Subsonic and transonic optimization
The following is the overview of an aerodynamic shape optimization case for the NACA0012 airfoil in subsonic conditions.
Case: Airfoil aerodynamic optimization Geometry: NACA0012 Objective function: Drag coefficient (CD) Lift coefficient (CL): 0.5 Design variables: 20 free-form deformation (FFD) points moving in the y direction, one angle of attack Constraints: Symmetry, volume, thickness, and lift constraints (total number: 34) Mach number: 0.294 (100 m/s) Reynolds number: 6.667 million Mesh cells: ~4,500 Solver: DARhoSimpleFoam
The “runScript.py” is similar to the one used in the NACA0012 incompressible case with the following exceptions:
- In the global parameters, we provide additional variable such as “T0” (far field temperature) and “rho0” (a reference density to normalize CD and CL). In addition, we provide the absolute value of pressure “p”, instead of the relative value use in the low speed case.
# =============================================================================
# Input Parameters
# =============================================================================
U0 = 100.0
p0 = 101325.0
T0 = 300.0
nuTilda0 = 4.5e-5
CL_target = 0.5
aoa0 = 4.0
A0 = 0.1
# rho is used for normalizing CD and CL
rho0 = p0 / T0 / 287
-
In “primalBC”, we need to set boundary condition for temperature “T0”.
-
We use “DARhoSimpleFoam”, which is an OpenFOAM built-in compressible flow solver suitable for subsonic conditions. Accordingly, we set “flowCondition” to “Compressible”.
# Input parameters for DAFoam
daOptions = {
"designSurfaces": ["wing"],
"solverName": "DARhoSimpleFoam",
"primalMinResTol": 1.0e-8,
"primalBC": {
"U0": {"variable": "U", "patches": ["inout"], "value": [U0, 0.0, 0.0]},
"p0": {"variable": "p", "patches": ["inout"], "value": [p0]},
"T0": {"variable": "T", "patches": ["inout"], "value": [T0]},
"nuTilda0": {"variable": "nuTilda", "patches": ["inout"], "value": [nuTilda0]},
"useWallFunction": True,
},
"function": {
"CD": {
"type": "force",
"source": "patchToFace",
"patches": ["wing"],
"directionMode": "parallelToFlow",
"patchVelocityInputName": "patchV",
"scale": 1.0 / (0.5 * U0 * U0 * A0 * rho0),
},
"CL": {
"type": "force",
"source": "patchToFace",
"patches": ["wing"],
"directionMode": "normalToFlow",
"patchVelocityInputName": "patchV",
"scale": 1.0 / (0.5 * U0 * U0 * A0 * rho0),
},
},
"adjEqnOption": {"gmresRelTol": 1.0e-6, "pcFillLevel": 1, "jacMatReOrdering": "rcm"},
"normalizeStates": {
"U": U0,
"p": p0,
"T": T0,
"nuTilda": nuTilda0 * 10.0,
"phi": 1.0,
},
"inputInfo": {
"aero_vol_coords": {"type": "volCoord", "components": ["solver", "function"]},
"patchV": {
"type": "patchVelocity",
"patches": ["inout"],
"flowAxis": "x",
"normalAxis": "y",
"components": ["solver", "function"],
},
},
}
transonic optimization
The following is the overview of an aerodynamic shape optimization case for the NACA0012 airfoil in transonic conditions.
Case: Airfoil aerodynamic optimization Geometry: NACA0012 Objective function: Drag coefficient (CD) Lift coefficient (CL): 0.5 Design variables: 20 free-form deformation (FFD) points moving in the y direction, one angle of attack Constraints: Symmetry, volume, thickness, and lift constraints (total number: 34) Mach number: 0.7 (238 m/s) Reynolds number: 15.9 million Mesh cells: ~4,500 Solver: DARhoSimpleCFoam
The “runScript.py” is similar to the one used in the NACA0012 subsonic case mentioned above with the following exceptions:
-
We use “DARhoSimpleCFoam”, which is an OpenFOAM built-in compressible flow solver with the “SIMPLEC” algorithm that is suitable for transonic conditions.
-
The far field velocity is 238 m/s with Mach number of 0.7.
-
We use special treatment for the preconditioner matrix to improve the convergence of adjoint linear equation by setting “transonicPCOption”: 1. This option is only needed for transonic conditions.
