Calculate Prandtl-Meyer functions for expansion waves
[mach, nu, mu]
= flowprandtlmeyer(gamma, prandtlmeyer_array, mtype)
[mach, nu, mu] = flowprandtlmeyer(gamma, prandtlmeyer_array, mtype) calculates the following: array of Mach numbers, mach, Prandtl-Meyer 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 Prandtl-Meyer types. You select the Prandtl-Meyer type with mtype.
The function assumes that the flow is two-dimensional. 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 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.
Array of real numerical values for one of the Prandtl-Meyer types. This argument can be one of the following:
A string for selecting the isentropic flow variable represented by prandtlmeyer_array.
Array of Mach numbers. In Prandtl-Meyer angle input mode, mach outputs are the same size as the array input or array inputs. If there are no array inputs, mach is a scalar.
Array of Prandtl-Meyer angles. The Prandtl-Meyer 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 Prandtl-Meyer relations for air (gamma = 1.4) for Prandtl-Meyer angle 61 degrees. The following returns a scalar for mach, nu, and mu.
[mach, nu, mu] = flowprandtlmeyer(1.4, 61, 'nu')
Calculate the Prandtl-Meyer 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 Prandtl-Meyer 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 Prandtl-Meyer 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 element-wise.
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.