the experimental thermonuclear fusion reactor will be...lamps with 240 mm long tungsten filament....

Thermal fatigue experiments versus

theoretical models

M. Merola, R. Matera

Commission of the European Communities, Joint

Ce re, T.f. 750,

Italy

ABSTRACT

One of the most critical issues of the experimental fusionreactor is the thermal fatigue of the so-called 'First Wall',i.e. the component directly facing the thermonuclear plasma. Inthe framework of the European Fusion Technology Programme,thermal fatigue experiments are carried out at the JointResearch Centre at Ispra. This work describes the numericalmodelling of the thermal fatigue cycles and compare numericalresults with experimental data. Particular attention is givento the various problems to be solved when modelling a realexperiment.

INTRODUCTION

components are heated, as during start up, and cooled,as during shut down, the resulting thermal gradients give riseto stresses. The continuous change of such stresses, due to theoperational cycles of the component, is called thermal fatigue.The stress range will depend mainly upon the thermal loads andthe physical properties of the material such as the coefficientof thermal expansion, the thermal conductivity, the elasticmodulus and so on. An important role is also played by thecooling efficiency and the component geometry. Therefore it ispractically impossible to perform standard experiments, as itis usually done in mechanical fatigue, but only those 'ad-hoc'experiments are relevant which attempt to simulate the realshape of the structure, the real heat loads and the realcooling system. The fatigue problem for thermal cyclinginvolves not just crack initiation and growth but also thepossibility of crack arrest as the thermal stresses are not dueto external loads but to the inhibition of a free thermalexpansion by both external and internal constrains.

Transactions on Modelling and Simulation vol 5, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X

278 Computational Methods and Experimental Measurements

The experimental thermonuclear fusion reactor will becharacterised by a pulsed operation with a very high number ofoperating cycles (about 10 ) and by high surface thermal loads.The reduced accessibility and the strong activation of thematerials, following the interaction with neutrons at highenergy, make replacement of the internal reactor componentsvery difficult. In particular the first wall (FW) , thecomponent which covers about eighty percent of the surfacefacing the plasma, has to be considered a permanent componentof the reactor. It is therefore essential that the FW bedesigned to withstand severe working conditions and to workreliably for the expected number of operating cycles. Becauseof the uncertainty in the actual working conditions and thelack of previous experiments on the effect which these can haveon the behaviour of complex FW structures, the design proceedswith the support of a vast experimental programme which isintended to check, for the most critical components, whetherthe choices made match the project requirements. In particularfor the FW the experimental activity is oriented towardsmanufacturing problems and towards checking the thermal fatiguelifetime.

In the framework of the European Fusion TechnologyProgramme, thermal fatigue experiments are carried out at theJoint Research Centre at Ispra. After a brief description ofthe apparatus prepared to simulate surface thermal loads on FWmodels, the problem of the numerical analysis of thermalcycling loads is tackled and computational results are comparedwith the experimental temperature values . This is part of theco-ordinated research programme on "Lifetime Behaviour of theFirst Wall of Fusion Machines" endorsed by the InternationalFusion Research Council and organised by the InternationalAtomic Energy Agency of Vienna.

DESCRIPTION OF THE THERMAL FATIGUE TEST FACILITY

A complete description of the thermal fatigue test facility canbe found in Matera, et Al. [1], Below just the maincharacteristics are summarized.

The components are placed in a cylindrical chamber withdiameter 1 m and length 1.2 m, with horizontal axis closed bytwo hatches which slide on wheels (fig. 1) . Both the chamberand the hatches have double walls; in the cavity there areindipendent water cooling circuits. The components arethermally cycled In an argon inert atmosphere.

The heat flux is ensured by an array of quartz infraredlamps with 240 mm long tungsten filament. The spectraldistribution is similar to that of a black body. The lamps arehoused in a gold-plated copper lamp holder (fig. 2), which isactively cooled by a water circuit.


