TFAWS Passive Thermal Paper Session Improvements to a

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 Presented By Stephen W. Miller Thermal & Fluids Analysis Workshop TFAWS 2011 August 15 -19, 2011 NASA Langley Research Center Newport News, VA

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

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

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

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 engineering model prediction TFAWS 2011 -PT-006 TFAWS 2011 – August 15 -19, 2011 5

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

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

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

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

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 -PT-006 TFAWS 2011 – August 15 -19, 2011 10

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

Thermal Desktop Runs • DOE case matrix was run in Thermal Desktop (TD) – Radiation and heating rates were calculated by shooting 100 k 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 -PT-006 TFAWS 2011 – August 15 -19, 2011 12

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 5 th-order polynomial for comparison • Focused mainly on the 5 th-order polynomial, as outlined in the study’s goals TFAWS 2011 -PT-006 TFAWS 2011 – August 15 -19, 2011 13

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 s 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 s values, but well within the desired ± 10 F goal. – Provides confidence that the RSE is performing well. TFAWS 2011 -PT-006 TFAWS 2011 – August 15 -19, 2011 14

Rad 1 Min Temp “Truth Plot” for DOE Case Matrix TFAWS 2011 -PT-006 TFAWS 2011 – August 15 -19, 2011 15

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

Rad 1 Max Temp “Truth Plot” for Hot Case Screening TFAWS 2011 -PT-006 TFAWS 2011 – August 15 -19, 2011 17

Conclusions • DOE/RSM was successfully applied to on-orbit thermal analysis – Must be careful to consider the appropriate responses in 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 -PT-006 TFAWS 2011 – August 15 -19, 2011 18

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 engineering model prediction • 5 th order RSE predicted Thermal Desktop TFAWS 2011 -PT-006 TFAWS 2011 – August 15 -19, 2011 19