Pintle Engine Design Pipeline

A comprehensive physics-based simulation pipeline for pintle injector liquid rocket engines. This pipeline takes tank pressures as input and solves for chamber pressure, mass flow rates, and thrust output.

Overview

Input: Tank pressures (LOX and RP-1)
Output: Thrust, chamber pressure, mass flow rates, O/F ratio, Isp, and all combustion parameters

Key Feature: Chamber pressure (Pc) is solved, not input. The system balances propellant supply (from injectors) with combustion demand (from nozzle) to find the equilibrium operating point.

Repository Structure

examples/pintle_engine/
├── README.md                          # This file
├── config_minimal.yaml                # Engine configuration (geometry, fluids, etc.)
├── run_full_pipeline.py              # Single-point evaluation example
├── comprehensive_performance_plots.py # 16-panel performance dashboard
├── chamber_3d_plots.py               # 3D chamber behavior visualization
├── validate_chamber_intrinsics.py    # Validation against Huzel & Huang
├── compare_ideal_vs_actual.py       # Ideal CEA vs chamber-driven comparison
├── pressure_sweep_example.py         # 2D pressure maps and slices
└── plot_performance_summary.py        # 9-panel summary plots

pintle_pipeline/                      # Core pipeline modules
├── constants.py                      # Fluid properties
├── config_schemas.py                 # Pydantic validation schemas
├── cea_cache.py                      # CEA lookup table management
├── combustion_eff.py                 # L*-based combustion efficiency
├── feed_loss.py                      # Feed system pressure losses
├── regen_cooling.py                  # Regenerative cooling model
├── io.py                             # YAML loading, CSV/JSON export
└── visualization.py                  # Plotting utilities

pintle_models/                        # Physics models
├── geometry.py                       # Pintle geometry (areas, hydraulic diameters)
├── discharge.py                      # Discharge coefficient (Re-dependent)
├── spray.py                          # Spray physics (J, θ, We, SMD, x*)
├── closure.py                        # Mass flow closure (iterative solver)
├── chamber_solver.py                 # Chamber pressure root finder
├── nozzle.py                         # Thrust calculation (momentum + pressure)
└── runner.py                         # Main pipeline orchestrator

Quick Start

1. Installation

pip install numpy scipy matplotlib pandas pyyaml pydantic rocketcea

2. Basic Usage

from pintle_pipeline.io import load_config
from pintle_models.runner import PintleEngineRunner

# Load configuration
config = load_config('examples/pintle_engine/config_minimal.yaml')

# Initialize pipeline
runner = PintleEngineRunner(config)

# Evaluate at specific tank pressures
P_tank_O = 1000 * 6894.76  # 1000 psi in Pa
P_tank_F = 950 * 6894.76   # 950 psi in Pa

results = runner.evaluate(P_tank_O, P_tank_F)

print(f"Chamber Pressure: {results['Pc']/6894.76:.1f} psi")
print(f"Thrust: {results['F']/1000:.2f} kN")
print(f"Mass Flow (O): {results['mdot_O']:.3f} kg/s")
print(f"Mass Flow (F): {results['mdot_F']:.3f} kg/s")
print(f"O/F Ratio: {results['MR']:.2f}")
print(f"Isp: {results['Isp']:.1f} s")

3. Run Examples

# Single operating point
python examples/pintle_engine/run_full_pipeline.py

# Comprehensive performance dashboard
python examples/pintle_engine/comprehensive_performance_plots.py

# 3D chamber behavior plots
python examples/pintle_engine/chamber_3d_plots.py

# Validate against Huzel & Huang data
python examples/pintle_engine/validate_chamber_intrinsics.py

# Compare ideal vs actual performance
python examples/pintle_engine/compare_ideal_vs_actual.py

# 2D pressure sweeps and maps
python examples/pintle_engine/pressure_sweep_example.py

Workflow

Step 1: Configuration

Edit config_minimal.yaml to define:

• Fluid properties: Density, viscosity, surface tension
• Pintle geometry: LOX orifices (n, d), fuel annulus (d_pintle_tip, h_gap)
• Feed system: Inlet diameters, loss coefficients
• Discharge coefficients: Cd values (fixed or Re-dependent)
• Chamber: Volume, L*, throat area
• Nozzle: Expansion ratio, exit area, efficiency

Step 2: Pipeline Execution

The pipeline follows this sequence:

1. Input: Tank pressures (P_tank_O, P_tank_F)
2. Feed Losses: Calculate pressure drop from tank to injector
   • Δp_feed = K_eff(P) × (ρ/2) × (ṁ/(ρ×A_hyd))²
   • Optional: Add regenerative cooling pressure drop for fuel
3. Injector Flow: Calculate mass flow rates from injector to chamber
   • ṁ = Cd × A × √(2×ρ×Δp_injector)
   • Δp_injector = P_injector - Pc
4. Spray Physics: Validate atomization quality
   • Momentum flux ratio (J), spray angle (θ)
   • Weber numbers, Sauter Mean Diameter (SMD)
   • Evaporation length (x*)
5. Chamber Solver: Find Pc where supply = demand
   • Supply: ṁ_supply = ṁ_O + ṁ_F (from injectors)
   • Demand: ṁ_demand = Pc × At / c*_actual
   • c*_actual = η_c* × c*_ideal (CEA with L* correction)
6. Nozzle: Calculate thrust
   • Momentum: F_momentum = ṁ × v_exit
   • Pressure: F_pressure = (P_exit - Pa) × A_exit
   • Total: F = F_momentum + F_pressure