Computational Methods and Experimental Measurements 279

Figure 1. Cylindrical chamber where components are placedduring the thermal fatigue test.

Figure 2. Lamp holder partially filled with heating elements



The maximum heat flux compatible with a long lamp lifetimeis 0.6 MW/m , higher fluxes can be obtained at the expence ofshorter lamp life up to values in excess of 1 MW/m .

The test chamber and lamp-holder circuits use industrialwater at room temperature and pressure, without recirculation.The test components are cooled by means of a closed primarycircuit, with circulation pump of maximum flow of 40 m /h andwater/water heat exchanger between primary and secondary.

Two indipendent active systems, made of two Orion Deltadata loggers from Solatron, with their own programming andstorage capacity, monitor the control of the equipment and theacquisition of experimental data.

DESCRIPTION OF THE EXPERIMENT

Fig. 3 shows the component under investigation. It consists ofa block of AISI 316L austenitic stainless steel In which fivecooling channels were made by drilling. Two identicalcomponents were tested simultaneously (fig. 4). One of them wasinstrumented by 40 thermocouples while the other was notinstrumented. The former was used to measure the temperaturefield during the thermal cycle while the latter was used forthe lifetime evaluation.

\

Figure 3. The component used in the thermal fa.L±gue test.



ooooo ooooo

Q O O 0 O O O O O O O O O

Figure 4. Layout of Che experiment. The components are placedabove the lamp array.

Fig. 5 shows the final geometry, the position of thethermocouples and the reference axis. Table 1 gives thecoordinates of the thermocouples tip location, with respect tothe reference axis indicated in fig. 5.

Fig. 6 shows the thermal cycle applied to the component. Itis worth noting that it is not the heat flux absorbed by thecomponent. To obtain this value the emitted flux should bemultiplied by the component absorptance. A black Cr-platingprocess was performed on the component in order to increase theabsorptance which proved to be around CX95; therefore theabsorbed heat flux is about 520 and 75 kW/m during the heatingand dwell phase, respectively.

During the increase in power of the infrared lamps theiremission spectrum changes; the effective absorptance of thecomponent therefore also change as it is a mean value over thewavelength. Fortunately this fact does not influence in asensible way the absorbed heat flux. It was proved that thewavelength in which the emitted power reaches its maximum is1.32 and 2.13 m at the end of the heating and dwell phase,respectively. In this range the absorptance value is ratherflat and therefore the above assumed constant figure of 0.95 iscompletely justified.

Each component is cooled by water at a pressure of 0.2 MPa;the flow rate is 1.2 m /h.



ooooo

Y

7

Figure 5. Position of the thermocouples.

TABLE I. LOCATION OF THE THERMOCOUPLES (DIMENSIONS IN MM)

No.

9101112131415161118192021222324

CcZ

105105757575000

-45-45-45-105-105-10510590

:>ord

-1932-32-619

-32-619-196

32-32-619-6

-19

inatesX

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

44

1.1.1.1.1.1.1.1.1.1.1.1.1.1.3.3.

-Y

4312035603623401

No.

25262728293031323334353637383940

Z

903030

-15-15-75-751056060151515

-30-30-75

Coord

19-326

-1932

-32-6196

32-19-619-321932

inatesX

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

.5

44

3.3.3.3.3.3.3.4.5.5.5.5.5.5.5.5.

-Y

0010032045666666



Figure 6. Thermal cycle emitted by the infrared lamps.

NUMERICAL ANALYSIS OF THE EXPERIMENT

Geometric modellingThe geometric discretization was undertaken using PATRAN codeand the numerical analysis was performed using ABAQUS finiteelement code vers. 4.8. The three-dimensional analytical modelconsists of 2667 nodes and 448 twenty-nodes elements and isshown in fig. 7. As can be seen, just half a model was analysedbecause of the geometric and experimental symmetries.

Figure 7. 3D Analytical model.



Material modellingThe physical properties introduced in the ABAQUS code aresummarized in table II. A linear variation of the materialproperties vs temperature was taken into account in thecomputations.

