nozzle_design

This code was develloped by Nicolas LINDEN and Charles MALITOURNE as part of a third year qualifying project at École Nationale Supérieur d'Arts et Métiers. Its goal is to help design the geometry of supersonic nozzles. It is based on the method of characteristics and is in part inspired by the algorithm described in John D. Anderson's book 'Fundamentals of Aerodynamics, Fifth Edition'. It uses an ideal gas model and make the assumption of an iso-entropic flow, and allows the user to modify the nozzle's parameters to their liking. It makes use of the CoolProp python3 wrapper available at coolprop.org. Development is still ongoing but basic options are all available.

The code allows you to design two types of nozzle :

• standard nozzle with an expansion section :

• minimum length nozzles :

Required Python3 library

This code only work on python3. Necessary packages are : CoolProp, csv, matplotlib, numpy, math, time.

Creating a Nozzle

First create a new file that will contain the parameters for your nozzle. In this file, type :

#!/usr/bin/python3
from Nozzle import *
Nozzle(
physics = {
'mass_flow' : 4 ,  #kg/s
'tank_pressure' : 10e5 , #Pa
'tank_temperature' : 573 , #K
'specific_gas_constant' : 287.05 , #J/kg/K
'exit_pressure' : 1e5,  #Mach
'gamma' : 1.4
},
geometry = {
'nozzle_type' : 'expansion' ,
'initial_angle' : 0.01 ,
'step_number' : 100,
},
results = {
'display_tables' : True ,
'save_tables' : True ,
'display_figure' : False ,
'save_figure' : True ,
},
)

This example is provided in the tuyere.jdd file in the repository. To launch the program simply use the ./file_name command (Don't forget to chmod it adequately). You should adapt the python3 path to your system, or alternatively delete the line and just use the "python3 file_name" command. You can then modify the parameters to your liking.

Physics dictionnary

Parameter	Values
mass_flow	float
tank_pressure	float
tank_temperature	float
specific_gas_constant	float
exit_mach	float
gamma	float

The physics dictionnary contains the physical characteristic of the nozzle, they are :

• The mass flow going through the nozzle
• The tank pressure and temperature are the P/T condition in the tank upstream from your nozzle, this is used in the code as a way to define totale temperature and pressure (i.e. the dynamic Pressure (resp. Temperature) is zero for a Mach number of zero)
• The specific gas constant of the fluid, the default 287.05 J/kg/K is for Air. You can find data for other fluids in the CoolProp library.
• The exit pressure you want at the nozzle's exit.
• Alternatively, you can use the exit_mach parameter to specify a Mach number at the nozzle's exit (Don't use both exit pressure and Mach parameters)
• gamma is the Heat capacity ratio, equal to 1.4 for diatomic real gases, and to 1.67 for monoatomic real gases. You can use CoolProp to get more values for any fluid.

Geometry dictionnary

Parameter	Values
nozzle_type	'expansion', 'minimal'
initial_angle	0.01
step_number	int

These parameters pertain to the nozzle geometry, and to the algorithm's initial data line.

• The nozzle type parameter allows you to choose to create either a minimal length nozzle, or a standard nozzle with an expansion section.
• initial_angle allows you to define the angle of your very first right-running characteristics, a smaller angle will results in a better precision in the region just right of the initial data line.
• step_number allows you to choose to number of initial node in the initial data line, move step means better precision, but also longer computation time. The following graph represent the computation time with respect to the number of steps.

Results dictionnary

Parameter	Values
display_tables	True, False
save_contour	True, False
contour_format	'csv', 'CATIA'
display_figure	True, False
save_figure	True, False

• 'display_tables' is used to display your nozzle's characteristics after it is computed, it uses a custom made vtable class provided with the files. It works well with the monospace regular font.
• 'save_contour' allows you to save the nozzle's contour as a csv file to the results folder.
• 'save_format' lets you choose which format you want for your saved contour. The two possibilities are 'CATIA' and 'csv', the first produces a file easy to import in CATIA, the latter just saves the values.
• 'save_figure' allows you to save the nozzle's graph to the results folder.

Creating multiple nozzle in one script

If you wish to do a parametric study (for instance if you want to graph the exit section's area with respect to the exit mach number). You can use the Nozzle.iterate() function, and input a list of parameters in the desired fields. You can also add the 'iter_out_param' keyword to the results dictionnary, the program will then display a table with two columns, one for the parameter you changed, and the other for the studied quantity (for now, it only work with computation_time and area_ratio). The data set for a nozzle iteration should look something like this :

#!/usr/bin/python3
from Nozzle import *
Nozzle.iterate(
physics = {
'mass_flow' : 4 ,  #kg/s
'tank_pressure' : 10e5 , #Pa
'tank_temperature' : 573 , #K
'specific_gas_constant' : 287.05 , #J/kg/K
'exit_mach' : [2,3,4,5],  #Mach
'gamma' : 1.4
},
geometry = {
'nozzle_type' : 'expansion' ,
'initial_angle' : 0.01 ,
'step_number' : 100,
},
results = {
'display_tables' : True ,
'save_tables' : True ,
'display_figure' : False ,
'save_figure' : True ,
'iter_out_param' : 'area_ratio',
},
)

An example of such an iteration is the following graph :