Step 3: Visualization

Generate plots for:

• Performance: Thrust, Isp, Pc, MR vs tank pressures
• Combustion: Tc, c*, gamma, R vs O/F ratio
• Injector: Mass flow rates, pressure drops, velocities
• Spray: J, θ, We, SMD, x* diagnostics
• Chamber: 3D plots of Pc, Thrust, Isp vs MR and mdot_total

Key Physics Models

Pintle Injector

LOX (Axial Flow):

• Flows through N orifices on pintle tip
• Area: A_LOX = N × π × (d_orifice/2)²
• Hydraulic diameter: d_hyd = d_orifice

Fuel (Radial Flow):

• Flows through annulus gap between pintle tip and reservoir
• Area: A_fuel = π × (R_outer² - R_inner²)
• Hydraulic diameter: d_hyd = 2 × h_gap (thin annulus)

Discharge Coefficient

Re-dependent model:

Cd(Re) = Cd_∞ - a_Re/√Re
Cd_min ≤ Cd ≤ Cd_∞

Set a_Re = 0 for fixed Cd (matches spreadsheet approach).

Combustion Efficiency

L*-based correction for finite chamber:

η_c* = 1 - C × e^(-K×L*)

Where:

• L* = V_chamber / A_throat (characteristic length)
• C, K: Empirical coefficients (default from Huzel & Huang)

Chamber Pressure Solver

Uses Brent's method to find Pc where:

residual(Pc) = ṁ_supply(Pc) - ṁ_demand(Pc) = 0

• Supply: From injector flow (depends on P_injector - Pc)
• Demand: From combustion (depends on Pc, MR, c*_actual)

Nozzle Thrust

High-fidelity calculation:

F = ṁ × v_exit + (P_exit - Pa) × A_exit

Exit conditions calculated using isentropic relations with actual gamma (frozen flow corrected).

Configuration Guide

Pintle Geometry

pintle_geometry:
  lox:
    n_orifices: 16
    d_orifice: 0.001779  # m (1.779 mm)
  
  fuel:
    d_pintle_tip: 0.019050  # m (19.05 mm = 0.750")
    h_gap: 0.000313  # m (0.313 mm)

Feed System

feed_system:
  oxidizer:
    d_inlet: 0.009525  # m (3/8" = 9.525 mm)
    K0: 2.0  # Base loss coefficient
    K1: 0.0  # Pressure dependence (0 = constant)
  
  fuel:
    d_inlet: 0.009525  # m
    K0: 2.0
    K1: 0.0

Regenerative Cooling (Optional)

regen_cooling:
  enabled: true
  d_inlet: 0.009525  # m
  L_inlet: 0.5  # m
  n_channels: 12
  channel_width: 0.002  # m
  channel_height: 0.001  # m
  channel_length: 0.18162  # m (chamber length)
  d_outlet: null  # Same as inlet
  L_outlet: 0.1  # m

Output Files

Running the examples generates:

• comprehensive_performance.png - 16-panel dashboard
• pressure_sweep_2d.png - 2D contour maps (Thrust, Pc, MR, Isp)
• chamber_3d_plots.png - 3D scatter plots
• chamber_2d_projections.png - 2D projections
• chamber_intrinsics_validation.png - Validation plots
• ideal_vs_actual_comparison.png - CEA vs chamber-driven comparison
• pressure_slices.png - 1D slices through pressure grid

Validation

The pipeline has been validated against:

• Huzel & Huang: Chamber intrinsics (Tc, c*, gamma, R) vs O/F ratio
• Spreadsheet calculations: Mass flow rates and O/F ratio
• Physical constraints: Spray quality (We, x*), pressure drops

Notes

1. Chamber pressure is solved, not input. The Pc_range in config is only for CEA lookup table generation.

2. Injector pressure drop varies with operating conditions. The 150 psi in spreadsheets is a design target, not the actual operating point.

3. Area calculations use exact formulas:

   • LOX: A = N × π × (d/2)²
   • Fuel: A = π × (R_outer² - R_inner²) (annulus)

4. CEA cache is automatically generated on first run. Subsequent runs use cached values for speed.

Troubleshooting

Solver fails: "No solution: Supply > Demand at all Pc"

• Tank pressures are too low or mismatched
• Try increasing P_tank_O or reducing P_tank_F
• Check that P_tank_O > P_tank_F (typical)

O/F ratio too low/high:

• Adjust fuel gap (h_gap) or LOX orifice diameter
• Check discharge coefficients (Cd values)

Mass flow rates don't match spreadsheet:

• Verify geometry matches spreadsheet exactly
• Check that Cd values are correct
• Remember: pressure drops vary with operating conditions

References

• Huzel & Huang, "Design of Liquid Propellant Rocket Engines"
• RocketCEA documentation
• Pintle injector design literature

License

See repository license file.