Text

Submits Response to NRC RAI Re Ampacity Derating Analyses for Thermo-Lag 330-1 Fire Barriers Per IE Info Notice 94-022
	ML20115F327
Person / Time
Site:	Byron, Braidwood
Issue date:	07/12/1996
From:	Hosmer J; COMMONWEALTH EDISON CO.
To:	; NRC OFFICE OF INFORMATION RESOURCES MANAGEMENT (IRM)
Shared Package
ML20115F333	List: ML20115F327; ML20115F353; ML20115F368;
References
	IEIN-94-022, IEIN-94-22, NUDOCS 9607170199
	Download: ML20115F327 (5)
	v • d • e

(;onunonweahh lilison Osmpany 1400 Opus Place Downers Grove, IL (0515

'Ju(v 12,1996 -

Document Control Desk U.S. Nuclear Regulatory Commission Washington, D.C. 20555

Subject:

Byron Station Units 1 and 2 Braidwood Station Units 1 and 2 Response to the NRC Request for Additional Information Regarding Ampacity Derating Analyses NRC Docket Numbers 50-454. 455. 456 and 457

Reference:

1)

February 15,1995, M. J. Vonk letter to USNRC 2)

March 28,1995, K. L. Kaup letter to USNRC i

3)

March 29,1995, K. L. Graesser letter to USNRC 4)

November 2,1995, R. R. Assa letter to D. L. Farrar 1

5)

December 4,1995, G. F. Dick letter to D. L. Farrar i

6)

December 15,1995, D. Saccomando letter to USNRC i

7)

March 21,1996, D. Saccomando letter to USNRC l

8)

June 12,1996, R. A. Capra letter to D. L. Farrar i

Reference (1) provided the Commonwealth Edison Company (Comed) White Paper that compared the NRC test results provided in Nuclear Regulatory Commission (NRC) Information Notice (IN) 94-22 for determining the ampacity derating factors for cable trays wrapped with three-hour rated Thermo-Lag 330-1 fire barriers with the Comed analytical techniques and results used to derate the ampacities of cables installed in wrapped trays. Reference (1) also provided the i

calculation that determined the ampacity derating factors for the potential Darmatt KM-1 Fire Barrier System to be installed at Braidwood Station.

i Reference (2) provided the response to the NRC Request For Additional

)

information, pursuant to 10CFR50.54(f), dated December 29,1994, for j

Braidwood Station. Reference (3) provided the response to the NRC Request For Additional Information(RAls), pursuant to 10CFR50.54(f), dated December g g' 29,1994, for Byron Station. Reference (4) was the NRC Request For Additional Information regarding the ampacity derating analyses performed for Braidwood Station. Reference (5) was the NRC Request For AdditionalInformation 9607170199 960712 PJR ADOCK 05000454 Ird PDR 1

A t'nicom n>mpan) m

regarding the ampacity derating analyses performed for Byron Station.

Reference 6 transmitted Comed's request to respond to the Braidwood and Byron RAls (references 4 and 5) concurrently because many of the issues discussed in the Braidwood RAI apply to Byron Station. Reference 7, provided the Comed concurrent response for Byron and Braidwood. Reference 8,is the NRC RAI that requests a description of the detailed plan and schedule of the actions to resolve the ampacity derating issue.

The following provides the Comed response to that request.

General: As stated in reference 7, Comed has been reevaluating the Byron and Braidwood Thermo-Lag 330-1 ampacity analyses and has concluded that additional actions were necessary. This reevaluation had determined that the existing analyses did not completely envelope allinstalled configurations.

Because the as-installed Thermo-Lag 330-1 board thickness, in some cases, is greater than the nominal value supplied by TSI, this thicker Thermo-Lag 330-1 board value was not used in the prior ampacity derating calculations. Also, some installations have an air gap between the Thermo-Lag panel and the cable tray, that was not modeled in the prior ampacity derating calculations. These identified conditions are being addressed at both stations, as discussed below.

Appropriate calculations have been or are beirig revised as necessary. During this reevaluation, Comed has compared the ampacity analytical methodology used, to valid industry test data provided by Tennessee Valley Authority (TVA) and Texas Utilities (TU). As a result Comed is no longer relying on the test results cited in IN 94-22 as support of our analytical model.

The plan and schedule to resolve the concerns related to the cable ampacity for cables routed in raceway wrapped with Thermo-Lag 330-1, consist of the following tasks:

1. Develop an analytical model for the wrapped raceways to calculate the temperature of the cables in the raceway. This modelis calibrated, using actual industry test data, to validate the results. This task is comoleted and the results are documented in Calculation #BYR-96-059/G-70 092. Rev. O. (coov attached). This task comotetes the action stated in Comed resoonse item A.8 in reference 7,

2. Develop cable ampacity derating factors for bounding raceway configurations based on the analytical model. These bounding configurations are selected from a review of allinstallations at the Byron and Braidwood Stations. Any installations found that are outside of these bounding configurations are to be evaluated individually, on a case-by-case basis. This task is comoleted and the results are documented in Calculation #BYR-96-082/BRW-96-194. Rev. O. (coov attached). This 2

i

task comoletes the action stated in Comed resoonse item B.1 in reference 7.

3. Revise Calculation G-63, which applies to Byron Station only and addresses ampacity derating for cable routing in raceways wrapped with Darmatt KM-1 fire barrier material. Specifically, the revision considers an air gap between the raceway, and the Darmatt material, incorporates the annular model for conduit and eliminates described configurations not installed at Byron or Braidwood Station. This task is comoleted and the results are documented in Calculation #G-63. Rev. 4. (coov attached).

i This task comoletes the action stated in Comed resoonse item A.3 in reference 7.

4. Perform an analysis to address the ampacity of cables routed in conduits wrapped with the Thermo-Lag material. This task is on aoina and is scheduled to be comoleted by Juiv 31.1996.

5. Pedorm an initial screening by applying the ampacity derating factors established in Step 2, to the actual installations. ' This is performed using the ampacity evaluation report in the SLICE cable management program.

The report calculates the ampacity of each cable at a given routing point (applying any applicable ampacity deratings) and compares the i

calculated value to the potential full load current for the load fed by the l

cable. Any instances where the potential full load current may exceed the calculated ampacity are identified in the report. This task is acoroximatelv 60% comolete and is beina comoleted in oarallel with Task in.

6. Perform a refined analysis on the routing points that are identified in the SLICE ampacity report as potentially overloaded. This refined analysis includes consideration of the specific configuration (rather than using the bounding configuration) and includes consideration of the diversity in the cable load currents. The installations that are not covered by the bounding configurations are to be addressed in this analysis. The SLICE ampacity report discussed in Task #5 will be an attachment to this analysis. This task is on aoina and is scheduled to be comoleted by Auaust 30.1996. This task will address the 30 inch section of ladderback cable trav discussed in Comed resoonse item A.1 in reference 7.

7. Address the adequacy of the cable for continued service for the life of the plant. Provide recommendations for those raceways where potential overloading of cables exist. ' These recommendations may include the removal of the Thermo-Lag 330-1 materialin specified locations. As items are identified, they are to be assessed for impact on system continued l

3

f operability. This task will follow Task #6 and is scheduled to be comoleted by October 31.1996.

To the best of my knowledge and belief, the statements contained in this document are true and correct.

If there are any further questions concerning this matter, please contact Denise Saccomando of the Nuclear Licensing office.

Sincerely, i

M John B. Hosmer i

Engineering Vice President 1

........:: ---. ::::::::::::: 3

,i Subscribed and sworn to before me OFFICIAL SEAL j;

i this

/2 u day of Gm

.1996 MARY JO YACK ll;

/ /

/

many evene sim or umois;

