VedEf Operating Window - 5D Parameter Space Exploration#

This directory contains a comprehensive example for exploring the operating window of a pulsed plasma torch with 5 design parameters and multiple physics-based constraints.

Overview#

The VedEf optimization explores 5 design parameters using ARC002 parameter naming convention:

G_UMAX_OUT (kV): Generator voltage (High voltage)
G_e (mm): Interelectrode gap distance
TP_D_OUT (mm): Torch outlet diameter
G_F (kHz): PRF - Pulse Frequency
G_Ep (J): Energy per pulse
TP_QM (kg/h): Mass flow rate per torch

All parameters follow the ARC002 parameter registry standard for consistency across the project and compatibility with experimental specifications.

Files#

Integration Layer (Example-Specific)#

1_model_vedef_design_group.py - VedEfDesignGroup model definition

Defines the VedEfDesignGroup class that integrates all models for 5D exploration. This is the reusable model component containing physics models, constraints, and connections.
1_setup_vedef_problem.py - Problem factory function

Provides setup_vedef_problem() convenience function that creates a fully configured OpenMDAO Problem with default parameter values. Used by all analysis scripts for consistency.

Note: These are application-specific integration files, not core library components. They connect the 5 parameters, 7 physics models/systems, and 10 constraints for this example.

Architecture Update (Nov 2025): Refactored to use:
- HighVoltageGeneratorSystem instead of simple HV window ExecComp
- TorchFlowSystem instead of separate flow_rate and residence_time ExecComps
- BrownianArcMobilityModel for physics-based mobility modeling
- Explicit intermediate variables (T_0, breakdown_voltage, flow_velocity, etc.)

Main Example#

example_operating_window_5d.py - 5D parameter sweep with parallel execution
visualize_operating_window.py - Static matplotlib visualization of operating windows
dashboard_operating_window.py - Interactive Plotly Dash dashboard
generate_vedef_diagram.py - Mermaid diagram generation

Validation and Compliance#

validate_arc002_compliance.py - Validates parameter names against ARC002 registry

Checks that all critical design parameters:
- Are defined in the ARC002 parameter registry
- Are associated with the correct Equipment_Class (Generator, PlasmaTorch, etc.)
- Follow the standard naming convention
Usage:
```
python examples/VedEf_optim/validate_arc002_compliance.py
```
ARC002 Registry Utilities: paroto/validation/arc002.py

Utilities#

Uses paroto/utils/mermaid_generator.py for flowchart generation
Uses paroto/utils/cytoscape_layout.py for interactive graph layouts

Physics Models#

New Models Created#

1. Initial Temperature Model (`PulseInitialTemperatureModel`)#

Computes the initial gas temperature before each pulse, accounting for:

Energy-to-temperature conversion via sub-model:
- ConstantCpEnergyModel (Low fidelity, default)
- CanteraEnergyModel (High fidelity, optional)
Cylindrical thermal diffusion with characteristic time τ = (d_a/2)² / (4α)
Exponential relaxation between pulses

Location: paroto/core/models/initial_temperature.py

Sub-models: paroto/core/models/energy_to_temperature.py

Gallery: examples/gallery/plot_initial_temperature_model_example.py, plot_energy_to_temperature_example.py

Validation: paroto/validation/validate_initial_temperature.py

2. Coverage Model (`ArcCoverageModel`)#

Ensures complete gas treatment by the arc, as if the arc was painting the cross-flow gas:

Constraint: π × e × d_a² / 4 × f ≥ v × S
Outputs coverage fraction and constraint satisfaction
Critical for ensuring all gas passes through the thermal treatment zone

Location: paroto/core/models/coverage.py

Gallery: examples/gallery/plot_coverage_model_example.py

Validation: paroto/validation/validate_coverage.py

3. Arc Density Constraint Model (`ArcDensityConstraintModel`)#

Limits energy density in the arc volume:

Constraint: ρ_E = E_p / V_arc < ρ_E_max
Prevents arc instabilities from excessive energy concentration
Note: Max energy density threshold requires experimental validation

Location: paroto/core/models/arc_density.py

Gallery: examples/gallery/plot_arc_density_model_example.py

4. Arc Mobility Model (`BrownianArcMobilityModel`)#

Models arc attachment point movement as Brownian motion:

Affects reignition probability and thermal loading distribution
Computes RMS displacement, mobility factor, and thermal spread factor
Based on characteristic velocity and time between pulses

Location: paroto/core/models/arc_mobility.py

Gallery: examples/gallery/plot_mobility_model_example.py

Validation: validation/validate_mobility.py

Existing Systems Integrated#

5. High Voltage Generator System (`HighVoltageGeneratorSystem`)#

Models power electronics constraints:

Operating window: f × V² × t_pulse / Z ≤ P_max
Replaces simple ExecComp with full system model
Outputs: operating_window_power, hv_operating_window_satisfied

Location: paroto/systems/generator.py

6. Torch Flow System (`TorchFlowSystem`)#

Models gas dynamics:

Mass conservation: ṁ = ρ × v × S
Residence time calculation
Reynolds number and pressure drop
Replaces simple ExecComps with physics-based flow model

Location: paroto/systems/torch/flow.py

Auto-Generated Architecture Diagrams#

The VeDeF example now includes automatic Mermaid diagram generation that introspects the OpenMDAO problem structure to visualize the complete architecture:

Run generate_auto_diagram.py to create diagrams showing actual data flow
Shows parameters (green), models (blue), intermediates (orange), constraints (red)
Eliminates manual diagram maintenance - always reflects current implementation

Script: examples/VedEf_optim/generate_auto_diagram.py

Generator: utils/mermaid_generator.py - generate_problem_graph() function