外文.pdf

Optimisation and thermal control of a multi-layered structure for space electronic devices and thermal shielding of re-entry vehicles$ Riccardo Monti a,n, Renato Barbonia, Paolo Gasbarria, Leonardo D. Chiwiacowskyb aDipartimento di Ingegneria Meccanica e Aerospaziale Universit? a degli Studi di Roma La Sapienza, Rome, Italy bPrograma de Po s Graduac - ao em Computac -ao Aplicada, Universidade do Vale do Rio dos Sinos, Sao Leopoldo/RS, Brazil a r t i c l e i n f o Article history: Received 27 June 2011 Received in revised form 4 November 2011 Accepted 15 January 2012 Available online 18 February 2012 Keywords: Unsteady thermal problems Pyroelectrics Deterministic optimisation Stochastic optimisation a b s t r a c t All electronic devices, due to Joule effect, present heat dissipation, when they are electrically fed. The heat overstocking produces effi ciency and performances reduction. On account of this the thermal control is mandatory. On small electronic equipments, the diffi culty or impossibility of using a cooling fl uid for the free or forced convection heat dissipation imposes the presence of cooling systems based on another kind of functioning principle such as the conduction. In this paper the thermal control, via pyroelectric materials, is presented. Furthermore, an optimisation of geometric, thermal and mechanical parameters, infl uencing the thermal dissipation, is studied and presented. Pyroelectric materials are able to convert heat into electrical charge spontaneously and, due to this capability, such materials could represent a suitable choice to increase the heat dissipation. The obtained electric charge or voltage could be used to charge a battery or to feed other equipments. In particular, a sequence of different materials such as Kovars, molybdenum or coppertungsten, used in a multi-layer pyroelectric wafer, together with their thicknesses, are design features to be optimised in order to have the optimal thermal dissipation. The optimisation process is performed by a hybrid approach where a genetic algorithm (GA) is used coupled with a local search procedure, in order to provide an appropriate balance between exploration and exploitation of the search space, which helps in the search for the optimal or quasi-optimal solution. Since the design variables used in the optimisation procedure are defi ned in different domains, discrete (e.g. the number of layers in the pyroelectric wafer) and continuous (e.g. the layers thickness) domains, the genetic representation for the solution should take it into account. The chromosome used in the genetic algorithm will mix both integer and real values, what will also be refl ected in the genetic operators used in the optimisation process. Finally, numerical analyses and results complete the work. 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) 4250 In order to perform costs reduction and to enhance the effi ciency and the performances, an optimisation proce- dure could be introduced in the design process. In this paper different optimisation techniques, in order to control the temperature distribution inside multi-layered walls, are presented and many numerical simulations are performed. 2. Unsteady thermal problem Before addressing the problem of the structural thermal control on a multi-layer structure and introducing the optimisation technique for the choice of the materials and their mechanical and geometrical properties, let us introduce a brief insight on the one-dimensional unsteady thermal problem of a multi-layered structure. In the following for- mulation the mechanical and thermal characteristics will be considered constant through thickness of the generic layer. Fig. 1 shows the considered multi-layered wall confi guration. The multi-layer confi guration in order to represent typical space thermal problems has been chosen because it is suitable to represent microelectronics packages, made up of electric circuits, support boards and relevant housing, or to represent a classic thermal shield confi g- uration. In fact a large number of TPS are based on the superposition of different material layers, typically cera- mics, in order to brake the thermal fl ux that fl ows through the thickness. The generic thermal problem is ruled by the classic Fourier Law that reads as follows 1: kr2T?rc T t ?qv ATB:C:I:C:;1 where k,rand c are the thermal conductivity, the density and the heat capacity of the material, respectively, qvis an internal heat source/sink, T is the temperature, t is the time variable and A is a non-linear operator in order to take the boundary and initial conditions into account. The problem defi nition 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) becomes simpler ki 2Tiz,t z2 ?rici Ti t ?qi v 0,2 where apex i 1, .,N indicates the generic i-th layer of the wall. In order to solve the problem the boundary and the initial conditions must be considered B:C:- q0,t ?k1dT 10,t dz qu, TNhN,t Tl, 8 : I:C:-Tz,0 T0,3 where hNis the end abscissa of the N?th layer, quis the heat fl ux on the external upper surface, Tlis the lower external surface temperature of the wall and T0is the internal temperature distribution through the wall thick- ness at the initial time t0. These conditions are not suffi cient to solve the problem. It is necessary to add the temperature and fl ux continuity conditions, defi ned at the layers interfaces with i 1, .,N?1: Ti9z hi Ti19z hi, ?ki dTi dz ? ? ? ? ? z hi ?ki1 dTi1 dz ? ? ? ? ? hi :4 The temperature distribution, through the thickness of each layer, can be expressed as the sum of a steady state distributionFz and an unsteady distributionCz,t. By combining them we have: TiFizCiz,t:5 The stationary solutionFz for the generic i-th layer is given by 2 Fiz 1 2 qi v ki z2HizGi,6 where H and G are the coeffi cients obtained by the solution of the stationary problem by imposing boundary and continuity conditions. The unsteady solution we have reads as follows: Ciz,t X 1 k 1 jkT0Ai k coszkokBi k sinzkok?ea io2 kt: 7 The coeffi cientsjkT0 are determined by imposing the initial condition jkT0 P i R hik iT 0wiz,ok dh P i R hik iwiz,o kwiz,ok dh ? P i R hik iFiwiz,o k dh P i R hik iwiz,o kwiz,ok dh ,8 wherewiz,ok are the thermal eigenvectors of the thermal problem andokare the associated eigenvalues. The algebra and the solving procedure is widely reported in 3,4. 3. Thermal control As mentioned above the structural thermal control is a primary problem for space systems. In this paragraph two different examples, the former one applied to control the temperature 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 materials Concepts and numerical techniques presented so far to analyse 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 confi guration. R. Monti et al. / Acta Astronautica 75 (2012) 425043 This module is designed by exploiting miniaturisation and hybrid materials techniques with an overall length of 75 mm and a width of 20 mm. The RF module, designed for the operations of transmission and reception, foresees a high power amplifi er (HPA) mounted on its upper surface to amplify the incoming/outcoming signals. Dur- ing the activation phase the HPA dissipates, due to Joule effect, a heat fl ux that overheats the metallic carrier of the device. This thermal fl ux provides a heat overstocking that is not compliant with the European Space Agency (ESA) design rules. These rules are defi ned in the MIL STD 883G that prescribes a maximum reached temperature of 120 1C for all the electronics and equipment onboard the satellites. By taking this into account a thermal control is mandatory, eventually following an optimisation proce- dure to enhance its effi ciency. The RF module has a very simple layout as shown in Fig. 3. In this schematic it is possible to recognise the carrier made up of an iron-based alloy, Kovars, where the HPA is mounted on. In order to control the heat fl ux and the temperature 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 fl ux into electrical charge, or voltage, or current 36. In particular, a patch of pyroelectric is attached to the bottom surface of the RF carrier. The pyroelectric patch is made up of three different layers. The fi rst and the last ones are the electrodes constituted by a Nickel Chrome alloy, the middle layer is the 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 fl ux into electrical charge we can consider the pyroelectric patch as a capacitor whose thermo-electric coupling reads as follows 6: DV pe0er h DT,9 where p is the pyroelectric coeffi cient,e0is the vacuum dielectric 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 subsystem The function of thermal protection system is to protect the re-entry vehicle from aerothermodynamic heating during atmospheric entry. Ablative materials such as phenolic nylon, elastomeric silicon material (ESM), and white oak have been used in the past to protect against excessive heating. For the protection against the consid- erably higher heating rates, that occur on the conical skirt of the vehicle, two types of thermal protection systems have been used: (i) the ablative type and (ii) a ceramic- based surface insulation type. Other methods have been investigated in the past, and eventually used, such as reusable heat shields (Fig. 4). It is well known that in order to reduce the mass of the heat-shield, it is important to lower the heat loads during re-entry. Two main methods generally can be applied, lift and a lower ballistic coeffi cient. Lift requires stable aero- dynamic conditions over a wide range of fl ow conditions and a complex attitude control system. A low ballistic coeffi cient, on the other hand, requires either low mass or a large area 7. Once the re-entry trajectory is defi ned together with the front shield area which is in turn connected to the dimension of the satellite the only possibility we have to reduce the heat-fl ux which is connected to the reduction of the mass of the satellite. One of the possible choices to Fig. 2. RF module. Fig. 3. Breadboard confi guration with the thermal diffusion cone (red). (For interpretation of the references to color in this fi gure legend, the reader is referred to the web version of this article.) Table 1 Kovarsthermal properties. QuantitySymbolValueUnit of measure Densityr8360 kg=m3 Ther. conductivityk17.3W/(mK) Heat capacityc439J/(kg K) Table 2 Pyroelectric material characteristics. QuantitySymbolValueUnit of measure Densityr5300 kg=m3 Ther. conductivityk2.9W/(mK) Heat capacityc322J/(kg K) Pyroel. coeff.p238 mC=m2K Elec. permittivityer10,000 Table 3 Ni20% Cr thermal properties. QuantitySymbolValueUnit of measure Densityr8410 kg=m3 Ther. conductivityk11.3W/(mK) Heat capacityc435J/(kg K) R. Monti et al. / Acta Astronautica 75 (2012) 425044 reduce the mass of the satellite is the reduction of the mass of the heat-shield providing that the thermal protec- tion is guaranteed. In view of this with the present work we want to explore the possibility to use pyroelectric material as one of the layers constituting a thermal protection system. The heat-fl ux inside these layers can be converted into electric charge (accumulated inside the satellite power supply), at the same time reducing the increasing of temperature inside the structure. 