ML19339B691

Response Time Qualification of Resistance Thermometers in Nuclear Power Plant Safety Sys.

ML19339B691
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Site:	Millstone
Issue date:	09/11/1980
From:	Kerlin T ANALYSIS & MEASUREMENT SERVICES CORP.
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ML19339B688	List: ML19339B687 ML19339B691
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NUDOCS 8011070478
Download: ML19339B691 (126)

Text

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RESPONSE TIME QUALIFICATION OF RESISTANCE TEERM0 METERS IN l NUCLEAR POWER PLANT FAPETY SYSTEMS l MILLSTONE NUCLEAR POWER STATION, UNIT NO. 2 i

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NORTHEAST UTILITIES TOPICAL REPORT l

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1 DOCKET No. 50-336 RESPONSE TIME QUALIFICATION OF RESISTANCE THERMOMETERS IN NUCLEAR POWEP ' ~ 9AFETI SYSTEMS MILLSTONE NUCLEAR POWER STATION, UNIT NO. 2 i

NORTHEAST UTILITIES TOPICAL REPORT PREPARED BY _

]7-f-JO N DR. T. W. KERLIN f - 8 SE ' U N Analysis and Measurement Services Corp. S- 6 /f -52f- /6 3 2. (Ahl) 1617 Euclid Ave.

Knoxville, Tennessee 37921 m we y -

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.z-TABLE OF CONTENTS CHAPTER PAGE

SUMMARY

. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . S-1

1. INTRODUCTION .. . . . . . . . . . . . . . . . . . . . . . . . .- 1 1.1 Regulations and Standards . . . . . . . . . . . . . . . . . 1 1.2 Candidate Test Procedures . . . . . . . . . . . . . . . . . 3 1.3 Organization of this Report . . . . . . . . . . . . . . . . 5

2. RESISTANCE THERMOMETER CHARACTERISTICS . . . . . . . . . . . . . 6 2.1 Construction Features . . . . . . . . . . . . . . . . . . . 6 2.2 Environmental Effects on Response Time . . . . . . . . . . . 13 2.2.1 Ambient Temperature Influence . . . . . . . . . . . . 13 2.2.2 Fluid Flow Rate Influence . . . . . . . . . . . . . . 16 2.2.3 Ambient Pressure Influence . . . . . . . . . . . . . 16 2.3 Modes of Response Time Degradation . . . . . . . . . . . . . 17 2.4 Effect of Heating Current on RTDs . . . . . . . . . . . . . 21

3. TIME RESPONSE CHARACTERIZATION OF SENSORS . . . . . . . . . . . . 23 3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4. SENSOR HEAT TRANSFER . . . . . . . . . . . . . . . . . . . . . 31 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Homogeneous Systems . . . . . . . . . . . . . . . . . . . . 31 4.2.1 Solid Cylinders . . . . . . . . . . . . . . . . . . . 32 4.2.2 Hollow Cylinders . . . . . . . . . . . . . . . . . . 36 4.3 Multi-Layer Modal Models . . . . . . . . . . . . . . . . . . 38 4.4 Results of Simulation Studies . . . . . . . . . . . . . . . 39

5. LOOP CURRENT STEP RESPONSE THEORY . . . . . . . . . . . . . . . . 42-5.1 Derivation of the Loop Current Step Response Trans fo rma t ion . . . . . . . . . . . . . . . . . . . . . . . 42 5.2 Correction Factors . . . . . . . . . . . . . . . . . . . . . 44

6. THE SELF HEATING TEST . . . . . . . . . . . . . . . . . . . . . . 47

7. EQUIPMENT . . .. . . . . . . . . . . . . . . . . . . . . . . . . 48 7.1 Constant Current Source with Voltage Measurement Across I the Resistance . . . . . . . . . . . . . . . . . . . . . . . 48 7.2 Bridge, Constant Voltage . . . . . . . . . . . . . . . . . . 48 7.3 Bridge, Constant Current . . . . . . . . . . . . . . . . . . 51 7.4 Conclusions Concerning Equipment . . . . . . . . . . . . . . 52 i

8. TYPICAL TEST AND ANALYSIS PROCEDURES . . . . . . . . . . . . . . 53 8.1 Performing a LCSR Test . . . . . . . . . . . . . . . . . . . 53 8.2 Analyzing LCSR Data' . . . . -. . . . . . . . . . . . . . . . 53 4

8.2.1 Craphical Analysis . . . . . . . . . . . . . . . . . 55 8.2.2 Computer Analysis . . . . . . . . . . . . . . . . . . 57 8.3 The Self-Heating Test . . . . . . . . . . . . . . . . . . . 57 8.4 Self-Heating Test Analysis . . . . . . . . . . . . . . . . . 59

PAGE

9. ACCURACY LIMITATIONS . . . .. . ... . . . . . . . . . . .. . . 61 9.1 Mathematical Crrors . .. . . . . ... . . . . . . . . . . . 61 9.2 Measurement Errors . . .. .. . . . . . . . . . . . . . . . 61

10. LABORATORY TESTING . . . . .. . . . . . . . . . . . . . ... . . 63 10.1 Description of Facilities .. .. .. . . . . . . . . . . . _3 10.1.1 University of Tennessee Thermometry Laboratory . . . 63 10.1.2 EDF Facility . . . . . . . . . . . . . . . . . . . . 64 10.2 LCSR Test Results . . . . .. . . . . . . . . . . . . . . . 64 10.2.1 University of Tennessee Thermometry Laboratory . . . 64 10.2.2 EDF Facility . . . . . . . . . . . . . . . . . . . . 64-10.3 Self-Heating Test Results . . . . .. . . . . . . . . . . . 64

11. IN-PLANT TESTING . . . . . . . . . . . . . . . . . . . . . . . . . 69 11.1 University of Tennessee Program . .. . . . . .. .. . . . 69 11.2 Test Procedure . . .. . . . . . . . . . . . . . . . . . . . 76 11.3 AMS Test Program . ... . .. . . . . . . . . . . . .. . . 76 ll.? Millstone 2 Tests . . . . .. . . . . . . . . . . . . . . . 85 11.4.1 First Test Program . . . . . . . . . . . . . . . . . 85 11.4.2 Second Test Program . . . .. . . . . . . . . . . . 85 11.5 Conclusions From In-Plant Testing . . . .. . . . . . .. . 89

12. CONCLUSIONS ........................... 92 APPENDIX A. EFFECT OF JOULE HEATING ON RTDs . . . . . . .. . . . . . 93 APPENDIX B. TIME RESPONSE CHARACTERIZATION OF SENSORS . . . .. . . . 100 B.1 The Concept of Time Constant . . .. . . . . .. . 100 B.2 Higher Ordar Dynamic Systems . . . . . . .. .. . . 101 B.3 Ramp Response . . . . . . .. . . . . . . . . . . . 105 B.4 Relation Between Time Constant and Ramp Time Delay . . . . . . ... . . .. . .. . . . . .. . 108 APPENDIX C.- THE LOOP CURRENT STEP RESPONSE TRANSFORMATION . .. . . 110 C.1 Introduction .. . .. . . . . . . . . . . . . . . 110 C.2 Mathematical Development of the LCSR Transformation . . . . . . . . . . . . . . . . . . 110 C.3 Steps in Implementing the LCSR Transformation . . . 121 APPENDIX D. TEST PROCEDURE , . . . . . . . . . . . . . . . . . .. . 122 REFERENCES ............................. . 126 i

Sunnary Met hods for measuring the response characteristics of resistance thermoneters are presented and verified. The methods include loop cur-rent step response testing for quantitative response characterization and self heating for monitoring for changes in response time. The loop cur-rent step responcc test provides the transfer function of the sensor (out-put signal / fluid temperature change). The measured transfer function may be used to give any index of response desired (i.e. response vs. time for a step input, response vs time for a ramp input, time constant, ramp delay time, etc.).

The loop current step response test or the self heating test may be performed at the end of the sensor leads where they are normally connected to their transmitter. The sensor must be disconnected during testing; but, otherwise, normal plant operation is not affected.

The testing procedures have been verified by extensive laboratory testing. Laboratory conditions varied from room temperature and pressure and low flow to full PWR operating conditions. Laboratory tests permitted direct response measurements and loop current step response tests with the sensor in the same condition. Loop current step response results and direct time constant measurements were found to agree very well (within ten percent). I The procedures also have been applied in operating plants. Experiences at six plants are reported herein which show the practicality of the pro-cedures for in-plant testing.

The methods have been found to be reliable, accurate, and practical.

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1. Introduction New techniques for response time testing of resistance thermom-eters installed in nuclear power reactors have been developed, validated and applied. The techniques are described and their validity is estab-l lished in this report.

1.1 Regulations and Standards U.S. Nuclear Regulatory Guide 1.118( provides criteria, re-quirements and recommendations on periodic testing of electric power and protection systems. This guide refers heavily to two Institute of Elec-trical Engineers Standards (IEEE Std 279-1971( ) and IEEE Std 338-1975(3)),

The Regulatory Guide states that the criteria, requirements and recommenda-tions in IEEE Std 338-1975 are considered to be generally acceptable sub-ject to sixteen stated exceptions and/or clarifications. The key points relative to sensor testing in the Regulatory Guide are:

- (Section C - Item 1). "Means shall be included in the design to facili-tate response time testing from sensor input to and including the actuated equipment."

- (Section C - Item 5). " Designs that do not require the use of bypasses in order to test all or part of a safety system, are preferred over those that require bypasses."

- (Section C - Item 6). " Instrumentation channel tests should include perturbing the monitored variable wherever practical. Wherever this is not practical, it should be shown that the substitute tests are adequate."

- (Section C - Item 12). "6.3.4 Response. Time Verification Tests. Safety system response time measurements shall be made periodically to verify the overall response time (assumed in the safety analysis of the plant) of all portions of the system from and including the sensor to operation of the actuator.

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2 "Where it-is not possible to include sensors in in-plant individual or system response time tests, the sensors.shall be periodically removed from their normal installations and tested. When this is necessary, the test i

installation shall duplicate as nearly as possible the expected environment and mechanical configuration of the actual installation.

"For channel testing, not including sensors, test equipment shall include that necessary to simulate sensor output over its full range and simul-taneously record input and output conditions for determining the overall response time. The test input.should span the normal trip setpoint suf-ficiently to reset the channel for the untripped condition and ensure com-plete tripping for the tripped condition.

"For protection tripping functions where two or more variables enter into the tripping-action (for example, the trip point is computed from tempera-ture, differential pressure, and nuclear flux signals), the channel re-sponse time shall be verified using each of the variables to produce the tripping action. During this tripping action, the test signals for the re-i maining variables shall be adjusted to within their expected operating range, but to a value that will produce conservative test results.

"The response time test shall include as much of each safety system, from censor input to actuated equipment, as possible in a single test. Where the entire set of equipment from sensor to actuated equipment cannot be tested at once, verification of system response time may be accomplished by measuring the response times of discrete portions of the system and 4

showing that the sum of the response timas of all portions is equal to or less than the overall system requirement.

" Response time testing of all safety system equipment per se.is not re-quired if, in lieu of. response time testing, the response time of safety

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3 system equipment is verified by functional testing and/or calibration checks where it can be demonstrated that changes in response time beyond acceptable limits are always accompanied by changes in performance charac-teristics that are detectable during these routine periodic functional tests and/or calibration checks."

These criteria, requirements and recommendations, along with those in IEEE Std 279-71 and IEEE Std 338-75, were taken into account when develop-ing and evaluating a testing procedure for resistance thermometers. Full compliance with these criteria, requirements and recommendations is demon-strated in subsequent sections of this report.

1.2 Candidate Test Procedures The response of a resistance thermometer is controlled by the rate at which heat diffuses from the fluid to the sensing element. There-fore, a suitable test procedure will involve a variation in the heat dif-fusion rate.

Several candidate test procedures have been identified and evaluated. These are:

A. Remove and Plunge. 1The plunge test is the classical response time qualification test for temperature sensors. Most tests involve rapid in-sertion of the sensor from room temperature air or an ice bath into flow-ing water. The most common water flow rate is three feet per second.

These tests are of questionable value for proper evaluation of the response time of reactor sensors because the conditions in the reactor (flow, pres-sure, *emperature and possibly conditions inside and outside of a thermo-well) are different than in the laboratory. Partial resolution of this problem is possible by simulating flow, pressure, and/or temperature con-ditions, but other environmental condition 4 (such as the thermowell) cannot

4 he simulated with confidence. Consequently, the removal and plunge test procedure is judged ~to have limited usefulness for practical response measurements.

B. Plant Maneuver. Fluid temperature changes can be induced by enanging reactor power or by changing the steam flow. This will provide a sensor output transient that depends on its response characteristics. However, there is no way to determine the actual fluid temperature so,that the sensor dynaics can be identified. Simulation might be used to estimate the fluid temperature, but the uncertainty in this would be significant.

Consequently, the plant maneuver approach is considered to be unsatisfac-tory.

J C. Internal Heating. It is possible to induce a heat diffusion transient by passing an electric current through the normal sensor leads. Since a small current must be used in the bridge used for normal temperature measurement, this approach involves an increase in current from its normal level to a level suitable for obtaining adequate test data. The Joule heat-

! ing causes a temperature transient which is controlled by heat diffusion from the sensing (and heating) element to the fluid. This is exactly the reverse of the normal heat diffusion path, but the same physical properties control the heat diffusion regardless of the path. This intuitive approach led to the development of an internal heating test method called the loop current step response (LCSR) test. The key to this test method is the l

ability to construct the response of interest (the response to a fluid temperature change) from information that is measureable in a LCSR test

(the response to an internal heating' change). This transformation has been developed and validated.(4J,6,7) The method is suitable for complying with the' criteria, requirements and recommendations of Regulatory Guide 1.118. It is discussed in subsequent sections of this report.

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I D. Fluctuation Analydis. The output of a temperature sensor that experiences random fluctuation in fluid temperature depends on the sensor response characteristics. Methods have been developed for analyzing these fluctuating signals to determine the response time, but quantitative re-sponse time determinations depend on satisfaction of an assumption about the statistics of the process temperature fluctuations. Since this assump-tion cannot be validated, this method is considered unsuitable for quanti-tative measurements.