)q Au, o, 7ve i d_"??.S??.17.5I"'IO*.$.Y!N3

^ ' / No,tdty'Publid

~~~~~

Date Commission expires:

lt +1 A 7 Attachments:

(A)

Calculation #BYR-96-059/G-70-96-092, Rev. O.

Calculation #BYR-96-082/BRW-96-194, Rev. O.

Calculation #G-63, Rev. 4.

cc:

G. Dick, Byron Project Manager-NRR R. Assa, Braidwood Project Manager-NRR H. Peterson, Senior Resident Inspector-Byron C. Phillips, Senior Resident inspector-Braidwood H. Miller, Regional Administrator - Rlil i

Office of Nuclear Facility Safety - IDNS i

4

l Attachment "A" Calculations cited in the response:

1

1) BYR-96-059/G-70-96-092, Rev. O.

2) BYR-96-082/BRW-96-194, Rev. O.

l

3) G-63, Rev. 4.

1 I

j I

5

Exhibit C NEP-12-02 Calculation Title Page Revision 2 Calculation No.: G-63 Page No.: 1 of 141 g Safety Related O Regulatory Related O Non-Safety Related Calculation Tit;e: Darmatt firewrap matenalcable ampacity derating calculation Station / Unit: Byron /Braidwood System Abbreviation: Vanous Equipnuent No. of appu Vanous Project No. of appo 09050-051/09135-200 l

Rev.: O Status:

QA Serial No. or Chron No. 210548 Date:

Prepared by: _ Roman Gesior Date: _Aug.30,1994 Revision Summary:

i i

Electronic Calculation Data Files Revised:

(Name ext / sue /date/ hour /. marw erificatiori method / remarks) w Instralissue Do any assumptions in this calculation require later verification? O Yes a No Reviewed by: _B. Perchiazzi / G. Hinshaw Date: _ September 1,1994 Review Met' hod:

Comments (C or NC):

Approved by: _B. Rybak Cate: Sept. 2,1994 i

l f

I I

Exhibit C I

NEP-12-02 i

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION REVISION PAGE PAGE NO.: 2 of 141 CALCULATION NO. G-63 REV:1 STATUS:

QA SERIAL NO. OR CHRON NO. 210740 DATE:. January 3.1995 PREPARED BY: Roman Gesior DATE;.Janusry 3,1995 REVISION

SUMMARY

I Change iteration process to utilize Mathcad built in

Root" command which iterates for a solution. Entire calculation restructured to provide calculation of each case individually and not as a vector as was done for Rev. O. Also a case l

was added to the conduit section of the calculation which calculates the derating for a 4" conduit with a 500 kemit i

l cable, per request of Byron Station. Also a change to section 4 6.5 case 47 and 48 is made, the results were switched in the onginal calculation.

CALCULATION FILES REVISED:

(Name ext / size /date/ hour: min / verification method / remarks)

DO ANY ASSUMPTIONS IN THIS CALCULATION REQUIRE LATER VERIFICATION O YES O NO REVIEWED BY:.B. Perchiazzi DATE: January 3,1995 REVIEW METHOD:

COMMENTS (C OR NC):

APPROVED BY: B Rybak DATE: January 3,1995 REV: 2 STATUS:

OA SERIAL NO. OR CHRON NO. 210744 DATE: January 23,1995 PREPARED BY: Roman Gesior DATE: January 20,1995 REVISION

SUMMARY

Clanfy that the vertical length design inputs are used to determine relative derating of vertical trays and all cases

)

considered in Rev. O of the calculation are included in Rev.1.

CALCULATION FILES REVISED:

(Name ext / size /cate/ hour: min / verification method / remarks)

I DO ANY ASSUMPTIONS IN THIS CALCULATION REQUIRE LATER VERIFICATION: O YES @ NO j

{

REVIEWED BY: B Perchiazzi DATE: January 23,1995 REVIEW METHOD:

COMMENTS (C OR NC):

APPROVED BY: B.Rvbak DATE: January 23,1995 i

r

- -}

.A Exhibit C NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION REVISION PAGE CALCULATION NO. G-63 PAGE NO..

3 of 141 REV:3 STATUS:

QA SERIAL NO. OR CHRON NO.

DATE.

PREPARED BY:.

DATE.

REVISION

SUMMARY

Delete unneeded configurations. Include convection and radiation in the air gaps in the fire wrap system for conduits, only.

CALCULATION FILES REVISED:

(Name ext / size /date/ hour: min /venfication method / remarks)

DO ANY ASSUMPTIONS IN THIS CALCULATION REQUIRE LATER VERIFICATION O YES S NO REVIEWED BY:.

DATE.

REVIEW METHOD:

COMMENTS (C OR NC).

APPROVED BY:

DATE.

FEV: 4 STATUS:

QA SERIAL NO. OR CHRON NO.

DATE.

EEPARED BY: 04M4fi/IIm DATE.

// /9f 6

/

REVISION

SUMMARY

I References to "Thermolag" fire wrap material were corrected. No changes were made to the numencal results.

CALCULATION FILES REVISED:

i (Name ext / size /date/ hour: min /venfication method / remarks) 2c4h.mcd / 44306 / 07-11-96 / 8:44 a 2c6n.med / 44297 / 07-11-96 / 8:52a 500c6n.med / 44286 / 07-11-96 / 8:56 a 6c0r75h.med / 44296 / 07-11-96 / 9:01a 8c0r75h.med / 44294 / 07-11-96 / 9:09 a new g-63. doc / / 07-11-96 / 9:54 a DO ANY ASSUMPTIONS IN THIS CALCULATION REQUIRE LATER VERIFICATION: 0 YES S NO

/r A

/

REVIEWED BY: A/Adil

/ALRh DATE: "7////9f De/,////gey/gg COMMENTS (C OR NC): 4/ (,

REVIEW METHOD:

APPROVED BY: d//e D

/

DATE.

7/ gj j 9 g,

Exhibit D NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION TABLE OF CONTENTS PROJECT NO. 09050-051 /09135-200 CALCULATION NO. G-63 REV..NO. 4 PAGE NO. 4 of'141 DESCRIPTION PAGE NO.

SUB-PAGE NO.

TITLE PAGE 1

2 REVISION

SUMMARY

TABLE OF CONTENTS 4

6 PURPOSE / OBJECTIVE METHODOLOGY AND ACCEPTANCE CRITERIA ASSUMPTIONS 15 16 DESIGN INPUT REFERENCES CALCULATIONS 22

SUMMARY

AND CONCLUSIONS 141

l I

l Exhibit D l

N EP-12-02

(

Revision 2 i

COMMONWEALTH EDISON COMPANY CALCULATION TABLE OF CONTENTS PROJECT NO. 09050-051/09135-200 CALCULATION NO. G-63 REV. NO. 4 PAGE NO. 5 of 141 l

DESCRIPTION PAGE NO.

SUB-PAGE NO l

ATTACHMENTS 1-1 to 1-3 l

1-Byron NDIT BYR-94-029, Chron 0302309, Approved 8/ 5/ 94 (Reference 1) 2-1 to 2-6

(

2-La Salle Calculation 4266-EAD-13, Rev 0, l

Transmitted by DIT BB-EXT-0836, July 21,1994 (Reference 2) 3-1 to 3-2 3-Tests at Braidwood Station on the Effects of Fire l

Stops on the Ampacity Rating of Power Cables l

(Reference 3) 4-1 l

4-Heat Transfer by Holman, Table 7-4 (Reference 5) b##

5-General Electric Heat Transfer Data Book (Reference 4) 6-Transco Transmittal of Darmatt Data Sheets 6-1 to 6-15 (Reference 6) l l

l i

7 j

1 i

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO. 6 09050 051109135-200 of 141 PURPOSE / OBJECTIVE The purpose of this calculation is to determine the amount of cable ampacity derating required for 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months fire barriers installed utilizing Darmatt fire wrap material. The scope of this calculation covers 18" x 4" cable trays with a 1" depth of fill. The calculation will also evaluate the relative derating for a vertical cable tray (24" x 12") relative to an i

unwrapped horizontal cable tray. Also the ampacity of cables in conduits installed with 3 hour3.472222e-5 days 8.333333e-4 hours 4.960317e-6 weeks 1.1415e-6 months rated Darmatt fire wrap will be compared to the ampacity in conduit without fire wrap.

P I

i

)

l REVISION NO.: 4 l

l

6 4

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO. 7 09050-051/09135-200 of 141 l

METHODOLOGY AND ACCEPTANCE CRITERIA Wranoed Cable Trav The allowable heat generation for a tightly covered cable tray is first calculated. The allowable heat intensity versus depth of fill for an uncovered l

i cable tray (see figure 1)is derated by 15% for the covered cable tray.

l The total thermal resistance of the cable mass, air space and cable tray is I

then determined. The allowable heat generation for a tightly covered cable tray is used to calculate the surface temperature of the cable tray. The difference between the rated conductor temperature and this surface l

temperature is then divided by the allowable heat generation for a tightly covered cable tray in order to obtain an equivalent thermal resistance from the conductor metal to surface of the tightly covered cable tray (see figure 2).

The surface temperature of the tightly covered cable tray, TGS, is found by manually adjusting this value until QTGS, the calculated value of the total heat transferred from the closed cable tray surface, nearly matches QCB. the allowable heat generation in a tightly covered cable tray.

Next, a composite thermal resistance of the Darmatt fire wrap and an l

assumed air gap (to compensate for potentialinstallation problems and fire wrap thickness variations)is calculated and added to the equivalent resistance from the conductor metal to the surface of the cable tray which was calculated previously.

i 1

1 The same formulas for the total heat transfer (convection and radiation) from the tray surface to the surroundings, as modified for the higher emissivity of the Darmatt material as compared to the galvanized steel, are then used to calculate the total heat transfer (convection and radiation) from the wrapped cable tray to the surroundings (see figure 3).

i The surface temperature of the wrapped cable tray, TWT, is manually adjusted using the MATHCAD program until the calculated maximum temperatt e of the conductor, TCCR, is nearly equal to the rated conductor tempera' re, TCR. The variable, calculated rated conducted temperature, TCCR, is calculated from the formula TCCR= TWT +QTWTxRTOT, where QTWT is the total heat transfer from the wrapped cable tray, and RTOT is the total thermal resistance from the conductor metal to the surface of the fire wrap.

Since the heat generated in the cable is proportional to the square of the current, the square root of the ratio of the allowable heat for a wrapped cable l

l REVISION NO.: 4 l

l

1 Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. :G-63 PROJECT NO.

PAGE NO. 8 09050-051109135-200 of 141 tray to an unwrapped cable tray is the ampacity factor. The derating factor is 1 minus the ampacity factor. Calculations were performed for a horizontal cable tray and for a nser with a 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months rated system.

O l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO. 9 I

i 09050-051 /09135-200 of 141 l

I Uncovered Cable Tray 4 TAR.

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h QuCS l

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=

w QucB : B1 Aeg a = w. det (?)

Figure 1 l REVISION NO.: 4 l

Exhibit E N EP-12-02 Resision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 10 of 141 Tightly Covered Cable Tray der &S

TSR et6s i

QM

-y i

m ots ERia

=A%c5 "-I g.

C W

OtM oc.MS GTG5 = QG5 +ec%s, + o CT4s oc.865 C Qt2 )

RC.m = 3 A O QC B Figure 2 l

l l REVISION NO.: 4 l

l Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 11 of 141 witAffFD.CA8LE TAAY auf

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4 etw oowr QTWT* QEkif y GCiWT e GCTshe QC8 ki'i~

TCCRs TWT + QTWT* ItTUf" RTOT = (CM e Rcomp Figure 3 Vertical Cable Travs The same methodology was used for evaluating the relative derating for vertical cable trays. The calculation w as done for A 19' tray length. The calculation was performed for the actuallength of the tray and not per linear foot of tray as was done for the horizontal trays. An assumption is made that the relative thermal resistance of the cable mass and vertical tray assembly is the same as for a horizontal tray cable mass and tray assembly of equal size and material. A 24" wide tray is used for the vertical tray ampacity derating calculation. Per Reference 1 vertical trays are 12" deep.

l REVISION NO.: 4 l

l

Exhibit E N EP-12-02 Revision 2 f

COREBONWEALTH EDISON COMPANY CALCULATION NO. : G-EB 1 PROJECT NO.

PAGE NO. ~

09050-051 1 09135-200 12 of 141 Conduits The model for conduits uses basic heat transfer relationships outside of the conduit andtie Neher McGrath equations inside the conduit (Ref.13). The heat dissipated by the cables inside of the conduit is calculated first. Energy balance equationa can then be written at each interface or discontinuity in the fire wrap system. The temperature at the interfaces can then be determined so that the amount of heat being transferred across the interface is equal to the amount of heat being generated by the cables.

The first interface is at the surface of the conduit. Heat will be dissipated from the sudace of the conduit by radiation and convection. The radiation relationship assumes that the conduit is located in free space, and the area dissipating heat per unit length is equal to the circumference of the wrapped conduit (Equation 8-43a of Reference 14). Convection is calculated using th' simplified relationship for a horizontal cylinder in air (Table 7 2 of Reference 14). The resulting non-linear equations are solved using the solve block feature of Mathcad (Reference 15).

The outer layer of fire wrap is treated as a cylindrical shell. The temperature drop can be calculated using Equation 2 8 of Reference 14.

Heat conduction across the air gap between the inner and outer layer of fire wrap is assumed to be by radiation, conduction, and in some cases convection. The heat transferred by radiation is taken into account by treating the two layers of fire wrap material as concentric cylinders (Equation 8 43 of Reference 14). The heat transferred by conduction is calculated by treating the gap as a cylindrical shell. Since the thermal conductivity of air is a function of temperature, a section of the calculation makes a linear interpolation of the conductivity based on data points taken from Reference 14. The conductivity is calculated for the average of the temperatures on either side of the gap. Depending on the size of the gap and the temperature difference, convection may or may not be significant in the air gap. Any convection is taken into account V an adjustment factor to the thermal conductivity of air. This adjustmen altiplier is given in Section 7-2, Equations 7 49 and 7-60, and Table 7-3 of Reference 14. The Prandtl number and the kinematic viscosity of air are non-linear functions of the i

temperature. Cubic splines are used to perform interpolations of the values l

of these quantities taken from Table A-5 of Reference 14. The function for the adjustment of the conductivity of air is placed in an "if" statement so that its minimum value is 1 (no additional heat transfer due to convection). A l

Mathcad solve block is used to solve the heat transfer equations at the gap.

l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 13 of 141 The temperature drop across the inner layer of fire wrap material is calculated in the same way that the temperature drop was calculated acrosa the outer layer of fire wrap material. The temperature drop across the gap between the conduit and the inner layer of fire wrap material is calculated in the same manner as was used for the air gap between the inner and outer layers of fire wrap material. In cases where there is no gap between the conduit and the fire wrap or where there is only a single layer of fire wrap material, the gap between the conduit and the inner layer of fire wry material or the gap between the inner and outer layers of fire wrap material can be made infinitesimally small.

The temperature drop across the conduit is calculated by treating the conduit as a cylindrical shell.

The temperature drop in the gap between the outside of the cable and the inner wall of the conduit is calculated using Equation 41A of Reference 13.

This equation is partly based on experimental data. Since the cable rests on the bottom of the conduit, an analysis of this temperature drop based on simple heat transfer theory is not possible. The circumscribed diameter of the conductors can be calculated by trigonometry, and the numeric value of the multiplier is tabulated in Table 1 on page 80 of Reference 16.

The temperature rise through the insulation is calculated using Equation 39 of Refererice 13. The coefficient of 0.00522 used in this equation includes various unit conversion factors. Since the Mathcad calculation uses consistent units, the appropriate coefficient is 1. Because of the presence of 2x the other three conductors of the four conductor bundle, a geometric factor from Figure 2 of Reference 17 is used, as recommended in Reference 1. The basic arrangement of the modelis shown in Figure 4.

Calculations were performed for 3/C, #6 AWG,600V and 1/C, #8 AWG. 600 V cables in a %" conduit, a 3/C,500 MCM, SkV cable in a 4" conduit, and for 3/C, #2 AWG,5kV and 3/C,500 MCM, SkV cables in 6" conduits.

Vertical Conduits A similar approach is used for vertical conduits. The main difference is that the coefficients for convection are changed to reflect the vertical configuration. Six inch conduits containing 3/C,500 MCM, SkV cables 19 and 30 feet long are considered.

l REVISION NO.: 4 l

k Exhibit E N EP-12-02 Resision 2 1

COMMONWEALTH EDISON COMPANY i CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

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Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 15 of 141 ASSUMPTIONS Assumptions not requiring verification 1.

The increase in surface area available for convection and radiation caused by wrapping the tray will be ignored on the basis that the heat flow through the corners of the fire wrap is non-uniform. This assumption does not require validation because it provides a conservative result.

2.

A 1/16" air gap is assumed in the Darmatt system installation even though installation is expected to be consistent from the cable tray to ambient with no gaps (Reference 8). This will allow for potential installation problems and j

variations in the Darmatt thickness.

3.

There are no gaps at the corners of the Darmatt boards which would allow air flow from the cable tray. This assumption is conservative because it reduces the heat transfer from the wrapped cable tray to the surroundings and therefore does not require validation.

4.

No contact resistance between boards and cable tray is considered the boards will adhere directly to the cable tray and any contact resistance will be minimal.

5.

The heat intensity values obtained from Reference 2 assume a 24" wide tray.

The Reference also indicates that for other tray widths such as 18" and 36" results are close to those for a 24" width since about 2/3 of the heat is dissipated by radiation and since h (heat transfer coefficient for convection) is proportional to W 94 (width of tray).

6.

The thermal resistance of a vertical tray cable mass, tray assembly and Darmatt fire wrap is the same as a horizontal tray mass, tray assembly and Darmatt fire wrap of same geometric dimensions since it is a function of the material properties and thickness.

l REVISION NO.: 4 l

... ~

+

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 16 of 141 DESIGN INPUT 1.

The ambient temperature is 40'. 50', and 60'C (Reference 1); the calculation is performed for a 40' C ambient temperature. Methods for determining the ampacity deratings for other ambient temperatures are provided in the conclusion.

2.

The cable tray are 18 x 4 (includes 2" side rail) and 24 x 12 (vertical only) all dimensions are in inches (Reference 1).

3.

Depth of fill considered will be 1" (Reference 1) 4.

The allowable heat intensity is 6.7 (W/ft-in2) for a 1" depth of fill (Reference 2 page 25) 5.

A tightly covered cable tray requires a 15% ampacity derating (Reference 3 Table III) i 6.

The emissivity of a galvanized, iron, bright surface is.23 (Reference 7, page I

4-111) i 7.

The emissivity of Darmatt surface is.7 (Reference 8) 8.

The rated conductor temperature is 90 C (Reference 9 page 3 section 3.2) 9.

The thermal conductivity of air is.0158 Btu /hr ft *F at 104 'F linearly interpolated from data in Reference 7 page 4 94 10.

The thermal conductivity of the Darmatt materialis 0.783 Btu in/hr-ft2 *F or O.0653 Btu /hr ft *F @ 156'F mean (Reference 8) 11.

The Darmatt firewrap material has the following total thickness' including tolerance for the 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months and 3 hour3.472222e-5 days 8.333333e-4 hours 4.960317e-6 weeks 1.1415e-6 months barrier, respectively: 1.25", 2.61" (Reference 8). For conduit the thickness is 1.25" and 3.00" for a 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months and 3 hour3.472222e-5 days 8.333333e-4 hours 4.960317e-6 weeks 1.1415e-6 months barrier respectively.

12.

The Stephan Boltzman constant is equal to 0.1713x10-s Btu /hr ft *R4 2

or i

5.67x10-8 W m 2 K d (Reference 7, page 4108).

13.

The verticallength of a wrapped cable tray is 19 ft. These values are used to determine the relative derating due to vertical cable risers compared to horizontal trays. The ampacity derating factor for vertical trays will be qualified by this length.

l REVISION NO.: 4 l

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Exhit'it E N EP-12-02 i

Revision 2 COMMONWEALTH EDISON COMPANY 1

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CALCULATION NO,. G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 17 of 141 14.

Thermal resistivity of the cable insulation, jacket, and overall jacket is 500

C-cm/ Watt, (Reference 9 Table 1 & 2).

15.

The thermal resistivity of a steel conduit wall is 2.08 oC-cm/ Watt (Reference l

9 Table 2) 16.

Parameters of the selected cables are identified below (Reference 12. Table C) These cables were selected to provide a representative sample of cable I

installations to provide a relative value of derating of cable in wrapped conduit to cable in wrapped cable trays.

Cable Cable Overall 1/C Insul.

Jacket Overall Descr.

Sl#

OD OD Thick.

Thick.

Jacket 1

i 1/C-8 363E38

.34

.045 n/a

.03 3/C-6 363F17

.87

.33

.06 n/a

.06 3/C 2 363D35 1.90

.632

.14

.03

.08 363D38 3.34 1.193

.14

.05

.14 500 kcm

)

Note: All dimensions are in inches where 1 mil =.001 inch j

i 1

17.

Conduit sizes used to perform this review are 3/4",4" and 6" Two sizes were j

l selected (3/4"and 6") to bound the relative affect of conduit diameter (Reference 1).

18.

Conduit outside diameter is 1.05",4.5"and 6.625" for a 3/4". 4"and 6" conduit respectively (Reference 11).

19.

Conduit wall thickness is.107",.335" and.266" for 3/4", 4" and 6" conduit respectively (Reference 11).

20.

The characteristics of Air are as follows (Reference 2, Table A 5):

l REVISION NO.: 4 l

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Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 18 of 141 Temperature (K)

Thermal Kinematic Viscosity.

Prandtl Number.

(m tri)

Pr Conductivity, k 2

(W mi K 1) 300 0.02624 16.84 10-8 0.708 350 0.03003 20.76 10-8 0.697 400 0.03365 25.90 104 0.689 450 0.03707 31.71 106 0.683 21.

The diameters of Class B copper conductors used in insulated cables are as follows (Reference 18):

Conductor Size Diameter (in)

8 AWG 0.146

6 AWG 0.184

2 AWG 0.292 500 MCM 0.813 22.

The resistance of Class B copper conductors is a follows (Reference 19):

Conductor Size Conductor Resistance (ohm per 100')

8 AWG 0.0818

6 AWG 0.0513

2 AWG 0.0203 500 MCM 0.00254 23.

The grouping factor given by Reference 17 is as follows:

l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 19 of 141

}

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Asene Q' Fig. 3-Geometric factors for eingle-conductor cable and multi conductor belted cable with round or sector conductors Geovnetric factors can be obtained by calestating the ratsas (T + O/d and 1/T (# bems denned for sector cables as the daameter of a round conductor of the same area as the sector), and thee read.ng the required value el geometne factor from a curve almve. The value thus obtaaned will be the correct geometric factor for a round conductor cable. For sector con-ductors the values ao obtained shouki be mulupbed by the sector correctmn factor. In cables of the non-type H form without behs.

I ru......

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-. _. - -. _ _ ~ ~. -. -...

-. - -.. _ -. - ~.

... ~... -

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050 051 109135-200 20 of 141 REFERENCES 1.

Byron NDIT No. BYR 94 029 approved July 1994 (Attachment 1) 2.

La Salle calculation 4266-EAD-13. Rev. O titled " Cable Tray Heat Intensity" transmitted via S & L EDIT BB-EXT-0836 dated July 21,1994 (Attachment j

2) 3.

Tests at Braidwood Station on the effects of fire stops on the ampacity rating of power cables, Proceedings of the American Power Conference.1982. by Haddad, Bloethe, Lamken, Stolt, Sykora (Attachment 3) 4.

Fundamentals of Heat and Afass Transfer,2nd Edition, J. Wiley and Sons. F.

l Incropera and D. DeWitt 5.

Heat Transfer, J. Holman, McGraw Hill Book Company,1968 (Attachment'4) 6.

Heat Transfer Data Book, D. Kaminsky, General Electric Co,1977 (Attachment 5) 7.

Standard Handbook for Mechanical Engineers. Baumeister and Marks, 7th Edition 8.

Darmatt Material Specification Sheets transmittal from Transco. Letter date July 27,1994 (Attachment 6) t 9.

Sargent & Lundy Electrical Standard, ESA 105, Rev. 8-4-86.

l 10.

Sargent & Lundy Calculation for LaSalle Station 4266/19G52 Rev. O.

1 11.

Allied galvanized rigid conduit specifications, NEIS-CAT-205, CAT NO:

)

i ATC L-1127 3, Rev.1/92.

l 12.

Electrical Installation Standard, EIS N EM-0035 Table C, Rev. 5.

}

~

13:

Neher, J. H. and Mc Grath, M. H.1957. The Calculation of the Temperature j

Rise and Load Capability of Cable Systems. AIEE Transactions, Part III

{

Power Apparatus and Systems 76 (October): 752-772.

