ML18052A655

Forwards Response to NRC 860425 Request for Addl Info on Expansion of Spent Fuel Pool Storage Capacity.Tech Spec Change Request & Supporting SAR Will Be Submitted to NRC

ML18052A655
Person / Time
Site:	Palisades
Issue date:	07/24/1986
From:	Berry K CONSUMERS ENERGY CO. (FORMERLY CONSUMERS POWER CO.)
To:	Office of Nuclear Reactor Regulation
References
NUDOCS 8608210088
Download: ML18052A655 (140)

Text

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consumers Power Kenneth W Berry Director POWERING Nuclear Licensing MICHlliAN'S PIUJliRESS General Offices: 1946 West Parnell Road: Jackson, Ml 49201 o (617) 788-1636 July 24, 1986 Director, Nuclear Reactor Regulation US Nuclear Regulatory Commission Washington, DC 20555 DOCKE.T 50-255 - LICENSE DPR PALISADES PLANT -

EXPANSION OF THE SPENT FUEL POOL STORAGE CAPACITY - RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION Consumers Power Company letter dated February 20, 1986 submitted a Request for Change to Palisades Technical Specifications and supporting Safety Analysis Report (SAR) to increase the storage capacity of the Plant spent fuel pool and tilt pit. This increased capacity will be achieved by installing new spent fuel storage racks in approximately one-half of the main pool and in a portion of the spare tilt pit. By letter dated April 24, 1986, Consumers Power Company committed to submit the Summary Reports for all the analyses performed to support the conclusions in the SAR.

NRC letter dated April 25, 1986 transmitted a request for additional informa-tion regarding the expansion of the spent fuel pool. Additional requests for information were also received during discussions with the Palisades Plant NRC Project Manager. Attachment 1, including Enclosure A, provides responses to the questions in the April 25, 1986 NRC letter. Attachment 2, including Enclosure B, provides responses to questions received from the Project Manager. Attachment 3 provides information referenced in the responses to certain questions.

To respond to a specific NRC recommendation (NRC letter dated April 25, 1986, question 82), Consumers Power Company has decided to revise the Technical Specifications Change Request and supporting SAR submitted by our letter of February 20, 1986. These revised documents, which will be submitted to the

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Director, Nuclear Reactor Regulation 2 Palisades Plant Expansion of Spent Fuel Pool Storage Capacity - Additional Information July 24, 1986 NRC shortly, together with the responses provided by this letter, are being submitted in lieu of the Summary Reports described above and in our letter of April 24, 1986.

Kenneth W Berry (Signed)

Kenneth W Berry Director, Nuclear Licensing CC *Administrator, Region III, USNRC NRC Resident Inspector - Palisades Attachments OC0786-0116-NL02

consumers Power Kenneth W _Berry Director l'OWERING Nuclear Licensing llAIUllliAN"S PRatiRESS General Offices: 1945 West Parnall Road, Jackson, Ml 49201 * (517) 788-1636 July 24, 1986 Director, Nuclear Reactor Regulation US Nuclear Regulatory Commission Washington, DC 20555 DOCKET 50-255 - LICENSE DPR PALISADES PLANT -

EXPANSION OF THE SPENT FUEL POOL STORAGE CAPACITY - RESPONSE TO REQUEST FOR ADDITIONAL INFORMATION Consumers Power Company letter dated February 20, 1986 submitted a Request for Change to Palisades Technical Specifications and supporting Safety Analysis Re~ort (SAR) to increase the storage capacity of the Plant spent fuel pool and tilt pit. This increa$ed capacity will be achieved by installing new spent fuel storage racks in approximately one-half of the main pool and in a portion of the spare tilt pit. By letter dated April 24, 1986, Consumers Power Company committed to submit the Summary Reports for all the analyses performed to support the conclusions in the SAR.

NRC letter dated April 25, 1986 transmitted a request for additional informa-tion regarding the expansion of the spent fuel pool. Additional requests for information were also received during discussions with the Palisades Plant NRC Project Manager. Attachment 1, including Enclosure A, provides responses to the questions in the April 25, 1986 NRC letter. Attachment 2, including Enclosure B, provides responses to questions received from the Project Manager. Attachment 3 provides information referenced in the responses to certain questions.

To respond to a specific NRC recommendation (NRC letter dated April 25, 1986, question #2), Consumers Power Company has decided to revise the Technical Specifications Change Request and supporting SAR submitted by our letter of February 20, 1986. These revised documents, which will be submitted to the

• OC0786-0116-NL02

Director, Nuclear Reactor Regulation 2 Palisades Plant

• Expansion of Spent Fuel Pool Storage Capacity - Additional Information July 24, 1986 NRC shortly, together with the responses provided by this letter, are being submitted in lieu of the Summary Reports described above and in our letter of April 24, 1986. ,;

Kenneth W Berry (Signed)

Kenneth W Berry Director, Nuclear Licensing CC Administrator, Region III, USNRC NRC Resident Inspector - Palisades Attachments OC0786-0116-NL02

ATTACHMENT 1 Consumers Power Company Palisades Plant Docket 50-255 SPENT FUEL POOL STORAGE CAPACITY EXPANSION RESPONSE TO QUESTIONS TRANSMITTED BY NRC LETTER DATED APRIL 25, 1986 July 24, 1986 84 Pages OC0786-0116-NL02

• RESPONSES TO NRC REQUEST FOR ADDITIONAL INFORMATION PALISADES SPENT FUEL STORAGE EXPANSION Question 1: What type of administrative controls are employed to evaluate the burnup of a fuel assembly prior to its placement in Region II?

Response: The following is an outline of the administrative controls that will be invoked.

1. Unless a documented engineering analysis and associated safety evaluation proves the present criticality analysis and burnup verse enrichment curve to be bounding for fuel batch K and future batches, only batches A through J will be considered for storage in Region II.

t.n 2. Assembly burnup values will be obtained from the incore analysis system which calculates the individual assembly burnup values based on core power distribution and core average burnup. This system is the same one used to monitor

, Technical Specification limits for peaking factors.

3. A 10% uncertainty will be applied to the documented burnup value. A lower uncertainty value may be utilized in the future if: 1) The current incore detector analysis system, INCA, is determined to be more accurate, 2) INCA is replaced with an improved code such as CECOR, or 3) assemblies are actually tested to verify burnup. Any change in the uncer-

!:':) tainty value will be documented.

'-" 4. The active fuel documentation file maintained by the Reactor Engineer will be utilized to identify assemblies that have r--... been modified from their original condition (eg, reconstitu-

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tion, poison rod removal or fuel rod removal). The modified assemblies will be evaluated to determine if the criticality analysis bounds the "as-is" condition.

5. Actual serial numbers will be read on either: 1) assemblies that are acceptable for Region II storage, or 2) assemblies that are NOT acceptable for Region, II storage. Both methods have advantages and~disadvantages, and the best option is presently being evaluated. When a serial number is read, the assembly will be physically marked. The marker should be designed to be visible (with adequate lighting) from the 649 foot elevation in the spent fuel pool area. These markings should allow easy, definitive verification of correct assembly storage at any desired time.

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6. During refueling operations, items 1 through 4 above will be applied to an assembly prior to placement into Region II.

Within 90 days following completion of all refueling opera-tions (ie, after the new core loading is verified), item 5 above will be performed, as necessary.

7. New fuel assemblies will not be allowed in Region II. New fuel can be easily distinguished from spent fuel and special identification marking is unnecessary.

8. Plant procedures will be revised to require all fuel assem-bly movements into Region II rac,ks be approved first by the Reactor Engineer or designate.

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3 Question 2: Since the spent fuel burnup requirements for storage in Region II are given in terms of weight percent of U-235, we recommend that the references to 41.24 grams of U-235 per axial centimeter in Tech Spec 5.4.2 be changed to weight percent of U-235 for consistency.

Response: A revised Technical Specifications change request will be submitted which will include the change to section 5.4.2 recommended by the NRC.

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• Question 3: 'Please identify the organization and provide assurance that the organization that performs the criticality analyses has be~n previously qualified to perform these type of calculations.

Response: The Westinghouse Nuclear Fuel Division is responsible for the criticality analysis. This division performs all Westinghouse core design calculations and has been responsible for fuel rack and shipping container criticality analysis since the early 1970's.

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5 Question 4: The standard deviation of the K f values for the 27 critical experiments used as benchmarks tfable 3-1) is significantly lower than that previously obtained by other licensees using the same calculational method. Describ~ your derivation of the 95/95 uncertainty in the method bias in more detail.

Response: It has long been known that the original Westinghouse procedure for handling the.bias uncertainties in the criticality.analysis was conservative. As a result, a new procedure was implemented in _1984 based on the method presented in "Statistical Methods in Nuclear Material Control" by John L. Jaech. This method has been used by Westinghouse since that time and has been licensed in the Zion fuel rack analysis.

From the 27 critical experiments modelled in KENO, the mean Keff of the benchmarks is 0.9998 which demonstrates that there is no significant bias associated with the method *. The original treatment of the uncertainty associated with the bias resulted in a 95% probability with a 95% confiden~e level of 0.013 delta-K. This was based on a standard deviation of the mean of Hl 0~0057 delta-K for the 27 benchmark K f values. However, a more correct treatment of the uncertain~ies can be used to determine the uncertainty of the bias term applied to the KENO results. This treatment is based on the method in the reference mentioned above. Based on this treatment, the square of the standard deviation of the mean, and the average KENO uncertainty for the 27 critical benchmarks were added and divided by _27. As a result, the uncertainty of the bias term is 0.0014 delta-K.

The 95/95 one-sided tolerance limit factor for 27 values is 2.26. Thus, the 95/95 in the bias reactivity due to the method is not greater* than 0.0032 delta-K

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6 Question 5: What are the values of the worst case K ff and of the biases and uncertainties referenced in Section 3 .17Zj. .1.1 for Region II?

Response: The values of the worst case Keff' biases and uncertainties are:

K - 0.899 worst Bmethod - O.O B - 0.0045 part Ks - 0.0035 worst Ksmethod - 0.0032 Ks - 0.01 re Substituting the calculated values results in a maximum Kef f -

0 0.9155.

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• • Question 6: It appears that the only certainty accounted for due to reactiv-ity equivalencing is that due to uncertainty in the plutonium reactivity. Justify why the uncertainty in reactivity as a function of burnup was not included also.

Response: Although the reactivity uncertainties associated with plutonium and fuel burnup are not independent, it should be considered that the reactivity of fuel as a function of irradiation depends implicitly on the production rate of plutonium. These uncer-tainties are so closely related that accounting for them twice is considered very conservative. As a result, a term was defined to account for the uncertainty associated with the burnup dependent reactivities.

A value of 0.01 delta-K is given to the uncertainty term associ-ated with the burnup dependent reactivities computed with PHOENIX. This uncertainty is considered to be conservative since comparison between PHOENIX results and the Yankee Core experiments and the 81 benchmark experiments indicates much closer agreement *

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8 Question 7: What is the maximum clad temperature predicted to occur in the spent fuel pool for normal storage condition and for any abnor-mal or accident condition?

Response: Maximum clad temperatures were calculated for three conditions

- normal storage; 80% flow blockage of the rack coolant inlet at the rack base plate; and total loss of cooling in the spent fuel pool. For the first two cases water inlet temperature was conservatively taken as 150°F. For the third case water inlet temperature was 212°F. Decay heat value correspond to 36 hours4.166667e-4 days <br />0.01 hours <br />5.952381e-5 weeks <br />1.3698e-5 months <br /> after reactor shutdown. The chart below shows maximum clad surface temperature for a peak rod of 1.6 times heat output for an average rod.

Condition Max. Clad Surface Temp (°F)

Normal Operation 258.2 80% Flow Blockage at Base Plate 291.8 Loss of Cooling < 300 Note that the calculations were performed for fuel stored in the main pool and the spare tilt pit. Therefore the results given above apply to fuel stored in either location.

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• Question 8: The request for Technical Specification change from Consumers Power Company dated February 20, 1986, does not provide suffi-cient information to perform an adequate review of certain aspects of mat~rial considerations mentioned in (or omitted from) Section 4 of PALSFP-4-NL02. The following information is needed for the staff to complete this review:

a. Identification of subsections, articles, subarticles and paragraphs of Sections III and IX of the ASME Boiler and Pressure Vessel Code that pertain to spot welding referenced in PALSPF-4-NL02,

b. The fabrication, control, and inspection methods utilized in spot welding, and

c. The long term environmental compatibility of the spot welds with fuel pool storage conditions.

Response: Spot welding is used on the spent fuel rack to attach the poison wrapper to the cell. The function of the poison wrapper is to cover the Boraflex poison material. Thus, the spot welds are not part of the primary load path of the rack structure and are, therefore, outside the jurisdiction of the ASME Boiler and Pressure Vessel Code.

The spot welds on the racks are made using the plasma arc fusion welding process or the gas tungsten arc welding process, West-inghouse has developed process specifications for this weld using the intent of American Welding Society specification C~.l.

The procedures were qualified by testing using the same material alloy and thickness as the wrapper and cell. Testing included visual examination, peel tests, shear load tests and material

.... ... sensitization tests. In each case, on the sheer load test weld strength greatly exceeded design requirements. For the material sensitization test the weld and heat affected. zone were tested and passed per Practice A of ASTM A262.

Spot welds are made using calibrated equipment on which all welding variables are preset. Prior to each working shift a weld sample is made with each welding head using the same material alloy and thicknesses as the wrapper and cell. Each sample is visually inspected and peel tested to determine fusion migget- diameter-. -- In -a-ddition~ each weld made during- a shift is visually inspected.

Sample spot welds were tested and passed per ASTM A262 Practice A during procedure qualification. This test showed that the material is not sensitized by the spot welds. Thus the long term environmental compatibility of the spot welds in the fuel storage pool conditions will be the same as 304 stainless steel and should not be a problem.

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10 Question 9: SPENT FUEL RACK STRUCTURAL ANALYSIS With respect to the analysis of spent fuel rack modules, please provide the following information:

a. For the Region I racks already in place, provide descrip-tions and sketches of the fuel racks, their method of lateral restraint (attachment to the pool walls), and a full description of the displacement analysis indicating that the Region I racks will not be displaced to impact the new Region II racks.

Response: The existing Region I racks are 8x8 with 10.25 inch center-to-center cell spacing and are supported on the pool floor at four locations. The rack-to-wall lateral restraint assembly (see Sketch 9a) is a bolt with integral bearing pad which threads into the ends of both the top and bottom gri~ members. (Note that the north end of the Region I racks will have no lateral restraint.)

The non-linear time history analyses of the Region I and Region II racks show that the maximum relative displacement between the Region I and Region II racks due to sliding, rocking, structural deflection, and thermal effects is 0.54 inches. This is much less than the 1.75 inch minimum clearance and therefore pre- .

eludes impact between the Region. I and Region II racks.

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11 SKETCH 9a TYPICAL REGION I RACK - PLAN VI~

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• • Question 9b: Document the source of the earthquake data and describe the methods by which the earthquake acceleration time histories were generated for use in the rack displacement analysis.

Response: The acceleration time histories applied to the fuel rack models were obtained by synthesizing the 1940 El Centro earthquake such that the resulting response spectra envelop the Palisades Floor Response Spectra. The Palisades Floor Response Spectra employed here is that of the original design of the Plant. That response spectra was generated from the modified Taft 1952 earthquake *

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• Question 9c: Describe the number of independent horizontal earthquake accel-eration components used, as well as the directional orientation of the horizontal components relative to the long and short sides of the racks analyzed.

Response: The analysis accounts for two horizontal shocks and one vertical shock simultaneously. Since the North-South and East-West horizontal shocks are identicai, the rack response is indepen-dent of the directional orientation

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• Question 9d: Identify the rack modules chosen for analysis and provide the technical justification that the choice of racks for analysis brackets, or bounds, the response of all the rack modules in the spent fuel poo~ and tilt pit.

Response: The main spent fuel pool has two (2) llxll rack modules and two (2) 7xll rack modules, while the tilt pool has a 6x6 rack module and 6x7 rack module. In order to determine which rack response would be limiting, loads were calculated for both the llxll and 7xll in the main pool. For racks in the tilt pool, loads were calculated for the 6x7 rack, which enveloped the response of the 6x6 rack.

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• Question 9e: Provide the clearance space between each adjacent rack module and between the rack modules and the pool walls.

Response: The minimum clearance space between each adjacent rack module is 1.50 inches. The minimum clearance between the rack modules and the pool walls is 1.80 inches .

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• Question 9f: For adjacent rack modules, describe how the clearance space between the rack modules was apportioned to each module for the purposes of comparing the rack displacement to the available apportioned clearance space.

Response: The maximum rack relative displacement between rack modules was found' to be 0.439. This value is much less than the available 1.50 inch clearance space.

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17 Question 9g: Document the computer codes used for the three-dimensional elastic analysis and for the nonlinear dynamic displacement analysis. Include justification of the choice of the computer codes.

Response: An analysis of the racks is performed on the Westinghouse Electric Computer Analysis (WECAN) Code, wh.ich has been devel-oped over many years by Westinghouse. It is a general purpose finite element code with a great variety of static and dynamic capabilities. These elements have been fully verified by benchmark problems and are on a configuration control code which is maintained in compliance with strict quality control requirements.

The general WECAN code has been reviewed by the NRC through the submittal of Westinghouse document WCAP-8929, "Benchmark Problem Solutions Employed for Verification of the WECAN Computer Program." For review of additional capabilities which pertain to the fuel rack non-linear dynamic analysis, the following documents are provided in the "References" section of this letter.

a. Shah, V N, Gilmore, C B, "Dynamic Analysis of a Structure with Coulomb Friction," ASME Paper No. 82-PVP-18, presented at the 1982 ASME Press~re Vessel Piping Conference, Orlando, FL, June 1982.

b. Gilmore, C_ B, "Seismic Analysis of Freestanding Fuel Racks,"

ASME Paper Number 82-PVP-17, presented at the 1982 ASME Pressure Vessel Piping Conference, Orlando, FL, June 1982.

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• Question 9h: Describe the features and limitations (if any) of the frictional model used to compute static and sliding friction in the dynamic displacement analysis.

Response: The three-dimensional friction element used in the non-linear model is composed of a gap in series with a parallel combination of impac~ spring and impact damper with a frictional spring orthogonal to the gap. This element, which is used to model the support pad interface with the pool floor, is designed to represent two surfaces which may slide relative to each other, and may separate or contact each other. The dynamic displace-ment analysis is performed for friction coefficients of mu = .2 and .8. The maximum sliding distance (rack base horizontal displacement) of the rack module is obtained for the mu = .2 case. The maximum rack loads and structural deflections are obtained for the mu = .8 case

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19 Question 9i: A statement on Page 4-9 indicates that "the hydrodynamic mass of a submerged fuel rack assembly is modeled by general mass matrix elements connected between the cell and the pool wall." Please provide the thebretical premise by which this was modeled, and justify the use of the model for hydrodynamic mass and hydrody-namic coupling between adjacent rack modules, between a rack module and the pool walls and walls, and between a fuel assembly and the storage cell walls. Does this underestimate or overes-timate the hydrodynamic coupling?

Response: The hydrodynamic mass between the rack cells and the pool wall was calculated by evaluating the effects of the gap between the rack modules and the po9l wall using the method outlined in the paper by R. J. Fritz ("The Effect of Liquids on the Dynamic Motions of _Immersed Solids," Journal of Engineering for Industry, February 1972). The close proximity of adjacent racks, as well as the size of the racks relative to the gap -

between racks, is such that extremely large hydrodynamic masses are produced if the racks attempt to respond out of phase. It is this large hydrodynamic mass which causes the racks to respond in phase. The seismic analysis treats the racks as if they are hydrodynamically coupled (move in phase), which gives the highest loads and displacements. The hydrodynamic mass between the fuel assembly and the cell walls is based upon the fuel rod array size and cell inside dimensions using the tech-nique of potential flow and kinetic energy. The hydrodynamic mass is calculated by equating the kinetic energy of the hydro-dynamic mass with the kinetic energy of the fluid flowing around the fuel rods. The concept of kinetic energy of the hydro-

--* dynamic mass is discussed in a paper by D F Desanto ("Added Mass and Hydrodynamic Damping of Perforated Plates Vibrating in Water." ASME Journal of Pressure Vessel.Technology, May 1981).

Both papers cited above are provided in the "References" section of this letter

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20 Question 9j: Document the source of the impact spring stiffness and impact damping between a fuel assembly and the storage cell walls, and justify the value of impact damping used.

Response: To determine the spacer grid impact stiffness and impa~t damping, the following test was performed in air. (Note that water will increase the damping effects from those of air.) A weight was dropped onto a spacer grid mounted vertically to a load cell. The top end of the spacer grid is free. Sections of fuel rod cladding are inserted into the spacer grid to simulate the fuel's effects on stiffness and damping. A displacement transducer follows the vertical motion of the dropweight and displacement of the top surface of the spacer.

The results of this test are summarized below.

Drop Height of Weight; in 0.25 0.50

=================== ================= . ===========

Direction Relative to Spacer Orientation x ~ x y

=================== ======== ======== ======== ==

Natural Frequency; Hz 31.6 21.0 26.2 21.2 Spacer Impact Stiffness; 14,544. 6,402. 9,970. 6,510.

lbs/in Spacer Impact Damping; 15.8 12.3 18.0 17.7

% of Critical Damping

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• Question 9k: For the non-linear dynamic displacement analysis, describe the numerical integration method used, as well as the procedures that were employed to assure that the numerical integration remained stable and that the resulting displacements represent a fully converged solution.

Response: For the non-linear dynamic analysis, the modal superposition method was employed to obtain displacements as a function of time. In order to determine of the solution was full converged, a time increment study was performed. Different time increments were used, and it was shown that the results were the same for the time increments of 0.0013 seconds and 0.0025 seconds. Thus, for the seismic analysis, the time step chosen was 0.0025 seconds.

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22 Question 91: Provide a summary of rack displacements that includes elastic distortion (if significant), sliding.and tipping displacement as well as their sum.

Response: The maximum single rack displacement including elastic distor-tion and tipping is 0.2579 inches, and the maximum single rack sliding displacement is 0.0053 inches. The maximum relative displacement between adjacent racks is 0.439 inches.

0

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• Question 9m: Provide tables of computed stresses in the rack structure and support legs, and their comparison to allowable values in accordance with the acceptance criteria cited in the licensing report.

Response: The following table provides a summary of the computed stresses in the rack structure and support structure along with the allowable values and their margins of safety.

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24 REGION II RACKS

SUMMARY

OF DESIGNS STRESSES AND MINIMUM MARGINS OF SAFETY NORMAL & UPSET CONDITIONS Design Allowable Margin Stress Stress of (psi) (psi) Safety l.O Support Pad Assembly 1.1 Support Pad 2801 11000 2.93 Shear Axial and Bending 11538 16500 .43 Bearing 9805 24750 l. 52 1.2 Support Pad Screw Shear 8030 11000 .37 l.3 Support Plate Shear 2802 11000 2.93 Weld Shear 16100 24000 .49 2.0 Cell Assembly

2. 1 Cell Axial and Bending .86 1 .O** .16 2.2 Cell to Base Plate Weld Weld Shear 17695 24000 .36 2.3 Cell to Cell Weld Weld Shear 22652 27500* . 21 2.4 Cell to Wrapper Weld Weld Shear 9053 11000 . 21 2.5 Cell Seam Weld Weld Shear 19173 24000 .* 25 2.6 Cell to Cover Plate Welds

• ~

Weld Shear 20431 24000 .18

• Thermal Plus QBE.Stress is limiting

,**Allowable per Appendix XVII-2215 Eq (24)

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25

• Question 9n: Provide the amount and characteristics of mounting foot lift-off from the pool floor associated with dynamic rack displacement, and show that the resulting impacts with the floor were consid-ered in the stress analysis.

Response: The maximum pad (mounting foot) lift-off from the pool floor is 0.342 inches. This pad is modeled using an impact/gap element which allows impact to be accounted for in the dynamic analyis.

The loads developed from this dynamic analysis are in turn used in the stress analysis.

• .~

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26 Question 9o: Provide an analysis of rack module stability in the tipping mode, considering the worst case of off-center fuel load possible.

Response: For the evaluation of rack stability, the rack is evaluated for both partially and fully loaded conditions. It was determined that the partial loading of two rows of fuel, coupled with the limiting condition of the six-cell direction of the rack (ie, the side of the rack comprised of six storage cells), yielded a minimum factor of safety against overturn of 32. This value is much greater than the 1.5 minimum required by the NRC Position Paper.

.J

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27 Question 9p: Provide a detailed description of the recessed cask area (cask pit), showing its location in the spent fuel pool and geometric relationship of the cask pit to any adjacent spent fuel rack modules. Include full descriptions of any structures, or other provisions, present to the preclude damage to any adjacent fuel rack modules during cask operations, or to prevent any adjacent fuel rack modules from entering the pit.

Response: A 9-foot by 9-foot area in the northeast corner of the spent fuel pool is recessed to accommodate a shipping cask. Technical Specifications section 5.4.2, item "f", prohibits fuel shipping casks from being moved to the fuel storage building until the NRC approves the cask drop evaluation. With regard to prevent-ing any adjacent fuel rack from entering the recessed cask pit, a review of the Region II rack configuration shows that the centerline of the* fuel rack support closest to the cask pit is 3.5 inches from the edge of the pit. Comparing this distance to the sliding distance given in the response to Question 91 (0.0053 inches), shows that the racks will not enter the pit.

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28 Question !Oa: SPENT FUEL POOL STRUCTURAL ANALYSIS With respect to analysis of the spent fuel pool under the increased loads of higher density fuel storage, the Licensee is requested to provide the following information to supplement the analysis outline provided in the licensing report:

a. Describe how the dynamic interaction between the pool structure and the rack modules was considered, including the value of any associated dynamic amplification factors.

Include all assumptions made regarding the summation and phase of all rack loads.

Response: The response of the spent fuel racks was determined by a non-linear time history analysis. The seismic time histories applied to the racks were 'synthesized from pool floor response spectra which account for the pool floor amplification. Apply-ing the time histories to the nonlinear dynamic fuel rack model, the loads on the pool were determined. Since the dynamic model accounts for possible rack lift and then pad impact on pool floor, the results of the nonlinear dynamic analysis provide the proper rack to pool interaction and the use of additional dynamic amplification factors is not necessary. The structural model of the pool was loaded assuming that all the individual racks were responding in phase. See also the response to Question 9c *

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• • Question lOb: Provide analysis proving the adequacy of the pool floor and liner under the local maximum rack module dynamic mounting foot loads.

Response: .The analysis of the pool floor is discussed in the response to Question lOc. This analysis considers the local maximum rack module dynamic mounting foot loads. From the stress summary Tables provided in the response to Question lOc, it is apparent that the pool floor is adequate for these local loads. The structural adequacy of the liner for these local loads is demonstrated bel9w.

Two types of fuel racks (W and NUS) are used in the pool. Both racks are free standing with circular pads used to transfer the rack loads to the pool floor. The basic design characteristics are shown in Figure 1-lOb. The W pad and the NUS pad are 5 inches in diameter. The liner o~ which the pads rest is 3/16 inches in thickness and is SA-167, Type 304L stainless steel anchor plate. The liner rests on the concrete pool floor. This is also shown in Figure 1-lOb.

