COOLING SYSTEM TRANSIENT ANALYSIS USING AN ELECTRIC CIRCUIT PROGRAM ANALOG

Transcription

1 OOLING SYSTE TANSIENT ANALYSIS USING AN ELETI IUIT OGA ANALOG J. O'Loughln ξ, and D. Loree Ar Force esearch Laboratory, Drected Energy Drectorate, 3550 Aberdeen Ave. SE Krtland AFB, N, USA Abstract By explotng the common mathematcal smlartes between electrcal and thermal crcuts, an electrc crcut transent analyss program may be used to analyze the transent behavor of thermal crcuts. Ths s an especally convenent approach for the analyss and optmzaton of the coolng performance of burst mode type electrcal apparatus such as hgh power transmtters. The relatons between electrcal components and the equvalent thermal components are establshed such that gven the thermal component characterstcs, one may then wrte and electrc crcut wth the proper values and then run the model to determne the performance n electrcal parameters that are then easly nterpreted as thermal parameters. Smlar technques have been used for the thermal analyss of components such as semconductor devces [1] and analog hardware [2]. In ths paper the -Spce T program s used as an example; however, the same procedures may be mplemented usng any electrc crcut analyss program. I. ELETO-THEAL ANALOGS A. Objectve In general, an electrc crcut or a thermal crcut wth n energy storage elements s descrbed by an nth order dfferental equaton. Electrc crcut analyss programs provde the requred soluton by means of fnte element analyss technques. It s the objectve here to establsh an analog relaton between a thermal crcut and an electrc crcut such that the soluton of the analog electrc crcut provdes a soluton of the thermal crcut. B. Electro-Thermal omponent Analogs In order to set up an electro-thermal analog, we need to dentfy the correspondence between the electrcal and thermal parameters and varables. Because of the dualty opton n electrc crcut analyss, we can use ether nductance or capactance to correspond to thermal mass. We choose capactance as the analog of thermal mass. Ths choce mposes the nterpretaton of electrc current as power flow and the voltage as temperature. Ths analog model par s llustrated n Fgure.1 T(t) V(t) Fgure 1. Thermal ass, apactor Analog odel The tme dependent equatons that descrbe the varables n Fg 1, are: T ( t) = T (0) + dt (1) V ( t) = V (0) + dt (2) where: T =temperature of thermal mass, o =ower nput to the thermal mass, Watts =Thermal mass, Joules/, o V =voltage on capactance, volts =current nput to capactance, amps = value of capactance, farads omparng the equatons (1) and (2) we fnd that temperature corresponds to voltage, power (thermal) corresponds to current, and thermal mass corresponds to capactance. Had we chosen to use nductance as the analog of thermal mass, then we would have found current as the analog of temperature and voltage that of power. Havng chosen capactance as thermal mass, then there s no use for nductance n the electrcal analog of a thermal crcut. Snce current s the analog of power, then an electrcal current source can be the analog of ether a heat power source or a heat exchanger, dependng upon whch drecton the current s ntroduced nto the crcut. Let us consder a lqud to ar heat exchanger, commonly called a radator, whch s characterzed by a Q that relates the power transferred n terms of the dfference between the nlet ar and coolant temperature. In general the Q ξ emal: james.oloughln@krtland.af.ml U.S. Government work not protected by U.S. copyrght. 767

