Analysis of Space Radiators

ANALYSIS OF SPACE RADIATORS : ANALYSIS OF SPACE RADIATORS M. DEIVEEGAN Guide Dr. SUBRAHMANYA S. KATTE Senior Lecturer M.Tech [THERMAL PLANT ENGINEERING] SHANMUGHA Arts, Science, Technology & Research Academy SASTRA Deemed University Thanjavur-613 402, India May 2004


LIST OF PUBLICATIONS BASED ON THE PRESENT WORK : LIST OF PUBLICATIONS BASED ON THE PRESENT WORK 1. Title: Analytical Expressions for View Factors with an Intervening Surface Edition: Vol. 18, No. 2, 2004, pp. 273-277. Authors: Deiveegan. M, Ramamoorthy. V, and S. S. Katte Journal: Journal of Thermophysics and Heat Transfer Publishers: American Institute of Aeronautics and Astronautics (AIAA). 2. Title: One Dimensional Analysis of Hollow Conical Radiating Fin Edition: Vol. 18, No. 2, 2004, pp. . 277-279 Authors: Deiveegan. M and S. S. Katte Journal: Journal of Thermophysics and Heat Transfer Publishers: American Institute of Aeronautics and Astronautics 3. Title: Thermal Modelling of Radiative Micro Heat Pipe Array Authors: Deiveegan. M, S. S. Katte, and Santhosh Kumar. S Journal: International Journal of Heat and Technology Publishers: Edizioni ETS, Pisa, Italy.


Organization of Presentation : Introduction Review of Literature Hollow Conical Radiating Fin Radiative Micro Heat Pipe Array Analytical Expressions for View Factors with an Intervening surface Conclusions Organization of Presentation


1. Introduction : 1. Introduction Introduction to Space Radiators Spacecraft subjected to heating - Internal sources - External sources Thermal Control System Space Radiators Mass is at a premium Need not augment heat transfer always


1. Introduction continued … : Introduction to Radiative Micro Heat Pipe Array Array of Aluminum wires brazed between two thin Aluminum sheets. Higher heat transport capacity. Flexible, light weight, able to operate in any position Need for the Theoretical model To predict the performance of MHP array in space environment, useful for design. 1. Introduction continued …


1. Introduction continued … : Analytical Expressions for View Factors Thermal analysis of space radiators involves computation of view factors. Minimum overall resolution of at least six digits required Shadowing effect of intervening objects cannot be ignored while calculating the view factors 1. Introduction continued …


2. Review of literature : 2. Review of literature Space Radiators


2. Review of Literature continued … : 2. Review of Literature continued … Radiative Micro Heat Pipe Array


2. Review of Literature continued … : 2. Review of Literature continued … Motivation for the present work Space Radiators Most of the previous investigations For space at 0 K Neglected radiation interaction between fin and base Only a few attempts to modify geometry Micro Heat Pipe Array Almost all investigations applicable only for convection environment Previous numerical models Not “Two-dimensional model”-- Radiative loss by edges not considered. Heat loss by conduction through insulation not considered. Monte Carlo method used for view factor calculation. View factors are not accurate. [Ref. Emery et al.] Analytical Expressions for View factors with an Intervening surface Analytical expressions for view factors between a finite area and a coaxial differential element, in the presence of a finite intervening surface -- not available


Slide10 : Objectives To propose a hollow conical space radiator to augment the heat transfer per unit mass To carry out an analysis of such a space radiator To study the effects of various parameters To propose correlations for optimum parameters 3. Hollow Conical Radiating Fin


Slide11 : Assumptions One-dimensional heat conduction No solar heating Steady state All surfaces are diffuse and gray 3. Hollow Conical Radiating Fin Analysis


Slide12 : For a differential element, the energy conservation gives Formulation T(x = 0) = TB where with boundary conditions Radiosity-irradiation method is used 3. Hollow Conical Radiating Fin


Slide13 : View factors calculated using - parallel coaxial disks of unequal radii - annular disk to coaxial truncated cone - view factor algebra Assume the temperatures Calculate radiosities using Gauss-Seidel technique for inside and outside enclosures With these radiosities, calculate temperatures using TDMA for linearized energy balance equations in FD form Repeat steps 3 and 4 until all temperatures converge Solution Methodology 3. Hollow Conical Radiating Fin


Slide14 : Improvement in heat loss per unit mass over unfinned base where Qim= (Q-QUB)/m Solution Methodology continued… 3. Hollow Conical Radiating Fin


Slide15 : Results and Discussion 3. Hollow Conical Radiating Fin Grid Sensitivity Study optimum grid size: 2 mm θ=50°, H=0.1 m, t=1 mm, ε=0.85, TB=313 K, Te=4 K and k=177 W/m K


Slide16 : For limiting case, heat loss = 0.5596 W Pin fin with adiabatic tip & no base interaction (D.Q. Kern, 1972) Error is 0.018 % Validation Pin fin (θ=90°) outside dia. = 4 mm ε=0.85 H=107.6 mm RB=2.001 mm adiabatic tip at 300K 3. Hollow Conical Radiating Fin


