Shocks

gas_dynamics.shocks.shocks.shock_mach(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the Mach number after a standing normal shock

Notes

Given a starting Mach number M1 and the ratio of specific heats, return the Mach number M2 that immediately follows the shock. The default fluid is air.

Parameters

  • mach (float) – The Mach number before the shock

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The Mach number after the shock

Return type

float

Examples

>>> M2 = gd.shock_mach(mach=1.5)
>>> M2
0.7010887416930995
>>>
gas_dynamics.shocks.shocks.shock_mach_before(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the Mach number before a standing normal shock

Notes

Given the Mach number after the shock and the ratio of specific heats, return the Mach number that immediately precedes the shock. Default fluid is air.

Parameters

  • M (float) – The Mach number after the shock

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The mach number before the shock

Return type

float

Examples

>>> import gas_dynamics as gd
>>> M2 = 0.7010887416930995
>>> M1 = gd.shock_mach_before(mach = M2)
>>> M1
1.4999999999999998
>>>
gas_dynamics.shocks.shocks.shock_pressure_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the pressure ratio after a standing normal shock for a given Mach number

Notes

Given a starting Mach number and a ratio of specific heats, this function returns the ratio of pressure 2 over pressure 1 across a standing normal shock.

Parameters

  • mach (float) – The starting Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The pressure ratio p2/p1

Return type

float

Examples

>>> import gas_dynamics as gd
>>> p2_p1 = gd.shock_pressure_ratio(mach=1.5)
>>> p2_p1
2.4583333333333335
>>>
gas_dynamics.shocks.shocks.shock_mach_from_pressure_ratio(pressure_ratio: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the mach number across a standing normal shock given a pressure ratio

Notes

Given the ratio of pressure behind the shock over pressure before the shock and the ratio of specific heats, this function returns the Mach number before the shock. Default fluid is air.

Parameters

  • pressure_ratio (float) – The pressure ratio p2 / p1

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The mach number prior the shock

Return type

float

Examples

>>> import gas_dynamics as gd
>>> p2_p1 = 6
>>> M1 = gd.shock_mach_from_pressure_ratio(pressure_ratio = p2_p1)
>>> M1
2.29906813420444
>>>
gas_dynamics.shocks.shocks.shock_temperature_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns the temperature ratio after a standing normal shock for a given Mach number

Notes

Given a starting Mach number and a ratio of specific heats, this function returns the ratio of temperature 2 over temperature 1 across a standing normal shock. Default fluid is air.

Parameters

  • mach (float) – The starting Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The temperature ratio T2/T1

Return type

float

Examples

>>> import gas_dynamics as gd
>>> T2_T1 = gd.shock_temperature_ratio(mach=1.5)
>>> T2_T1
1.320216049382716
>>>
gas_dynamics.shocks.shocks.shock_dv_a(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns change in velocity over the local speed of sound after a normal shock.

Notes

Given a starting Mach number and a ratio of specific heats, this function returns the velocity change across a standing normal shock divided by the local speed of sound. Default fluid is air

Parameters

  • mach (float) – The starting Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The change in Mach number

Return type

float

Examples

gas_dynamics.shocks.shocks.shock_stagnation_pressure_ratio(mach: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns stagnation pressure ratio after a normal shock.

Notes

Given a starting Mach number and a ratio of specific heats, this function returns the ratio of stagnation presure 2 over stagnation pressure 1 across a standing normal shock. Default fluid is air.

Parameters

  • mach (float) – The starting Mach number

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The stagnation pressure ratio pt2/pt1

Return type

float

Examples

>>> pt2_pt1 = gd.shock_stagnation_ratio(mach=2)
>>> pt2_pt1
0.7208738614847454
>>>
gas_dynamics.shocks.shocks.shock_tables(range=[1, 5], step=0.01, gas=<gas_dynamics.fluids.fluid object>) → str

Returns shock tables for a range of Mach numbers.

Notes

Given a range of Mach numbers and a ratio of specific heats, generate the standing normal shock tables for every incremental Mach number in between.

Parameters

  • range (list) – The starting and ending Mach # in a list, ie: [1,5].

  • step (float) – The step size for the tables.