2 eport Documentaton age Form Approved OB No ublc reportng burden for the collecton of nformaton s estmated to average 1 hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and eports, 1215 Jefferson Davs Hghway, Sute 1204, Arlngton VA espondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OB control number. 1. EOT DATE JUN EOT TYE N/A 3. DATES OVEED - 4. TITLE AND SUBTITLE oolng System Transent Analyss Usng An Electrc rcut rogram Analog 5a. ONTAT NUBE 5b. GANT NUBE 5c. OGA ELEENT NUBE 6. AUTHO(S) 5d. OJET NUBE 5e. TASK NUBE 5f. WOK UNIT NUBE 7. EFOING OGANIZATION NAE(S) AND ADDESS(ES) Ar Force esearch Laboratory, Drected Energy Drectorate, 3550 Aberdeen Ave. SE Krtland AFB, N, USA EFOING OGANIZATION EOT NUBE 9. SONSOING/ONITOING AGENY NAE(S) AND ADDESS(ES) 10. SONSO/ONITO S AONY(S) 12. DISTIBUTION/AVAILABILITY STATEENT Approved for publc release, dstrbuton unlmted 11. SONSO/ONITO S EOT NUBE(S) 13. SULEENTAY NOTES See also AD IEEE ulsed ower onference, Dgest of Techncal apers , and Abstracts of the 2013 IEEE Internatonal onference on lasma Scence. IEEE Internatonal ulsed ower onference (19th). Held n San Francsco, A on June U.S. Government or Federal urpose ghts Lcense., The orgnal document contans color mages. 14. ABSTAT By explotng the common mathematcal smlartes between electrcal and thermal crcuts, an electrc crcut transent analyss program may be used to analyze the transent behavor of thermal crcuts. Ths s an especally convenent approach for the analyss and optmzaton of the coolng performance of burst mode type electrcal apparatus such as hgh power transmtters. The relatons between electrcal components and the equvalent thermal components are establshed such that gven the thermal component characterstcs, one may then wrte and electrc crcut wth the proper values and then run the model to determne the performance n electrcal parameters that are then easly nterpreted as thermal parameters. Smlar technques have been used for the thermal analyss of components such as semconductor devces [1] and analog hardware [2]. In ths paper the -SpceT program s used as an example; however, the same procedures may be mplemented usng any electrc crcut analyss program. 15. SUBJET TES 16. SEUITY LASSIFIATION OF: 17. LIITATION OF ABSTAT SA a. EOT unclassfed b. ABSTAT unclassfed c. THIS AGE unclassfed 18. NUBE OF AGES 4 19a. NAE OF ESONSIBLE ESON Standard Form 298 (ev. 8-98) rescrbed by ANSI Std Z39-18

3 depends upon the partcular unt and the ar and coolant flows. The characterstcs of a typcal commercal heat exchanger are shown n Fgure 3. Fgure 3. haracterstcs of a typcal lqud to ar radator. The electrc analog s mplemented by a voltage controlled current source as shown n Fgure 4. T AI T Q=W/(Inlet Temperature Dfference) Fgure 4. adator-urrent Source Analog odel The equatons relatng to Fgure 4 are: = Q( T TAI ) = G( V VAI ) The equatons are arranged such that, f the ar temperature s greater than the coolant, then the power s transferred to the ar and has a postve sgn. A resstor n an electrcal crcut can be nterpreted as the analog of heat beng transferred by coolant flow n a thermal crcut. A dagram of ths component par s shown n Fgure 5. T IN Q Flow T OUT V AI Fgure 5. oolant Flow-esstor Analog for Heat Transport In order to relate the value of to the "Flow" of the coolant, we must consder the specfc heat as well as the V V IN G (3) (4) V OUT mass or volumetrc flow of the coolant. The power transported by the flow s gven by: = fδσ T OUT T ) (5) ( IN where: f=volumetrc flow of coolant, lters/second δ=densty of coolant, kg/lter σ=specfc heat of coolant, Joules/kg-degree The current flow n the electrc crcut s: ( VIN VOUT ) = (6) omparng (5) and (6), the value of s determned as: 1 = (7) fδσ The flow of coolant n the electrc crcut s mbedded n the value of the resstor. onfuson can arse f one attempts to assocate coolant flow n the confguraton of the electrc analog model of a coolng system, n that the flow of the coolant appears to be opposte from the flow of heat power. Ths confuson s a result of determnng f the power s beng removed or added, and from what or to what. We have now establshed enough thermal-electrc analog components to model a complex coolng system consstng of multple thermal masses, heat sources, heat exchangers and other elements. II.ALITION EXALES We shall frst mplement a smple example of the coolng dynamcs of a hgh power electron beam devce and then expand to a more complcated example of an entre transmtter. A. Thermal odel of Electron Beam ower Devce Lqud cooled hgh power electron beam devces such as klystrons, gyrotrons, etc, have massve collectors that account for nearly all of the power dsspaton. Under pulse or burst mode operaton the thermal mass of the collector as well as the coolant flow s an mportant consderaton n the analyss of the thermal performance. A smple electrcal analog model of a pulsed beam devce s shown n Fgure 6. A pulsed voltage source, V(t), gates a current source wth transconductance G that smulates the power dsspaton of the collector. The mass of the collector s modeled by the capactor and the coolant analog s mbedded n the resstor. 768

