Presented By Stephen W. Miller

1. TFAWS Passive Thermal Paper Session Improvements to a Response Surface Thermal Model for OrionStephen W. Miller – NASA JSCWilliam Q. Walker – West Texas A&M Presented ByStephen W. Miller Thermal & Fluids Analysis WorkshopTFAWS 2011August 15-19, 2011 NASA Langley Research CenterNewport News, VA

2. Talking Points • Simple Design of Experiments (DOE) introduction • Goals of Study • Orion Outer Mold Line Model Overview • Response Surface Equation Development • Factors • Responses • Case Matrix • Results • Conclusions • Summary TFAWS 2011 – August 15-19, 2011

3. DOE/RSM Introduction • What is Design of Experiments? • Mathematical/Statistical approach to complex problems • Identify quantifiable measurements and controllable factors (or variables) • Then implement purposeful changes in factors and measure changes in response • Can then use statistical analysis to quantify the effect of each factor (and combination of factors) on the response • What is Response Surface Methodology? • Extension of DOE to produce a polynomial equation that can be used to create a surface of the response for any combination of identified factors • Note that extrapolation beyond defined factor limits is inherently dangerous due to the behavior of polynomials TFAWS 2011 – August 15-19, 2011

4. Introduction, Continued • DOE is different from changing one factor at a time • Changing one factor each case leads to a large number of cases and doesn’t do a good job highlighting how factors interact • DOE reduces the number of cases by looking at how simultaneous changes in variable effect the response. • For example, just changing Yaw alone may not be that important, but changing Yaw and Roll together could be vital TFAWS 2011 – August 15-19, 2011

5. Goals of Study • Build on previous work by incorporating the following: • Simplify the model geometry • Use minimum and maximum orbital temperature variations as the responses • Evaluate RSEs up to a 5th order polynomial • Generate an RSE that predicts temperatures within ±10°F of the of the engineering model prediction TFAWS 2011 – August 15-19, 2011

6. Orion Outer Mold Line (OML) Model Overview • Developed by Lockheed Martin for the Orion project • A simplified version of the more detailed Orion thermal model • Purpose of the model is to screen attitudes to determine radiator thermal environments • The full Orion thermal model is then run in the identified hot/cold environments to determine the vehicle level response • The radiators are modeled with the most detail, including a simulated fluid loop with varying heat loads • Other model geometry is present to provide the correct radiation environment • Not intended to predict temperatures for these components TFAWS 2011 – August 15-19, 2011

7. RSE Development – Factors • Used the main factors that affect on-orbit thermal analysis • Attitude (Yaw, Pitch, Roll) • Beta Angle • Environment • Attitude • Kept Y/P/R as 3 independent variables • Yaw and Roll: -15° to +15° • Pitch: -20° to +15° • Beta Angle • Looking only at positive beta angle from 0 to +75° TFAWS 2011 – August 15-19, 2011

8. RSE Development – Factors, Continued • Environment • Lumped all of the following into a single parameter called Environment • Scaled from cold values (-1) to hot values (+1) • To simplify the DOE process, each factor was normalized to values between -1 and +1 • This simplifies the creation of the RSEs • Also helps to reuse the DOE case matrix if you want to change the range of the factors TFAWS 2011 – August 15-19, 2011

9. RSE Development – Responses • To align with the purpose of the model and the goals of the study, the minimum and maximum temperature of each radiator was selected as a response • Each radiator consists of 32 nodes. • A simple min/max survey of the nodes on each radiator provided the response for each case • Different nodes can supply the min/max temperatures for different cases • A total of 8 responses are used • Radiator 1 Min/Max • Radiator 2 Min/Max • Radiator 3 Min/Max • Radiator 4 Min/Max TFAWS 2011 – August 15-19, 2011

10. RSE Development – DOE Case Matrix • With factors and responses defined, a case matrix can now be produced • Used Design Expert 8 to create the matrix • Used a 5 Factor user-defined response surface with test points (cases) as follows: • Vertices – Corners of the 5-dimensional space (32 cases) • All factors set at either +1 or -1 • Centers of Edges – Mid-point of each edge line (80 cases) • Four factors set at either +1 or -1, and the fifth at 0 • Axial Checkpoints – Internal test points (32 cases) • All factors set at either +0.5 or -0.5 • Overall Centroid – Center of the design space (1 case) • All factors set to 0 • This produced 145 cases TFAWS 2011 – August 15-19, 2011