The loads transferred through the pads are both vertical and horizontal. The maximum loads that a particular pad will

• transfer is a function of the type and configuration of the rack. This is seen in Table 1-lOb.

By the nature of free standing rack design, the only way that a horizontal load can be transmitted to the pool floor is by friction. The friction load, as well as the vertical load, is transferred directly to the pool floor at the location of a pad.

0 This is shown in Figure 2-lOb. As seen in this figure, two types of local stresses are induced into the liner, shear stress and bearing stress. Since the NUS fuel racks have the highest loads (See Table-lOb), the highest local liner stresses will occur at the location of the NUS pads. The maximum local stresses that will be produced in the liner for the defined design seismic events are given in the following.

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Local Liner Bearing Stress (P): 30

• Pad Bearing Area= 3.14 x (5/2) x (5/2)

Pad Bearing Area*= 19.63 sq in SSE Event: P = 94.2/19.63 P = 4.8 ksi OBE Event: P = 60.94/19.63 P=3.lksi The local liner bearing stresses calculated above are well within the liner plate allowable stresses defined below.

SSE Bearing Allowable Stress= 1.6 x 0.9 Fy Where Fy = Liner Yield Stress Fy = 25 ksi at 100 degrees Fahrenheit SSE Bearing Allowable Stress = 1.6 x 0.9 x 25

= 36.0 ksi OBE Bearing Allowable Stress = 0.9 Fy

= 0.9 x 25 = 22.5 ksi

31 Local Liner Shear Stress (V):

• SSE Event: v = 60.5/19.63 V = 3.1 ksi OBE Event: v = 30.24/19.63 V = 1. 5 ksi The local 11ner shear stresses are also well within the liner allowable shear stresses as seen below.

SSE Shear Stress Allowable= 1.6 x 0.4 x Fy rn = 1.6 x 0.4 x 25 = 16 ksi OBE Shear Stress Allowable= 0.4 x Fy

= 0.4 x 25 = 10 ksi As seen from the analysis given above, and the analysis reported in response to question lOc, the pool floor and liner is adequate for the local maximum rack module dynamic mounting foot loads.

The wall rack loads are bearing forces only. The bearing loads are smaller than the floor bearing forces and are therefore enveloped by the analysis performed above .

32 MAXIMUM PAD LOADS (kios)

WESTINGHOUSE RACKS i I NUS RACKS RACK ARRAY 11 x 11 11 x 7 7 x 6 6 x 6

---

~.

8x8

-SSE Load Condition Vertical* 75 75 68 68 94.2 Hor: N-S 25 25 16 16 60.5 E-W 47 47 16 16 13.83

-DBE Load Condition Vertical 46 46 46 46 60.94 Hor: N-S 12.5 12: 5 8.0 8.0 30.24 E-W 23.5 23.5 8.0 8.0 6.92 J

"."\~

M TABLE 10-lb: MAXIMUM PAD LOADS

~ ...

I

• II t\ ' b.' ' t '

. b. \, . . ' SECT

' I ' ...... , '

. I '

• 1

\ I"

~.

\* , ' ."* ,,

I, A

. ~

I ......A ' ' : RACK

• -

• I

• I: .: : ... *: . .6*:

~ .:. .~ ~

~

• (:;

0

.j 1*

I *

. ll '

I . A'. *. .'. ~

• ~*

w*

• A

• ~

' PAD

• ..... -J,,,,,,----~~lf

.. ..."'.j,." *: *. '.

POOL FLOOR FIGURE 1-lOb: RACK MODULE AND MOUNTING PAD pESIGN CHARACTERISTICS

RACK MODULE N ., NORMAL LOAD N

MOUNTING FOO~ LOADS S = SHEAR LOAD s

PAD LINER POOL FLOOR PAD

'J DIRECT TRANSFER THROUGH PAD T7TTs N

FIGURE 2-lOb MAXIMUM RACK MODULE DYNAMIC MOUNTING FOOT LOADS

35

• Question lOc: Provide identification of the most critical regions of the pool structure. List the stresses (thermal, deadweight, seismic and rack dynamic loads) and their comparison to allowable values, including the source and justification of the use of the allow-able values.

Response: The requested information is provided in Enclosure A that follows. The criteria and loading conditions employed to evaluate the Palisades Spent Fuel Pool Structure are given, as well as the stresses associated with the most critical regions of the pool. Specifically provided in this attachment are the following:

1. Loading Combinations

2. Material Properties

3. Design Allowable Stress Limits with Basis of Allowable Values 4." Table of Critical Stresses and Location (Al to A2)

5. Figures Defining Element No. Used to Define Critical Stress Locations per Tables Al to A2 (Figures Bl through B7 and Dl through D31)

AT0786-0116-NL02

36

• Question 11: FUEL ASSEMBLY ACCIDENT ANALYSIS The following information is requested with respect to the analysis of a dropped fuel assembly covered in Paragraph 4.6.4 of the Licensee's report:

a. For the first accident condition, provide the extent of deformation predicted by the analysis to occur on the top of the spent fuel rack as well as to occur on the dropped fuel assembly. Indicate whether there is a possibility for the damage to release radioactive material.

b. Documentation of the second accident condition should be provided in a manner similar to that requested for question lla ab.ove.

c. Provide a description of the analysis methods for the third 0 accident condition, including justification of assumptions.

Provide the maximum velocity reached by the fuel assembly and verify that the kinetic energy of the fuel assembly can be absorbed as strain energy in the structure without damage to the pool liner or release of radioactive material from the fuel assemblies

• Response: For fuel drop accident conditions, the double contingency principle of ANSI N16.1-1975 is applied. This states that one is not required to assume two unlikely, independent, concurrent events to ensure protection against a criticality accident.

Thus, for accident conditions, the presence of soluble boron in the storage pool water can be assumed as a realistic initial condition since not assuming its presence would be a second unlikely event.

........ -. The presence of approximately 1720 ppm boron in the pool water will decrease reactivity by about 30 percent 8K. In M perspective, this is more negative reactivity than is present in the poison plates (18 percent 8K), so K ff for the rack would be less than 0.95 even if the poisoneplates were removed by a drop accident. In fact, with 1720 ppm boron in the pool water, there is no deformation that could reasonably be achieved by the drop of a fuel assembly that would cause the criticality acceptance criteria to be exceeded for fuel meeting the burnup criteria for Region II storage. This applies to.all of the three drop accident conditions.

The radiological consequences of a fuel drop accident are described in Section 5.3.1 of February 20, 1986, submittal.

This Section shows that the potential offsite doses are less

• than the guidelines of 10CFRlOO. Furthermore, an analysis has been performed which shows that a large number of fuel elements could be failed without exceeding the guidelines of 10CFRlOO.

AT0786-0116-NL02

ENCLOSURE A Consumers Power Company Palisades Plant Docket 50-255 SPENT FUEL POOL STORAGE CAPACITY EXPANSION July 24', 1986 0

• OC0786-0116-NL02

ENCLOSURE A A. CRITERIA AND LOADING CONDITIONS T~is section presents the loading conditions, material properties, seismic requirements, criteria employed and design specifications and codes used to evaluate the structures.

A. l LOADS The following loads were considered in the evaluation of the pool integrity.

Dead Load, includes pool structure self-weight, racks and fuel assem-blies, and hydrostatic loads. In addition, all floor live loads, dead loads of adjacent structures and superstructure crane loads are included.

Operating basis earthquake Safe shutdown earthquake Thermal loads Hydrostatic loads are considered for a water level at elevation 648 feet in the spent fuel pool and tilt pits Sloshing effects of water - hydrodynamic loads To determine the adequacy of the structure, the criterion outlined in Appendix A "Design Bases" to the FSAR Update was adopted.

"*' Based on the Palisades FSAR Update (Reference Document 1) the following critical load combinations were considered in the analysis of the pool structure.

l.25D + l.25T + l.25E (Normal Operating Condition) 0 l.OD + l.OT + l.OE' (Abnormal Operating Condition) 0 where D = Dead load defined above including hydrostatic loads E Seismic (OBE) load including hydrodynamic (sloshing) loads E' = Seismic (SSE) load including hydrodynamic (sloshing) loads

• T 0

Thermal gradient load for normal operating condition AT0786-0116-NL02 1

Two additional load combinations were considered to evaluate the isolated effects of the mechanical loads and to evaluate.the abnormal event of a full core off load case. The additional load combinations are:

1. 25 D + 1. 25 E 1.0 D + 1.0 Tab where Tab Thermal gradient for abnormal operating condition AT0786-0116-NL02 2

A.2 MATERIAL PROPERTIES

• CONCRETE:

F'c = Compressive Strength at 28 days = 3000 psi W = Specific Weight of Concrete = 150 pcf Ee = Modulus of Elasticity of Concrete Ee = w 1* 5 (33) ~ = 3.32056 x 106 psi = 3.321 x 10 3 ksi v = Poisson's Ratio = 0.14 p = Mass Density = 4.6583 P-sec 2/ft 4 G = Modulus of Rigidity = 1.4563 x 103 ksi a = Coef. of thermal Expansion = 5.5 x 10-6 per °F REINFORCEMENT BARS:

ASTM-A-615, Grade 40 Yield Strength = 40 ksi Es = 29000 ksi

= Poisson's Ration = 0.33 G = 10694 ksi a = Coeff. of thermal Expansion = 6.5 x 10-6 per °F 3

A.2 DESIGN ALLOWABLE STRESS LIMITS The design allowable stress limits outlined in "Building Code Requirements for Reinforced Concrete (AC! 318-71)" were considered the basis of evalua-tion for the spent fuel structure.

To determine the adequacy of structure, the stress criterion outlined in FSAR Update Appendix A (Reference 1) was adopted. The load combinations considered for evaluation are:

1 (1.25D + 1.25T + 1.25E)

{

1. y =

~

(Normal Operating Condition) y = 1

2. -~- ( 1. 25D + 1. 25E)

• y = 1 (1.0D + 1.0T + 1. OE')

{

3. -~-

r..n (Abnormal Operating Condition) y = 1

4. (1.0D + 1.0 Tab)

T where:

D, T, Tab' E and E' are defined in Section A.l, and Y = Required yield strength of the material

~ = Yield capacity reduction factor per AC! 318-71 for both reinforcement and concrete A.3 STRESS

SUMMARY

~*

The reinforcement and concrete stresses of the critical sections in the pool walls and slabs, in the substructure walls and in the foundation mat M have been identified in Tables A-2 and A-3. Sketches to help identify the critical sections have been included in Attachment A in Figures B-1 to D-31.

A.4 REFERENCES Palisades FSAR _Update Appenclix A, De_s:l,gil. Bases for Structures, Systems, and Equipment for Palisades Plant.

AT0786-0116-NL02 4

TABLE A1 MAXIMUM REINFORCEMENT STRESSES DIRECTION 1 DIRECT"3N 2 REI NF ELEMENTl] LOAD~

LOCATION STRESS REI NF ELEMENT~ LOAD~

NO.

MAT &SLABS (ksi) - COMB. STRESS (ksi) - NO. COMB.

590 (MAT) 1 30.00 13 2 10.44 13 2 607 - 6" 1

17.30 54 1 15.8 53 1 610' - 0" 35.1 72 1 12.6 70 1 611' - 0" 34.9 128 1 15.5 128 2 EAST-WEST WALLS

'°

• ".°'.'

EW 1 19.3 618 2 28.9 618 2 EW 2 14.5 664 1 18.8 664 2 EW 3 4.0 683 3 31.9 683 4 NORTH SOUTH WALLS NS 1 24.8 311 1 20.3 311 4 NS -2

• -J NS 3 17.0 37.4 357 429 3

1 22.2 16.6 357 428 2

1

~'*'

NS 4 1.1 480 1 17.0 M

480 2 All reinforcement stresses are below the allowable stress of 40 ksi (yield strength of ASTM-A-615, Grade 40).

1. For Mat and Slabs: Direction 1 = NS, Direction 2 = EW

2. For Walls: Direction 1 =Horizontal, Direction 2 =Vertical

3. Attachment A for Element Locations.

4. load combinations are defined in Section A.6.

5

'79 71 2731 OSCSIH. i JA

TABLE Al (Continued)

MAXIMUM REINFORCEMENT STRESSES

• LOCATION REI NF STRESS

{ksi)

DIRECTION 1 ELEMENT~

NO.

LOAD~

COMB.

RE INF STRESS

{ksi)

DIRECTION 2 ELEMENT11 NO.

LOAD'1J COMB.

SUPPORT WALLS BELOW NS 4 20.30 466 2 28.19 466 2 NS 5 32.53 501 1 7.51 494 2 NS 6 29.0 513 2 2.0 513 2 NS 7 18.9 526 1 2.0 526 2 NS 8 6.1 536 1 6.1 536 2 NS 9 20.7 546 1 3.9 546 1 r-.. NS 10 35.7 561 2 18.1 561 2 f1t.

EW4 10.5 690 3 2.0 690 3 EW 5 16.6 696 2 28.0 696 2

• EW 6 EW 7 EW .S 23.9 35.2 29.8 705 715 718 4

1 2

2.0 2.0 3.9 705 715 718 1

2 3

.":'.) EW 9 21.1 720 2 23.7 720 2

~* EW 3 26.0 677 3 2.0 677 1

~

!"')

All reinforcement stresses are below the allowable stress of 40 ksi (yield strength of ASTM-A-615, Grade 40).

1. For Mat and Slabs: Direction 1 = NS, Direction 2 = EW

2. For Walls: Direction 1 =Horizontal, Direction 2 =Vertical

3. See Attachment A for Element Locations.

4. Load Combinations are defined in Section A.6.

6

• 1a11. 2ns. ososaa 1o.a.

TABLE A2 MAXIMUM CONCRETE STRESSES DIRECTION 1 DIRECTION 2 CONC.; ELEMENTII LOAD~ CONC. ELEMENTll LOAD!!

LOCATION STRESS NO. COMB. STRESS NO~ COMB.

(ksi) (ksi) --

MAT &SLABS 590' (MAT) 0.5 13 2 0.2 13 2 607' - 6" 0.3 53 1 0.3 54 4 610' - 0" 1.3 71 2 0.5 71 1 611' - 0" 0.5 128 1 0.3 128 2

('") EAST-WEST WALLS ry. EW 1 0.3 618 2 0.1 618 1 EW 2 0.7 664 1 0.6 664 1 EW 3 1.4 685 1 0.1 3 685 NORTH SOUTH WALLS NS 1 0.4 311 1 0.2

- 311 4

"°:) NS 2 0.6 360 1 0.6 353 4

'."V NS 3 0.6 428 1 0.4 428 1 M

NS 4 0.1 480 1 0.1 480 2 All concrete stresses are below the allowable stress of 3 ksi (concrete compressive stress at 28 days).

1. For Mat and Slabs: Direction 1 = NS, Direction 2 = EW

2. For Walls: Direction 1 =Horizontal, Direction 2 =Vertical

3. See Attachment A for Element Locations *

4. Load Combinations are defined in Section A.6.

7

'797s 2735. 05.:1986 * *JA

TABLE A2 (Continued)

MAXIMUM CONCRETE STRESSES DIRECTION 1 DIRECTION 2 CONC. ELEMENTll LOAD4.J CONC. ELEKENTl.J LOADg_i LOCATION STRESS NO. COMB. STRESS NO. COMB.

{ksi) (ksi) --

SUPPORT WALLS BELOW NS 4 0.1 466 2 0.3 465 3 NS 5 0.1 503 2 0.8 503 3 NS 6 0.3 512 2 0.8 512 .1 NS 7 0.3 518 2 1.5 526 1 NS 8 0.1 536 1 1.4 536 2

()'

NS 9 0.2 545 3 - 1.4 545 3

~

NS 10 0.1 561 3 0.1 561 2 EW 4 0.1 686 2 1.2 686 2 EW 5 0.1 692 2 1.0 692 2 EW 6 0.1 705 3 1.2 705 1 EW-7 0.1 715 3 0.7 715 3 0

EW 8 0.1 718 3 0.9 718 3 r.v EW 9 0.1 720 2 0.5 720 2 M EW 3 0.1 677 3 1.0 677 3 All concrete stresses are below the allowable stress of 3 ksi (concrete compressive stress at 28 days).

1. For Mat and Slabs: Direction 1 = NS, Direction 2 = EW

2. For Walls: Direction 1 =Horizontal, Direction 2 =Vertical

3. See Attachment A for Element Locations.

4. Load Combinations are defined in Section A.6.

8

• 787s 27Js c;;gaa

• JA

LIST OF FIGURES FIGURE*

~

8-1

• Plan at El. 590 ft 8-2 Plan at El. 611 ft

. 8-3 Section A-A - El. 590 ft to 696 ft 8-4 Section 8-B - El. 590 ft to 649 ft B-5 Section C-C - El. 590 ft.to 649 ft B-6 Section. F-F - El. 590 ft to 649 ft 8-7 Section H-H - El. 590 ft to 649 ft D-1 Perspective View - El. 590 ft thru 602 ft D-2 Perspective View - El. 602 ft thru 611 ft D-3 Perspective View - El. 611 ft thru 649 ft 0-4 Foundation Mat at El. 590 ft D-5 Slab at El. 602 ft D-6 Slab at El. 607.6 ft 0-7 Slab at El. 610 ft D-8 Slab at El. 611 ft D-9 Slab at El. 622 ft D-10 Slab at El. 634 ft D-11 North/South Wall 1 D-12 North/South Wall 2 D-13 North/South Wall 3 D-14 North/South Wall 4 D-15 North/South Wall 5 D-16 North/South Wall 6 0-17 North/South Wall 7 D-18 North/South Wall 8 0-19 North/South Wall 9 D-20 North/South Wall 10 0-21 East/West Wall 1 D-22 East/West Wall IA D-23 East/West Wall 2 D-24 East/West Wall 2A D-25 East/West Wall 3 0-26 East/West Wall 4 0-27 East/West Wall 5 0-28 East/West Wall 6 D"".29 East/West Wall 7 D-30 East/West Wall 8 0-31 East/West Wall 9 9

1754s IOA

N<i----

H~ F1

~48'0" - - - - - - - - - "

