Calculate PrandtlMeyer functions for expansion waves
[
mach
, nu
, mu
]
= flowprandtlmeyer(gamma
, prandtlmeyer_array
, mtype
)
[
calculates
the following: array of Mach numbers, mach
, nu
, mu
]
= flowprandtlmeyer(gamma
, prandtlmeyer_array
, mtype
)mach
,
PrandtlMeyer angles (nu
in degrees) and
Mach angles (mu
in degrees). flowprandtlmeyer
calculates
these arrays for a given set of specific heat ratios, gamma
,
and any one of the PrandtlMeyer types. You select the PrandtlMeyer type with mtype
.
The function assumes that the flow is twodimensional. The function also assumes a smooth and gradual change in flow properties through the expansion fan.
Note, this function assumes that the environment is a perfect gas. In the following instances, it 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, it cannot assume a perfect gas environment. If the stagnation temperature is above 1500 K, the function cannot assume constant specific heats. In this case, you must consider it a thermally perfect gas. See 2 for thermally perfect gas correction factors. The local static temperature might be so high that molecules dissociate and ionize (static temperature 5000 K for air). In this case, you cannot assume a calorically or thermally perfect gas.

Array of  

Array of real numerical values for one of the PrandtlMeyer types. This argument can be one of the following:
 

Isentropic flow variable represented by


Array of Mach numbers. In PrandtlMeyer angle input mode, 

Array of PrandtlMeyer angles. The PrandtlMeyer angle is the angle change required for a Mach 1 flow to achieve a given Mach number after expansion. 

Array of Mach angles. The Mach angle is between the flow direction and the lines of pressure disturbance caused by supersonic motion. 
Calculate the PrandtlMeyer relations for air (gamma
=
1.4) for PrandtlMeyer angle 61 degrees. The following returns a
scalar for mach
, nu
,
and mu
.
[mach, nu, mu] = flowprandtlmeyer(1.4, 61, 'nu')
Calculate the PrandtlMeyer functions for gases with specific
heat ratios. The following yields a 1 x 4 array for nu
,
but only a scalar for mach
and mu
.
gamma = [1.3, 1.33, 1.4, 1.67]; [mach, nu, mu] = flowprandtlmeyer(gamma, 1.5)
Calculate the PrandtlMeyer angles for a specific heat ratio
of 1.4 and range of Mach angles from 40 degrees to 70 degrees. This
example uses increments of 10 degrees. The following returns a 4
x 1 column array for mach
, nu
,
and mu
.
[mach, nu, mu] = flowprandtlmeyer(1.4, (40:10:70)', 'mu')
Calculate the PrandtlMeyer relations for gases with specific
heat ratio and Mach number combinations as shown. The following returns
a 1 x 2 array for nu
and mu
each,
where the elements of each vector correspond to the inputs elementwise.
gamma = [1.3, 1.4]; prandtlmeyer_array = [1.13, 9]; [mach, nu, mu] = flowprandtlmeyer(gamma,prandtlmeyer_array)
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.