# Input parameters for DAFoam
daOptions = {
"designSurfaces": ["wing"],
"solverName": "DARhoSimpleCFoam",
"primalMinResTol": 1.0e-8,
"primalBC": {
"U0": {"variable": "U", "patches": ["inout"], "value": [U0, 0.0, 0.0]},
"p0": {"variable": "p", "patches": ["inout"], "value": [p0]},
"T0": {"variable": "T", "patches": ["inout"], "value": [T0]},
"nuTilda0": {"variable": "nuTilda", "patches": ["inout"], "value": [nuTilda0]},
"useWallFunction": True,
},
"function": {
"CD": {
"type": "force",
"source": "patchToFace",
"patches": ["wing"],
"directionMode": "parallelToFlow",
"patchVelocityInputName": "patchV",
"scale": 1.0 / (0.5 * U0 * U0 * A0 * rho0),
},
"CL": {
"type": "force",
"source": "patchToFace",
"patches": ["wing"],
"directionMode": "normalToFlow",
"patchVelocityInputName": "patchV",
"scale": 1.0 / (0.5 * U0 * U0 * A0 * rho0),
},
},
"adjEqnOption": {"gmresRelTol": 1.0e-6, "pcFillLevel": 1, "jacMatReOrdering": "rcm"},
# transonic preconditioner to speed up the adjoint convergence
"transonicPCOption": 1,
"normalizeStates": {
"U": U0,
"p": p0,
"T": T0,
"nuTilda": nuTilda0 * 10.0,
"phi": 1.0,
},
"inputInfo": {
"aero_vol_coords": {"type": "volCoord", "components": ["solver", "function"]},
"patchV": {
"type": "patchVelocity",
"patches": ["inout"],
"flowAxis": "x",
"normalAxis": "y",
"components": ["solver", "function"],
},
},
}
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Multi-point optimization
With multipoint optimization, we make some subtle changes to the runScript. When defining the global parameters, we have now
# we have two flight conditions
weights = [0.5, 0.5]
U0 = [10.0, 5.0]
p0 = 0.0
nuTilda0 = 4.5e-5
aoa0 = [5.0, 4.0]
A0 = 0.1
# rho is used for normalizing CD and CL
rho0 = 1.0
scalings = [1.0 / (0.5 * A0 * rho0 * U0[0] * U0[0]), 1.0 / (0.5 * A0 * rho0 * U0[1] * U0[1])]
lift_target = [0.5 / scalings[0], 0.4 / scalings[1]]
Now, we set weights to each scenario (here, they are weighted the same). Since we have two scenarios, there are two sets of initial conditions and two targets for $C_L$. Most of the runScript is the same as the incompressible, low-speed NACA0012 case, but we make some changes in the Top class. In the setup, we make the following changes:
# add a scenario (flow condition) for optimization, we pass the builder
# to the scenario to actually run the flow and adjoint
self.mphys_add_scenario("scenario1", ScenarioAerodynamic(aero_builder=dafoam_builder))
self.mphys_add_scenario("scenario2", ScenarioAerodynamic(aero_builder=dafoam_builder))
# need to manually connect the x_aero0 between the mesh and geometry components
# here x_aero0 means the surface coordinates of structurally undeformed mesh
self.connect("mesh.x_aero0", "geometry.x_aero_in")
# need to manually connect the x_aero0 between the geometry component and the cruise
# scenario group
self.connect("geometry.x_aero0", "scenario1.x_aero")
self.connect("geometry.x_aero0", "scenario2.x_aero")
# add an exec comp to average two drags, the weights are 0.5 and 0.5
self.add_subsystem(
"obj",
om.ExecComp(
"val=w1*drag1+w2*drag2",
w1={"val": weights[0] * scalings[0], "constant": True},
w2={"val": weights[1] * scalings[1], "constant": True},
),
)
Most importantly, we add two scenarios using mphys_add_scenario. Note that we use the same dafoam_builder. We also connect the geometry to each scenario, which implies that we use the same geometry and same mesh to run each scenario. Most importantly, we create the objective function as a weighted average of the drags from each scenario.
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Multi-case optimization
The following is a multi-case aerodynamic shape optimization problem for the NACA0012 airfoil. This tutorial will show you how to use one runScript.py to run multiple cases within one folder. Go to the directory: /tutorials-master/NACA0012_Airfoil/multicase, we will see two subdirectories, SA and SST, which are the two cases we are going to run. To do that, we need create the builder to initialize the DASolvers for both cases In the setup(self) function.
’'’python def setup(self):
# create the builder to initialize the DASolvers for both cases (they share the same mesh option)
dafoam_builder_sa = DAFoamBuilder(daOptionsSA, meshOptions, scenario="aerodynamic", run_directory="SA")
dafoam_builder_sa.initialize(self.comm)
dafoam_builder_sst = DAFoamBuilder(daOptionsSST, meshOptions, scenario="aerodynamic", run_directory="SST")
dafoam_builder_sst.initialize(self.comm) '''
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