The research program for developing response time testing methods in-volved theoretical analysis, equipment design, laboratory testing and in-plant testing. The. laboratory work involved testing at room temperature, low flow conditions, and testing at plant conditions in a special test loop at Electricite de France. In these tests it was possible to compare the loop current step response test results with plunge tests or injection tests and thereby evaluate the validity of the methods.

1.3 Organization of this Report Subsequent sections of this report give a complete description of the loop current step response test. This includes basic theory, equip-ment requirements, analysis procedures, accuracy limitations,. laboratory validation and field testing experience. Most of the information.was ex-tracted from several earlier publications, but some new information is included also.

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2. Resistance Thermometer Characteristics d

2.1 Construction Features a A typical resistance temperature detector (RTD) consists of a fine platinum wire mounted inside a metal sheath (usually stainless steel).

Two construction methods are commonly used: mandrel mounting and wall mounting. In a mandrel-mount sensor, the platinum element is mounted on a support piece, inserted into the sheath, and held in place by a powder or cement filler (See Figure 2.1). In a wall-mount sensor, a platinum wire coil is attached to the inside wall of a hollow sheath by a cement that also serves to insulate the platinum electrically from- the sheath (See Figure 2.2).

Each of the construction methods has advantages. If a support l

structure is used to mount the filament, stress effects on sensor perfor-l mance can be minimized; however, the back-fill material needed for elec-trical insulation has significant thermal resistance. If the filament is I very close to the inner wall of the sheath, as is the case for the wall-mount sensor, the time response of the sensor is faster than when the fila-ment is mounted on a separate support. The fast time response is desired for some applications.

RTDs may be designed for direct immersion into a fluid stream (wet-type) or for installation into a well in the stream (well-type). To improve the heat transmission in well- type sensors, a thermal bonding material is of ten used in the gap between the sheath and the well.

The sensors found in pressurized water reactors manufactured by

-different vendors are quite different. Table 2.1 gives specifications on some of the commonly-used sensors. Figures 2.3 through 2.5 show some of I

these sensors.

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TABLE 2.1 SPECIFICATIONS OF THE RTDS USED IN THIS WORK Sensor Number of 2 Wire Resistance Sensor Model Plants Wet Type Sheath Well Sensing Elements 3 Wire Dummy 'at 0*F Manufacturer Number Where Used Or Well Type 0.D. 0.D. Per RTD or 4 Wire Wire? R (0)

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• 177-GY B&W wet .335" NA 2 4 no 100 REC 177HW B&W well .290" .410" 2 4 no 100 REC 104-AFC C.E. well .125' .281" 1 2 yes 200 .

REC 176-KF Westinghouse wet .375" NA 1 . 4 no 200 REC. 104ADA C.E. well .125" .25 1 2 yes. 200 REC 104VC C.E. well .125" .25 1 2 yes 200 Sostman 8606 Westinghouse wet .25" NA 1 4 no 200 Rosemount Engineering Company.

Babcock and Wilcox Co.

Combustion Engineering Inc.

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c:nn:ct:d configurations Sensors may be to lead wires that conn figurations shown in Figure 2.6 are used in The constructed with . acth sistance to obtain measurement systems tomultiple y wire with single accurate temperature compensate for leade w sensing elements per measurements. RTDs two independent mea are also ma.

2.2 surements sheath with the same and with dual el EnvironmentalsEffect sensor. ements that allo on Response Time ambient Environmental effects temperature, fluid flow that may influence sensor cussed below.

rate, and ambient pressresponse time at 221 ure.

These Ambient Temperature I f are dis-n luence Changes in ambient following mechanisms temperature can affect response tim temperature dependence e by the of heat tivities, specific h transfer parameters ( h eat capacities coefficients) . t ermal conduc-

- dimensional change and surface film transfer heat s with temperature.

The materials temperature dependenused commonly in RTDs ities ces of are is shown available for in . Table 2.2 es thermal From Table 2.2, we and specific heat capa conducti tion on c-the temperature depseveralr als, important so a see matethat no i informati on use endence of sensor conclusive answer to to of physical property da response time ta.

obtain quantitative inf Experiments on cannot be based e on th ormation. actual sensors must be used temperature.

The heat transfer This coefficient at the occurs becauseof sensor surface changes the temperature de with pendence of water

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. 4 15 Table 2.2 Effect of. Temperature on Thermophysical Properties of Resistance Thermometer Materials Percentage change in Prgperty for a Material. Temperature increase from 70*F to 600*F Specific Heat Thermal Conductivity 304 SS +18 +25 316 SS Negligible +25 i

Al 02 3 (porosity = 0) +43 -57 i Air +0.5 +70 Cement Used in RTDs  ?  ?

Thermal Bonding Compounds  ?  ?

! (for use as a filler between sensors and their wells)

Note - The thermal conductivity of A1 023 depends strongly on porosity.

The net effect depends on the combined effect of Al 02 3 conductivity and the conductivity of the air in the pores. Since the conductivity of A1 023 decreases with temperature and the conductivity of air increases with temperature, these are competing effects. For 53 percent porosity, the temperature dependence is nearly zero.

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l 16 thermal conductivity, specific heat capacity and viscosity. It has been shown(6) that the film heat transfer coefficient decreases by about a

- factor of two as water temperature increases from 70*F to 500'F.

An additional (and possibly dominating) factor in establishing the temperature dependence of the response time in the temperature effect on dimensions. The sensor is cimposed of several layers of materials.

Ideally, these materials are 'somogeneous and in perfect contact with one another. In actuality, it is likely that cracks and gaps exist within regions and at boundaries. As temperature increases, the gaps and cracks may open or close depending on the temperature coefficients of expansion of the sensor materials. Since gas-filled gaps and cracks have a large effect on the heat transfer resistance, this could be a large (but unpredictable) factor with the net effect being an increase or decrease in time constant with temperature.

2.2.2 Fluid Flow Rate Influence The film heat transfer coefficient for the sensor depends on the fluid flow rate. Correlations show that the film coefficient varies as the flow to the 0.8 power. The importance of the film coefficient in determin-ing the time constant depends on the relatlee importance of internal heat transfer resistance vs. surface heat transfer resistance. For example, a sensor whose internal heat transfer resistance is ninety percent of the

-total at low flow can experience only a maximum of ten percent improvement even at very high flow.

2.2.3 Ambient Pressure Influence If the sensor sheath were compressible, then increased pressure would compact the materials, improve the heat transfer, and reduce the time constant. The effect is insignificant for practical sensor designs.

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17 Ambient pressure also affects the thermophysical properties of water (density, specific heat capacity, thermal conductivity and viscosity), but the effect is small. The total effect of ambient pressure is small.

2.3 . Modes of Response Time Degradation Since the response time is controlled by heat diffusion, response time degradation could occur either by an increase in the overall heat transfer resistance or by an increase in the effective heat capacity of the sensor materials. Response time degradation has occurred, so it is useful to postulate causes. Possible causes are:

- Changes in properties of thermal bonding material. The NEVER-SEEZ com-pound used for thermal bonding in some well-type sensors undergoes changes with temperature. Experiments ( showed a tendency for NEVER-SEEZ to change from a pasty material at room temperature to a powder at elevated temperature (500*F). Consequently, tests were performed to determine the' influence of temperature on the time constant because of NEVER-SEEZ property changes. Results are shown in Table 2.3. These show that NEVER-SEEZ prop-erties change in a way that increase the time constant of the sensor-well assembly.

- Changes in properties of filler or bonding material. A special cement called PBX (manufactured by the Robert G. Allen Co. of Mechanicsville, N.Y.) is used in most currently used PWR sensors. It is the filler mate-rial in mandrel-mounted sensors and the cement used to hold the platinum in place in wall-mounted sensors.. Tests in air show that the' cement changes from a homogeneous, plastic-like material to a flaky, hard material when heated in air to 500*F. Additional tests (12) with PBX were performed in which special sensors were constructed for material evaluations. Small, iron-constantan thermocouples were placed in the center of 1/2 in tubes

18 TABLE 2.3 EFFECT OF NEVER-SEEZ PROPERTY CHANGES WITH TEMPERATURE ON THE TIME CONSTANT Test Number Condition Time Constant (Plunge Test) 1 Fresh NEVER-SEEZ in Well 3.70 sec.

2 After heating sensor and 4.55 thermowell with NEVER-SEEZ at 500*7 for 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br /> 3 Sensor and Well with NEVER-SEEZ 4.12 Removed-Sensor and Well cleaned with' alcohol (air now in Well) 4 Repeat of Test Number 1 (fresh 3.72 NEVER-SEEZ) 5 After heating' sensor and thermo- 5.08 well with NEVER-SEEZ at 550*F for 16 hours1.851852e-4 days <br />0.00444 hours <br />2.645503e-5 weeks <br />6.088e-6 months <br /> 6 Repeat Test Number 3 4.13 (Note: The sensor was a Rosemount 104 and matching thermowell) 1 1

l

'19 1

(13/16 inch long) and then the tubes were i

packed with PBX.

were then cured according to the manufacturer' The assemblies. i s instructions. These sensors were subjected co thermal shock tests, extended ture, and mechanical shock tests exposure at high tempera-and after these tests. The time constant was measured befor  ;

The results appear in Table 2.4.

These tests show changes (increases and decreaseE) in time constant

, indicating a' change in PBX properties or a change in its bonding t i

If similar effects occur in a reactor sensoo the thermocouple or th r, then a~ change in time constant 4

would occur.

Furthermore, if the main effect is PBX emb i r ttlement, then mechanical vibrations in a power plant would lik l heat transfer properties. e y affect the PBX and its

- Changes in conditions at the sensor-fluid ace.'

interf If any material s

(such as corrosion products or crud) adhe would increase the heat transfer resistanceres to the surface, then

- Changes in contact pressure or contact areaand increase the ti In a well-type sensor with '

no thermal bonding material .the contact pre surface and the inside wall of the well can ssure betwee affect the response time.

Righer contact pressure will give a fast er response.

' tion of a spring caused a gradual d If a gradual relaxa-I increase in time constant ccur. would o ecrease in contact pressure, then an with points or groves to establish' contact betAlso, some sen side wall of the well. ween the sensor and the in-b If vibration ~ caused relative motion en the betwe

' sensor and the well, then wear would cause dec t

response time. reased contact and-a slower

}

This short list of possibilities does not

-will occur, but sensor res

~

prove that these changes mechanisms are pisesible. ponse time changes do occur and the postulat e d

! Consequently, they amst be taken seriousl y.

7.

20 oo p g-se . . am TABLE 2.4 ENVIRONMENTAL L 7. CTS ON PBX CEMENT Number of Test Samples Effect Thermal shock (450*-550*F 4 small (<5%) increase then quench in room in time constant temperature water)

Exposure to h'gh 4 decrease (up to 35%)

temperature (450*F-550*F) in time constant for at least 4 hours4.62963e-5 days <br />0.00111 hours <br />6.613757e-6 weeks <br />1.522e-6 months <br /> Mechanical shock 4 increase (up to 21%)

(36 in. drop onto a in time constant hard surface)

/)ppu ou mo ' K73 r -s b 4J s ro sp c.<_

sa n n ete a a m k n y ,c/u u <tt

~

P2X ce m w/.  ?SX ha W polin *I h* C ' m o -}

b ri f/ k w/ 7/ap z4 L7 fcyn ;44/ .

4

l

'21 i

- 2.4- Effect of Heating Current on RTDs ,

i The response time testing' procedures presented in subsequent sec- ,

i tions involve heating the sensor filament by Joule heating. Consequently,

[ it is pertinent to consider the possibility of sensor Cegradation as a re-

< sult of passing a heating current through the filament.

The sensors used in power plants routinely experience a current 1

of a few mil 11 amperes as o result of the requirements for resistance mea-i surement with a Wheatstone bridge. RTD manufacturers normally specify ,

maximum currents to be used so as to avoid temperature measurement errors due to self heating. A typical maximum recommended value is ten milliam-peres. This would give a measurement error of about 0.l*C for a typical j PWR sensor. ,

Some manufacturers also specify maximum safe heating currents to avoid sensor damage. These include large safety factors because there is no need for high' currents in the normal temperature measurement applica-

) tions.

Now that sensor testing by internal heating is an important con-  ;

1 sideration, several sensor manufacturers have re-examined the question of maximum allowable cur ents. They agreed to provide their conclusions for use in this report- (See Appendix A). The consensus is that currents needed for sensor testing (up to 80 milliamperes) are acceptable.

Additional evidence that Joule heating needed for sensor testing l

t does not harm the sensor has been obtained at Oak Ridge National Laboratory.

These results are also documented in Appendix A.-

Further experience has been obtained in the EPRI-funded research  !

J program at the University of Tennessee. Sensors.have been subjected to thousands of Joule heating tests with currents:of up to 100 milliamperes

.with no resultant observable change in sensor characteristics.

l 1

- .

.- l t, l i l 22 1 k-1 It is. concluded that heating currents of'up

~

to-80 ma range needed

}

for' effective testing will cause no delet i

erious effects on the sensors.

[~

I

- l e

1 .

d 1 ,

l' i

i 4

.g i

e I

4 i

il e

l t

n 1

d 9

4 J

/

1 4

a d "

1 i

4 i

j_ -i l

j ..

i.-

4

=- 'O- , , , - - e.w,.-.,-, - - -- ,,,.g- , ~ ,p.,, /c,- m., .... ., ._w.g e,--m. - -

23

3. Time Response Characterization of Sensors (See Appendix B for details.)

3.1 General There is considerable confusion about the terms used to charac-terize the response time of sensors. An attempt will be made here to clari-i fy the situation. There are three basic ways to specify sensor dynamics:

A. Response to a Reference Input. In this case, a reference input (s uch as a step or a ramp) is imposed and the resulting output curve is recorded.

This is unambiguous, but the whole response curves must be specified rather than a single concise numerical index.