. 11'0'~

_J a*

~~~~~~~~~~~--..:C..:t:::::+/-:Ll~~--__,jt c c 1' t FIGURE B-1: PLAN AT EL. 590 FT 10

N<3i---

H+,

c FUEL TRAr\JS.

TUEE 121

- L-:

H FIGURE :B-2: PLAN AT EL. 611 FT

• 11

• • N<l---

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• FIGURE B-3: SECTION A-A - EL 590 FT TO 696 FT 12

N <l--

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FIGURE B-4: SECTION B-B - EL. 590 FT TO 649 FT 13

':'J IN I~

• r:u...~--. EL. 625 'o

'----21 *a**-~

FIGURE B-5: SECTION C-C - EL. 590 FT TO 649 n' 14

w <J----

CONT

---

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• • FIGUREB-6: SECTION F-F - EL.

15 590 FT T0.649 FT

W<J~-

---

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FIGURE B-7: SECTION H-H - EL. 590 FT TO 649 FT

• - 16

1 1'(~ECTlVE Vl~W I OF nc 'n9'U 1102 0

• FIGURE 0-1: PERSPECTIVE VIEW - EL.

17 590 FT. THRU 602 FT.

FIGURE 0-2: PEFSPECTIVE VIEW - EL. 602 FT. THRU 611 FT.

18

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FIGURE-0-3: PERSPECTIVE VIEW - EL. 611 FT THRU 649 FT.

19

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"°' "°' 504 CPP.lltl.ISllES SPENT FL£!. ...._TSIS FIGURE 0-4: FOUNDATION MAT AT EL. 590 FT.

20

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Structural slab not adjacent to spent fuel pool region. The reinforcement and concrete stresses in this slab are less than the allowables.

FIGURE D-5: SLAB AT EL. 602 FT .

21

• • N

.: I 28

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x z

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- I ICIOe  ;

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x J

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M FIGURE D-7: SLAB AT EL. 610 FT.

23

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• t I t t NS2 CPP "15'1DU 5'EIJT .Fl.!L --.rs1s FIGURE D-8: SLAB AT EL. 611 FT.

24

x N

26 l

z

- 2 NS4

-~.

i i

1a*ae ~ lllQI i llC~

/*a j L.U' i

~ t I I I J I ~ .

ll'JQI.

i NS3' Note:

Structural slab not adjacent to spent fuel pool region. The reinforcement and concrete stresses in this slab are less than the allowables .

• FIGURE 0-9: SLAB AT EL. 622 FT.

25

x l

?"'

S!XlH 63A I

...N z

NS4

~

+i-0' I

201ae

~ i 2DDC* 2020*

0 1noe

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NS3 Note:

Structural slab not adjacent to spent fuel pool region. The reinforcement and concrete stresses in this slab are less than the allowables.

C'!!.~l\.1~0£5.~~T_Fl.£L llMLfSJS FIGURE 0-10: SLAB AT EL. 634 FT.

26

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GIO CPP P'll. l SADES SPENT FI.EL '91111. r515 FIGURE D-11 : l~f'.:IRTH/SOUTH WALL 1 27

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FIGURE D-13: NORTH/SOUTH WALL 3 29

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FIGURE D-17: NORTH/SOLTTH WALL 7 33

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ATTACHMENT 2 Consumers Power Company Palisades Plant Docket 50-255 SPENT FUEL POOL STORAGE CAPACITY EXPANSION RESPONSE TO QUESTIONS RECEIVED FROM THE NRC PROJECT MANAGER July 24, 1986 14 Pages OC0786-0116-NL02

• RESPONSES TO NRC REQUEST FOR ADDITIONAL INFORMATION PALISADES SPENT FUEL STORAGE EXPANSION Question A: Dose rate changes at the sides of the pool concrete shield walls, where occupied areas are adjacent to these walls, should be reviewed as a result of the modification. Increasing the capacity of the pool may cause spent fuel assemblies to be relocated closer to the concrete walls of the pool, resulting in an increase of radiation levels in occupied areas. Discuss this potential problem.

Response: Increasing the capacity of the spent fuel pool and tilt pit will result in spent fuel assemblies stored in portions of the pool and tilt pit being located closer to the concrete pool (shield) walls than their current positions. Radiation levels in occu-pied areas adjacent to the spent fuel pool and tilt pit walls, 0 however, will increase by more than 1/10 of a percent (0.001)'.

This is due to the fact that occupied areas adjacent to the spent fuel pool and tilt pit walls will be separated from spent fuel assemblies by no less than five feet of concrete and the stainless steel pool and tilt pit liners (ref. NCRP46, App D, Figure 12). Supporting calculations using the Rockwell Nuclear Shielding Design Manual will be available on site *

• AT0786-0116A-NL02

2

• Question B: Provide or explain why the following descriptive information was not included in your modification for the spent fuel storage facility:

i. the manner in which occupational exposure will be kept ALARA during the modification including the need for and manner in which cleaning of the crud on SFSF walls will be performed to reduce exposure rates in the SFSF area; ii. vacuum cleaning of SFSF floors i f divers are used; iii. clean-up of the SFSF water; iv. the distribution of existing spent fuel stored in racks to allow. maximum water shielding to reduce dose rates to divers;

v. pre-planning of diver work as required; and vi. the provision for surveillance and monitoring of the work area by health physics personnel.

Response: i. Westinghouse, the organization performing the modification, does not intend to deviate from existing SFSF operations.

Water levels will be maintained at their normal height during SFSF modifications, thus ALARA concerns would be virtually unchanged. Nevertheless, ALARA concerns will be addressed during the ALARA reviews of procedures governing the modification process.

ii. SFSF Floors will be vacuumed only at spent fuel rack locations. Vacuum operations will be performed by using a

"""I

'* ...o:

swarp clean-up system. Rack removal and installation efforts will be done remotely. At this time, the use of divers is not anticipated.

iii. SFSF Water will be kept clean by utilizing Palisades SFSF Cavity Filtration System.

iv. Removal and installation efforts will be performed using remote tooling. Existing spent fuel stored in racks to be

__________________________________ removed _will be shuffled __ to empty:_ racks_._ We_stingho_usia cfoE!.S__

not intend to use divers.

v. At this time, the use of divers is not anticipated, and divers will only be used as a last option. A contingency plan will be developed, however, if diving operations are found to be necessary

• AT0786-0116A-NL02

3

• vi. All radiological protection monitoring and surveillance of work performed in conjunction with the expansion of the SFSF will be conducted by qualified Radiation Protection Department personnel. The monitoring and surveillance activities will be performed in accordance with approved Plant Health Physics and Administrative Procedures, and controlled by specific requirements on a standard Radiation Work Permit

• AT0786-0116A-NL02

4

• Question C: In Section 4.7.2, 3rd paragraph, pg. 4-12, provide the analyti-cal basis including specific assumptions that support your conclusion that the maximum gas generation would be less than 0.01 percent of the total room volume during irradiation.

Response: The calculation for gas generation being less than .01 percent of room volume uses the average gas generation over one year's time assuming the number of locations equivalent to one third core is filled with freshly discharged fuel and all other locations are filled with fuel one or more years old. The calculation also assumes the atmosphere in the spent fuel area is renewed at an average rate of the total room volume per week.

M

T N

AT0786-0116A-NL02

5 Question D: For the disposition of existing racks_, describe the following:

i. The method that will be used to remove, decontaminate and dispose of the old racks. Disposal alternative should include crating intact racks for disposal at a low-level waste burial site or cutting and drumming them for burial.

If the racks are to be decontaminated and stored on-site, then this alternative should be described.

ii. The number of workers that will be required for each operation including divers, if necessary.

iii. The dose rate associated with each phase of rack removal and disposal, occupancy times and the total man-rems that will be received by all workers.

Response: i. As part of the old rack removal process, each individual storage cell and all other surf aces of the rack shall be hydrolased. Decontamination shall proceed until average contact radiation readings are less than 50 mrem/hr.

The racks will then be removed from the spent fuel pool and dried in the cask washdown area *. They shall be moved to a loading area and placed in a fiber reinforced plastic bag.

This bag serves as ~ protective layer against the release of radioactive contaminants from the racks. The racks shall then be placed in strongtight shipping containers for transport to the Westinghouse Decontamination, Disposal and Recycling (DDR) facility located near Madison, Pennsylvania.

The number of workers necessary for the above efforts and their exposures have been addressed as part of the on site effort (see Enclosure B).

Upon arrival at the DDR facility the racks will be placed into a contaminated materials storage area while appropri-ate process areas are being cleared of other work. Once the processing area is free, the racks will be handled as follows:

1) The racks will be surveyed and appropriate samples

- obtained and analyzed' to meet the waste 'classification requirements of 10CFR61.

2) Any rack with excessive average contact radiation readings (greater then 50 mrem/hr) will be abrasively decontaminated to reduce the radiation levels and consequent man-rem dose. The decision.regarding abrasive cleaning of.the racks with hot spots will be determined on a per rack basis.

AT0786-0116A-NL02

6

• 3) Racks will be mechanically volume reduced and packed in strongtight shipping containers to both reduce total burial volume and meet licensed burial site waste stability requirements.

4) Volume reduced fuel racks will be shipped to a licensed commercial low level waste burial facility for burial.

Experience indicates that a crew of four men can volume reduce spent fuel racks of this type and number to approxi-mately 35% of their original volume in about 8 weeks.

Given the radiation levels above, exposures average approx-imately 15 to 20 mrem per man per week. Total man-rem exposure at the DDR facility for the volume reduction of the Palisades spent fuel racks will therefore range between

.480 and .640 man-rem.

r..n ii. Rack deconning, removal and packaging for shipment will be

• --~ performed by a seven (7) man crew: six (6) technicians and one (1) engineer. At this time, the use of divers is not anticipated.

iii. See Enclosure B.

• ~

• AT0786-0116A-NL02

7 Question E: Has the spent.fuel pool cooling system been modified to provide a direct cooling water supply for the tilt pit that is used for fuel storage?

Response: As stated in Consumers Power Company letter dated January 11, 1977, cooling water will be supplied to the tilt pit from the existing fill line which penetrates the pool wall near the top of this pit. A 90-degree elbow has been welded to the end of this pipe at the liner penetration to direct the cooling water downward. The nozzle welds are capable of withstanding seismic, thermal, and hydraulic loads. This line can be used to direct water from the spent fuel pool cooling pump discharge to the tilt pit for cooling purposes *

• AT0786-0116A-NL02

8

• Question F: Provide a summary of the evaluation of the spent fuel pool (bulk) cooling system. State the assumptions used and the results concerning (1) normal refueling heat loads, (2) full core offload heat loads, (3) temperatures with single failure, and (4) time to reach 212°F with no forced cooling.

Response: Fuel decay heat values for the spent fuel pool (bulk) cooling system were calculated using the method provided in NRC Branch Technical Position ASB 9-2. All storage cells were assumed to be filled (892 assemblies). Decay heat from fuel assemblies in the tilt pit was included with.the decay heat from fuel assem-blies in the main pool. Loading of the spent fuel pool was begun 36 hours4.166667e-4 days <br />0.01 hours <br />5.952381e-5 weeks <br />1.3698e-5 months <br /> after reactor shutdown and proceeded at the rate of 3 fuel assemblies per hour. For the full core offload case, the offload was assumed to occur just before a normal refueling which gives the highest decay heat values. The chart below shows the results of this analysis and lists the comparable results for the existing configuration.

798 892 Assemblies Assemblies Condition (existing) (expanded)

Normal Refueling Heat Load, BTU/hr 16.9E6 16.2E6 Outlet Temperature (2 pumps), °F 116 114.3 Outlet Temperature (1 pump), °F 118* 137.6 Time to Reach 212°F (0 pumps), hrs 8.5+ 8 Full Core Off load Heat Load, BTU/hr 26.4E6 34.1E6 Outlet Temperature (2 pumps), °F 134 141.5 Outlet Temperature (1 pump), °F 103* 191.9 Time to Reach 212°F (0 pumps), hrs 6.3+ 3

• This value was determined by accounting for the spent fuel pool cooling that is provided by the Shutdown Cooling System, assuming that fuel transfer tube is open and allows communica-tion between the spent fuel pool water and the containment refueling cavity.

+These times were calculated assuming an initial outlet tempera-

---*cure* of 18°F- -fcr:r- normar refi.ieTing coiidifions, - *and T03°F- for full core offload conditions.

Note that the normal refueling heat load for the existing configuration (16.9E6 BTU/hr) is greater than the expanded configuration (16.2E6 BTU/hr), even though the expanded configu-ration accounts for 94 more fuel assemblies. The major reason for this apparent anomaly is the difference in the times at which the decay heat load was calculated. For the 798 assem-blies case representing the current pool capacity, all 68 fuel AT0786-0116A-NL02

9

• assemblies discharged from the reactor were assumed to be in the spent fuel pool at 36 hours4.166667e-4 days <br />0.01 hours <br />5.952381e-5 weeks <br />1.3698e-5 months <br /> after reactor shutdown. In the 892 assemblies case representing the expanded pool capacity, refuel-ing (ie, discharge of fuel assemblies from the reactor) was assumed to begin 36 hours4.166667e-4 days <br />0.01 hours <br />5.952381e-5 weeks <br />1.3698e-5 months <br /> after shutdown and was completed at 60

• hours after shutdown, the time at which the maximum heat load occurred. Note that both of these cases are conservative since the Palisades Technical Specifications prohibits initiation of refueling operations until 48 hours5.555556e-4 days <br />0.0133 hours <br />7.936508e-5 weeks <br />1.8264e-5 months <br /> after reactor shutdown.

To put the two cases on a common basis, the heat load for the 798 assemblies case was corrected to 60 hours6.944444e-4 days <br />0.0167 hours <br />9.920635e-5 weeks <br />2.283e-5 months <br /> after shutdown using the NRC Branch Technical Position ASB 9-2. The resultant heat load is 14.6E6 BTU/hr, which is 10% lower than the heat load for the 892 assemblies case.

Also, for full core offload conditions, the heat load for the 798 assemblies case was calculated at seven days after shutdown, and the heat load for the 892 assemblies case was calculated at 108 hours0.00125 days <br />0.03 hours <br />1.785714e-4 weeks <br />4.1094e-5 months <br /> after shutdown.

Note also that all calculations for the expanded 892 assemblies case were performed for fuel stored in the, main pool and the spare tilt pit. Therefore, the results given above apply to fuel stored in either location.

~.!

AT0786-0116A-NL02

ENCLOSURE B Consumers Power Company Palisades Plant Docket 50-255 SPENT FUEL POOL STORAGE CAPACITY EXPANSION July 24, 1986 OC0786-0116-NL02

ENCLOSURE B

• SPENT FUEL RACK REPLACEMENT PERSONNEL EXPOSURE

SUMMARY

Page 1 of 4 The Personnel Exposure Estimate Worksheets contain the exposure estimate for various tasks involved in Spent Fuel Rack Replacement. These estimates include only the Westinghouse crew.

Summary of Exposure Estimates to W Personnel:

I. Prerequisite and Clean-up Task 0.122 man-rem II. Removal of Existing NUS Racks 0.688 man-rem III. Installation of W Racks 1.620 man-rem Total 2.430 man-rem Assumptions for Estimates:

The overall average exposure in the spent fuel building was found to be 0.69 0 millirem per hour. While the average dose rate directly above the SFP was 1.5 millirem per hour.

1.n

• AT0786~0116A-NL02 1

ENCLOSURE B Page 2 of 4 PALISADES PLANT SPENT FUEL RACK REPLACEMENT PERSONNEL EXPOSURE ESTIMATES I

I. Prerequisite and Clean-up Task Total Exp II of Times Radiation Number Task Per Task Task Total Description of Task Responsibility Levels mr/hr of Men Hrs (Man-rem) Performed Man-rem A. Fuel Shuff le CPCo 1.5 1 52.2 78.3 1 0.078 B. Interference R~moval CPCo 4 4 40 640 1 0.640

& Installation :

c. Temporary Shed, CPCo No Facility Erection Exposure D. W Personnel w No Platform Exposure rn E. Personnel Platform/ ~/ 1.5 5 8 60.0 1 0.060 N Positioning in

• CPCo 1.5 2 8 24.0 1 0.024 Spent Fuel Building 0

F. Rack Lifting ~/ 0.69 5 18 62.1 1 0.062 Drive Erection/, CPCo 0.69 3 18 16.6 1 0.017 Positioning/

Disassemb~y W Total of Task I 0.122 0 CPCo Total of Task I 0.759 Grand Total of Task I 0.881

~!

~

M AT0786-0116A-NL02

PALISADES PLANT SPENT FUEL RACK REPLACEMENT ENCLOSURE B Page 3 of 4 PERSONNEL EXPOSURE ESTIMATES II. Removal of ExistinG NUS Racks Total Exp # of Times Radiation Number Task Per Task Task Total Description of Task Responsibility , Levels mr/hr of Men Hrs (Man-rem) Performed Man-rem A. NUS Rack Lifting w 1.5 5 2 15.0 8 0.120 Rig Engaged B. NUS Rack Decon w 1.5 5 8 60.0 8 0.480

& Hydrolase

c. NUS Rack Transfer w 0.69 4 2 5.52 8 to Cask Wash Down 0.044 CPCo 0.69 2 2 2.76 8 Area 0.022 N

D. Rack Packing & w 0.69 4 2 H'i 5.52 8 0.044 Loading onto Truck CPCo 0.69 3 2 4 .14 8 0.033 N

0 w Total for Task I I 0.688 CPCo Total for Task I I 0.055 Grand Total for Task II 0.743 AT0786-0116A-NL02

• • ENCLOSURE B Page 4 of 4 PALISADES PLANT SPENT FUEL RACK REPLACEMENT PERSONNEL EXPOSURE ESTIMATES III. Installation of W Racks Total Exp II of Times Radiation Number Task Per Task Description of Task Responsibility Levels mr/hr Task Total of Men Hrs (Man-rem) Performed Man-rem A. Embediment Pad w 1.5 Elevation 4 9 *54.0 6 0 .324 Measurements B. ~ Rack Upending CPCo No Transporting Exposure

& Cleaning

c. W Rack Pre-level w No M & Drag Test Exposure

,n D. W Rack Transfer CPCo 4

~ . to Spent Fuel Building 4 8 128 1 0.128 0

E. Rack w 1.5 4 18 108 Positioning 6 0.648 F. Rack Leveling w 1.5 4 18 108 6 0.648

'J W Total for Task III 1.620 CPCo Total for Task III 0.128

~-.¥. Grand Total for Task III 1.748 M

AT0786-0116A-NL02

ATTACHMENT 3 Consumers Power Company Palisades Plant Docket 50-255 SPENT FUEL POOL STORAGE CAPACITY EXPANSION REFERENCED REPORTS H">

Shah, V N, Gilmore, C B, "Dynamic Analysis of a Structure with Coulomb Friction," ASME Paper No 82-PUP-18

• Gilmore, C B, "Seismic Analysis of Freestanding Fuel Racks," ASME Paper No 82-PUP-17.

Fritz, R J, "The Effects of Liquids on the Dynamic Motions of Immersed Solids," Journal of Engineering for Industry, February 1982.

Desanto, D F, "Added Mass and Hydrodynamic Damping of Perforated Plates

• .~ Vibrating in Water," Journal of Pressure Vessel Technology, May 1981.

July 24, 1986 33 Pages OC0786-0116-NL02

l 82-PVP-18

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DYNAMIC ANALYSIS OF A STRUCTURE WITH COULOMB FRICTION

[.n

""I V. N. Shah C. B. Gilmore Engineering Specialist Senior Engineer EG&C Idaho, Inc. Westinghouse Electric Corporation Idaho Falls, ID 83415 Pittsburgh, PA 15230 Hem. ASHE Hem. ASHE ABSTRACT may slide and tip during a seismic event. Iri addi-tion, a fuel rack may collide with other racks or A modal superpos1t1on method for the dynamic with the pool walls during an earthquake. In the analysis of a structure with Coulomb friction is seismic analysis of the freestandin*g fuel racks, Che presented. The finite element method i1 used to possibilities of sliding, tipping, and collisions derive the equations of motion, and the. nonlinear- must be evaluated. The main purpose of this paper ities due to friction are represented by a pseudo- is to present a c*omputationally '!Conomical method force vector. A structure standing freely on the to perform a seismic analysis of a freestanding fuel ground may slide during a seismic event. The rela- rack.

tive displacement response may be divided into two The direct integration methods(l,2) are widely parts: elastic deformation and rigid body motion. used for the nonlinear dynamic analyses, but their The presence of rigid body motion neceasitates the computer coat for the seismic analysis of a free-inclusion of the higher modes in the transient standing fuel rack is prohibitive. In order to analysia. Three single degree-of-freedom problems reduce computer cost, the application of the modal are solved to verify this method. In a fourth prob- superposition method to nonlinear analysis is lem, the dynamic response of

• platform standing considered.

freely on the ground is analyzed during a seiamic In the modal superposition methods, two event. approaches are used to integrate the nonlinear equa---

tion of motion. In the first approach, referred to INTRODUCTION as the incremental approach(3), the equation of*

motion is converted to an incremental form and non-Some component* in nuclear power plants are not linearities are treated by updating the natural anchored to the ground and may alide when subjected frequencies and mode shapes. In the second to external forces. These components are designed approach(4,5,6), the nonlinear terms are represented to with1tand hypothetical accidents resulting from as pseudoforce. In both approaches, the uncoupled an earthquake. In the seiamic analy1is of these modal equations are integrated analytically without component1, it i1 necessary to model the sliding introducing any artificial damping or phase between the components and the ground. For distortion.

inatance, one such component is a fuel rack to store In the dynamic analyses of the nonlinear struc-the 1pent fuel assemblies in a water filled pool. tures, such as spent fuel rack, the -source of non-Generally the fuel rac~s are anchored to the floor linearities is restricted to a small portion of the of the pool; however, some application* do not per- structure. In the finite element anlaysis, a large mit the fuel racks to be anchored to the floor. The portion of such nonlinear structure is modeled with unanchored fuel racks, standing freely on the floor, linear elements, while the remaining small portion

• is modeled with nonlinear element1. The computational co1t of the paeudoforce approach to analyze such non-1 inear structure* is lower than that of the incre-mental approach(5j. Therefure, the pseudoforce apporach i1 developed for the subject analysis.

Sliding of the structure is modeled with aid of Coulomb friction.

The modal superposition method using the pseudo-Friction force force approach was originally developed to 3nalyze the structures subjected to single-point translational excitations. The nonlinearity due to impact hetween various structural components was permitted. Later, the scope of this method was expanded[7] to analyzP.

the linear and nonlinear structures subjected to mul- Relative displacement tiple support motions. Recently, this method has between contact been further developed to analyze the structures surfaces with elastic-plastic material properties[8]. This method has now been expanded to analyze the struc-tures with Coulomb friction which is the suhject of this paper.

In the next section, an element representing Coulomb friction is described, followed by the dis-cussion on the pseudoforce approach. Then the use . INEL 2 0300.1 Fig. l Approximate friction behavior simulated by of the friction element in the seismic analysis is discussed. The results of four test problems are friction elP.ment shown in Figure 2 presented to verify the subject method and to gain y some insight in the use of the method. Gilmore[9]

has applied the subject method to the seismic anal-ysis of a freestanding fuel rack and reported a significant savings in the computer cost.

MODAL SUPERPOSITION METHOD The discussion of the modal superposition I M I

method is divided into the following three topics:

GAP

l. Friction element