l 1

14.

Holman. J. P.1981. Heat Transfer. (5th Edition,4th printing,1983) New j

l York and Tokyo: McGraw-Hill Kogakusha Ltd.

[

i l REVISION NO.: 4 l

i

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 21 of 141 15.

Mathsoft, Inc.1993. Mathcad 4.0 User's Guide. Cambridge, Massachusetts:

Mathsoft, Inc.

16.

Horton, H. L.; Schubert, P. B.: and Garratt. G. (ed.) 1973. Machinery's Handbook (19th Edition). New York: Indus, trial Press, Inc.

17.

Simmons, D. M.1932. Calculation of the Electrical Problems of Underground Cables. The Electric Journal. (May-November).

18.

ASTM Standard B8-1981, Standard Specification for Concentric-Lay.

Stranded Copper Conductors, Hard, Medium-Hard, or Soft 19.

Sargent & Lundy ESA 102, " Electrical Engineering Standard for Electrical and Physical Characteristics of Class B Electrical Cables", dated April 14.

1993.

l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

0905G-051/ 09135-200 22 of 141 CALCULATIONS Case 2 CW-'% of 09 Ammi$r Deratina For a 18" x 4" Cable Trav With 1" Death of Fill and a 1 Hour Firewrap A. Allowable heat generation calculation Eauivalent Cable Area For a 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months fire bamer dofa1 The depth of fig in inches (reference 1, Attachment 1) w = 18 Wxith of cable tray in inches (reference 1, Attachment 1) h=4 Height cable tray in inches (Ref.1 Attachment 1)

Acq =

dofw Acq = 14.137 Equivalent cable area in the bottom of the cable tray in square inches Allowable heat aeneration for an uncovered trav (Fiaure 1) 2 III = 6.7 The aNowable heat intensity in watts /ft-in QUCW = IU (Aeq)

The ellowable heat in watts /ft for an uncovered cable tray QUCW = 94.719 QUCB .29;9 The anowable heat in Stu/hr-ft for an uncovered cable tray QUCB = 323.383 Allowable heat aeneration for tiahly covered cable trays (Fioure 2)

QCB = (1.15)2-QUCB AHowable heat for a tightly covered cable tray in QCB = 233.645 l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 23 of 141 i

B. Temperature of ttu outside of a cable tray with tight covers i

Radiation Formula AT = f1 -(h + w) 2 Area in ft /ft, this includes 2. mes the sum of the heigth and width (for

\\12/

top, bottom and both sides) tmes i ft unit length AT = 3 667 Total Radiating area per linear ft o =.171310.s Stephan Boltzmann Constant in Btu /hr-ft -R4 2

cOS =.23 Emissmty of a galvanized steel surface (Ref. 7 page 4-111)

The ambient temperature in degrees C (Ref.1)

The ambient temperature in degrees Rankine TAR = (TAC + 273) 9 5

TAR = 563.4

~

TOS = 610 Guess Cable tray surface temperature in degrees Rankine.

QROS(TGS) = a CGS AT f(TGS)# - TAR ) Radiation heat transfer from the galvanized steel 4

surface of the cable tray in Stu/hr-ft.

Convection Formula (s)

Sides (2 total) hsGS(TGS) =.29-

~

AS = 2 I AS = 0.667

* * * 'I " ' " ' ' '

2 12 foot of tray in ft fft, m e es ans er kom me es oN @

QCSGS(TGS) = hsGS(TOS) AS-(TGS - TAR) tray in Btu /hr-ft l REVISION NO.: 4 l

i Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY cal.CULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 24 of 141 f

htGS(TOS) =.27-

~ ^

ff\\

\\12/

ATS= 1 ATS =1.5 Area of the top of cable tray in square ft/ft 12 QCTOS(TOS) = htGS(TGS) ATS-(TOS - TAR)

Convective heat transfer from the top of the cable tray Bottom Convective heat transfer coefficient for the bottom of the hbOS(TGS)

.12 TOS - TAR.25 cable tray in Btu /hr-ft -degree F 2

AB = E AB = 1.5 Area of bottom of the cable tray in square ft/ft 12 QCBGS(TGS) = hbOS(TOS). AB-(TOS - TAR) g, Total Heat Transfer QTGS(TGS) = QRGS(TGS) + QCSGS(TOS) + QCTOS(TGS) + QCBGS(TOS)

TGS = root (QTOS(TGS)- QCB.TGS)

TOS =630.623 Re ** of the convective. radiabon and total heat transferred Total heat transferred, QTGS, equals the allowable heat generation of a covered tray, QCB, therefore a solubon for TGS is obtained Q[GS(TGS) = 233.644QRGS(TGS) = 82.919 QCSGS(TOS) = 48.976 QCTGS(TGS) = 70.441 QCBOS(TGS) = 31.307 QCB = 233.645 l REVISION NO.: 4 l

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Exhibit E N EP-12-02 Revision 2 COWNONWEALTH EDISON COMPANY CALCUI.ATION NO. : G-O PROJECT NO.

PAGE NO.

09050-051109135-200 25 of 141 C. Thermal resistance of tN cable mass and cable tray assembly up to the surface of the cable tray.

TCC = 90 Rated conductor temperature in degrees centigrade (Ref. 9)

TCR = (TCC + 273) 9Rated conductor temperature in degrees Rankine 5

TCR =653.4 RCM =

~

Resistance of the cable mass in CF-br-ft/Bru QCB RCM = 0.097 D. Thermal resistance of the Darmatt firewrap material covermg the bottom, top and both sides of the tray (Figure 3) tdarl = 1.25 thickness of Darmatt in inches for a 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months banier (Ref. 8 Att. 6).

tair =.0625 thickness of air gap, in inches, between Darmatt and cable tray per assumption 2.

2 kdar =.0653

[(.783 Stu-in/hr-ft.oF)/12 in/ft] conductMty of Darmatt in Btu /hr-ft 0F Input 10 kair.0158 conductivity of air at 104 F in Stu/hr-ft oF Input 9 kdar x=-

x = 4.133 equivalent thickness of Darmatt for 1/16" air, multiplier katr ttot! = tdari + (x tair) ttot! = 1.508 Equivalent thickness of Darmatt in inches el=h el =4 bil = ttott b21 = ttotl b31 = ttotl b41 = ttotl e2 = w d = 18 b11 = 1.508 b21 = 1.508 b31 = 1.508 b41 = 1.508 1

Rcompt =

+.54 +

+.54 Rcompt =0.489 Thermal resistance of 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months banier wrapped tray in F-hr-ft/ Btu o

l REVISION NO.: 4 I

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 26 of 141 E. Total equivalent resistance of the cable mass and cable wrap RTOTl = RCM + Rcompi in f-br-ft/Stu o

RTOTl =0.586 F. Calculation of total heat transfer due to radiation and convection Total heat transfered from the wrapped cable tray TWT - 601 guess Surface temperature of a wrapped tray OR Fast guess in the iteration of the total heat transferred equations listed below.

Radiation heat tranfer formula EA

.7 Emissivity of the Darmatt fire wrap (Ref. 8 Attachment 6)

QR%T(T%T) = a cA AT-((TWT)# - TAR *)

Radiation heat transfer from the wrapped surface of the cable tray in Btu /hr-ft.

Qorvctive Heat Transfer Sides of Wracoed Trav hs%7(TWT) =.29

~

QCSWT(TWT) = hsWT(T%T) AS-((T%7)- TAR)

Convective heat transfer from the sides of the wrapped cable troy in Btultr-ft Too of Wracoed Trav htWT(TWT) =.27 QCTWT(TWT) = htWT(T%T) ATS-(1WT-TAR)

Convective heat transfer from the top of the wrapped cable tray in Btu /hr-ft l REVISION NO.: 4 l

P Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO, : G-63 PROJECT NO.

PAGE NO.

09050-051/ 09135-200 27 of 141 l

Bottom of Wrapped Trav hbwT(TWT) =.12

~

(i),

QCBWT(T%T) = hbWT(T%T) AB (TWT - TAR) wrapped cable tray en Btu /hr-ft Total Heat Transfer Total heat transfer from the unwrapped cable tray in Btu /hr-ft QTWT(T%T) = QR%T(TWT) + QCSWT(TWT) + QCT%T(TWT) + QCB%T(T%T)

TCCR(TWT) = T%T + QT%T(TWT) RTOTI Calculated maximum temperature of the conductor OR, the equations will be iterated until TCCR converges on TCR Rated conductor temperature 900C TCR = 653.4 TWT 3 root (TCCR(TWT)- TCR,T%T)

This solves the iteration problem where the calculated rated conductor temperature minus the rated conductor temperature is equal to zero.

TCCR(TWT) = 653.4 ace tempaue ome waW TWT a 586.123 tray QTWT(T%T) = 114.757 Total heat transferred G. Ampacity Factor

(

AF =

AF =0.5% Ampacity factor for Darmatt firewrap material QUCD 3

l REVISION NO.: 4 l

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 28 of 141 H. Ampacity Derating Factor Ampacity derate factor = 1 - Amapetty Factor (AF)

ADF = 1 - AF ADF = 0 404 P

t

[ REVISION NO.: 4 l

i

l l

l I

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Exhibit E NEP-12-02 j

Revision 2 COMMONWEALTH EDISON COMPANY 1

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 29 of 141 Case 26 Calculation of Cable Ameacity Deratina For a 12" x 24" Vertical Cable Trav With 1" Death of Fil8 and a 1 Hour Firewrao The calculation of the equivalent thermal resistance of the cable mass, RCM, will be calculated for a 12" x 24" honzontal l

tray. This resstance will then be used to caculate the total equivalent thermal resistance of vertical cable tray of length L.

L = 19 Length of vertical cable tray in ft l

A. Allowable heat generation calculation l

EauivalentCable Ares l

For a 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months fire barrier dof = 1 The depth of fliin inches (reference 1, Attachment 1) w = 24 Width of cable tray in inches (reference 1, Attachment 1) i h = 12 Height cable tray in inches (Ref.1 Attachment 1)

Acq =

dof w Acq = 18.85 Equivalent cable area in the bottom of the cable tray in square inches ARowable heat oeneration for an uncovered trav (Fioure il 2

ill a 6.7 The allowable heat intensity in watts /ft-in QUCW = 111(Acq)

The allowable heat in watts /ft for an uncovered cable tray l

QUCW = 126.292 QUCB =

The allowable heat in Btu /hr-ft for an uncovered cable tray

.2929 QUCB = 431.178 Allowable heat aeneration for a tichtly covered cable trav (Fiaure 21 j

l QCB = (I.15)2-QUCB Allowable heat for a tightly covered cable tray in Stu/hr-ft QCB = 311.576 i

l REVISION NO.: 4 l

l Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 I09135 200 30 of 141 B. Temperature of the outside of a cable tray with tight covers Radiation Formula 2)

[I2[I*

2 Area in ft /ft, this includes 2 times the sum of the heigth and width (for

^

I

(

top, bottom and both sides) times 1 ft unit length AT = 6 Total Radiating area per linear ft

)

o =.171310' 8 Stephan Boltzmann Constant in Btu /hr-ft -R4 2

rGS =.23 Emisamty of a galvanized steel surface (Ref. 7 pg. 4-111)

TAR = 563.4 The ambient temperature in degrees Rankine TGS = 600 The value of galvanized steel surface temperature, TGS.

QRGS(TGS) = c EGS-AT f(TGS)*.- TAR *) su*rface of the cable tray. Stu/hr-ft.

in i

Convection Formula (s)

Sides (2 total) hsGS(TGS) 29 TGS - TAR

.25 ht l

-12/

The total area of two sides of the cable tray for 1 linear AS'=2I AS== 2 2

12 foot of tray in ft /ft.

Conve at transfer from the sides of the cable QCSGS(TGS) = hsGS(TOS) AS-(TGS - TAR) g l

i i

l REVISION NO.: 4 l

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Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY i

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135 200 31 of 141 IDE From table 7-4 of Ref. 5 the conv'ective heat transfer coefficient for a heated plate facing upward is h=27(AT/L).25. This equation bill apply to the top of the cable tray :vith L equal to w/12.

htGS(TGS) =.27

~

ATS = *-

ATS = 2 Area of the top of cable tray in square ft/ft 12 QCTGS(TGS) = htGS(TGS) ATS-(TGS - TAR)

Bottom From table 7-4 of Ref. 5 the convective heat transfer coefficient for a heated plate facing downward is h=.12(AT/L) 25. This equation will apply to the bottom of the cable tray with L equal i

to w/12 feet.

Convective heat transfer coefficient for the bottom of the hbOS(TGS),.12 TOS - TAR '.25 2

cable tray in Stu/hr-ft -degree F W\\

\\I2/

4 i

AB =

AB = 2 Area of bottom of the cable tray in square ft/ft j

Convective heat transfer from the bottom of the cable QCBGS(TOS) = hbGS(TGS) AB (TOS - TAR) tray n Btu /hr-ft Total Heat Transfer QTGS(TGS) = QRGS(TGS) + QCSGS(TGS) + QCTGS(TGS) + QCBOS(TGS)

TOS = roc 4(QTOS(TGS)- QCB,TGS)

TGS =621.311 l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 32 of 141 l

Results of the convective. radiation and total heat transferred Total heat transferred, QTGS, equals the allowable heat generation of a covered tray, QCB, therefore a solution for TGS is obtained.

l QTGS(TGS) = 311.526 QRGS(TGS) = 114.088 QCSGS(TGS) = 92.657 QCTGS(TGS) = 72.541 QCBGS(TGS) = 32.241 QCB = 311.526 C. Thermal resistance of the cable mass and cable tray assembly up to the surface of the cable tray.

TCC = 90 Rated conductor temperature in degrees centigrade (Ref. 9)

(TCC + 273) ! Rated conductor temperature in degrees Rankine TCR4 5

TCR =653.4 This value represent the thermal rbtance, o F-hr-ft/ Btu, from cable mass to surface of RCM = TCR - TGS cable tray includmg air space and tray for a horizontal tray. This resistance will be QCB appied to a vertical tray (assumption 1) of length L RCM =0.103 D. Thermal resistance of the Darmatt firewrap material covering the bottom, top and both sides of the tray (Figure 3) tdarl = 1.25 thickrms of Darmatt in inches for a 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months barrier (Ref. 8 Att. 6).

tair 0625 thickness of air gap, in inches, between Darmatt and cable tray per assumption 2.

(.733 Btu-in/hr-ft AF)/12 in/ft conductivity of Darmatt in Stu/hr ft "F Input 2

kdar =.0653 10 kair 0158 conductivtty of air at 104 F in Blu/hr-ft DF Input 9 x=

x = 4.133 equivalent thicknca of Darmatt for 1/16" air, multiplier kair ttott 4 tdarl + (x tair) ttot! = 1.508 Equivalent thickness of Darmatt in inches

] REVISION NO.: 4 l

l Exhibit E N EP-12-02 l

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

j 09050-051109135-200 33 of 141 l

el = h el = 12

)

bli = tiott b21 = ttott b31 = tiotl b41 = ttott c2 = w c2 = 24 blI =1.508 b21 =1.508 b31 = 1.508 b4i = 1.508 i

1 kdar Roompi =

e2 el c2 +.54 l + el +.54 +

+.54

+.54 +

Rcompt =0.307 Thermal resistance of 1 hour1.157407e-5 days 2.777778e-4 hours 1.653439e-6 weeks 3.805e-7 months barrier wrapped tray in F-hr-ft/ Btu o

E. Total equivalent resistance of the cable mass and cable wrap for a tray of length L

E RTOTl.=

RTOTl =0.022 in 0F-hr/ Btu L

F. Calculation of total heat transfer due to radiation and convection of a vertical cable tray of length L Total heat transfered from the wraoned cable tray i

TWT lterated value of the surface temperature of the wrapped cable tray. This value is iterated until the calculated rated conductor temperature of the cable mass, TCCR, equals the rated conductor temperature, TCR.

l TWT = 586 guess Surface temperature of a wrapped tray OR Radiation heat transfer formula The radiation heat transfer equation used in section B of this calculation is used again here AR = 2 *

L The radiating area of the wrapped vertical cable tray of length L in 12 squareft cA 7 Emisemty of the Dermatt fire wrap (Ref. 8 Attachment 6)

QRWT(TWT) = o-cA ARI(M'T)# - TAR')

Radiation heat transfer from the wrapped surface of the cable tray in Stu/hr.

i l

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09050-051 109135 200 34 of 141 Convective Heat Transfer Vertical Surfaces of Wrapped Trav hs%T(TWT) =.29-

\\

L

]

Convective heat transfer from the vertical surfaces of QCS%T(TWT) : hsWT(twt)- AR-((T%T) - TAR) the wrapped vertical cable tray in Stu/hr Total Heat Transfer QTWT(T%T) = QRWT(TWT) + QCSWT(TWT)

TCCR(TWT) = T%T + QTWT(TWT) RTOTl Calculated maximum temperature of the conductor OR, the equations will be iterated until TCCR converges on TCR TCR = 653.4 Rated conductor temperature 90 CC TWT = tmt(TCCR(TWT)- TCR, TWT)

This solves the iteration problem where the calculated rated conductor temperature mnus the rated conductor temperature is equal to zero.

TCCR(T%T) = 653.4 T%T = 585.986 Surface temperature of the wrapped tray Total heat transferred in Btu /hr 3

QTWT(TWT) = 3.125 10 G. Ampacity Factor Ampacity factor for Darmatt firewrap material, the all weble heat of an uncovered cable tray, QUCB,

!QTWT(TW'T) must be multiphed by L because it was calculated in AF = 0.618 AF = d QUCB L section A per unit length

~

l REVISION NO.: 4 l

I Exhibit E NEP-12-02 Revision 2 l

COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 35 of 141 l

l l

H. Ampacity Derating Factor ADF = 1 - AF ADF = 0.382 1

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09050-051 109135-200 36 of 141 I

Case 37-Model for a Wrapped Conduit-3/C, #6 AWG,600 V Cable in a 3/4" Conduit l

Cable Data Cable is 3/C, #6 AWG,600V Conductor Resistance and Diameter cab ' O.051310-2 onmfr Conductor resistance at 90 *C I

r dcab = 0.184 in Conductor diameter tinsd 10.06-in Insulabon thickness t jacket = 0.00 in individualJacket thickness i

t jacket = 0.06 in Overau Jacket thickness o

d cab = 0.87 in Overed diameter of the cable o

Thermal Resstubes p insW = 5 K m watt'I insulation jacket = S K m watt individualjacket p

ojacket = 5 K m watt ' Overau Jacket p

Conduit Data inner and Outer Diameters, Thermal Conductmty, and Emissivity dcondi = 1.05 in - 2 0.107 in inside diameter of a 3/4" trade size conduit dg =0 836 in da = 1.05 in Outside diameter of a 3/4" trade size conduit g = 2.08 K cm watt' 3 Conduit thermal conductivity p

E g = 0.23 Conduit emissuty Darmatt Data Thermal Conductivity

= 0.783 BRJ in-br^ I 2

fr R'I k wrap E,p = 0 7 l REVISION NO.: 4 I

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Revision 2 COMMONWEALTH EDISON COMPANY i

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PAGE NO.

09050-051 109135-200 37 of 141 Thicknesses of Fire Wrap Outer Layer tTho = 3.00 in inner Layer t w = 0.000001 in Enter an infinitessimal value since there is only one layer Gap Thicknesses Gap between Conduit and inner Fire Wrap Layer B inner =

in Gap between the Two Fire Wrap Layers l

g outer = 0.000001 in Set to an infinitessimal value since there is only one layer of wrap Test Parameters l

Test Current I =45.89 amp Aminent Temperature l

l Converson factor between deyees Celsius and Kelvin CtoK = 273.16 K Tamb = 40.0 K +- CtoK Tamb =313.16 K j

Macellaneous Constants i

Stefan-Boltzmann Constant a = 5.6710^ 8 watt m g

-2 4

Acceleration due to pavity l

g = 9.8-m-sec 2 l

l l

I I REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2

' COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 38 of 141 Develop interpolation Functions for the Characteristics of Air which are Functions of Temperature. These parameters are required for the calculation of heat transfer by conduction and convection in air gaps.

Thermal conductuty of air 300 0.02624 watt m' ' K '

T K

k

=

arg 400 arg 0.03365 temperature and thermal conductmty

450, 0.03707 (Table A-5 of Ref.14) i = 0. 3 0.04 g

o.035 Since the variation of the conductivity with k

temperature is nearly linear, the use of us n,g3 linear interpolation is appropriate.

/

300 350 400 450 T,gi f

T, + T \\

Function to find the thermal conductivity of b

k,,(T,,T ) = linterp(Targ,karg*

2

/

air by linear interpolation of the average of b

two temperatures l REVISION NO.: 4 I

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Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

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09050-051 / 09135-200 39 of 141 Interpolate to calculate the kinematic vescoasty of air 16 M 10~'I Lookup table for kinematic viscosity. The 20.76 10 6 temperatures for these points were defined m,,,, I with the thermal conductivity of air (Table A-5 2

v T

25.9 10 '

of Reference 14) 31.71 10

-5 4 10 Plot shows that the kinematic 3'30

"" [/

viscosity is not a linear function of

' arsi temperature. Therefore, the use of

_/-

cubic spline interpolation is appropriate.

-5

- 2 10

-5 t

t 3 30 300 350 400 450

= cspime(Targ Vag Auxiliary vector for cubic sphne interpolation i

v aux Perform cubic sphne interpolation T,+Th n

b for kinematic vscosety

/

v ir(T,,T ) = interp v,,,Targ Varg*

2

)

2 (T,,T ) =

Volume coefficient of expansion (assuming air b

T,+Tb behaves as an ideal gas) i l

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PAGE NO.

09050 051 /09135-200 40 of 141 Prandtl Number 0'708,

Data points for lookup table. The correeponding temperature values are shown in the section on the thermal conductivity of air.

0.697 (Table A-5 of Reference 14)

W "'E

=

0.689

,0.683,

0.71 i

N "7

N

~

Since the Prandtl number is a non-knear argi function of temperature, cubic spline

~~

interpolation will be used.

o.69

\\

300 350 450 T,,,

Pr

= csplinc(Targ,Prarg) Aumliary vector for cubic spline interpolation aux Interpolation function using cubic f

T,+Tb Pr ir(T,,T ) = interp Praux,Targ Prarg.

2 a

b splines for the Prandtl number l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 41 of 141 Outer Diameter of Wrapped Conduit d 33em dcondo 2 (t g 4 g og 4 t g i g inner) 4 d,33,, = 7175 in Heat Generated by Cables 3

Q cab = 3 I rcab 9 cab = 3.241. watt if Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be wrtten as funcbons of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Dissipated by Radiabon Q r(T) = x dassem% rape

-Tamb Heat Dissipated by Convecton 1

amb} d 5

1, _,

Q c(T) = 1.32 watt K " m.2,4 assem (T - Tamb) x

\\ assem )

l REVISION NO.: 4 l

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1 Exhibit E NEP-12-02 Revision 2 l

l COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 42 of 141 Initial guess for iterative solution of the surface temperature of the wrapped conduit T

= 330 K guess Given Q cab"Q r(Tguess) + Q c(Tgues,)

Heat dissipated by radiation and convection must equal heat generated by cables.

l T

Find (Tguess) outer I

Touter = 315.646 *K Touter - CtoK = 42 486 K 'C Surface temperature of the I

wrapped conduit

)

Temperature Drop Across the Outer Fire Wrap Layer dgno=dcondo + 2.(tThi + Binner + 8 outer) inside diameter oflayer d gg = 1.175 in (d

Where Qcab s in watts per foot

[

i g

g assm In

-Q cab AT h 2.x k,3 p (d th ATg = 27.114 K Temperature drop through the outer fire wrap Layer Temperature on the inside of the Outer Fire Wrap Layer Tlh = Touter + ATg TITho = 342.759 K Tlh - 273.16 K =69.599 K

'C Grashof Number g S(T,,T )-(T,- T ).(d2-d)3 Grashof number for a d

b g

Gr(T,,T,d,d ) =

cylindrical space b i2 g(T,,T)

(Equation 7-21 of v

b Reference 14) The Grashof numberis a major parameter in determining convection.

I l REVISION NO.: 4 l

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PAGE NO.

09050-051 /09135-200 43 of 141 Heat Transferred across an Air Gap Heat Transfer by Conduction Function for heat transferred air (T,,T ) (T,- T )

2xk b

Q cond(T,,T,d,d ) '*

b by conduction across a g

b 2

fd I cylindrical shell(Equation 2

I".

2-8 of Reference 14)

Adjustment of the Heat Transferred by Conduction to Account for Any Convection The IF function is used to force the minimum value of the adjustment to be 1.

(Conduction and convection can't be worse than conduction alone.) The convection correlation is given in Equation 7-60 and Table 7-3 of Reference 2.

j 1'd ) = 011-(Gr(T,,T 'd 'd ) Pr ir(T,,T ))

krauo(T,,T 'd 2

b 1 2 a

b b

ratio (T,,T,d,d )=I) ratio (T,T,d,d )>I,k kfunc(T,,T,d g,d ) = if(k b 3 2 b

2 b 3 2 Q conv(T,,T,d,d )

Q cond(T,,T,d,d ) kfunc(T,,T,d j,d )

g b 3 2 g

b 3 2 b

2 l REVISION NO.: 4 l

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Exhibit E N EP-12-02 Resision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135 200 44 of 141 Heat Transferred by Radiation Heat transfer by radiation between concentric p

3 (T,, - Tb/

cylinders. Since the heat oxd Q rad (T,.T,d,d2,E y,E g) =

I_. _..,

g b i 1

transferred per Unit length

}

is desired, circumference d

is area per unit length. See ej 2(E7 j

Equation 8-43 of Reference 14.

Heat Transferred across the Air Gap between the Fire Wrap Layers don;=dcondo + 2-(tTid 4 g

) Outside diameter of the inner layer of fire wrap dOni = 1.175 ain Find the temperature of the outside of the inner fire wrap layer Tgua,ss) = 350 K Initial value for iterative solubon.

Given Heat transferred across the gap equals heat generated by cables.

ITho,d ni,d gno).

Conduction / convection l

0 cab"O cony (Tguess!,T O

s guessI.T g,d ogi,djgo cwrap Ewrap)

+Q rad (T Radiation i

g i

Toni = Find (T

,g) g i

-5 Temperature drop T ni - TITho = 9.771 10 k,

TOni = 342 "'6 m,.

O across gap (neglegible since there is no gap)

Review the relative contribution of the various mechanisms to heat transfer I

Q cond(TOThi,TITho,dOThi,dih) = 3.241 watt ff Heat transferred by cenduction s

Oui,d g) Pr,;,(TOThi,TITho) =0 Grashof number Gr(T ogi,TITho,d i

kratio(T ogi,T17ho,dOThi,d ;g) = 5.805 10 Raw multiplier for convection value indicates no convection I

Qconv(TOni TITho,dOThi,dIh) =3.241 watt ff Conduchon / Conve: tion g

I Q rad (T ni,Tgg,dOThi,dITho'Ewup'Ewnp) = 1.313 10

wart if Radiation g

O l REVISION NO.: 4 I

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Exhibit E NEP-12-02 I

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I 09050-051/09135-200 45 of 141 Temperature Drop through Sie inner Fire Wrap Layer d g3g; = dcondo + 2 g inner inside diameter of the inner fire wrap layer d11hi = 1.175 ir, Id I

OThi i

1 Thi

2.x k,,'I" d

Qcab Temperature drop (Equation 2-8 of AT

( IThi)

Reference 14)

ATThi = 2.551 10 K

Temperature of the inner surface of the inrier fire wrap layer T nhi = TOThi + AT1hi T nhi = 342.76 K i

Temperature at the Outer Surface of the Conduit T

= 375 K Initial value for iterative soluition guess Given The amount of heat trans-Qc'ab"Q conv(Tguess,TIThi,dcondo,dIThi) '

ferred across the air gap g

+Q rad (Tguess,TIThi,dcondo,d Rhi,Econd,Eunp) between the conduit and the g

