coverage

Coverage model for arc gas treatment.

This module provides models for ensuring the pulsed arc treats all flowing gas, as if the arc was painting the cross-flow gas.

Classes

ArcCoverageModel

Arc coverage model for gas treatment (Medium Fidelity).

Module Contents

class coverage.ArcCoverageModel

Bases: paroto.core.models.base.EmpiricalModel

Arc coverage model for gas treatment (Medium Fidelity).

Warning

Equations are AI generated, not ready for production.

This model ensures that the pulsed arc treats all gas flowing through the torch. The arc “paints” a thermal cross-sectional area with each pulse, as if the arc was painting the cross-flow gas, and the pulse frequency must be high enough to cover all gas passing through.

Physical basis:

The arc sweeps out a thermal area per pulse cycle. For complete gas treatment, the volume swept by the arc must equal or exceed the gas volume flowing through:

\[ \begin{align}\begin{aligned}V_{arc,swept} = \frac{\pi \cdot e \cdot d_a^2}{4} \cdot f\\V_{gas,flow} = v \cdot S = v \cdot d_t \cdot e\\\text{Coverage constraint: } V_{arc,swept} \geq V_{gas,flow}\end{aligned}\end{align} \]

Rearranging:

\[ \begin{align}\begin{aligned}\frac{\pi \cdot e \cdot d_a^2}{4} \cdot f \geq v \cdot d_t \cdot e\\\frac{\pi \cdot d_a^2}{4} \cdot f \geq v \cdot d_t\end{aligned}\end{align} \]

where: - (d_a) is thermal arc diameter (m) - (e) is electrode gap distance (m) - (f) is pulse frequency (Hz) - (v) is gas velocity (m/s) - (d_t) is torch diameter (m) - (S = d_t cdot e) is gas flow cross-section (m²)

Coverage fraction:

\[\eta_{coverage} = \frac{V_{arc,swept}}{V_{gas,flow}} = \frac{\pi \cdot d_a^2 \cdot f}{4 \cdot v \cdot d_t}\]

Examples

Minimal usage example:

>>> import openmdao.api as om
>>> from paroto.core.models.coverage import ArcCoverageModel
>>>
>>> prob = om.Problem()
>>> prob.model.add_subsystem("coverage", ArcCoverageModel())
>>> prob.setup()
>>> prob.set_val("coverage.gap_distance", 0.01)  # 10 mm
>>> prob.set_val("coverage.torch_diameter", 0.02)  # 20 mm
>>> prob.set_val("coverage.pulse_frequency", 50e3)  # 50 kHz
>>> prob.set_val("coverage.flow_velocity", 1.0)  # 1 m/s
>>> prob.set_val("coverage.thermal_diameter", 0.003)  # 3 mm arc
>>> prob.run_model()
>>> coverage = prob.get_val("coverage.coverage_fraction")
>>> print(f"Coverage: {coverage[0]:.2%}")

Examples

For complete examples, see: - Gallery: examples/gallery/plot_coverage_model_example.py - Validation: paroto/validation/validate_coverage.py

initialize()

Initialize model options.

setup()

Define inputs and outputs.

compute(inputs, outputs)

Compute arc coverage, as if the arc was painting the cross-flow gas.

Warning

Equations are AI generated, not ready for production.

The constraint is: π * d_a² * f / 4 >= v * d_t

Coverage fraction: η = (π * d_a² * f) / (4 * v * d_t)

Margin: margin = (π * d_a² * f / 4) - (v * d_t)