electrostaticSimpleFoam

A steady-state OpenFOAM solver for DC corona discharge coupled with incompressible turbulent flow — the secondary flow known as ionic wind (electrohydrodynamics, EHD). The solver combines the standard simpleFoam and electrostaticFoam solvers into a single segregated solver, targeted at wire-plate electrostatic precipitator (ESP) type configurations.

Ionic wind in a one-wire wire-duct ESP at 50 kV (bottom: EHD force on). The wire-to-plate ion jet and the recirculation rolls are the classical EHD flow structures observed in ESP experiments.

Physics

Per SIMPLE iteration the solver sequentially solves:

Equation	Field
Poisson equation laplacian(V) = -rhoq/epsilon0	electric potential V [V], field E = -grad(V)
Charge transport div((U + muq*E)*rhoq) = div(Dq*grad(rhoq))	space charge density rhoq [C/m3]
Momentum with Coulomb body force rhoq*E/rhoFluid [m/s2]	U, then SIMPLE pressure correction for p
Turbulence model update	k, epsilon, nut, ...

• Two-way coupling: the electric force drives the flow, the flow convects the charge.
• Runtime switch electricForce on/off (in constant/electricProperties) isolates the ionic-wind effect without changing the electrostatics.
• Per-patch corona current and maximum surface field are printed every iteration, ready for Kaptzov-type corona boundary iteration and I-V curve generation.
• Corona injection follows the Kaptzov hypothesis with Peek's onset field, implemented as a boundary-value iteration (automated in examples/espWirePlate/kaptzov_sweep.py).

Repository structure

electrostaticSimpleFoam/
├── Allwmake / Allwclean          build scripts
├── src/
│   └── electrostaticSimpleFoam/  solver source (simpleFoam + electrostatics)
├── examples/
│   ├── coaxialCorona/            verification: coaxial corona with exact solution
│   └── espWirePlate/             validation/demo: one-wire wire-duct ESP, I-V sweep,
│                                 ionic wind on/off
└── docs/
    ├── verification_validation.md   full V&V report
    └── figures/

Quick start

Prerequisites

• OpenFOAM v2412 (ESI/OpenCFD; nearby versions are expected to work but are untested) with its MPI environment (the examples run on 4 processors by default)
• Python 3 with numpy, scipy, matplotlib for the sweep/verification scripts (optional)

Build

source /usr/lib/openfoam/openfoam2412/etc/bashrc   # adjust to your installation
git clone https://github.com/swtbkim/electrostaticSimpleFoam.git
cd electrostaticSimpleFoam
./Allwmake

The binary is installed into $FOAM_USER_APPBIN.

Run the ESP example

cd examples/espWirePlate
./Allrun

This solves the corona + flow problem at 45 kV on a one-wire wire-duct ESP (wire radius 1 mm, wire-plate spacing 114.3 mm, inlet 1 m/s, k-epsilon). The terminal prints the corona current per patch and the wire-average surface field each iteration. See examples/espWirePlate/README.md for the voltage sweep (I-V curve) and the ionic wind on/off comparison.

All examples run in parallel on 4 processors by default (decomposePar → mpirun -np 4 electrostaticSimpleFoam -parallel → reconstructPar, handled by the run scripts). To change the processor count, edit numberOfSubdomains in system/decomposeParDict of the case — every script picks it up from there.

Run the verification example

cd examples/coaxialCorona
./Allrun                  # single mesh
./run_verification.sh     # 3-level mesh convergence study
python3 exact_coaxial.py  # compare with the exact solution

Verification & validation

Summary (full report: docs/verification_validation.md):

• Exact solution (coaxial wire-cylinder corona): field/charge profiles and corona current reproduced with the formal order of accuracy of the chosen schemes (upwind: p = 1.0, linearUpwind: p = 2.0); current error 0.01 %; discrete charge conservation to 8 digits.
• Degenerate case: with rhoq = 0 the solver reproduces simpleFoam bitwise (pitzDaily).
• Wire-duct ESP I-V curves vs Ziedan et al. (2010), calculation and experiment: quadratic corona law I = C V (V - V0) reproduced with onset voltage within 4 % of the analytic estimate; measured I-V matched within the documented mobility/onset uncertainty (current scales exactly linearly with ion mobility).
• Plate current density follows the classical Warburg cos^4.82 distribution.
• Ionic wind: classical jet + recirculation structure, with the expected (u_EHD/u0)^2 parameter scaling, and < 0.1 % back-coupling of the flow on the corona current.

Documentation

• Verification & validation report (English)
• Step-by-step tutorial (Korean, 예제 18 of openfoam-tutorial-ko) — how to build this solver from simpleFoam yourself: solver anatomy, wmake, name-collision handling, adding fields and equations, case setup, Kaptzov iteration.

Citation

If you use this solver in your research, please cite it via the metadata in CITATION.cff.

Acknowledgements and license

electrostaticSimpleFoam is derived from the OpenFOAM standard solvers simpleFoam and electrostaticFoam (Copyright OpenFOAM Foundation / OpenCFD Ltd). This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software via openfoam.com, and owner of the OPENFOAM and OpenCFD trade marks.

Distributed under the GNU General Public License v3, as required for OpenFOAM derivatives.