2. Pseudoforce approach

3. Seismic.analysis.

Friction Element Coulomb friction is used to represent the energy dissipation resulting ~rom the sliding between two contact surfaces. The external force INEL 2 0298.

acting ~n the contact surfaces has two components:

one acting normal to the contact surfaces and the Fig. 2 Friction element to represent approximate other acting in the plane of contact, The latter friction behavior shown in Figure 1 component is referred to aa shear force. A friction force exists between the contact surfaces and acts in contact surface. Node K is fixed in the space. The a direction opposing the 1hear force, The magnitude direction ~ is along the direction of sliding. The of the friction force i1 equal to that of the shear friction spring (Kf) between node1 K and I 1imu-force. A1 the magnitude of the shear force increases, lates the friction behavior between two contact 1ur-the magnitude of the friction force increases until faces. The damper (Ci), spring (K1) and the its magnitude become* equal to the product of the parameter GAP between two nodes I and J simulate the normal force (PH) and a 1tatic coefficient of fric- possibility of separation of and impact between two tion (u 1 ). Any further increase in the shear force contact surfaces. In the absence of the friction will cau1e the two contact surfaces to slide along spring, the friction element reducea to a gap ele-the direction of the force. During sliding, the fric- ment. In a gap element, the nonlinearity due to

--tion force is equal to -the *product of the.normal impact .is represented by a pseudoforce as described force and the dynamic coefficient of friction in Reference[8). In the following di1cuaiion; ana-Cud>* lysis of only sliding behavior i1 presented. When The sliding between two contact surface1 take1 the force in the friction spring is greater than the place when the shear force becomes greater than the static friction force u 11 PN 1 sliding takes static friction force <usPN)* This ideal place, At the initiation of eliding, the relative friction behavior is approximately simulated by the displacement between two 1urface1 in the direction friction element. The friction element allows a of 1liding is nonzero and i1 equal to UsPN/~f* Al small amount of relative displacement between two the stiffne11 of the friction 1pring increases, the contact surfaces before the shear force becomes magnitude of the relative displacement decreases; greater than the static friction force. The approx- and the behavior 1imulated by the friction element imate friction behavior simulated by the friction will be closer to the ideal behavior. The"magnitude element is shown in Figure 1. of Kf is selected auch that the relative di1place-The two-dimensional friction*element is shown ment UsPN/Kf is a small fraction of the total in Figure 2. Node* I and J are located on each displacement due to sliding.

2

• • PRP.udoforce Approach In chis approach, the nonlinear dynamic analy-sis of a structure is divided into two parts: modal analysis and transient analysis. In the modal anal-ysis, the nonlinear structure is linearized by treating the friction spring as a linear spring.

Then, the mode shapes and the natural frequencies of the linearized structure are calculated. In the and transient analysis, thesP. mode shapes are used to uncouple the equation of motion. Mode shapes and the natural frequencies of the linearized structure are not updated during the transient analysis.

The equation of motion of a structure with the resulting modal equations becomes Coulomb friction is

/q} (6)

[MJ!XJ +. [CJ{X} +. [Kntl /xi = /F} ( 1) where where

~ .

J percentage of the critical damping

[MJ mass matrix for the jth mode (CJ damping matrix fKn.t.1 nonlinear stiffness matri~

{QI generalized Arrays {xJ, {x}, {"x}, and {F} are applied force the displacement, velocity, acceleration, and vector applied force vectors, respectively.

generalize pseudo force Let vector.

ui Arrays {q}, {q} and {q} are the

[KJ + [KJ (2) modal displacement, velocity and acceleration vec-tors, respectively. For a given time step, the pseudofroce is approximated by the first two terms where of a Taylor series, provided the friction force is continuous during the previous time step. The

[KJ stiffness matrix representing the pseudoforce is expressed as linearized structurP.

[Kl stiffness matrix representing the nonlinearity due co Coulomb friction. T<t<T+4T (7)

Substitution of Equation (2) in Equation (1) gives where (11J {XJ + [CJ{X} ~ [KJ{X} "' {F} - {F nt} ( 3)

~--'

where 4T

{Fn 1 1 a (KJ{Xl

• pseudoforce vector. (4) If the friction force is not continuous during the previouu time step, then Initially, the pseudoforce vector is zero and T < t < T + 4T * ( 8) it remains zero as long as the force in the friction spring is less than the static friction force. When the force in the friction spring exceeds the static For a given time step, Equation (6) is inte-friction force, the sliding initiates and the pseudo-grated analytically. Then, the displacements and force becomes nonzero. The resultant of the force veiocities of the nodes associated with the friction in the friction spring and the pseudoforce is equal elements are calculated. Thia information is used to a friction force acting on node I. Pseudoforce to calculate the generalized pseudoforce vector and is a piecewise-linear function of displacement and its time derivative needed to integrate the modal velocity of node I relative to node J. Let ['"111,)

equation* during the next time step.

and !ti be the natural frequency and normalized mode shape matrix associated with the linearized, undamped structure. The transformation Seismic Analysis In the seismic analysis of a 1tructure sub-(X} * [tl{q} (5) jected to single-point translational excitations[lO),

i.e., all supports are subjected to the same trans-lational excitations; it is a normal practice to

• is substituted in Equation (3) premultiplied by calculate the disp-lacement response relative to a

[+JT, Then, employing the orthogonality fixed point on the ground. If the structure is relations expressed by anchored to the ground, the di1placement response 3

ie calculated relative to ite fixed ba1e. The y relative dieplacement re1ponee conei1t1 of the elaa-tic defonaation and can be ei11Ulated by the lover L.

mode ehape1 of the 1tructure. For a linear etruc-ture anchored to the ground, the number of 110de hapee 'o be included in the analy1i* i1 determined y the frequency content of the eei1mic excitation.

If a linear 1tructure ie etanding freely on the ground, its dieplacement re*ponee i1 calculated with reepect to a point on the ground that i1 initially in contect with its base. If the structure 1lidee INEL 2 0301 J during a 1eismic event, its relative displacement response consists of the elastic deformation super- Fig.3a Spring-mass system with Coulomb friction imposed on the rigid body motion of the structure.

The presence of the rigid body motion influences the y selection of the mode shapes.

The finite element model of a freestanding structure consist* of friction elements between the baee of the structure and the ground. The stiffness of the friction springs is kept high so that the base of the structure experiences little relative displacement before actual sliding takes place. In W = 1000 lbs (deadwelght) the modal analysis. of a freestanding structure, the M

friction springs are treated as linear springs. In the lower mode shapes, these springs act like rigid I X members, while in some of the higher mode shape1 the strain energy in the friction springs dominates the - 0.1 I n.(p.reload) total strain energy. These higher mode shapes should be included in the analysis to simulate the rigid body motion. Thus, in the seismic analysis of a freestanding structure, the selection of the

~ode shapes depends upon the frequency content of

~ the excitation and the stiffness of the friction triprings.

INEL 2 0299J Test Problems Fig.3b Finite element model of a spring-mass system

\""'1 with Coulomb friction The modal superposition method described in paper is incorporated in the WECAN (Westing-e Electric Computer ANalysis) computer Dynamic coefficierit of o.3 ram(8). This program also has a direct integra- friction (11d) n methodl2) to perform the transient dynamic analysis of a structure. Four test problemstare Normal spring stiffness (KI) 10,000 lb/in.

solved to verify the modal superposition method in ( 1. 75 x 106 N/m) the WECAN program.

• In the iirst two problems, respectively, free Friction spring stiffness (Kf) 10,000 lb/in.

and forced vibrations of a spring-mass system with (1.75 x lOi; N/m)

~ulomb friction are analyzed. In the third prob- GAP -0.l in.

• • rem, forced vibrations of a spring-mass-damper

,.,.s,Ystem with Coulomb friction are analyzed. In the (-0.254 x lo-2m).

fourth problem, the seismic analysis of a platform supported freely on the ground is presented. The The deadweight of the mass H is 1000 lbs f'iourth problem is solved by the direct integration (4448.2 N) acting along the negative Y-direction.

method and by the modal superposition method. The The deadweight is balanced by the preload in the

~parisona of the corresponding results and the normal spring. The transient displacement response computer coats are given. of the mass H consists of only the X-component.

The spring-mass system analyzed in the first Test Prohlem 1. The free vibrations of th~

two problems is shown in Figure 3. In the third spring-mRss system with Coulomb friction are anRl-problem, a viscous damper parallel to the spring is yzed in this problem. The initial conditions are added to the system. The physical parameters of the

• spring-mass system are x 4. 7 in. ( 0. 1194 m) x O.O in./s (Q,Q cm/s).

Spring stiffness (K) 1000 lb/in.

_(l. 751 x _ro5 N/m)

The pseudoforce acting-on the sliding mass is given by ~ne of the following four expressions.

Hau (H) 2.59 lb-sec2/in. For X < 0 (mass sliding along negative (1.1748 kg) X-axis)

Natural frequency (wn) 3.1273 Hz F

nt x > 0 Static coefficient of 0.3 fric_tion C1u) x < 0 4

For X > 0 (ma11 1liding along po1itive

• t5.736 in

• x-axi1) (t0.1457 111).

x >0 The dynamic responae of Che mass M calculated by the modal superpo1ition method is 1hown in Figure 4. The amplitude of Che steady state di1-x <0 placement ruponte varies from 5.6367 in. (0.1432 *>

co 6.048 in. (0.1536 m). The average frequency con-tent of the response over the last three cycles is where 2.5042 Hz--approximately equal Co the excitation frequency of 2.5018 Hz.

PN dead weight

• 1000 lbs.

- 10.0 The-analytical result for the decay in ampli-tude of vibrations per half cycle is given by(lll 7.1 Decay in amplitude

• 2 x friction force per half cycle K 0.6 in. (0.01524 m). 1.0 The decay in amplitude per half cycle is constant.

This problem is solved by Che modal superposi- z.s c ion method using two different time step sizes:

6T

• 0.01 sec and 6T

• 0.005 sec. Table 1 gives Che*

decay in the amplitude of vibrations per half cycle i

using both time steps. The results show that for a I 0 smaller time step, the decay in the amplitude per ~

half cycle is closer to the correct answer of o.~ in. (0.01524 m) and is approximately constant . z.s during the analysis. =

TABLE t. DECAY IN AMPLITUDE PER HALF CYCLE DURING

• 1.0 THE FREE VIBRATION RESPONSE OF A SPRING MASS SYSTEM WITH COULOBM DAMPING (1 in. = 0.0254 m).

• 7.5 Decay in Amplitude per Half Cycle . 10.0 I I I I I I (in.) 0 Z.5 u 7.1 10.0 1U 11.0 TIMI ISICI 6T

• 0.1 (sec) 6T .. o.oos (sec) Fig.4 Displacement response of a spring-mass sys-tem with Coulomb friction, subjected to sin-First hal{ cycle o.73588 o.62674 usoidal forcing function PSinwt, Second half cycle 0.72421 O.lil840 w

• 2.50184 Hz (l in.

• 0.0254 m)

Third half cycle o.745811 0.61798 Fourth half cyclP O.li7Rli3 O.lil410

• • ifth half cycle 0.64979 0.605611 Case 2* The ratio of the friction force (F)

Sixth half cycle 0.1"13398 O.li01i710 over the applied force (p) is less than w/4. During resonance, as explained in Reference (12), the amp-litude of the displacement response is unbounded.

Test Problem 2. The forced vibrations of a The results calculated by th~ modal superposition spring-mass system with Coulomb friction are ana- method are shown in Figure 5. The frequency content lyzed in this problem. The mass M is initially at of the displacement response is 3.1250 Hz--approxi-rest and has zero displacement. The harmonic force macely equal to the resonance frequency of PSinwt is acting on the mass in the X-direction. J.1273 Hz.

Test Problem 3. The forced vibrations of a The two cases considered are spring-mass-damper system with Coulomb *friction*are r.ase l: p analyzed in this problem. The spring-mass system 2100 lhs (9341 N) shown in Figure 3 is modified by adding a viscous w 2.so1q4 Hz damper (modal damping coefficient*~) in parallel r.ase 2: p ?100 lbs (9341 N) co a spring between nodes I and K. The mass is J.1271 Hz (* wnl

'" initially at rest and has zero initial displacement.

It is subjected co a harmonic force PSinwt.

~* The analytical results for the steady Den Hartog[l3) has given a complete analytical scac~ amplitude are given by(l2J solution of this problem. The numerical results for the amplitude (A) of the forced vibrations are plot-steadv state amplitude = A = t~ ted in the amplitude diagrams~ The horizontal axis represents the frequency ratio (w/wnl and the vertical axis represents the magnification factor 5

• 0.0301513 (Case l)

• 0.0497~10 (Case 2).

Equ~tion (q) gives the modified modal damping coefficient for a single degree-of-freedom problem.

The modified damping coefficients for a multidegree-of-frP.edom system may he calculated as follows. In the modal analysis ~f a system, the presence of the 211.0

- n "

friction springs may or may not modify the original natural frequency of a mode shape. If the natural frequency is not modified, then the modal damping

• coefficient need not be modified. If the natural I\~

i... frequency of the ith mode shape is modified, then the modified damping coefficient tm,i may be z

!I c

0 vv ~

calculated from 2

i5

~ "'i

• ti

• 21.D - ~ tm, i

"'m,i

( 10)

• IO.O where I I I I I I I original natural frequency-

• 11.0 D 0.1 1.1 2.0 4.0 modified natural frequency modal damping ~oef ficient.

TIMl!RCI 0 Fig.5 Displacement response of a spring-mass sys- Case 1. For this case, the frequency ratio tem with Coulomb friction subjected to sin- wlwn

• 0.8, and the force ratio F/P.* 0.2. From the usoidal forcing function PSinwt, w

• 3.1273 amplitude diagram fort

• O.l (Figure 8 in Refer-(* "'n system frequency) (1 in ** o.0254 m) ence [13)), the magnification factor is 2.26. The

' amplitude A of the steady state response is given by A*K/P). In each of the amplitude diagrams, several curves are plotted for a constant value of the modal A = 2.26

• f damping coefficient. Along each curve the ratio of the friction force (F) over the amplitude of the 3.39 in. (0.08611 m) applied force (P) is constant. These diagrams are used to calculate the amplitude of vibrations for The displacement response of the mass H .calcu-Che following two cases, and che results are com-lated by the modal superposition method is shown in pared with the corresponding results from the modal Figure 6. During the last four cycles, the ampli-superposition analysis.

tude of the steady state displacement *response var-

~ p ies from 3.3927 in. (0.08617 m) to 3.2952 in.

Case 1: 1500 lbs (6672 N)

(0.08370 m). The frequency content of the response 2.50184 Hz

""' "'t 0.1 is 2.5047 Hz--approximately equal to the excitation Case 2: p 250 lbs (1112 N) frequency of 2.5018 Hz.

r..... Case 2. For this case, the frequency ratio 2.50184 Hz

"'t 0.5 wlwn is equal to 0.8 and the force ratio F/P

• Q.4.

From the amplitude diagram for t

• 0.5 (Figure 12 in Reference [13)), the magnification factor is*o.6.

The magnitude of the remaining physical parameters The amplitude A of the steady state response is remain unchanged from those defined in Test given by Problem 1, except in Case 2 where coefficients of friction are reduced from Q,3 to O.l and the stiff-ness of the friction spring is increase~ from A

• 0.6 *~

10,000 lb/in. (1.75 x 106 N/m) to 100,000 lb/in.

(l,75 x 107 N/m). . ..

• 0.15 in. (0.00381 m) *

. The niltiira"f" frequency of a spring-mass system is increased due to the presence of the friction The displacement response of the mass H calcu-spring. This increased frequency is used in the lated by the modal superposition method is shown in transient analysis. Therefore it is necessary to Figure 7, During the last cycle, the amplitude of modify the modal damping coefficient t* The mod- the steady state displacement response varies from ified modal damping coefficient tm is calculated o.1448 in. (0.00368 m) to o.1455 in. (0.00369 m).

from The frequency content of the response is 2.4956 Hz.

It should be noted that during each cycle, the response curve has a flat portion near its peaks.

(9) No sliding takes place in this flat portion. This 6

l.O 2.0 1.G

...z 0.0 2

(.l

-' -1.0 Q

Fig.8 RllMIC IXCITATGlll Finite element model of a long, freestanding

-2.0 platform. F

• 1288 lbs, (5729.3 N),

(l in.

• 0.0254 m)

-l.O the nonlinearity due to friction is handled by mod-ifying the stiffnes* matrix. In the modal superpo-i I I I sition method, the nonlinearity due to friction ia

-*.o ~~ndled by the pseudoforce approach as described in o.o .u 5.0 7.5 10.0 1:1.110 this paper. Tile impact between the masa m and the TIMI !SKI platform is modeled by a gap element[S,8] and i1 Fig.6 Displacement*response of a spring-m~ss sys- used with both methods. The platform propertie1 are

• -0 tem with combined Coulomb and viscous damp-ing, wlwn = 0.8, F/P = 0.2 and C = O. l Modulus of elasticity 2.8 x 107 lb/in.2 (1 in. = 0.0254 m) (19,3 x lolO Pal 0.15 Length 107.50 in.

! (2.731 m)

...~ 0.05 Cross-sectional area 60.6275 in.2 2

(0.0391 m2)

~ -0.011

~ Area moment of inertia 5.70 in.4 Q -0.15 (0.237 x lo-5 m4) 100 1'6 1* uo TIMI! ISICI Density 1.5343 x lo-3 lb-12/in.4 Fig.7 Displacement response of*a spring-mass sys- (42.47 kg/m3).

tem with combined Coulomb and viscous damp-ing wlwn = 0.8, F/P "' 0.4 and C = O. 5 The friction element properties used with the (l in. = 0.0254 m) modal superposition method are particular characteristic of the displacement Normal spring stiffness 8.351 x 105 lb/in.

response is also predicted in Reference [13J. (Kr) (1.46 x 108 N/m)

Test Problem 4. The transient dynamic response of a long platform supported freely on the ground Friction spring stiffness 8.351 x 107 lb/in.

and subjected to seismic e~citation is analyzed in (Kf) Ct.46 x lolO N/m) this problem. The platform is supported at both ends as shown in Figure 8. The platform is repre- GAP 1.0 x 10-6 in.

sentative of the base of a spent fuel rack and its (-0.254 x 10-7 m) supports are representative of t.he ~uppor~_ p_ads of l

the rack. A. concentrated mass, m, is located at the Mass (H) O.O lb-s2/in.

center of the platform. There is a clearance between the mass and the platform along the horizon- Coefficient of friction 0.8.

tal direction, and the mass is free to move relative <us

• lid}

to the platform. During a seismic event, the mass may collide with the platform. The impact between The friction element used with the direct inte-the mass m and the platform is a simplified repre- gration method has the same propertie1 except the sentation of the impact phenomena between the fuel normal spring stiffness is 8.351 x 107 lb/in.

assemblies and storage cells in a spent fuel storage (1.46 x 1010 N/m}.

rack. The magnitude of the concentrated masa, m, at

. This problem is solved by the direct integra- the center of the platform i1 equal to 4.0 lb-s2/in.

tion and the modal superposition methods present in (1.8144 kg). The initial clearance Ge between the the WECAN program. Both methods use different fric- mass m and the platform i1 equal to 0.2145 in.

tion elements. In the direct integration method, (0.005448 m}. The energy loss due to impact between 7

....

• and the ph.tform ia ne1lected. In the 0.70 detailed docU111entation of thi* proble*(l4], the ener1y 1011 due to impact i1 taken into account. o.ao The deadveight of the platfol'll ia modeled by three

~oncentr1ted force* 1ctin1 at the Node* 1, 3, and 5.

he magnitude of each force ia 1288.0 lb1 (5729.3 N). 0.50 The tran1ient di1placement reaponae of the platform con1i1t1 of only the x-component. ...:r ii 0.40 The platform i1 modeled vith two two-dimensional beam element1. The finite element model ha* ten degree1 of freedom; nine *re as1ociated with the ...~

platform and the tenth ia a1sociated with the con- ...:Iz 0.30 centrated mas* m. The modal analysis of the plat- ...

form gives ten natural frequencies and mode shapes. ~

..... 0.20 The fir1t frequency is Q.O Hz and is associated with Ill Q

the concentrated mass. The next six frequencies 0.10 repre1ent the bending mode shapes of the platform.

The three highest frequencies are 990.9 Rz, 1323.0 Hz, and 1836.0 Hz and* represent the axial 0 mode shapes of the platform. A rigid body motion of the platform can be represented by the linear -0.10 superpoaition of these three mode shapes.

Seismic excitation applied to the platform along the X-direction is shown in* Figure 9. The -0.20 platform may 1lide during the seismic analysis, and 0 0.1 0.2 0.3 0.4 its displacement respon1e consists of the rigid body TIME (SECONDS) motion superimposed on the elastic deformation. As explained earlier, the three axial mode shapes must (a) Modal superposition be included in the modal auperpoa1t1on analysis to represent the rigid body motion. 0.70 311.fl . . - - - - - - - - - . . . . . . . - - - - - - - - - - - ,

300.0 0.60

-0

.u 200.0 ii 0.50

...,::! 100.0 "':r<J 0.'D

~ ~

z 0 0 z... 0.30 C(

a: ...u

I

"'..... *100.0 C(

0.20 u Ill

~ Q

-200.0 0.10

-300.0 0

?

-311.6 -0.10

,.,. ' 0 0.2 0.4 0.1 0.1 1.0 TIME !SECONDS!

Fig.9 Acceleration time history applied co the -0.20 freestanding platform in X-direccion 0 0.1 0.2 0.3 0.4 0.5 (lin/sec2

• 0.0254 m/sec2) TIME !SECONDS)

Results of the modal superposition and the (b) Direct integration direct integration analyses sre presented in Figures 10 to 13. All the mode shapes are included Fig.10 Displacement response of Node l along in the modal superposition analysis. The displace- X-direction, Test Problem 4.

ment response of Nodes l and 6 respectively, along (l in. = 0.9254 m) the X-direction is shown in Figures 10 and 11. The time history of the friction force at Node l is pre-sented in Figure 12. The time history of the impact CONCLUSION force between ,mass M and the platform is shown in Figure 13. The comparison of time history results l. The modal superposition method may be used to in Figures 10 to 13 show that the modal superposi- analyze a structure with Coulomb friction.

tion method and the direct integration method give 2. The dynamic analysis of a structure with approximately the same results. The computer cost Coulomb friction requires that the mode shapes with of using modal superposition method is found co be higher frequencies be inclu~ed so chat the rigid four times leas than that of using the direct body motion due to sliding of the structure is cegration method[l4). correctly represented.

8

• . O.M !MIU O.IO 14114A Q.40 . .A

...iii:z: i 4M.4

~

0.20

=

Ill u

ac

...z 0

...a 0

~

... u i... *Mii.i Q -0.20

-104l.I

-0.40

• 11C5.I

-0.57 0

0 0.1 0.2 0.3 0.4 0.5 TIME (SECONOll TIME (SECONDSI (a) Modal superposition (1) Modal superpodtion*

0.13 1!54&.I O.llO 14154.4 tl

. .o 0.40 954.4 N ...iii:z: i u

0.20 =

"'ac u

454.4

...z ...0

... -45.11

...au 0 z 0

...c u i

IllQ -0.20 ... -546.1

• 104l.8

-0.40

~

-0.57 *111411.1 I"\',

0 0.1 0.2 0.3 OA 0.5 0 0.1 0.2 0.3 0.4 0.5 TIME (SECONDSI TIME (SECONDS!

M Fig. ll Displacement response of the concentrated mass m at Node 6 along X-direction (l in. '" 0.0254 m)

Fig.12 Tr1n1ient response of the friction force It the left support of platform, element 1 (1 lb

• 4.448 N)

3. The computer cost of using the modal *superposi- 2. Chan, s. P., Cox, H. L., and Benfield, w. A.,

