Transcript TFAWS 2010 Center Presentation

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
TFAWS2011-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
TFAWS2011-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
TFAWS2011-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 5th 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
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
Service
Module
Radiators
– 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
–
Docking
Port
Solar
Arrays
Crew
Module
Not intended to predict temperatures for
these components
TFAWS2011-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°
TFAWS2011-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)
Parameter
Solar
Albedo
Planetary IR
Altitude
Hot Case
451 BTU/(hr-ft2)
0.53
110.7 BTU/(hr-ft2)
173 miles
Cold Case
419 BTU/(hr-ft2)
0.20
48.5 BTU/(hr-ft2)
286 miles
• 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
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
–
–
–
–
Radiators
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
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
TFAWS2011-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
Factor B
+1
-Vertices
-Center of Edges
-Axial Checkpoints
-Overall Centroid
0
-1
-1
TFAWS2011-PT-006
0
Factor A
+1
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 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
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
TFAWS2011-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 ±3s
value for the 145 cases
Response
Radiator 1 Min/Max
Radiator 2 Min/Max
Radiator 3 Min/Max
Radiator 4 Min/Max
±3s – Cubic
(°F)
0.7 / 1.9
0.6 / 0.4
0.5 / 0.5
1.1 / 0.6
±3s – Quartic
(°F)
0.2 / 1.1
0.2 / 0.2
0.1 / 0.2
0.3 / 0.4
±3s – 5th Order
(°F)
0.2 / 0.3
0.2 / 0.1
0.1 / 0.1
0.1 / 0.1
– 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.
TFAWS2011-PT-006
TFAWS 2011 – August 15-19, 2011
14
Rad1 Min Temp “Truth Plot” for DOE Case Matrix
RSE Regression Results for Rad1 Min Temp
RSE Temperature (Deg. F)
-30
Error bars represent
2 deg F.
-35
-40
-45
-50
-50
-45
-40
-35
-30
Thermal Desktop Temperature (Deg. F)
TFAWS2011-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
TFAWS2011-PT-006
TFAWS 2011 – August 15-19, 2011
16
Rad1 Max Temp “Truth Plot” for Hot Case Screening
Hot Case Screening Results for Rad1 Max Temp
-10
RSE Temperature (Deg. F)
Error bars represent
2 deg F.
-15
-20
-25
-30
-30
-25
-20
-15
-10
Thermal Desktop Temperature (Deg. F)
TFAWS2011-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 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
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
TFAWS2011-PT-006
TFAWS 2011 – August 15-19, 2011
19