B. Mathematical Relation. In this case, a mathematical relation such as a transfer function, a differential equation or a response equation may be used. These may be obtained experimentally. As such, they may be viewed

as condensed representations of the same information contained-in the re-sponse curves. Furthermore, once the mathematical relation is known, it can be used to determine the response to any input.

It is well known( ) that the following mathematical relations are valid for giving the response of temperature senaors to temperature changes:

- Transfer function

= (3*1)

T(s) (T s+1) (T 2s+1) . . .

W "

- where O(s) = output- E// L 7 '>l' ,1.

~

\

T(s) = temperature .

This transfer function has an infinite number of poles (denomi-nator terms), but the higher ones have decreasing importance. The transfer-function shown has no numerator terms (zeroes) because experience has shown

}

that they do not occur in typical RTDs used in current PWRs.

24 It is important to note that a measurement of the transfer func-tion is the preferred way to identify sensor dynamics. Once the transfer function is identified experimentally, all essential information is avail-able. The response to any input (such as a temperature transient expected in a postulated accident) can be determined easily and reliably.

- Response to a step change in fluid temperature.

0(t) = a, + ya e~!*1+ae 2  ! 2 + ... (3.2)

Again, an infinite number of terms is required in theory, but the higher terms have a small influence.

- Response to a ramp change in fluid temperature.

0(t) = K [t - (ty+T2 + ...))+ b ye~ !*1 4- b2 e~! 2y ... (3.3) where' K = ramp rate C. Time Constant and Ramp Delay Time. The concept of a time constant (al-so sometimes called a response time) was introduced to permit characteriza-tion of system dynamics with a single numerical index. The standard defini-tion of the time constant is the time required for the response to cover 63.2 percent of its span following a step input (other definitions based on other percentage s are also used sometimes). Figure 3.1 illustrates the ,

concept of a time constant.

Another index is the ramp delay time. It is the time displace-ment between input and response af ter the curves become parallel during a ramp input (See Figure 3.2).

Both the time constant and the ramp delay time are very useful, -

but they are unambiguous only for certain cases. That is, it is possible

O E U

e I R 1 i T

m T -

N ,

A T

S N

O C

E M

I T

A F

O T

P E

C N

O C

R E 2 L H

3 Jy T 6 1 O

3 T E R

M U GI F

$8e&

. . l 26 I

s Time Delay 8

B E

E E

N

(

Temperature Ramp Measurement Error Measured Temperature t

l l

Time  !

l FIGURE 3.2. ILLUSTRATION OF A RAMP RESPONSE AND THE RAMP TIME DELAY.

I

27 to have two systems wit's different dynamic characteristics, but identical time constants (See Figure 3.3).

The time constant is a unique index in the special case of a first order system (only the term involving ry is significant 2.c Equation 3.1, Equation 3.2 or Equation 3.3). In that case, there is only one re-sponse for a system characterized by a certain time constant. Furthermore, the time constant and the ramp delay time are numerically identical. (See Appendix B.)

For a higher order system (terms involving'ty, T3, etc. are sig-nificant as well as the tern. involving Ty in Equations 3.1, 3.2, and 3.3) it is still possible to use the concept of a time constant or a rap delay time, but it is not unambiguous as in the case of a first order system.

That is, two systems can reach 63.2 percent of cheir final value at the same time, but have different dynamic characteristics (See Figure 3.3). Figure

.,.3 also illustrates a common feature of real sensors that is not observed with a first order system. That is the S shaped curve (derivative equal to zero at the initial time).

The time constant and ramp delay time are useful to characterize even sensors with higher order dynamics in apite of the ambiguity. Formulas have been derived ( ) to relate the overall time constant to the T in Equa-ticas 3.1, 3.2 and 3.3. These t are usually called modal time constants.

The m$dal time constants are related to the overall time constant, t, and the ranp delay time, D, as folloss:

T = ry [1 - in (1 T2/T1) - In (1 *3/ty) ...] (3.4)

D=ty+T2+T3 + ... (3.5)

While t and D are numerically equal for first order systems, they are

i 10- -

[

C R O.632- --------

lC a l I

i y 1

1 1

1 I

I i

1 I

7 Time FIGUFa.3.3. TWO RESPONSES WITH IDENTICAL TIME CONSTANTS

~

30 i

8-R 7-w a Note: The step response time y constant is always greater p than thejtime delay, a 6- ra aj E

$ Note: A typical value for te/7 3 e is < 0.2. Therefore, the E difference is < 2%

g 5-5 E

O O

y4-i; E

Sj 73 = slowest time constant t 3-aa g ra = fast time constant in a 2 g time constant representation b

2-O Y

i 8 b

o. 1-O I I I I l l 0 .1 .2 .3 .4 .5 .6 Ratio of 7e/73 FIGURE 3.4: RELATION BETWEEN PLUNGE TIME CONSTANT AND RAMP TIME DELAY

. o 31 l

4. Sensor Heat Transfer 4.1 Introduction Theoretical heat transfer analysis has a very important role in developing LCSR data analysis procedures and in determining limitations on accuracy. However, the theory is suitable only for determining how to use data from experiments. Any analysis or correction based entirely on theory is unsuitable because of the impossibility of specifying adequately the geometrical, dimensional and physical property information that would be required. Consequently, this section is devoted to heat transfer theory as a tool for using the information in a LCSR transient.

The approach will be to study a range of sensor configurations in search of correlations (which are independent of geometry, dimensions, or physical properties) that are useful in LCSR data analysis. Exact solu-tions for homogeneous solid cylinders and for homogenous annular cylindrical geometries will be used. Also, finite difference methods will be used for non-homogenous assemblies. The results will reveal the sensor character-istics and environmental conditions that control response time and will pro-vide information needed to improve the accuracy of test results (from ap-proximately twenty-five percent maximum without the improvement to ap-proximately ten percent maximum with the improvement).

4.2 Homogeneous Systems Sensors are not really homogeneous assemblies. They consist of layers of materials with varying heat transfer properties. Nevertheless, homogeneous models provide a useful starting point in analyzing sensor heat transfer.

Many standard references give the equations, boundary conditions and solutions for unsteady state heat transfer in homogeneous cylinders

l 32 (solid'or hollow). The heat conduction equation is: i 2

.!LT(r,t) , . [a2 T(r,t) , l_ aT(r,t)) , g(r,t) (4.1) at Br r 3r oc where T = temperature r = radius t = time a = thermal diffusivity = k/pc k = thermal conductivity p = density c = specific heat capacity Q = heat generation rate.

The solution is specialized to selected geometries and surface conditions by selection of suitable boundary conditions. ,

4.2.1 Solid Cylinders The proper boundary conditions for a solid cylinder are:

T(0,t)y= (4.2) kff (R,t) = h (T(R,t) - 0(t)) (4.3) where K = outer radius h = film heat transfer ccefficient A = heat transfer area 0 = bulk fluid temperature The second boundary condition is called Newton's law of cooling. The solu-tion of Equation 4.1 for a step change in 0 with these boundary conditions is:

2 T(r,t) - T(r.=) , g ,-(An ") (4.4)

T(r,0) - T(r,=) - n n=1

33 where 2 J7(M )J,(M r/R)

K =- (4.5) n [J (M ) + J (M )]

s Mn =ARn AR J (A R)

~

• J (A R) k J,,Jy = Bessel functions There are several key points to note:

a. The response is an infinite sum of exponentials

b. The exponential coefficients depend on the solution of a trans-cendental equation (Equation (4.6)) . The A that cause validity of Equa-tion (4.6) are called eigenvalues. The model time constants, T , are inversely proportional to At.

hR This very important

c. The quantity, p , appears in Equation 4.6.

parameter is called the Biot Modulus, NBi. It represents the ratio of internal heat transfer resistance to surface heat transfer rasistance. It will prove to be a very important item in developing LCSR theory and in understanding sensor behavior.

The eigenvalues (values of A that cause the equality in Equation (4.6) to be valid) may be found by a graphical procedure. The procedure requires specification of the following information about the sensor:

- outer radius

- Biot modulus A plot with separate curves for the lef t hand side (N A vs. A) and for the J (AR)- Bi right hand side (J (AR) Ns. T) w 11 h e 6 tersections at values of A that satisfy Equation 4.6. A plot of this type is shown in Figure 4.1. 'From

34 14 --

12- -

10- -

Ns, = 0.5 B- -

Na, = 1.0 6- -

4- -

2- -

C C 6

- 6 , . . .

,e ,- O .

.m 3 .

1 2 4 5 6 7 8 9 10 11 E AR 6 6 C 2

-B - -

FIGURE 4.1. GRAPHICAL SOLUTION OF EQUATION 4.6 i

i

35 this curve, several properties relative to the eignvalue spacing (which will be useful in subsequent development of LCSR transformation theory) can be determined:

- The smallest Ag (largest T ) is much more sensitive to the Biot modulus than the other A g.

- The value of J (AR)/J y(AR) goes to infinity at values of AR equal to (n + 1/4)w for large, integer values of n. The intersections occur near these values for-large n. Since the exponential terms in the response equation involve A1 , we observe that the modal time constants, t , are inversely related to A1 Therefore Ry an (1 + 1/4)

- The value of J,(AR)/Jy (AR) goes to zero at values of (n - 1/4)w for large integer values of n.

- Since the straight line (with slope 1/NB1) neersects the J o(AR)/J yOR) curve at progressively larger values of the abscissa, the intersections occur nearer the vertical asymptotes at the larger values of AR. This means that the larger values of A are given by y , (1 + 1/4 h i R The rntio of the higher eigenvalues is given by:

T i , (1 + 1.25)

'i + 1 (1 + 0.25)2 This is independent of the Biot modulus.

The response to a step change in heat generation rate is also possible. The results are:

at/R T(r,t) - T(r,0) = L,e n (4.7) n=1

36 where Q,-Q, J,(Ag t)J o(Ag R)

(A R )[Jy (A R) + J, ( A R)]

Q = initial heat generation rate Q,= final heat generation rate The eignvalues (A ) are the same as for the previous case. Consequently, the exponential terms are the same for both cases, but the factors that multiply the exponentials are different.

The modal time constant ratios for different values of Biot Modulus are shown in Table 4.1. It is clear that for a solid cylinder, the eigenvalue ratios increase when the Biot modulus decr.ases (internal heat transfer resistance decreases relative to surface heat transfer re-sistance) . This shows that higher modes are more important wh(n the Biot modulus is large (internal heat transfer resistance dominates over surface heat transfer resistance).

4.2.2 Hollow Cylinders The heat conduction equation (Equation 4.1) applies for hollow cylinders as well as solid cylinders. Also, the Newton's law of cooling boundary condition at the surface (Equation 4.3) is still applicable. The i

other boundary condition must be changed. A suitable choice is to assume that there is no heat transfer at the inner radius. This means that the surface is insulated or that the material across the inner boundary has no heat capacity. In this case, the boundary condition becomes:

3T(R y,t) at

= 0. (4.9)

As for the solid cylinders, the response to a fluid temperature step or an internal heat generation step is a sum of exponentials. As

l

, . l 37

.r'

~ TABLE 4.1 EFFECT OF THE BIOT MODULUS ON THE MODAL TIME CONSTANTS Biot Modulus T

2!*1 i

.4 21.69 4 il 10.49 3 i

! 2 7.18 i

d

< 5 5.64 4

i E 10 5.34 20 5.28 d

.i.

4 s

I i

C 4

N

'I  !

a .,c e

h i r e

J k

w g ye- =

g n.' ~ - ,

38 I

before, the exponentials are the same for both types of coefficients, but '

i i the factors that multiply the exponentials differ. The solutions are given in reference (12).

4.3 Multi-Layer Modal Models Transient heat transfer models may also be constructed using a  ;

finite difference approach. Dynamic energy balances may be written over each section. This method gives results that approach the exact solution as the number of sections increases. For a one-dimensional case, the equa-tion for the temperature of the ib node is:

dT y y y .

~

i+1} + ki

~ ~

(MC)f.de "R1,1-1 i-1 i R 1,1+1 (i

where Tg = average temperature in the ith section R

_f

= heat transfer resistance between section i and section 1-1 M y= mass in section i Cg = specific heat capacity of material in section i

= heat generation rate in section i The advantage of a model of this type is that it is easy to simu-late non-homogeneous syscems. The variations in heat transfer charac-teristics in different regions shows up in the model in values for the resistances which differ in different equations in the set.

The cierall model for the sensor consists of a set of coupled, linear differential equations. The solution for the temperature response in the ib section is: M OL A #6

'f%t f a !*s . 140 fk 5 an k 's f%l @

Tg (t) = a01 + age1At+a 21 e2X t + ... );3 njw f ,

tf If the model involves a equations, there will be n exponential terms in

39 the response equation. Note that the response equation for each section contains the same exponentials, but the coefficients that apply for dif-ferent sections are different. Also, note that the solution is a sum of exponentials, just like for the analytical approach in the previous section.

The eouations may be solved to give the time responses of interest or they may be solved to give the Ag . The approach used(l ) was to solve the finite difference equations for homogeneous systems as a first step.

Comparisons with analytical results confirmed that the coefficients were being cr.lculated correctly and that a sufficie c number of sections was being used. Subsequently, the coefficients were re-formulated to approxi-mate the multi-layer structure of typical commercial sensors and simulations were performed.

4.4 Results of Simulation Studies A large number of simulations was performed to find general cor-relations of potential use in interpreting sensor response tests. One question that was considered is, "Is it possible to find a correlation that permits estimation of higher mode effects when only the first few dominant modal time constants are knowni Particularly, can one use a knowledge ofy t and 2T t estimate the influence of T3, t4, etc. on the sensor response?

The atnroach is to define an approximate time constant t(N) based on N edes. For example:

T(1) = t y T(2) = ty(1 - in(1 - T2 /T1))

t(3) = ty(1 - In(1 - T 2/ *1) - in(1 - T3 /Ty))

Note the t(=) is the true thne constant (infinite number of modes) .

