Shocks and detonations module#

In this section, you will find the documentation of the routines implemented to solves processes that involve strong changes in dynamic pressure, such as steady state shock and detonation waves in either normal or oblique stream configurations within the limits of regular shock reflections.

Note

The kernel of the incident, reflected, and Chapman-Jouguet detonations are based on Gordon, S., & McBride, B. J. (1994). NASA reference publication, 1311.

Routines
det_cj(self, mix1, varargin)#

Compute pre-shock and post-shock states of a Chapman-Jouguet detonation

This method is based on the method outlined in Gordon, S., & McBride, B. J. (1994). NASA reference publication, 1311.

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture in the post-shock state

Examples

  • [mix1, mix2] = det_cj(self, self.PS.strR{1})

  • [mix1, mix2] = det_cj(self, self.PS.strR{1}, self.PS.strP{1})

det_compute_guess(self, mix1, phi, drive_factor)#

Obtain guess of the jump conditions for a Chapman-Jouguet detonation. Only valid if the mixture have CHON. It computes the guess assuming first a complete combustion, next it recomputes assuming an incomplete combustion from the composition obtained in the previous step.

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • phi (float) – Equivalence ratio [-]

  • drive_factor (float) – Overdriven ratio [-] respect to the sound velocity of the mixture

Returns:

Tuple containing

  • P (float): Pressure ratio [-]

  • T (float): Temperature ratio [-]

  • M1 (float): Pre-shock Mach number [-]

  • R (float): Density ratio [-]

  • Q (float): Dimensionless Heat release []

  • STOP (float): Relative error [-]

Example

[P, T, M1, R, Q, STOP] = det_compute_guess(self, self.PS.strR{1}, 1, 2)

det_compute_guess_CEA(self, mix1)#

Obtain guess of the jump conditions for a Chapman-Jouguet detonation as in NASA’s CEA code (see Sec. 8.3 of [1])

[1] Gordon, S., & McBride, B. J. (1994). NASA reference publication, 1311.

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

Returns:

Tuple containing

  • P (float): Pressure ratio [-]

  • T (float): Temperature ratio [-]

  • STOP (float): Relative error [-]

Example

[P, T, STOP] = det_compute_guess_CEA(self, self.PS.strR{1})

det_oblique_beta(self, mix1, drive_factor, beta, varargin)#

Compute pre-shock and post-shock states of an oblique detonation wave given the wave angle (two solutions)

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • drive_factor (float) – Drive_factor [-]

  • beta (float) – Wave angle [deg] of the incident oblique detonation

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-detonation state

  • mix2_1 (struct): Properties of the mixture in the post-detonation state - weak detonation

  • mix2_2 (struct): Properties of the mixture in the post-detonation state - strong detonation

Examples

  • [mix1, mix2_1, mix2_2] = det_oblique_beta(self, self.PS.strR{1}, 2, 60)

  • [mix1, mix2_1, mix2_2] = det_oblique_beta(self, self.PS.strR{1}, 2, 60, self.PS.strP{1})

det_oblique_theta(self, mix1, drive_factor, theta, varargin)#

Compute pre-shock and post-shock states of an oblique detonation wave given the deflection angle.

Two solutions:

  • Weak detonation

  • Strong detonation

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • drive_factor (float) – Drive factor [-]

  • theta (float) – Deflection angle [deg]

Optional Args:

  • mix2_1 (struct): Properties of the mixture in the post-shock state - weak detonation (previous calculation)

  • mix2_2 (struct): Properties of the mixture in the post-shock state - strong detonation (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-detonation state

  • mix2_1 (struct): Properties of the mixture in the post-detonation state - weak detonation

  • mix2_2 (struct): Properties of the mixture in the post-detonation state - strong detonation

Examples

  • [mix1, mix2_1, mix2_2] = det_oblique_theta(self, self.PS.strR{1}, 2, 30)

  • [mix1, mix2_1, mix2_2] = det_oblique_theta(self, self.PS.strR{1}, 2, 30, self.PS.strP{1})

det_overdriven(self, mix1, drive_factor, varargin)#

Compute pre-shock and post-shock states of an overdriven planar detonation

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • drive_factor (float) – Overdriven factor [-]

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture in the post-shock state

Examples

  • [mix1, mix2] = det_overdriven(self, mix1, 1.5)

  • [mix1, mix2] = det_overdriven(self, mix1, 1.5, mix2)

det_polar(self, mix1, drive_factor, varargin)#

Compute detonation polar diagrams

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture at the post-shock state with the shock polar results

Examples

  • [mix1, mix2] = det_polar(self, mix1, 3000)

  • [mix1, mix2] = det_polar(self, mix1, 3000, mix2)

det_underdriven(self, mix1, drive_factor, varargin)#

Compute pre-shock and post-shock states of an overdriven planar detonation

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • drive_factor (float) – Underdriven factor [-]

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture in the post-shock state

Examples

  • [mix1, mix2] = det_underdriven(self, mix1, 1.5)

  • [mix1, mix2] = det_underdriven(self, mix1, 1.5, mix2)

shock_ideal_gas(gamma, M1)#

Compute jump conditions assuming a thermochemically frozen gas (calorically perfect gas)

Parameters:

  • gamma (float) – Adiabatic index [-]

  • M1 (float) – Pre-shock Mach number [-]

Returns:

Tuple containing

  • R (float): Density ratio [-]

  • P (float): Pressure ratio [-]

  • T (float): Temperature ratio [-]

  • Gammas (float): Rankine-Hugoniot slope parameter [-]

  • M1 (float): Pre-shock Mach number [-]

Example

[R, P, T, Gammas, M1] = shock_ideal_gas(1.4, 2.0)

shock_incident(self, mix1, u1, varargin)#

Compute pre-shock and post-shock states of a planar incident shock wave

This method is based on the method outlined in Gordon, S., & McBride, B. J. (1994). NASA reference publication, 1311.