inner layer of fire wrap must equalthe amount of heat Tcondo = Fmd(Tguess) generated by the cables.

Tcondo =348.586 K Temperature of the outer surface of the conduit Tcondo - TIThi = 5.826 K l REVISION NO.: 4 l

1 Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 46 of 141 Review the breakdown of how the heat was transferred I

condo,d g;) = 2.946 watt if Conduction Q cond(Tcondo,Tgni,d g

g Gr(Tcondo,TIThi,dcondo,d IThi) Pr ir(Tcondo,TIThi) = 8.895 Grashof number a

kratio(Tcondo,T gg;,dcondo,d gg;) = 0.207 Raw convection multiplier; value indicates no convection I

Q conv(Tcondo,T gni,dcondo,d gg;) = 2.946 watt fr Heat transferred by convection g

Q rad (Tcondo,Tgni,dcondo,dgg;,e g,ewrap) = 0.295 watt ff ' Heat transferred by radiation g

Temperature Drop through the Conduit Idcondo\\

g cond

2 x Pcond'I"'

I'Qcab See Equation 2-8 of Reference 14 AT (dcondi/

i ATcond =0.008 K j

Tcondi = Tcondo + ATg T g =348.594 K Temperature of the inside wall of the conduit Temperature Drop through the Air Gap inside the Conduit Diameter of a Single Cable d Icab = dcab + 2-(tinsul+8 jacket) i d Icab =0.304 in Circumscribed Diameter of Three Cables

!1+ 2 \\d d3 cab *i Icab i

d3 cab =0.655 in l REVISION NO.: 4 l

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CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 47 of 141 Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap

-I A' - 3.2 K ft watt in B' = 0.19 in A*

ca@ee @uah M omeference u AT condpp B' + d over_ cab ATcondpp " 9 784'K Temperature at the outside surface of the cable' Tjacket = Tcondi + ATcondgap Tjacket = 358 378 K Tjacket - 273.16 K = 85.218 K ('C)

Temperature Drop through the Overau Jacket p ojacket k-(

d cab o

ATojecket

Q cab' i s over_ cab - 2.t jecket).

d 28 o

AT

=1.256 K ojacket l

Toinsul = Tjacket + AT jacket Toinsul - CtoK = 86.474 K (*C) o Geometric Factor for Three Cables Ratio (t+T)/d

. insul + t jacket I

i insul,

dcab Rati insul = 0.326 0 3 = 1.25 This value is obtained by looking it up on the curve in Reference 17 Temperature Rise through the Cable insulation and Jacket Qcab ATinsul '

P nsul'G 1

= 1.08 watt 11'I i

3 ATinsul = 3.526 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductor = Toinsul + ATinsul Conductor temperature l

Tconductor= 363.159 K Tconductor-273.16 K = 89.999 K

'C In45.89 amp l REVISION NO.: 4 l

l 1

l' Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 48 of 141 Calculate the Free Air Ampacity of the Cable Test value of free air ampacity Ihee =60.7 amp l

Heat Generated by Cables I

Q w 3Igee*r Q ee = 5.67 watt if cab Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equabons for the heat desapated by the wrapped assembly wid be written as funcbons of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Dissipated by Radiaton

[

Q rcond(D = x dcondgE go-(T" - Tamb )

Heat Dissipated by Convection I.

t 3

I

/

id m

,4, T - T 2

amb d

xdcondd (T - Tamb)

Q c_cond(D = 1.32 watt K (dcondoj initial guess for iterative solubon of the surface temperature of the wrapped conduit Tp.,, = 330 K Given Q ee"Q reand(Tguess)'Qccond(Tguess) Heat dissipated by radiation and convection h

must equal heat generated by cables.

Touterf = Find (Tguess)

Touterf = 337.65 K Touterf-CtoK = 64.49 K *C Surface temperature of the wrapped conduit l

l REVISION NO.: 4 l

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Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

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09050-051 109135-200 49 of 141 l

Temperature Drop through the Conduit (d

1 condo 'O ree See Equation 2-8 of Reference 14 AT I

condf * ~~3'P cond "i condi f

d ATcondf =0.014 K Tcondif = Touterf + ATcondf Tgf =337 665 K Temperature of the inside waf of the conduit Temperature Drop through the Air Gap inside the Condta I

A'

' Q ,

See Equation 41 A of Reference 13 l

AT condgapf

g.+d I

over_ cab j

ATcondgapf"17 II8*K f

Tjacketf = Tcondif + ATcondgapf Temperature at the outsioc surface of the cable Tjacketf = 354.783 K Tjacketf-273.16 K = 81.623 K (*C)

Temperature Drop through the Overall Jacket P ojacket dover cab AT,,p,gr = Q ree-in oj f

2x (dover _ cab-2 t jacket),

o ATojacketf =2.197 K Toinsulf = Tjacketf + AT jacketf Toinsulf-CtoK = 83.82 K ('C)

]

o Temperature Rise through the Cable Insulation and Jacket ATinsulf*

P nsul~O 1

= 1.89 watt ftd i

3

- ATinsulf =6169 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductorf = Toinsulf + ATinsulf Conductortemperaturs Tconductorf = 363.149 K Tconductorf-273.16 K = 89.989 K 'C Ifree = 60.70 amp l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 1 COMMONWEALTH EDISON COMPANY l

CALCULATION &lO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 50 of 141 4

Ampacity Fedor F

nmpeity g Fnmpcin. = 0.756 Derating Factor l

Fderating = 1 - Fampacity t

Fht4 =0.244 i

l 1

l i

I REVISION NO.: 4 I

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Exhibit E t

N E P.12-02 Revis.on 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 51 of 141 Case 42 Model for a Wrapped Conduit-3/C,500 MCM,5000 V Cable in a 6" Conduit Cable Data Cable is 3/C,500 MCM,5 kV Conductor Resistance and Diameter cab = 0 0025410 2 ohm frConductor resistance at 90 *C 3

r dcab = 0 813 in Conductor diameter tinsul = n.14 in Insulation thickness t jacket = 0.05 in Individualjacket thickness i

t jecket = 0.14 in OverallJac5t thickness o

dover _ cab ' 3.34 in Overall diameter viiiie cable Thermal Resstubes p insul = 5 K m watt' 3 Insulation jacket = 5 K.m watt'3 IndividualJacket p

P jacket = 5 K.m watt OverallJacket o

Conduit Data inner and Outer Diameters, Thermal Conductivity, and Emisemty dcondi = 6 625 in - 2 0.266 in inside diameter of a 6" trade size conduit dcondi = 6.093 *in dcondo = 6 625 in Outside diameter of a 6" trade size conduit g = 2.08 K-em watt'IConduit thermal conducrivity p

c g = 0.23 Conduit emissmty i

Darmatt Data Thermal Conductivity fr R'3 2

wrap = 0.783 BTU in hr~ 3 k

E

=0.7 wrap l REVISION NO.: 4 l

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 52 of 141 TNeknesses of Fire Wrap Outer Layer f

t g = 3.00 in inner Layer t g = 0 0(0001 in Enter an infinitessimal value since there is only one layer Gap TNcknesses Gap between Conduit and inner Fire Wrap Layer 8 inner

'in Gap between the Two Fire Wrap Layers g outer = 0.000001 in Set to an infireitessimal value since there is only one layer of wrap Test Parameters Test Current I = 341.95 amp Ambient Temperature Conversion factor between degrees Celsius and Kelvin I

CtoK = 273.16 K 1

Tnmb a 40.0 K + CtoK Tamb =313.16 K Mocellaneous Constants Stefar> Boltzmann Constant o = 5.6710' 8 watt m'* K" Acceleration due to gravity 2

g = 9.8-m-sed 1

l REVISICjlIOI4 I

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I Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 53 of 141 Develop interpolation Funcbons for the Charactenstics of Air which are Functions of Temperature. These parameters are required for the calculation of heat transfer by conduction and convection in air gaps.

Thermalconductivityof air 300 0.02624 350 0.03003 i.

Lookup tables of T

=

arg 400 arg 0.03365 temperature and thermal conductivity 450 0.03707 (Table A-5 of Ref.14) i = 0. 3 0 04 i

i 0.035 Since the variation of the conductMty with temperature is nearly linear, the use of 0.03 linear interpolation is appropriate.

0.025 300 350 400 450 ag j

T, +T \\

i d

kair(T,,T ) = 1m.terp(Targ,karg' 2

/

air by linear interpolation of the average of b

Function to find the thermal conductMty of i

two temperatures l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 CWSMONWEALTH EDISON COMPANY l

CALCULATION NO. : Ge;3 PROJECT NO.

PAGE NO.

09050-051/09135-200 54 of 141 Interpolate to calmide the kinematic viscosity of air im10 Lookup table for kinematic viscondy. The 6

temperatures for these points were defined 20.76 10 2

1 with the thermal conductivity of air (Table A-5 v

=

m see yg 25.9106 of Reference 14) 31.71 10~ '

-0 4 10 Plot shows that the kinematic 3'30 '

/

~ iscosity is not a linear function of v

art, temperature. Therefore, the use of v

- 2 10 cubic spline interpolation is appropriate.

~8 3 30'S 300 350 400 450 v,, = cspline(Tyg,yyg Auxiliary vector for cubic spline interpolation Perform cubic sphne interpolation

/

T,+T \\

b) for kinematic viscosity v,;,(T,,T ) = interp v,,,Tyg,yyg, b

2 (T,,T ) =

Volume coefficient of expansion (assuming air b

T,+Tb behaves as an ideal gas) l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 55 of 141 Prandtl Number

.708 -

Data points for lookup table. The corresponding temperature 0

values are shown in the section on the thermal conductmty of air.

0.697 (Table A-5 of Reference 14) g B 0.689 0.683 0.71 N~\\

"7

~

Since the Prandd number is a non-linear h

function of temperature, cubic spline

arg, o 69 interpolation will be used.

I I

0.68 300 350 400 450 T arg; Pr

= esphne(Targ,Prarg) Auxiliary vector for cubic spline interpolation aux Pr,i,(T,,T ) = interp(Pr Interpolation funcbon using cubic T,+Tb splines for the Prandt! number b

aux,Targ,Prarg*

2 l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO, PAGE NO.

09050-051109135-200 56 of 141 Outer Diameter of Wrapped Conduit d

=dcondo + 2-(tTho ' S ouw + tThi

S h) assem d 33, = 12.75 in Heat Generated by Cables I

Q cab

3'I cab Q cab = 8.91. watt ff Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be written as functions of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

P Heat Dissipated by Radiation o-(T' - Tamb )

Q r(T) = x dassem'Eap Heat Dissipated by Convection 1

'fT-T""fxd

)

assem (T - Tamb)

Q c(T) = 1.32 watt K m'* m -

d d

( assem /

l REVISION NO.: 4 l

I

- ~ -.

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 57 of 141 Irntief guess for iterative solubon of the surface temperature of the wrapped conduit Tguess = 330%

i Giwn Q cab"9 r(Tguess) + 0 c(Tguess)

Heat dissipated by radiation and convection must equal heat generated by cables.

Touter = Find (Tguess)

Touter = 317.032 K Touw - CtoK = 43.872 K 'C Surface temperature of the wrapped conduit Temperature Drop Across the Outer Fire Wrap Layer dth = dcondo + 2-(t g + g w + g e) Inside diameter of layer dgo =6.75 in ld l

i assem Where Q i

cab s in watts per foot AT b

h *2xk d

wrap i Th /

ATg = 26.201 K Temperature drop through the outer fire wrap Layer Temperature on the inside of the Outer Fire Wrap Layer TTh = Touter + ATh TIb = 343.233 K T mo - 273.16 K = 70.073 K

'C Grashof Number gS(T,,T )-(T,- T )-(d2-d)3 GrW numWor a b

b j

Gr(T,,T,d ;,d ) '"

yhndncal space b

2 v,;,(T,,T )2 (Equeh 7-21 of h

Reference 14) The Grashof numberis a major parameter in determining i

convection.

l REVISION NO.: 4 l

1 l

Exhibit E NEP 12-02 Revision 2 l

COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 58 of 141 Heat Transferred across an Air Gap Heat Transfer by Conduction Funcbon for heat transferred air (T,,T ) (T,- T )

2xk b

by conduction across a Q eond(T,T,d,d )

b g

b 3 2 fd I cylindrical shell(Equation 2

in f)'

2-8 of Reference 14) i1 Adjustment of the Heat Trsnsferred by Conduction to Account for Any Convection The IF function is used to force the minimum vakse of the adjustment to be 1.

(Conduchon and convection can't be worse than conduction alone.) The convection correlation is given in Equation 7-60 and Table 7-3 of Reference 2.

k,,go(T,,T,d,d ) = 0.11-(Gr(T,.T,d,d ) Pr ir(T,,T ))

b g 2 b g 2 a

b rado(T,,T,d,d )*l) rabo(T,,T,d,d )>l,k kfunc(T,,T,d,d ) = if(k b 3 2 b 3 2 b 3 2 Q conv(T,,T,d,d )

O cond(T,,T,d,d )hc(T,T,d,d )

g b j 2 s

b 2

b 3 2 1

i l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

l CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050 051 109135-200 59 of 141 i

Heat Transferred by Radiation Heat transfer by radiation between concentnc 3 (T,4 - T *)

cylindws. Since the heat oxd b

Q rad (T,,T *d 'd2,E g,E2)=

transferred per unit length g

b I 1

_I. I I is desired, circumference

d2E, is area per unit length. See eg i

Equation 843 of l

Reference 14.

Heat Transferred across the Air Gap between the Fire Wrap Layers dOlhi = dcondo + 2'(I'!hi + 8 h) _ Outside diameter of the inner layer of fire wrap dOlhi =6.75 in Find the tempeteture of the outside of the inner fire wrap layer Tguessi = 400-K Initial value for iterstwe solubon Giwn Heat transferred across the gap equals heat generated by cables Qcab"Q conv(Tguess1.TITho,dOThi,d ITho).

Conducbon/ convection g

guessi.T g,d ogg;,d '!ho'Ewnp Ewnp)

+Q rad (T g

I Radiation g

TOlhi = Find (Tguessl)

~5 Temperature drop TOlbi = 343.233 K T olhi - T g = 4.67 10 K

i pg there is no gap)

Review the relative contnbubon of the various mechanisms to heat transfer

)

I Q cond(TOlbi,TI h,dOThi,d th) = 8.91 watt ff Heat transferred by conduction g

Or(TOThi,TITho,dOIhi,d Ih)Pr,;,(TOlhi,T jg) = 0 Grashof number kratio(TOlhi,Tlb dOlhi,dITho) = 4.678 10 Raw muluplier for convection value indicates no convection I

Q eonv(TOlbi,T gg,d Olhi,d g) =8.91 watt if Conduchon / Convection g

g Q rad (TOThi.TIb dOThi,dgg.c,,p,c,,p) = 3.786 10'#

I watt fr Radiation g

l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 60 of 141 Temperature Drop through the inner Fire Wrap Layer d 11hi dcondo + 2 g.

Ire.ide diameter of the inner fire wrap layer d nd =6.75 in I

dOlhik 1

1

'I TQ ab Temperature drop (Equation 2-8 of AT Tid * ~2.x k,7,p d 11hi/

Reference 14)

Thi = 1.221 10" K AT Temperature of the inner surface of the inner fire wrap layer TIThi = TOlhi + ATThi T11hi = 343.233 K Temperature at the Outer Surface of the Conduit T

= 420 K initial value for iterstwe sokAon guess Given The amount of heat trans-Qcab"Qconv(Tguess,Tilhi,dcondo,dng).

ferred across the air gap g

i

+Q rad (Tguess,TIThi,dcondo,d11hi'Econd,EuTap)between the Conduft and the g

inner layer of fire wrap must equal the amount of heat Tcondo = Find (Tguess) generated by the cables.

Tcondo =345.894 K Temperature of the outer surface of the conduet Tcondo - TIThi = 2.661 K l REVISION NO.: 4 l

l Exhibit E l

N EP-12-02 l

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G 63 PROJECT NO.

PAGE NO.

09050-051109135-200 61 of 141 I

l Review the breakdown of how the heat was transferred I

Qeond(Tcondo TIThi'dcondo,dfib) = 8.076 watt ff Conduction g

Gr(Tcondo,T IThi,d g,dflhi).Pr ir(Tcondo TIThi) = 4.118 Grashof number a

i kratio(Tcondo,TIThi,dcondo,dfihi) = 0.166 Raw convection multiplier; value indicates no convection f

I Q oonv(Tcondo,TIThi'dcondo,d !Thi) = 8.076 watt ff Heat transferred by convection l

g 9 rad (Tcondo,TIThi,dcondo,d11hi'Econd'8 map) = 0.834 watt if ' Heat transferred by radiation g

Temperature Drop through the Conduit fdcondM i

cond

2E Pcond'In

'Qcab See Equation 2-8 of Reference 14 j

l AT (dadif AT g =0.008.K Tcondi = Tcondo + ATcond Tcondi = 345.902 K Temperature of the inside wall of the conduit I

Temperature Drop through the Air Gap inside t'ie Conduit 1

Diameter of a Single Cable i

d Icab

dcab + 2-(t nul + 1 jacket) i d Icab " I I93 *in Circumsenbed Diameter of Three Cables I+2)d d3 cab *

. Icab

/

d3 cab = 2.571 *in l REVISION NO.: 4 l

l E-

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Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 62 of 141 Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap A' = 3.2 K ft watt. l. ;,

B' = 0.19-in condgap

D' + d ca@ee Ewabon M omefereme 13 AT over_ cab ATcondgap = 8 077 K Temperature at the outside surface of the cable Tjacket = Tcondi + ATcondgap T;,cLeg =353.979 K Tjacket - 273.16 K = 80.819 K (*C)

Temperature Drop through the Overall Jacket P jacket d

o over_ cab ojacket, cab, 2x d

g - 2 t p[

AT jecket = 2.037 K o

Toinsul = Tjacket + AT jacket Toinsul - CtoK = 82.856 K (*C) o Geometnc Factor for Three Cables Ratio (t+T)/d tinsul + t jacket i

dcab Ratio insul = 0.234 G g = 0.92 This value is obtained by loolung it up on the curve in Reference 17 Temperature Rise through the Cable Insulation and Jacket Q cab,797,,,, g.

P nsul O 3 ATinsul

i ATimul =7.134 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductor = Toinsul + ATinsul Conductor temperature Tconductor = 363.15 K

- 273.16 K = 89.99 K

C

!= 341.95 amp Tconductor

[ REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 63 of 141 Calculate the Free Air Ampacity of the Cable Test value of free air ampacity I gee = 469.35 amp Heat Generated by Cables I

Qge,=31ge,2 Q ree = 16.786 watt ff Icab f

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be written as funcbons of the sur! ace temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Dissipated by Radiation cond o-(T' - T Q ud(T) = x dcondo E amb Heat Dissipated by Convection 1

'I amb)#

Q c cond(T) = 1.32-watt K "-m-2,,4. 'T - T dcondo-(T - Tamb)

(dcondo j initial guess for iterative solubon of the surface temperature of the wrapped conduit T

= 330 K guess Given Q ee"Q reond(Tguess)

Qc cond(Tguess) Heat dissipated by radiation and convection must equal heat generated by cables.

Touterf = Find (Tguess)

Touterf = 330.651 K Touterf-CtoK =57.491 K 'C Surface temperature of the condurt l REVISION NO.: 4 l

. -..-.~.. _..- - - -. -

_ _ ~ -,.... ~ _.......

4 1

l Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135 200 64 of 141 i

Temperature Drop through the Conduit fd I

'O ree See Equation 2-8 of Reference 14 condo I

I AT

'PW f

condf"' 2 (dcondi j AT g = 0.015 K j

Tcondif = Toutcrf + ATcondf T gr = 330.666 K -

Temperature of the inside wa8 of the conduit Temperature Drop through the Air Gap inside the Conduit 4pr =,

- Q r,,,

See Equation 41 A of Reference 13 j

AT over_ cab l

AT4pr= 15.217 K Temperature at the outside surface of the cable Tjackett = Tcondir+ AT4pr Tjacketf=345.883 K Tjackett-273.16 K = 72.723 K ('C)

Temperature Drop through the Overau Jacket P ojacket dover cab dT jacketf

9 ree' I"

2.x (dover _ cab-2 t jecketf.

o f

o AT jecketf"3 837*K o

Toinsulf = Tjacketf+ AT jecketf Toinsulf-CtoK = 76.56 K ('C) o Temperature Rise through the Cable insulation and Jacket g

Qg 3

O AT insulf*{Pinsul y

= 5.595 watt ff 3

3

'ATinsulf = 13.44 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductorf = Toinsulf + ATinsulf Conductortemperature T gg = 363.16 K 1,,,. 469.35 amp Tconductorf-273.16.K =90 K

'C 7

l REVISION NO.: 4 l

l

~

l Exhibit E N EP-12-02 Revision 2 f.

l COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-631 PROJECT NO.

PAGE NO.

09050-051 109135-200 65 of 141 i

Ampacity Factor i

E F ampucity 3 l

= 0.729 F ampacity Derating Factor Fgg4 1-F ampacity Fht4 =0.271 l

l i

I t

i l

l I

l 4

l REVISION NO.: 4 l

8 e

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY i

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 66 of 141

]

s Case 42a Model for a Wrapped Conduit-3/C,500 MCM,5000 V Cable in a 4" Conduit i

Cable Data Cable is 3/C,500 MCM,5 kV Conductor Resistance and Diameter cab e 0.0025410 2 ohm ffConductor resistance at 90 'C 3

r dcab = 0.813 in Conductor diameter t gg = 0.14 in insulation thickness t jacket = 0.05-in IndmdualJacket thickness i

t jacket = 0.14 in OveralJacket thicknees o

dover _ cab = 3.34 in OveraN diameter of the cable Thermal Resstmties p bd = 5 K m watt'I Insulation p,ct,g = 5 K m watt IndividualJacket j

-3 pojacket = 5 K m> watt OveralJacket Conduit Data inner and Outer Diameters, Thermal Conductuty, and Emissivity I

dcondi = 4.50-in 0.225 in inside diameter of a 3/4" trade size condimt dcondi =4.05 in dcondo = 4.50 in Outside diameter of a 6" trade size conduit cond = 2.08 Keem watt'IConduit thermal conducrivity p

E g = 0.23 Conduit emesuty Darmatt Data Thermal Conductivity k,,p = 0.783 BTU in hi tr.R

I 2 e,,p = 0.7 l REVISION NO.: 4 l

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Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 67 of 141 Thicknesses of Fire Wrap Material Outer Layer t go = 3 00 in inner Layer 1

!Thi = 0.000001 in Enter an infinitensimal value since there is only one layer Gap Thicknesses Gap between Conduit and inner Fire Wrap Layer 8 inner -

in Gap between the Two Fire Wrap Layers g a = 0.000001 in Set to an infiniteseimal value since there is only one layer of wrap l

l Test Parameters l

Test Current i

I = 315.36 amp Ambient Temperature 1

Conversion factor between degrees Celsius and Kelvin i

CtoK = 273.16 K Tamb = 40.0 K + CtoK Tamb = 313.16 K Miscellaneous Constants l

Stefan-Boltzmann Constant 2

o '= 5.67 10- s,,,,, yf.g-4 l

Acceleration due to gravity g = 9.8 m sec.2 i

l l REVISION NO.: 4 l

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Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09060-051 109135-200 68 of 141 Develop Interpolation Functions for the Characteristics of Air which are Functxms of Temperature. These parameters are required for the calculation of heat transfer by conduchon and convection in air gaps.

Thermal conductMty of air

.300.

.0.02624.

350 0.03003 1'E.1 Lookup tables of T

K k

arg g

arg 0.03365 temperature and thermal conductMty

450,

,0.03707 (Table A-5 of Ref.14) i = 0. 3 0.04 i

a035 Sirce the variation of the conductMty with k a%

temperature is nearly linear, the use of

~

0.03 linear interpolabon is appropriate.

0.025 300 350 400 450

)

l T,g

[

T,+Tbl Function to find the thermal conductMty of air (T,,T )

Iint*8P(Ty8,kar8, 2

/

air by linear int &T- ' ' - of the average of k

b two temperatures t

I I

l REVISION NO.: 4 l

._l

i

(

l 1

l l

Exhibit E N EP-12-02 Revision 2 l

COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050-051109135-200 69 of 141

)

Interpolate to calculate the kinematic viscosity of air 4

16 h 10 Lookup table for kinematic viscosity. The 20.76 10 6 temperatures for these points were defined 2

i v

=

m

,,c with the thermal conductivity of air (Table A-5 arg 25.9 10 '

of Reference 14) 31.71 10

~0 4 10 Plot shows that the kinematic

-5 3'30

~

vocoedy is not a linear function of

, arg, temperature. Therefore, the use of

- 2 10 cubic spline interpolation is appropriate.

4

-3 l

3.jo 300 350 400 450

= cspline(Targ Varg Auxiliary vector for cubic spline interpolation v aux

/

T,+T \\

Perform cubic spline interpolation b

I v,9(T,,T ) " interp v,,,Targ Varg*

2 b

for kinematic viscosity 2

S(T,,T'b) = T, + T Volume coefficient of expansion (assuming air j

b behaves as an ideal gas) l l

l l REVISION NO.: 4 l

)

Exhibit E N E P-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 70 of 141 Prandtl Number Data points for lookup table. The corresponding temperature i

0'708 values are shown in the section on the thermal conductivity of air, 0.697 (Table A-5 of Reference 14) h "'8

=

0.689

,0.683 0.71 i

N N

07

~

Since the Prandtl number is a non-linear

*rsi function of temperature, cubic spline 0.69 NI N > d b8 US#d-0.68 300 330 400 450 arg; Pr

= cspline(Targ,Prarg) Aumhary vector for cuMc spline interpolation aux rpolation function using cubic f

T,+Tb Pr ir(T,.T ) '=

Praux,Targ,Prarg.

2 sp es for the Prandtl number a

b l REVISION NO.: 4 l

_ _ _ _ = _ _ _ _ _ _.

i i

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 71 of 141 1

Outer Diameter of Wrapped Conduit d,,, e d a + 2 (t go i g ouw4 Ini

8 h) d,,, = 10.625 in 1

Heat Generated by Cables I

Q cab = 31 rcab Q cab = 7.578 awatt ff Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be written as funcbons of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

l Heat Dissipated by Radiation 4

Q r(T) = x d ast,ed y,p o T - Tamb E

Heat Dissipated by Convection 1

8 I IT-T amb d

-2.,4 xd assed(T-Tamb)

Q c(T) = 1.32-watt K

-m

( assem /

l l

l i

l l REVISION NO.: 4 l

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Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 72 of 141 j

inibal guess for iterative solubon of the surface temperature of the wrapped conduit T

= 330 K guess Given 9 cab"9 r(Tguess) + 9 c(Tguess)

Heat dissipated by radiation and convection must equal heat generated by cables.

Touter Find (Tguess)

T

= 317.05 K T

- CtoK =43.89 K

'C Surface temperature of the outer ouw Wrapped Conduit Temperature Drop Across the Outer Fire Wrap Layer dth =dcondo + 2.(t g + g inner + 8 outer) inside diameter of layer i

d g = 4.625 *in ld cab s in watts per foot i

Where Q g

i N assem ATh *, x k,7,p (dITho ATh = 29.144 K Temperature drop through the outer Fire Wrap Layer Temperature on the inside of the Outer Fire Wrap Layer T gg = Touter + ATh Tlh =346.193 K T g-273.16 K =73.033 K

'C Grashof Number gj(T,,T )-(T,- T )-(d2-d)3 Grashof number for a b

b i

Gr(T,,T,d g,d ) '

yhndrical space b

2 v,;,(T,,T)2 (EW L21 of b

Reference 14) The Grashof numberis a major parameter in determining convection l REVISION NO.: 4 l

l Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 73 of 141 J

Heat Transferred across an Air Gap Heat Transfer by Conduction Function for heat transferred air (T,,T ) (T,- T )

2nk b

Q eond(T,,T,d.d ) "

g3 b

by conduction across a g