4. Optimisation techniques The RF module design was done by using an optimisa- tion procedure based on the successive use of a Genetic Algorithm (GA) and of a classical gradient-based Sequen- tial Quadratic Programming (SQP) 8. The GA is used to perform a preliminary search in the solution space for locating the neighborhood of the solution. Then, the SQP method is employed to refi ne the best solution provided by the GA. The aim of the optimisation is to fi nd out the best values of the thicknesses of the layers and their relevant disposition inside the structure in order to have the maximum effi ciency on the performance of the pyro- electric material. Constraints on the maximum values of the temperature on fi xed check points will be also assigned. It is worth to note that the above approach was introduced because of the large number of the design variables involved in the optimisation process coupled with the complexity of the process in itself. In fact the GA method is able to perform a more comprehensive scan on the search space than that obtainable with the SQP method so as to avoid being trapped at local optima. Furthermore, with GAs, constrained requirements are usually handled by adding penalty terms in the fi tness function, penalising unfeasible solutions. However, there are no general guidelines on designing 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 defi ne some constraints that must be introduced into the opti- misation procedure. Let us now give some insights on the GA algorithm proposed here. The GAs are essentially optimisation algorithms whose solutions evolve some- how from the science of genetics and the processes of natural selectionthe Darwinian principle. As a class of general-purpose search methods, the GA approach gives a remarkable balance between exploiting the promising regions of the search space and exploring the search space. GAs differ from more conventional optimisa- tion techniques since they work on the whole population of encoded solutions, called chromosomes or individuals, and each possible solution is encoded as a set of genes. In general, the most important phases in standard GAs are selection (competition), reproduction (recombi- nation), mutation, and fi tness evaluation. Selection is an operation used to decide which individuals to use for the reproduction in order to produce new search points. Reproduction or crossover is the process by which the genetic material from two parent individuals is combined to obtain one or more offsprings. Mutation is usually applied to one individual in order to produce a new version of it where some of the original genetic materials have been randomly changed. Fitness evaluation is the step in which the quality of an individual is assessed 10. By conducting the search in a global domain, the GA approach reduces the chance of converging to local optima and makes it possible to solve problems involving many parameters. Other advantages of using GA are that it is a self-start method with no special requirement on the initial value of unknown parameters, other than defi ning a search range, and also it does not need information 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 defi ned in both contin- uous and discrete domains, appropriate genetic represen- tation, and also genetic operators, should be employed. The genetic representation of the solution, i.e. the chromosome, is described by an array of real and integer values, as shown in Fig. 5. The real values are related to the carrier, pyroelectric and electrode layer thicknesses, which are continuous vari- ables in the optimisation procedure. On the other hand, the integer values are related to the materials employed in the carrier, pyroelectric and electrode layers. The material choice is based on a mapping between integer values and a list of available materials to be used on each layer. Concerning the genetic operators, each numerical representation leads to specifi c crossover and mutation operators. The arithmetic crossover 11 is applied on the fi rst section of the design vector, i.e. on the real values of thickness, while the one-point crossover 11 is used on the second section of the design vector, i.e. on the integer values indicating the material to be employed. When the mutation is performed, different operators are applied depending on the portion of the design vector. Only one position of each section is chosen, randomly and not necessarily the same. For the thicknesses portion, the non-uniform mutation operator 11 is applied. On the Fig. 4. Schematic of a thermal shield. Fig. 5. Genetic representation for the solution. R. Monti et al. / Acta Astronautica 75 (2012) 425045 other hand, for the material portion, the uniform muta- tion operator 11 is applied. Finally, the selection phase is based on the tournament selection operator 11, while the replacement strategy is based on steady state updates. 5. RF design variables and optimisation procedure In this paragraph optimisation procedure and design variables for thermal design of the microelectronic equip- ment will be presented. The RF module is modelle