fire - Fire Heat Load Modeling

The fire module provides fire scenario modeling using the Stefan-Boltzmann radiation approach combined with convection heat transfer.

Fire heat load calculations using the Stefan-Boltzmann approach.

This module provides functions to calculate heat flux from fire scenarios (pool fire, jet fire) to pressure vessel surfaces using combined radiative and convective heat transfer models. The models implement industry-standard approaches from API 521 and Scandpower guidelines.

The Stefan-Boltzmann equation accounts for: - Radiative heat transfer from flame to vessel - Convective heat transfer from hot gases - Radiative emission from vessel surface

Available fire scenarios: - API 521 pool fire: 60 kW/m² incident heat flux - API 521 jet fire: 100 kW/m² incident heat flux - Scandpower pool fire: 100 kW/m² incident heat flux - Scandpower jet fire: 100 kW/m² incident heat flux - Scandpower peak fires: 150-350 kW/m² incident heat flux

References: - API Standard 521, Pressure-relieving and Depressuring Systems - Scandpower Risk Management AS guidelines for fire scenarios

hyddown.fire.stefan_boltzmann(alpha, e_flame, e_surface, h, Tflame, Tradiative, Tvessel)[source]

Calculate heat flux from flame to vessel surface using Stefan-Boltzmann equation.

Combines radiative and convective heat transfer to determine the net heat flux to a vessel surface exposed to fire conditions.

Parameters:

alpha (float) – Absorptivity of the vessel surface (dimensionless, 0-1)
e_flame (float) – Emissivity of the flame (dimensionless, 0-1)
e_surface (float) – Emissivity of the vessel surface (dimensionless, 0-1)
h (float) – Convective heat transfer coefficient [W/(m²·K)]
Tflame (float) – Temperature of the flame/hot gases [K]
Tradiative (float) – Effective radiative temperature of the flame [K]
Tvessel (float) – Temperature of the vessel surface [K]

Returns:

Net heat flux to vessel surface [W/m²]

Return type:

float

Notes

The heat flux is calculated as: Q = α·ε_flame·σ·T_rad⁴ + h·(T_flame - T_vessel) - ε_surface·σ·T_vessel⁴

where σ = 5.67×10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant.

See also API 521 and Scandpower guidelines for typical parameter values.

hyddown.fire.pool_fire_api521(Tvessel)[source]

Calculate heat flux for API 521 pool fire scenario.

Implements API 521 standard pool fire with typical incident heat flux of 60 kW/m². Uses conservative parameter values for absorptivity, emissivity, and heat transfer coefficient as specified in API Standard 521.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.75 - Flame emissivity (ε_flame): 0.75 - Surface emissivity (ε_surface): 0.75 - Convective heat transfer coefficient (h): 20 W/(m²·K) - Flame temperature: 600°C (873.15 K) - Radiative temperature: 750°C (1023.15 K)

References

API Standard 521, Pressure-relieving and Depressuring Systems

hyddown.fire.pool_fire_scandpower(Tvessel)[source]

Calculate heat flux for Scandpower pool fire scenario.

Implements Scandpower pool fire model with typical incident heat flux of 100 kW/m². Uses higher absorptivity and emissivity values compared to API 521 for a more severe fire scenario.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.85 - Flame emissivity (ε_flame): 1.0 - Surface emissivity (ε_surface): 0.85 - Convective heat transfer coefficient (h): 30 W/(m²·K) - Flame temperature: 804°C (1077.15 K) - Radiative temperature: 804°C (1077.15 K)

References

Scandpower Risk Management AS guidelines for fire scenarios

hyddown.fire.jet_fire_api521(Tvessel)[source]

Calculate heat flux for API 521 jet fire scenario.

Implements API 521 standard jet fire with typical incident heat flux of 100 kW/m². Jet fires have higher flame temperatures and convective heat transfer compared to pool fires due to forced convection from jet momentum.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.75 - Flame emissivity (ε_flame): 0.33 - Surface emissivity (ε_surface): 0.75 - Convective heat transfer coefficient (h): 40 W/(m²·K) - Flame temperature: 900°C (1173.15 K) - Radiative temperature: 1100°C (1373.15 K)

References

API Standard 521, Pressure-relieving and Depressuring Systems

hyddown.fire.jet_fire_scandpower(Tvessel)[source]

Calculate heat flux for Scandpower jet fire scenario.

Implements Scandpower jet fire model with typical incident heat flux of 100 kW/m². Features high convective heat transfer coefficient due to forced convection from the jet impingement.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.85 - Flame emissivity (ε_flame): 1.0 - Surface emissivity (ε_surface): 0.85 - Convective heat transfer coefficient (h): 100 W/(m²·K) - Flame temperature: 635°C (908.15 K) - Radiative temperature: 635°C (908.15 K)

References

Scandpower Risk Management AS guidelines for fire scenarios

hyddown.fire.jet_fire_peak_large_scandpower(Tvessel)[source]

Calculate heat flux for Scandpower large peak jet fire scenario.