Slide17 : H=50 mm RB=50 mm ε=0.85 Top radius=2 mm Thickness =0.2 mm Qim is 4.8 times that of solid fin 3. Hollow Conical Radiating Fin Comparison with pin fin


Slide18 : Effect of Fin Angle 3. Hollow Conical Radiating Fin H=0.1 m t=1 mm ε=0.5


Slide19 : Effect of Fin thickness 3. Hollow Conical Radiating Fin θ=70° H=0.1 m ε=0.85


Slide20 : Effect of Fin Height 3. Hollow Conical Radiating Fin θ=70°, t=0.001 m ε=0.85


Slide21 : Effect of Emissivity 3. Hollow Conical Radiating Fin H=0.1 m θ=55° t=1 mm RB=0.398 m


Slide22 : Index of correlation : 0.9916 RMS error : 2.59% Number of data points: 596 Index of correlation : 0.9937 RMS error : 5.51% Number of data points: 118 Optimum thickness Optimum emissivity Index of correlation : 0.9916 RMS error : 4.54% Number of data points: 271 Optimum angle Correlations for optimum parameters 3. Hollow Conical Radiating Fin


Slide23 : Index of correlation : 0.9975 RMS error : 6.89% Number of data points: 1443 Improvement in heat loss per unit mass over unfinned base Correlation for heat transfer 3. Hollow Conical Radiating Fin


Slide24 : Range and values of parameters considered 3. Hollow Conical Radiating Fin


Slide25 : Experimental setup of Wang et al. 4. Radiative Micro Heat Pipe Array MHP Array is treated as a plate of thickness t formulated by radiosity-irradiation method Vacuum chamber Black painted cold plate Thin film electric heaters Bottom surface insulated Objective To propose 3 theoretical models To suggest a comprehensive theoretical model


Slide26 : Heat conduction is one dimensional along x direction The insulation material is divided in to a number of strips along x-axis In each strip the heat conduction is one dimensional along z direction The bottom surface of the insulation to radiate heat to the surroundings Accounts for the heat loss by conduction through the insulation Radiative loss by the edges considered Energy balance equation: Uniform heat flux supplied only to the evaporator section Boundary conditions: Quasi one-dimensional model Analysis 4. MHP Array


Slide27 : In each strip of insulation, the heat conduction is one dimensional along z direction For interface - constant temperature boundary condition (No contact resistance) For the bottom surface of the insulation -- radiative boundary condition N number of divisions along x-axis & M divisions along z-axis Equations represented by central difference finite difference scheme Energy balance equation linearized: For intermediate nodes i=2 to N Solution Methodology 4. MHP Array


Slide28 : For node i=N+1 View factors calculated using analytical expressions & view factor algebra Nodal temperatures coupled with heat loss by conduction through insulation and radiosities Radiosities are calculated using Gauss-Seidel technique Temperature distribution in each strip of insulation material -- using TDMA Temperature distribution in MHP array -- using TDMA Convergence criteria 10-7 % For node i = 1 4. MHP Array


Slide29 : One-dimensional model Bottom surface of the MHP array is adiabatic heat loss due to conduction through the insulation is not considered 4. MHP Array


Slide30 : For a differential element energy balance equation Two-dimensional model Heat conduction is two-dimensional along x and y directions Bottom surface assumed to be adiabatic boundary conditions 4. MHP Array


Slide31 : Equations represented by central difference finite difference scheme. N number of nodes along x & M number of nodes along y direction. Totally [(N+1) (M+1) +2] surfaces. View factor matrix calculated using analytical expressions and view factor algebra. Nodal temperatures coupled with radiosities. Radiosities are calculated using Gauss-Seidel technique. Temperature distribution in MHP array is calculated using Gauss-Seidel technique. 4. MHP Array Solution Methodology


Grid sensitivity study : Grid sensitivity study Optimum grid sizes: 1Dimensional: 5 mm Quasi 1Dimensional: 5 mm Two Dimensional: 6mm 4. MHP Array Results and Discussion


Slide33 : Parameters considered for modelling Properties of insulation corresponding to 8.4% of insulation loss 4. MHP Array


Comparison of temperature distributions predicted by theoretical models with experimental results : Comparison of temperature distributions predicted by theoretical models with experimental results Quasi 1D model predicts least temperature levels 4. MHP Array


Isotherms predicted by the two-dimensional model with out working fluid : Isotherms predicted by the two-dimensional model with out working fluid Two-dimensional temperature field not significant. Radiative loss by two edges: 1.6 % of the power input. ΔTY, Max = 0.53 K. ΔTX, Max = 26.6 K. 4. MHP Array


Isotherms predicted by the two-dimensional model for the best case : Isotherms predicted by the two-dimensional model for the best case Parameters: Qin = 19.35W, ε = 0.98. Radiative loss by 2 edges: 1.9 % of the power input. ΔTY, Max = 0.68 K. ΔTX, Max = 44.1 K. 4. MHP Array