TABLE II. PHYSICAL AND MECHANICAL PROPERTIES

Temperature (°C) 20 400

DensityThermalThermalSpecificYoung ' sPoisson

(kg/m")expansion (10conduct. (W/mheat (J/kg K)

modulus (GPa)modulus

VK>K)

796316.214.64761920.29

781217.820.05441610.34

Determination of the heat transfer coefficientThe heat transfer coefficient 'h' depends on the temperature ofthe cooled surface. It therefore changes temporally andspatially. It was estimated that this variation is of the orderof 20% in the present experiment. This variation was taken intoaccount in the analysis as described below.

As L/d < 400 the entrance effects cannot be neglected andthe following formula is recommended by Nusselt [2]:

Nu = 0.036 Re°^ Pr^

The heat transfer coefficient was computed for different cooledsurface temperatures T . The relationship between h andsurfT was evaluated by the least squares technique and the

following expression was obtained:

h = -0.0401 T^ + 39.824 T + 7047surf surf

Determination of the coolant sink temperatureFigg. 8 and 9 show the variation of the coolant sinktemperature vs time. Thermocouple 1 refers to the entrancemanifold and thermocouples 2 to 6 refer to the outlet of eachcooling channel. The irregular behaviour of the plots is due tothe fact that the component length (300 mm) is not enough toassure a complete mixing of the water and thus an uniform bulktemperature is not achieved. With respect to that, it is worthnoting that the heat flux is applied on one sigle surface ofthe component, therefore the heat removal Is not uniform alongthe cooling channel circumference.

As can be seen, the sink temperature varies from one tubeto another and vs time. The different temperature of eachcooling channel was taken into account, whereas for the



variation vs time a mean value was calculated.

17

T16

PE 14RA 13TU 12RE 11

D 18GC 9

20 40160

180

' - 1 - '100

TIME 5

120 H0 160 180 200

Figure 8. 1/ariaCion of Che coolanC sink CemperaCure vs Cime.

100 120 140 160 180 200

TIME 5

Figure 9. Variation of the coolant sink temperature vs time.



Time discretizationWhile performing a numerical transient thermal analysis, timeis discretized in several steps. Going from one step toanother, the temperature of each point of the investigatedstructure changes by a certain amount. Using the ABAQUS finiteelement code, the user can choose the maximum temperature range(called DELTMX) allowed in each temporal step. This is a focuspoint; in fact if too a large temperature range is allowed,numerical errors may become sensible; this fact means that thenumerical results are hardly comparable with experimentalvalues. The smaller the value of DELTMX is, the more accuratethe results obtained are but the higher the cpu time required.

A parametric study was performed to quantify the influenceof DELTMX on cpu time and on the amplitude of the thermalcycle. A rapid increase of the cpu time occurs for DELTMXvalues less then 30 C. The maximum temperature range, i.e. thedifference between the temperature at the end of the heatingphase and the temperature in the same point at the end of thedwell phase, increases linearly if DELTMX decreases. Below aDELTMX value of 20 °C the curve begins to be flat.

As a conclusion, it can be affirmed that the value of themaximum temperature range per each time step must be evaluatedwith care. A DELTMX of 25 °C seems to be a good compromise toobtain quite accurate results without increasing the cpu timetoo much; therefore this value has been adopted throughout thiswork.

THERMAL RESULTS

IntroductionThe thermal analysis was performed in two steps:

1) steady state analysis and experiment.2) thermal transient analysis and thermal fatigue experiment.

The former step was performed to compare numerical andexperimental data in the absence of transient numericalproblems. Two boundary effects were quantified concerning theheat flux spatial distribution:

- latitudinal effects due to the finite number of infraredlamps. This caused a lower heat flux on one edge of thecomponent;

- longitudinal effect due to the following reason: finitelength of the infrared lamps and the lower temperature of thelamp filament at the lamp extremities. Both of these factsleads to a lower irradiated heat flux.