4 The dc voltage source, V IN, models the nlet temperature of the coolant. V(t) G V IN Fgure 6. Electrcal Analog of ollector of a ulsed Beam ower Devce To better understand the example, the followng numerc values are assgned to the parameters. The power nput to the collector s a 50kW pulse wth a one second duraton and a three second perod. The collector mass s 50kg of copper wth a specfc heat of 380J/kg o thus the value of n the electrc crcut s 19000Farads. The collector coolant s water wth a flow of 0.125lters/second and an nlet temperature of 60 o. The value of the from equaton (7) s mΩ. Intally the temperature of the collector s stablzed at the coolant nlet temperature. The crcut n Fgure 6 as wrtten n - Spce s shown n Fgure 7. + B. Example of a Transmtter Wth oolng System The -Spce model of a beam power devce transmtter ncludng the coolng system s shown n Fgure 10. The waveform begns wth a 30 second pulse followed by a 30 pulse burst of 10 Second pulses wth a 20 Second perod, then followed by a 60 second off perod. The peak collector dsspaton s 50kW wth the same mass as the prevous example. The coolng system has a water capacty of 10kg, a flow of lters/second and a radator wth a Q=2400W/ o. The ambent ar temperature and the ntal temperatures of the water and the collector are 40 o. The waveform s generated by two pulse generators and a logc statement n the dual voltage controlled current source. The frst pulse generator produces a sngle ntal pulse of 30 seconds. The second generator produces a repped 10 second pulse wth a perod of 20 seconds after an ntal 50 second delay. The logc statement n the current source blanks any output after 150 seconds. The nlet water temperature of the radator, modeled by a dual voltage nput current source, s the collector temperature or equvalently the water ext temperature from the collector. The ar temperature nput to the radator s the ambent ar temperature, Tar=60. The radator removes heat from the coolant and dumps t nto the ambent ar at 60. In the model ths s represented by a current beng removed from the capactor 2 and then sunk to ground as shown n Fgure 10. The resstor, 1, models the collector coolant flow and the transfer of heat from the collector to the coolant reservor. The thermal mass of the coolant, 10kg=41800Joules/ o s modeled by 2 set to Farads. The results of the smulaton are shown n Fgure 9. Fgure 7. -Spce rcut of Fgure 6 odel III.SUAY We have shown that an electrc crcut smulaton program can be used to analyze the transent thermal response of heat flow crcuts. The complexty of the thermal crcut may be much greater that the examples gven. By followng the analog smulaton rules the only lmt to the number of heat sources, thermal masses, flow loops, heat exchangers, and other components s that of the smulaton program whch typcally extends to hundreds of components. V(ABII1:out-) Tme Fgure 8. ollector Temperature as Determned by the odel n Fgure 7, Scales; Tme=0 to 30 Seconds, Temperature 60 to 80 (Volts) 769

5 SEL>> V(2:1) V(1:2) I(AB2I2)*.5 Fgure 9. esults of Smulaton n Fgure 10. Upper plot Tme top trace collector temperature, Upper plot lower trace water reservor temperature; Temperature scale 80 to 100. Lower plot collector power dsspaton, 50kW peak. Tme scale 0 to 300 Seconds IV.EFEENES [1] A.. Hefner and D. L. Blackburn, "Thermal omponent odels for Electro-Thermal Network Smulaton", n roc. Nnth IEEE SEI-THE T Symposum, pp.88,98. [2] X. Huang and H. A. antooth, "Event-Drven Electrothermal odelng of xed-sgnal rcuts", n roc. 37th Desgn Automaton onference, pp.10-15, June Fgure 10. -Spce odel of Transmtter Includng the oolng 770