電子機(jī)箱結(jié)構(gòu)設(shè)計,電子,機(jī)箱,結(jié)構(gòu)設(shè)計 Optimisation and thermal control of a multi-layered structure forspace electronic devices and thermal shielding of re-entry vehicles$Riccardo Montia,n, Renato Barbonia, Paolo Gasbarria, Leonardo D. ChiwiacowskybaDipartimento di Ingegneria Meccanica e Aerospaziale Universit?a degli Studi di Roma La Sapienza, Rome, ItalybPrograma de Po s Graduac -ao em Computac -ao Aplicada, Universidade do Vale do Rio dos Sinos, Sao Leopoldo/RS, Brazila r t i c l e i n f oArticle history:Received 27 June 2011Received in revised form4 November 2011Accepted 15 January 2012Available online 18 February 2012Keywords:Unsteady thermal problemsPyroelectricsDeterministic optimisationStochastic optimisationa b s t r a c tAll electronic devices, due to Joule effect, present heat dissipation, when they are electricallyfed. The heat overstocking produces efficiency and performances reduction. On account ofthis the thermal control is mandatory. On small electronic equipments, the difficulty orimpossibility of using a cooling fluid for the free or forced convection heat dissipationimposes the presence of cooling systems based on another kind of functioning principle suchas the conduction. In this paper the thermal control, via pyroelectric materials, is presented.Furthermore, an optimisation of geometric, thermal and mechanical parameters, influencingthe thermal dissipation, is studied and presented. Pyroelectric materials are able to convertheat into electrical charge spontaneously and, due to this capability, such materials couldrepresent a suitable choice to increase the heat dissipation. The obtained electric charge orvoltage could be used to charge a battery or to feed other equipments. In particular, asequence of different materials such as Kovars, molybdenum or coppertungsten, used in amulti-layer pyroelectric wafer, together with their thicknesses, are design features to beoptimised in order to have the optimal thermal dissipation. The optimisation process isperformed by a hybrid approach where a genetic algorithm (GA) is used coupled with a localsearch procedure, in order to provide an appropriate balance between exploration andexploitation of the search space, which helps in the search for the optimal or quasi-optimalsolution. Since the design variables used in the optimisation procedure are defined indifferent domains, discrete (e.g. the number of layers in the pyroelectric wafer) andcontinuous (e.g. the layers thickness) domains, the genetic representation for the solutionshould take it into account. The chromosome used in the genetic algorithm will mix bothinteger and real values, what will also be reflected in the genetic operators used in theoptimisation process. Finally, numerical analyses and results complete the work.& 2012 Elsevier Ltd. All rights reserved.1. IntroductionIn the last decades the space design research hasbeen involved in the optimisation of missions, of costs,of primary and secondary structures and of all otherequipments onboard the spacecraft. The thermal designis one of the most important and expensive issuesof a spacecraft design. In fact the designer must pro-vide a thermal protection system (TPS) in order tocontrol effects of external thermal sources (i.e. theSun heat flux) and efficient internal thermal devices todraintheheatfluxesgeneratedbytheelectronicequipments.Actually most of the internal thermal control isprovided by thermal pipes or by exploiting the thermalcharacteristics of equipments constituting materials suchas the thermal conductivity in order to increase the heatdissipation and to reduce the heat overstocking.Contents lists available at SciVerse ScienceDirectjournal homepage: Astronautica0094-5765/$-see front matter & 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.actaastro.2012.01.006$This paper was presented during the 61st IAC in Prague.nCorresponding author. Tel.: 39 0644585301;fax: 39 0644585670.E-mail addresses: riccardo.montiuniroma1.it (R. Monti),renato.barboniuniroma1.it (R. Barboni),paolo.gasbarriuniroma1.it (P. Gasbarri),ldchiwiacowskyunisinos.br (L.D. Chiwiacowsky).Acta Astronautica 75 (2012) 4250In order to perform costs reduction and to enhance theefficiency and the performances, an optimisation proce-dure could be introduced in the design process.In this paper different optimisation techniques, inorder to control the temperature distribution insidemulti-layered walls, are presented and many numericalsimulations are performed.2. Unsteady thermal problemBefore addressing the problem of the structural thermalcontrol on a multi-layer structure and introducing theoptimisation technique for the choice of the materials andtheir mechanical and geometrical properties, let us introducea brief insight on the one-dimensional unsteady thermalproblem of a multi-layered structure. In the following for-mulation the mechanical and thermal characteristics will beconsidered constant through thickness of the generic layer.Fig. 