Effect of heat input and emissivity on the heat loss by conduction through insulation : Effect of heat input and emissivity on the heat loss by conduction through insulation Heat loss by conduction through the insulation: [ε = 0.92] 10.8 % to 3.6 % of Qin Total heat loss : [ε = 0.92] 13.8% to 7.2 % of Qin. For ε = 0.5, & Qin = 10 W, total heat loss=15.8 % of Qin. ε decreases with lifetime Heat loss by conduction through the insulation significant Better insulation warranted 4. MHP Array


Effect of heat input on maximum temperature and maximum temperature difference : Effect of heat input on maximum temperature and maximum temperature difference Tmax - very sensitive to Qin Working fluid reduces temperature level MHPA useful only if Qin > 10 W (ΔT)max increases almost linearly with Qin (ΔT)max variation not significant 4. MHP Array


Slide39 : 5. Analytical Expressions for View Factors with an Intervening Surface Analytical expressions for view factor. View factor with showing object. Contour Integration method. Finite area and Coaxial differential area, in the presence of finite intervening object. Analysis View factor : S2 = x22+y22+z22. C - Visible portion of A2 as seen from dA1 dA1 A2 x y L z


Slide40 : arc I:- x3 = R3 cos θ, y3 = R3 sin θ; dx3 = − R3 sin θ dθ, dy3 = R3 cos θ dθ. θ varies from θ2 to θ1 line II:- yS = (2+BS), dyS = 0, xS varies from to (1−WS). line III:- xS = (1−WS), dxS = 0, yS varies from (2+BS) to (2−BS). line IV:- yS = (2−BS), dyS = 0. xS varies from (1−WS) to . View Factors Between dA1 and Disc with a Rectangle in Between 5. Analytical Expressions for View Factors


Slide41 : Closed form solutions of five configurations are combined Five different configurations are possible Substituting limits expression for view factor becomes Checking: If there is no intervening surface F1d-2 reduced to form available in literature 5. Analytical Expressions for View Factors


Slide42 : Five different configurations: 5. Analytical Expressions for View Factors Configuration 1a Configuration 1b Configuration 1c Configuration 1d Configuration 1e


Slide43 : line I: x3 = W3, dx3 = 0, y3 varies from to −B3. line II: y3 = −B3, dy3 = 0, x3 varies from W3 to − W3. line III: x3 = −W3, dx3 = 0, y3 lies from –B3 to B3. line IV; y3 = B3, dy3 = 0, x3 varies from −W3 to W3. line V: x3 = W3, dx3 = 0, y3 varies from B3 to . arc VI: xS = 1+RS cos θ, yS = 2+RS sin θ; dxS = −RS sin θ dθ, dyS = RS cos θ dθ. θ varies from θ1 to θ2, where View Factors Between dA1 and Rectangle with a Disc in Between 5. Analytical Expressions for View Factors


Slide44 : Four different configurations are possible Closed form solutions of 4 configurations are combined Substituting limits expression for view factor becomes where Checking: If there is no intervening surface F1d-2 reduced to form available in literature 5. Analytical Expressions for View Factors


Slide45 : Four different configurations: 5. Analytical Expressions for View Factors Configuration 2a Configuration 2b Configuration 2c Configuration 2d


6. Conclusions : 6. Conclusions For hollow conical fin, improvement in heat loss per unit mass is 4.8 times than that of solid pin fin There exist optimum angle, thickness and emissivity Optimum angle increases with increasing height, emissivity and decreases with increasing thickness Optimum thickness increases with increasing height, emissivity and decreases with increasing angle Optimum emissivity increases with increasing angle, thickness and decreases with increasing height For optimum parameters, improvement in heat loss per unit mass over unfinned surface correlations are presented Hollow Conical Radiating Fin


Slide47 : Three theoretical models for radiative MHP array are proposed, [accounting for the radiative loss by the edges, heat loss by conduction through insulation and two-dimensional temperature field, if any] Two-dimensionality in the temperature field could be ignored Heat loss by conduction through the insulation can not be ignored MHP array is advantageous only if the heat input is higher than 10 W quasi one-dimensional model proposed is best suited for predicting the performance of micro heat pipe array Radiative Micro Heat Pipe Array Conclusions continued…


Slide48 : Closed form solutions presented for view factors between a finite area and a coaxial differential element, intervening finite area at an arbitrary position is present in between Totally 4 different combinations of geometries considered Analytical expressions presented for 9 configurations totally Analytical expressions for View Factors with an Intervening Surface Conclusions continued…


Scope for Future Work : Scope for Future Work Hollow conical fin: Effect of specularly reflecting surface Effect of solar heating on the performance Array of conical radiating fins on an isothermal base View factors with an intervening surface: View factors between finite areas, accounting for the shadowing effect Analytical expressions for view factors between differential element and finite areas of various regular geometry, when another finite area is intervening Micro Heat Pipe Array: Investigation of effect of extended surfaces to augment the performance