NENZF1D is a program for estimating flow conditions in reflected-shock tunnels, when the test gas reaches temperatures high enough for chemical reactions to occur and when nonequilibrium chemistry effects are expected to be important. The calculation proceeds in two parts. Assuming thermochemical-equilibrium, a state-to-state calculation is done for the shock-tunnel processing of the test gas until it reaches sonic conditions at the nozzle throat. Then a calculation with finite-rate chemical reactions is made of the supersonic flow of the gas through the nozzle expansion.

1. Getting started

The nenzf1d program is built upon the core gas model and flow modules of our gas-dynamics tool kit. General getting started notes can be found at There, you will see how to get a copy of the source code, a list of what other software you will need to build and install the tool kit, and a collection of environment variables that need to be set.

To install the nenzf1d program, move to its source directory and use the make utility.

cd dgd/src/nenzf1d
make install

This will also install files associated with the gas models. Note that you will need a compiled version of the NASA Lewis cea2 program installed in a location that the gas models module can find it.

2. Getting command help

When run as an application, this program accepts a single command line argument that specifies an input file with the detailed calculation parameters.

To see what other command-line options are available, start the program as:

nenzf1d --help

3. Example shock-tunnel calculation

Let’s consider shot 10559 for the T4 shock tunnel. This particular run of the wind tunnel was part of Wilson Chan’s PhD studies and used air as the test gas, with the Mach 6 nozzle providing expansion of the air to test-flow conditions.

To start, you are going to need a set of consistent gas model files in your working directory. There is a guide ( to the gas-model module that is worth reading but, for the moment, let’s set up a 5-species model of air by copying the gas-model files from the samples in the source code repository.

cp ${DGD_REPO}/src/gas/sample-data/cea-air5species-gas-model.lua .
cp ${DGD_REPO}/examples/kinetics/air-chemistry-1T/air-5sp-1T.inp .
cp ${DGD_REPO}/examples/kinetics/air-chemistry-1T/GuptaEtAl-air-reactions.lua .
prep-gas air-5sp-1T.inp air-5sp-1T.lua
prep-chem air-5sp-1T.lua GuptaEtAl-air-reactions.lua air-5sp-1T-reactions.lua

3.1. Input file

# Sample input file for nenzf1d is a YAML 1.1 file.
# t4m6-air.yaml
# Data for T4 shot 10559 obtained from Wilson Chan's PhD thesis, Table D.1, page 158.
# PJ 2020-10-17
title: "T4 shot 10559 with Mach 6 nozzle."    # Any string will do.

species: ['N2', 'O2', 'N', 'O', 'NO']         # List
molef: {'N2': 0.79, 'O2': 0.21}               # Map of nonzero values will suffice.
# Gas model and reactions files need to be consistent with the species above.
# Gas model 1 is usually a CEAGas model file.
# Gas model 2 is a thermally-perfect gas model for the finite-rate chemistry.
gas-model-1: cea-air5species-gas-model.lua
gas-model-2: air-5sp-1T.lua
reactions: air-5sp-1T-reactions.lua

# Observed parameter values for shock-tube operation.
T1: 300         # K
p1: 130.0e3     # Pa
Vs: 2434.0      # m/s
pe: 34.07e6     # Pa
ar: 127.0       # Mach 6 nozzle

# Define the expanding part of the nozzle as a schedule of diameters with position.
xi: [0.0, 0.150, 0.280, 0.468, 0.671,  0.984]  # axial-distance metres
di: [1.0,   4.0, 6.232,  8.44,  9.92, 11.268]  # diameter (may be normalized)

# Optionally, we can adjust the stepping parameters for the supersonic expansion.
# x_end: 1.0
# t_final: 1.0e-3
# t_inc: 1.0e-10
# t_inc_factor: 1.0001
# t_inc_max: 1.0e-7

3.2. Results

Run nenzf1d with the command:

nenzf1d t4m6-air.yaml

to get the result

NENZF1D: shock-tunnel with nonequilibrium nozzle flow.
  T4 shot 10559 with Mach 6 nozzle.
Initial gas in shock tube (state 1).
  pressure    130 kPa
  density     1.5036 kg/m^3
  temperature 300 K
  H1          0.00187216 MJ/kg
Incident-shock process to state 2.
  V2          0.362529 km/s
  Vg          2.07147 km/s
  pressure    7711.1 kPa
  density     10.0951 kg/m^3
  temperature 2648.54 K
Reflected-shock process to state 5.
Isentropic relaxation to state 5s.
  entropy     8483.2 J/kg/K
  H5s         5.4437 MJ/kg
  H5s-H1      5.44183 MJ/kg
  pressure    34070 kPa
  density     27.947 kg/m^3
  temperature 4147.1 K
Isentropic flow to throat to state 6 (Mach 1).
  V6          1155.62 km/s
  mflux6      20077.8
  pressure    19158.3 kPa
  density     17.374 kg/m^3
  temperature 3775.48 K
Isentropic expansion to nozzle exit of given area (state 7).
  area_ratio  127
  V7          3.15445 km/s
  pressure    10.7819 kPa
  density     0.050117 kg/m^3
  temperature 746.49 K
  mflux7      20077.7
  pitot7      479.342 kPa
End of part A: shock-tube and frozen/eq nozzle analysis.
Begin part B: supersonic expansion with finite-rate chemistry.
Throat condition:
  velocity    1.1908 km/s
  sound-speed 1.18961 km/s
  (v-V6)/V6   0.0304407
  pressure    19158.3 kPa
  density     17.3739 kg/m^3
  temperature 3775.48 K
  massf[N2]   0.726242
  massf[O2]   0.17141
  massf[N]    2.27571e-05
  massf[O]    0.014889
  massf[NO]   0.0874362
Exit condition:
  x           0.98406 m
  area-ratio  126.968
  velocity    3.10966 km/s
  Mach        6.04831
  p_pitot     506.509 kPa
  pressure    10.1286 kPa
  density     0.0523794 kg/m^3
  temperature 669.499 K
  massf[N2]   0.732318
  massf[O2]   0.190771
  massf[N]    5.02429e-17
  massf[O]    0.00244285
  massf[NO]   0.0744683
Expansion error-indicators:
  relerr-mass 0.000390353
  relerr-H    8.22724e-06