tion method is less than that of using the direct "Transient Analysis of Forced Vibration* of integration method to analyze a structure with complex Structural-Mechanical Sy1tem1," Journal Coulomb friction. of the Royal Aeronautical Society, 66, 1962, PP* 457-460._

AC:KNOWLEOCHENT* ). Nickle, R. ii;., "Nonlinear Dynamics by Mode Superposition," Co111puter Method* in Applied The authors wish to thank D. F. Miller for Mechanics and Engineering, 7 1976, PP* 107-129.

providing encouragement on this project* and for 4. Stricklin, J. A., and Haider, w. !. , "Formula-suggesting Reference (13). A. J. Kuenzel's assis- tions and Solution1 Procedure* for Nonlinear tance in solving the fourth test problem is also Structural Analysh," Computers and Structure1, acknowledged. No. 7, 1977, PP* 125-136.

5. Shah, v. N., Bohm, G. J. 0 and Nahavandi, A. N.,

° FERENCES "Modal Superposition Method for Computationally Economical Nonline1r Structural Analysil," ASME Houbalt, J.C., "A Recurrence Matrix Solution Journal of Pressure Ves1el Technology, ~~

for the Dynamic Response of Elastic Aircraft," Vol. 101, Hay 1979, pp. 134-141.

Journal of AP.ronautical Science, Vol. 17, 1950, 6. Molnar, A. J. Vashi, K. H., and Gay, c. w.,

PP* 540-551). "Application of Normal Mode Theory and 9

0 0

-IOl3.1 -1000.0 i -2083.11 i -2000.0

!..."' "'a:u

~

-:JIMl3.11 ...0 u

• 3000.0 l  :

..telll3.ll -4000.0

-5013.11 *fiC!OO.O

-<<113.1 -5978.11 0 0 TIME fSECONDSI TIME ISECONDSI (a) Modal superposition (b) Direct integration Fig.13 Transient response of impact force on the concentrated mass m (1 lb

• 4.448 Ni Pseudoforce Methods to Solve Problem* with 10. Biggs, J. H., Introduction to Structural Nonlinearities," ASHE Journal of Preuure Dynamic, HcGrav-Hill, N.Y., 1964, PP* 245-248.

Ve1ael Technology, Hay 1976, PP** 151-156. 11. Tse, F. S., Hor1e, I.E., and Hinkle, R. T.,

1. Shah, v. N., and Hartmann, A. J., "Nonlinear Mechanical Vibration*, .Prentice-Hall, 1963, Dynamic Analysis of a Structure Subjected to PP* 175-178.

Multiple Support Hotion1," ASHE Journal of 12. Timoshenko, S., and Young, D. H., Vibration Pressure Vessel Technology, Vol 103, February Problems in Engineering, 3rd Edition,-

1981, PP* 27-32. D. VanNosrand, 1955, pp. 92-95.

• O 8. WECAN User's Manual. ed. A. W. Filstrup, 13. Den Hartog, J. p., "Forced Vibrations with Westinghouse Research Laboratories. Combined Coulomb and Viscous Friction", ASHE Gilmore, c. B., "Seismic Analysis of Transactions, Vol. 53, 193lt PP* 107-115-.-

Freestanding Fuel Rack11". Submitted for 14. "WECAN, Westinghouse Electric Computer presentation at 1982 Orlando Pressure Vessel Analysis, Verification Manual," Westinghouse

. and Piping Conference. Research Laboratories

• 10

. i'

.f SEISMIC ANALYSIS OF FREESTANDING FUEL RACKS c.e. Gilmore Senior Engineer.

Nuclear Technology Division Westinghouse Electric Corporation r.n Pittsburgh, Pennsylvania Men. ASHE ABSTRACT analysis of one of these components, i.e., free-standing spent fuel storage rack, is presented. The This paper presents a nonlinear transient primary functions of the freestanding spent fuel dynamic time-history analysis of freestanding spent storage rack are to contain the spent fuel assem-fuel storage racks subjected to seismic excitation. blies in a water-filled pool and protect the fuel This t,Ype of storage rack fs structurally un- assemblies fran excessive mechanical loads.

restrained and submerged in water in the spent fuel pool of a nuclear power complex, holds (spent) fuel The spent fuel storage rack consists of an array assemblies which have been removed from the reactor of individual storage cells made of stainless core. Nonlinearities in the fuel rack system steel. The top of the storage cell is flared to include impact between the fuel assembly and sur- facilitate insertion of the fuel assembly into the rounding cell due to clearances between then, fric- storage cell and precludes placing the fuel assembly tion due to sliding between the fuel rack support in an inappropriate location. The inside dimension structure and spent fuel *pool floor, and the of the cell is such that clearance (a gap) exists lift-off of the fuel rack support structure from the* between the fuel assembly and cell. The cells spent fuel pool floor. The analysis of the fuel within a spent fuel storage rack are interconnected rack system includes impacting due to gap closures, by top and bottom grid structures to form an energy losses due to impacting bodies, Coulomb damp- integral module. The bottom grid structure is con-ing between sliding surfaces, and hydrodynamic mass nected to a support plate which provides the level effects. Acceleration time history excitation support surface required for the fuel assembly.

development is discussed. Modeling considerations, Support screws (pads) attached to the support plate, such as the initial status of nonlinear elements, via leveling pads, raise the rack above the pool number of mode shapes to include in the analysis, floor, yet provide contact with it. The support modal damping, -and integration tfme-step- sue are pads also transmit loads from-the fuel rack module presented. The response of the fuel rack slbjected to the pool floor. For some applications, the sup-to two-dimensional seismic excitation is analyzed by port pads are anchored to the pool floor by bolts the modal superposition method, which has resulted which react to the seismic loads. Other applica-in significant computer cost savings when compared tions require the fuel rack modules to be neither to that of direct integration. anchored to the pool floor nor braced to the eool walls; thus, giving rise to the *freestanding fuel INTRODUCTION rack terminology. A typical freestanding spent fuel storage rack module is shown *in Figure 1*

Various structures, systems, and components important for safety in nuclear power plants are In the analysis of freestanding spent fuel designed to withstand the effects of earthquakes storage racks, hereafter referred to as fuel storage (seismic events) without loss of capability to rack(s), various factors are considered. First, the perform their functions. In this paper, a seismic effects of water, in terms of frequency and forces,

The methods described herein include analytical techniques used for determination of hydrodyn111ic mass and acceleration ti111e-history excitation.

Dyn1111ic modeling considerations, i.e., initial status of nonlinear elements, number of mode shapes to include in the analysis, modal damping, and integration time-step, are discussed. The nonlinear response of the fuel rack system subjected to two-dimensional seismic excitation is presented. *'"1e use of the modal superposition method has resulted in significant computer cost savings when compared to that of the direct integration method.

FUEL RACK SYSTEM DEFINITION The data required to formulate the finite eleinent model of the fuel storage rack consists of structural mass, structural stiffness, and hydro-dynamic mass properties of the fuel rack system.

The structural mass and stiffness properties of the fuel rack system are determined using well-known analytical techniques. Discussion concerning derivation of hydrodynamic mass for the fuel rack system is found as follows:

Fuel Rack System Hydrodynamic Mass For this application, the flufd motion is con-sidered to be described by incompressible potential flow, so that the dynamic fluid effect on the fuel rack system can be accounted for by hydrodynamic mass. Various sources for h~drodynamic mass can be found in the.literatureC4, 5 ,ti,7J. Many of these Figure 1 Typical Freestanding Spent Fuel Storage sources have experimental data to substantiate the Rack Module potential flow*theory results. However, the cross-N sectional geometry and/or bodies for which hydro-must be considered. During seismic excitation, the dynamic mass is available, are quite simple. Due to fuel assembly and cell respond, accelerating the the complexity of the fuel assembly geometry (an surrounding fluid. The accelerating fluid in return array of N x N rods), the finite element method induces an added mass effect on the two structures. discussed by Yu(BJ is used to determine fuel Secondly, the presence of nonlinearities in the fuel assembly hydrodynamic mass.

rack system (fuel rack structure and fuel assembly) are considered. Sources of nonlinearities in the The finite element model used to determine the fuel -rack system include geometrical nonlinearities fuel assembly hydrodynamic mass is shown in (impact) and a combination of material (friction) Figure 2. The.45-degree segment model shown in and geometrical nonlinearities (impact). These Figure 2 is for a 15 x 15 (rod array) fuel nonlinearities are located at the fuel assembly assembly. Because of the large number of elements grid/nozzle-cell interface (impact) and rack support involved in this model, substructure technique is pad-pool floor interface. The nonlinearities at the used to generate the full model. The results later interface consists of Coulomb or friction obtained from this model include a full matrix (452 damping due to sliding and impact due to support pad x 452 mass matrix) and a reduced matrix (2 x 2 mass lift-off, The possible sliding and impact phenomena matrix). The elements of the full mass matrix are which may occur at the support pad-pool floor inter- the hydrodynamic mass coefficients and represent the face result from coupled, horizontal, and vertical inertia coefficients that give the forces on each fuel rack system response. body (225 rods and 1 cell) when the accelerati9ns in two directions of each body are specified; namely, Due to the highly nonlinear characteristics of 452 degrees of freedom (DOF).

• The 2 x 2 matrix the fuel rack system, a nonlinear, transient, represents the hydrodynamic mass for two-body (fuel dynamic, time-history analysis is required. For assembly and cell) motion in one direction with nonlinear analysis, direct integration methods are fluid coupling and is based on identical motion of widely used; however, the computer cost for seismic all fuel rods in the fuel assembly rod array,*

analysis of structures employing large finite relative to the cell.

element models is very high. To re<luce the computer -

cost, the modal superposition method found in The 2 x 2 hydrodynamic mass matrix is imple-WECAN(lJ is applied. The nonlinear behavior due mented in the fuel rack system model using a to impacting Df fue1 ~ssembly and cell is modeled general, mass matrix, element. This technique models hydrodynamic mass effect on both frequency using a gap element 2J, The friction element presented in Reference (3) is used to model the and force response ~f the fluid coupled bodies 8' discussed by Fritz( , and Stokey and Scavuzzol l l.

nonlinear behavior due to lift-off and/or sliding of the support pad relative to the pool floor. Verifi- System modeling of fuel storage rack module hydro-cation of the modal superposition method for struc- dynamic mass coupling with the pool wall follows the tural problems wf th nonlinearities due to impacting method used for the fuel assembly. Hydrodynamic components and Coulomb friction is demonstrated in mass coupling between adjacent cells was found to References ( 2) and ( 3). have an fnsignfficant effect on the response of the 2

7UI I

l

-~

157 .*

31.11 i 18.32

~ ~

~

z 0

c

~

8c *19.32 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 T1MElll!~

Figure 3 Synthesized Horizontal Acceleration Time History ( 1 ln/sec2

• 25.4 11111/Sec2 Figure 2 Finite Element Model (45 degrees segment) of 15xl5 Fuel Assembly Used to Determine Fuel Assembly Hydrodynamic Mass rack module. However, the mass of water between adjacent cells was taken as part of the structural mass of each cell. i 19.32 ii!

~*

ACCELERATION TIME HISTORY EXCITATION z 0

The acceleration tfme history seismic excitation  ;"

used in this analysis is developed using the design response spectra ao~ damping va1ue$ given in Regu- ~

latory Guides 1.601 1) and 1.61 121, respec- *19.32 tively. - The seismic excitation is synthesized using spectrum amplification and suppression techniques per Reference (13). The 1940 El Centro earthquake record is the basis for the synthesized time-history excitation. The spectral characteristics of the synthesized time-history fs similar to the original El Centro earthquake record. Consequently, statis- ll 5.0 7.5 10.0 TIME lll!CONDll 12.5 115.0 11.6 20.0 tical characteristics of the El Centro ear.thquake are maintained in the synthesized time-history exci- Figure 4 Synthesized Vertical Acceleration Time tation. The synthesized horizontal and vertical History (1 In/Sec2

• 25.4 11111/SecZ) acceleration time-history excitation fs shown in Figures 3 and 4, respectively. pad and spent fuel pool floor. These two surfaces .

may slfde relative to each other~ separate frOlll each FINITE ELEMENT MODEL OF FUEL RACK SYSTEM other, and impact during the seismic event. The friction behavior is represented by a linear spring, The finite element model of the fuel rack system hereafter referred to as friction spring. The

'*f is shown in Figure 5. The fuel rack system model is composed of three-dimensional beams, three-purpose of the friction spring fs to calculate the shear force at the friction interface.

t dfme.nsf ooal sp.rfngs, two-dimenstona 1 . rotary springs, ...

general matrix elements, gap elements, and friction The fuel rack system 1110del *shown *1n Ff gure 5 elements. These elements are discussed in Reference consists of 119 elements (99 linear elements and 20

( 1). nonlinear elements) and 60 unique nodes, which results in 339 gross DOF. Boundary conditions are The gap elementCl,2) is used to model the imposed on 206 DOF. The reinaining DOF's are speci-nonlinear behavior due to impacting of the fuel fied in the ensuing modal and time-history analy-assembly and cell. The gap element is a combination sis. The imposed boundary condftfons are on all of ~ spring and a dashpot (damper) in parallel, DOF's associated with the spent fuel pool wall, coupled to t gap in series. The friction floor, and Uz, Rx, and Ry fuel rack system element< ,31 is used to model the friction inter- structural motion. Thus, the fuel rack module or face (two surfaces) between the fuel rack support system can slide only in the X-direction and respond 3

Initial Status of Nonlinear Elements The status of the nonlinear elements, i.e.,

l.EGINO* "open* or "closed", in a finite element model should

§ GROUND llllOTIOfrll INft.IT POINT be such that initially it represents the linear, reference st4te of the structure, as implied by

~ HVOAOOYNAMIC MASS MATRIX Shah, et al.12) For some structures, with various 0 NONLINEAR ELEllllNT NUllllJl" preloads and nonlinearities, determination of the

• NODE NUl'nlll reference state may require a nonlinear static .

(iterative) analysis. However, for this applfca-tion, the reference state of the fuel rack system is determined by inspection.

Prior to the seismic event, the fuel rack system is in static equilibrium, resting on the spent fuel pool floor. The support pads are preloaded due to weight of fuel assemblies and module, including bouyant effects. Clearance exists between the fuel assembly and cell since external forces are not acting on the system. Therefore, the initial state of the nonlinear friction and gap elements is "closed" and "openu, respectively. Having defined the reference state of the fuel rack system, the natural frequencies and mode shapes associated with the linear system are calculated. As the nonlinear elements change status during the til!Ml-history analysis, changes in the natural frequencies and.

mode shapes associated with the linear system are y represented by pseudoforces, as discussed in References (2) and (3).

l

)-* Modal Dampint _

Differen values of damping are specified for the elements which-define the fuel rack system.

Since the damping is not uniform in the system for a given natural rreguency, ft is called nonpropor-tional damping l4T. For nonproportional damping, Figure 5 Finite Element Model of Fuel Rack System an additional computation is required to calculate equivalent modal damping coefficients to be used in two-dimensionally in the X-Y plane. The seismic the time-history analysis.

excitation shown in Figures 3 and 4, which repre-sents the motion of the pool wall and floor, is For this application, modal damping is assumed transmitted to the fuel rack structure via the to be proportional to the strain energy in each frict4on and mass matrix (hydrodynamic mass element. This type of damping is used to represent coupling) elements. the energy loss due to stru~tural damping. The method presented by Whitman115J is used to calcu-To ensure that the spent fuel storage rack late equivalent modal damping coefficients.

modules function during a seismic event, design requirements stipulate, in part, that the rack Mode Sha~ Selection

• modules must be analyzed for any possible fuel Fore fuel storage rack system, consideration assembly loading configuration. To satisfy this was given to the number of mode shapes to include in requirement, analysis is performed to simulate full, the analysis to achieve the correct deadweight and partially filled (half-full), and empty fuel sliding (rigid body) solution. In the fuel rack assembly rack module loadings. The analysis to system model, the weight is distributed uniformly simulate the full fuel assembly rack module loading throughout the structure (represented by mass times is based on the fuel rack system model shown in acceleration due to gravity) *. Thus, a portion of Figure 5. This model is a two-cell representation the structural weight (mass) fs associated with each of a fully loaded rack module. The partially filled node in the system model. Since the vertical fre-anc empty fuel assembly loading configuration system quencies associated with these nodes are generally model is derived from the model shown in Figure 5 by high, the higher mode shapes should be included to removing one and two fuel assemblies, respectively. achieve the correct static equilibrium solution. To This analysis also encompasses variations in fric- support this reasoning, a study was performed to tion coefficient µmin (0.2) <µ<-µmax (0.8) - determine the number-of mode shapes required to

• between rack module support pads-and pool floor. achieve static equilibrium. The results of this study showed that 95 percent of the system mode MODELING CONSIDERATIONS shapes are required to achieve the correct static equilibrium support pad load.

In determining the transient <tynamic response of a structure when using the modal superposition In modeling the friction interface between the method in Reference (1), consideration must be given support pad and pool floor, the value for the to the initial status of nonlinear elements, modal friction spring stiffness is set high such that: al damping, mode *shape selection, and integration time small elastic deformation occurs in the friction step. These considerations are discussed in detail spring prior to rigid body motion; and b) the in the following sections. lateral frequenr.y response of fuel rack system is 4

., not affected significantly (lowered) due to the Figures 6 through 12 show plots of the typical fuel rack systell response due to the two-dimensional

• . * . friction spring (llltlich fs a flexibility between the

. support pads of the rack module and the pool floor seismic excitation. The response in these figures

' and is included in the modal analysis of the fuel is obtained frOll the partially filled fuel rack

. ' rack system). Note that the friction spring stiff- system model during the time interval 9.75 sec < t <

ness is not set so high that ft governs the integra- 11.70 sec. The partially filled fuel rack systiin -

tion time-step used fn the analysis. Sfnce the mode model is derived by removing the fuel assembly on shapes associated with the friction springs possess the right side of the full fuel rack system model.

high strain energy and frequencies, these mode shown fn Figure 5.

• shapes must be included in the analysis to obtain

• • the correct rigfd body solution, as discussed by Figure 6 shows the impact force response of Shah and Gflmore<3J. Therefore, based on dead- element 5. Element 5 represents the interaction l weight and rfgf d body motion considerations, all mode shapes are included fn the analysis.

between the fuel assembly and cell. This element is located at the center of the fuel assembly and cell. The maximum impact force for this element is Integration Time-Ste~ -260.3 lb (-1157.8 N), which occurs at 11.48 sec.

sing the tfme h story excitation shown fn Figures 3 and 4, with acceleration due to gravity added (superposed) to the vertical excitation, a study was performed to determine the integration tfme step required for converged results. Thfs 0 study utilized the partially filled fuel rack system model. This conffguraion was chosen because ft is more sensitive to an integration time-step (due to stability considerations), as compared to the full and empty fuel rack system models.

Based on previous analyses, an integration time-step of 2.000 io-4 sec. was used to calculate the rack response during the time interval o.oo sec

~

w

(.J a:

-50.0

-100.0 (7' 0

• -0

< t < 1.95 sec. The rack response was calculated aur1ng this time interval to provide for: al time for the fuel rack system to respond to the initial

(.J

-150.0

~~

portion of the seismic event; and b) initial condf-tions for calculating rack response due to strong motion exeitation (1.95 sec < t < 3.90 sec). Usfng the restart capability in Rererence (ll from thfs point in the time-history excitation (1.95 sec), the

-200.0

-250.0 - I

• integration time-step study is performed ¥sing -260.3 I I I I I integration time-steps of 6T/6 (8.333 10- sec), 9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.70 6T/8 (6.250 10-4 sec), 6T/12 (4.167 io-4 secl, TIME (SECONDS) 6T/25 (2.000 10-4 secl, and 6T/50 (1.000 io-4 sec). ~T is the time interval (0.005 sec) between successive points in the time history data. Figure 6 Fuel Assembly Impact Force at Element 5 for Time Interval 9.75 sec < t < 11.70 sec Based on a comparison of support pad and fuel (1 lb* 4.448 N) - -

assembly force response versus integration time-step, the results indicate a converged solution is A plot of the vertical force on.the pool floor achieved (within 7 perientl using an integration from element 10 is shown in Figure 7. Element 10 tfme step of 2.000 10- sec 1 Thus, the integra- represents the support pad on the right side of the tion time-step of 2.000 10-~ sec fs used in the fuel rack module. The minimum vertical force full, partially filled, and empty fuel rack system response for this element is 0.0 lb (O.O N), which analysis. occurs during the time interval 11.50 sec < t <

11.54 sec. The value of o.o lb (O.O N) for the FUEL RACK SYSTEM DYNAMIC RESPONSE vertical force of this element indicates that this support pad lost contact (lift-off) with the pool The fuel rack system dynamic response consists floor. The vertical force on the pool floor from of spent fuel pool floor loads, fuel assembly-cell the support pad on the left side of the fuel rack impact loads, and rack module displacements. As module, element 11, is shown in Figure 8. The mentioned previously, the seismic analysis of the maximum and Minimum vertical force response for this fuel rack system includes all possible fuel assembly support pad is -2023.2 lb (-8999.2 N) and -830.7 lb loading configurations, as -well as variations in (.~3694.5-N), respectively. The-minimum vertical friction coefficient, µmio < µ < µlllilX' The force for element 11, -830.7 lb (-3694.5 Nl, indi-results of this analysis fnaicate the maximum spent cates that this support pad does not lfft off the fuel pool floor loads, i.e., vertical and friction pool floor. The maximum vertical force for element load, and fuel assembly-cell impact loads are 11, -2023.2 lb*(-8999.2 Nl, occurs at time t = 11.52 derived from the full fuel assembly loading configu- sec., the time at which the support pad on the right ration, wlth maximum friction coefficient, µmax* sf de of the rack module has no contact with the pool The maximum rigid body, or sliding motion of the floor. The vertical force response for the right rack module was also determined from the full fuel (element 10) and left (element 11) support pads are assembly loading configuration; however, with out of phase with each other and are* centered about minimum friction coefficient, µmin* the static equilibrium position of -570.0 lb

