axialfans

Spanwise-resolved analytical solver for multistage axial turbomachinery

Quasi-1D pointwise solver for arbitrary sequences of rotating and stationary axial blade rows (rotors, stators, counter-rotating fans) using Newton-Raphson iteration on coupled thermodynamic equations at each radial station. Designed for preliminary turbomachinery design and uncertainty quantification.

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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, State
import numpy as np

M = 25  # radial stations

solver = MultistageFanSolver(
    N=1, M=M,
    direction=[1],
    sigma=0.9,
    omega=1800,
    beta=45,
    rp=0.25, rm=0.18,
    eta=0.85,
    R=287.05, cp=1004.7, gamma=1.4
)

T0   = 288.15
P0   = 101325.0
rho0 = P0 / (287.05 * T0)

inlet = State(0, M, 0.18, 0.25, T0, P0, 50.0, rho0, 0)
solver.solve(inlet)

perf = solver.performance()
print(f"Pressure ratio:        {perf['PR']:.3f}")
print(f"Temperature ratio:     {perf['TR']:.3f}")
print(f"Isentropic efficiency: {perf['eta_isen']:.3f}")

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Examples

See the examples/ directory:

Example	Description
01_single_rotor.py	Basic single-stage fan
02_rotor_stator.py	Fan with straightening vanes
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 (jet engine architecture)
06_monte_carlo_uq.py	Uncertainty quantification with LHS

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Key Concepts

State Object

All inlet conditions are passed as a State:

inlet = State(
    n=0,        # stage index (0 = inlet)
    M=25,       # radial stations
    rm=0.18,    # hub radius [m]
    rp=0.25,    # tip radius [m]
    T=288.15,   # temperature [K]
    P=101325,   # pressure [Pa]
    vax=50.0,   # axial velocity [m/s]
    rho=1.225,  # density [kg/m³]
    vtheta=0    # tangential velocity [m/s]
)

Spanwise Resolution

M radial stations are solved independently at each blade row. Spanwise variation arises from blade twist. Pass a 2D (N x M) beta array for full control, or np.linspace(beta_hub, beta_tip, M) for linear twist:

beta_row = np.linspace(65, 71, M)           # single twisted row
beta_matrix = np.array([row1, row2])        # N x M for multistage

Slip Factor

Supplied externally before calling solve(). The modified Stodola model developed in Wang (2026) is recommended for axial machines:

sigma = 1 - C / Z   # Z = blade count, C calibrated from NASA Rotor 37

Unlike Qiu, Wiesner, and classical Stodola — which were derived for centrifugal machines and degenerate toward σ ≈ 1 for low-twist axial geometries — this model explicitly encodes blade count as the primary slip mechanism, which is physically correct for axial blade rows. It applies consistently to both rotors and stators.

Direction Array

Configuration	direction
Single rotor	[1]
Rotor + stator	[1, -1]
Counter-rotating pair	[1, -1]
LP + stator + HP	[1, -1, 1, -1, ...]

Stators have omega=0. Direction still alternates to correctly handle the velocity triangle frame at each interface.

Variable Area

Pass per-stage radii as arrays:

rp=[0.30, 0.25, 0.20]
rm=[0.20, 0.18, 0.15]

Tunable Solver Constants

import axialfans.fan_solver as solver_module

solver_module.MAX_ITER = 2000   # Newton-Raphson iteration limit
solver_module.TOL      = 1e-10  # convergence tolerance
solver_module.ALPHA    = 0.5    # line search step (reduce if NR diverges)

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Performance

• ~10,000 Monte Carlo evaluations in ~20 minutes on a standard workstation
• Enables UQ studies that would be computationally prohibitive with RANS CFD
• A single RANS CFD evaluation for an equivalent geometry takes hours on a cluster

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Validation

Validated against NASA experimental data across two independent transonic rotors:

Test Case	Configuration	PR Error
NASA Rotor 37	Transonic single rotor, deterministic	2.0%
NASA Rotor 67	Transonic single rotor, uncertain geometry, 50,000-sample UQ	2.54%
NACA TR 729	Low-speed rotor-stator, regime of validity characterization	—

The NACA TR 729 case identifies the solver's validity boundary: the inviscid compressible model breaks down at low rotor speed and high inlet axial velocity where viscous effects dominate.

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Important Note

This solver is a preliminary design and research tool. Outputs must be independently verified before any engineering application. See LICENSE for full liability disclaimer.

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Citation

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

@software{wang2026axialfans,
  title={axialfans: Spanwise-Resolved Analytical Solver for Multistage Axial Turbomachinery with Uncertainty Quantification},
  author={Wang, Sean H.},
  year={2026},
  url={https://github.com/sean-h-wang/axialfans},
  version={2.0.0}
}

@article{wang2026analytical,
  title={Spanwise-Resolved Analytical Solver for Multistage Axial Turbomachinery with Uncertainty Quantification},
  author={Wang, Sean H.},
  journal={AIAA Journal},
  year={2026},
  note={submitted}
}

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License

MIT License — see LICENSE for details.

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Contributing

Issues and pull requests welcome. For bug reports include Python version, NumPy version, and a minimal reproducible example.

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Author

Sean H. Wang

• Personal: seanwangpiano@gmail.com
• Institutional: swang122@montgomerycollege.edu
• GitHub: @sean-h-wang