Steady state thermal analysis: evaluation of the resultsThe numerical and experimental results are compared below. Themaximum calculated temperature was 465 C. For better



understanding, the thermocouples are grouped into sets. Beforediscussing these tables it must be pointed out that thenumerical values are calculated by interpolating thetemperature of the two closest nodes at each thermocouple. Thisis quite onerous and time consuming but cannot be avoidedbecause thermocouple coordinates cannot be stated a priori withenough accuracy due to manufacturing tolerances. It isimportant to point out that exact metrology of the thermocoupletip location was necessary as a little uncertainty in thisvalue can lead to a large difference in the measuredtemperature because of the strong temperature gradient (up to40 °C/mm).

Table III groups the thermocouples which give the bestagreement with the numerical results. The difference neverexceed a few percent.

Table IV groups together the thermocouples which are placednear the manifolds. The differences from the experimentalresults can therefore be justified by considering the edgeeffects concerning the heat flux distribution which can be onlyroughly quantified in the numerical analysis. Another sourcesof discrepancy can be that the manifold was only partiallymeshed and that the material is thermally altered in thisregion because of the welding process.

TABLE III. THERMOCOUPLES WHICH GIVE THE BEST AGREEMENT

Therm.No.

111315172527303338

Exper .

263385370355305332252255206

Numer .

273391370358303331238262207

Therm.No.

1214162426283136

Exper .

370280386260240303309244

Numer .

369280385264252304313253

TABLE IV. THERMOCOUPLES PLACED NEAR THE MANIFOLDS

Therm. Exper.No.

Nume r. Therm.No.

Exper. Numer.

9202232

245254220216

253202284230

102123

299340225

314273237

Table V groups the thermocouples which are placed at one edge



of the component. The heat flux was considered to be constantin this region, whereas a lower heat flux was absorbed by thecomponent due to the latitudinal boundary effect. Thisjustifies the lower experimental temperature.

TABLE V. THERMOCOUPLES PLACED AT ONE EDGE OF THE COMPONENT

Therm.No.

1934

Exper .

379286

Numer .

421313

Therm.No.

2940

Exper .

352200

Numer .

384303

It is likely that thermocouples in table VI were not correctlyembedded in the hole. Either they did not touch the holesurface properly or they may even have stopped before reachingthe bottom of the hole. This justifies the lower experimentaltemperature. This point is particularly critical as thermalfatigue is characterized by high temperature gradients and evena small uncertainty in the point of measurement can lead to bigerrors.

TABLE VI. THERMOCOUPLES WHICH GIVE THE WORST AGREEMENT

Therm.No.

1837

Exper.

168251

Numer .

380268

Therm.No.

3539

Exper .

217223

Numer .

234267

Thermal transient analysis: evaluation of the resultsFour thermocouples were chosen from those which gave the bestresults in steady state analysis. In order to save cpu time,only one cycle was numerically simulated. Operating in such away, the focus point is to determine the initial temperaturefield. This was done according to what is stated in table VII.

TABLE VII.

ThermocoupleNo.

SS TR

141516

280370386

271361370

The meaning of the symbols is the following:

SS is the experimental steady state temperature;TR is the maximum experimental transient temperature.



Let F be defined as

TR-cool ant temperatureF = SS-coolant temperature

The mean value for factor F is 0.966, so a rounded value of0.97 was considered. The following three steps were thereforeperformed:

1) steady state analysis at 97% of maximum heat flux;2) numerical analysis of the cooling phase;3) numerical analysis of the heating phase.

The following graphs summarize the results obtained. The solidlines refer to the experimental temperature, whereas the dashedline refer to the numerical results.

The first comment that can be made is that the calculatedand experimental temperature ranges agree quite well. This is aconfirmation that the right choice was made for the parameterDELTMX.

THERMOCOUPLE 12

18 20 38 40 50 66 70 88 90 188 118 120 130 140 150 168 178 188 190TIME I SEC)

Figure 10.