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture in the post-shock state

Examples

  • [mix1, mix2] = shock_incident(self, mix1, u1)

  • [mix1, mix2] = shock_incident(self, mix1, u1, mix2)

shock_incident_2(self, mix1, u1, varargin)#

Compute pre-shock and post-shock states of a planar incident shock wave

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture in the post-shock state

Examples

[mix1, mix2] = shock_incident_2(self, mix1, u1) [mix1, mix2] = shock_incident_2(self, mix1, u1, mix2)

shock_oblique_beta(self, mix1, u1, beta, varargin)#

Compute pre-shock and post-shock states of an oblique shock wave given the wave angle (one solution)

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

  • beta (float) – Wave angle [deg] of the incident oblique shock

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture at the post-shock state

Examples

  • [mix1, mix2] = shock_oblique_beta(self, mix1, u1, beta)

  • [mix1, mix2] = shock_oblique_beta(self, mix1, u1, beta, mix2)

shock_oblique_reflected_theta(self, mix1, u2, theta, mix2, varargin)#

Compute pre-shock and post-shock states of an oblique reflected shock wave given the deflection angle.

Two solutions:

  • Weak shock

  • Strong shock

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state of the incident shock

  • u2 (float) – Post-shock velocity [m/s] of the incident shock

  • theta (float) – Deflection angle [deg]

  • mix2 (struct) – Properties of the mixture in the post-shock state of the incident shock

Optional Args:

  • mix5_1 (struct): Properties of the mixture in the post-shock state of the reflected shock - weak shock (previous calculation)

  • mix5_2 (struct): Properties of the mixture in the post-shock state of the reflected shock - strong shock (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state of the incident shock

  • mix2 (struct): Properties of the mixture in the post-shock state of the incident shock

  • mix5_1 (struct): Properties of the mixture in the post-shock state of the reflected shock - weak shock

  • mix5_2 (struct): Properties of the mixture in the post-shock state of the reflected shock - strong shock

Examples

  • [mix1, mix2, mix5_1, mix5_2] = shock_oblique_reflected_theta(self, mix1, u2, theta, mix2)

  • [mix1, mix2, mix5_1, mix5_2] = shock_oblique_reflected_theta(self, mix1, u2, theta, mix2, mix5_1, mix5_2)

shock_oblique_theta(self, mix1, u1, theta, varargin)#

Compute pre-shock and post-shock states of an oblique shock wave given the deflection angle.

Two solutions:

  • Weak shock

  • Strong shock

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

  • theta (float) – Deflection angle [deg]

Optional Args:

  • mix2_1 (struct): Properties of the mixture in the post-shock state - weak shock (previous calculation)

  • mix2_2 (struct): Properties of the mixture in the post-shock state - strong shock (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2_1 (struct): Properties of the mixture in the post-shock state - weak shock

  • mix2_2 (struct): Properties of the mixture in the post-shock state - strong shock

Examples

  • [mix1, mix2_1, mix2_2] = shock_oblique_theta(self, mix1, u1, theta)

  • [mix1, mix2_1, mix2_2] = shock_oblique_theta(self, mix1, u1, theta, mix2_1, mix2_2)

shock_polar(self, mix1, u1, varargin)#

Compute shock polar diagrams

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

Optional Args:

mix2 (struct): Properties of the mixture in the post-shock state (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture at the post-shock state with the shock polar results

Examples

  • [mix1, mix2] = shock_polar(self, mix1, u1)

  • [mix1, mix2] = shock_polar(self, mix1, u1, mix2)

shock_polar_limitRR(self, mix1, u1)#

Obtain polar curves for the given pre-shock conditions using Broyden’s method

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state

  • u1 (float) – Pre-shock velocity [m/s]

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state

  • mix2 (struct): Properties of the mixture in the post-shock state - polar diagrams from mix1 (incident)

  • mix2_1 (struct): Properties of the mixture in the post-shock state - weak shock

  • mix3 (struct): Properties of the mixture in the post-shock state - polar diagrams from mix2_1 (reflected)

Example

[mix1, mix2, mix2_1, mix3] = shock_polar_limitRR(self, mix1, u1)

shock_reflected(self, mix1, u1, mix2, varargin)#

Compute pre-shock and post-shock states of a planar reflected shock wave

This method is based on the method outlined in Gordon, S., & McBride, B. J. (1994). NASA reference publication, 1311.

Parameters:

  • self (struct) – Data of the mixture, conditions, and databases

  • mix1 (struct) – Properties of the mixture in the pre-shock state of the incident shock

  • u1 (float) – Pre-shock velocity [m/s]

  • mix2 (struct) – Properties of the mixture at the post-shock state of the incident shock

Optional Args:

mix5 (struct): Properties of the mixture in the post-shock state of the reflected shock (previous calculation)

Returns:

Tuple containing

  • mix1 (struct): Properties of the mixture in the pre-shock state of the incident shock

  • mix2 (struct): Properties of the mixture at the post-shock state of the incident shock

  • mix5 (struct): Properties of the mixture in the post-shock state of the reflected shock

Examples

  • [mix1, mix2, mix5] = shock_reflected(self, mix1, u1, mix2)

  • [mix1, mix2, mix5] = shock_reflected(self, mix1, u1, mix2, mix5)