axialfans 1.0.1

Analytical solver for multistage ducted axial fans.

axialfans

Fast analytical solver for multistage axial turbomachinery

Generalized solver for arbitrary sequences of rotating and stationary axial stages (rotors, stators, counter-rotating fans) using Newton-Raphson iteration on coupled thermodynamic equations. Designed for preliminary turbomachinery design and rapid parameter exploration.

Key Features:

• ⚡ Fast: 333 solves/second enables real-time Monte Carlo (10,000 samples in ~30s)
• 🎯 Validated: 6% accuracy vs NASA experimental data (Rotor 37, Report 729)
• 🔧 General: Rotors, stators, counter-rotation, variable area in unified framework
• 📊 Production-ready: Type hints, error handling, comprehensive documentation

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Installation

pip install axialfans

Requirements: Python 3.9+, NumPy

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Quick Start

from axialfans.fan_solver import MultistageFanSolver

# Single stage fan
solver = MultistageFanSolver(
    N=1,                # Number of stages
    direction=[1],      # Rotation: +1=CCW, -1=CW
    sigma=0.9,          # Slip factor
    omega=1800,         # Angular velocity [rad/s]
    beta=45,            # Blade angle [degrees]
    rp=0.25,            # Tip radius [m]
    rm=0.18,            # Hub radius [m]
    eta=0.85,           # Efficiency
    R=287,              # Gas constant [J/kg-K]
    cp=1005,            # Specific heat [J/kg-K]
    gamma=1.4           # Heat capacity ratio
)

# Solve from inlet conditions
solver.solve(
    T0=288,         # Temperature [K]
    vax0=50,        # Axial velocity [m/s]
    P0=101325,      # Pressure [Pa]
    rho0=1.225      # Density [kg/m³]
)

# Results
print(f"Pressure ratio: {solver.P[1]/solver.P[0]:.2f}")
print(f"Exit velocity: {solver.vax[1]:.1f} m/s")

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Examples

See the examples/ directory for detailed usage:

Example	Description
01_single_rotor.py	Basic single-stage fan
02_rotor_stator.py	Fan with straightening vanes (NASA 729 config)
03_counter_rotating.py	Swirl cancellation with opposite-spinning rotors
04_variable_area.py	Converging/diverging ducts
05_multi_spool.py	LP + stator + HP compressor configuration
06_monte_carlo_uq.py	Uncertainty quantification (1000 samples)

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Key Concepts

Indexing Convention

State arrays indexed 0 → N:

• solver.T[0] = inlet temperature
• solver.T[n] = temperature exiting stage n

Direction Array

Specifies rotation sense:

• direction=[1] = counter-clockwise rotation
• direction=[-1] = clockwise rotation / mirror frame
• direction=[1, -1] = rotor + stator pair

Stage Types

Configure via parameters:

• Rotor: omega > 0, any direction
• Stator: omega = 0, set opposite direction from previous
• Counter-rotating: Adjacent stages with opposite direction values

Variable Area

Different radii per stage:

rp=[0.30, 0.25, 0.20]  # Decreasing tip radius
rm=[0.20, 0.18, 0.15]  # Decreasing hub radius

Area decrease → velocity increase, pressure ratio decrease

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Performance

• Single solve: ~3 ms
• 1,000 solves: ~3 seconds
• 10,000 solves: ~30 seconds
• 4-5 orders of magnitude faster than RANS CFD

Enables real-time design space exploration and Monte Carlo uncertainty quantification.

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Validation

Validated against NASA experimental data:

Test Case	Configuration	Error
Rotor 37	High-speed single rotor (Re ~ 10⁶)	6.2% on pressure ratio
NASA 729	Low-speed rotor-stator (Re ~ 10⁵)	Correctly identifies inviscid breakdown

Uncertainty quantification with 10,000 Monte Carlo samples shows 99.8% convergence rate. See notebooks/rotor37_validation.ipynb for detailed analysis.

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Documentation

Full API documentation available in code docstrings. Quick reference:

MultistageFanSolver(
    N,              # Number of stages
    direction,      # Rotation sense: +1 (CCW) or -1 (CW)
    sigma,          # Slip factor (0.85-0.95 typical)
    omega,          # Angular velocity [rad/s] (unsigned, use 0 for stators)
    beta,           # Blade angle [degrees] (unsigned)
    rp, rm,         # Tip and hub radius [m]
    eta,            # Efficiency (0-1)
    R, cp, gamma    # Gas properties
)

All parameters accept scalars (same for all stages) or arrays (per-stage values).

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Citation

If you use this software in your research, please cite:

@software{wang2026axialfans,
  title={axialfans: Fast Analytical Solver for Multistage Axial Turbomachinery},
  author={Wang, Sean},
  year={2026},
  url={https://github.com/sean-h-wang/axialfans},
  version={1.0.0}
}

Associated paper:

@article{wang2026analytical,
  title={Analytical Solver for Multistage Axial Turbomachinery with Variable Area and Counter-Rotation},
  author={Wang, Sean},
  journal={AIAA Journal},
  year={2026},
  note={submitted}
}

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License

MIT License - see LICENSE file for details.

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Contributing

Issues and pull requests welcome! Please see CONTRIBUTING.md for guidelines.

For bug reports, include:

• Python version
• NumPy version
• Minimal reproducible example
• Error message / unexpected behavior

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Author

Sean H. Wang

• Email: [e-mail]
• GitHub: @sean-h-wang

Developed as part of hypersonic propulsion research.