(-2535.4 Nl and -1400.0 lb (-6227.2 N), respectively.

5

.0 -200.0 249.5 200.0 150.0

~.o 100.0 i i:!

...u -600.0 ...u 50.0 ac:

ac: ...0 0

0

-800.0

-50.0

-1000;0

-100.0

-144.8 ,..___ _ _ _ _ _ _........._ _ _ ..____..___~

9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.70 9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.70 TIME (SECONDS) TIME* (SECONDS)

Figure. 7 Vertical Force on Pool Floor fran Support Figure 9 Frictfon Force on Pool Floor frCll Support Pad. Element 10. Ouring Time Interval 9.75 Pad, Element 10, Durfng Tfme Interval 9.75 sec~ t ~ 11.70 sec (1 lb= 4.448 N) sec~ t ~ 11.70 sec (1 lb* 4.448 N) the Ux response of node 53 fndicate no slfding and sliding motfon, respectively. Figure 10 shows that sliding motion of the support pad fs initiated at times t

• 10.80, 11. 27. 11. 32. 11. 38, and 11. 52 sec. During the time fnterval shown fri Figure 10,

-1023.2 u

ac:

0

-1423.2

-1823.2

...iii::c u

~

0.0204 . . . . - - - - - - - - - - - - - . . . . . . . . , . . . - -.....

0.0~00 0.0190 0.0180 loo

...z

-1823.2

...:I

~

..... 0.0170 8J 2i

-2023.2 .___..___..___~_....__....__...L...._...L.-J 9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.70 0.0190 TIME (SECONDS)

Figure 8 Vertical Force on Pool Floor fra11 Support 0.0150 c::.__:L---L---L---L--__.L--__JL--.....J~-

Pad. Element 11, During Tf111e Interval 9.75 9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.70 sec~ t ~ 11.70 sec (1 lb* 4.448 N) TIME (SECONDS)

The friction force on the pool floor frCll the support pad on the right side of the rack module, Figure 10 Lateral (Ug) Displacement of 54.lpport element 10, is shown in Figure 9. The inaxi1111111 and Pad, Node 53, During Time Interval 9.75 rainimum friction -load on the pool .floor is 249.5 lb.

(1109 *.7 N) and -144.6 lb (-643.2 N), respectively.

_ sec < t < U *.lO sec (1 In. * --25.4 ma) -

During the time interval 11.50 sec < t < 11.54 sec, the right support pad experiences 11axinA11 sliding the friction force for this element-is lJ.O lb (O.O 1110tfon of 0.0055 in. (0.1397 1111), fra1t 0.0204 fn.

N). This follows fran Figure 7, which shows the (0.5182 111) to .0.0149 fn. (0.3785 m). The Ux vertical force for element 10 to be 0.0 lb (O.O N) displacement plot for node 57 is shown fn Figure during this time interval. 11. Node 57 represents the support pad on the left side of the rack 110dule (Figure 5). A comparison of F.fgure 10 shows the lateral (Ux) displacement Figures 10 and 11 shows nodes 53 and 57 to be fn se of node 53. Node 53 represents the support phase. The phase relationship between nodes 53 and the right side of the rack module (Ffgure 57 indicates that the rack module experiences rigid

.* n Figure 10, horizontal and vertical lines for body sliding 1n0tion during the tfme interval shown.

6

A review of Figure 6 indicates that the fuel assanbly impacts the cell at times t=9.90, 10.85, 11.29, 11.48, and 11.61 sec. The impact of the fuel assembly with the cell at these times is indicated in the vertical and friction force response of the support pads as shown in Figures 7 through 9. Specifically, the impact between the fuel assembly and cell at time t *11.48 sec results 3

in lift-off of the support pad from the pool fJoor at time 11.55 sec. Comparison of Figures 6 and 10 indicates that rigid body motion of the support pad occurs as a result of the fuel assembly-cell impact. Thus, the results indicate that the fuel rack system response is significantly influenced by the strµctural interaction (impact) between the fuel assembly and cell.

CIJilPUTER COST The response of the partially filled fuel rack system model (with rms wave front equal to 96.7£ was calculated using the direct integration method( >.

The computer cost, i.e., cost per integration time-11.50 11.70 step, of this analysis was compared to that of the modal superposition method, which included all (103) mode shapes in the solution. An integration time-Jport step of 2.0 io-4 sec was used for both analyses.

al 9.75 The comparison showed the modal superposition method 4 mn) to cost less by a factor of 22.1 than that of the direct integration method. Only 0.8 percent of the e for modal superposition cost is associated with the ack modal analysis; i.e., calculation of natural he maximtsn frequencf es and mode shapes. The cost advantage of pad is the modal superposition method reported here makes for this use of the option in WECAN to bypass(the calculation d has of the forces in the linear elements 1,2),

f Ff cal CON CL US IONS e.

1i 1. The modal superposition method can be used to e support determine seismic response of detailed struc-tures which have nonlinearities due to gap closure and Coulomb damping or dry friction

- between two sliding surfaces.

2. Mode shapes with high frequencies must be included in the analysis to represent static equilibri1111 (deadweight) and rigid body motion of the fuel rack system.

3. The maximum spent fuel pool floor loads and rigid body (sliding) rack module displacement result from the full fuel assembly loading configuration.

4. The fuel rack system response is significantly influenced by the structural interaction between the fuel assembly and cell.

5. Significant reduction in computer cost has been realized by using the modal superposition method in lieu of the direct integration method to determine dynamic response of freestanding spent fuel storage racks subjected to seismic excf tati on.

S 11.50 11.70 ACKNCMLEDGEMENTS The author wishes to express his appreciation to upport Dr. V. N. Shah for his valuable cornnents in using rval. WECAN Modal Superposition Method. Ms. C. Culbertson

.4 assisted in model development for determination of fuel assembly hydrodynamic mass. Mr. T. P. Murphy 7

of Hydrodynamic fte Element 00- P-117.

of on the \

ds," E, Journal

• 94 ,""TI72, pp.

• UZZO, R. J., ;'Normal oncentric No. 77-PVP-37.

ission, Directorate cry Gui de l. 60, smic Design of 1, Dec., 1973. -.

ission, Directorate ory Gui de l. 61, gn of Nuclear Power nm-Comp ati b1e CE J. Enar* Mech.

, (No. E 2).

of Vibration with lewood Cliffs, N.J.,

ucture Interaction,"

Plants, (R. J.

ridge, Mass., 1970,

-* ----~-*---

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'711111 ........ "' "' ll'L.t*t .. *1** .. 11:11.alt* 1:1*rc1r1;.-t.*.... ,,l .. , .. 1 ** t l'**~n.:r t 'u11tr,l 1 uri... I 11\' 1ltu l tC' .. i~:*1 1*::1,i...1111.*cnu.: l>i,*L~iun :11111 1*rt':ioae>uh:'I aL ll1t.* \'1i11,,ru.1,, C *111f1*n*1wc. T111011lu, ( 'au:ul:.. Sc1*lt'Uthcr K-10, 0

l!J;t, "' ........\\lt:ICll'\"' s .......:I'\..... ~l*:1*11A,****.u. l*'.-.1;1st:*:1&1&. A {11r11111f ....1111i1111

\l.11111 ... *ril'I r1*1*1*1**~.1 al ,\~.\I K ll~ad1 1 uarh:r~. J1111u 11. 1u;J. l'.*1ier

~ ... ;1.\ il1r*llJIJ.

J-:11rnal ol En~inccrln~ lor lndu~trv

'i' 1 ~ j'",. Jur~* *.~- prl.tlrt!O~ I",' + l'i') (13)

Frol'I 1~c111:\l.ic111" (i), (1'), (i:.!), nnJ (l:lj F11 .. -.ll uir + (,\/, + .\1 11 )i 1 (H)

/*'n ,.. (.1/ 1 + ,\( 11 ).?1 - (,\/ 1 + J/, + ,\/ 11 ).r, (lj)

• I wlll'n' /*'11 nml F" nrc lh1* ll11i,I n*!wli1111 furn:-" \he i1111<'r l\ll*I onlt*r cyli111kr,., ; C-*P*'l"l ivdy, :rnd

• --**, "\

(~t ,** ~ -,r11' l.p \, 111:1:*:* ul f111icl 11i"ph1'\*1I 11,\' I he* i1111cr l l, I - ~ rylimkr

.If: Tri*'l.p ma"""f f111itl 1h:111:11ulcl lill llw co11lcr cy-li11dri1*al ravily i11 llll' ali:-c111*t* uf the (IGj

. -i1,_ucr rylimlcr

-* i.,2 + ~! *

.( .11 11 ., .11 1 ---

~  : - " - 11! 1

\...l )

-Fur thc-t*as<* 11(*1*0>11rt*111rir "Jlht*rt'l< ,.cparal1.'tl hy a fricli1111k.,_..,

i11c1111111n.,,,.ihle lluid (s<*c Fi;:. I), l!u.* !111ill fur,*~ :haL rc~11IL Crum u :<i111ilul' a11:ily,:is an~ :ii:-** ~:ivc11 h~* 1.*<1\mti1111" ( 14) :\lu.l (l:i) wher~

1"1 1 1111<1 1'.'!1 *arc 1111.* lluid r1.*:1r1i1111 (11rt.'l":j 011 the i1111cl' nnd oukr 1<J1h**n*s, fl"'l"Livcl~*, aull

• 1'1, .,. - r.a 1p 3*

1a:t.."4 11( nuid Ji,.plat'l'(I hy i1111cr "Jlhcrc r*r + rJ' - I ,. o (0) 111:1~ of lli;i<11l1<"1i;*:al ravil.\' i111lo1*1.l...,*111,*uf Lhu

• rlu* ,..,,_li=t :1111 t*r ii.; .. '"'Illa\ iun j...; l"C.'~L...,n:alil,v ~1 rui~?il furwurd.

{'J 'J'l;i* lin11l ,_11J11l j, >II j., ium*r "i'lll'n'

"'* ,,. + '.!11*

I' r .. (-,2' II

,! ) ('II: c (i) ,\/II

.! Ii' - "'

.. " e~,. +

I ~ ..t

\J ~1.1. ()

(S) Sy11lhc~is of filiid forces. !ur TWO* nouy Problem l-:*11111li1111.' (HJ 111Hl (I ... ) 111ay In* dt*vc*lujl\*l.in a 11111rc gc11c111l

..l\lit*1c w:..i.j'. Cu11:-idcr the c~*c *,*;here fl11id mu:iuoi i.~ c.!t*1cr111i11c<l br tl;c

/, 1a 1 motion of imme:rsnJ soii1.1.i. Similar to LnmlJI:!, p. I.SS}, the fluid lJ - - - -1 (+/ .t:) (9) kineti~ ;,*ncq;y is taken a." :i q1111<lr:.t.ic fo11ctio11 v' - a l*IJ li.L' ;; *. ~ .* \,:>., .i :11.i:\* .. ._' 0 1.;,.~.~-*~1,,_. ~*,,1 ******-****- . ...; ,.,.,.,.;. 11 t*r.l:;,:: :did n  :~y \.~ '"dl:!J l:ll iiilr\i~d L~;;1u1:,~::111. :--y~l ... HL 'l.i1e H1i:J n*:,1 ti*.111 f.ir1*c f ia Stir.I-. 11 ~y.:lt<ll\ :,-, i:ivl:*: 11~* L~.r,r:rnl':c':1 A;&* For lk, ~\\'C>-l>;;i..!)' prulili:-n\

1; Cill!:1!i1*U (20)

(1 l) Fru1>1 C*Jlli>'.'.ol\s (!:.?) i:ml (~u)

A1:.l\ (:!I)

\:h;. 1t!1 J, ;1 n.: l !.~ t~ca~*r:tli.-'"*d i..:*.l:.,nli111~~t* .. ; ~ 1:~u~ii1:1 :.nr~ ',, i*; tlir?

fluid ~*i: 1 ,.1 i;..* *,*::z*. i.'Y* I!~ thi*; !l:*rl.r 7: *~*.*ill ~:f*l**"\r.d!y l1r: t ::~ lr~uu: * * ('..!:!)

-i*I:.&& A::i1

];..,ti.1 .... ~ II\:*~;,,:\.,; a :--t.t:\~ lHh!y (b:.JJy i), ,,11<1 F 1 , wili l11,; t!1 ~ C11i\J j';.*;1r\i;111 (1HTt' 11~1 ~ii;.t:. ii',l IJ11*;y, wl1*:r* i1!~**i:1, f.1 1 :rncl f<'n nm lhu !!uiil rc*ll'li1*11 for,*~ u11 !'.<1licJ lt i~. na:**111: :,~,. lr1 :;*:.~\ :..,:t.. tb1; turlr,huti*.. n oft!~*-' i:.~.*.. \!.;i"lll lu l1111li1*.-; l 1.1111 :?. Tho *~1t*liit*ic11l>1 ,1 will 1111w lio 1h:l".!rmi1,cJ.

~';1.::~J11:: i? l: ii 1L~* ~1;J1tl :*~t..<ti.1:i~ t*1*1;. ::.* ...... ~1::\:..-~! \u !>'.! ~.n10~ll ,,_.i~h  :\.~*111nc f:1r tl:is t;Xa111p:c tiu.I. l.uJy :? "11rr111111ol:< U.i<l}' I, hin.i:ar n***!*'"*! l!' Cul'.! ,*,1:"!::1:\ \L:1*l~n:* ...... l:~. ~~t~,*~, au r.s ... \1~ *. : .* ~:1.11 i~ (11 1!1.! cul'dition u{ ti *.: prn!ilt*lll a\>o\':.J r11;* lhu c:yliaukr; 1:.nc!

!1*.*.* ' * !:1 ti,:.: 11.q: :r, J. :.:id; l:..!J ,uu... i.J1:r.""J h fl"*'; C:l:,1~:.: <1f ~*;r .. ~!~~**  ::pl:;*r;.~.  :\11\\' c'111:1ticrns (".'l) :111<l (:'.:!) :111: 1:c1oc1:1lly tnr<? (or 11:1

• : i:, 1:i* :::.;,  :::r-:" ::\.;~ 1i.1.* 1:.* =. \'..:li\:.  :\**~_':.* ..*t.i:1.', !:, . : :.~**l l1*l1i~ V:*k**; ui .i*1 :u::l .:',. lf J1 "'" ..i',, \l.t*11 Lli,* fl*;id ac*n:ll:mlio11 L* ;,

. rpi t .,,*;.1;,.:* (I'>.'*'***:~ .. :,~;:**' ti .. 1~ {1.rt....: ;.; it\ :.:'.'t-.y 1':1i11 1. i11 :~11 l!i1*11111p1~:-.* ilJll* {}l1id a:n~ h prr... ,ur1..' }~rad:L"*Ll

,, / t.:**.,*,.\) ~*:i~L..; U11u*t~h.:ut. the :iu1d ,!:11* l.:.> \he lluld iH~:*t.ia, r ... r. I , .. ( l:')

I ,, \\.*:I/ i>!'

lJJ. ... ,. ,.,

.,. *. ., r: ; .J.... ~ cf i'.!c: l} * (

.* nil j'~ IH(' l'f\11:11. Fur thi- l'lll&!itiun thc.l111i.I rurt'I... :ire* 11*11:111~*

'Ii .. : p:-1**-1111* .Ii .:rih11!iott1 r*.iv*'"' ri-1* 111 a l.u .. ~*a111*y f111r1* of 1*11"ily .!;*!rr111i11:1lill*, ,.jrnilnr tu tl.4! h\"11-luuly 1':\*t' 11ln*aolv 1!1'-

\rt"l:it*'.,*d.*- tr;***,"' Llaal.

,.,*riht'<L \\'ilh th,*:.(* ll11itl r.. n~ ... 1h*h*rmi11:1hh*, II i"1*1:1:in1t* 1ir1*

f-'11 *. , *-(A II + 11 .,},;*, r' .lf 1 i'1 ('.,!*() l'*'l:1h!i .* hr1l i11\*11lvi11i:: tht* r*u111pcrncnh of ,I. Tlll'rc* :ire* 11111 +

• 1 )/'~ c*11tnpo11r11f,1 11( ,1 whirh nm.:!. lir. 1lrlt*n11i111*1l. Thr r1'-

f-tl" -CA,,+A~).r,,. -.11,i, ('..!!"1) 111:1i11i111-t t**111al i1111,. 111:1~* lit* l'.-111hli,.f11 .. I l1y 'l'lliui: 1111 r,

• ti 1*s-from whit-h rcpt. our, i ;r n111I ll'lli11~ j =- l tu n. The vnh1r.-1 uf t hl' ll11i1l f111'N.'S fll"C mo~L Cl\-~ily dct1*rmiill'd if nnl~* nllC hod~* 111 au~* u11r.

A11 + A11..., -.ll 1 (:?G) time is :illowt.:cl to 1111r\'c. ll j,. .. uc-r;l.,,l<.'tl th:1l lhrs1~ l111i1l fon*N A1i + A1i .. M, (2i) wm1ld he clrlcrmin<:<I from 1hc nmti1111ity nf flow nucl h~- 11,.1* uC L'<tllnti1111 (12). Alth1111i::h it i:- ditlir11IL to prcrlirt nil tlll' pu--ihlu

"~" n111fii.-;11r:1tio11s thnl mny he nwL in pr111'1ir1*, it. i* >'lll?L:"'"I ihaL

,1[ 1 ~. l!u* It<'<<< ur 011itl <Ii: plnr1*d l1y I hr: i1111c*r Lu<!.'* in ,,,,Jvi11~ ll1c c1,;ili1111it~* 1*q11:1tim., ~om<! mt'lhml 11( .*Nil*,. nncl J( 1 ~ t!.c ***'"'-~ uf Ouit! ilia\ wnnl<l fill I.ht* hod~* 2 i11 thr. :ilt- 1inrnHcl flow i111prd1111rr:< mii:ht he ronsiilcrr.tl, n1111l11i::1111* 111 1111

,.<*1"*~* .. r th** i11111*r 1.....1y l'h*1*1rir 111*lw11rk :111:i.l~*,i:-. l~*tlluwint: thi* prr~1*ripli1111, 1111' **n111-fl<lll('l\\s o( tl1r fi11i(\ 11\:L" malri:rc A in rq11:1li1111 l:IO\ :1rr 1lt*!r*r-Eqnnt i1111~ (:!ii) :1111! ('.!i) pnivi1k* I w11 n*l:ll i1111><. Tu c\':1l11:1tr. mi11c;I, Thl':<e fluid f:*rrrs arr. I hen rm1,..itlrrrtl :1l1111:t with crtl11*r ll1r thrr<' 1111l::.,1w11s :1 11 , :1 1:, :1 :1 , :-. thiul n*lali1111 is 11r1*drd. f11rrc:< pr!',.l'nl, l,1 :ir;ivc al thc cumplclc dy11:1111ir ~11l11ti1111.

A.~sanw tlw n*illaii;;u~ brnl~* :? lo lw ><lnli1*, .i' 2 "' 0, Frum For I lie n\lllt iplc-l111dy pr11hlrm th<: :u1:\ly:<I 11111y fi11d i1 tnorr.

cqu:ilion (:.!I ) oonvc:nicnt. \11 11y11the:<i7.e the dyn:imir prnhlrm h~* ro11,.i1lcrini::

(1lt*f:aC>< .If 11) (2:-1) the n"'Jl°~ 11f "in:tlc rh111111<"L"'. The prC".*11rc tJj,t ril 1111 i1111 of F11 .. -A11i1 "' - .If 1111 t.he::<c d1:i.11nrls r :Ill hC' writtr11 in ll'rm-; or l'llt r:tlll'l~ :uni rxil lhtiil l' A:* indirntr1l, <-<l11111i1111 !:?~) d<!lill<':"I \}IC' It-rm .\1 11 * ,lf 11 rnny hu VC'ltll'il i'"' :1ml .ri11rn11rl wall mot i111~" <lclrrmin<>rl h~* t lu* 11111t ion e'r'ahml<*.I h~* ::..---11111i!lt: Lhc hody I tu have 11 YC'lll1'ily i1 and h~* of imllll'l"'."C'd ~olid:<. l3y 1*1111sid<*ri11p: ru11ti1111it~* nnll m11111r11l11m th" r1111ti1111it:-* of now, thr. A11id v1*l:.('ity cii.:tri 1iuti1111 m:*y r.lsri be or c11nti1111i1~* nn<l Lai::rnni::r'>< Cf111nti11n, n "erie>t of C'<pt!lti1111" r<'-

• ' C\'11!11:1\e<I. Tl:c lh1iu fon-c 111:1~* lil' c*vah1atrcl 11sinr, ll1r: ro11,cr\'n-* >'lllt. The prt.,..~mre tJi,.trihutiuns :ne then r1111si1lcrctl as r!l'mrnl.'i

.:: linn 11r m11m<'nt11m nr h~* u,:in~ <:q11~lin11 (12), whi1-h rc-i;lls in of clynnmir *fnrrc J!:r11,..rn1i11i1 in the cq11:1tio11" of 111nti1111 nf the

. tn solitl:<. An cii::c11vnl11c pruhlem n.,.uJL..;, whir*h 1*1111 hl* ,;ol\'t-d l<J

~ 11*,

.vu "' -.- .:r.

(for :i', =- C) (Z'J) dc-velop lhc l'0!11tion for rri*q;1e11rr nnd clcflcl'lio11:1l rr,.p<mse>c, r~vl'n the ncrc ..:s:i.rr hounclary rta1ditio11s. In manr ('f\."C.C, it.

~ 1 m:1~* he llC'<'C'~"'nry f11r n fluid i:p<*<>i:ili.:t In wrirk .wil h thC' rl~*11nmic...

f"'J wl:o:-1e T 1 i.-* th:: 1111!1! !dn~t ii' c,;;c*rr:~*. ~i:1rc the m11111('11!um rC'ln-

<.*  :<p1*1*iali><l I 11 dr,; **cl11p \.111* ,..,1111 ion fur 1111' r:1111pl(*:ot 11 nirl :"nl;<I

• :"" will 1::vc :::c !hid pn*:<.~1111* wlti1*lt 11111,.t Ill' i11kl{r:1l1*cl lo ol>-

' 1. llnid f11i.*;~ 11!1 :111 i111111:*r~<**l hod~-. Iii:- 11~<' of <'1jll:llii11t (:.!!l) prnhl1*m. *

,!11 s111111* *':L~('"* l111id 1*11<t11'H"'*if.iliL~* nrl" in **1*.11j11111*1io1t wilh

"*"tall)* I>.' ,.i:111'li*r. Fn*ll' ('t(ll:tfin11:< (:!I), (:.!:!), (:.!Ii), (:.!i),

.cl'~'."\), c-.111:,ii,,,,, (!*'} :ual n:\) f1:1ttn\*. 'l'hu~:, tlu*--(' ~c!:'\ti1111~

Hui:! inl'rl in11**c r1r h;-dr .. d:.*11:1mir- m:I"-" In r*~i:~c frl'q11:::11r'.\' m11dc.~

l:u~r-1~* d1w lo !hr* l111id. ;\11 l'X:l.!:tpl1~ j,. a ll1*l111b11ll': l'l'St111alor

• ": :. !, "*':\"' i!t :-;\"<"! fr11111 h:"'.*'i1* :illicl 1;.H*c*li:~11i1*..- :::i* al..;u 01it.nii1*

f11rnwtl h;* n 111! ~..:h('{'t vil1rati11)! r1."l111ivc to 1111 1ulj:u*c11l pk*i.1101.

a.~,:* by th,.* ni~:h~1d ,,f ~~*nthc*:-ii:-< dL ...-rri!Jl*d "bu*.*c.

Osrilla! i1111 or I he I 11l11**ltC'f'I 11111,f hr. nc 1'1111lp:111il'rl hy rli-pl:1* ,..

0

'l"!zc- c:ath i11 'Ta!>~** I :1rr* t~*pit*;d u( .. nnH' l\V:i.ithl;1c~ inforrnl\linn 11w111 of lho llui<I. Thi.: 1li,.rpl11.-i*111c11t. rn11 he nr1~111*111*1d:1!ctl

i\'i11i

l,~*;l~117"!y11:1111i1* 111:1"" n*hli;i:1s wlicrc 11 ,,i11i.:ll* l1ocly is in hy the 1*11111prr><>:ihilit~* .. r ti)(' :ulj:ircnt. fh:i<l 111111 hy the How m11!i1>'1 :<11cl i.* "11rro:111;h*1l 1*illwr hy :111 1111h111111d:*d ll11id i11itinlly t hru1111;h t hr. I 11hl's wlrir-h rall-C"' :m i111*rl"in1ir*r* !'ITc*1*L Tiu* :111! hrrr*

111 ri"'I 11r h~* 11 ,.!:11ir 1*111ilai1:1*r. B~* 11:<1* 11f 1111' :1IM1v1* pr;ll'l'r111r1*,

<lc\'l*l11pe 1 C'q1rntir111s11f 111111io11 for ,.111*h ,;y,.rlt'llL" hy fir,..\ =~*,..11min1t 0th~~ 111b11l.1kd .111~:1 11n* lr:111~rurmahlt* into h~'(lro.ly11r1mir 111as.i 1hnl ('111 *n*,.:,.jltilir~* wa* "" low th11t 11111~* 111lm fl11w'.w:1* im-

.' " rcl:1ti1111" wl:.*r1* 11 ... ,:i11:.:l1* 1i .. i1.1* i.* C'ilhl'r st11T1111111l**il 1,_,. :1 m11vi11~

porlm1I. The method ... d :111:ily,.i~ uf I his p:1pN w1*n* 1hC'11 ll"C'll

','.",.~ro11t11in\:r wh:i*~ Ji111e11.-i1111s fll"I! l:trJ!l' 1*11;11p:1n*il In Ilic ,.;i11~lc to rlcv1*!

• tl~*nnmi<* r111:i 1i11:i,.:. Th<!11, the t 11hc flow impr<l:mcc t.n1l:; ior th'.' "*'*'<':i *:,-hr*rc 11 ,..i;1;.:ll! IH11l;- j,; slr11w11 i11 Table: I 11r W:\." II'* lC'cl lu l:t; ,..., hii.:h lhn~ romprt'*"ihilit~* r*ITl'**l,c flrl..

'"'d1~rr lhe 111:!*:-r "'"f;"" fnr C::i.-:t'~ s, !I, Ill, II, 1u11I H 111:1:.* h(!

cluminal lit s11rh n 1*:1,.c ii wns c:i,::-* \11 write the cq11nti1111 hlt1.*id~1 rd i11 ll*otl ;,.II, for n fl1 : spri11~. Tl """" 1hr11 :111 <'ll"'Y >'lep to wrilt* 11 1~111-M Th<! rr1\ll"r tllfl\' 1:11;1' i11 <"1*::11i1111 CH) th:~t -r*hr11 i1 "' :!'1, tlte t i1111it~* 1 111iremc11I 1~111-idC"ri11r, hol h (*ITcl'l:<. ,\11111 her cx:unplc hyd.-11(l,Y1H\t:1ir* m!l.-:.: ,!/ 1 i*: llli: 1!i~11l:11-l'd mass nri,:itti.: !ro111 Utlll,\'-

of ~11rh :1 1lclmhob: r~111:1111r whirh internrrs with the me(*hnnirnl h.111*~** The h;-.: ** or!y11:1111i1* in:1:*.-* ;II 11 i11 (*111mli11:i (I*!) is 11.<,:p1*i-r.t1*1I wil Ii r1*la'. !*.-., 11".111 ina :11111 n::1y 111* 1*111t.,i1l<'rbl i;11 in~rli:il ~~-..11,111 ol't"11rs in I he anah*~i- 11f vi11li11.i.

St.jll\'l'Z!:-film *.*:;to;*L 111 ~:,*t:(*rnl.- tb* hydrud~*1111111i1* ma.-:* i::in be COn,.;il!lcll'cl to **::::-i<l or tlw*:~ h1111ynnt*y aud i11c11i:\J ,.;r1'1'.'l'1.l'-filnl f,Hnp,~1\Ci\\...:.

The Eifcct cf Fl~i~ Dar:iplng Till' 1111*1*t~li111t 1111::!~-,; .. a-,tHlll.,. 11 fri(*tio11lc,...-; 011irl. The l-1~!il!}i!~*r;ci!:* :.:(:t!~iiS \'t'ilh F:~1id c~,(li~;:n~ ('!11-":i11C'rri11i:: d1::,i1:nc:r 11111-1 h:.vc- i:ornc 11:11icla111*c lo j1Hlp;c whru l\

l111i1l 111a~* 1,,. r1111,.ider,:d frirti1111l,**:<. Home ~11ichu1rc is prr.~cntC'cl

'\"h**:*t~ i.i.\11:: Ln*\i,*....: :u*t* inltH(*:*:.*:.l in=-~ fri**l:1111k ....... , hu*o1np**"""~

lw n~.

iL!0 !i;11*id t\ ... i :u*;* n*ll!=~t*d l1r t:1: . . tiq::id, tl11* 11w\)1.,.J of ~~*1\lht.* .... i...: Tiu* fri1*1 i1.11al prC'--sll! l' rlr11p i:* n,:,..1111\C'<l to lir. lm~cil 111; the 1h-,1*rili-.*.l 11l,,,.,.,. f,,r ;I"' 1,... ,,.111:*.:y pn1Ll .. 111 ,!:ol'lil f:11*ilit:1l'.: th1*

I >:rn*y I ri1*1 ion f~ttors, .,1,1 :1i11l1 frnm ,:\l'ndy-lluw d:o.tn, d:'\r.rr.ii:i:1ti::n .. { ~ ;.c l1~*,!r1~tly1t:l:.~!,* fu1Tt*~:. 'i'h:.., 1r:1*li1:1d i."l"lllll*

r,;nr;;.,f*'~ f.*r I;,,. ;~i:d1i;>'*** !1<1dy pn*!:li*:i:. From 1*11:1:i1 io11s (I !l) an:! lll' '.., fl. l'1 c:11 >

I~) 011 2 p

-*Jo', **~ ~:.r (:l.J)

"-"ht*.n:

.. 11 *H.* F1 1~'.1:~ .' .. !\' (1. )~ I~ 1* *. :1::~1n *:l*: :1.1:. H:1*.: .t i*: 1~ ;.,l11~1r,*

") i'l" **l1;1 1, ... ~ri'. (1.  : ' 1: ). /'

11 i. \!a* \'t*,*lc11 . 111.i:'* 11.r J:I 1

,,f 1 11id t..' i' friC"l1*nrnl :1:**:=-.l1n' dn1p furr" *Iii~ .11 :1 ** :'.i1'. lu,1!_* \*'Le"" r 1 j., lh1* :;i*.(:1*111":.****.: :1c"l'f*l<11t:1ll\ .r I i1iri.,,* f* i1*ti .. *1 h***11r (it lh* 1 ~ 111.,: i*, 1.\'. *:., .l**ll*:,;1:*~ !?;" ,,1;. 1111.:** .. !. ,:;* :l, .,..-,. 011-  ?*111:1l1or 1*it.11nd

-. 'I' ."I' 'h**' .*I 1**p*:'1°'11:1 ,:,'lj . ot,,,  :.;* ~*.< ,,;*j .:l\ 1111**, ji Hilbt

'* **11:11:11* l ',.1 .. ,.~1~*. 11 .... ,, .... .J 111airur111 ;., **l11~11ur~1

t I! I~. (I*; I* I;.'* **1, *I1 1 t ti i;: j:: rt ', . *1 *I , *I ...1 * ' \ ' *

• I: *:I:,'* (ii *.I. l ! ~ ,L l. /' llt1id Ill~:":~ ,:1*11 . . i~ f

.,. ,,., ., I tr"*

f*bl* 1 i-l;*drad 1ru11l"i< ~o** 101,,tio,.a t*...- .. tiu1 onl.- ono budy I* uivon, It Ir. r&*ur"od 1hut 'ha clim*r.~iGlll gf c.lher avuoundir.p b.,d:e1 are luro*

c*onpars.f I* lh* giYOft hndy; srnoll d*.,.1,. ** ,,,.,.,, r.re ouu1nul)

Olrc.ctSca et Rrd.*~te ru1 htt.

--*-+----' -----** -----4----

r..,11ua

~~----~--~-+---~~~~~~i--~-~-,--~~*~~~-~

"* IIJlrf'Ct.109 vr

~\I"'"

1 .,,

• TTn. ,P'r* ~" 1uiu1 e. W...J C'1U~l~*l Tra.11***r** \,I')

• r.n~1u. ut ,,.,.

1 \A ...... h f, TlolD StzlJ

@t

'* alc....,.,.ior Prha

• • ,_""~'.. . I. ~. . . "

A.A:luha - A&U 1

0

. Aals.!. Flaw eO 1 10 1.1* *<<*

) 1.21

_J 1-~ _J 2

l l/~

1.)6 l.,l

1. 70 ta\o pl:u* at u.:r. <r..d 1./) l.~

l/10 *2.2) 1,(,. rieU* L,11. .;\b s

1...,.u. L 'fl'tlD .uat:ul.o*

C~b L:a*UO::::t. or he.* p.* ...s y

~U U*;.r"6lr.&\.c fQn"\lla i'~COI wu.tb o \o 12.~ ?s:.::.cr "::a.:i "M U.11'"' 41r.-.n-.lo:oal *=lwLlcia ot

(. t il l

l.Jz

.e>

.7,

.67 U. ~.. n1. l.l'D\IJ*

~*** l~ lot o/*

• 9 1/5 ,61. C..rCMt 4lr~ .... .:, u i'GC..\lr~ J~r C)'lllohr c

• ai..:.ulul '" lchA'll a * .011.to1lY£ rLJiu*, * >>

b

• IDt:\llWI bOrfUI, .. ):,;. 6

~1..

C')

l.****

1.*.) .t'!'I.

6.CO .~;.

),OJ .:1'::0 l.~o

!.*** .~,7 10 Awal \0 Pl.o.u I.

2

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• c.

Ytrtlt-.i '"a:* l .,, rr P *?>~ J.

-./1. Kul*'- '**fl.Sf"t,.l

--1 1..0"J .~

Q~;.

.')l.tJ

~-'>> ,20') .1in

-  !.M 1~

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.c;i.,

1.C'=ll

})II "" hyJr1111li1: ilLal\lt!lCr__ ,.. :!r r11r II_ d1:_l!~l_l*:J \\ii !i IJ:lraJld As.'<~ll>l* 111°.* llo1ii! velocity \*1 he 1:y1*1i:*,

w:1lh 111111 ,:1?p:1ratiu11 1liic*l.11c,.:.-; ; 1 \*1hi1*h will l>u 1-1*:1.\r in Lhi>H:xpu:-.i1i.1n 1' "" l'o ,..ju <**I U.:1i11;~ ~:i1111lio?i~ (aa), 1:11'111Liu11 (:U) :n:1y *LcJ i11Lt*~r~leu i;vc~ u hr.l!-1*y1*lc* 111 i~ivc (3t)

(3:!)

... .rJ.~~--.,r 'tll Ir 1:1c lh1:11 1l111:,pi111~ fon*c Wl!ru linear 111111 c:.111u.l lu bl', u,. .. ,

lhc 1*10:*;-ry  !~ 1* **Ver i: J,*,![.,*y1*:c is

• 1c wb:ru J:':

A Iii:.**

• • ----****--**-** ....... ----*****-.-*** ...... -----*------...--.....-----~-- ___,,,,,,., ______

liH1*nr 1:a11:;:i11r~ r:i:*ffi1*i;*111 /, 111:::* hr* clr*IC'i 111ir:.-:I ~**r*1111*;l 111 "l!r<*1* 1*x:1rtl~* with pn .. li.-1i1111. Fur 111lu*r p.. iut .. r,f hi-1*:1 , with lh.: rc*.*ult 1~rnphcd d:11a, the V!lriati1111 IJ1:lwrc11 lllt':1"111*t'tl 11:1l11ral £rl*q111*11c*~*

111111prr<lil'lt*d11:il11r:11 frc1111rnr:; was 1~*pir:il1y 11*so.; llm11:.!1wn*1*11t.

'.? fl *,r,f.A Fur 11/n "' I.:! n11d a frcq1u:1u*:** 111:.l!l1*ps, the m11si11111rn value

. /1 <* - *- --**- *--

~hi~ (; 11£ thn l!c:~*111oltls u:unl*,('r 1l11ri11:: lhr \'ihralor~* 1*y1*1c i.< t*stimalc'll (nrl*I I\1*:111c',. tlaln 111 111* :.!*l,l!iKI. T11rl111lr111*<* 111:1~* hr* :1ss111111*cl 1.o 1::*1*11r if lite Hc~*11111d* 1111111lwr is i:rl.':\lc1* th:m :moo. Thu,.,

11 lhr water s11rro11udi11i:: the l>t*:un r:\11 hr ro11,.id1*1*1*d t111"h11h*111.

2~ ~ 1t .. Jati1111 (:~~l) i:iv1*s :\ \':tlil? nr :!~ "' 0.0:1, 11si11i: :I fril'li1111 farl111'

• "/"' ,,[II.ti:.?.... This rrit*li1111 fal'lur i" lakt'll fr11111 :\l1111rl~* Iii. :'i1wc nml .1/ / :: fiuid m:'""* :!~ i" the r:11i11cf1111' d:1111pi11~ i111p<><blll'C  :!~ = O.O:l is 111111*h ~111:11!rr tl1:m I, the m111*cpl n( I his cl:impi11i.t 111 tlw inrrlial i1qJ1*rln1"" ~ i.~ ,.i111ibr ta fr:;..ti.111 11f 1*rilir:1l par:llll!'lrr would i111pl,l' 1h;1t 11.r. l111id 1*1111lcl 111* 1*1111,.idr*n*d t"t*11-ilampi11r. l11r :i 11Hr-dq.:n*(:-i.f-!rc*('d11m l'y.* 1,*111 with lim*ar rlamp- ti:11i.1* fri1*:i:1:1k-,:s, Thr far*! 1h:11 th<' dal:a 1111 11a1*1rnl fn*<(llC'l\C'~'

i11g I*, 111r.".' .H 1; 111111 natural !1 N111r11ry t.:l. Fr11m t'<jn:.ti11n:: (:l!i) :11,n*r:'d "" wrll wit:11hr11r~* w1111l<l *c11<l l11 vali1ln11~ lh1* a"*1tmp1i1111 nnrl (:Ii) :11HI with .\! 1 ~- p/,,t, or :1 fri1*ti1111ll's."' !l11i1I. Tl11* amplilirali1111 in 1\1':1111' ~

