pypbomb.sd

Pypbomb requires the use of some functionality from the shock and detonation toolbox from the Explosion Dynamics Laboratory at Cal Tech [1]. SDToolbox is, as yet, not installable via pip or conda, and not all of its functions are needed for this package. Therefore, the functions needed for pypbomb’s purposes are located here, in pypbomb.sd. Some of these functions, such as Detonation.cj_speed, have been modified to speed up the calculation process. If you are planning to do any sort of actual detonation work outside of tube design it is recommended to use the full SDToolbox.

[1] SDToolbox Numerical Tools for Shock and Detonation Wave Modeling,

Explosion Dynamics Laboratory, Contributors: S. Browne, J. Ziegler, N. Bitter, B. Schmidt, J. Lawson and J. E. Shepherd California Institute of Technology, Pasadena, CA USA http://shepherd.caltech.edu/EDL/PublicResources/sdt/

class pypbomb.sd.Detonation

Bases: object

Methods specifically relating to Chapman-Jouguet speed and state calculation

classmethod cj_speed(initial_pressure, initial_temperature, species_mole_fractions, mechanism, use_multiprocessing=False, return_r_squared=False, return_state=False)

Calculates the Chapman-Jouguet detonation velocity of a gaseous mixture.

This is a modified version of sdtoolbox.PostShock.CJspeed. Specifically, it has been changed to allow for CJ state output, and to allow the use of multiprocessing to speed up the curve fit.

Parameters:

  • initial_pressure (float) – Initial pressure in Pascals

  • initial_temperature (float) – Initial temperature in Kelvin

  • species_mole_fractions (str or dict) – Reactant species mole fractions

  • mechanism (str) – Cti file containing mechanism data (e.g. gri30.yaml)

  • use_multiprocessing (bool, optional) – Use multiprocessing to speed up CJ speed calculation

  • return_r_squared (bool, optional) – Return the \(R^2\) value of the CJ speed vs. density ratio fit

  • return_state (bool, optional) – Return the CJ state corresponding to the calculated velocity

Returns:

Dictionary with the following keys:

  • "cj speed": Chapman-Jouguet wave speed (float)

  • "R^2": R-squared value of the CJ speed vs. density ratio fit (float). Only exists if return_r_squared is set to True.

  • "cj state": Cantera solution object describing the CJ state (ct.Solution). Only exists if return_state is set to True.

Return type:

dict

classmethod cj_state(working_gas, initial_state_gas, error_tol_temperature, error_tol_velocity, density_ratio, max_iterations=500)

Calculates the Chapman-Jouguet state and wave speed using Reynolds’ iterative method.

This function corresponds to sdtoolbox.PostShock.CJ_calc

Parameters:

  • working_gas (cantera.Solution) – Working gas mixture used for calculations.

  • initial_state_gas (ct.Solution) – Working gas mixture in its initial, undetonated state.

  • error_tol_temperature (float) – Temperature error tolerance for iteration, in Kelvin.

  • error_tol_velocity (float) – Velocity error tolerance for iteration, in m/s.

  • density_ratio (float) – Density ratio.

  • max_iterations (int, optional) – Maximum number of loop iterations used to calculate output. Default is 500.

Returns:

A tuple containing:

  • Gas mixture at equilibrium state (ct.Solution)

  • Initial velocity resulting in the input density ratio, in m/s (float)

Return type:

tuple(ct.Solution, float)

class pypbomb.sd.GetError

Bases: object

Methods for calculating error in enthalpy and pressure from a given velocity.

static equilibrium(working_gas, initial_state_gas, initial_velocity_guess)

This function uses the momentum and energy conservation equations to calculate error in current pressure and enthalpy guesses. In this case, working state is in equilibrium.

Original function: FHFP_CJ in PostShock.py

Parameters:

  • working_gas (ct.Solution) – Working gas mixture used for calculations.

  • initial_state_gas (ct.Solution) – Working gas mixture in its initial, undetonated state.

  • initial_velocity_guess (float) – A guess for the initial velocity in m/s

Returns:

A tuple containing:

  • Enthalpy error (float)

  • Pressure error (float)

Return type:

tuple (float, float)

static reflected_shock_frozen(shock_speed, working_gas, post_shock_gas)

This function uses the momentum and energy conservation equations to calculate error in current pressure and enthalpy guesses during reflected shock calculations. In this case, working state is frozen.

Original function: sdtoolbox.reflections.FHFP_reflected_fr

Parameters:

  • shock_speed (float) – Current post-incident-shock lab frame particle speed

  • working_gas (ct.Solution) – Working gas mixture used for calculations.

  • post_shock_gas (ct.Solution) – Working gas mixture in its post-incident-shock state.

Returns:

A tuple containing:

  • Enthalpy error (float)

  • Pressure error (float)

Return type:

tuple (float, float)

class pypbomb.sd.Properties

Bases: object

static equilibrium(gas, density, temperature)

This function calculates the equilibrium pressure and enthalpy given temperature and density.

Original function: sdtoolbox.Thermo.eq_state

Parameters:

  • gas (ct.Solution) – Working gas object.

  • density (float) – Mixture density in kg/m^3.

  • temperature (float) – Mixture temperature in K.

Returns:

Dictionary containing pressure and temperature values. Keys:

  • "pressure" (float)

  • "enthalpy" (float)

Return type:

dict

class pypbomb.sd.Reflection

Bases: object

static get_eq_state(particle_speed, post_shock_gas, working_gas, error_tol_temperature=0.0001, error_tol_specific_volume=0.0001, max_iterations=500)

This function calculates equilibrium post-reflected-shock state for a specified shock velocity

Original function: sdtoolbox.reflections.PostReflectedShock_eq

Parameters:

  • particle_speed (float) – current post-incident-shock lab frame particle speed

  • post_shock_gas (ct.Solution) – Working gas mixture in its post-incident-shock state.

  • working_gas (ct.Solution) – Working gas mixture used for calculations.

  • error_tol_temperature (float, optional) – Temperature error tolerance for iteration.

  • error_tol_specific_volume (float, optional) – Specific volume error tolerance for iteration.

  • max_iterations (int, optional) – Maximum number of loop iterations

Returns:

working_gas – gas object at equilibrium post-reflected-shock state

Return type:

ct.Solution

classmethod reflect(initial_state_gas, post_shock_gas, working_gas, incident_shock_speed)

This function calculates equilibrium post-reflected-shock state assuming u1 = 0.

Original function: sdtoolbox.reflections.reflected_eq

Parameters:

  • initial_state_gas (ct.Solution) – Working gas mixture in its initial, undetonated state.

  • post_shock_gas (ct.Solution) – Working gas mixture in its post-incident-shock state.

  • working_gas (ct.Solution) – Working gas mixture used for calculations.

  • incident_shock_speed (float) – Incident shock speed in m/s.

Returns:

A tuple containing:

  • post-reflected-shock pressure in Pascals (float),

  • reflected shock speed in m/s (float),

  • Gas object at equilibrium post-reflected-shock state (ct.Solution)

Return type:

tuple of (float, float, ct.Solution)

pypbomb.sd.cj_curve_fit(x, y)

Determines least squares fit of parabolic data. This is a vectorized version of sdtoolbox.PostShock.LSQ_CJspeed using np.linalg.lstsq.

Parameters:

  • x (np.array) – Independent data points for curve fitting

  • y (np.array) – Dependent data points for curve fitting

Returns:

A tuple containing (a, b, c, r_squared) where a, b, and c are the coefficients of quadratic function \(ax^2 + bx + c = 0\) and r_squared is the \(R^2\) value of the curve fit.

Return type:

tuple