1 shows the considered multi-layered wall configuration.The multi-layer configuration in order to representtypical space thermal problems has been chosen becauseit is suitable to represent microelectronics packages,made up of electric circuits, support boards and relevanthousing, or to represent a classic thermal shield config-uration. In fact a large number of TPS are based on thesuperposition of different material layers, typically cera-mics, in order to brake the thermal flux that flowsthrough the thickness. The generic thermal problem isruled by the classic Fourier Law that reads as follows 1:kr2T?rcTt?qv ATB:C:I:C:;1where k,rand c are the thermal conductivity, the densityand the heat capacity of the material, respectively, qvisan internal heat source/sink, T is the temperature, t is thetime variable and A is a non-linear operator in order totake the boundary and initial conditions into account. Theproblem definition is completed by the boundary (B.C.)and initial conditions (I.C.).For a generic multi-layered wall and in the case of one-dimensional unsteady thermal problem Eq. (1) becomessimplerki2Tiz,tz2?riciTit?qiv 0,2where apex i 1, .,N indicates the generic i-th layer ofthe wall. In order to solve the problem the boundary andthe initial conditions must be consideredB:C:-q0,t ?k1dT10,tdz qu,TNhN,t Tl,8:I:C:-Tz,0 T0,3where hNis the end abscissa of the N?th layer, quis theheat flux on the external upper surface, Tlis the lowerexternal surface temperature of the wall and T0is theinternal temperature distribution through the wall thick-ness at the initial time t0. These conditions are notsufficient to solve the problem. It is necessary to add thetemperature and flux continuity conditions, defined at thelayers interfaces with i 1, .,N?1:Ti9z hi Ti19z hi,?kidTidz?z hi ?ki1dTi1dz? hi:4The temperature distribution, through the thickness ofeach layer, can be expressed as the sum of a steady statedistributionFz and an unsteady distributionCz,t. Bycombining them we have:TiFizCiz,t:5The stationary solutionFz for the generic i-th layer isgiven by 2Fiz 12qivkiz2HizGi,6where H and G are the coefficients obtained by thesolution of the stationary problem by imposing boundaryand continuity conditions. The unsteady solution we havereads as follows:Ciz,t X1k 1jkT0AikcoszkokBiksinzkok?eaio2kt:7The coefficientsjkT0 are determined by imposing theinitial conditionjkT0 PiRhikiT0wiz,ok dhPiRhikiwiz,okwiz,ok dh?PiRhikiFiwiz,ok dhPiRhikiwiz,okwiz,ok dh,8wherewiz,ok are the thermal eigenvectors of thethermal problem andokare the associated eigenvalues.The algebra and the solving procedure is widely reportedin 3,4.3. Thermal controlAs mentioned above the structural thermal control is aprimary problem for space systems. In this paragraph twodifferent examples, the former one applied to control thetemperature inside an electronic device used for trans-mission operations and the latter one applied to a Re-entry Thermal Protection Subsystem, will be analysed.3.1. RF electronic devices and pyroelectric materialsConcepts and numerical techniques presented so far toanalyse the temperature distribution inside a multi-layered structure will be applied.In particular, we will deal with a Radio Frequency (RF)module, see Fig. 2 used to transmit and receive operations.Fig. 1. Multi-layered wall configuration.R. Monti et al. / Acta Astronautica 75 (2012) 425043This module is designed by exploiting miniaturisationand hybrid materials techniques with an overall length of75 mm and a width of 20 mm. The RF module, designedfor the operations of transmission and reception, foreseesa high power amplifier (HPA) mounted on its uppersurface to amplify the incoming/outcoming signals. Dur-ing the activation phase the HPA dissipates, due to Jouleeffect, a heat flux that overheats the metallic carrier of thedevice. This thermal flux provides a heat overstockingthat is not compliant with the European Space Agency(ESA) design rules. These rules are defined in the MIL STD883G that prescribes a maximum reached temperature of120 1C for all the electronics and equipment onboard thesatellites. By taking this into account a thermal control ismandatory, eventually following an optimisation proce-dure to enhance its efficiency.The RF module has a very simple layout as shown inFig. 