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The shock table

Return type

str

Examples

>>> import gas_dynamics as gd
>>> gd.shock_tables(range=[1,2], step=.1)
Normal Shock Parameters for γ = 1.4
M: 1.00   |   M2: 1.0000   |    p2/p1: 1.0000   |    T2/T1: 1.0000   |   dV/a: 0.0000   |   pt2/pt1: 1.000000
M: 1.10   |   M2: 0.9118   |    p2/p1: 1.2450   |    T2/T1: 1.0649   |   dV/a: 0.1591   |   pt2/pt1: 0.998928
M: 1.20   |   M2: 0.8422   |    p2/p1: 1.5133   |    T2/T1: 1.1280   |   dV/a: 0.3056   |   pt2/pt1: 0.992798
M: 1.30   |   M2: 0.7860   |    p2/p1: 1.8050   |    T2/T1: 1.1909   |   dV/a: 0.4423   |   pt2/pt1: 0.979374
M: 1.40   |   M2: 0.7397   |    p2/p1: 2.1200   |    T2/T1: 1.2547   |   dV/a: 0.5714   |   pt2/pt1: 0.958194
M: 1.50   |   M2: 0.7011   |    p2/p1: 2.4583   |    T2/T1: 1.3202   |   dV/a: 0.6944   |   pt2/pt1: 0.929787
M: 1.60   |   M2: 0.6684   |    p2/p1: 2.8200   |    T2/T1: 1.3880   |   dV/a: 0.8125   |   pt2/pt1: 0.895200
M: 1.70   |   M2: 0.6405   |    p2/p1: 3.2050   |    T2/T1: 1.4583   |   dV/a: 0.9265   |   pt2/pt1: 0.855721
M: 1.80   |   M2: 0.6165   |    p2/p1: 3.6133   |    T2/T1: 1.5316   |   dV/a: 1.0370   |   pt2/pt1: 0.812684
M: 1.90   |   M2: 0.5956   |    p2/p1: 4.0450   |    T2/T1: 1.6079   |   dV/a: 1.1447   |   pt2/pt1: 0.767357
M: 2.00   |   M2: 0.5774   |    p2/p1: 4.5000   |    T2/T1: 1.6875   |   dV/a: 1.2500   |   pt2/pt1: 0.720874
>>>
gas_dynamics.shocks.shocks.shock_flow_deflection(mach: float, shock_angle: float, gas=<gas_dynamics.fluids.fluid object>) → float

Returns flow deflection angle from Mach number and oblique shock angle

Notes

Given the Mach number prior to the oblique shock, the angle of the oblique shock in degrees, and the ratio of specific heats, this function returns the angle that the flow is turned. Default fluid is air.

Parameters

  • mach (float) – The Mach number before the shock

  • shock_angle (float) – The shock angle in degrees

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The deflection angle

Return type

float

Examples

>>> import gas_dynamics as gd
>>> deflect = gd.shock_flow_deflection(mach=2, shock_angle = 157.5)
>>> deflect
10.856560004139958
>>>
gas_dynamics.shocks.shocks.shock_angle(mach: float, flow_deflection: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the shock angle given the Mach number prior to the shock and the deflection angle

Notes

Given the Mach number prior to the oblique shock, the angle of the flow deflection, and the ratio of specific heats, this functions returns the angle that is formed by the shock. Default ratio of specific heats is for air

Parameters

  • mach (float) – The Mach number before the shock

  • flow_deflection (float) – The flow deflection angle in degrees

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The shock angle

Return type

float

Examples

>>> import gas_dynamics as gd
>>> shocks = gd.shock_angle(mach=2, flow_deflection = 10)
>>> shocks
[23.014012220565785, 96.29991962425305]
>>>
gas_dynamics.shocks.shocks.shock_mach_given_angles(shock_angle: float, flow_deflection: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the Mach number before a shock given shock angle and flow deflection

Notes

Given the angle of the shock and the angle that the flow has turned, return the mach number that preceded the shock.

Parameters

  • theta (float) – The shock angle in degrees

  • delta (float) – The flow deflection angle in degrees

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The mach number

Return type

float

Examples

>>> import gas_dynamics as gd
>>> M = gd.shock_mach_given_angles(theta=22.5, delta=10)
>>> M
3.9293486839798955
>>>
gas_dynamics.shocks.shocks.shock_oblique_charts(mach_max=6, gas=<gas_dynamics.fluids.fluid object>, points=40000, dark=True)

Generate 2-D Oblique Shock Charts

Notes

Displays two plots, 1) Mach number versus oblique shock wave angle and the corresponding deflection angles for each case. 2) Mach number versus resulting Mach number after an oblique shock and the corresponding deflection angles for each case. Default ratio of specific heats is for air.

Parameters

  • mach_max (float) – The upper limit Mach number for the chart

  • gas (fluid) – A user defined fluid object. Default is air

  • points (int) – The number of points to evaluate on the mesh

  • dark (bool) – Dark mode for the plots. Default is true.

Examples

>>> gd.shock_oblique_charts()
>>>
gas_dynamics.shocks.shocks.shock_flow_deflection_from_machs(mach_initial: float, mach_final: float, gas=<gas_dynamics.fluids.fluid object>) → float

Return the flow deflection angle given the mach number before and after the oblique shock

Notes

Given two mach numbers, iteratively solve for the shock angle and flow deflection to satisfy the system.

Parameters

  • mach_initial (float) – The initial mach number

  • mach_final (float) – The mach number after the event

  • gas (fluid) – A user defined fluid object. Default is air

Returns

The flow deflection angle

Return type

float

Examples

>>> import gas_dynamics as gd
>>> flow_deflect = gd.shock_flow_deflection_from_machs(M1=3, M2=1.5)
>>> flow_deflect
28.589471710648365
>>>