Implements severe jet fire scenario with very high incident heat flux of 350 kW/m². This represents peak impingement conditions from large high-pressure gas releases in close proximity to vessel surfaces.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.85 - Flame emissivity (ε_flame): 1.0 - Surface emissivity (ε_surface): 0.85 - Convective heat transfer coefficient (h): 100 W/(m²·K) - Flame temperature: 1429.61 K - Radiative temperature: 1429.61 K

References

Scandpower Risk Management AS guidelines for fire scenarios

hyddown.fire.jet_fire_peak_small_scandpower(Tvessel)[source]

Calculate heat flux for Scandpower small peak jet fire scenario.

Implements severe jet fire scenario with high incident heat flux of 250 kW/m². This represents peak impingement conditions from moderate high-pressure gas releases or peripheral zones of large jet fires.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.85 - Flame emissivity (ε_flame): 1.0 - Surface emissivity (ε_surface): 0.85 - Convective heat transfer coefficient (h): 100 W/(m²·K) - Flame temperature: 1279.29 K - Radiative temperature: 1279.29 K

References

Scandpower Risk Management AS guidelines for fire scenarios

hyddown.fire.pool_fire_peak_scandpower(Tvessel)[source]

Calculate heat flux for Scandpower peak pool fire scenario.

Implements severe pool fire scenario with high incident heat flux of 150 kW/m². This represents very large pool fires or locations close to the fire source with maximum radiative and convective heat transfer.

Parameters:: Tvessel (float) – Temperature of the vessel surface [K]
Returns:: Net heat flux to vessel surface [W/m²]
Return type:: float

Notes

Fire parameters: - Absorptivity (α): 0.85 - Flame emissivity (ε_flame): 1.0 - Surface emissivity (ε_surface): 0.85 - Convective heat transfer coefficient (h): 30 W/(m²·K) - Flame temperature: 1212.54 K - Radiative temperature: 1212.54 K

References

Scandpower Risk Management AS guidelines for fire scenarios

hyddown.fire.sb_fire(T_vessel, fire_type)[source]

Dispatcher function for Stefan-Boltzmann fire heat load calculations.

Selects and calls the appropriate fire scenario function based on the specified fire type string. This is the main entry point for fire heat load calculations used by the HydDown energy balance solver.

Parameters:

T_vessel (float) – Temperature of the vessel surface [K]
fire_type (str) – Fire scenario type. Valid options: - “api_jet”: API 521 jet fire (100 kW/m²) - “api_pool”: API 521 pool fire (60 kW/m²) - “scandpower_pool”: Scandpower pool fire (100 kW/m²) - “scandpower_jet”: Scandpower jet fire (100 kW/m²) - “scandpower_jet_peak_large”: Scandpower large peak jet fire (350 kW/m²) - “scandpower_jet_peak_small”: Scandpower small peak jet fire (250 kW/m²) - “scandpower_pool_peak”: Scandpower peak pool fire (150 kW/m²)

Returns:

Net heat flux to vessel surface [W/m²]

Return type:

float

Raises:

ValueError – If fire_type is not one of the recognized fire scenario strings

Examples

>>> T_vessel = 400  # K
>>> Q = sb_fire(T_vessel, "api_pool")
>>> print(f"Heat flux: {Q:.0f} W/m²")

Predefined Fire Scenarios

The module provides predefined fire scenarios with different heat flux intensities:

api_pool: ~60 kW/m² incident heat flux per API 521 (pool fire)
api_jet: ~100 kW/m² incident heat flux per API 521 (jet fire)
scandpower: Higher intensity fire per Scandpower guidelines

Stefan-Boltzmann Calculation

Fire heat load is calculated using:

\[\begin{split}Q = \\varepsilon \\sigma A (T_{fire}^4 - T_{wall}^4) + h_{conv} A (T_{fire} - T_{wall})\end{split}\]

where:

\(\\varepsilon\) is surface emissivity (built-in value)
\(\\sigma\) is the Stefan-Boltzmann constant (5.67×10⁻⁸ W/m²K⁴)
\(A\) is the exposed surface area
\(T_{fire}\) is the fire temperature
\(T_{wall}\) is the vessel wall temperature
\(h_{conv}\) is the convective heat transfer coefficient

Usage Example

To use a fire scenario in your input file:

heat_transfer:
  type: "s-b"        # Stefan-Boltzmann radiation model
  fire: "api_pool"   # API 521 pool fire scenario