3. In this schematic it is possible to recognise the carriermade up of an iron-based alloy, Kovars, where the HPA ismounted on. In order to control the heat flux and thetemperature distribution and to avoid the heat overstocking,an innovative thermal device, based on pyroelectric mate-rial, is used. Pyroelectric materials demonstrate a sponta-neous capacity to convert a thermal flux into electricalcharge, or voltage, or current 36. In particular, a patchof pyroelectric is attached to the bottom surface of the RFcarrier.The pyroelectric patch is made up of three differentlayers. The first and the last ones are the electrodesconstituted by a Nickel Chrome alloy, the middle layer isthe pyroelectric made up of a classic piezoelectric material(PZT). Tables 13 show the mechanical and thermal char-acteristics of the materials constituting the RF module.Due to the inherent capacity to transform heat fluxinto electrical charge we can consider the pyroelectricpatch as a capacitor whose thermo-electric coupling readsas follows 6:DV pe0erhDT,9where p is the pyroelectric coefficient,e0is the vacuumdielectric constant,eris the relative electrical permittiv-ity, h is the thickness of the pyroelectric active layer,DV andDT are the voltage and temperature variation,respectively.3.2. Thermal protection subsystemThe function of thermal protection system is to protectthe re-entry vehicle from aerothermodynamic heatingduring atmospheric entry. Ablative materials such asphenolic nylon, elastomeric silicon material (ESM), andwhite oak have been used in the past to protect againstexcessive heating. For the protection against the consid-erably higher heating rates, that occur on the conical skirtof the vehicle, two types of thermal protection systemshave been used: (i) the ablative type and (ii) a ceramic-based surface insulation type. Other methods have beeninvestigated in the past, and eventually used, such asreusable heat shields (Fig. 4).It is well known that in order to reduce the mass of theheat-shield, it is important to lower the heat loads duringre-entry. Two main methods generally can be applied, liftand a lower ballistic coefficient. Lift requires stable aero-dynamic conditions over a wide range of flow conditionsand a complex attitude control system. A low ballisticcoefficient, on the other hand, requires either low mass ora large area 7.Once the re-entry trajectory is defined together withthe front shield area which is in turn connected to thedimension of the satellite the only possibility we have toreduce the heat-flux which is connected to the reductionof the mass of the satellite. One of the possible choices toFig. 2. RF module.Fig. 3. Breadboard configuration with the thermal diffusion cone (red).(For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)Table 1Kovarsthermal properties.QuantitySymbolValueUnit of measureDensityr8360kg=m3Ther. conductivityk17.3W/(mK)Heat capacityc439J/(kg K)Table 2Pyroelectric material characteristics.QuantitySymbolValueUnit of measureDensityr5300kg=m3Ther. conductivityk2.9W/(mK)Heat capacityc322J/(kg K)Pyroel. coeff.p238mC=m2KElec. permittivityer10,000Table 3Ni20% Cr thermal properties.QuantitySymbolValueUnit of measureDensityr8410kg=m3Ther. conductivityk11.3W/(mK)Heat capacityc435J/(kg K)R. Monti et al. / Acta Astronautica 75 (2012) 425044reduce the mass of the satellite is the reduction of themass of the heat-shield providing that the thermal protec-tion is guaranteed. In view of this with the present workwe want to explore the possibility to use pyroelectricmaterial as one of the layers constituting a thermalprotection system. The heat-flux inside these layers canbe converted into electric charge (accumulated inside thesatellite power supply), at the same time reducing theincreasing of temperature inside the structure.4. Optimisation techniquesThe RF module design was done by using an optimisa-tion procedure based on the successive use of a GeneticAlgorithm (GA) and of a classical gradient-based Sequen-tial Quadratic Programming (SQP) 8. The GA is used toperform a preliminary search in the solution space forlocating the neighborhood of the solution. Then, the SQPmethod is employed to refine the best solution providedby the GA. The aim of the optimisation is to find out thebest values of the thicknesses of the layers and theirrelevant disposition inside the structure in order to havethe maximum efficiency on the performance of the pyro-electric material. Constraints on the maximum valuesof the temperature on fixed check points will be alsoassigned.It is worth to note that the above approach wasintroduced because of the large number of the designvariables involved in the optimisation process coupled withthe complexity of the process in itself. In fact the GA methodis able to perform a more comprehensive scan on the searchspace than that obtainable with the SQP method so as toavoid being trapped at local optima. Furthermore, with GAs,constrained requirements are usually handled by addingpenalty terms in the fitness function, penalising unfeasiblesolutions. However, there are no general guidelines ondesigning penalty functions 9.On account of this it is possible, as we will see later,not only to enhance the solution, but also to better definesome constraints that must be introduced into the opti-misation procedure. Let us now give some insights onthe GA algorithm proposed here. The GAs are essentiallyoptimisation algorithms whose solutions evolve some-how from the science of genetics and the processes ofnatural selectionthe Darwinian principle.As a class of general-purpose search methods, the GAapproach gives a remarkable balance between exploitingthe promising