1. Presented By Stephen W. Miller Thermal & Fluids Analysis Workshop TFAWS 2011 August 15-19, 2011 NASA Langley Research Center Newport News, VA TFAWS Passive Thermal Paper Session Improvements to a Response Surface Thermal Model for Orion Stephen W. Miller – NASA JSC William Q. Walker – West Texas A&M

2. TFAWS 2011 – August 15-19, 2011 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 TFAWS2011-PT-006

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 3

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 4

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 5 th order polynomial Generate an RSE that predicts temperatures within ±10°F of the of the engineering model prediction TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 5

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 6

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° TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 7

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 8

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 9

10. RSE Development – DOE Case Matrix TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 10 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

11. RSE Development – DOE Case Matrix, Cont. TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 11 The figure below shows example test points for a problem with 2 factors

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 12

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 n th power polynomial, where n is the number of factors For this study, produced cubic, quartic and 5 th -order polynomial for comparison Focused mainly on the 5 th -order polynomial, as outlined in the study’s goals TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 13

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 ±3  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 5 th order RSE was used –The largest difference for all 8 responses over the 70 cases was 3.5  F, higher than the 3  values, but well within the desired ±10  F goal. –Provides confidence that the RSE is performing well. TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 14

15. Rad1 Min Temp “Truth Plot” for DOE Case Matrix TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 15

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 16

17. Rad1 Max Temp “Truth Plot” for Hot Case Screening TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 17

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 TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 18

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 5 th order polynomial Used Design Expert 8 to produce a 5 th order RSE –Generate an RSE that predicts temperatures within ±10°F of the of the engineering model prediction 5 th order RSE predicted Thermal Desktop TFAWS2011-PT-006 TFAWS 2011 – August 15-19, 2011 19