THERMOCOUPLE 15

a 19 .?9 53 ^0 S3 o3 70 30 93 100 ] 10 128 138 148 158 168 178 188 198TIME (SEC)

Figure 11.

THERMOCOUPLE 27

3 10 20 39 48 53 68 30 90 108 na 129 138 140 153 160 170 I S8 190Tine (SEC)

Figure 12.



THERMOCOUPLE 33

50 63 70 80 98 108 110 128 138 140 158 168 178 188 198TIME (SEC)

Figure 13.

From the analysis of the graphs it becomes evident that theagreement between computed and experimental temperature isquite good. The following general comments can be made,however:

1) there is a better agreement in the heating phase than in thecooling phase for the thermocouples located near the heatedsurface (i.e. No. 12 and 15). The opposite seems to happen forthe thermocouple located at a larger distance (i.e. No. 33).This can be explained by the fact that during the heating phasethe temperature field near the heated suface is mainlydetermined by the heat flux whose value is imposed. On theother hand, during the dwell phase the coolant temperature isthe main factor influencing the temperature field near thecooling channels.

2) During the cooling phase the computed temperatures aregenerally lower then the experimental, while during the heatingphase they are higher. A priori it is difficult to say whetherthis fact is due to numerical errors or to non-ideal factorsconcerning the power supplied by the electronic equipment andthe heat flux absorbed by the component. It may also be thatthe material modelling has led to a higher value of the thermaldiffusivity. This would also justify why in the first secondsof both the heating and cooling phase a higher slope can benoticed for the computed line.



CONCLUSIONS

The measurements of the temperature by thermocouples Is quitecritical in high temperature gradient regions and can beaffected by several factors which cannot be evaluated a priori.Moreover an experimental result may be influenced by a largenumber of non-ideal factors which can be hardly modellednumerically.

While comparing numerical with experimental results itshould be clear in mind that each idealization will contributeto increasing the discrepancy from the experimental data.Therefore great attention should be paid to each assumptionmade during the numerical analysis. This is why we had to takeinto account the material properties variation vs temperature,the heat transfer coefficient variation vs time and space, thecoolant sink temperature change during the cycle, the timediscretization as well as a deep understanding of theexperimental facility and the measurement problems. When suchuncertainties are sufficiently under control, however, there issatisfactory agreement between experimental and numerical data.

Such satisfying results cannot be extended to numerical andexperimental data concerning strain and deformation. In fact,as the stress field is above the yield stress limit, anelastoplastic analysis is needed. This may lead to bigdifferences in the numerical results according to the assumedboundary conditions and to the adopted hardening model (seealso Merola [3] and Diegele et Al. [4]). Now, our effort is torealize which are the most suitable modellistic approximationsto obtain mechanical numerical values comparable withexperimental results.

REFERENCES

1. Matera, R., Merola, M., Antidormi, R. and Sevini, F.Experimental results of the I.A.E.A. benchmark on lifetimebehaviour of the first wall of fusion machines. Comm. Europ.Commun., EUR Report, Ispra site, 1992, in print.

2. Nusselt, W. 'Der Warmeaustausch zwischen Wand und Wasser imRohr' Forsch. Geb. Ingenieurwes., vol. 2, p. 309, 1931.

3. Merola, M. Numerical analysis and nuclear standard codeapplication to thermal fatigue, Comm. Europ. Commun., EURReport 14028, Ispra site, 1991.

4. Diegele, E., Jakeman, R., Klischenko, A., Matera, R.,Merola, M. , Munz, D. , Suzuki, S. 'Structural analysis of afirst wall component - Results of benchmark calculations', tobe published in J. of Nucl. Mater.; presented at the 5th Int.Conf. on Fusion Reactor Materials, Clearwater, Florida, U.S.A.,November 17-22, 1991.


the experimental thermonuclear fusion reactor will be...lamps with 240 mm long tungsten filament....

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