b 3 2 cyhndrical shell(Equation I",{2 2-8 of Reference 14)

Adjustment of the Heat Transferred by Conduction to Account for Any Convection The IF function is used to force the minimum value of the adjustment to be 1.

(Conduction and convection cant be worse than conduction alone.) The convection correlation is given in Equation 7-60 and Table 7-3 of Reference 2.

ratio (T,,T,d j,d ) = 0.ll-(Gr(T,,T,d,d ) Pr,;,(T,,T ))

k b

2 b 3 2 b

kfunc(T,T,d j,d ) = if(k ratio (T,,T,d,d )>1,k ratio (T,,T,d,d ),1) b 2

b 3 2 b j 2 Q conv(T,,T,d,d ) ' Q cond(T,,T,d,d ) kfunc(T,,T,d,d )

g b j 2 g

b j 2 b 3 2 l

i l REVISION NO.: 4 I

Exhibit E NEP-12 02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050 051 /09135-200 74 of 141 1

1 Heat Transferred by Radiation Heat transfer by radiation between concentric g(T,4 43 oxd

-T b/

cyhnders. Since the heat gid(T,,T,d,d

,E y,E7) =

I 9

b 3 2 transferred per unit Q I

3 is desired, circumference

]

d is area per unitlength. See Eg 2

e2

)'

Equation 8-43 of Reference 14.

Heat Transferred across the Air Gap between the Fire Wrap Layers dOlhi = dcondo + 2-(tThi

8 h) Outsede diameter of the inner layer of fire wrap dOlhi =4.625 in Find the temperature of the outside of the inner fire wrap layer Tguesst = 400 K Initial value for iterative solubon Given Heat transferred across the gap equals heat generated by cables.

g SuessI,TITho,dOThi,d th).

Conducbon/ convection Qcab"9 conv((T

+ 9 rad Tguessi TI h,dOlhi,d.ggo,co p,cwrap) g g

Rh TOlhi = Find (Tguessi)

~s Temperature drop TOlhi = 346,194 k, TOlhi - TITho = 5.753 10 L.

pg there is no gap)

Review the relatwe contribution of the various mecherusms to heat transfer 3

Q cond(TOlhi TIW,dOlhi,d gg) = 7.578 watt E Heat transferred by conduchon s

Or(TOlhi,T11ho,dOlhi,d ITho) Pr ;,(TOThi,TITho) =0 Grashof number 3

, kratio(TOW.T gg,dOThi,dIlho) = 4.91910' Raw mulbplier for convechon vaiueindicatesno ean I

Q conv(TOThi,T gg,dOlhi,dth) =7.578 watt K Conduction / Convechon g

Q rad (TOThi,T gg,dOlhi,dITho Cwrap* Emp) =3.27910 watt E t

Radiation g

l l REVISION NO.: 4 l

1 I

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

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PAGE NO.

09050-051109135-200 75 of 141 Temperature Drop 'hrough the Inner fire wrap Layer dTIhi = dcondo + 2 g inner inside diameter of the inner fire wrap layer d13gi = 4.625 in Id I

' 1 1

OThi I"

'Qcab Temperature drop (Equation 2-8 of AT'!hi

2 x k d

gap q 11hi)

Reference 14)

~8 AT1hi = 1.515 10 K

T11hi = TOThi + ATThi Temperature of the inner surface of the inner fire wrap layer T gIhi = 346.194 K Temperature at the Outer Surface of the Conduit T

= 420 K Initial value for iterative soluition guess Given The amount of heat trans-Q cab"Q conv(Tguess,TIThi,dcondo,dIThi) -

feed am h ak gap g

+Q rad (Tguess,TIThi,dcondo,d ggj,Econd'Ew' rap' g

g between the conduit and the inner layer of fire wrap must equal the amount of heat Tcondo = Find (Tguess) generated by the cables.

Tcondo =349.479 K Temperature of the outer surface of the conduit Tcondo - T gIhi = 3.285 K l REVISION NO.: 4 l

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Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 76 of 141 i

Review the breakdown of how the heat was transferred Q cond(Tcondo.T ggj,deog,d ggj) = 6.858 watt if ' Conduction s

Or(Taindo,T gg;,dcondo,d ggj) Pr ir(T g,,T gn;) = 4.887 Grashof number a

condo d g;) =0.174 Raw convection multiplier; value indicates krauo(Tcondo Tggj,d g

no convection I

Q conv(Tcondo,T ggj,dcondo,d ggj) =6.858 watt fr Heat transferred by convection g

O rad (Tcondo,Tgg;,dcog,d ggi,E g,Emp) = 0.72

watt ff ' Heat transferred by radiation i

g Temperature Drop through the Conduit r

g =1pgn

-Qcab See Equation 2-8 of Reference 14 i

AT 2x

( condil ATcond =0.009 K Tcondi = Tcondo + ATcond Tcondi " 349 487 *K Temperature of the inside wall of the conduit Temperature Drop through the Air Gap inside the Conduit i

Diameter of a Single Cable d Icab = dcab + 2-(t nsul + t jacket) i d Icab " I I93 *i" Circumsenbed Diameter of Three Cables 3 cab * ' I + -[2 )

d d

~ Icab i

3/

d 3 cab = 2.571 ain l REVISION NO.: 4 l

1 e

l l

Exhibit E i

NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 77 of 141 l

Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap l

N 3.2 K ft watt'I in l

B' = 0.19 in j

Q c,g ee Equation 41 A of Reference 13 AT S

4p =

over_ cab ATcondgap =6.87 K Tjacket = Tcondi + ATcondgap Temperature at the outside surface of the cable Tjacket =356.357 K Tjacket - 273.16 K = 83.197 K ('C)

Temperature Drop through the Overau Jacket P jecket d o g cab o

ATojecket " Q cab' 2x (dover _ cab - 21 jacket).

o AT

= 1.732 K ojadet Toinsul-CtoK =84.929 K ('C)

Toinsul = Tjacket + ATojacket Geometric Factor for Three Cables Ratio (t+T)/d Iinsul

I jacket i

dcab Ratio insul = 0.234 G = 0.92 This value is obtained by looking it up on the curve in Reference 17 Temperature Rise through the Cable insulation and Jacket 9 cab ATinsul

P nsul'O 1

= 2.526 watt ft

i j

3 3

l Temperature drop through the cable insulation. See Equation 39 of ATinsul =6.068 K Reference 13 Tconductor = Toinsul + ATinsul Conductor temperature Tconductor = 364.157 K Tconductor-273.16 K = 90.997 K *C,

!= 315.36 amp l REVISION NO.: 4 l

l l

Exhibit E N EP-12-02 Revision 2 QDMMONWEALTH EDISON COMPANY I

CALCULATION NO. G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 78 of 141 Calculate the Free Air Ampacity of the Cable Test value of free air ampacity I g =444.72 amp Heat Generated by Cables I

O ce = 15.071 watt ff Q ree

3'I free rcab f

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equebons, the equations for the heat i

dumpeted by the wrapped assembly will be written as funcbons of the surface temperature. The area of the wrapped condut per unit length is equal to x times the diameter of the wrapped assembly.

l Heat Desipated by Radsbon l

Q rcond(T) = x dcondo e ga T* - Tamb )

Heat Dempated by Convection t

5 1

4 T-T 4

4 amb Q c_cond(T) = 1.32 watt Km.2 m-xdcondo-(T - Tamb) i dg Initial guess for iterative solubon of the surface temperature of the wrapped conduit Tp,, = 330 K Given j

Q free"O reand(Tguess) ' Q c cond(Tguess) Heat dissipated by redebon and convection must equal heat generated by cables Touterf = Find (Tguess)

Touterf = 333.%8 K Ter-cioK =60.808 K 'C Surface temperature of the wrapped conduit i

l REVISION NO.: 4 l

i

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Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 79 of 141

)

Temperature Drop through the Conduit Idcondo\\

1

'Q ee See Equation 2-8 of Reference 14 AT I

condf* 2-x P cond "(d h

condi!

ATgf =0.017 K Tcondif = Touterf + ATcondf Tconds = 333.985 K Temperature of the inside war of the conduit Temperature Drop through the Air Gap inside the Conduit N

free b EW Nf Rehm u AT condgapf'* g. +d over_ cab ATcondgapf = 13.662 K Tjacketf = Tcondif + ATcondgapf Temperature at the outside surface of the cable Tjacketf = 347.647 K Tjacketf-273.16 K = 74 487 K (*C)

Temperature Drop through the Overau Jacket P jacket d

o o m cab ATojacketf

9 ree-In f

2x (dom _ cab - 2 t jecket) o ATojacketf =3.445 K To nsulf = Tjacketf + ATojacketf oinsulf-CtoK = 77.932 K (*C)

T Temperature Rise through the Cable insuiabon and Jacket ATinsulf*

Pinsul-O j I

3

=5.024 watt ff 3

ATinsulf = 12.066 K Temperature drop through the cable insulabon. See Equation 39 of Reference 13 l

Tconductorf = Toinsulf + ATinsulf Conductor temperature Tconductorf =363.158 K l

Tconductorf-273.16 K =89.998 K *C I g,a 444.72 amp l REVISION NO.: 4 l

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050 051 /09135-200 80 of 141 Ampacity Factor F cmpacity

j I

F

= 0.709 ampacity Derating Factor Fdemting " 1 - Fampacity F gg =0.291 i

l REVislON NO.: 4 l

l i

1 l

Exhibit E l

N EP-12-02 l

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 81 of 141 Case 44-Model for a Wrapped Conduit-3/C, #2 AWG,5000 V Cable in a 6" Conduit Cable Data Cable is 3/C, #2 AWG,5 kV Conductor Resistance and Diameter cab - 0 020310 2 ohm fr Conductor resistance at 90 'C I

r dcab = 0.292 in Ccnductor diameter tinsd = 0.14 in insulation thickness t jacket = 0.03 in Individualjacket thickness i

t jacket.= 0.08 in Overe8 jacket thickness o

dover _ cab = 1.90 in OveraR diameter of the cable Thermal Resotmbes p insd = 5 K m watt

Insulation

-I p acket = 5 K m watt IndividualJacket j

ojacket = 5 K m-watt OverallJacket p

Conduit Data inner and Outer Diameters, Thermal Conductivity, and Emissmty dcondi = 6 625 in - 2 0.266 in inside diameter of a 3/4" trade size conduit dcondi = 6 093 in dcondo = 6.625 in Outside diameter of a 6" trade size conduit I

pg = 2.08 K cm watt Conduit thermal conducrivity cg = 0.23 Conduit emissmty Dermatt Data Thermal Conductmty d

2 fr R-'

'k

= 0.783 B1Uin hr wrap E

=0.7 op l REVISION NO.: 4 l

.._. =_. _ _

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 82 of 141 Thicknesses of Fire Wrap Outer Layer tgo 3.00 in inner Layer t n; = 0.000001 in Enter an infinitessimal value since there is only one layer Gap Thichwsses Gap between Conduit and inner Fire Wrap Layer 8 inner

I" Gap between the Two Fire Wrap Layers g a = 0.000001 in Set to an infinitessimal value since there is only one layer 7f wrap Test Parameters Test Current 1 = 110.26

amp Ambient Temperature Conversion factor between degrees Celsius and Kelvin CtoK = 273.16 K 1 aab = 40.0 K + CtoK Tamb = 313.16 K Miscellaneous Constants Stefan-Boltzmann Constant o = 5.67105 watt m'

K

Acceleration due to gravity g = 9.8 m sec.2 e

l REVISION NO.: 4 I

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Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 83 of 141

?

Develop Interpolation Functions for the Characteristics of Air which are Functions of Temperature. These parameters are required for the calculabon of heat transfer by conducbon and convection in air gaps.

Thermal conductmty of air 1

'300'

'O.02624' 350 0.03003

.i.i Lookup tables of T

^

arg 400 "TB '

O.03365 temperature and thermal conductmty

450, 0.03707 -

(Table A-5 of Ref.14) l i = 0. 3 l

l 0.04 y

a035 Since the variation of the conductuty with j

g "8 temperature is nearly lineer, the use of i

~~

linear interpolation is appropriate.

0.03 0.025 l

300 350 400 450 T,,

T'+Tb air (T.T ) = linterp Targ karg*

2

)

air by linear interpolation of the average of l

i k

a b Function to find the thermal conductmty of i

two temperatures l

5 l REVISION NO.: 4 l

l Exhibit E N EP.12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 84 of 141 Interpolate to calculate the kinematic viscosity of air i

1ml04l Lookup table for lunematic viscosity. The 20.76 10 6 temperawes fw these points were defined 2

m,,,, I with the thermal conductivity of air (Table A-5 y

=

arg 25.9 10~ 6 of Reference 14) 31.71 10

4 10-Plot shows that the kinematic

-5 3'30

'~

visconstyis not a linear funchon of

waj temperature. Therefore, tne use of

- 2 10 cubic spline interpolation is appropriate.

-5 l

3 30'S I

300 350 400 450 v,, r espline(T,,g,v Auxiliary vector for cabic spline interpolation arg

[

T,+T \\

Perform cubic spline interpolabon b

f r kinemabc viscoasty v,;,(T.T ) = interp v,,,Targ Varg*

2 b

2

$(T,,T ) =

Volume coefficient of expansion (assuming air b

T,+Tb behaves as an ideal gas) l REVISION NO.: 4 l

=

Exhibit E NEP-12-02 Revision 2 i

COMMONWEALTH EDISON COMPANY l

I CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 85 of 141 j

Prandt! Number 0'708,

ata poh for bo@Me correspondng temperahe l

values are shown in the section on the thermal conductivity of air.

l 0.697 (Table A-5 of Reference 14)

Pr

=

arg 0.689 0 683 0.7)

N "7

~

Since the Prandtl number is a non-linear "8

function of temperature, cubic spline i

~~ 0 69 interpolation will be used.

t 0.68 300 350 400 450 T,,

Pr

= cspline(Targ,Prary Auxiliary vector for cubic spline interpolation aux l

T,+T )

Interpolatior, function using cubic b

air (T,,T ) = interp Praux.Targ,Prarg.

2 j

l splines for the Prandt! number PT b

l l

l l REVISION NO.: 4 l

l

. -~

l I

i Exhibit E N EP-12-02 Revision 2 i

COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135 200 86 of 141 Outer Diameter of Wrapped Conduit d

= d a + 2 (tgo

F outer + tThi

8 inner) assem d,,, = 12.75 in i

Heat Generated by Cables Q cab = 31 rcab Q cab = 7.404 watt ft'I Calculate the Surface Temperature of the Wrapped Assembly l

Note: in order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be wntten as functions of the surface temperature. The area of the v. rapped condtat per unit length is equal to x hmes the diameter of the wrapped assembly.

I l

l Heat Dissipated by Radiation 4

Q r(T) = x d E

o T -Tamb assem wrap Heat Dissipated by Convection 34 m,,4.

7 _ 7 2

am d

ndassem (T - Tamb)

Q c(T) = 1.32 watt K assem i I

e i

j l

l REVISION NO.: 4 l

A_a-_..--..#

ea-Ja

+4 1&wa

+>+a m

.,_-a

+.

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 87 of 141 inibal guess for iterative solubon of the surface temperature of the wrapped conduit Tguess " 330'K l

Given 4

i 9 cab"O r(Tguess) + 9 c(Tguess)

Heat dissipated by radiation and convection must equal heat generated by cables.

i T

= Find (Tguess) outer T

=316A28 K T

- CtoK = 43.268 K 'C Surface temperature of the outer outer wrapped conduit i

Temperature Drop Across the Outer Fire Wrap Layer djno=dcondo + 2-(t3; + g inner + 8 outer) inside diameter of layer d gno = 6.75 m fd I

Where Qcab s in watts per foot 1

1 assem i

AT Tho

22 k.

I" d gno j'Qcab m,p ATgo = 21.772 K Temperature drop through the outer fire wrap layer Temperature on the inside of the Outer Fire Wrap Layer T gno = Touter + ATgo TITho = 338.2 K TITho - 273.16 K =65.04 K

'C Grashof Number g p(T,,T )-(T,- T )-(d2 - d )3 Greshof number for a b

b j

Gr(T,,T,d,d ) =

cylindrical space b 3 2 v ir(T,,T )

(Equation 7-21 of a

b Reference 14)The Grashof number is a major parameter in determining convection.

1 l REVISION NO.: 4 l

j

1

(

l l

I l

I Exhibit E l

N EP-12-02 Revision 2 l

l COMMONWEALTH EDISON COMPANY

)

l CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 88 of 141 Heat Transferred across an Air Gap Heat Transfer by Conduction Funcbon for heat transferred Q cond(T,,T,d,d )

2 x k,yT,,T ) (T,- T )

b by conducbon across a b

g b

2 yd I cyhndrical sheH (Equation i

2 l

I" 24 of Reference 14)

Adjustment of the Heat Transferred by Conduction to Account for Any Convection The IF function is used to force the minimum value of the adjustment to be 1.

(Conduchon and convechon can't be worse than conduchon alone.) The convection correlation is given in Equation 740 and Table 7-3 of Reference 2.

k,go(T,,T,d,d ) = 0.11-(Gr(T,,T,d,d ) Pr ir(T, T ))

r b 3 2 b 3 2 a

b rano(T,,T,d,d )'l) rano(T,,T,d,d )>1,k kfunc(T,,T,d,d;) = if(k b 3 2 b g 2 b 3 1,d ) kfunc(T,,T ad.d )

Q conv(T.T d.d )

Q g(T,.T d 2

h t 2 s

b 1 2 g

b i

l t

l REVISION NO.: 4 l

i l

Eshibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

CALCULATION NOL : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 89 of 141 l

Heat Transferred by Radiation Heat transfer by radiation between concentric b) cylinders. Since the heat 3 (T,4 4

-T oxd 9 rad (T,,T d I'd E l'E2)*

transferred per unit length g

b 2

d 3(g

)

I is desired, circumference 3

c3 2 {E y is area per unit length. See d

Equation 8-43 of Reference 14.

Heat Transferred across the Air Gap between the Fire Wrap Layers dOThi = dcondo i 2-(t g; 4 g mna) Outside diameter of the inner layer of fire wrap dOni =6.75 in Find the temperature of the outside of the inner fire wrap layer Tguessi = 400 K Initial value for iterative solution.

Gim Heat transferred across the gap equals heat generated by cables.

4 9 cab"9 eonv(Tguess! Tt h,dOThi,d no).

Conduction / convection g

g

+9 rad (Tguess!.Tl b,dOThi,dgno,c,,p,c wnp)

Radiation g

T ni = Find (Tguess1)

O

~

T n - T gno = 3.93210 ' K TOThi = 338 2 K O

oss ap (neglegible since there is no gap)

Review the relative contribution of the vanous mechanisms to heat transfer 3

Q oond(T ui,TI h,dOni dIh) =7.404 watt if Heat transferred by conduction g

O 1

Or(Toni,T gg,dOThi,dIh) Pr ir(Toni,T gg) =0 Grashof number a

kratio(TOThi,TI h,dOThi,dgg) = 4.529 10~

Raw multiplier for convechon value indicates no convection 8

ITho,d ui,dIh) =7.404 watt ff Conduction / Convection 9eonv(TOThi,T O

g

~8 I

9 rad (TOThi,T ggo,dOni,dITho Ewnp*Ewnp) = 3.04910 watt ff Radiation g

I l

l REVISION NO.: 4 l

I Exhibit E NEP-12-02 l

Revision 2 COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 90 of 141 Temperature Drop through the inner Fire Wrap Layer dgng=dcondo + 2 g ;,

inside diameter of the inner fire wrap layer dITid =6.75 +in I

In[dORd 1

1 t

-Q cab Temperature drop (Equation 2-8 of AT pg

2 x k,7,p gdIThi /

Reference 14) d ATTh = 1.014 10 K

Tempe o% W Mace of h W ke map byw TIRd = TOThi + ATpg l

TIRd = 338.2 K L

Temperature at the Outer Surface of the Conduit l

T

= 420 K Initial value for iterative soluinon guess Given The amount of heat trans-s Qcab"Oeonv(Tguess,TIThi'dcondo,dIThi) '

fened am N a'r gap g

+Q rad (TFucss*TIThi.dcondo,dgpg,Econd'uTap) between the cW and the g

inner layer of fire wrap must equal the amount of heat Icondo = Find (Tguess) generated by the cables.

Tcondo = 340.448 K Temperature of the outer surface of the conduit l

Tcondo - TfThi = 2.248.K 1

1 l REVISION NO.: 4 l

l Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050-051 /09135-200 91 of 141 i

Review the breakdown of how the heat was transferred I

Qcand(Tcondo,Tllin,dcondo,d gg;) =6.731 watt ff Conduction s

Gr(Tcondo.TIThi,dcondo,d gg;) Pr ir(Tcondo,T jn;) = 3.705 Grashof number a

krauo(Tcondo,T gg;,dcondo,dgg;) = 0.161 Raw convection multiplier; value indicates no convection 3

Q conv(Tcondo,Tgg,dcondo,dgg;) =6.731 watt ff Heat transferred by convection g

3 Q rad (Tcondo,Tgni,dcondo dIniEcond,E,

=0.673 watt ff Heat transferred by radiation g

Temperature Drop through the Conduit I

I dcondo AT

-Pcond'I Qcab See Equation 2-8 of Reference 14 cond " ~2 x d condij ATcond =0.007 K Tcondi = Tcondo + ATcond Tg =340.455 K Temperature of the inside wall of the conduit Temperature Drop through the Air Gap inside the Conduit Diameter of a Single Cable d Icab = dcab + 2 (tinsul + t ;;,g) d Icab = 0 632 in Circumsenbed Diameter of Three Cables I

3 cab

l 1 + 2 i;-d Icab d

l

(

)

d3 cab = 1.362 in i

l REVISION NO.: 4 l

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Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 92 of 141 Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap

-I A' = 3.2 K It watt in B' = 0.19 in condgap

D' + d ca@e epm A of Reference 13 AT

+

over_, cab ATcondgap = 11.336 K Temperature at the outside surface of the ceble T;,ct,g Tcondi + ATcondgap Tjacket =351.79I K Tjacket - 273.16 K = 78.631 K ('C)

Temperature Drop through the Overall Jacket P ja ket d owr _ cab AT ecket = Q cab-oj 2'E

,(dowr_cah-2 t jacket);

o AT

= 1.7 K i

ojecket Toinsul-CtoK =80.331 K ('C)

Toinsul = Tjacket + ATojacket Geometric Factor for Three Cables Ratio (t+T)/d Iinsul + t jacket dcab Rati insul = 0.582 O g = 1.50 This value is obtained by looking it up on the curve in Reference 17 Temperature Rise through the Cable insulation and Jacket 1

Ocab I

AT insul * {P nsul O g-i 3

=2.468 watt ff

\\

ATinsul = 9 665 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductor = Toinsul + ATinsul Conductor temperature Tconductor = 363.156 K

- 273.16 K = 89.996 K

'C I a 110.26 amp Tconductor l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G43 PROJECT NO.

PAL,5 NO.

09050-051 /09135-200 93 of 141 Calculate the Free Air Ampacity of the Cable Test value of free air ampacity Ig = 140.34 amp Heat Generated by Cables Q g = 3 I g,,2 I

Q ee = 11.994 watt if rcab h

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be written as funcbons of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Dissipated by Radiation Q rcond(T) = x d ge g o-(T* - Tamb )

Heat Dissipated by Convection 5

I d

Q c_cond(T) = 1.32 watt K ni ' m'-

xdcondo-(T - Tamb)

(dcondo /

Initial guess for iterative solution of the surface temperature of the wrapped conduit Tguess ' 330 K Given Q ree"Q reond(Tguess) ' 9 e cond(Tguess) Heat dissipated by radiation and convection f

must equal heat generated by cables.

Touterf = Find (Tguess)

Toutcrf = 326.369 K Touterf-CtoK = 53.209 K *C Surface temperature of the wrapped conduit l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 94 of 141 Temperature Drop through the Conduit Id I

1 condo condf' 2 x'P cond "d "Q free See Equation 2-8 of Reference 14 AT I

( condi; ATcondr=0.011 K Tcondif = ToutcIf + ATcondf Tcondif = 326.38 K Temperature of the inside war of the conduit Temperature Drop through the Air Gap Inside the Conduit

^'

4 pr = B' d Q free See Equation 41A of Reference 13 AT over_ cab 4p = 18.365 K AT g

Temperature at the outside surface of the cable Tjacketf = Tcondif + ATcondgapf TjacLett= 344.745 K Tjacketf-273.16 K = 71.585 K (*C)

Temperature Drop through the OveraR Jacket P ja ket d

cab AT acketf O ree-oj f

2x

, (dover _ cab-2 t jacket) o AT jacketf =2.755 K o

Toinsulf = Tjacketf+ AT jacketf Toinsulf - CtoK -74.34 K ('C) o Temperature Rise through the Cable insulation and Jacket ATinsulf*

P nsul'O 1

= 3.998 watt if 1

i 3

ATinsulf = 15.658 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductorf = To nsulf + ATinsulf Conductor temperature Tconductorf =363.157 K Tconductorf-273.16-K -89.997 K 'C I g e l40.34 amp l REVISION NO.: 4-

)

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY '

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 95 of 141 Ampacity Factor F ampacity

g F

=0.786 nmpacity Derating Factor Fderstmg = 1 - Fampacity Fhting =0.214 i

l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 96 of 141 Case 45-Model for a Wrapped Conduit-3-1/C, #8 AWG,600 V Cables in a 3/4" Conduit Cable Data Cable is 3-1/C, #8 AWG,600V Conductor Resistance and Diameter cab ' O.081810 2 ohm fr Conductor resistance at 90 *C I

r dcab = 0.146 in Conductor diameter tinsul = 0.045 in insulation thickness t jacket = 0.03 in IndividualJacket thickness i

t jecket = 0.00 in Overau jacket thickness o

d cab = 0.34 in OveraH diameter of the cable o

Thermal Resstubes p but = 5 K m watt'I insulation jacket = 5 K m watt'I IndmdualJacket p

ojacket = 5 K m watt'I Overa'ilJacket p

Conduit Data inner and Outer Diameters, Thermal Conductmty, and Emissivity dcondi = 1.05 in - 2 0.107 in Inside diameter of a 3/4" trade size conduit dcondi = 0.836 *in dcondo = 1.05 in Outside diameter of a 3/4" trade size conduit cond = 2.08 K em watt'IConduit thermal conduermty p

Econd = 0.23 ConM emW Darmatt Data Thermal Conductmty I 2 k

= 0.783 BTU in hi fr R-I wrap E

= 0.7 uup l REVISION NO.: 4 l

t l

1 t

Exhibit E NEP-12-02 j

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 97 of 141 Thicknesses of Fire Wrap Outer Layer l

1Tho = 3 00 in Inner Layer tThi = 0.000(X)l in Enter an infinitessimal value since there is only one layer l

Gap Thicknesses l

Gap between Conduit and in.ier Fire Wrap Layer 1

/1 S inner !,16}/ -

i Gap between the Two Fire Wrap Layers l

g outer = 0.000001 in Set to an infinitessimal value since there is only one layer of wrap Test Parameters Test Current l

I = 36 amp Ambient Temperature l

l Conversion factor between degrees Celsius and Kelvin CtoK = 273.16 K Tamb = 40.0 K + CtoK Tamb =313.16 K Miscellaneous Constants Stefan-Boltzmann Constant 2

o = 5.6710~ 8 watt m g l

Acceleration due to gravity g = 9.8 nr sec-2 l REVISION NO.: 4 l

1 l

1

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 98 of 141 Develop interpolation Funcbons for the Characteristics of Air which are Funcbons of r

Temperature. These parameters are required for the calculation of heat transfer by conduchon and convecton in air gaps.

l ThermalconductMtyof air j

'300'

'0.02624' 350 0 03003 i

Lookup tables of K

k T

~*'

l arg 400 arg 0.03365 temperature and l

thermal conductMiy 450 0.03707 (Table A-5 of Ref.14) i = 0. 3 0.04 y

. a035 Since the variation of the conductMty with l

k %

temperature is nearly linear, the use of l

linear integ ' t-. is appropnate oa3 0.025 300 350 400 450 ars;

/

T,+Tb Funcbon to find the thermal conductMiy of k,;,(T,.T ) = 1mterp(Targ.karg-2 ar' by her interpolation of the average of b

two temperatures I

i s

0 l REVISION NO.: 4 l

Exhibit E N EP-12-02 Resision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 99 of 141 Interpolate to calculate the kinematic viscosity of air 4I 16 M 10 Lookup table for kinematic viscosity. The 20.76 10~ '

temperatures for these points were defined 2

i v

=

m see with the thermal conductivity of air (Table A-5 yg 25.9 10' of Reference 14) 31.71 10-'

da10

4 6

Plot shows that the kinematic

-5 3'30

~

viscosityis not a linear funcbon of

' "si temperature. Therefore, the use of