0

,,.,, \\'a" ah-!*ILL I:, al rr:;on:1;11*c, whil'!1 r:m :1ls11 It(' ,.,,11,.id1*rr1l as r1*irl1*1irc (h:tl. thr. 11\'crall i11cr\i:11 inqh!*l:uwe j,. 1*1111,.ide.rnhl~* grr:11er than lhn 11vcr:il11l:impi11i: imprdanre.

l*'urthc*r, if l'o ca;,, from t*qn:it inn (33) Dul:i of Fritz and Kia, Fril7. and Kis" !SJ repurl<'il lhr rr,.1111:1 or :1 l<'>'L nn a ,.nlid :-.!11111i1111111 r~*lirulc*r llrxihl~* "11Jlporl!*d wit.hi11 :1

-~- /!_o (lurlntlcut nuw) .

rir,iil ryli111lri1*al c11111:1i11rr. The cq11ipmc11l wa.s vihrnletl 011 11 3ir r. ~hnkc-lnhlr. Thr lr11i:1l1-lo-1li:Lmeler or the- 1*yli11drr "'n .. :1h1111l 1.11. Thr r:-*1i11drr wn." :<11rr1111111ll'<I hr R I hi11 11111111l11r l111id whii*h

• I'.. Equali:.11 (:i'l) d~f.nC'" r1 dtnwnsiottl<>ss n11111hrr, a il:1mpi1tl'.!: "".. frl'<? 111 !111w 11xinll,l' 11" wrl1 ns rifr1m1frrr111i:\ll~*. Th<' 11al11rnl

)mr:\llH*l1*r, lhat. sho!:ld pruvid:* a r1'f"""llahl1! 111<':\."lill' 11! lhl' taliu fn*q11c*ul'y was takl*n as 1111' f1*L.. lllCt11*~* :ll whi1*h the vihra I i1111al

• i'.i1ffluid fri .. 1i1111 to ilnid i1::-~tin. '.'.'c n*1*111l that in c(\11alin11 (:l!l) nmplit 11dr of the c*~*lind!'r rr:u*hcd it:; nrnxin111111 value with :i r1111-lh~ 1>:.r1*~* lrii*1:0.a fn!:ltor fur lurlrnlcul. !low l'ln11L t:1h!~ nr.1p!i111dc. Tiu~ :1xinl :111<1 1*itr11mfrrrn!inl h~*dr11-

!= dx11:1111i1* ma-.*rs wcrt* 1*11111hi11t'<l 11~ s1111w11 in i;<:rn .Jll nf Table* I.

lhr r1:,1:1?1rr tlint I hr ll1:id 11111v..; in r.tt o~l'illator,1* 1:yl'I~

(n.1np1il11d~!nf !-i:.n .. .,id:ll r1111tio11) Tlw 11:1111ral f~C\11r1ll'~* nl thr- rylindr.r i11 nir "-'a..: :1.*1.:11*1>"* \'."ith 11:1* n.iic: ,-!1*:!!1\t*? :--p:~1*i11J.: 11*:1l1*r sqrr11111:tli1:~ I )11? ,._1*i:11rl1*r, I he (ri*<p1t*111*y wa" rt"1h11*<*d I 11 li.11 rps, whirh ,c::~vr. 1*1*r.1* >:1ti,.farlnrr :u:ri-c1n<.*11t with the prc-

! . sitr.ii:\.r r.n:~~ ..-~; .. fnr dic*li1111 11! l(i.!l rp..:.

111 n*f(:H*:11*c [SJ ll1r l:L*y1111ld:< 11111111rl'r \\'as <"'limall.'d 111 lie

• lSOll whirh 11*:1s 1.in.*idl'n*d I 11rl111lcnt. Tiu: vnluc: 11f :!~ is 1*alc*11-

• Jt (1:1111i11:ir fl;1w) l-111) lalt*d fn1111 l'l)llali1111 (:SS) t11'"'11.11:1 1 11,.i111t llm cl:lln fr11111 rd<*n*11rc

!SI: f = 11.0-4, \', = :l.:! fps, w ""' :!r (Ii rp,.), r ,. 11.11!10 in.

O:im*r. :?~ i:< 111t11*h IC'Ss lh:111 I, 1111' 11:;.-i1tnptiu11 of 11 Crirli1111li*si1

!l11irl >'h11111d he valid. Thi .. i,. v11lidah.. t in 1 lmt 1 hP """ 11C the v fluid kinrmal ir vi,.ro,.ily h~*1lrmly11amil' 11111s.1 1*011r<'pL i11 rr(r.nm1*<: !)<II pi*11vi1!1*il a v1*ry r*11~.11!:1r fr*:*ptl*111*:-* ,.f o>'rillator~* r.10Li1111

~~ "'c = f111ici r!.:u:;1d :-p:wi11;:;

~ Tr lhr r1mrL*pt of ti1i' d:111.pi11~ pnr11nll'tN :?~ is rra,..1111:\hlt',

lhc11 th;- :;.-...:un:11lim1 **fa fridio:1ll.S fluid 11111..:t rc<i11irt' that:?~

Mmw~ lil* 1::1ll'h sm:.llcr 1h:,11 1. The qn:mtity :?~ will Ir.lei' h:*

ra!cuhtrrl for ~:ill:l(' 1...,..1 !':*"'""*

Fl iii ti f:a i*ii;r ~~~-:tilil)*

Tlie r,,.,,, C'*lin.'. rt*":J:.*,,;,, :."..:11111c:l an i11r*11111pn~.-.-*ihlc ll11iil.

\\'hrn: tia* l'..... ;1.iliiy 11f :, n11it! "J'l;!I;!. i..: pr1**:c11t, ii. b u..:11:\liy :1

~trnii!1:'fqi \'."o.h: 1*~l**11la\in;1 t11 dr*tt"'i"l11i11('1 if thr* *"*1d1111H* ~-tor;iJ~C of I\ fi11LI ,,, .. ;**.,. -,,*jl! an ... *t !he* ('<lldi1:11itr lo:i!a111*c. Tiu* nppli**ali**ll of lhi..: (IJl;*r i<< f11rthn p*.,tri1°lhl tu r:l"C" of ~.111:111:\f:wh11111111><!1' (h*.*' th:.i: ,,t..,*1l. 10 l**'n ,..,r) :11111 t':l*L'*' 1d\('r1* 11.1* 11 .* 1*: 1*h:.!11*1*l 1~11:-:::h i*; ~il?~;~!l ~*n:t,p*an*d lt* r?h.~ w:1\*r k~1r.1h fo1* pri>=~!~a1i11).!

vil1r;il111.1* ,i:~111rl::111*T' ll**:<.; 1lt:1:1 al:o11L Ill p:~ri*<*111.), i11 11rcl1*r tu n\*ni;! tln~ 1,,,...... jt ilily of :-t:i.!Hl;t1}!**\\'!\VC rff~<*t.~ .

1 i1:-~:i*;(::i!t:irJ'1,-..i:;

~c.1 :.:.'r 1

• . P. :,,, Jo::*:*:t1~ lLJ Yi 1 *~* tC':i 1:. 1*i11-.1~ar l'::!lti!~*vc1 t 1dL1

!~l\:*111*:; .* !**:: h*; :.:\ ;:.*::1; 1 ~:*r '::'.*i: v. 'i'h1~ i*1:~ 1 ~;:: :--,l:1*'l' *::.i~ 'd1**d

\': i IL :. 1".:; I:.!. ** :i :1 : 1: .. ': .. t l; .. f; .... t ' 11!' .. i .I ,*1 \: \*, it i \ ii c*; I\ :*, u~ . r .\I.:~'

I l (,h1.* 1.*i:*:~'. .. n,. ~: ..<1 .. : .. 1*~ l~j L i;:.*1!*.- <*.,:\:11i1.1*d li***dll':~I

• ,* jl I, .l I : ~ . : ' I :* ':

• I :. ";:: .'.' ., ,., ~ ! I. <ticutt af  :<;, relC'tion* (39) or (40), tor equlpnHnl 1how*

ll11*1i-1'11o! Inf iy. :I I

i

. rtco v, ... u:i-..11* .,, n Coru.ehl1ic c.,liru.lo;r. ..\ l"UIH"CUtri,* l \'li1Hh*r a ..c.- ..........-

0

~-~.

u ..:....

--~~-*- ..-,, .....

-.

• t-1*1nl1(,* :L1~n~ ill Fi;~. '..! \\'a."' :l\':,ilal1!1* f~*r h*,L ,\n nlt111\lll1llll 1*yli11d.*r 1p;111 ."11 i- ll1*'<il1ly ""l'll"llc1l hy l'll(\111111 ~lruts (part..

I

~

...... ...... ....**V .....

.. iL:

I). Tl,,. 1*.,*1.,,.l.*1 i*: *ll1'1*111111h*1I lo~* :111 a111111lus. Fh1i1l h*aka;.:1*

... ... .. '-......"'",***.. ... . - ..,. ... ** ..... ... u ..... n fr11111 llil* a:ii.1d:i .* i, li111ill*il by du*,l-dl*:11*ai11*c 111cl11l ~1*als, parl.s

-1. Tli*.* 1:i11li,,., uf-thc 1-.di111h:r WIL" rnc:1:-11n*d li,\' Ilse u! :\ 1*:1111i-ll'\'l'l' d1 -p!:i,*,*111*'!1 ~ ~:1 1 '.c, lil ll*J "il h ::-I rain ~::~~l'*'* part S. Tl,ll

.n

.n .,. ... ,,. ....

.. ' ~

~

lluiil '""'"111- wi,hh c was \':1ri1*d by lll:ll'hi11i11~ tl11l ~yli11ilcr cli:111wl1* r. Ta I il1* '!. ;:.I ac1*s,. ~ull\*.' 111111wri1*a I tin la from l hr.*c l<*sls.

(

Fi~;. :1 -1:* ..... ,... 11*,,* l.,,*p!1*al 11*1*ill11:'.raph n*1*1111b u! the !rel! vibrn-li1111**. 1.,\:,*:1 d:1:i"~ 1\11*-1* lc."l'" Tlw vihrnli1111s \*:ith uir :iml llw tu *11.1 ...,.., ..

~*!..  ! ,.

• .-i1 **J.:, -U-- *"'lf** ,,.._ . .,. qu....., ":':.. u* ** ,,., ... *a. rwa t.

1;l~*1*,*111: ""Ii:: i1111 Wl'rl' 1:rc:1 l1:1I hy n*l11l*i1y-sh11ddn1: l he t*ylindcr

1) ~,.... , IJ

• JJT' ~I*.* 1 1 *

• I " ' ' ' ' - - ' .. " '

1/11 I* lrtnt* tMt*

\IJ*WJ" t.aMa f f

• Y9 * - - : * , ,. . . . . . .

L.I * ._.,, I* .-4i& ,.,_

• I with a brr*-' 1.1:.!!1*\. Tlw Yihr:i1iu11< with waler nncl uil W1!rC &.-1...r1 ,, * ., ,,,~.* I cn*;1l1*:! 11\' l':lll-i1:;'. all i11i1i:1l lar;:l' udh*cliun.

Th*: 1;,:d, -

. .. d*:ua111i1: Wl'i**hL ., was cuk!1b11*il from item S, Tah!c lion (I) of [SI) th:11 :m~ l'11u:<i:<te11t with <'t1uati1111 l 14) oi thi..

J. Tli" l'..1*1!r11il~*1i:1111il' l*i:~hl \"a:; :.1::-11 1.:ak1:l:itcd from the l<:st p:1pl'r. 'fhc*l' l'llll:lt inn:; fur t.wu-hod.'* 11101 i1111s µrr,.l'ntcd in fn*q111*1:1 j .... )ha(* In 11'1* 11ac.111u of llu: cq*iipmcnL it w:~-; Cc~i.

this papur 1*1111ncl'l lmuy:im*y 11ml i11*!l'li11l Sl\lll'<'Zl'-lilm c-ITert.1.

1h .. 1 :l,.*tt* ,,.., .. " -111:oll.u111111111i. u( lcal::i1;l' pn~l Lhc cud :<cals Tlicrdc;rn, 1dcrcm'(" (G) nml ISi lll'C r1111.*i.*lc111 wi1h the moJel

\\'li:**L *.... 111.J ,.,.,.,,. 1li1* :11*lu:1l hy,lr ... 1.,*11:1111i1* 'n*i1:hl l:i hll ""dlcr p1*t'.*C11te<l i11 thi.... papt*r. ln rcforc111*1*,. IGI a11cl (XI the l*1111y-

\hau 1h1* 1ia*11r1*1i1.:al v:dll'.'. En*11 tl11111;.(h the valn*! uC :.!~ W:L-; :l:i 1111l'y 1crn1 i111plie<l ncitli~iblc clTt*l'l::I 1111 1111111rnl (n-<1111:11<")', but did hi1:h a" 11.i, \hi.' 1*ah*1d:i11*1I h~*1lr11dy11a111i1* wciv.ht wns Cell lu be

• irnpl~* 11. 11ig11i!ic-:ml clTccL ,, .. the pn'llit*lcd 1unplili1*ati1111"- Thia i11 rc:1*111rnl1l1* a~11.:1*1111*111 "'ilh Ilic tc-l \'ahic*,

cll'cei 011 :unplili1*:tli1&1L wn..-; "l:Kll'ifil*:1ll)' nutcd in rclt*rcnt-e l!!-I.

ll j, 111111*:1 1ha1 1hi* :q>para\ll* w:&"' :1lsu 11,-cd to mcas11rc the llcforc11cc:1 l!il 1111d (1'1 du rc:<11h. in some L~111linnati1111 uf tl:e h.nlr11dy11:r111i.* l'!:r" uf a 1l,i11 a1m11l:1s ar11111ul a rul:1ti11g cyli111kr.

mrnk*L" p1u].1<1.-.t..J in Lhi,. pap'cr. ,\J111illl'llly, 11111r11: 1~ui1irn111~i1>11 The: n*:.i:li- w1*11: p11h!i.-lt!:1l i11 ll ll.

i.c dcsimhlc. lluwevur, :>in<'C t.hc i11(ur111:1fiu11 11( \hi.* 11.11.cr l*

c.;or.~.*~! Cooi'HUVnli 011 Tho,,, CC1ompari1on* to l'o:I DQtn. *rhu nl)41Vl?

lmsL"<l 1111 ha.. ii* pri11ci11Ji*.,., it j,. cx1nwk.J llmL lhc c'<111:*Liun.. -..*111 1-.1:11p .ti ... *;,.* lo l<**l ilala appl~* \11 thl' clfo1*t uC tlm inertial ~llll!.:c1.u he 111*1*11rnw fur the :<(>et'ificd co11diti1111~.

ti!:11 ~,, ,. l 01 i:1* ~i.._,. l,f 1 I"' d:i u1pi'11;.c parn111*~*<*r :!~. *r1ic ph,*110111<~11011 11[ lh:* !1:.*; 1.,d "i'"'l'Z<' lil111 11r, iu 01 hl*r w11r.J.;, lhi! \'irt11al 111:L,.;

N l*ffc*1*t, ,,.;,.; li!-.-1 pn*1!i1*l1*.I lir ~1 .. la*s l LJ, 1;i.J ha.-; ~incc hL"c11 Commentli of Multi*Dcgrce-of*freedom Dynamic Analysis widt:l.'* :1:**.l'l'h:d. 'J'h~;*d11rl:, t*111dirn1:11i11u of this rlfocL L-; nul A salic11L lcali1n: uC the 11111:;~ widely ll>'l'll 11111hi-<lc;!,rl't'-<IC-11c1*:. I h*.n*vl':*, lw: h rl'in*.:H'l""' lul :111cl l~;j i11vu!ve: :Lu1111l:u* Crccdum <lr1u1mic 111i:1ly~cs uf *1i11c:1r :<y:<t'!llls whid1 ure CXl*iteJ U11id :-.p'.1c , ... ln*n* tJn! 11Uh*r n*ul i111a\*l" Lui.11.laric*~ 11! \.lu- fluid hy """"' 11rl1i1 ,.,:,*~* l11L*.c 111111 io11 i.... th* ! r:111,.r11rr11:11i1111 .. r 1111 11rhi-ua:i11h:- !,;,\\, 1::1J\'t'. B1*\!1 r.-fc1e111*(!., (lil ;111d (Iii rcporl fornL'< tr:1ry l'llllli~urali1111 "' uy1mmi.: c11:11p<1!1t*lll.- iul.l.J ll UClulllJh:U 11( lluid 1a11i: .. 11 l'(l'1ali11:i:; (l'f. c11u:oti1111. (*l.:.!.i.-1) o~ IGI m:d c:lllll'- nrrny uf simple 11~1*ill;\\m'i; whi1*h :t1*e cxL*itcd by the base motiuii.

0 ti-***-r . U/,/~- . ...... --... **r~r. r I..

i  !

L.. ,....

• .' 1 t.!l ; I .I

• i I*

/ ........ I

/" lf- \

. .,, r--i~- :1-; *r-*:*-;t '--F-,*-jj

• • • • .--,-' J:. 1-*;: -

• --' * ;. II '(: . I  : !_,....'....;

-*-*"j

-: A'. \ -

\-\~.

.. _\"":" ~ - ,-\!- ... -**

-1 \X 1*** : \~ \*. \!

... -*I -

-\t\..._\ -\*-:*\\

. .* j .

~-

'.. -*~~--1 __,t __ ._

I\ ' \ \ \ ,

~. *

\ ~

/,.i:; I' .., ':'!.(* cpr.1  ;....

--- - - ~--

r~r..-/-{r--rr*,r-:1-r:T *t**r*-1-r-!*:

-*-:- -* **. . . . ~*.-1

• ,i;dS'(;(;*t'***:*~ **I--~;..~

• • f . '

__ ,- -- -,*_-;-:-~

I t

• 1-.- - * ~

.. *.Ii._,I ... * . ~~-*-~r-:- r-=-f-*.:.:

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lrl':1li11~ l\11id 1*ITt C'I.* in a 11111lti-dC';:n*t'-<>f-frC': dn*n nnnl~*sis.

0 0 1\8:\H:, \'ol. GG, HIH, pp. G'i1 .. r.-...:.

f, Frilz, II. J., nnol l\i.-.,, 1:., "Thr \'ihration He*1*1111'<'*ol a Canti-lrn*n-.1 ( *~*li1ul"r ~:uc rn1111dr.l Ii~* .\*1 A111111lar Fl11iol." )\.\ l'J. ..\t ..

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10 l'ri\'ale<*om11n111i~:.li<1*i: ikm" 12, 13 aretluc .I. If. C:1*r111cr, C:c11cral 1-:lcl'lrir: ( '11.

r,11id,l'li11t*~ :r1 l' pr11p.,*l'tl to l"'l:1l;lish the r1mdit.i*1n:; 11{ fril'li1111l".!ss, I I Fri:!, IL J., "The EIT<:t*" o! nn Annular Fluirl c111 the \'ihr::*

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or D H:Hlial \':rne r11tcrni\I f;lc:uu Gc11Nal11r :'tructurc:* ,\:ST.-71i~.~.

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~ 1 [:*~kt'", r.:. (: .. "C>11 f.:m:c c ...c~ or Fluid ::\lolion," l'r,1crrdi11as Syslrm ('11111/>'nrn/1, ;\la~* Hl<O. ,\r1.:111111e :Satiou:LI J.:dior:,lory,

• • T'a111/11itl~r l'/,1/n.o.,J>'"'cd -"*** \'ol. s. ~la,\' 1!'~3. pp. I0.~-1:r;, ,\r:;unnc, Ill.

-~

~ H'  : *, .:

~ * : ' :: : I ~ ' I ~ I y '/'] I 173

1 *Added Mass .and Hydrodynamic Damping of Perforated Plates D. F. De Santo Vibrating in Water Senior Engineer (Dynamics). Experiments are described in which the fluid dynamic forces acting on perforated Westinghouse Research and Development Center.

plates vibrating in water were measured. The test results are expressed in terms of Pittsburgh. Pa 15235 added mass. and hydrodynamic damping. Dimensionless formulas are presented

• which give accurate values for rhe added mass of the plates tesred and whi<'h yield I

Mem. ASME satisfactorily conservative lower bounds for the hydrodynamic damping force in both the lineur and nonlinear (/urge-amplitude) clumping run~e. The formulas for added mass and for low-amplitude damping apply to plates of any thickness thar have any uniform square pattern of circular perforations. All of the results are general in that fluid density, viscosity, vihrution umplitutle, u11d frequem*y ure ul/

free parameters.

• lnlroduction Th~ purpo'ie of 1he invcs1iga1ion described in lhis paper i~ In rhis paper, lhe apparatus rhar w;1' 1.Jcvclopcd 111 rm:;r,1111.*

.z 10 Jc1crminc 1hc fluid-,1ructurc in1crac1ion cHccts of coolanl* rhl' in-waler added ma" anc.J hydrody11a111i1.: da111p111f! 111

• uid on lhc na1ural frequency and damping of vibraling pcrrora1cd rlari:, is dl.',1.:rihed, and re'! rc,ull\ arc rrc,i.:1111.:d in J'ora1cd plales (such as lower core 'upporl plalcs), which general dimcn,ionle" form. S1.*111i-e111p1r11:al for1111il*" ;111.*

l\liltrlc impor1an1 cu111pone111s of nuclear re;1clor inlernal~. given for l.:lllllJllllillg lhe olUUcd lllilSS anU J'luiU Uamping vi Na1ural frequency and damping are critical fac1ors in pla1es vibrating with arbi1rary ampli1udes and frequencii:s in Jcrermining 1he responses of reactor in1ernals structures 10 fluids of arbitrary dcn,iry and visco\ily. Compari,om arc

'arious excitations including '1eady lluw forces, pump made between the result\ ol' the presenl 'ludy and e\i,riHg ruha1ions, and sei.,mic mvtiom. Natural frequency is af- rheory, showing close agri:emenl over lhe er11ire ;unplitudc rc*rcd by the added mass associaled with 1hc incriia of lhe range invcsligated in the case of added mass and, in 1hc 1.:ase rluid 1ha1 is forced 10 oscillale when lhe structure vibrale~. or fluid damping, giving satisfactory corrcla1ion in the low-i".' 1"01al damping is the sum of the hydrodynamic damping and

' qhc mechanical damping. Thus, it is necessary 10 evaluale 1he JJdcd mass and hydroc.Jynamic dampi,1g when predicling and

~nalyLing 1he vibratory responses and slrcsscs of imernals amplilude range within which 1he lheory is valid.

2 Physical Hascs ot' Added Mass and 1-t)drodynamic:

I .:omponen1s.

r"'.. lmporiant information perlinent lo 1he added mass and Jamping of pcrl'oraled plales has been publish""tl in references t'll and 21. as well as in 01her sources. The scope of lhal in-1orma1ion is limi1ed, however, in lhat ii is reslriclcd to eilher Damping The Jcrm "added mass" refers 10 1he apparcnl inerca'e in rhe inertia of a solid objecl immersed in a fluid over ils inert i<1 in a vacuum, 1he in-fluid incrlia being defined in lerm' or aceeleralion with respccl 10 a fluid eon1aincr 1ha1 is fixed in

,ingle (mainly 1hin-pla1e) orifices, or 10 1he linear small- ineriial 'pace. The added 111;1" clTea.:t j, a 111anife,1ario11 of lhl*

.ampli1mk re~irm.-. or lo 11-*1'"* Thl* 1ne,e111 invc,1i1w1io11 was i11l*rti;1 of lhl' fluid rim! 1111"1 hi: 'I. in 111111i1111 ;i, !Ill" i1111111.*rwd nulli\alcd hy 1hc llWll lo ac111:in* .-cli;1hlc l'Xpcri111cnl;1l dalil 1111 houy i' accdl.'lollcd; !hi: audcd lllil" j, !hl*rclorc JllllJllllllllll;d

.-11nfig11ra1iorrs arrd condi1io11s rcpn*,cn1;11ive of rl.'aclllr 111 fluid dcmiry. In rhc ca'l.' of a pl*rJornrcd plare. rill' addl.'d

-.1pplica1io11,. Thew cornpri\I.': ma" a.:an_hc very_ h11g1.* 1.*11111p;11.cd with rhl' 111'"' 111 rhe pl;il*:

11\cll 11 the t111;1I hole arc;1 j, 'ub,1a111i;dly le" than Ille lolal

• rcl;llivdy rhid. plall.'s having 111ul1ipk pcrloratiun' wi1h (hole plus 'olid) plale area. Then, the flow musl bl* ac-I aa.Jjai:cnt holes 'paced \ul'ficiently clo'e 10 each olhcr to in*

f tcrai:1 apprcdahly a liquid medium (waler)

• large-ampli1ude vibranons in which nonlinear effec1s arc cclera1ed 10 high vcloci1ies in and near the perforatious a' lhe plale rnuves through lhe fluid. Thi~ involve~ high incriia forces.

1 1mpor1ant.

The added ma~s assoeialed wi1h an aceclcraling imrnef\cd body can be e"-pre\sed in lerms of lhe kine1ic energy of lhc nu id 1111hu1rd hy 1hc Prc<\urc Vc"c and Pi11in~ Di.h1nn fnr ruhlicali<>n in "i:..,

L'"

= .,I Ill,, v*~ (I)

,oUUIAI OF Pus.<1*u VH\H Tt..-11~"'"""'* l\.fanu,<rirr rttrl\rd al .\SMF llrJdquarrcr*. h*hruary 9, lllHI. or Journal of Pressure Vessel Technology MAY 1981, Vol. 1031175

t.!) p1111,*d liy 11.11 i'llhk \(111111'*' \II lil.11 11.11.dkl 1*11111\'d ,., ........ - -

l where 111. i~ 1111: added mai.' and V, i~ I he vclucily ul a lhc plalc "p1,,1011" j, adlll'\/Cll. "i11111-.111dal .,,ull.1111*11 .ii plate is prudul*cd by an elec1romagnc11c \hakcr; th~* a111pl1111d .

r I

. reference point on the body. Physically, lhe inertia force a:.\ociated with the added mass consists of the resultant of and frequency uf the plate mo1ion arc mca\urcd w11h *'

i

! nuid pressure forces acting on the: body surface; this resultant calibrated ac1,;cleromc1c:r. Diffc:rc:nt re\onan1 frequcnc:ic' ,.J,.

force vector is collintar with and opposite in sense to the body be obtained by using different titanium tuning springs.

• acc~leration vector. In the case of a rigid perforated plate Where the rod penetrates the end wall \>f the c:hamber 111 accelerating normal to its plane, the difference in lluid which the plate vibrates, a metal bellows is usc:d 10 seal again':

i::ressures determined a short distance away from the plate leakage of lluid around the rod. An identical bellow' is u,,.J surface on either side provides an accurate measure of 1he on the other side of the plate, so that a5'the rod is 1ramla11:J.

added mass. (See Sections 3.2.1 and 4.1.) the volume source effect of the expanding bellows is com*

The term '*'hydrodynamic damping" is used to signify pcn!>alcd exactly by the volume sink effect or the oth**

mechanical energy dissipation associated with the motion of a bellows. This circumvents the large springlike force (oppo,in~

solid through a nuid. The hydrodynamic damping force is a the motion) which would exist if an unsymmetrical bello\\'

arrangement were u~ed.

drag force 1ha1 is veloci1y-depc:nden1 rather than accelera1ion-dependc:n1. In the case of a ricrfora1cd plate, this rorcc The radial dearance between the edge of the pla1e and 1h~

comprb1..-s not only the 'trcamwi~c i.hcar forccll along 1hc imidc diamc1er of 1he cylindrical chamher i' alm111 l(Jt, surfaces that are parallel to the direction of motion (i.c*., 1he mic:roni., which ill ~ul'ficicnt lo guara111ee frccdo111 I r11111 hole in:c1 ior surfaces), but also the normal-pressure force' on rubbing and from any significant damping effecl due ll.' ;h~;i:

!he plate face:-. a!>l>OCiated wi1h flow separaliun and olher ,, rc\\e~ developed in lhe nu id in I he annuhl\. Thi". lll~t'I i1l:

energy-loss effects. These normal-pressure and shear t'orces with lhc guide )pring dc~ign employed, 1hc u~c ul IU\\*

are in phase with velocity and act in a sense opposing the plate damping bellows seals, and the mounting of the model on a motion. They arc ullimalcly due 10 lluid vi)tcmily, and al ma\\ivc 71 cm ..,, 71 cm x ~cm 'lccl 'Prini:-,11ppor1ed wi"lll*

ba~c. ai.i.urci. I hat the cxtra111.:ou~ (i.e., mechanical) d;i111p111g 1, relatively low velocities are proportional to the square rm>I of the viscosity. (Sec Section 4.2.) of a \ulTicicntly lower order of magni1udc than the hydrodynamic damping hcing mca,un:d.

Stainlc)~ !>Ice! and brall) arc u~cd fur all ~cited part~. 11*

J Tesl Apparalus and Procedure avoid corrosion problems.

J. l Ex~rimcntal Model. A sectional drawing of the ex- . Three plate~ were tested. The\e. arc \hown in Vig. 2. Plate I perimental model used in this investigation is !>hown in Fig. I. I!> a quartcr-i.cah: partial model of lhc orificl.."' portion or a In the model, a perforated plate is mounted on a rod ~up- prc~surized water reactor lower core support plate. Plate 2 ha'

- - - - Nomenclalure

( 11 effective length of hole A cylinder area = A = KE, kinelic energy of fluid Y.. ;11.:ccleralion nwgnilulk wl> 2 I 4 111111 ion 111 I il'I ~*ydc ol tkcayin~

A,, = effective piston area of "' ma~~ or \inglc-dcgrcc-of- 11ibra110n one bellows seal frecdom sy~1em y, acceleration rnagnilutk A,, hole area plu~ annulus U.m rncc:hanical ma\i. in- after N cycle' ol area c:rcmcnl dccayini,: v1hra1ion

- A,. effective solid area of Ill;, added mas~ due lo fluid ir - rac1or 11\Cd i11 computin~

plate = A,. = A - A 1, inertia <.lamping h}* handwit11i1

-A,,

• m, s1ruc1ural mass method (\cc equation (7)

A,, = A,*. =A - A 1, =A~ + m, = total mas.~ = 111 1 = m., and Table I)

A,, + 111,  ;; log decremcnl <.!;imping b pitch of holes in a square

• N number of cydc' u~cd tu b1 log decrcmc111 damping array compute damping by due to fluid c1 = l'luid damping coef- decay met hod h, log dccrcmenl dampinj!

ficient fl{J O\cillatory di 1Terc11t ial due to 111cd1;111ical anJ d = hole diameter pressure across plate windage IO\\C:~

D = cylinder diameter vibrating in nuid o 1 total log decrement F = vibratory force applied Q volume llow rate of lluid damping: b 1 = 11 1 + o, by shaker through open arcct of " = kinematic vi\cmily ol F1 hydrodynamic damping plate fluid force r = lcmpcralurc or water ,, ma" dcn,ily or i'l11id

_ }~. _=. natural frequency of V ah,ol111c velocity of l'luid 11, ma" dc11,11y 111 '1ru..:1ur,*

vihrntfon in hole\ w circular _ rreq11cuq: _ u!

/ 1,/~ = frequcncic~ (above and v, rel al ivc vcl01.:ity or rluid 11 i hr at ion he 1ow I h c rw 111 r a I in hole' w,. cir~ular 11;111iral rrc*

frequency /,,) al which V, velocity uf rcfcrcn1,;c 4ucncy drive force amplitude is point on moving body w,.,.., c:ircular na1ural fre*

staled multiple of value x di,placcmcnl or plate q11cncy in air al natural frequency, for (normal to it\ 'urfaccl w,.""'"' c:ircular natural frc*

cono;lant motion am- .i: vcloc:ily of plate with qucn~y in water plitude rc,pccl Ill cylinder w ... .l.., circular nal 11r;il l'ro.:*

lcnglh or hole (lhicknes~ x acceh:ralion or pla1c 411ency wi1h 111'1\\ in*

of rlatc) with rC\f'lCCt 10 cylii1dcr cn:mcnl ::.111 176 /Vol. 103, MAY 1981 Transactions of the ASME

• ** fo Y<<.uum * *

'..;! or Almo\Qf\trt ~

I. I:

I

,~:~

~ ll-i.*

. Alr_lrr:;}

• • l Pr1nure r..,

- Bletd ...,.

YllVIS Prr\\utt I'll Sm111iw Acceleromtter Accelerametu I ~*

tii.n1um-Tuni119 Sprinq

(

II

[

Fig. 1 Apperatua tor determining added m111 and hydrodynamic damping of perforated plates vibrating In water t

t~

- N.

t Pl;ite 1 -.

~

s

~J

_J 1.-o. 96 cm 1r*l.Z7 0.038 i~ .......

Pliite 2 0.79 j~

N L 2.85 cm Cl Fig. 3 Perlorattd*pl1te model 1111 configuration with electrom1gnellc

{-~

sh1kerdri.,.

• Pliite 3 J l:o.96cm

-- J.2 Tesl Procedure Cylinder I. D. 10.450 cm 3.2./ Mt*u.~urc*mc*111 <~/Added Muss. For each of 1he three perrprated plate,, _the ma uf the vibra1i11g 'Y'lcm wa' fi"I Fig. 2 St11lnles1 steel plat11 used In eaperlment*I inwestlgatlona ot determined in air. Then 1hc- -appareni mass in water -wa!>

added m111 ind hydrodyn1mlc damping determined. The added mas' was found by 'ubtracting 1hc in-air value from 1he in-waler value.

the same hole pauern as Plate I but is rhree limes as thick; it The vibrating mass 111 of a *single-degree-of-freedom was tested to determine lhc effect of hole lcnglh. Plate 3 is nor syslcm 1 is given by

.. perforated. Its diameter was specified to yield the same llow 1 area as Plates I and 2 but in the form of annular clearance tween the plate outside diameter and cylinder in,idc 1 The JlCrlnra1t.*c.J.rl.1lt. modd ma'.i he: c.:rnhitkrctJ 111 0

he 11 ,i11v.lt*-tJcJ.!fl'c:*nf*

amclcr. All lhrce plales arc slainle\s eel, and in all ca'e' lri.:1,,*Jo111 \)'\h.*m hn*au'c 1lu: &.:)*li11Jcr/ha'c a\\cmhl)' \U 111m:h muu.* 111a"1v1.*

• e lest fluid wa' waler in room 1empera1urc. 1ha11 1hc 1-..:rl111a1cc.J plalc a'wmbly 1ha1 1hc haw" "c1111ally mul1<*11lc". rim Figure 3 is a pho1ograph of 1he model. ""a' H'fl I11..*t.I hy llll"~l\111 c1111.*111\ 111 1hL* hJ\C v1hra1ory a1.*1.:dcrn 1u111.

Journal of Pressure Vessel Technology MAY 1981, Vol. 1031177

j111 T.-IJlo I U,11utw1dth mclhull lo* dulf*rn11n11u1

,,, :.. wibr*tion amphludo.

d,1111p111q 11 ....

( ~'.'_.): - I Drive Force Amplitude

"'"*~" 3 6 10 2~8 d8 up where w" and w~ ..l"' arc 1hc na1ural frcquem:ics of lhe W'lem --*- ~

with and withoat 1he addition or an incremental ma!ts i1m. Drive Force Amplitude, Thus, if 1he natural frequency or the model is measured Multiple of Value 1.414 2.00 3. 16 10.0 before and aflcr allaching a known mass tl111 10 1he moving at Resonance.

pla1form, equalion (3) can be used lo compule lhe ma~~ 111. >---

Performing 1he computation for the* dry model and fluid- a l . ~IT 3 9.9S rilled model yields the difference in apparent mass, or added mai.s.

