Documentation

flowisentropic

Isentropic flow ratios

Syntax

[mach, T, P, rho, area] = flowisentropic(gamma, flow, mtype)

Description

[mach, T, P, rho, area] = flowisentropic(gamma, flow, mtype) returns an array. This array contains an isentropic flow Mach number (mach), temperature ratio (T), pressure ratio (P), density ratio (rho), and area ratio (area). This function calculates these arrays given a set of specific heat ratios (gamma), and any one of the isentropic flow types. You select the isentropic flow with mtype.

This function assumes that variables vary in one dimension only. It also assumes that the main mechanism for the change of flow variables is the change of cross-sectional area of the flow stream tubes.

This function assumes that the environment is a perfect gas. In the following instances, the function cannot assume a perfect gas environment. If there is a large change in either temperature or pressure without a proportionally large change in the other, the function cannot assume a perfect gas environment. . If the stagnation temperature is above 1500 K, do not assume that constant specific heats. In this case, the medium ceases to be a calorically perfect gas. Consider it a thermally perfect gas. See 2 for thermally perfect gas correction factors. If the temperature is so high that molecules dissociate and ionize (static temperature 5000 K for air), you cannot assume a calorically or thermally perfect gas.

Input Arguments

gamma

Array of N specific heat ratios. gamma must be a scalar or array of N real numbers greater than 1. For subsonic area ratio input mode and supersonic area ratio input mode, gamma must be a real, finite scalar greater than 1.

flow

Array of real numerical values for one of the isentropic flow relations. This argument can be one of the following:

• Array of Mach numbers. flow must be a scalar or an array of N real numbers greater than or equal to 0. If flow and gamma are arrays, they must be the same size.

Use flow with the mtype value 'mach'. Because 'mach' is the default of mtype, mtype is optional when this array is the input mode.

• Array of temperature ratios. The temperature ratio is the local static temperature over the stagnation temperature. flow must be a scalar or an array of real numbers:

• Greater than or equal to 0 (as the Mach number approaches infinity)

• Less than or equal to 1 (at Mach number equal 0)

If flow and gamma are both arrays, they must be the same size.

Use flow with mtype value 'temp'.

• Array of pressure ratios. The pressure ratio is the local static pressure over the stagnation pressure. flow must be a scalar or an array of real numbers:

• Greater than or equal to 0 (as the Mach number approaches infinity)

• Less than or equal to 1 (at Mach number equal 0)

If flow and gamma are both arrays, they must be the same size.

Use flow with mtype value 'pres'.

• Array of density ratios. The density ratio is the local density over the stagnation density. flow must be a scalar or an array of real numbers:

• Greater than or equal to 0 (as the Mach number approaches infinity)

• Less than or equal to 1 (at Mach number equal 0)

If flow and gamma are both arrays, they must be the same size.

Use flow with mtype value 'dens'.

• Scalar value of area ratio. flow must be a real value greater than or equal to 1.

Use flow with mtype value 'sup'.

mtype

Input mode for the isentropic flow in flow.

TypeDescription
'mach'Default. Mach number.
'temp'Temperature ratio.
'pres' Pressure ratio.
'dens'Density ratio.
'sub'Subsonic area ratio. The subsonic area ratio is the local subsonic stream tube area over the reference stream tube area for sonic conditions.
'sup' Supersonic area ratio. The supersonic area ratio is the local supersonic stream tube area over the reference stream tube area for sonic conditions.

Output Arguments

All outputs are the same size as the array inputs. If there are no array inputs, all outputs are scalars.

 mach Array of Mach numbers. T Array of temperature ratios. The temperature ratio is the local static temperature over the stagnation temperature. P Array of pressure ratios. The pressure ratio is the local static pressure over the stagnation pressure. rho Array of density ratios. The density ratio is the local density over the stagnation density. area Array of area ratios. The area ratio is the local stream tube area over the reference stream tube area for sonic conditions.

Examples

Calculate the isentropic flow relations for air (gamma = 1.4) for a design subsonic area ratio of 1.255. This example returns scalar values for mach, T, P, rho, and area.

[mach, T, P, rho, area] = flowisentropic(1.4, 1.255, 'sub')

Calculate the isentropic flow relations for gases with specific heat ratios given in the following 1 x 4 row array for the Mach number 0.5. This example following returns a 1 x 4 row array for mach, T, P, rho, and area.

gamma = [1.3, 1.33, 1.4, 1.67];
[mach, T, P, rho, area] = flowisentropic(gamma, 0.5)

Calculate the isentropic flow relations for a specific heat ratio of 1.4. Also calculate range of temperature ratios from 0.40 to 0.70 in increments of 0.10. This example returns a 4 x 1 column array for mach, T, P, rho, and area.

[mach, T, P, rho, area] = flowisentropic(1.4, (0.40:0.10:0.70)', 'temp')

Calculate the isentropic flow relations for gases with provided specific heat ratio and density ratio combinations. This example returns a 1 x 2 array for mach, T, P, rho, and area each. The elements of each vector correspond to the inputs element-wise.

gamma = [1.3, 1.4];
rho = [0.13, 0.9];
[mach, T, P, rho, area] = flowisentropic(gamma, rho , 'dens')

References

1. James, J. E. A., Gas Dynamics, Second Edition, Allyn and Bacon, Inc, Boston, 1984.

2. NACA Technical Report 1135, 1953, National Advisory Committee on Aeronautics, Ames Research Staff, Moffett Field, Calif. Pages 667–671. 