regions of the search space and exploring thesearch space. GAs differ from more conventional optimisa-tion techniques since they work on the whole population ofencoded solutions, called chromosomes or individuals, andeach possible solution is encoded as a set of genes.In general, the most important phases in standardGAs are selection (competition), reproduction (recombi-nation), mutation, and fitness evaluation. Selection is anoperation used to decide which individuals to use for thereproduction in order to produce new search points.Reproduction or crossover is the process by which thegenetic material from two parent individuals is combinedto obtain one or more offsprings. Mutation is usuallyapplied to one individual in order to produce a newversion of it where some of the original genetic materialshave been randomly changed. Fitness evaluation is thestep in which the quality of an individual is assessed 10.By conducting the search in a global domain, theGA approach reduces the chance of converging to localoptima and makes it possible to solve problems involvingmany parameters. Other advantages of using GA are thatit is a self-start method with no special requirementon the initial value of unknown parameters, other thandefining a search range, and also it does not needinformation such as gradients or derivatives of the func-tion to be minimised.Concerning the RF module design by the GA metaheur-istic, since the design variables are defined in both contin-uous and discrete domains, appropriate genetic represen-tation, and also genetic operators, should be employed. Thegenetic representation of the solution, i.e. the chromosome, isdescribed by an array of real and integer values, as shown inFig. 5. The real values are related to the carrier, pyroelectricand electrode layer thicknesses, which are continuous vari-ables in the optimisation procedure. On the other hand, theinteger values are related to the materials employed in thecarrier, pyroelectric and electrode layers. The material choiceis based on a mapping between integer values and a list ofavailable materials to be used on each layer.Concerning the genetic operators, each numericalrepresentation leads to specific crossover and mutationoperators. The arithmetic crossover 11 is applied on thefirst section of the design vector, i.e. on the real values ofthickness, while the one-point crossover 11 is used onthe second section of the design vector, i.e. on the integervalues indicating the material to be employed.When the mutation is performed, different operatorsare applied depending on the portion of the design vector.Only one position of each section is chosen, randomly andnot necessarily the same. For the thicknesses portion, thenon-uniform mutation operator 11 is applied. On theFig. 4. Schematic of a thermal shield.Fig. 5. Genetic representation for the solution.R. Monti et al. / Acta Astronautica 75 (2012) 425045other hand, for the material portion, the uniform muta-tion operator 11 is applied. Finally, the selection phase isbased on the tournament selection operator 11, whilethe replacement strategy is based on steady state updates.5. RF design variables and optimisation procedureIn this paragraph optimisation procedure and designvariables for thermal design of the microelectronic equip-ment will be presented. The RF module is modelled as afour-layered wall where the first layer represents thecarrier, the second and the fourth ones are the electrodesand the third one is constituted by the pyroelectric layer.In Table 4 the thickness of each layer is reported.On the upper surface of the RF module a constantheat flux qu 62:5 kW=m2corresponding to a dissipatedpower of 10 W is applied, whereas on the bottom surfacea constant temperature value Tl60.0 1C is imposed. Thetemperature distribution at the starting time is consid-ered equal to T060.0 1C.The optimisation process was formulated as follows:Findwto maximise FOw10subjected to inequality constraints grrgnr; r 1, .,Nrand a limitation on the lower and upper bounds of thedesign variableswlrwrwu,11where FOw is the electric power generated by the pyro-electric device defined as follows:FO1DtZtf0DV2Rdt,12whereDt is the simulation period,DV is the voltagedefined in Eq. (9), R is the equivalent circuit resistanceand tfis the end simulation time. In this optimisationprocesswis the design variable vector, containing thethicknesses of the layers of the RF module and thethermal conductivities of the materials; Nris the numberof the constraints; the subscripts l and u represent thelower and upper bounds on the design variables, respec-tively, and grare the equality constraints defined as:gr Tscp,gnr Tmax,13where Tscp(whit s 1;2,3) is the check points temperaturemeasured at one fourth s 1, half s 2 and threefourth s 3 of the RF carrier thickness. This value mustbe less than Tmax 115 1C, see Fig. 6. It is worth to notethat the design vector lower and upper limits are definedas shown in Table 5.Eqs. (10)(13) represent