It was found that t(=)/t(2) correlates uniquely with T2/T1 regard-less of sensor geometry, size or materials. The basis for this may be i

i

. . l l

40 reasoned as follows:

- The ratio of r /*1 2 e rrelates uniquely with the Biot modulus

- The Biot modulus completely defines the required sensor heat transfer informat(on

- The availability of the required sensor heat transfer infrarmation allows assessment of higher mode contributions.

The correlation appears in Figure 4.2. It shows results for homogeneous solid cylinders, hemogeneous annular cylinders, and inhomogeneous (multi-layer) assemblies. Clearly, they all follon the same correlation.

t l

l

1.20 -- Y ~ ' ~

~_ l] N vJ) Y' ' e*

p yL sf i /AJ'- It/f - vi 7 A> a , >- o ~ <.

1.18- - - M G 9

• • e g 1.16-- 1 lA r's ic de ve fsju ) ,,' , y

' l96O / /// 7 ' # Fifth Order Polynomial Fit O 1 14 } (~ / , ,,' / ) f'" / g e w g" 1.1 E +-

• . a a

W is ,

• W N 1.10-- *^

A

• • ^

u. b 8 . A Multi-Node 5 1.08--

e

. e Analytical E

I5 a u 1.06- -

a 4 M"k p3y- N e .

1.04 -- ,

^ ' "' '+ ~ t ' 'H i !L v o IH fs v A,/A, a

• ' #'# # - "#

• I- 3 8 1.02 - -

7 ao t /r, = (# /z .3o)*: o,f cf l l l l

, 1.00 l --

l l l _

.025 .050 .075 .100 .125 .150 .175 .200 72 /7 3 FIGURE 4.2. CORRECTION FACTOR FOR CYLINORICAL SENSOR ASSEMBLIES.

m = - . .

. s. l 42 i

5. Loop Current Step Response Theory 5.1 Derivation of the Loop Current Step Response Transformation l The loop current step response transformation provides a means to determine the. response to a fluid temperature change from information extracted from a loop current step response transient. The transformation provides the sensor transfer function. Consequently, it enables one to determine the response of the sensor output to any fluid temperature dis-turbance. In addition the time constant or the ramp delay time may be de-termined.

The mathematical details of the development of the transformation are given in Appendix C. The key points to understand about the basis for the transformation are:

- No physical property information or dimensions are required to implement the transformation. All information needed in the transformation is con-tained in the loop current step response transient data.

- The validity of the mathematical model used in the analysis is assured.

The deriviation depends only on the form of the model. The form assumed is I

based on a model developed by performing dynamic energy balances on a series of adjacent slices to represent the sensor. The LCSX transformation theory doca not require a specification of the number of sections or the coef-ficients. The model used in the theory can then be said to be free of any restrictions that limit the validity of the transformation.

Two assumptions are made about sensor geometry.

A. The heat transfer is one dimensional B. There is insignificant heat capacity between the sensing element and the center line of the sensor.

The implications of these assumptions are important in assessing

43 the validity of sensor response time evaluation by' loop current step re-sponse testing. The effects of imperfectly satisfying the assumptions have been evaluated theoretically and experimentally. These topics are dis-cussed in Chapters 9 and 10 of this report.

Analysis based on the model-and the two required assumptions gives the following results (See Appendix C for details):

- LCSR transient.

x(t) = a +ae g 1+ae 2

+ ... (5.1)

- Sensor transfer function 60(s) , 1 (5.2) 60(s) (r ys + 1)(r 28 + 1)***

where 60 = sensor output variation 60 = fluid temperature variation

- Sensor response to a step change in fluid temperature 60(t) = b +be y 1+be 2

+ 1 ... (5.3) where b t = f(3g) f ( 7,, n , g ,.., )

The noteworthy aspect of these results is that the r are necessary and f

! sufficient to specify the sensor transfer function. Furthermore, the same r{ determine the LCSR transient and the response to a fluid temperature-perturbation. Consequently, identification of the r from the LCSR tran-sient provides all of the information needed to determine the sensor's re-sponse to fluid temperature changes. The result for a step change in fluid temperature given above is one example.

The steps in a LCSR test and analysis program are:

44 A. Measure the time varying resistance following a step change in Joule heating of the sensor.

L Identify the T byg analyzing the LCSR transient.

C. Use the i to identify the sensor's response to fluid temperature changes. Identification may provide any of the following:

- transfer function (sensor output / fluid temperature changes)

- response vs. time for a fluid temperature step change

- response vs. time for a fluid temperature ramp change

- time constant (time required to reach 63.2 percent of the final

-output following a fluid temperature step)

- ramp time delay.

This list illustrates the completeness of the information from a LCSR test and analysis. The usual desired quantity is the Mme constant, but much more information is available if desired.

5.2 Correction Factors It has been shown that the sensor response can be specified if all o# the.tg are identified. For example, the time constant can be evaluated from the T using i=T g [1 - In(1 - T 2/ *l) - In (1 - T3/ty) ...] (5.4)

The contribution of the term involving Tg gets smaller as i gets larger.

Nevertheless, a good determination of T may require a number of Tg. In analysis of practical data sets, it is possible to identify only two, or possibly three, t from g a LCSR transient. If the additional, unmeasureable

~

T contribute a significant fraction to the total response, then the time constant based on two or three terms will be too small.

The results of the theoretical studies may be used to develop correction factors that account for the important modes (terms containing

.. ._ l l

i 45 l l

1 the exponential factors) that cannot be identified from practical LCSR data. l The relation between the modal time constan .T , and the overall time con-stant, t, was given in Equation 5.4.

This is rewritten as follows:

t- T 7 [1 + +C2 + ...] (5.5) where C1 = - in(1 - Tg/ty) (5.6)

The true time constant (based on an infinite number of terms) is r=1 1 [1 + 1 25c]1 (5.7)

The approximate time constant (based on a finite number of terms, N)' is N

T(N) = t [1+ d2 C] g (5.8)

A correction factor is defined as:

Correction Factor = F =

"" * " "" "" = *(*

N Time constant based on N terms T(N)

If two modal time constants (Ty and T2) can be identified experi-mentally, then the appropriate correction factor is F . The theoretical 2

studies show that a measurement of T /T provides all of the information 2 1 required to give F 2. This very important correlation appears in Figure 4.2.

Note that F varies from 1.0 to 1.2. It should be noted that the correla-2 tion is based on simulations that include a wide range of geometries, dimensions and physical properties. The striking feature is that the cor-relation is independent of these properties. The procedure for determining the time constant is:

- perform a LCSR test

- identify Ty and T fr a the test data 2

- evaluate T(2) based on yt and r 2 I I

l

j 46 l

- determine F2 fr a the measured T2/Tl

- evaluate the true-time constant T = F2 T(2).

The validity of this approach is confirmed experimentally in Chapter 10.

Other correction factors besides F2 are sometimes useful. Par-ticularly, F may 1

be required in cases where experimental conditions make it imposaible to identify T2 In this case, Ty is the only available modal time constant and it may be inadequate to evaluate the overall time con-stant. In this case, it is not possible to evaluate the higher mode con-tributions without know1ng the Biot modalus. Since the Biot modulus is just as poorly known as the time constant that is being measured, it is not possible to specify a proper value to use in order to give F y. However, we can use F to set an upper limit on T. The theoretical studies show that the maximum value for yF is 1.4. Since T = F T the maximum possible T is 1.4T .

. a 47

6. The Self Hear' . rest l The heat transfer resistance affects two measurable quantities following a change in internal heating: the rate of temperature change and the magnitude of the resulting steady state temperature change. The heat capacity affects only the rate of change. Consequently, a change in heat transfer resistance (and a concomittant change in time constant) may be detected by measuring the magnitude of the temperature change per unit of power dissipated in the filament. Since the temperature change in an RID is proportional to its change in resistance, the measurement may also in-volve determination in the steady state change in resistance per unit of power (typics11y ohms / watt). This index, which is called the self-heating index, is easily measureable. Its suitability for detecting changes in response characteristics is demonstrated in Chapters 10 and 11.

l l

l

48

7. Equipment Several options are available for the test equipment needed in a loop current step response test. The instrument should permit switching from one constant power condition to another constant power con /.ition while simultaneously providing a measurement of the time-varying resistance.

Bridge-type instruments are well suited for this. The bridge may be run using a constant voltage source or a constant current source. Also, a simple voltage measurement on a resistance element being heated by a con-stant current may be used. These are considered below.

7.1 Constant Current Source With Voltage Measurement Across the Resistance In this case, the equipment involves the simple circuit shown in Figure 7.1. Tte resistance changes because of Joule heating and this af-fects the voltage measurement. The voltage drop increases linearily as the resistance increases and the power also increases linearily as the resis-tance inc ases. Therefore, if the resistance changes significantly, the constant power assumption used in the development of LCSR theory is not valid. This can be overcome, but at the expense of a more complicated analysis procedure.

7.2 Bridge, Constant Voltage The voltage drop, V, across the arms of a Wheatstone bridge with applied voltage E is (See Figure 7.2):

)

(RRT V = (g +D (7.1)

Rd }(~1d+1RTD} E If the bridge is initially balanecd, then R ~

RTD d and 1 6R Ry+Rd(1+ d+ }

V S

l ---+

[ -

R FIGURE 7.1. CIRCUlT FOR LCSR TESTING

50 Switch E

& I i R3 R3 Rd V

R3 p

ATO 1

FIGURE 7.2. WHEATSTONE BRIDGE FOR LCSR TESTING l

l'

1 I

51 l

he power dissipated in the RTD is E (Rd + 6R)

P= 2 (7.4)

(Ry+Rd+

The relation between resistance change and measured voltage is 6R =

(R7+R) d

(*

9 PRE 1 y L1+ d J 1

The relation between V and 6R is nonlinear, but, if 6R is small compared to g + R d, then assuming linearity is satisfactory. -Typical values for 6R are two to ten ohms and R s 200 to 500 o b . Ry may be chosen large d

enough to ensure adequate linearity, but 100 to 500 ohms is generally satisfactory.

-2.

For a bridge with constant voltage, the power changes when the resistance changes. For typical cases where 6R is small compared to Ry and R , ee ec s saa . cases are enc un ere w ere s sig-d nificant compared to Ry and R , then the analysis procedure may be modified d

to account for the varying power 4

7.3 Bridge, Constant Current In this case, the relation between voltage measured and resistance change is R1 1

~ * (7.6) 2Ry + 2Rd + 6R t

The power dissipated in the sensor is (1+ d I (Rd + 6R) (7*7) 3 2(g + Rd ) + R L -

The linearity of V vs. 6R and the effect of resistance change on power are similar to the previous results for a constant voltage bridge.  ;

l i

4

- . w , . - . - - - ,- - -- ..

1

-52

~

-7.4 Conclusions Concerning Equipment j l

The equipment is simple and its operation is fully understood.

Equipment design or data processing features may be specified so as to ensure adcquacy of the data collected by the instrumentation.

t 1

i 4

(

e d

(

l 4

8 4

i k

1 1

g - . . - - - - ,-. ,

53

8. Typical Test and Analysis Procedures 8.1 Performing a LCSR Test The loop current step response is performed as follows:

a. ' connect a lead from each side of the resistance element to the test equipment. The additional leads used in multiple wire sensors are not needed since the absolute temperature is not measured.

b. set the bridge to the low voltage condition. The voltage is selected to give a sensor current of 1 to 4 ma so as to cause negligible Joule heating.

c. balanca the bridge by adjusting the variable resistor so as to give a zero voltage drop, V, across the arms of the bridge.

d. Switch to the high voltage condition. The voltage is selected to give 25 to 75 ma through the sensor. For a 400 ohm sensor this gives 0.25 to 2.25 watts. This causes a resistance chant;e of 2 to 20 ohms in typical PWR sensors. The temperature increase is 3 to 30'C. A typical transient is shown in Figure 8.1.

It is also possible to use the data obtained upon switching from high voltage to low voltage. However, the measured signal is smaller and the signal-to-noise ratio is lower. Consequently, the preferred test involves a transition from Jwe voltage to high voltage.

Appendix D gives a detailed test procedure.

8.2 Analyzing LCSR Data The data analysis procedure discussed in Section 5.1 requires the identification of exponential coefficients from step response data.

This may be done graphically using well-known exponential peeling tech-niques or it may be done using a computer fit. The fit is usually based on a least squares principle that finds the coefficients in a sum of ex-ponentials that give the best fit to the data.

E 0

-_ 2 8

1 A

- T A

D E

6 S N

l 1

O P

S E

R

. l 4 P 1 E

-_- T S

- T N

_ E l

2 R 1 R

) U s C d

n P o O

0 ce O 1

(

s L e Y R

im T

O T

A I

8 R O

B A

L L

l 6 A C

I P

Y T

1 l

4 8 E

R U

GI F

l 2

. . . . . O

}Ca g!t.e3mEoSog 2

o

55 8.2.1 Graphical Analysis The function has the form X(t) = ga +ae

_t/ty + a "_t/r2 + *** (0*1) y 2 Since a = X(=), we may write

_t/T y _t/t 2 X(=)-X(t) = - a ge -ae 2

e ... (8.2)

If Ty > r 2, then higher terms (t for i > 1) hree a small influence relative to the t term as time increases. If one waiis until the higher terms are negligible,-then X(=)-7(t) 1 - aye" . (8.3)

In this portion of the data, a sem?-logari;hmic plot of X(=)-X(t) is a straight line and 1 is the slope. The intercept of this line at t = 0 1

gives the value of a y.

The identification of the second exponential involves using the identified ay and t y-to construct a modified data set:

_t/t y _t/r2 + a3 e t/*3 + ...

y(t) = X(t)-X(=) - a ye =aey (8.4)

The same procedure may be applied to find 2T that was used to find t y.

In principle, this could go on until a large number of I were identified. In practice, the small influence ri the higher terms and the limited accuracy of actual test data restrict the graphical analysis to identification of one or two T 1

An example of a graphical analysis of laboratory data is shown in Figure 8.2

56 l

l 1.0 --

.,e LCSR Raw Data c FirstOrderFit Data Remaining after Subtracting the First Order .

Fit from the Data .,

! O.1 - -

g .. .,

g ..