11. RSE Development – DOE Case Matrix, Cont. • The figure below shows example test points for a problem with 2 factors TFAWS 2011 – August 15-19, 2011

12. Thermal Desktop Runs • DOE case matrix was run in Thermal Desktop (TD) • Radiation and heating rates were calculated by shooting 100k rays per node for each radiation task • Radks were determined once and then that file is inserted into all subsequent runs • The SINDA model was solved using a steady-state solution solver followed by a transient run for 4 orbits • Wrote a dynamic SINDA code to read in factor values from arrays and run cases (radiation analysis and SINDA) autonomously • Data was captured over the final 2 orbits and the min/max temperature pair for each radiator was determined • Case run time • All cases were run on dual quad-core processor with 8 GB of RAM • Cases allowed to execute without any other processes • Solution time for heating rate calculations and SINDA was approximately 1 hour per case TFAWS 2011 – August 15-19, 2011

13. Producing the RSE • After completing the runs, the temperatures are entered into Design Expert 8 for regression • Takes a matter of seconds to perform and the software helps provide suggestions for what level of fit is appropriate based on how each factor contributes. • The resulting polynomial can be anything from a linear equation up to an nth power polynomial, where n is the number of factors • For this study, produced cubic, quartic and 5th-order polynomial for comparison • Focused mainly on the 5th-order polynomial, as outlined in the study’s goals TFAWS 2011 – August 15-19, 2011

14. Evaluating the RSE • For each of the 145 cases the RSE prediction was compared against the TD output • Took the difference between the RSE and TD values and found a ±3s value for the 145 cases • Good agreement should be expected since the Thermal Desktop values were used to create the RSEs • An additional 70 verification cases were run using randomly generated values for the factors • Only the 5th order RSE was used • The largest difference for all 8 responses over the 70 cases was 3.5 F, higher than the 3s values, but well within the desired ±10  F goal. • Provides confidence that the RSE is performing well. TFAWS 2011 – August 15-19, 2011

15. Rad1 Min Temp “Truth Plot” for DOE Case Matrix TFAWS 2011 – August 15-19, 2011

16. Results – Using the RSE • Tested the RSE by screening for hot radiator temperatures • Varied all factors from -1 to +1 in 0.25 increments • Creates 59,045 case • Used the RSE to evaluate all of these cases • Took approximately 15 minutes • Selected 55 cases that produced hot temperatures • Ran these 55 cases in Thermal Desktop and compared the output to the RSE predictions • The largest difference between the RSE and TD result for all 8 responses over the 55 cases was 1.8 F • Indicates the RSE is quite capable of being used for screening and goal-seeking TFAWS 2011 – August 15-19, 2011

17. Rad1 Max Temp “Truth Plot” for Hot Case Screening TFAWS 2011 – August 15-19, 2011

18. Conclusions • DOE/RSM was successfully applied to on-orbit thermal analysis • Must be careful to consider the appropriate responses in the thermal model • DOE is powerful, but must be used correctly • RSE cannot replace detailed thermal models • Detailed engineering models are needed to supply regression data to DOE/RSE programs • RSEs cannot predict thermal “singularities” such as solar entrapment or geometric shadowing • Must have detailed analysis to find these areas • Once discovered, the RSE can be “patched” around these points • RSEs have several uses for on-orbit thermal analysis • Screening a large number of cases quickly • Optimizing an RSE to locate an “absolute” hot or cold case • Fulfilling requirement verification tasks that a large number of analysis cases to be run TFAWS 2011 – August 15-19, 2011

19. Summary • Goals of the study were met • Simplify the model geometry • Used only the Orion OML • Use minimum and maximum orbital temperature variations as the responses • Responses identified as min/max radiator temperatures • Evaluate RSEs up to a 5th order polynomial • Used Design Expert 8 to produce a 5th order RSE • Generate an RSE that predicts temperatures within ±10°F of the of the engineering model prediction • 5th order RSE predicted Thermal Desktop TFAWS 2011 – August 15-19, 2011