~~~ 2 10 cubic spline interpolation is appropriate.

~3

~3 1 10 300 350 400 450 v,, = cspline(T,,g,y Auxiliary vector for cubic spline interpolation arg

/

T, + T \\

Perform cubic spline interpolation b

v,;,(T,,T ) = interp(v,,,Targ. Vug.

2 f

f rkinematicviscosity b

(T,,T ) =

Volume coefficient of expansion (assuming air b

T,+Tb behaves as an ideal gas) l l

l REVISION NO.: 4 l

1 i

l l

l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G 03 PROJECT NO.

PAGE NO.

09050-051 109135-200 100 of 141 Prandtl Number

'O.708 -

Data points for lookup table. The corresponding temperature values are shown in the section on the thermal conductMty of air, 0.697 (Table A-5 of Reference 14) b "'E

=

O689 0.683 0.71 g

3

\\

"7 - \\

Since the Prandtl number is a non-linear "8:

function of temperature, cubic spline 0.69 interpolation Will be Uned.

N 0.68 300 350 400 450 T,,gi Pr,, = cspline(Targ,Prarg) Auxiliary vector for cubic spline interpolation Interpolation function using cubic T

Tb Pr ir(T,,T ), interp Pr,,,Targ'P' ars' a

a b

2 l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 101 of 141 Outer Diameter of Wrapped Conduit d33, = d a + 2 (t go g og 4 t g; 4 g %)

4 d,,, = 7. I 75 in Heat Generated by Cables Q cab

3 I 'Tcab Q cab = 3.18 watt if '

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat 4

dissipated by the wrapped assembly will be written as funcbons of the surface j

temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembiy, 4

Heat Desapated by Radiation

-o-(T" - Tamb )

Q r(T) = x d E

assem map Heat Dissipated by Convection 1

5 i

4 f

3 ni,,4.

7 _ 7 2

amb d

xdassem (T - Tamb)

Q c(T) = 1.32 watt K i assem j l REVISION NO.: 4 l

I Exhibit E l

N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY cal.',LATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 I09135 200 102 of 141 initial guess for iterative solution of the surface temperature of the wrapped condurt Tgo,,,=330.K Given Q cab"O r(Tguess) + Q c(Tguess)

Heat dissipated by radiation and convection must equal heat generated by cables.

Touter = Find (Tguess)

Touw = 315.603 *K Touter - CtoK = 42.443 *K 'C Surface temperature of the wrapped conduit Temperature Drop Across the Outer Fire Wrap Layer d go = d g + 2-(t m + g inner + 8 outer) Inside diameter of layer d no = 1.175 in (dasM hre Qg is in watts pr foot l

l h

ATh *2ak (d no j wrao ATh = 26.607 K Temperature drop through the outer fire wrap layer Temperature on the inside of the Outer Fire Wrap Layer T mo = T

+ ATg Tih = 342.21 *K T gg - 273.16 K =69.05 K

C Grashof Number g $(T,,T )-(T,- T )-(d2-d )

Greehof number for a b

b 1

Gr(T,,T,d,d)=

cylindrical space b 3 2 vg(T,,T )

(Equation 7-21 of b

Reference 14) The Grashof numberis a major parameter in determining convection.

l REVISION NO.: 4 l

i l

j Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 103 of 141

)

Heat Transferred across an Air Gap i

Heat Transfer by Conduction Function for heat transferred 2 x k,;,(T,,T ) (T, - T ).

b Q eond(T,,T,d.d ) =

(d I b

by conduction across a g

b j 2 2

cyhndrical shell(Equation I"

2-8 of Reference 14)

Adjustment of the Heat Transferred by Conduction to Account for Any Convection The IF function is used to force the minimum value of the adjustment to be 1.

(Conduction and convection can't be worse than conduction alone.) The convection correlation is given in Equation 7-60 and Table 7-3 of Reference 2.

rado(T,T,d,d ) = 0.11-(Gr(T,,T,d ;,d ) Pr,;,(T,.T ))

k b i 2 b

2 b

kfunc(T,,T,d,d ) = if(k rano(T,,T,d,d )>l,k ratio (T,,T,d,d ).l) b 2

b 2

b 3 2 Q conv(T,.T,d,d ) O eond(T,,T,d,d ) kfunc(T,,T,d,d )

s b 3 2 g

b 3 2 b g 2 l

l l REVISION NO.: 4 I

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l Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 104 of 141 Heat Transferred by Radiation Heat transfer by radiation between concentric i(T,4 oxd

-Tb cylinders. Since the heat

,T

2)

I Q radt,,T

,d,d

E l'E transferred per unit length g

b g 2 d i j i

g is desired, circumference eg d; e2 is area per uret length. See 3'

Equation 8-43 of Reference 14.

Heat Transferred across the Air Gap between the fire wrap layers dOThi ' dcondo 4 2 (tn; 4 g

) Outside diameter of the innerlayer of fire wrap dOni = 1.175 *in Find the temperature of the outside of the inner fire wrap layer Tguessi = 350 K Initial value for iterstrve solubon Given Heat transferred across the gap equais heat generated by cables.

Ocab"Oconv(TguessI.Tgno,dOThi,d no).