1 ..

y Fit to tne Remaining Data 0.01 l l l l l l l

.08 .16 .24 . 3 12 .40 .48 .56 Timeiseconds)

FIGURE 8 2. GRAPHICAL EXPONENTIAL STRIPPING l

1

57 8.2.2 Computer Analysis Numerous algorithms are availahly for identifying exponential coefficients from data records. Most involve minimization of the error

.between the data and the equation prediction of the response:

2 E=gy j cf (8.5)

_t/t y _tg/T2 e = X(t ) - a -a l " ~ "2 e ... (8.6) where

.E = error N = number of samples The identification involves finding the parameters (ag and r ) that minimize 1

E. Experience has shown that two gT can usually be identified using com-puter fitting methods.

Results of a computer fit are shown in Figure 8.3. The figure shows the raw LCSR data, the fitted curve and the predicted response to a step change in fluid temperature as determined from the identified trans-fer function. It is seen that the fit is indistinguishable from the raw data. This is typical of LCSR analysis results.

8.3 The Self-Heating Test In a self heating test, the sensor is connected to the test j equipment as for the LCSR test. The steps are as follows:

a. Set the applied voltage to obtain a low current (typically 5 to 10 ma)'through the sensor, b.. Measure the sensor resistance. In a bridge-type instrument, this means adjusting the variable resistor to achieve a voltage drop of zero across the arms of the bridge. I c.. Measure the power (I R) dissipated in the sensor.

10-9- -

8 -

4 LCSR Raw Data and Least Squares Fit

~

m

.e 7--

C 3 4 Predicted Response to a Step Change in Fluid Temperature g 6--

b j 5--

z E 4--

8 a y 3--

2--

1- l O l l l l l l l l l l l 0 3 6 9 12 15 18 21 24 27 30 33 Time (seconds)

FIGURE 8.3. TYPICAL LABORATORY RESULTS FROM A LOOP CURRENT STEP RESPONSE TEST ON A ROSEMOUNT 104 ADA.

59

d. Repeat steps a through c for several different applied voltages (usually ten or more values are measured).

A detailed self heating procedure is included in Appendix D.

8.4 Self Heating Test Analysis l

The self heating data are plotted (steady state changes in resistance vs. power). The plot is a straight line. The slope (ohms / watt) is called the self heating index. The self heating index is proportional to the overall heat transfer resistance for the sensor. Typical laboratory l results appear in Figure 8.4. Self heating index values for typical PRR resistance thermometers are 5 to 10 ohms / watt.

i 221 -

~

m E

r O

Self Heating index = 5.7 ohms / watt ,

o C

220- -

$ 8 9 .

m o

E 219  ;  ;  ;  ;  ;  :

0 100 200 300 400 500 600 700 Power (milliwatts) ,

1 FIGURE 8.4. SELF HEATING CURVE FOR ROSEMOUNT RTD i

I l

l l  !

I

61

9. Accuracy Limitations The accuracy of the results of a loop current step response test depends on the significance of two types of errors:

Mathematical errors _- Those errors due to violation of the conditions for validity of LCSR transformation' theory.

Measurement errors - Those errors due to measurement conditions that prevent accurate identification of all of the exponential coefficients (t ) that are needed to permit accurate specification of sensor dynamics.

These errors are assessed below.

9.1 Mathematical errors The LCSR transformation depends on the absence of zeroes in the transfer function for the sensor. This is guaranteed (See Appendix C) if the following two essential assumptions of LCSR transformation theory are satisfied:

1. insignificant branching in the heat transfer path between the sensing filament and the fluid.

2. insignificant heat capacity between the sensing filament and the sensor center line.

Analysis shows(13) that the presence of zeroes that would occur if these -

e,rrak E assumptions were violated causes the7 response to be slower than the true ,~

1 value. Consequently, if these assumptions are violated, the results are conservative and there is no possibility of failing to detect an unsafe ,'

condition because of mathematical errors.

9.2 Measurement errors Measurement errors have to do with the test conditions that limit the amount of necessary information that can be extracted from the data, in an ideal test, the LCSR transient will obey the following type l

i l

62 s

aof equation:

X(t) = a, + a ge_t/T1 +2 a '_t/T2 t/*3

+

+ "3" *** ( )

? Experimental and data handling problems that limit the accuracy of the identification of the t are:

- noise (either due to electrical pick-up or process fluctuations)

I

- drift in the process-

-- finite resolution in the sampling of the data and in the digital computa-

' tions.

The noise problem can be overcome by using large heating currents or by averaging multiple data sets. In some power plants, adequate signal-to-noise ratios have been obtained with moderate heating currents (50 ma) .

In others, the noise was too high to overcome with safe heating currents so averaging was used.

Drif t is easily removed by identifying the drif t rate and sub-tracting it from the data before analysis.

The finite resolution in data sampling and computer calculations is unavoidable. This effect-usually limits-the analysis to identification of two modes (T y and t2). These alone are inadequate to specify the com-plete response for some sensors. However, the identification of Ty and t 2 has been shown to reveal all of the information required about sensor heat transfer and permits evaluation of the contributions of T3' T4' *E** (8**

Section 5.2 for details).

.Further assessment of the validity of the method must rely on testa performed :ader conditions when the response can be measured directly and compared with the prediction. This is reported in Chapter 10.

i f

i

63-

10. Laboratory Testing Laboratory tests were performed to check the validity of the test procedures. These were performed by University of Tennessee personnel in .

two different laboratories: the Thermometry Laboratory in the Nuclear Engi-neering Department at the University cf Tennessee and the RTD test facility at the Renardieres facility of Electricite de France in France. In each laboratory, it was possible to perform the tests developed for use in a power reactor and to perform a direct response time measurement for the l

RID under the'same conditions (ambient tenperature, flow, pressure) . Com-parison then showed the adequacy of LCSR testing and analysis.

4 10.1 Description of Facilities 10.1.1 University of Tennessee Thermometry Laboratory The tests at the Thermometry Laboratory at the University of Tennessee were performed in a rotating tank of water. The radial position where e velocity of three feet per second occurs was found and used for the tests. For LCSR or self heating tests, the sensor was mounted vertical-ly with an insertion depth of about six inches. For direct response time measurements, the following procedure was used:

1. Mount the RTD vertically on the shaft of a pneumatic cylinder positioned such that the stroke of the shaft carries.the sensor from air down into the flowing water.

2. Place a container of ice water under the RTD. The container had a thin membrane at the bottom. j

3. Actuate the solenoid to move the cylinder down (penetrating the membrane).

4. Record the sensor resistance and a timing signal that marks the entrance of the RTD into the water.

l

65 TABLE 10.1 RESULTS OF LCSR AND PLUNGE TESTING IN THE UNIVERSITY OF TENNESSEE THERMOMETRY LABORATORY LCSR Estimate of Time Constant Without Higher With Higher-Plunge Time Mode Correction Mode Correction Percent Sensor Constant (Sec.). of Section 5.2 of Section 5.2 Error Rosemount 176KF 0.38 0.39 0.41 + 7.9 J

Rosemount 104ADA 3.1 2.9 3.1 0 (without thermowel'.) -

Rosemount 104ADA 7.1 5.9 7.2 + 1.4 (with thermowell)

Rosemount 104VC 2.3 1.7 2.1 - 8.7 (without thermowell)

Rosemount 104VC 5.3 4.5~ 5.5 + 3.8 (with thermowell)

Rosermunt 177CY 5.8 5.1 6.2 + 6.9 Rosemount 177GY 6.1 5.2 6.3 + 3.3

.L Sostman 8606 2.0 1.7 2.1 + 5.0 I

1 66

' TABLE 10.2 RESULTS OF LCSR AND INJECTION TESTING IN THE EDF FACILITY LCSR Estimate of Time Constant Time Constant Without Higher With Higher from Injection Test Mode Correction- Mode Correction Percent Serar r (Sec.) of Section 5.2 of Section 5.2 Error Rosemount 176KF 0.14- 0.11 0.13 - 7.1 Rosemount 177HW 8.8 7.0 8.4 - 4.5 (with thernowell)-

Rosemount 104 6.2 4.9 5.9- - 4.8 (with therm well with air in gap)

Rosemount 104 4.1 3.3 3.7 -9.8 (with thermowell with NEVER-SEEZ) 2 I

i l

l 67 )

flowing at three feet per second. The main purposes of the tests were to develop testing proc 9dures and to determine the sensitivity of the measured self-heating index to changes in the sensor's response characteristics.

Typical self-heating test results appear in Figure 8.4.

l The sensitivity of the self-heating index to changes in response characteristics was evaluated using sensors with artifically degraded heat transfer. This involved application of insulat?,; material (plastic tape or rubber tubing) to the surface of the sensor. lar each different applica-tion of insulator, self-heating tests and plunge n ats were performed.

Typical results are shown in Figure 10.1. The sensitivity of the self-heating index to changes in time constant were evaluated around the sensor's normal, unmodified condition. Tests on two different sensor designs showed that a nne percent change in the self-heating index indicates about a 0.2 percent change in time constant.( }

-l

\

68 24 - -

22 - -

20 - -

g 18- -

16- -

O g 14- -

2 .O E

5 12- -

E O -

O c) 10- -

.E w

8- -

e 6- - -

4- -

g. .

O  :  ;  :  :

5 6 7 8 9 Self Heating Index(ohms / watt) 1 i

l FIGURE 10.1. Lo7 ORATORY RESULTS FOR RELATION BETWEEN THE TIME CONSTANT AND THE SELF-HEATING INDEX.

i i

. o 1

69  ;

1

! 11. In-Plant Testing 11.1 University of. Tennessee Program Tests were performed on three pressurized water reactors as part of the University of Tennessee research program.( ' } Tests were performed on control system RIDS rather than safety system RTDs. The main purposes of the tests were to establish suitable test procedures and to determine wheth-er plant conditions (such as background noise, process temperature fluctua-tions, etc.) interferred excessively with the testing. Measurements were made at Turkey Point (a Westinghouse plant), at St. Lucie (a Combustion Engineering plant) and at Oconee (a Babcock and Wilcox plant).

The program included self-heating tests and loop current step re-sponse tests. Typical self heating test results appear in Figures 11.1 through 11.3. The expected linear relation between resistance change and power is evident and the scatter is quite small. Consequently, it is con-cluded that self-heating tests are feasible in operating plants.

LCSR tests were also performed and rypical raw data traces ap-pear in Figures 11.4 through 11.6. The results from St. Lucie and Oconee tests are very similar to results obtained in the laboratory. The curves were smooth and repeatable and analysis was accomplished without difficulty.

The Turkey Point results were quite different than typical labora-tory data. The data had fluctuations due to fluctuations in the process temperature that interferred with effective analysis of the data. The problem occurred because only a small heating current was used (20 ma) and the sensor is very responsive to process temperature fluctuations because of its fast response. Subsequent tests on the same type of sensor in an-i other Westinghouse plant showed that the problem could be overcome readily i i I with a larger heating current and averaging - (See Section 11.3) .

w v

439--

E E 438- -

5

- e g Self Heating index = 5.2 ohms / watt 8

.M_

E 437- - g E

436  :  :  ;  ;  ;  ;  ;

O 100 200 300 400 500 600 700 Power (milliwatts)

FIGURE 11.1. TYPICAL SELF HEATING RESULTS FROM TURKEY POINT TESTS (Rosemount 176KF)

6 417 "

m r

E 416-2 m

E Self Heating Index = 6.4 ohms / watts B -

.m

@ 415- - .

a- -

y 414  :  :  :  ;  ;  ;  ;

C 100 200 300 400 500 600 700 Power (milliwatts) .

FIGURE 11.2. TYPICAL SELF HEATING RESULTS FROM ST. LUCIE TESTS (TE 1125 at 540oF)

E 220 -

219- -

'5i E

E i;

E 218- -

5

$ Self Heating index = 7.9 ohms / watt

$ M 217- -

• 216  ;  ;  ;  ;  ;  ;  ;

O 100 200 300 400 500 600 700 Power (milliwatts) 4 FIGURE 11.3. TYPICAL SELF HEATING RESULTS FROM OCONEE TESTS

l .

i LCSR raw data i

7 1

~

-f f _

g-_-

Least Squares Fit to LCSR data g ..

.tf E

t. .

E il c_

S ..

8 E Predicted Response to a Step Change in Fluid Temperature O

E

:  : l l l l  :  :  :

3 6 9 12 15 18 21 24 27 30 Time (seconds)

FIGURE 11.4. TYPICAL RESULTS FROM A LOOP CURRENT STEP RESPONSE TEST ATST.LUCIE NUCLEAR STATION

LCSR Raw Oata and Least Squares Fit g ..

.e 5

g ..

E

.e S

h. < Predicted Response to a Step Change in Fluid Temperature R

K ~

l l  :  ; l l  ;

O 3 6 9 12 15 18 21 24 27 30 Time (seconds)

FIGURE 11.5. TYPICAL RESULTS FROM A LOOP CURRENT RESPONSE TEST 4

AT OCONEE NUCLEAR STATION

I'  !

uv _.

_. l 4

- T

_. _ N I

O P .

Y l

3 E K

R U

T T

A

_ A 1

s T

= d A n

o D c R

_ l 2 e s S

( C e L m L b.

i T A C

I P

Y T

6

• 1 1

l 1 E R

U GI F

__ * . u

~

^m f E t 2 ^h f e E m 8 e E

_ 4 i

76

! 11.2' Test Procedure A standard test procedure was developed based on laboratory amperience and in plant testing experience. It is shown in Appendix D.

i' 11.3 AMS Test Program AMS Corporation has performed five testing programs in three

, pressurized water reactors for utility customers. The plants were Millstone 2, Arkansas Nuclear One-Unit 2, and Farley 1. The test procedures of Ap-pendix D were followed.

Typical self heating test results appear in Figures 11.7 through 11.9. As in the earlier in-plant tests, the data were adequate to define a reliable self-heating curve.

Typical LCSR raw data appear La Figures 11.10 through 11.12. The data from the Combustion Engineering plants (Millstone 2 and Arkansas Nu-clear One - Unit 2) are similar in quality to the earlier tests at St.

