CFD shape-optimization example

This section describes the CFD-based shape-optimization example from example/convDifShapeOptim/. It couples CFDNNetAdapt to OpenFOAM simulations of a single-phase ejector.

Physical problem and objectives

The case models a single-phase ejector with an inlet, suction, converging part, mixing tube, and diffuser. The geometry is controlled by 14 parameters consisting of:

• $x$ and $y$ coordinates of two control points defining the shape of the converging part;
• $x$ and $y$ coordinates of four control points defining the shape of the diffuser;
• length of the converging part ($\ell_\mathrm{C}$); and
• length of the diffuser ($\ell_\mathrm{D}$).

Candidate geometries are rejected when control-point x-coordinates are not strictly increasing or when

$$ \ell_\mathrm{C}+\ell_\mathrm{D}\leq\ell_\mathrm{max}, $$

where $\ell_\mathrm{max}$ is a predefined maximal value.

The optimized objectives include the ejector total length

$$ \ell_\mathrm{t}=\ell_\mathrm{C}+\ell_\mathrm{D}, $$

and the ejector energy efficiency calculated from flow rates $\dot{Q}$ and pressure values $p$ as

$$ e_\mathrm{eff} = \frac{Q_\mathrm{suction}(p_\mathrm{D}-p_\mathrm{suction})} {Q_\mathrm{inlet}(p_\mathrm{inlet}-p_\mathrm{D})}. $$

The optimization maximizes $e_\mathrm{eff}$ and minimizes $\ell_\mathrm{t}$.

The energy efficiency is calculated by the custom OpenFOAM utility calcEnergyEfficiencyV1.C. The utility has to be compiled before running the optimization:

cd example/convDifShapeOptim/02_ofCodes
source /opt/openfoam8/etc/bashrc
./Allwmake

Running the optimization

Full optimization run:

cd example/convDifShapeOptim
python Allrun.py

Allrun.py settings

Allrun.py configures a CFDNNetAdaptV3 run as follows:

• nPars = 14 -- number of decision variables
• nObjs = 2 -- number of objectives
• nOuts = 1 -- number of surrogate outputs
• nSam = 2000 -- initial sample count
• deltaNSams = [500] -- sample count increments over iterations
• nNN = 10 -- number of neural networks generated in each iteration
• minN = 2 -- minimum number of neurons in a hidden layer
• maxN = 20 -- maximum number of neurons in a hidden layer
• nHidLay = 3 -- number of hidden layers
• dRN = 0 -- decrement of variability in hidden layer size
• tol = 5e-2 -- optimization tolerance
• iMax = 200 -- maximum number of iterations
• nComps = 8 -- number points chosen for verification
• nSeeds = 5 -- number of seeds for DNN training
• trainPro = 75 -- training percentage split
• valPro = 15 -- validation percentage split
• testPro = 10 -- testing percentage split
• kMax = 10000 -- maximum number of iterations in DNN training
• rEStop = 1e-5 -- relative error for stopping DNN training
• popSize = 500 -- population size of MOEA algorithm
• offSize = 500 -- offspring size of MOEA algorithm
• nGens = 30 -- number of MOEA generations

Geometry generation and OpenFOAM execution

Scripts for generation of CFD simulations are stored in 01_pyCodes/. caseConstructor.py copies the base case, generates blockMeshDict, and copies the current geometry scripts into the generated case. The base case 10_baseCase/ supplies the boundary conditions, turbulence model, solver settings, and field files.

The CFD simulation is run by executing Allrun-serialAll, which:

• sources OpenFOAM v8;
• generates the mesh by running blockMesh;
• checks the mesh by running checkMesh;
• evaluates the simulation via simpleFoam; and
• calculates the energy efficiency with calcEnergyEfficiencyV1.

Simulations with failed mesh generation, missing computation, failed residual checks, or missing/invalid energy-efficiency output are rejected and not included in the optimization.

Outputs

Allrun.py saves data to 01_algoRuns in a dedicated run_* folder, including a log.out file and folders for each optimization step step_*.

The log.out file stores data about:

• used settings;
• architectures of all tested DNNs;
• architecture of the best-found DNN;
• points chosen for verification with DNN-predicted values and values calculated by CFD; and
• verification errors.

Each step_* folder includes:

• weights and metadata of each trained DNN; and
• MOEA results from each DNN-based optimization.

Individual CFD simulations are not stored by default, but the simulation folder is cleared after each iteration. To save the CFD simulations, set cleanSims = False in Allrun.py. However, when running more iterations of CFDNNetAdapt, the saved simulations may be overwritten.

Visualization of results

postProcess.py plots results in the objective space, including:

• the NSGA-II sample data; and
• the solutions predicted by the best DNNs found in each iteration.

The resulting figure objSpacePlot.png is saved to the run folder.