Conduction / convection s

g

+Q rad (Tguessi,Tino,d(ygg,d gn o,E ung,cwrap)

Radiation g

Togi = Find (Tguessi) i W'

T og; = 342.21 K T oni-TITho = 9.602 10 K

,,,gs (negl gible since t

there is no gap) l Review the relative contribution of the various mechanisms to heat transfer 3

Q cond(TOTh.TITho,dOni,d th) =3.18 watt ff Heat transferred by conduction g

Gr(T og.T gno,dOThi,dITho)PTair(TOThi,TITho) =0 Grashof number kratio(TOThi,T mm,dOThi,dgno) = 5.786 10'#

Raw multiplier for convection j

value indicates no convection Q conv(Tog;,TITho,dORi,dITho) = 3.18 watt-ff '

Conduction / Convection g

Q rad (TOThi,TITho,dOThi,dI h,Eggp, E wrap) = 1.343 10

watt if I Radiation g

l REVISION NO.: 4 l

l

-.m_._..

m Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050-051/09135-200 105 of 141 l

l Temperstwe Drop through the inner fire wrap layer dgg;=dcondo + 2 g w Inside diameter of the inner fire wrap layer d gg; = 1.175 in Id i

1 1

Oni AT In

-Q cab Temperature drop (Equation 2-8 of Thi = 2 x k,7,p d

g Ihi j Reference 14)

~#

ATThi = 2.503 10 K

TIThi = TOThi + ATg; Temperature of the inner surface of the inner fire wrap layw Tgg; =342.21 K Temperature at the Outer Surface of the Conduit l

l T

= 375 K Initial value for iterative solulbon guess l

I 1

l Given l

The amount of heat trans-l Qcab"Qeony(Tgue,s, TIT}u,dcondf,dgg;)..

ferred across the air gap g

l

+Q rad (Tguess,T gnj,dcondo,dIThi,Econd,Ewrap}

the Conduit and the g

I inner layer of fire wrap must equal the amount of heat i

Tcondo = Find (Tguess) generated by the cables.

l l

Tgo =347.938 K Temperature of the outer surface of the conduit Tcondo - T gg = 5.728 K l REVISION NO.: 4 l

t' Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 106 of 141 Review the breakdown of how the heat was transferred I

Q oond(Tcondo IIRi.dcondo,d gg;) = 2.892 watt ff Conduction g

Gr(Tcondo,T g;,dcondo d Ini) Pr ir(Tcondo,TIThi) = 8.808 Greshof number i

a kratio(Tcondo.TIThi,d g,dgg;) = 0.207 Raw convection multiplier; value indicates no convection I

Q conv(Tcondo,TIThi,dcondo,dIThi) = 2.892 watt ff Heat transferred by convection g

3 Q rad (Tcondo, TITH,dcondo,d gni,e g,eop) =0.288 watt fr Heat transferred by radiation g

Temperature Drop through the Conduit cond

2-x'Pcond "

'Qcab See Equanon 2-8 of Reference 14 I

AT

( condi/

ATg = 0.008 K Tcondi = Tcondo + ATcond Tcondi = 347.946 K Temperature of the inside well of the conduit Temperature Drop through the Air Gap inside the Conduit Diameter of a Single Cable d Icab = dcab + 2-(tinsul + 1 jacket) i d Icab =0.296 in Circumscribed Diameter of Three Cables f

I 1+2 d Icab d 3 cab =

7

(

/

d3 cab =0.638 in l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 107 of 141 Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap A' = 3.2 K fl watt-1,;,

B' = 0.19 in condgap

D' +

Q cab See Equation 41 A of Reference 13 AT ATcondpp = 12.294 K Tjacket = Tcondi

ATcondgap Temperature at the outside surface of the cable Tjacket =360.24 K Tjacket - 273.16 K = 87.08 K (*C)

Temperature Drop through the Overau Jacket l

P j""k*t d over_ cab AT acket 4 Q cab-b oj

, (dover _ cab - 2 t jecket),

,#K o

AT

=0 K ojecket i

Toinsul - CtoK = 87.08 K

(*C)

Toinsul = Tjacket + ATojacket Geometric Factor for Three Cables Ratio (t+T)/d insul, insul + L jacket t

i dg Rati insul = 0.514 G

1.41 This value is obtained by looking it up on the curve in Reference 17 Temperature Rise through the Cable insulation and Jacket Q cab, g,

g. t ATinsul

P nsul O i i

3 ATinsul = 3.903 K TemperaaJre drop through the cable insulation. See Equation 39 of Reference 13 Tconductor eToinsul + ATinsul Conductor temperature Tconductor =364.143 K Tconductor-273.16-K = 90.983 K

'C Ie 36.00 amp l REVISION NO.: 4 l

~

4 Eshibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY i

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 108 of 141 4

Calculate the Free Air Ampacity of the Cable Test value of free air ampacity Ifree =46.38 amp 7

Heat Generated by Cables l

3 2

I I

Q gee = 3 I gee Q ree = 5.279 watt ff rcab f

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations. the equations for the heat dissipated by the wrapped assembly will be written as functions of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Dissipated by Radiation Q rcond(T) = x dcondo E g o-(T - Tamb )

4 Heat Dissipated by Corrvection 1

'(T-T d

amb 2

d m

,4, xdcondo-(T - Tamb)

Q c_cond(T) = 1.32 watt K (dcondo

)

Initial guess for iterative solution of the surface temperature of the wrapped conduit I

1 Tguess 330 K j

Given Q ree"Q reand(TFuess)

Q c cond(Tguess) Heat dissipated by radiation and ccnvection f

must equal heat generated by cables.

Toutcrf = Find (Tguess)

Touterf =336.258 K Touterf-CtoK =63.098 K 'C Surface temperature of the wrapped conduit j

l REVISION NO.: 4 l

i Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 109 of 141 1

Temperature Drop through the Conduit fd i

condo condf*

8-'P cond'I" d

'9 hee See Equation 2-8 of Reference 14 AT i condi ATcondr=0.013 K Tcondif = Touterf + ATcondf Tcondif =336.271 K Temperature of the inside waH of the conduit Temperature Drop through the Air Gap inside the Conduit 4pr = B' +

free See WWM omeference G AT 3 cab ATcondgapf = 20.406 K Temperature at the outside surface of the cable Tjacketf = Tcondif + ATcondgapf Tjacketf =356.677 K Tjacketf-273.16 K = 83.517 K ('C)

Temperature Drop through the Overau Jacket jacket d over_ cab A'rojacketf = 9 ree-f 2'K

, (dover _ cab - 2 t jacket) o ATojacketf =0 K Toinsulf = Tjacketf + ATojacketf omsulf-CtoK = 83.517 K (*C)

T Temperature Rise through the Cable insulation and Jacket

'P nsul-O j h

ATinsulf

I i

= 1.76 watt ff 3

ATinsulf =6.478 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductorf = Toinsulf + ATinsulf Conductor temperature Tconductod = 363.155 K I,es46.38 amp Tconductod-273.16 K = 89.995 K 'C g

l REVISION NO.: 4 l

e Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G 63 PROJECT NO.

PAGE NO.

09050-051 109135 200 110 of 141 Ampacity Factor F ampacity

g F

= 0.776 ampacity Derating Factor F sq = 1 - Fampacity F3,4 =0.224 l REVISION NO.: 4 l

a Exhibit E N E P-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 111 of 141 Case 47-Model for a Wrapped Conduit-3/C,500 MCM,5000 V Cable in a 6",30' Long Vertical Conduit Cable Data Cable is 3/C,500 MCM,5 kV Conductor Resistance and Diameter cab - 0 0025410-2 ohm ff Conductor resistance at 90 *C I

r dcab = 0.813 in Conductor diameter tinsul = 0.14 in Insulation thickness t jacket = 0.05 in IndividualJacket thickness i

t jacket = 014 in Overalljacket thickness o

dover _ cab = 3.34 in Oerall diameter of the cable Thermal Resistivities p insd = 5 K m watt'I Insulation p acket = 5 K m watt'I IndividualJacket j

1 pojacket.= 5 K m watt OverallJacket Conduit Data inner and Outer Diameters, Thermal Conductivity, and Emissivity dcondi = 6.625 in - 2 0.266 in inside diameter of a 6" trade size conduit dcondi = 6 093 in dcondo = 6 625 in Outside diameter of a 6" trade size conduit cond = 2.08 K-cm watt'IConduit thermal conducrivity p

Ead = 0.23 Conduit emissmty Lcond = 3011 Conduit Length Darmatt Data Thermal Conductivity k

= 0.783 BTUin hr fr* R'I I

wrap E,y,p = 0.7 l REVISION NO.: 4 l

l

=

s i

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Revision 2 l

COMMONWEALTH EDISON COMPANY l

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PAGE NO.

09050-051 109135-200 112 of 141 l

Thicknesses of Fire Wrap Material l

Outer Layer t no = 3 00 in Inner Layer tThi = 0.000001 in Enter an infinitessimal value since there is ordy one layer l

Gap Thicknesses Gap between Conduit and inner Fire Wrap Layer l

8 inner -

in l

Gap between the Two Fire Wrap Layers g mter = 0.000001 in Set to an infinitessimal value since there is ordy one layer of wrap Test Parameters Test Current I = 339.36 amp Ambient Temperature i

Conversion factor between degrees Celsius and Kelvin CtoK = 273.16 K l

Tamb = 40.0-K + CtoK Tamb = 313.16 K Miscellaneous Constants Stefan-Boltzmann Constant 4

2 a o = 5.6710 watt-m,g Acceleration due to gravity 2

g = 9.8 m-soci l

i l.

l REVISION NO.: 4 l

l I

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Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050-051 109135-200 113 of 141 i

Develop interpolation Functions for the Charactenstcs of Air which are Funebons of Temperature. These parametws are required for the calculabon of heat transfer by conduchon and convection in air gaps.

Thermal conductivity of air 300 0.02624 i

350 0.03003

.. i Lookup tables of T arg "

arg 0.03365 temperature and

^

400 thermal conductivity 450j

,0.03707 (Table A-5 of Ref.14) i = 0. 3 0 04 i

0.035 Since the variation of the conductMty with l

k l

arsi temperature is nearly linear, the use of linear interpolabon is appropriate.

0.03 I

0.025 300 350 400 450 T

l arsi l

I l

T,+T I b

air (T,,T ) = linterp Targ,karg, 2

)

air by linear interpolation of the average of k

b Functon to find the thermal conductivity of two temperatures l

l i

i i

1 l REVISION NO.: 4 l

j

l i

l Eshibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050-051 /09135-200 114 of 141 l

l l

Interpolate to calculate the kinematic viscosity of air 4

16 M-10 l

Lookup table for kinematic viscosity. The 20.76 10-6 temperatures for these points were defined I

v

=

-m sec with the thermal conductuty of air (Table A-5 arg 25.9 10^ 5 of Reference 14) 31.71 10

4 10 '

~

Plot shows that the kinematic 3

3'80 vocoedy is not a linear function of j

v ar; temperature. Therefore, the use of

- 2 10 '

cubic spline interpolation is appropriate.

1 10

300 350 400 450 V,, = cspline(Targ Varg Auxiliary vector for cubic spline interpolation

/

T,+T \\

Perform cubic spline interpolation b

f rkinematicviscosity v,9(T,,T ) = interp v,,,Targ Varg' 2

b 2

(T,,T)=

Volume coefficient of expaen (assuming a'r b

l T,+Tb behaves as an ideal gas) l REVISION NO.: 4 l

i 1

f i

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PAGE NO, l

09050-051 /09135-200 115 of 141 1

Prandtl Number

-0'708 -

Data points for lookup table. The corresponding temperature values are shown in the section on the thermal conductivity of air.

0.697 (Table A-5 of Reference 14)

"'8 0.689 0.683 0.71 g

3 N

'N.

0.7 Since the Prandt! number is a non-bnear h arsi funcbon of temperature, cubic spline 0.69 d8 0.68 300 350 400 450 T arg; t

csp ne(Tyg,Pryg) Auxiliary vector for cubic spline interpolation Pr li aux Pr ir(T,,T ) = ing(Pr I

T,+Tb sphnes for the Prandtl number a

b aux,Targ Prarg*

2 l

l 1

I o

E l REVISION NO.: 4 l

l t

l a

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. ; G-63 PROJECT NO.

PAGE NO.

09050 051 / 09135-200 116 of 141 Outer Diameter of Wrapped Conduit condo + 2-(tgo e gouter + tni g g) d

=d 4

33.

d,,, = 12.75 *in Heat Generated by Cables Q cab = 8.776 watt ff '

2 Q g =31'Tcab Calculate the Surface Temperature of the Wrapped Assembh Note: in order to sohre the energy balance equebons, the equations for the heat dissipated by the wrapped assembly will be written as funcbons of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Doespated by Radiabon d

Q r(T) = x d T

-o T - Tamb assem wrap i

Heat Dissipated by Convection 1

5 I

m,,4, T - T 2

amb d

! xdassem (T - Tamb)

Q c(D '= 1.42 watt K L

i cond )

i e

1 l REVISION NO.: 4 l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 117 of 141 Initial guess for iterative solution of the surface temperature of the wrapped conduit T

= 330 K guess Given Q cab"O r(Tguess) + 0 c(Tguess)

Heat dissipated by radiation and convection must equal heat generated by cables.

Touter = Find (Tguess)

Touter = 317.74 *K Tog - CtoK =44.58 K

'C Surface temperature of the wrapped conduit Temperature Drop Across the Outer Fire Wrap Layer dg =dcondo + 2.(t n; + g inner + 8 mter) Inside diameter of layer d m = 6.75 in Id

\\

g g

assem Where Ocab s in watts per foot i

ATg =2xk dgj wrap ATgo = 25.806 *K Temperature drop through the outer Fire Wrap Layer i

Temperature on the inside of the Outer Fire Wrap Layer Tg = Touter + ATgo T g = 343.546 *K T g - 273.16-K = 70.386 K

C Grashof Number g S(T,,T )-(T,- T ) (d2-d)3 Grashof number for a b

b g

Gr(T,,T,d,d;) =

cyhndrical space b g v,9(T,,T )

(Equation 7-21 of b

Reference 14) The Grashof number is a major parameter in determining convection.

l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 118 of 141 Heat Transferred across an Air Gap Heat Transfer by Conduchon Funcbon for heat transferred Q dT,T 'd 'd )

2.rkg(T,,T ) (T,- T )

b by conduchon across a b

g b I 2 in[d 3 cyhndrical shell(Equation 2

2-8 of Reference 14)

Adjustment of the Heat Transferred by Conduction to Account for Any Convection The IF function is used to force the minimum value of the adjustment to be 1.

(Conduction and convection can't be worse than conducbon alone.) The convection correlation is given in Equation 7-60 and Table 7-3 of Reference 2.

.I 1

9

-IL I

cond ratio (T,,T,d d ) = 0.197 /Gr(T,.T,d j,d ) Pr g(T,,T ))

d k

b 3 2 b

2 b

2-d g ratio (T,T,d,d )'I) ratio (T,,T,d,d )>1,k kfunc(T,,T,d g,d ) = if(k b 3 2 b g 2 b

2 Q cons.(T,,T,d,d )

O cond(T,,T,d j d ) kfunc(T,,T,d,d )

g b g 2 g

b 2

b 3 2 l REVISION NO.: 4 l

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Exhibit E N EP-12-02 i

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO, : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 119 of 141 Heat Transferred by Radiation Heat transfer by radiation o

between concentric i (T,4 oxd

-Tb) cyhnders. Since the heat 9 rad (T,,T,d,d2,e,c 2) transferred per urut length g

b g d

3 ( I. 1) is desired, circumference I

c d2 e3 is area per unit length. See g

I-Equation 8-43 of Reference 14.

i Heat Transferred across the Air Gap between the Fire Wrap Layers dOThi = dg 4 2 (t pg + g g) Outside diameter of the inner layer of Fire Wrap dODd = 6.75 *in Find the temperature of the outsede of the inner fire wrap layer Tguessi = 400 K Initial value for iterative solubon Giwn Heat transferred across the gap equals heat generated by cables.

Q cab"O conv(Tguess1,T gg,dOui,d gg) _.

Conduchon/ convection g

+9 rad (Tguess!,T gg,dOui,dI h 'Ewnp,E unp)

Radiation g

T ni = Fir.d(Tguessi)

O

~5 Temperature drop T ni = 343.546 K T on;- TITho = 4.5%10 K

O agoss gap gible h there is no gap)

Review the relative contnbubon of the various mechanisms to heat transfer Qoond(TOThi,TI h,dond,d gg) = 8.776 watt ft' 3 Heat transferred by conduction g

Gr(Tog;,T go, DOR,dgg)Prir(TOui,T gg) =0 Grashof number g

a ratio (T ogi T gno d on;,dIh)=5.55410 Raw mulbplier for convection k

value indicates no convection 3

Qconv(TOThi,TDho,d on;,dIh) = 8.776 watt E Conduchon / Convection g

-5 3

9 rad (T07hi,T ggo,dODd,d j gg,Eunp,E,,p) = 3.736 10 watt K Radiation g

l REVISION NO.: 4 l

o 1

l Exhibit E NEP-12-02 Revision 2 l

COMMONWEALTH EDISON COMPANY l

CALCULATION NO. : G43 PROJECT NO.

PAGE NO.

09030-051109135-200 120 of 141 l

I Temperature Drop through the inner Fire Wrap Layer d IThi = dcondo + 2 g i, inside diameter of the inner fire wrap layer dIThi = 6.75 in IdOThik 1

1 in

-Q cab Temperature drop (Equation 2-8 of l

ATg = 2.x k,,p d

4 IThi /

Reference 14)

-8 ATg = 1.202 10 K

Temperature of the inner surface of the inner fire wrap layer T m; = T og + ATThi TIThi =343.546 K Temperature at the Outer Surface of the Conduit T

= 420 K Initial value for iterative solultion guess Oiwn The amount of heat trans-9 cab"9 cony (Tguess,TIThi,dg,dIThi) -

ferred across the air gap g

+9 rad (Tguess,TIThi,dcondo,d g,econd,Eunp) between the conduit and the g

g inner layer of fire wrap must equal the amount of heat Tcondo = Find (Tguess) gerersted by the cables.

l Tcondo = 346.165 K Temperature of the outer surface of the conduit Tcondo - T m; = 2.619 K I

t l REVISION NO.: 4 l

._- -...~-._

e

?

Exhibit E NEP-12-02 i

Revision 2 COMMONWEALTH EDISON COMPANY t

L CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 121 of 141 l

l Review the breakdown of how the heat was transferred I

Q cond(Tcondo,TIThi,dcondo,d gg;) =7.952 watt ft Conduction g

Gr(Tcondo Tjni,dcondo d!Thi) Pr,;,(T condo,T n;) =4.038 Greahof number i

kratio(Tcondo,T g;,dcondo,d gn;) = 0.115 Raw convection multiplier; value indicates g

no convection I

i l

Qeoov(Tcondo,T gg;,dcondo,dgg;) =7.952 watt ff Heat transferred by convection g

I Q rad (Tcondo TIThi,daindo,dggj,econd,Egp) =0.823 watt ff Heat transferred by radiation g

l Temperature Drop through the Conduit cond ' 2 E P cond'I" d

Qcab See Equation 2-8 of Reference 14 AT

( condij l

ATg =0.(08 K Tcondi = Tcondo + ATcond Tcondi = 346.173 K Temperature of the inside well of the conduit i

(

Temperature Drop through the Air Gap inside the Conduit l

Diameter of a Single Cable d Icab = dcab + 2-(tinsul + t jacket) i l

d Icab " I I93*I" l

l i

Circumscribed Diameter of Three Cables f

2\\

d d Icab 3 cab = 1 + bl

\\

d3 cab = 2.571 in l

l l REVISION NO.: 4 l

. ~. _

a Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : C-63 PROJECT NO.

PAGE NO.

09050-051109135-200 122 of 141 Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap 3

A' = 3.2 K ft watf in B'

0.19 in A'

ca@ee @h M oNerence O ATNP D* + d over_ cab AT4p =7.955 K Temperature at the outside surface of the cable Tjacket = Tcondi + ATcondgap Tj,ct,g =354.128 K Tjacket - 273.16 K = 80.%8 K (*C)

Temperature Drop through the Overau Jacket P j" k t d over_ cab AT jacket = Q cab-6 2'8 (dover _ cab-2 t jacket),

o o

AT,;,cteg = 2.006 K Toinsul - Ctc,K = 82.974 K (*C)

Toinsul = Tjacket + ATojacket Geometric Factor for Three Cables Ratio (t+T)/d tinsul + t jacket j

dcab Rati insul = 0.234 I

0 g = 0.92 This value is obtained by loolung it up on the curve in Reference 17 Temperature Rise through the Cable insulation and Jacket 1

Qcab Qcab AT insul*gPnsul-Og.