Lucia. The curves show some influence of process temperature variations, but they are generally smooth and quite suitable for analysis. The data from Farley are much better than the earlier-data from Turkey Point (both are Westinghouse plants) because a higher heating current was used. The Farley data are not as smooth as the data from the Combustion Engineering plants because the Farley sensor (Rosemount 176KF) is much faster than the sensors used in Combustion Engineering plants (Rosemount 104) and more responsive to process temperature fluctuations. Nevertheless, the Farley data are suitable for analysis. The benefits of averaging several tran-sients to reduce noise effects are illustrated in Figures 11.13 and 11.14.

These may be compared with corresponding individual transients shown in Figures 11.10 and 11.12. The averaged data sets are preferred for analysis.

I

e 420 - ,

419- -

~

m E 418--

^5 I

8 5

h417' Self Heating Index = 7.4 ohms / watt a

416- -

e e

415  :  :  :  :  :

0 100 200 300 400 500 600 700 Power (milliwatts)

FIGURE 11.7. SELF HEATING CURVE FOR MILLSTONE 2 RTD

424 -

m E 423- -

~O E Self Heating Index = 4.7 ohms / watt 8

m M

}422- - 5 E

421  ;  ;  ;  ;  ;  ;  :

0 100 200 300 400 500 600 700 Power (milliwatts)

FIGURE '1.8. SELF HEATING CURVE FOR ARKANSAS NUCLEAR ONE UNIT 2 RTO

452 -

4 451- -

~

m E

E 8

g 450- -

M rn y Self Heating index = 5.7 ohms / watt 0

.449--

448  ;  ;  ;  ;  ;  ; e O 100 200 300 400 500 600 700 Power (milliwatts)

FIGURE 11.9. SELF HEATING CURVE FOR FARLEY 1 RTD

.O

_ v +-_.-_-_ suy<^=^ ;: : _ =w

^ ^

f g ..

.M C

3 t

g ..

.e f

a g ..

E, a

8 m

o E ..

l l l l l l l l  ;

O 5 10 15 20 25 30 35 40 45 50 Time (seconds)

FIGURE 11.10. TYPICAL LCSR DATA AT MILLSTONE 2

~ 7 .. g

~

O' e

t

-W

=a>

W 4 n

y

' - -b 10 1.2 14 1.6 18 2O Time (sec.)

FIGURE 11.12. A TYPICAL LCSR TRANSIENT FROM FARLEY TESTS T

9 59,

_ __ _ . ,_ ,,- m  : = ;_- _=_-:~ _ _ --

=

.e E

D jo ..

.e f

e

!-- 0 R

W E ..

[

0 5 10 15 20 25 30 35 40 Time (seconds)

FIGURE 11.13. TYPICAL DATA SET OBTAINEU BY AVERAGING MULTIPLE TEST RECORDS AT MILLSTONE 2 e

~ _____

____.,w = =_-::- = ' - - : - -- = :- .~ -- . = - _

t

'E a

t .. .

2

.e O <

L

'1

} I m ..

m C

O a

m co e o~

E i c

O

-9 w 1 .

C I e ,

tn >

i A e a a R I e I A A 3

y I 3 5 m = u 3 3 0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8 2.0 Time (Sec.)

FIGURE 11.14. A TYPICAL AVERAGED LCSR TRANSIENT

- FROM FARLEY TESTS

85 11.4 Millstone 2 Tes?s The reference plant for this report is Millstone 2. Consequently, l the detailed results will be presented for tests on that plant. ,

l 11.4.1 First Test Program  !

The first test program was performed by AMS Corporation in December, 1977. Northeast Utilities contracted for these tests in order to evaluate the test procedure as a method for subsequent tests to be per-formed for compliance with Regulatory Guide 1.118. The procedure of Ap-pendix D was used to test sixteen safety system sensors.

Results of a typical self heating test performed in 1977 appear in Figure 11.15. Self heating index results for all sensors tested appear in Table 11.1. For comparison, laboratory values for the self heating index for other similar RTDs (with thermowell) varied from 6.1 to 8.8 ohma per t watt.

Typical LCSR raw data from 1977 appear in Figure 11.16. Analysis results appear in Table 11.1. These analyses were performed before the correction factors (Section 5.2) had been developed to accoi t for unde-tectable modes in the transient. Consequently, the results in Table 11.1 have a bias that causes the estimates to be low by as much as twenty per-cent.

11.4.2 Second Test Program i

The Millstone 2 sensors were tested a second time in December 1978. The test procedures were the same as for the first Millstone 2 test.

The analysis was modified because of the development of the correction factors to correct for higher mode contributions. Consequently, two sets of LCSR results are of interest: the uncorrected values for comparison with the first tests and the corrected values for giving the best estimates of sensor behavior.

t 1

i 419 -

~

m E 418- -

o .

E Self Heating Index = 5.5 ohms / watt E  ?

B

.e E'417- -

E 416  :  :  :  :  :

0 100 200 300 400 500 .600 700 Power (milliwatts)

FIGURE 11.15. SELF HEATING CURVE FOR MILLSTONE 2 RTD

• y,y. - - w--- -4w --

e3s- -.->- -,,,,m 9% , - m,- -- - --%% 7 -y y ,- ._,r_

1 87 MrYJ hs Tefobe f Table 11.1 l Comparison of Response Time Test Results at Millstone 2*

Tests of August 1977 Tests of December 1978

. Time Constant Self Heating Time Constant Self Heating Sensor S/N (sec) Index (ohns/ watt) (sec) Index (ohms / watt)

A7770 3.2 5.6 5.2 7.4 A7765 2.8 4.5 3.2 4.8 75313 4.7 6.2 5.6 6.5 A7774 3.8 5.8 4.3 6.2 4 2456 - ** - ** 5.3 7.5 2455 ** ** 4.5 6.4 2454 ** - ** 4.7 7.5 2453 ** - ** 4.5 5.2 75294 3.7 6.0 4.4 6.4 75299 5.5 8.6 9.3 9.1 75310 4.6 6.2 4.9 6.5 75300 4.6 6.5 4.7 6.5 75297 3.6 4.7 3.6 4.9 80364 4.0 5.6 4.4 6.1 75309 4.0 5.5 4.7 5.8 A7769 3.1 4.8 3.6 5.0

• Since the correction factor had not been developed at the time of the August 1977 measurements, 111 t Se constants shown here are uncorrected values.

• • These sensors were not included in August 1977 measurements.

thk : us.:j ek k n G a L .! ,, .h /f /Arg ; )s

,l as ,y s & u'.-s Jy a 1 ) nd a 4~ re ,a<J / af,4ed ]

p~ ,,, , . a J.

9 u , v .u .

f a s i

l l

1 i

I l

l

,s -

,- a4 s r.-, ,s y 1.. - - u. ,- w 1.

1

~ - -

• 6"6* - _ .N eh am.._

. -e jmspa"" "! .~ ~ '

y f

-,[

s.

'^--

'T.

__ _ J_

~ ~ ~ ~

N 2'I N .I 23 U l_ 5 -Y "

l

/ . if  :- .

5- :z 1  ?: .- ?- __

= E '= = -

s l

g

'I , .^' ~

'~

.~ _ _

~'

h r.__ _ _

/ __

.__ q_... . _ ._7__.___ _ _

_ ____) ,

_i_ _t._

_g_

. .L. _ _ _ l

_r _L g! . _,_m. '

i

. ._Lt__ ___ ___

___.L . :. , ! . i FIGURE 11.16. LCSR TEST TRANSIENT OF MILLSTONE 2 RTD.

BRIDGE BALANCED AT LOW CURRENT.

e 4

89 A typical self heating curve from the 1978 test appears in Figure 11.7. Table 11.1 shows self-heating index results along with comparable results from the first test.

Figure 11.17 shows a typical LCSR transient along with the fit 1

and the predicted respom.e to a step change in fluid temperature. Table 11.2 shows time constant results obtained by analysis of the LCSR data.

The table shows uncorrected values and the final corrected values. The re-sults reveal the following:

- The sensor time constants (uncorrected) increased "oy up to sixty-nine percent between December 1977 and December 1978. The average increase was twenty-one percent.

- The self heating index results revealed the same trends as the time coh-stant measurements. (Sensors had increases in self heating indices that were roughly proportional to the increases in time constants.)

11.5 Conclusions from In-Plant Testing The conclusions that following fr;m the in-plant testing experience are:

a. By selecting an appropriate combination of heating current and number of cases to be averaged, in-plant LCSR. data of comparable quality to laboratory data can be collected.

b. Reliable self-heating data can be collected easily.

c. Self heating data cannot be converted into time constant data using correlations 'obtained from a given sensor design because of de-pendence on construction details. However, the self heating index was found to be a sensitive indicator of changes in response character-istics.

E

E  : Raw Data and Fit t l m

h j: Predicted Response to a Step Change in Fluid Temperature 2

3 m ..

O M $

3 8

,E ..

(D

.m l l l l l l l l l l 0 3 6 9 12 15 18 21 24 27 30 Time (sec.)

FIGURE 11.17. TYPICAL LCSR TRANSIENT AND ANALYSIS RESULTS

. FROM MILLSTONE 2

91 Tsble 13.2 Response Time Test Results for Millstone 2 RTDs (Test of December 1978) 4 Uncorrected

• Corrected ** Self Heating Sensor S/N Time Constant (Sec) Time Constant (sec) Index (ohms / watt)

A7770 5.2 6.2 7.4 A7765 3.2 3.6 4.8 75313 5.6 6.7 6.5 A7774 4.3 5.2 6.2 4 2456 5.3 6.4 7.5 2455 4.5 5.4 6.4 2454 4.7 5.2 7.5 2453 4.5 5.4 5.2 75294 4.4 5.3 6.4 75299 9.3 11.2 9.1 75310 4.9 5.5 6.5 75300 4.7 5.6 6.5 75297 3.6 4.1 4.9 80364 4.4 5.0 6.1 75309 4.7 5.6 5.8

, A7769 3.6 4.3 5.0

• The uncorrected time constants are based on identification of two ex-ponentials in the experimental data. The higher mode correction factor of Section 5.2 was not used for these results.

• • Correction factors ranged from 1.11 to 1.20 for these tests.

1

i

)

l i

92

12. Conclusions Loop current step response testing has been developed thoroughly and is completely adequate for testing resistance thermometers in nuclear i

power reactors. The proof given in this report guarantees its suitability as a substitute test as required in Section C, Item 6 of U.S. Nuclear Regulatory Guide 1.118 (See Section 1.1 of this report for information on the Regulatory Guide).

The proof of adequacy of loop current step response testing has three bases:

- extensive theoretical analysis (Chapters 3, 4 and 5 of this report).

- extensive laboratory testing. In these laboratory tests, it was possible to measure the response of the RTD directly (by plunge testing or injection testing) for comparison with LCSR results. Good agreement was obtained.

- in-plant testing. In-plant tests show that the sethods developed in the laboratory are also suitable for plant testing. The test connections are simple and safe, and require little interference to normal operation. In fact, the desired plant condition for testing is full power operation.

l l

f i

93 Appendix A Effect of Joule Heating on RTDs l

4 4

3 i

1 4

i I

I f

4 9 e

f 94 -

I; Rosemount FIDsEMOUNT INC 12301 WEST 70th STREET / EOEN PRAIRIE, MINNESOTA 55344 Mailing Address: P.O. BOX 35129 / UINNEAPOLIS, AllNNESOTA $$435 ,

TEL: (612) 9415560 TWX: 910-576-3103 TELEX: 29 0183 Nay 21, 1979 a-Professor Tom Kerlin Nuclear Engineering Department University of Tennessee Knoxville, Tennessee 37916

Dear Sir,

i In response to your questions of using the Loop Current Step Response Test method on primary loop temperature sensors furnished to Combustion Engineering, Rosemount finds no problem with applying currents up to 30 millinmps to these sensors.

Currents in excess of this magnitude have been used during testing at Rosemount i

. without damage to the sensor. Recent testing conducted at Rosemount indicates that currents in excess of 300 milliamps with the sensor being at a temperature of 500 F did not cause open elements, h'hilo Rosemount does not have test data available to certify the sensors that have

] been shipped, it's my opinion that this testing will not damage the sensors.

]

Please contact me if I can answer further questions.

Si cerely, faf ' .G&Q lL.E. Anderson Temperature Sensor Design Supervisor LEA:dd-l 4

.g_ , -- -- --

r

f ggjg Y

95 0 23 Elm Avenue L% O '

Hudson. New Hampshire 03051

f. ..}._ .,. . ,~,.j... Tct:(603) 882-5195 TWX:710 228-1882 b

CORRORATIOi a . :?

v.orWi h-? f hM.'

i":ng;Qw we i: *5l&t kmELCW

&'hf$~??!$

May 21, 1979 University of Ten:wasee Dept of Nuclear Encpneering' Knoxville, Tennes me 37916 Attention: Dr. T.W. Karlin Page 1 of 2

Dear Dr. Kerlin:

In response to our telephone conversation on May 17, 1979, concern-ing RrD's for Nuclear Application: RID's are usually designed to meet specific tine response requiresmnts. This is acocarplished, by thermally coupling the sensor as c30sely as possible with the process nedium.

'Ihis allows energy to be transmitted between the sensor and medium as rahidly as possible.' Under these conditions, an intemittant current of 50 - 60 milliamperes generally will not cause self heating in the sensce to be substanHally above the nedium terryture, thus not cause any panranent damage to the sensir.g eiermnt. Sensing elements with merhanical drage to the sensing wire are susceptible to early failum.

RdF has tested "off the shelf" standard cc:mercial units at 100 millimperes with the element sheath irmersed in 70 F water, ficwing'at three (3) feet per second. Resistance shifts af*e_r exposure to 100 millic.rperes are usually less than .08 F.

enne intiere In Tnmnerature Instrumentation

96 Dr. T.W.Eerlin May 21, 1979 University of 'Ihmessee Page 2 of 2 You may use this letter as part of your re,mrt to the Nuclear P% tory C=Ndmn on loop current response tine testing, and if I can be of further help, please do not hesitate to call.

