ssnreduce 0.1.1

Supersonic-nozzle condensation data-reduction pipeline: isentropic inversion, diabatic ODE (Wyslouzil 2000), CNT/MKNT nucleation rates (Kalikmanov 2006; Bhabhe 2012), Gyarmathy droplet growth.

ssnreduce

ssnreduce is a Python library for reducing supersonic-nozzle (SSN) condensation experiments and computing nucleation rates. It implements the standard four-stage data-reduction pipeline for dilute vapour–carrier gas mixtures (e.g. CO₂/Ar, H₂O/N₂) developed in the Wyslouzil group (Wyslouzil et al. 2000) and validated extensively in Bhabhe (2012) for cryogenic systems.

A landscape scan found no dedicated, open-source CNT/MKNT nucleation-rate Python package — this library fills that gap.

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What it does

Given the measured centreline pressure profile p(x) from a supersonic nozzle experiment, ssnreduce recovers the full condensing flow state:

Stage	Output	Key equations
1 — Isentropic	M(x), T(x), A/A*(x), choked-throat state	Wyslouzil 2000 Eq 5; Streletzky 2002 Eqs 2–3
2 — Diabatic ODE	T(z), ρ(z), g(z), q(z)	Wyslouzil 2000 Eqs 10–12, 17–18
3 — Nucleation rates	J(x) for CNT family + MKNT	Bhabhe 2012 Eqs 2.17–2.34; Kalikmanov 2006
4 — Droplet growth	dr/dt(x), Td(x), Kn(x)	Gyarmathy 1963; Peters & Paikert 1989

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Nucleation models

nucleation_rates() computes six rate variants at each streamline point:

Model	Reference
Classical nucleation theory (CNT)	Becker & Döring 1935
Courtney correction	Courtney 1961
Girshick–Chiu (self-consistent)	Girshick & Chiu 1990
Wölk–Strey (empirical H₂O correction)	Wölk & Strey 2001
Hale scaled model	Hale 1986
Mean-Field Kinetic Nucleation Theory (MKNT)	Kalikmanov 2006; Bhabhe 2012

MKNT is the central modern alternative to CNT for cryogenic gases, validated for Ar and N₂ within 1–3 orders of magnitude (Bhabhe 2012 Ch 4–5).

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Install

pip install ssnreduce

Requires Python ≥ 3.10 and CoolProp ≥ 6.6.

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Quick start

import numpy as np
import ssnreduce as ssn

# --- nucleation rates on any T(z), p_v(z) streamline ---
co2 = ssn.species("co2")
z   = np.linspace(0, 40, 80)          # mm (synthetic)
T   = np.linspace(200.0, 90.0, 80)    # K
p_v = np.linspace(3000.0, 400.0, 80)  # Pa (partial pressure)

nuc = ssn.nucleation_rates(T, p_v, co2, phase="liquid", mknt=True)
print(f"J_CNT  max: {nuc.J_CNT.max():.2e} m⁻³ s⁻¹")
print(f"J_MKNT max: {nuc.J_MKNT.max():.2e} m⁻³ s⁻¹")

# --- Stage 2: diabatic ODE ---
# see examples/02_nucleation_growth.py for a full worked example

# --- available ODE solvers (Stage 2) ---
ssn.describe_solvers()

Run the worked examples:

python examples/01_stage1_isentropic.py
python examples/02_nucleation_growth.py
pytest -q

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Phase convention (CO₂ below the triple point)

Cryogenic CO₂ in an SSN sits below its triple point (216.6 K), so the thermodynamically stable condensate is solid (desublimation). Every property function accepts phase="liquid" (metastable supercooled, the historically used branch) or phase="solid" (Span–Wagner sublimation line, Halonen 2021 MD surface tension). Pass phase= consistently — it changes p_eq, σ, ρ, and L together.

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ODE solver selection (Stage 2)

The diabatic coupled ODE is stiff near onset (rapid rise in condensed fraction g). The default solver is "LSODA" (auto-switching Adams/BDF, equivalent to MATLAB's ode15s). All SciPy solvers are available:

ssn.describe_solvers()   # prints the full table with guidance

result = ssn.solve_diabatic(..., method="BDF")     # fully implicit
result = ssn.solve_diabatic(..., method="Radau")   # high-accuracy reference
result = ssn.solve_diabatic(..., method="RK45")    # explicit, dry runs only

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References

• Bhabhe, A. (2012). Nucleation and Condensation in Cryogenic Gas Mixtures. PhD thesis, The Ohio State University.
• Girshick, S. L., & Chiu, C.-P. (1990). Kinetic nucleation theory. J. Chem. Phys. 93, 1273.
• Gyarmathy, G. (1963). Zur Wachstumsgeschwindigkeit kleiner Flüssigkeitstropfen. Z. Angew. Math. Phys. 14, 280.
• Hale, B. N. (1986). Application of a scaled homogeneous nucleation-rate formalism. Phys. Rev. A 33, 4156.
• Halonen, R., et al. (2021). Homogeneous nucleation of CO₂ in supersonic nozzles. Phys. Chem. Chem. Phys. 23, 4517.
• Kalikmanov, V. I. (2006). Mean-field kinetic nucleation theory. J. Chem. Phys. 124, 124505.
• Peters, F., & Paikert, B. (1989). Nucleation and growth rates of homogeneously condensing water vapor in argon from shock tube experiments. Exp. Fluids 7, 521.
• Span, R., & Wagner, W. (1996). A new equation of state for carbon dioxide. J. Phys. Chem. Ref. Data 25, 1509.
• Streletzky, K. A., et al. (2002). CO₂ condensation in a supersonic nozzle. J. Chem. Phys. 116, 4058.
• Wölk, J., & Strey, R. (2001). Homogeneous nucleation of H₂O and D₂O in comparison. J. Phys. Chem. B 105, 11683.
• Wyslouzil, B. E., et al. (2000). Nonisothermal droplet growth in the free molecular regime. J. Chem. Phys. 113, 7317.

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Status

30 pytest invariants green. MIT licensed. See PUBLISHING.md for the JOSS roadmap.