3 i

= 2.925 watt-ff 3

l

)

ATinsul = 7.026 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductor = Toinsul + ATinsul Conductor temperature Tconducu = 363.16 K Tconductor - 273.16 K = 90 K

'C Ie 339.36 amp j

l REVISION NO.: 4 l

l

\\

i 4

Exhibit E NEP 12-02 j

COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 123 of 141 Calculate the Free Air Ampacity of the Cable Test value of free air ampacity I ge, = 423.15 amp Heat Generated by Cables I

Q gee

3-1 ge, r cab 9 rec = 13.644 watt ff f

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equations, the equations for the heat dissipated by the wrapped assembly will be wntten as functions of the surface i

temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

Heat Dissipated by Radiation Q reond(T) = x dcondo Econd o

-Tamb Heat Dissipated by Convection 1

i IT-Tamb 4

Q c_cond(T) = 1.42 watt K, m,2 m-ndcondo-(T - Tamb)

L t

cond )

initial guess for iterative solution of the surface temperature of the wrapped conduit TSuess '= 330-K Giwn Q ree"Oreond(Tguess)

Q c cond(Tguess) Heat dissipated by radiation and convection f

must equal heat generated by cables.

l Touterf = Find (Tguess)

Touterf =336.736 K Touterf - CtoK = 63.576 K 'C Surface temperature of the conduit l

l REVISION NO.: 4 l

l l

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 124 of 141 Temperature Drop through the Conduit ATcondf*

P cond'I" d

~Q hee See Equation 2-8 of Reference 14 cx

( condii ATeondf =0.012 K 1

Tcondif = Toutcrf + ATcondf Tcondif = 336.749 K Temperature of the inside wou of the conduit Temperature Drop through the Air Gap inside the Conduit AT 4pr = D' + d 0**

over_ cab ATcondgapf = 12.369 K Temperature at the outside surface of the cable Tjackett = Tcondif + ATcond apf 6

Tjacketf"349 Il7'K Tjacketf-273.16 K = 75.957.K ('C)

Temperature Drop through the OveraN Jacket P ojacket dover cab AT jacketr

Q a-In o

2-x (dom _ cab-2 t jacket) o ATojacketf"3 Il9 *K Toinsulf = Tjacketf+ AT jacketf Toinsulf - CtoK = 79.076 K ('C) o Temperature Rise through the Cable insulation and Jacket P nsul-O g I

ATinsulf

i

=4.548 watt ff 3

gf = 10.924 K Temperature drop through the cable insulebon. See Equation 39 of AT Reference 13 Tconductorf = Toinsulf + ATinsulf Conductor temperature Tconductorf = 363.16 K Tconductorf-273.16-K = 90 K

'C I g,, e 423.15-amp l REVISION NO.: 4 l

Exhibit E N E P-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 125 of 141 Ampacity Factor F ampacity " g F

= 0.802 ampacity Derating Factor Fderating = 1 - Fampacity F

= 0.198 derata l REVISION NO.: 4 l

Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 126 of 141 Case 48 Model for a Wrapped Conduit-3/C,500 MCM,5000 V Cable in a 6" 19' Long Vertical Conduit Cable Data Cable is 3/C,500 MCM,5 kV i

Conductor Resistance and Diameter cab = 0.0025410 2 ohm E Conductor resistance at 90 *C I

r dcab s 0 813 in Conductor diameter tinsul = 0.14 in Insulation thickness t;j,cteg = 0.05-in indudualjacket#wckness t jecket : 0.14 in OveraN jacketthickness o

d cab = 3.34 in OveraN diameter of the cable Thermal ResetMbes p insul = 5 Kcm-watt' 3Insulabon p acket = 5 K m-watt'I IndMdualJacket j

p ;g = 5 K m watt'I OveraN jacket o

Conduit Data inner and Outer Diameters, Thermal Conductmty, and Emissmty dcondi = 6.625 in - 2 0.266 in inside diameter of a 6" trade size conduit d g = 6.093 *in dcondo = 6.625 in Outmode diameter of a 6" trade size conduit g = 2.08 K cm watt' 3 Conduit thermal conduenvity p

c g = 0.23 Conduit emissmty Lcond = 19 ft Conduit Length l

Dermatt Data Thermal ConductMty

= 0.783 B1Uin h(I E R'I 2

k op e

= 0.7 op l

{ REVISION NO.: 4

i i

l Exhibit E N F.P-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 127 of 141 l

Thicknesses of Fire Wrap Material l

Outer Layer t no = 3.00 in inner Layer t n; = 0.000001 in Enter an infinitessimal value since there is only one layer Gap Thicknesses Gap between Conduit and Inner Fire Wrap Layer 8 inner

ID l

Gap between the Two Fire Wrap Layers 1

g outer = 0.000001 in Set to an infinitessimal value since there is only one layer of wrap Test Parameters Test Current I = 339.69 amp Ambient Temperature Conversion factor between degrees Celsius and KeMn CtoK = 273.16-K j

Tamb = 40.0 K + CtoK Tamb =313.16 K l

Miscellaneous Constants Stefan-Boltzmann Constant o = 5.67 10- s,,,,.,- 2, ga Acceleration due to gravity g = 9.8 m sec.2 l REVISION NO.: 4 l

1

l e

1 I

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051109135-200 128 of 141 Develop Interpolation Functions for the Characteristics of Air which are Functions of Temperature. These parameters are required for the calculation of heat transfer by corduction and convection in air gaps.

Thermal conductmty of air 300 0.02624 350 0.03003

.i 1

Lookup tables of T

~

temperature and arg 400

fB 0.03365 thermal conductmty

450,

,0.03707 -

(Table A-5 of Ref.14) i = 0. 3 0.04 i

0.035 Since the variation of the conductivity with g "S temperature is nearly linear, the use of i

0.03 linear interpolation is appropriate.

/

0.025 300 350 400 450 T,,i T,+Tb Function to find the thermal conductivity of k,,(T,,T ) = hnterp Targ,karg, 2

air by linear interpolation of the average of b

two temperatures I

i l

l REVISION NO.: 4

-.~.-

~

e 4

Exhibit E N EP-12-02 Revision 2 9

COMMONWEALTH EDISON COMPANY

,l CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 129 of 141 v

interpolate to calculate the kinematic viscosity of air 4

16 M 10 Lookup table for kinematic viscosrty. The 20.76-10

temperatures for these points were defined 2

m sec'I with the thermal conductivity of air (Table A-5 v

=

arg 25.9-10

of Reference 14) 31.71 10

4 10

3 3

Plot shows that the kinematic

_3 3'30

~

viscosity is not a linear funcbon of

' "si temperature. Therefore, the use of cubic spline interpolation is appropriate.

-3

- 2 10 7

f

-5 e

i 3.jo 300 350 400 450 v,, = cspline(Targ Varg Auxiliary vector for cubic spline interpolation

/

T,+T )

Perform cubic spline interpolation b

f r kinematic viscosity v,;,(T.,T ) = m.terp v,,,Targ Varg-2 b

2 (T,,T ) =

Volume coefficient of expansion (assuming air b

T,+Tb behaves as an ideal gas) i i

l l REVISION NO.: 4 l

1

Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 130 of 141 Prandtl Number

*Y'*

0'708 '

values are shown in the section on the thermal conductuty of air.

0.697 (Table A-5 of Reference 14)

'8 0.689 0.683 j 0.71

\\

07

~

Since the Prando number is a non-knear

"si funcbon of temperature, cubic spline

~

interpolation Will be uSed.

0.69 t

I 0 68 300 350 400 450 T,,,

Pr

= csplinc(Targ,Prarg) Auxiliary vector for cubic spline inteirc:'J::a aux I"I

" N f

T,+Tb sphnes for the Prando number Pr ir(T,,T ) = mterp Praux.Targ,Prarg*

2 a

b e

l REVISION NO.: 4 l

l l

s Exhibit E NEP-12 02

)

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09060-051109135-200 131 of 141 i

Outer Diameter of Wrapped Conduit d.3, ' = dgo 2 (tgo + g outer + t g; + g w) 4 d

= 12.75 in assem Heat Generated by Cables Q cab ' 3'I 4 cab Q cab = R 793

watt ft^

Calculate the Surface Temperature of the Wrapped Assembly Note: In order to solve the energy balance equabons, the equations for the heat dissipated by the wrapped assembly will be written as funcbons of the surface temperature. The area of the wrapped conduet per unit length is equal to j

x times the diameter of the wrapped assembly.

)

l Heat Dissipated by Radiation Q r(T) = x d,,ge po-(T-Tamb )

d i

1 Heat Dissipated by Convection I

Q c(T) = 1.42-watt K ni,,4,(T - T d

2 amb

.x dassem (T - Tamb)

( 'cond /

l REVISION NO.: 4 l

i

a Exhibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 132 of 141 IrWial guess for iterstrve solubon of the surface temperature of the wrapped conduit T

= 330 K guess Given Q cab"O r(Tguess)+Qc(Tguess)

Heat dissipated by radiation and convection must equal heat generated by cables.

Touter = Find (Tguess)

T

=317.651 K T

- CtoK = 44.491 K 'C Surface temperature of the outer outer wrapped condurt Temperature Drop Across the Outer Fire Wrap Layer g = d a + 2 (t g + g inner + S mter) inside diameter oflayer d

dIh =6.75 in

)

fdasM Where Q ab s in watts per foot i

1 1

c In

'~Q cab ATh

2.x k (dITho /

37,p l

ATg = 25.856 K Temperature drop through the outer fire wrap layer Temperature on the inside of the Outer Fire Wrap Layer TIh = Touter + ATh Tg =343.507 K T gg - 273.16 K = 70.347 K

'C Grashof Number gf(T,,T )-(T,- T )'(d2 - d g)3 Greshof number for a b

b Gr(T,,T,d,d ) =

cyhndncal space b 1 2 v,;,(T,,T)

(Equation 7-21 of b

Reference 14) The Grashof numberis a major parameter in determining convecton l REVISION NO.: 4 l

1 J

Exhibit E NEP-12-02 l

Revision 2 3

COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

1 1

09350-051 /09135-200 133 of 141 Heat Transferred across an Air Gap Heat Transfer by Conduction l

at tamfened Q cond(T,,T,d,d ) > 2 x k,;,(T,,T ) (T,- T )

b g

b 3 2 Id b

by conduction across a 2

cyhndrical shell(Equation I"

2-8 of Reference 14) l Adjustment of the Heat Transferred by Conduction to Account for Any Convection The IF function is used to force the minimum valse of the adjustment to be 1.

(Conduchon and convection can't be worse than conduction alone.) The convection correlation is given in Equation 7-60 and Table 7-3 of Reference 2.

.)

I g

bcond pgo(T,,T,d,d ) = 0.197-(Gr(T,,T,d.d ) Pr ir(T,,T ))4'd2-d g k

b 3 2 b 3 2 a

b kfunc(T,,T,d,d ) = if(k,,go(T,,T,d,d )>1,k rano(T,,T,d g,d )'I) b g 2 b j 2 b

2 gM(T,,T,d.d ) kfunc(T,,T,d,d )

Q conv(T T,d,d )

Q g

b 3 2 b 3 2 b 3 2 b

1 2

4

.J 4

4 4

l REVISION NO,: 4 l

-~..

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY t

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050 4 51109135-200 134 of 141 Heat Transferred by Radiation Heat transfer by radiation 4g between concentric o x d g-(T,4-Tb) cylinders. Since the heat Q rad (T,, rb,d g,d E 1,E2) trafmed per unit M g

2 dg r g i

. _. _ +

. __1 is desired, cir::umference d

is area per unit length. See ei 2

e2 Equation 8-43 of Reference 14.

Heat Transferred across the Air Gap between the Fire Wrap Layers ON>d g 42(t1hi + 8 h) Outsede diameter of the inner layer of fire wrap d

dOlhi =6.75 in Find the temperature of the outside of the inner fire wrap layer Tguessi = 400 K Initial value for iterative solution Oiwn Heat transferred across the gap equals heat generated by cables.

Ocab"Oeony(Tguesst T r!ho,d01hi,drgg).

Conduchon/anvection i

g

[

+O rad (Tguess1.Tl b,dUlhi,d g g c,,p,c,p)

Radiation g

w TOThi = Find (Tguessi) e op TOlhi = 343.507 K TOlhi-T17ho = 4.605 10 K

g there is no gap)

Rwiew the relative contribubon of the various mechanisms to heat transfer I

Q cond(TOIbi,TI h,dOlhi,drik) = 8.793 watt ff Heat transferred by conduction g

Gr(TOThi,TI h,dOlhi,d ygg) Pr ir(T og,T gg) =0 Grashof number a

kratio(T01hi,T g,dOlhj,dng) = 5.847 10 Raw mulbplier for convection g

4 value indicates no convection I

Qconv(TOlhi TI b,dOlbi,d ng) =R.793 watt ff Conduction / Convechon g

4 013i.d g,c.,,,c,,p) = 3.743 iO watt fr' Radiation Q rad (Tongrnw.d i

g i

l REVISION NO.: 4 l

l i

1 Exhibit E N E P-12-02 4

Revision 2 COMMONWEALTH EDISON COMPANY 1

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 135 of 141 1

i l

Temperature Drop through the inner fire wrap layer

]

i I

d ny = dcondo + 2'8 inner inside diameter of the inner fire wrap layer l

I dRhi =6.75 in

/d ggy)

Q cab 1

1 Inl AT gy = 2.x k rap \\dIThi)

Reference 14)

Temperature drop (Equation 2-8 of ATThi = 1.205 10 K

TU bi = TOThi + ATThi Temperature of the inner surface of the inner fire wrap layer T11hi = 343.507 K Temperature at the Outer Surface of the Conduit T

= 420 K Initial value for iterative solulbon guess Given The amount of heat trans-Qcab"Q eonv(Tguess,TUhi,dg,d gy)

ferred across the air gap g

+Q rad (Tguess,TUhi,dcondo,dg73,ccond,Ewrap) the CW and the g

inner layer of fire wrap must equal the amount of heat Tcondo = Find (Tguess) generated by the cables.

Tcondo = 346.131 K Temperature of the outer surface of the conduit Tcondo - T nhi = 2.624 K I

l l REVISION NO.: 4 l

Exhibit E NEP 12-02 Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 109135-200 136 of 141 Review the breakdown of how the heat was transferred I

Qoond(Tcondo,Tgni,dcondo,d gg;) = 7.%8 watt K Conduction g

Or(Tcondo,T gg;,dcondo,d gg;) Pr ir(T g,T ggj) =4.048 Grashof number a

kratio(Tcondo,T gni,dcondo,dIThi) = 0.121 Raw convection mulbpher; value indicates no convection I

Qoonv(Tcondo,Tgg;,dg,dIThi) =7.%8 watt W Heat transferred by convection g

Q rad (Tcondo,Tggi,dcondo,d g;,su d,Ey,p) =0.825 watt E ' Heat transferred by radiabon g

g Temperature Drop through the Conduit

~Pcond"fdcondo\\

I I

'Ocab See Equation 2-8 of Reference 14 AT cond " ~2 x (dcondij ATg =0.008 K Tcondi = Tcondo + 4T g Tcondi = 346.139 K Temperature of the inside war of the condist Temperature & g, through the Air Gap !:mide the Conduit Diameter of a Single Cable d Icab

dcab + 2-(t gg + t ;;,g) d Icab = 1.193 in Circumsenbed Diameter of Three Cables 2\\

3 cab = 1 + bl-d Icab d

\\

d3 cab = 2.571 in l REVISION NO.: 4 g

~

Exhibit E N EP-12-02 Revision 2 i

COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051/09135-200 137 of 141 Constants for Neher-McGrath Formula for Temperature Drop in the Conduit Air Gap A' = 3.2 K ft watt'I in B' = 0.19 in N

condpp

D' + d ca@ee Mon M omehe u AT over_ cab ATcondpp "7 97I *K Tjacket Tcondi + ATcondgap Temprature at the outside surface of the cable Tjacket =354.11 K Tjacket - 273.16 K = 80.95 K (*C)

Temperature Drop through the Overall Jacket f

cab AT jacket *Ocab in (dover _ cab - 24 jecket) o 22 o

1 AT jacket = 2.01 K o

Toinsul - CtoK = 82.959 K (*C)

Toinsul = Tjacket + ATojacket Geometric Factor for Three Cables Ratio (t+T)/d tinsul + t jacket i

I"8"I dcab Rati insul = 0.234 0 3 = 0.92 This value is obtained by looking it up on the curve in Reference 17 Temperature Rise through the Cable insulation and Jacket Qcab ATinsul

P nsul'O 1

=2.931 wattE 3

i 3

ATinsul = 7.04 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductor = Toinsul + ATinsul Conductor temperature Tconductor = 363.159 K Tconductor-273.16 K = 89.999 K

'C I s 339.69-amp l REVISION NO.: 4 l

~.

1 u

i Exhibit E NEP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY

' CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 138 of 141 1

4 i

Calculate the Free Air Ampacity of the Cable Test value of free air ampacity I g =428.45 amp l

Heat Generated by Cables i

I Q ree = 13.988 watt-fr Q free

3 I free 'fcab f

Calculate the Surface Temperature of the Wrapped Assembly l

Note: In order to solve the energy balance equebons, the equations for the heat dieospated by the wrapped assembly will be wntten as funcbons of the surface temperature. The area of the wrapped conduit per unit length is equal to x times the diameter of the wrapped assembly.

l Heat Dissipated by Radiation Q rcond(T) = x d w go-(T - T d

e amb 4

Heat Dissipated by Convection 1

h I

m,,4, /T - T 2

amb 4

'8'dcondo-(T - Tamb)

Q c_cond(T) = 1.42 watt K

\\Lemd /

Initial guess for iterative solubon of the surface temperature of the wrapped conduit T

330 K guess Given Q ree"Q rcond(Tgy,,,) + Q c cond(Tguess) Heat dissipated by radiation and convection f

must equal heat generated by cables.

Tg = Find (Tguess)

Touterf = 336.07 K Touterf-CtoK =62.91 K 'C Surface temperature of the Conduit i

l REVISION NO.: 4 l

a

Exhibit E N EP-12-02 i

Revision 2 COMMONWEALTH EDISON COMPANY CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050 051109135-200 139 of 141 Temperature Drop through the Conduit

'cond"fdcondo\\

AT I

Q ree See Equation 2-8 of Reference 14 con #

2 (dcondi/

f ATecng=0.013 K Tcondif = Touterf + ATcondf Tcondif = 336.083 K Temperature of the inside wou of the conduit Temperature Drop through the Air Gap Inside the Conduit A'

i condppf

D' + d free h hahn NNerne Q AT over,, cab ATcondppf = 12.68 K Tjacketr Tcondif + ATcondppf Temperature at the outside surface of the cable Tjacketf = 348.763 K Tjacketf-273.16 K = 75.603 K (*C)

Temperature Drop through the Overall Jacket jacket d over_. cab AT acketf = Q ree-oj f

,(dover _ cab ~ 2-I jacket) 2x o

ATopcketf " 3 I98 *K Toinsulf-CtoK = 78.801 K (*C)

Toinsulf = Tjacketf + ATojacketf Temperature Rise through the Cable insulation and Jacket Q free AT nsulf '

P nsul O 3

=4 663 watt fr I i

3 ATinsulf = 11.199 K Temperature drop through the cable insulation. See Equation 39 of Reference 13 Tconductorf = Toinsulf + ATinsulf Conductor temperature Tconductorf = 363.16 K Tconductorf-273.16 K =90 K

'C Ifree ' 428.45-amp I

l REVISION NO.: 4 l

l

iV l

Eshibit E N EP-12-02 Revision 2 COMMONWEALTH EDISON COMPANY

?

CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

09050-051 /09135-200 140 of 141 Ampacity Factor -

Fampacity *

= 0.793 F ampacity Derating Factor Fderating

I - Iampacity Fhting =0.207 l

l l

I f

I I

r 1

l I

l l

4 f

l REVISION NO.: 4 l

(

1 l

l t

i l

t Exhibit E NEP 12-02 Revision 2 i

COMMONWEALTH EDISON COMPANY l

[

l CALCULATION NO. : G-63 PROJECT NO.

PAGE NO.

l 09050-051 109135-200 141 of 141 t

Summary and Conclusions l

Case Raceway Orientation Depth Fire Ampacity Derating Comments l

Size of Fill Rating Factor Factor (in)

(hours) l 2

18"x 4" H

1 1

0.596 0.404 26 24"x12"x19' H

1 1

0.618 0.382 37

%" Conduit H

3 0.756 0.244 3/C. #6 AWG. 600V l

42 6" Conduit H

3 0.729 0.271 3/C. 500 MCM. 5 kV 42a 4" Conduit H

3 0.709 0.291 3/C. 500 MCM. 5 kV 44 6" Conduit H

3 0.786 0.214 3/C. #2 AWG. 5 kV l

45

%" Conduit H

3 0.776 0.224 3-1/C. #8 AWG. 600V i

t 47 6" Conduit V, 30' Long 3

0.802 0.198 3/C. 500 MCM. 5 kV l

48 6" Conduit V,19' long 3

0.793 0.207 3/C. 500 MCM. 5 kV l

+

l l

i l REVISION NO.: 4 l

\\

l

ML20115F327

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