Yours truly, BdF Cbrporation i/-

n!

Randal A Gauthier Odef ' Transducer Engineer 4

RAG:vb l

t l

r o e

The U LEWIS ENGINEERING

/el.&c..

r y1 Company P. O. Box 268 Norwich, New York 1381s Tel. 007-334-3939 May 24, 1979 The University of Tennessee Nuclear Engineering Department Knoxville, Tennessee 37916 Attention: Dr. T. Kerlin

Subject:

Effect of Loop Current Step Response. Test on Lewis Temperature Sensors for Nuclear Applications

Dear Tom:

Lewis Engineering hos furnished temperature sensors with standard plunge test response time data for use in coolant loops of nuclear reactors. These platinum resistance-temperature detectors, Models 56BPA2 and 56BPA4, are single element, 200 ohm, four wire, thermowell type sensors.

The Loop Current Step Response (LCSR) method of measuring sensor time constant as described in report hP-834, Volume I for EPRI would not be detrimental to these Lewis sensors. In-situ response time testing using the LCSR method, with electric current transients up to 70 milli-amperes, should cause no degradation of the sensors' parameters.

Should you desire to copy or use this statement in your report, per our conversation, please feel free to do so.

Very truly yours ,

THE LEWIS ENGINEERING COMPANY p@L b . =

James E. Dann

. Engineering Manager Transducer Division JED/mlk Corporate Headquarters: 238 Water Street Naugatuck. Conn. 06770 ,

Tel. 203-729-5253 Telex 962a39 , ,

98 OAK RIDGE NATIONAL LABORATORY optmatto sv UNION CARBIDE CORPORATION NUCLEAR DIVISION O

Po1T OFFICE 80X X OAK RIDGE. TENNESSEE 37830 July 17, 1979 Professor T. W. Kerlin Department of Nuclear Engineering University of Tennessee Knoxville, Tennessee 37916 Loop Current Step Response of Thermocouples and Resistance Thermometers Extensive use of Loop Current Step Response (LCSR) techniques has been made at ORNL over the past 8 years to measure response times of sheathed thermocouples in reactor experiment capsules in the HFIR, plant thermo-couples in ORR, and sheathed thermocouples in sodium test loops. Comparisons were made of the results of LCSR tests and mere conventional plunge response tests for a wide variety of sheathed thermocouples. Using heating currents typically of 1-1.5 nmps for LCSR tests on thermocouples, agreement between LCSR and plunge tests of better than 10% is typical. A few disparities as high as 20% were found, but could be attributed to differences in test conditions, such as surface heat transfer conditions. I estimate several hundred thermocouples have been tested ranging from some as small as 0.020 in.

OD to others as large as 0.125 in. OD. No dauage from LCSR testing was ever observed.

Tests of the LCSR method were also made for determining response times of platinum resistance thermometers (PRTs) using heating currents typically of 60 ma. No effects on calibration, as determined by changes in the ice pnint resistance (R ), were f und, although it is customary to restrict the O

normal measuring currents to 1-3 ma to avoid self-heating effects. In a 3 recent study to use the self-heating effect in a PRT as a means for deter-mining whether there was water surrounding the PRT sheath (in the Three Mile Island pressurizer), we ran currents of 200-250 ma through a Rosemount Engineering Model 104MB PRT for periods of 5-6 hours repeatedly over a period of a week with the thermometer at temperatures as high as 550*F.

After these tests, the ice point resistance of the PRT was rechecked and found to be 100.003 ohms, well within the normal calibration tolerance. It l

2 l

1

4 99

1. .

Professor T..W. Kerlin

- July 17, 1979.

Page 2 is our judgement that currents'of as high as 200 ma can be used in LCSR and self-heating tests for PRTs which are properly manufactured to meet RDT and i ASTM specifications, so long as the internal platinum element temperature does not exceed'the rated temperature for these PRTs.

Very truly yours, j

s R. 1.. Shr,ard f*'fm Thermome:.ery Development RLS:wt cc: R. M. Carroll f

i I

i J

l 1

4 1

1 i

1 F

T k

9

, . . . , .  : r-- . _ . . , e_ , ,, , -_.m', . _ . .,. . . 4 - , __ ,_ ,. .~.. , ,

100 APPENDIX B TIME RESPONSE CHARACTERI2.ATION OF SENSORS B.1 The Concept of Time Constant The time constant _is commonly used to represent the response charac-teristics of a dynamic system. It has unambiguous meaning only for first order systems (described by a first order differential equation or equiv -

alently, a first order transfer function);

(B.1)-

{f+ax=au or G(s) =us*((*) = 1 ,,1 . (B.2) a If Equation B.2 is solved for a unit step change in the input, u; one obtains x(t) = 1 -e *'. (B.3) 1 If the response is evaluated for t = , then x(t = a) = 0.632. (B.4)

Thequantity,f,isdefinedasthetimeconstant,T. It is easily identi-fied from test data by measuring the time required for the respons: to achieve 63.2 percent of its final value following a step change in the input.

. - w - _

101 B.2 Higher Order Dynamic Systems The first order approximation is usually inadequate to represent the dynamics of typical temperature sensors. This ueans that highet order differential equations or transfer functions are required to represent the dynamics. As is shown in Appendix C, a transfer function without zeroes (no numerator dynamics) is usually adequate:

a G(s) = (*

sn + a sn -1 + . . . + a s+a or a

(B.6)

G(s) = (s-s y )(s-s 2

) . . . (s-s )

For a step change in the input, the response is a a e yst

+

x(t) = (-sy )(-s2 ) . . . (-s ) -sy (s -s2 ) . . . (s y-s )

8 a e 2

+

s2(82-s . . . (s 2-s ) + * * * (I*7}

or a (-sy ) (-s2 ) . . . (-s") 8 E x(t) = (-sy )(-s2 ) . . . (-s ) [l+ sy(sy 2-s ) . . . (s y-s ) e 1

(-s y

+ s- 8(1) (-s ) . . . ( s,,) e ,2 t +...] (B.8) 2 2-s ) . . . (s ~"n) 2 The sy are the poles of the system transfer function. They are all  ;

negative real numbers for transfer functions for temperature sensors. It is common to introduce the concept of a time constant for each mode of the solution:

l w

-l 102 l

l l

e si t , ,-t/ti. (B.9)

Thus, we may write 1

x(t) ,y , *1*2 * * * *n ,-t/tl

X(*) 1 (l-t+y J.t y) ...(l

+ 3. )

-t y -T y T, 1 _gjT tty2** ** n *

+ . . .

+ (* }

1

_t 2

(1

_t 2

+1) 71

. . ( _1t 2

+1)

T n It is clear that there is no simple relation between the multiple time con-stants in the response equation. However, it is still accepted practice to define an overall time constant, t, as the time required to achieve 63.2 percent of the final response following a step change in the input.

It is possible to develop an expression that relates the overall time constant, T, to the individual time constants, Tg, using an assumption that is well satisfied in typical temperature sensors. The faster time con-stants have a decreasing effect on the response compared to the slowest one as time progresses since they decay faster. For example, if we let t y be the slowest time constant and evaluate the second exponential at t/ty = 1, we obtain the following:

e ~! 2 (at t=t T y/T2 y) 2 .135 3 .050 i

4 .018 5 .007 Since ty/t2 is 5 or greater for a sensor, the T term c ntribution is small 2

by the time t = Ty. Since the Ty term has the most important effect on t,

. 9 a -- _ __

103 we can also assert that:T and higher terms have a small influence when 2

t = T. Thus, we may write 1

x(t) I 2 * * * *n T T

,-t/Tl (B.ll) x(=) g y , 1

-t (1

-t y

+L)...(l t -T y

+ L) y y t, Now, we can set x(t)/x(=) = 0.632 and solve for T to obtain:

e ~*!*1 = .368 (1 - ) (1 - ). . . (1 - ) (B.12)

T I 1 l *1 or T T T T =t y (1 - in(1 - f ) - in(1 - f) . . . In(1 - ")) (B.13) 1 1 1 To illustrate the effect of the faster time constants on the overall time constant, the ratio, T/ty, was evaluated for various values of T2 /Tl with i = 0 for i greater than 2. The results are shown in Figure B.l.

I 104 i

i 2.0 - -

Basis T;= 0 for i > 2 1.8 - -

1.6 - -

T T

3

\

l 1.4 - -

1.2 - -

1  ; l l l l 0 .1 .2 .3 .4 .5 2/T $

s FIGURE B.1. EFFECT OF FASTER TIME CONSTANT ON OVERALL TIME CONSTANT.

e =

.I l

105 l 1

l B.3- Ramp Response-The ramp response 'of sensors is of interest because safety studies generally involve ramp changes. The ramp response is obtained readily

' from the transfer function of a system. First, let us consider a first order system:

1 G(s) = ,y '(B.14) s The ramp response is evaluated using the Laplace transform of a ramp with ramp rate K as follows:

L {Kt) = -s f (B.15)

Then:

' K (B.16) x(s) =s'2(Ts + 1)

The response may be obtained by inverse Laplace transformation:

x(t):= K [t-T + T e ~ ! *] (B.17) \

For t>>T, the exponential term is insignificant. The response is as shown in Figure B.2. The output, x(t), is delayed relative to the true process value, Kt, by a time that is less than or equal to T. The asymptotic delay is-called the system ramp time delay and is equal to the time constant for a first order system. Note that the ramp time delay is independent of the ramp rate. The asymptotic measurement error is Kr.

Now, we will evaluate the ramp time delay and measurement for sensors described by higher order dynamic models. Consider the transfer function:

i i

106 I

Time Delay

! 2

E E

E E

A 6

Measurement Error Temperature Ramp '

, Measured Temperature l

Time FIGURE B.2. TYPICAL RAMP RESPONSE AND ILLUSTRATION OF RAMP TIME DELAY AND MEASUREMENT ERROR.

107 a

(B.18)

G(s) = (8-8 )(8-82) . . . ( -s )

a, = (-s 1) (-s2) * *

• C-8n) and the input, Kt, with Laplace transform, . The Laplace transform of a

the output is Ka .

x(s) = (B.19) s2 (s-sy ) (s-s 2 ) . . . (s-s )

The sensor response may be evaluated by inverse Laplace transformation.

The partial fraction method gives A A A A 3 4 x(s) ql + -2 + + +... (B.20) s s s-s s-s 2

The arbitrary constants must be evaluated if the complete response is re-quired. However, we are interested only in determining the ramp delay time and the asymptotic measurement error. Consequently, the exponential terms are of no interest, and we can concentrate on g and A .2 These may be evaluated ,

to give the following result.

A =K (B.21) 1 A2 " "K I'l + T2 + * * * *n] (B.22)

Therefore x(t) N K[t-(ty+T2+...+t )] (B.23) in this case, we obtain:

ramp time delay = Ty+T2+***I n (B.24) and asymptotic measurement error = K[ty+T2 + * * * *n] (B.25).

108 B.4 Relation Between Time Constant and Ramp Time Delay The time constant and the ramp time delay ar'e given by:

T T time constant = T y [1.- An(1 2) - in(1 3) . . . ] (B.26) 1 1 and ramp time delay - T 1[1 +T y2 +t y *3 + . . . ]. (B.27) insertion of numerical values into these expressions shows that the ramp delay time is always less than the time constant, but the difference is small for values of the ty that are typical of temperature sensors. To

illustrate this, the percent differences between the time constant and the ramp time delay was evaluated for a two-term representation (Ty and T2)*

The error is shown in Figure B.3. We note that for a typical ratio of 0.20, the difference is less than two percent.

(

109 8--

j 7--

O m

.E w

R6- - Note: The step response time 8 constant is always greater E than the time delay.

Im j 5-Note: A typical value for7 2/7, M is < 0.2. Therefore, the 8 difference is< 2%.

U

@4- -

F E

~

3 Y2-ca 8

E 71= slowesttimeconstant Ei

=2- -

O T2= fast time constant in a 2

{ time constant representation.

E s' 1 - -

O  :  :  :  :  :  :

O .1 .2 .3 .4 .5 .6 Ratioof 72/73 FIGURE B.3. RELATION BETWEEN PLUNGE TIME CONSTANT K,3 vg/j AND RAMP TIME DELAY.

-.F s,l, /

na 1. 4l,s.

sy C W .s'.

sLff d,x n/r,=o.t a.~ + y,y u W Jo o %

l 110 APPENDIX C THE LOOP CURRENT STEP RESPONSE TRANSFORMATION C.1 Introduction The result of interest is the time constant associated with a step change in fluid temperature external to the sensor. The time constant is defined to be the time required for the sensor output to reach 63.2 per-cent of its final steady-state value after a step change in fluid tempera-ture. This time constant is usually obtained from a plunge test in a laboratory environment. Since the plunge test cannot be used to obtain the time constant of an installed RTD, the LCSR test is proposed as one method to obtain an estimate of the desired plunge test time constant.

A transformation is needed to convert LCSR data into a prediction of the response that would occur following a fluid temperature step change.

The transformation may be developed using a general nodal model for sensor heat transfer. The development is independent of the number of nodes in-cluded in the model, so use of this approach does not imply any restrictive assumptions. The following sections give some details on RTD heat transfer that permit formulation of a transformation and that define the conditions for validity of the-transformation.

C.2 Mathematical Development of the LCSR Transformation An analytical transformation for converting loop current step response (LCSR) test results into plunge test results may be developed using a general nodal model for sensor heat transfer. Consider first a system with predominantly one-dimensional heat transfer. In this case, the nodal model

/

may be represented schematically as shown in Figure C l. The accuracy of such a model may be made as great as desired by using enough nodes.

1 I

112 l

1

)

The. dynamic heat transfer' equation for node i is:

(MC) =

R ( i-1

~

i

~

(i

~

i+1 +9 1 (*

i-1 i-where Q = heat generation rate in node i-M = mass of. material in node i C g= specific heat capacity of material in node i R g= heat transfer resistance for node 1-1 to node i T g= temperature of node 1.

