Nozzle — MOC Rocket Nozzle Design Tool

Method of Characteristics solver for axisymmetric supersonic nozzle design. Designs optimized contours (MLN, Rao, TIC, Sivells), generates parabolic approximations, and compares them — all from YAML config files.

Try the live web demo — runs entirely in your browser via Pyodide.

Nozzle Types

Type	Method	Use Case
Conical	Straight divergent wall	Baseline / simplest design
Rao parabolic	Cubic bezier bell (Rao 1960)	Industry-standard short nozzle
TIC	Truncated ideal contour	Trade length vs. performance
MLN	Minimum length nozzle (MOC)	Theoretical optimum (uniform exit)
Sivells	MOC + mass flow (AEDC-TR-78-63)	High-fidelity design to M~6
Custom	User CSV contour	Evaluate any arbitrary shape

Install

pip install -e .

Requires Python 3.9+ and numpy, scipy, matplotlib, pyyaml, unyt.

Quick Start

# Compare all nozzle types at M=2.0
nozzle run examples/configs/all_types.yaml

# Quick example (no config file needed)
nozzle example --M-exit 2.5

# TIC truncation trade study
nozzle run examples/configs/tic_comparison.yaml

# High-Mach (M=4) with Sivells MOC
nozzle run examples/configs/high_mach.yaml

# Launch interactive web interface (Pyodide)
nozzle web

Example Output

  Conical 15.0°: Cf=1.3992, λ=0.9830, M_exit=2.000
  Rao 80% bell: θ_n=17.0°, θ_e=8.5°, Cf=1.4156 (λ=0.9945)
  TIC 80% M=2.0: θ_e=3.1°, Cf=1.4177 (λ=0.9993)
  MLN M=2.0: Cf=1.4234, M_mean=2.000, efficiency=1.0000

Nozzle          Cf   % Ideal   Notes
-------   --------   -------   -----
conical     1.3992     98.3%   lambda=0.9830
rao         1.4156     99.5%   theta_n=17.0 theta_e=8.5
tic_80      1.4177     99.9%   lambda=0.9993
mln         1.4234    100.0%   M_mean=2.000

Outputs per config: contour PNG, contour CSV, exit plane CSV, and a summary.json with all performance metrics. Comparison runs also produce overlaid contour plots, shape delta plots, tolerance band analysis, and performance bar charts.

YAML Configuration

configs:
  rao:
    type: rao
    gamma: 1.4
    M_exit: 2.0
    bell_fraction: 0.8

  mln:
    type: mln
    gamma: 1.4
    M_exit: 2.0
    n_chars: 30

outputs:
  - contour
  - performance

Features:

• Config inheritance — base: key merges parent config with overrides
• Flexible exit conditions — specify any one of M_exit, area_ratio, or exit_radius
• Dimensional I/O — set throat_radius: 15 mm for physical units in output CSVs

See examples/configs/ for all available examples.

Python API

from nozzle.contours import minimum_length_nozzle, rao_parabolic_nozzle
from nozzle.analysis import moc_performance, quasi_1d_performance

# Design an MLN at M=3.0
x, y, mesh = minimum_length_nozzle(M_exit=3.0, n_chars=30)
perf = moc_performance(mesh)
print(f"Cf = {perf['Cf']:.4f}")

# Rao 80% bell at AR=10
x, y, theta_n, theta_e = rao_parabolic_nozzle(area_ratio=10, bell_fraction=0.8)

Web Interface

The interactive web viewer runs the full Python solver in-browser via Pyodide. Toggle nozzle types, adjust parameters, and see contour overlays, performance tables, tolerance band analysis, and exit plane distributions — all without a server.

• Live demo: evand.github.io/nozzle
• Local: nozzle web (or python web/serve.py)

Validation

359 tests, validated against published references:

Source	Coverage
Anderson Modern Compressible Flow Tables A.1/A.5	Gas relations (exact to 4+ digits)
Sutton & Biblarz Tables 3-3/3-4	Rao angles, conical lambda, Cf
CONTUR Fortran (Sivells AEDC-TR-78-63)	122 tests at machine precision
Physics invariants	Monotonicity, conservation, ordering

See docs/VALIDATION.md for the full module-by-module matrix.

pytest tests/

Project Structure

nozzle/
  gas.py        — Isentropic + Prandtl-Meyer relations
  kernel.py     — Hall transonic initial data line
  moc.py        — MOC unit processes and mesh
  contours.py   — Nozzle contour generators
  sivells.py    — Sivells CONTUR port (AEDC-TR-78-63)
  analysis.py   — Performance analysis (Cf, efficiency)
  config.py     — YAML config with inheritance
  cli.py        — CLI entry point
  plots.py      — Visualization (contours, deltas, tolerance bands)
web/            — Browser-based interface (Pyodide)
tests/          — 359 tests
examples/       — YAML configs for common use cases
docs/           — Algorithms, references, validation matrix

References

• Sivells, AEDC-TR-78-63, 1978 — Axisymmetric nozzle design via MOC
• Anderson, Modern Compressible Flow, 3rd ed., McGraw-Hill 2003
• Zucrow & Hoffman, Gas Dynamics Vol. 2, Wiley 1977
• Rao, Jet Propulsion 1958; ARS Journal 1960
• Sutton & Biblarz, Rocket Propulsion Elements, 9th ed.
• Hall, QJMAM 1962 — Transonic kernel
• NACA 1135, 1953 — Isentropic flow tables