Actually, since the stiffness is the same with air or water, allaching tlln need be done only for one model condition (full 6:

or empty). For example, if the incremental mass is u~ed wi1h

• the empty model the approi'riate expression for the added massm,, i:o; Ill 2 6 = damping I log decrement I

( -2....) -I = frequency at resonance 111., =llJll[ - Ill"****** *--]. (4) = frequencies I above and below f n l at

. (- Ill"ii"

)2 -I which the drive force amplitude is the

"'~air.~" stated number of dB above value at resonance where the sub!tcripls have lhc obvious definilion!t.

a In 1he experimenls, mass tlln or 190 g was used, and the na1ural frequencies were determined by varying the excitation frequency or the shaker unlil maximum motion or lhe plate (resonance) was obtained for a given applied force amplitude.

The results or these experimenls were verified by bump 1es1s. where De1erminations were made at various natural frequencies or N = number or cycles vibration, corresponding to different stiffnesses and masses y,, trace am(llitudc or the firsl cycle of 1he syslem. Differen1 ampliludes were also inves1.igated. y, trace ampli1udc after N cycles

• The added mass was abo determined by measuring lhe oscillatory differemial pressure across the vibrating pla1e using two transducers !lush-mounted in the cylindrical The 101al damping 0 1 is1hc :-.um of 1he mechanical Llampi1111;.

chamber wall a ~horl dis1ance from eilher ~ide of 1hc pla1c and lhc hydrodynamic dampini: Ii,, all eval11a1cd al 1hc 'amr (Fig. I). The value ol' added ma!t~ implied by lhe re~ull\ of lhi' rrcq111.:11l*y ;111d a111pli1mh.: or vilu al i1111.

lypc of lest is given by A second 111c1hoJ u'cd lo dc1crm1111.: tla111pi11g Wil\ 1h1:

hunclwiclrll 111t:1hod, in which 1hc pla1cirod/pla1f11r111 mu=A,l~l/lil (5) assembly wa' driven al con~1an1 vibration ampliluLle "'hilc lhl.'

where A, is the effcc1ive solid area or the plale (cylinder area exci1a1ion frequency was varied. The frequencic' / 1 and f.* a1 1111i1u!t 1u1:1l open :1rca minu~ lhc cfl'cclive pi~1011 an.:a uf one which lhc drivl' lull'l' 111a~*11i1mlc illl.ll'il'l'd hy a 'l'l'l'1l1,*d bellows sea1 2 ), l~I is 1he magnilude of differen1ial pressure amou111 over lhe force al lhc re~unant frc4uc11cy ),, were across 1he plate and Iii is the magni1ude or 1he pla1e ac- recorded and 1hc log decremenl damping, o, was calcula1eu by celera1ion (see Appendix). /J =7r(f: - /i)/(crj,,) 171 1.1.1 M<*usur<'ltl<'nt of .Jlytlrm/y11umi<' Du11111in>:. Three where" depends 011 lhe 'pccificd illlllllllll of rml l' i11creaw 1111 0

differenl me1hods were used 10 measure lhe damping of lhe rc!tu11a111.:c; \CC Table I. In lhcsc lc!tb lhl* \*1bra111111 <1111plilulk plates in water al various vibralion ampli1udes and natural was held cons1an1 by an automalic conirol s}*,1em while 1he frequencies. These me1hods a~e described in the ror1hcoming. frequency was vari\.'t.I manually and 1he force mca,ured by a 1

The firsl or 1hcse techniques was also used 10 mea!ture lhe pieloclcclric l'orcc gage 1hat cou(llcd lhc !thaker drive rod 111 damping in air, so that allowance could be made for 1his 1hc moving platform (figs. I and 3).

relatively small nonhydrodynamic componenl of 101al A third me1hod employed in 1he damping measuremenh damping when interpreting the in-waler 1es1 resulls. was the dumpinR jtJrc:e method, in which lhc logari1hmi.:

The Jvgurilhmit* dec:uy method was employed 10 delermine decrement damping was delermined by mca,uring 1he 1he damping in air and at relatively low amplitude!t in waler. magni1ude of lhc drive force, I Fl, al re.,onance al gi\*cn Wilh the shaker disconnected, lhe movabte platform of 1he magnitude~ of (llale vibralory accclera1ion, 1.\: I. The equal ion model wa~ given an impulsive mo1ion by culling a !tlre1ched U!ted wa!>

siring or 'lriking 1he (lla1form with a rubber malh.:1. l'rom (XJ h=ll'IFl/(mlil>

pholographs of o~cilloscopc lrace!li of lhe ensuing 1rn11,ic111 signal from the platform-mounted accelerometer, the Uo1h lhe bandwidth mclhod and lhe damping rorcc mc1hud logarithmic decrement 6 was determined using the following are useful in ca\cs where the damping is sirongly cJepcndeni well-known equation hce e.g., reference 13)): on amplitude, as wa~ found 10 be 1hc ca!>e in waler cxcepl al very low am(lliludci.. The decay method is pariicularly good when 1he damping i!t low and 1101100 nonlinear.

• --f-- 4 Discussion or Tesl Resulls

• The cffeclive J'll\lon area or each ol 1hc 1wo bellow* wal\ u,cJ 111 1he c**

~nmcnl* i* J.4M cm:. 4.1 Addl'd Mass. Result!> ob1aincd for the 1hrec pla1e' 178/Vol.103, MAY 1981 Transactions of the ASME

equal ion ( 1S) .:an be \Hillen in 1hc following ui111c11sionks\

form Plate l: ~ =i.~ =.79 (16)

Plate 2: ~ = ~ = 2. 33 Equation (16) was used to compute values of ( 11 /d for P~ates I am.J 2. These arc plot11:d in Fig. 4 for lhc value\ or //r/

5 corresponding to the: two plates(/ is the: platc:'thicknc:ss). Al~o shown in Fig. 4 is the theoretical relation between /" 11 /d and

//d obtained when values or the te~t parame1cr~ arc !>ub-stituted in the following analytical expression (references (I 4 1. 22* and 2)) for circular holes in a square array:

'*"d = d~ + Jr _!_ (1 - 2b ~) ( 17) where di b is the diameter/pitch ratio. The agreement is seen 10 be very good.

Computations made using equation (15) and the added mass determined experimentally for Plate 3 yielded the value 2 .I effective_  ! + !. 11 _ .! 1 /,. 11 = 2.57 cm for this plate. This is 55 percem grea1er lhan d - d 311 2b

• the value 1.65 cm similarly computed for l'lale l, which ha' the: same: thickness (0.96 cm) as Pla1e 3 and has the same open d=l.22cm. b =2.46cm area. The greater effective length for Plate 3 (i.e., grealer added mass for the same erfective solid area) implie~ 1hat Experiment I Plate 11 greater fluid kinetic energy is involved in pumping the water through a peripheral annular orifice than through distributed 0 .___ __..__ _ _.....__ ____..__--,-_ _..._ _____. holes having lhe same total now area. This is consistent wi1h lhe fact thal for circular holL"S, reducing 1h1: number of hole' 0 2 3 4 5 while keeping the: tota'I opc:n arc:a and the solid area (Ah and

\

t/d Ar) constant will cause d, 1.11

• and mu 10 increase: (equations flt- 4 ValuH of '*flecliweld used for determining 1dded mHI of a (17) and (14)).

perforated plate vibrating In fluid

'* .~ 4.2 llydrodyn:amic l>:ampin~. In a numhcr or ca'>C'> more

\ing equation (4) are shown in Table 2. *1 Because of the 1han one melhod was.u~cd 10 determine damping in 1hc ~amc calcr amounl of waler in lhe longer holes of Plate 2 com- amplitude and frequency range. In many of 1he'>e ca\e\ 1hc aml wi1h Plate I, lhc added ma~\ or Plaic.2 i~ grcalcr. agt<.:cmcnl hclwccn lhc'c rc,ull' wa' v.:ry good and 1h1: vah1c' The volume llow rate of water lhrough 1he open area of the were averaged.

11la1c i~ In other cases lhe rc,ul" differed by as much a' 20 pcn:cnl.

The reasons ror lhc'c di'>crcpancie'> arc nol known, hul i11 (9) view of the fact that damping is usually difficult 10 measure "here A,, is the total open area (hole area plus annulus area) accurately and that experimental values generally exhibi1 and.\* i~ Ilic plate velocity relative lo the cylinder. The: average considerable i.cauer bee, e.g., reference ( l )), 1he prc.,cnl

\clocity V, (relative: to the plate:) of the water in the: holes is outcome is not surprising. The: overall damping result!; are considered to be reliable.

V,=QIA 1, (10) (In all Cil'>e\, the mca\llred val UC\ of h1. the lolal damping The ab\olutc veloci1y is in water, were corn:c1cd by ~ublracling oul 1he nonhydrodynamic component, o,, of damping obtained from V= V,-i (11) in-air decay measuremenl,. Thi'> lauer component compri'e' ur. u~ing cqualion!'t (9) and ( W),

• mechanical ('>pring plu' bellows) and wind:ige lu... ... c~. II V=A,.i/Ah (12) represents a relatively small correction; typically much le'>s Representing the: moving nuid by a volume: of cross sect*ion than 10 percent. Measured values of or ranged from 0.0165 to 0.524, where a!> o, ranged rrom 0.0016 to 0.0070.)

area Ah and effective length 1.11 , we can cxpresi. its kinetic The damping re.,ull' were Irani.formed into non-energy as dimcmional form in accordance wi1h 1he procedure of reference ( l ). This compri.,ed two steps. Fir\t, 1hc (13) hydrodynamic damping n1 WU\ cxpre\\ed in ICrlTI\ Of lhc

• di1i1en,i*onlcs\da111ping p;iramcter F 1 !(11 V,p J1*wJ, in. whid1 1-"rom equation (2) wi1h V, replaced by i, and from cqualiun F 1 i' lhe hydrodynamic damping force whme mai:ni1udc i' 113) we ohwin 1he folluwini: ~*,pre"ion fur 1hc add.:d nlil" given hy 1

• mu= pA ,,l,. 11 CA,./ A,, I~ ( 14) IF, I =m,.,n lilo 1 /11' , (18)

From equation (14), lhe relative lluid velocity .V, i~ given by

.'f ' ,

mulCA,.IA 1, ) *

"" = --* --**--***

pAh

-- ( 15) V,= (A,. + l)x (19)

A~

r any number of idenlical hole' of lcnglh I and diame1er d, J n1c <la111p111~ l11rw 111a~*1111111.k 11 1 I" 11 1 ~ .- 1 1 rl, 111 which lhc 11111<1 1

't*nr Pl:.llc. I anf..I ~. lhC\C IC\Ulh \t;\'IC 1,;unlHlllc.'d h~* rrt."\\llfC llU.'it\llH.'111\.'lll\ Ua111p111i* ""'*:I I 11.:1c111 1 / \.all hl* c.-'prc"l"tJ ii' c 1 -* mw 11 i> 1 11 f'.n*. l".J.' .. rdt*n*11u*

l 1*'4llalnrn 1~11. 1111 Journal of Pressure Vessel Technology MAY 1981, Vol.103/179

V r.:. 11~111lulk.o ul rclt1hv1: 11.,,. 'fl.:i1J1.1I; ll1n111*1l1 11ol1** Ip' 1\ 1,/1\hl um F1 = l!Wqnitude ol nydroOy11dm1C !l4ni~1nq lort1:; A =*n t*.'/ ~: ~ = llulll ~*n\tly

\

11 ,.circul1r villrilion lrequericv: v *~kin .. lllitic vi~~*.*::~:;* lluid Cylinder iMiJt didrneler O = Hi.a'.AI w*

~ ...

... Plate 1: ~ = i:~=. 79 Pl1te 2: ~ = 2.8S =2 3J d 1.22 .

c "i. 100 I

£ Y/ ./w l*

Q 0 ¢e Q

10 Exoerimental values Llne.r theory-, Pl'J.' 2 c.51

...c Lin Hr theory*, Plate l 6

,., ' . 7 Yr/ ./W o Piiie l, 13. 2 Hz t:i. Plate I, 53.* Hz

~ D Piiie 2, 211. 7 Hz 2

Ci

• F,JIAVr pJW1J(d! + l ""'. i (~) ] o Piiie 2, CJ. 8 Hz l .__~.__ ............................~_._......._._.................__~..__...._...........................~.......__._,_.................

o. l l 10 100 l!XXI Dimensionless rel1llve llow velocity Yr/ JW Fig. 5 D1mplng ver1u1 rel11lve llow velocity through hol11 of perforeted pl1t&11 vibrating lnw1ter Vr " llliCJnltude of rel11lve llow velocity throuqh 1nnulus =VD I Al Ahl Fr s llliCJnltude of h)'drodyn1mlc dimping lorce; A.,, 11 o2/ *: ~ =fluid density

!I $

r.n ~

...... 11 s clrculu vibration frequency, 11 = tlne1111tlc viscosity of lluid

~

l 100 Cytl"""'"" ..." D*l**50<m 1' '7 c

~...

. I

~-l i jL t =0.96 cm Annular flow pas~qe

~

~

• s.

E Q

. 10 c

.51 c

0 E

Ci 1 ~----.t.....l-'-L.U..U.....~-'--'-..L-l....L.LJ..U.~-L--1_,_..............

0.1 l . 10 100 l!XXI Dimensionless Rel1tlve flow Velocity v,J ./W Fig. 8 D1mplng versu1 rel11lve !low velocity through the peripheral annul~r clearance of 1 1olld clrcul1r pl1te vlbretlng In w11er at 1 frequency ol 50.45 Hz in accordance with equations (9) and (10), A is the cylinder plo11cd in dimcmionle\!I form.' In 1hi\ form 1hc rc,ull\ arc area, w is the vibration frequency and w,, the natural generally valid l"or plate\ of any 'i1c 1ha1 arc gcomc1ricall~

II frequency, and ,, is the kinematic* viscosity of the lluid. The similar 10 tho'e 1c,1cd, anu the rc,ult' .ire valid for value' 01 dimensionless damping parameter is then expressible a' vibration frcqucm:y, rluid vi,co,i1y, and dcn,ity dil lcri:111 from the cxpcrimcn1al unc,. /\t low a111ph111dc' lhl* l'\*

I- . -

. -F 1 / (A V,pv1""') = .

lllw,,!'1 Ir/,/

_ (20) pcrimcntal rc.,-1111' Jor the pcrf11ra1cd pla1c,, hg. !i, arc cll"i:l~

1rACAr+Ah)P .J11w approximatcd by linear theory (reference\ I I and 21): namcl)*

Next, the amplitude of vibration was expressed in terms of the dimensionless amplitude parameter V,/ .J;w which in ac-

' F,!(AV,pv11w)=.J8 ,- ['(j+I- 4~(cl)~] b mi cordance with equation (19) can be written which give' \lightly conservative re,ults (the calculatcc.I v,1.J;w=(~: +1)x1.J;.., (21) damping value\ arc aboul IS pcrceni lower than the measured The parameters given by equations (20) and (21) constitute . "I u f,.h.*h:r111111\ \o,ilrn;' 111 111'-' ah\l."l\\a 0

h.J111u:11\11111lt.*" t.1111plt111d1.*). llu.: 411a11l11\

the axes of Figs. S and 6, in which the expcrimcn1al da1a arc ""I.ti h;" hcc:n '11h,111u1c ...l lur x 111 c4ua11011 f21).

180/Vol.103, MAY 1981 Transactions of the ASME

T~blo :l Me*'\urod naturnl lro111111nc1n*. a111I ;1111111<.I lor*ted pl*I**

Pt1le No.

• In-1ir Natural ln -water Natural Added Mass.

• 111 11tc \1lii;1111111 ol p..:1 to1a1c<.l pla1c, 1~p1\:al ,,, I'\\ R 111*

• _ __.__ Ficiquency, Hz Frequ~ncy, Hz kg 1crnal'. 1hc ;tddcd 111a" duo.: lo llll" \loater can he a 'i!!11ilil*a111 l'ractio11 lll 1hc \lrtll'llll .11 111..0.,,, I he a<.ldcd 111<1\\ can rcuucc 15.05 13.15 0.45 the natural frequem.:y to a \Jluc si11-nificantly below the in-air

• 60.15 53. 60 .45 value .

• Me<i'ured values of the a<.lded ma'\ 111,, of 1he perforated' 47.J> 40.68 .99 plates teslcd in this \ludy arc accurately given by 1hc following

59. 70 50.45 .70 formula, which applies 10 uniform circular holes .ju square array':

m,, =p A~ -* [t + Sd*- ( I - -d )]

A,, 3ir . 2b

\alues). The range of validi.ty of the linear theory is about VJ

"!'Ill < S for Plate I and V, I ..f~w < 3 for Plate 2. Thus, for In this formula*, p = rluid dcmity, A,. = effective solid area low amplitudes equa1ion 122) is universal in ihat ii applies to of the plate, A,, = total open area, I = hole length (plate

~c1wral 'qua re arr_ays or cin:ular holes in plalcs of arbitrary thicknes'i), d = hole diameter, and h = hole pitch. No thidnes' as well as arbi1rary vibralion frequency, fluid 'Y'tcmatic v:iriation of :1d<.lcd ma" occurred over the range of

\ i'cosily, and lluid Jensity-. ~ amplitudes and frequencies \Urveyed.

Whcrea-; al low values of V,/ ../;w the damping force is

• The hydrodynamic damping of vibrating pcrfora1ed plate~

proportional 10 the first power of velocity and 10 the square comprises two regimes: I) a small-amplitude linear (con*

root of viscosity (equation (22)), al higher values of this slant log decrement) regime where the damping is propor-parameter 11':e damping force is proportional to the square of tional 10 the square root of kinematic viscosity; 2) a larger-the \*eloci1y and is independent of viscosity. In this nonlinear amplit ude nonlinear regime where the damping log dcc.:rement range ( V, I ../~w greater than about 20), the experimental data is proportional to the vibrational velocity and i' independent of viscosity. ~.

arc satisfactorily correlated by i.

• The nondimcnsionalized hydrodynamic damping of a 0.96-F1 /(AV,pv'11W) =0.7 V,/../;w for Plate I (23) cm-thick plate with multiple perforations was found to be less than 1ha1 of a 2.115-cm-thick plate having the same hole F 1 /IA V,p../;w) = V,t.J;w for. Plate 2 (24) pattern, an<.J ,lighlly greater 1h:111 th:1t of a O.%-c.:111-thick pt.ttc f; The values of the numerical coefficients have been chosen to

~iq}slighlly more conservative (i.e., lower) damping values 1han would be given by a least-squares fit. Unlike lhe linear with the same solid area but ha\'ing all or the open area in the form ol an annulus al the periphery.

. ,;~

t

• The cxperimcnt:il rc,1ilt' ror 1hc two perforated plates can .

r~1e, in the nonlinear regime there is no analytic expression be correlated to yield the following analytical e.'<pre\\ion' ror .*

~i~ing 1he dependence of damping on ltd and hid. Therefore

,;11i,fac1orily con~crvative values of the hydrodynamic ~  :

fo"'.'\'alUCS Of these IWO parnmeler\ \ignific:tnlly far outside <.l:1mpi11_g force F,:

1hc

• ngc investigated, accura1e determination of damping "quire furl her testing. 2.8~-cm-thick plate 011di111c11sio11ali1ed d:1111pi11g result\ for l'l.a1e 3 arc separately in Fig. 6. The damping is slightly lower than 1h;s. .,f 1he perforated plate of the same thickness (i.e., Plate F, = /, v, µ-..* l'W\ x l:, I I _: ( ~ r* J.v. I .... ,.""< J I). Comparison of the results on an analytical ba-;i~ is difficult F, =A v;p, V, /...:~w>20

!>\.'Cause of the difference in 'hape of the flow openings. It 0.%-cnl-lhick plate 1.nay be noted, however, that the strcamwisc wetted area of Plate 3 is considerably less than that of Plate I, whic.:h implies lcs)..Qrag from thal source.

• F,=AV,p.J;wv8[~ +I - ; (~) ~ ].v,N;w<5 R6ults of reference (I) indicate that for single orifices in F, =0.7 AV;p,V,/..[;w?20 thin r.1a1es, the lran!tilion from the linear to lhc nonlinear

\*ifC"bSity-independen1 regime begins al a value of where A = cylinder area. V, = average relative flow \clocity V, /J;w= 3. This is in general agreemen1 with the experiments of fluid in the holes, " = fluid kinematic viscosity, w =

rc~lctl here, a!> arc the other 1u:11ernl result\ or 1hc rcfcn:ncc circul:ir frequency of vibration, and th~ other 'iymbols arc a' Ill damping i.1udics. . defoicd previomly.

i'l'Re experiments performed thus far have been restricted 10

• In those regimes where comparisons are valid, the results of the case of systems with zero 'ileady now component. Similar this investigation arc in g'!neral agreement with those reported i1wcs1iga1ions of vibrating perforated lllales in a flowing in reference 111. which deal\ wi1h single orifices in 1hin plates.

water system would he dellirablc; such lcsts would be con-

• J\ri extension of the cxpcrimcntll <.lcscribed to the ca\c of

'itlcrahly more cmnple.'c 1hm1 1hnsc performed llll to now. llowill!l w411er sy,tem~ i' dc,irable and would be likely to With steady flow, lhe characlcrislics of the hydrodynamic rcve:il .,ignific<llll cllect' ol 1he ~tea<.ly 1'111w co111po11e111, 'i

\lamping c:m hl* cxpl'l"lcd In change 'ignificanlly: specifically, c'pcl*ially 011 the hydrodyn:1111il* damping.

1he linear rl'!liti1e nii!lhl di;.,appcar for 'lcmly flow vclocil ie'

\:lllllp:irahle to lhll\e in lypic;il 1111dea1* rcaclOr applica1i1111'. At*knowll*d~llll'lll.,

However, for configuralion'i 'iimilar to 1ho!>c that have been The author wi~he\ to acknowle<.lgc the valuable con-te'ited, ii is believed that th~ damping is likely 10 remain tributions of D. V. Wrighl, H.J. Connors, A. R. Hess, and relatively low and that the effects of the steady now on 1he K. B. Wilner of the Westinghouse R&D Center to the ex-added mass would not be great. perimental phase of this investigation.

l(cfercnccs c*ulh presented in reference I l I sug11est that this and the other per*

rora1cu:p1a1e lc\I r~'ulr\ may!>.: applicable 10 J!!a'c' a' well a' to liquid\. l Panton. R. L.. and Goldman. A. I ... "Correlation or Nonlinear Orifi~c Journal of Pressure Vessel Technology MAY 1981, Vol.103/181

l1npinl~rh:r," .1111111111/ ul .,,,,.,,,,,.,, ,,,.,,.,, ,., ,,,,,.,,.,,_ \'111 t.o . .-...u * ,,,, l'"'lll *l'llW \J.1llh111.1li..11i\. 1111-. ll l.111.,11.l1q1 ,.. I'" ***

0 1'17'., 1'1' I 11111 I l'lt" 2 lltt.snck, I.. L .* "AcOU\llc l'umponrnh," (.hap. '* Ac*11umn. ~l*l*<il"'*

Hi(I, ,_.,. Ycwl. 1954. I'* IJll. wl,J.,,ldV!dtl.-' l~1ll.-l-A,.1-111.,lrl 1:~1 l Thom"""'* W. T .. "l>:1111110:d l'rc~*V1hrn11e111," *"1/1ru1u"' """'"""

Aptllic'fllttHll, (.'ha11. 2. l'rrnllc~*lhdl, !'.11,1,.,.,,kKI ('hlh, N J., l'IM. IJ1 I lcrc1111;11111g equal 11111 I I: 1 ~ 1dlh APP~NDIX Sub,lituting equation C?6) inlo 125) and 1carrn11ging pwLlu..:c' (111,, +p...-l,.(. 11 )1.\'I = l~pl (11-.*1 1,)  !.:?.71

.1eriv111ion of Equation (5) finally, u~ing equation (14) in (27) 1ogct'hcr \\ith the The magnitude of the force that accelerates the fluid dct'ini1ions of lhe areas give~

through the openings of the pi!lton i!1 equal to the vec1or ~um Ill,, 1.\'1 = l~Jl.-1,.

of the force mu Iii exerted on the nuid by the piston and the pressure force IApl (A -A,.) ac1ing on the fluid in the op- which j, lhc 'amc ~1' c411<1linn 15).

• !1:

• II

• 11

~~ '*

i!1 1 I") *;i ..

lk

q l~

l'll i:1!*

'I'

!i **

l'i<-

"l'1111"'

Ii**:

'* jlit

• 182/Vol.103, MAY 1981 Transactions of the ASME Jr;

j.

consumers Power Kenneth W Berry Director l'OWERINli Nuclear Licensing MICHlliAN"S PROliRE.55 General Offices: 1945 West Parnall Road, Jackson. Ml 49201 o (517) 788-1636 October 16, 1986 Director, Nuclear Reactor Regulation US Nuclear Regulatory Commission Washington, DC 20555 DOCKET 50-255 - LICENSE DPR PALISADES PLANT -

EXPANSION OF SPENT FUEL POOL STORAGE CAPACITY -

TECHNICAL SPECIFICATION CHANGE REQUEST - REVISION 1 Consumers Power Company letter dated February 20, 1986 submitted the Technical Specification Change Request and supporting Safety Analysis Report (SAR) associated with the proposed installation of new spent fuel pool storage racks in_approximately one-half of the Palisades Plant spent fuel pool. At the time of that submittal, the analyses referred to in the SAR were incomplete.

Consumers Power Company letter dated April 16, 1986 provided confirmation that the analyses had been completed and the conclusions given in the SAR, with the exception of those for the pool structure, are valid. Additionally, it reported the results of analyses that showed that no modifications to the Region I racks are necessary. It also provided revised pages containing tables, figures and descriptions which were either incomplete or editorially incorrect in the February 20, 1986 submittal. Consumers Power Company letter dated April 24, 1986 confirmed that analysis of the Spent Fuel Pool structure was complete and that conclusions given in the SAR regarding the Spent Fuel Pool structure are valid.

NRC letter dated April 25, 1986 transmitted a request for additional information __ regardi~g the -~xpansion of the spent fuel pool storage capacity.

Requests for additional information were-also received during discussionwith-the Palisades Plant NRC Project Manager. The additional information requested by letter and during discussion was provided by Consumers Power Company letter dated July 24, 1986 which also informed the Staff that Consumers Power Company would revise the Technical Specification Change Request and supporting SAR. \

Additionally, the July 24, 1986 Consumers Power letter informed the staff that submittal of the revised Technical Specification Change Request and supporting SAR, together with the information contained in that letter would be considered as submitted in lieu of the Summary Reports described in the Consumers Power Company letter dated April 24, 1986.

OC0886-0129-NL04

Director, Nuclear Reactor Regulation 2 Palisades Plant Rev 1 - TSCR Spent Fuel Pool Capacity October 16, 1986 Attachment I to this letter contains the revised (Revision 1) description of the proposed Technical Specification Changes and analysis which determines that this installation and license amendment involve no significant hazards.

Attachment II contains the revised Technical Specification Change. Attachment III contains Revision 1 of the supporting SAR. The completed detailed analyses referred to in the SAR are available* for review. Changes from the original February 20, 1986 submittal and from the revised pages included with our April 16, 1986 submittal are summarized as follows:

1. References to results of analyses are stated in the past tense and refer to the results of completed analyses.

2. Information provided by the completed Thermo-Hydraulic Analysis has been incorporated into Section 3 of the SAR.

3. The maximum initial U-235 loading of the fuel is stated in w/o.

0

4. The effect of 1,720 ppm boron in the pool water has been H') conservatively stated as 25 percent ~K.

"'T Changes made to* the SAR by our letter dated April 16, 1986 have been included in the attached Revision (. Therefore, the changes indicated by a vertical line in the right margin include those ~ade at that time.

After approval, the specification changes requested in this Technical Specification Change Reque~t will become effective when the installation of tha new racks commences.

This letter supersedes and withdraws the May 11, 1981 Consumers Power Company letter entitled Technical Specification Change Request - Fuel Storage.

A check for $150.00 as required by 10CFR170.21 was included with Revision 0 which was submitted on February 20, 1986.

Kenneth W Berry/rws (Signed)

Kenneth W Berry Director, Nuclear Licensing _ ..

CC Administrator, Region III, USNRC NRC Resident Inspector - Palisades Attachments

• OC0886-0129-NL04