Dividing through by (MC)g and defining constants gives dT dt " *i,1-1 1-1 ~ 81,1 i + *i,1+1 1+1 + 110 (*

where 1

8 1,1-1 " (Mc)1 R_

• i,i-" (MC)g (R _t

• i,1+1 (MC Rg i )g The nodal equations may be applied to a series of nodes, starting at I the node closest to the center (i=1) and ending with the node closest to the surface (i=N) . The equations have the form:

1 l

[

l

...-m

113 dT 7

de " -*1l 1 + *12 2+ 1 91 dT

de " *21 1 - *22 2.+ "23 3+ 2 92 dT 3

de " "32 2 -8 33 3 + "34 4+ 3 93 1

dt " *N,N-1 N-1 ~ "N,N N+ N,F F+ N ON where T = fluid temperature.

F Ttase equations may be written in matrix form:

a; - - -

p=Ax+Bq+cTy (C.3)

.i where p- _ _

Ty -a g a 0 0 .. .

l2 T a -8 0 . ..

2 21. 22 *23 T 0 a **

• 3 32 ~*33 *34 i= . A= .

N N,N-1 ~*N,N O

-.m-,- -, , . , . , _ - - . -

l 114 by 0 0 Q 1

0 b 0 _ Q2 2

B= q=

0 0 b ... Q3 3

-b N .

ON

. Laplace transformation gives:

[sI-A] x(s) = c T y(s) + B q(s) . (C.4)

The Laplace transform solution for the responae of any node, x 1, may be found using Cramer's rule. Let us consider several cases:

Case 1-no heat capacity in region between the filament and the center of the sensor, no heat generation in any nodes, fluid temperature pertur-bation, one dimensional heat transfer F(s)

(C.5) 1(8}"lsI-Al where 0 -a 0 0 ...

l2 0 ***

(s+a22) ~"23 O -a ***

32 (s+a33) -"34 0 0 -a 34 ("+"44) * * *

. . . . ... )

l C

N,F F(s) . .- . . . . -a N,N-1 (s+aN,N 1

(C.6) y

115 This may be written 0 0 ...

-ai2 (s+a22) ~*23

^*32 (s+a33) ~*34 * *

• F(s) = CN,F F(s) (-1)(N+f) , _ , ,,_

. . -a _1,3_1-y (C.7)

This determinant is for a matrix in lower triangular form (all elements-above the diagonal are zero). The determinant is given by the product of x

the diagonals, all of which are constants. Therefore, for a fluid tem-perature perturbation in a one-dimensional heat transfer system, the response of the innermost node is characterized by a transfer function with no zeroes. If the sensing element in an RTD is centrally located, or if there is insignificant heat capacity between the filament and the center of the sensor, then this type of transfer function describes the response characteristics of the sensor.-

The transfer function may be written Tl (s) K T(s)"lsI-Al y _

= (C.8)

(s-p1) (s-p2} * *

• where.

p = poles (identical to eigenvalues of A).

. .s 116 For a unit step changa in Tp , T y(s) = 1, and we may write:

T1 (s) = s(s-p ) (s-p ) ** *

(C.9) y 2 Inversion of this Laplace transform using the residue theorem gives:

Pt i

T1 (t) = K[(-py ) (-p2) +

.. . (-PN) (P1 ) (Py-P2 ) ***

Pt 2

+ . . .]. (C.10)

+ (P2 ) (P2-Py) ...

Thus, we make the following important observation:

For an RTD with predominantly one-dimensional heat transfer and with insignificant heat capacity between the sensing element and the center of the sensor, the poles alone (no zeroes) are adequate to characterize the response due to a fluid temperature change.

The implication is that if one can identify the poles by some other test (such as the LCSR), then he can construct the response to a fluid tempera-ture step.

Case 2-significant heat capacity between the filament and the center of the sensor,.no heat generation in any nodes, fluid temperature perturba-tion, one-dimensional heat transfer This case may be analyzed for the response of any non-central node, but for notational simplicity, let us consider the response of the second node. In this case T2 (s) = (C.11)

I 117

.1

'where-(s+ayy) 0 0 0 ...

-4 0 -a ***

21 23 0 0 ***

(s+a33) ~"34 F(s) = . . . . ... (C.12)

. C N,F F(8) * * ***

This may be written 0 0 0 ...

(s+a 1)

-a * **

21 ~"23 O

(s+a33)

-a 34

• • • (*

)

F(s) = CN,F F(s) (-1) . . . . ...

Agair, we' observe that the matrix is triangular, but the diagonals are not all constant. In this case, the transfer function will have one zero.

For the response of nodes further from the center, there will be more zeroes. Thus, the poles alone are not adequate to construct the response l i

for an RTD if the sensing element is not loceted at a position with in- i l

significant heat capacity between the filament and the center of the sensor.

.: 4-118 Case 3--insignificant heat capacity between the filament and the center of the sensor, heat generation in central node, constant fluid tempera-ture, one-dimensional heat transfer

^ (S) (C.14)

T(s)=lsI-AI, 1

where by Q -a 0 0 ...

l2 0 ***

(s+a22) ~*23 O -a ...

(s+a33) 4 (C.15)

F(s) =

This may be written 0 0 ...

(s+a22) ~*23

-a -a * * * '

32 (s+a33) 34

~ -a ***

43 (s+a44) 45 (C.16)

F(s) = byQy l

In this case, the matrix is not triangular, and the transfer function will have zeroes.

The transfer function may be written:

, Ty (s) 1 (s-z ) (s-z2) * * * (8-*M)

Qy (s) " (s-p1 ) (s-p2) ... (S-P N *

. e

'119 For a unit step change in Qy(Q y (s) = 1), we obtain K (s-zy ) (s-z 2) * * * (8~*M)

T1 (s) = s(s-p ) (s-p ) . . . -(C.18) 1 2 (8-P N Inversion by the residue theorem gives:

y (-zy ) (-z 2) *

• * (~*M) (Pl ~*l) (Pi-z2 ) . . .

(Pi %) Pt i 1 (-py ) (-p3) .. . (-p N) (Pt ) (Py -P 2 ) . . . (P y -PN )

(p2 ~*1) (P2 ~*2) . . - (P2'*M) Pt 2

+ (P2 ) (P2 -P e + . . .). (c.19) 1 ) . . . (P 2-PN }

Note that the response is determined by the zeroes as well as the poles.

However, the poles are the same as for the fluid temperature change case.

Thus, if we can identify the poles from a LCSR test, we can construct the equivalent fluid perturbation response using Equation (C.10) .

Case 4-insignificant heat capacity between the filament and the center of the sensor, no heat generation in any nodes, fluid temperature perturbation, multi-dimensional heat transfer In chis case, there is branching in the heat transfer (see Figure C.2).

This means that the temperature of a node may be influenced by more than just two neighboring nodes as in the one-dimensional case. In the one-dimensional case, all of the elements of the A matrix are on the diagonal or in the position adjacent te the diagonal. In the multi-dimensional case, coupling terms appear in other positions (always symmetrically positioned around the diagonal). Thus F(s) may be written

e e

VV% W< ---

2 I

i 1

FIGURE C.2. SCHEMATIC OF A MULTI-DIMENSIONAL NODE-TO-NODE HEAT TRANSFER

'* .h 121 0 -a * * ***

2 O ***

(s+a22) ~*23

. .-a (s+a 33 -*34 ***

32 F(s) = (C.20)

CN,F . ...

F(s) . .

where

• = possible new coupling terms.

In this case, the matrix is not triangular and zeroes can occur. This means that the availability of the poles through some sort of measurement is not sufficient for construction of the response to a fluid temperature step.

C.3 Steps in Implementing the LCSR Transformation The steps for obtaining the plunge test time constant are:

1. perform a LCSR test

2. identify the poles associated with the LCSR data

3. construct the step response for a fluid temperature perturbation using Equation (C.10) .

1 I

1

a a 122 l

I l

APPENDIX D i TEST PROCEDURE l A test procedure for performing a combined self heating. loop current step response test program is presented below.

1. Set up the equipment as near as possible to the cabinet where the RTD leads are connected to the plant transmitters. The equipment includes:

- The test instrument (bridge, switchable power supply, adjustable decade resistors, adjustable-gain amplifier to -amplify the voltage drop across the bridge, and a digital voltmeter that can monitor the amplifier output or can be switched to measure the voltage x drop across a fixed bridge resistor to provide the current).

- A strip chart recorder connected to the bridge amplifier output.

- A data recording system (analog or digital) connected to the bridge amplifier output and to the current switch status (open or closed) indicator output.

2. Connect a spare RTD to the test instrument. The RTD should be immersed in water to within two inches of the top connector on the RTD.

3. Turn on the power supply with the current selector switch set to LOW and the power supply voltage at its lowest setting.

4. Adjust the power supply to give 1-5 ma.

5. Balance the bridge . (adjust the decade resistor until the bridge amplifier output goes to zero).

6. Check to be sure that the resistance is correct for the water temperature.

-7. Switch the current selector switch to HIGH.

a >

l 123 1

8. Adjust the power supply to give 40 ma (typical) through the sensor. I I

9. Adjust the amplifier gain to give an output voltage that is suit-able for the recording equipment.

10. Switch the current selector switch to LOW.

11. Wait until the bridge amplifier output settles out.

12. Turn on the strip chart recorder.

13. Switch the current selector switch to HIGH.

14. Wait until the bridge amplifier output settles out.

15. Measure the time required for the output to reach 63.2 percent of its total variation.

16. Compare this time with a reference value (obtained on previous tests on the same sensor in still water).

17. If the difference in times is more than fifteen percent, check equipment and procedure.

18. If the difference in times is less than fif teen percent, set the .

current selector switch to LOW and continue. Otherwise, check equipment.

19. Turn off the power supply

20. Disconnect the spare RTD.

21. Remove the selected plant RTD leads from its in-plant transmitter.

22. Connect the in-plant RTD leads to the test instrument. If the RTD has more than two leads, select only one from each side of the filament.

23. Turn on the power supply and adjust to give 1-5 ma through the RTD.

24. Balance the bridge.

i .

1 124 , l

25. Check the noise level at the bridge amplifier output.

26. Set the power supply to its lowest value.

27. ' Switch the current selector switch to HIGH. I

28. Start the self heating test. Increase the power supply voltage to give a current through the RTD of about 10 ma.

29. Wait unti1~ the bridge amplifier output settles out.

30. Rebalance the bridge.

31. Calculate the power dissipated in the RTD filament.

32. Record the resistance and power.

33. Repeat steps 23 through 32 for current values up to 40 ma (typical).

34. Plot resistance versus power on linear graph paper. If the data indicate a well-defined straight line, go to step 35. If the data indicate scatter, repeat steps 23 through 32 for more data points.

35. Start the Loop Current Step Response (LCSR) tests. Balance the bridge at low current then set the current selector switch to HIGH.

36. Set the power supply voltage to give a current of 40 ma (typical) through the RTD.

37. Adjust the amplifier gain to give an input voltage that is suit-able for the. recording equipment.

38. Set the current selector switch to LOW.

39. Wait for the bridge amplifier output to settle out.

40. Start the strip chart recorder and the data recording equipment.

41. Switch the current selector switch to HIGH.

42. Wait until the bridge amplifier output settles out.

43. Switch the current selector switch to LOW.

w i  ;

125 1

44. Repeat steps 38 through 43 at least five times (more for noisy or unstationary data).

45. Set the current selector switch.to LOW.

46. Turn off the power supply.

47. Disconnect the sensor.

48. Repeat steps 22.through 47 for the next sensor to be tested.

49. Complete tests on all sensors.

50. Remove test equipment.

4 i

l 4 - .n. - - e , .-- ., -

w. ,

126 References

1. U.S. Nuclear Regulatory Commission, " Regulatory Guide 1.118 - Periodic Testing of Electric Power and Protection Systems" USNRC, Washington, D.C. , Revision 1, November 1977

2. The Institute of Electrical and Electronics Engineers, "IEEE Standard:

Criteria for Protection Systems for Nuclear Power Generating Stations" Standard 279-1971, IEEE, New York, 1971

3. The Institute of Electrical and Electronics Engineera, "IEEE Standard Criteria for the Periodic Testing of Nuclear Power Generating Station Class IE Power and Protection Systems," Standard 338-1975, IEEE, New York, 1975

4. T. W. Kerlin, " Analytical Methods for Interpreting In-Situ Measure-ments of Response Times'in Thermocouples and Resistance Thermometers,"

Oak Ridge National Laboratory Report ORNL-TM-4912 (March 1976)

5. T. W. Kerlin, et. al. , "In-Situ Response Time Testing of Platinum Resistance Thermometers," EPRI Report NP-459 (January,1977)

6. T. W. Kerlin, et. al. "In-Situ Response Time Testing of Platinum Resistance Thermometers," EPRI Report NP-834 (July,1978)

7. T. W. Kerlin, L. F. Miller and H._M. Hashemian, "In-Situ Response Time Testing of Platinum Resistance Thermometers," ISA Transactions, p,,

71-88 (1978)

8. B. R. Upadhyaya and T. W. Kerlin, "In-Situ Response Time Testing of Platinum Resistance Thermometers - Noise Analysis Method" EPRI Report NP-834, Vol. 2, July 1978

9. B. R. Upadhyaya and T. W. Kerlin, " Estimation of Response Time Characteristics of Platinum Resistance Thermometers by the Noise Analysis Technique" ISA Transactions, 17,, 21-38 (1978)

10. H. M. Hashemian, T. W. Kerlin, B. R. Upadhyaya, " Apparatus for Measur-ing the Degradation of a' Sensor Time Constant" Patent Application filed with U.S. Patent Office

11. M. Skorska, personal communication, Nuclear Engineering Department, University of Tenenssee, Knoxville, Tennessee

12. W. P. Poore, " Resistance Thermometer Characteristics and Time Response Testing" Thesis, Nuclear Engineering Department, University of Tennessee, Knoxville, Tennessee (to be published)

13. T. W. Kerlin, " Accuracy of Loop Current Step Response Test Results" (to be published)

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