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Fanno line flow relations
[mach, T, P, rho, velocity, P0, fanno]
= flowfanno(gamma, fanno_flow, mtype)
[mach, T, P, rho, velocity, P0, fanno] = flowfanno(gamma, fanno_flow, mtype) returns an array for each Fanno line flow relation. This function calculates the arrays for a given set of specific heat ratios (gamma), and any one of the Fanno flow types. You select the Fanno flow type with mtype.
This function uses Fanno variables given by the following. F is the Fanno parameter given by F = f*L/D. f is the friction coefficient. L is the length of constant area duct required to achieve sonic flow. D is the hydraulic diameter of the duct.
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.
If the temperature experiences large fluctuations, the perfect gas assumption might be invalid. If the stagnation temperature is above 1500 K, do not assume 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 perfect gas.
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 reference static temperature for sonic flow. |
P |
Array of pressure ratios. The pressure ratio is the local static pressure over the reference static pressure for sonic flow. |
rho |
Array of density ratio. The density ratio is the local density over the reference density for sonic flow. |
velocity |
Array of velocity ratios. The velocity ratio is the local velocity over the reference velocity for sonic flow. |
P0 |
Array of stagnation (total) pressure ratio. The total pressure ratio is the local total pressure over the reference total pressure for sonic flow. |
fanno |
Array of Fanno parameters. The Fanno parameter is F = f*L/D. f is the friction coefficient. L is the length of constant area duct required to achieve sonic flow. D is the hydraulic diameter of the duct. |
Calculate the Fanno line flow relations for air (gamma = 1.4) for subsonic Fanno parameter 1.2. The following returns scalar values for mach, T, P, rho, velocity, P0, and fanno.
[mach, T, P, rho, velocity, P0, fanno] = flowfanno(1.4, 1.2, 'fannosub')
Calculate the Fanno line flow relations for gases with specific heat ratios given in the following 1 x 4 row array for the Mach number 0.5. The following yields a 1 x 4 row array for mach, T, P, rho, velocity, P0, and fanno.
gamma = [1.3, 1.33, 1.4, 1.67]; [mach, T, P, rho, velocity, P0, fanno] = flowfanno(gamma, 0.5)
Calculate the Fanno line flow relations for a specific heat ratio of 1.4 and range of temperature ratios from 0.40 to 0.70 in increments of 0.10. The following returns a 4 x 1 column array for mach, T, P, rho, velocity, P0, and fanno.
[mach, T, P, rho, velocity, P0, fanno] = flowfanno(1.4, [1.1 1.2], 'temp')
Calculate the Fanno line flow relations for gases with specific heat ratio and velocity ratio combinations as shown. The following returns a 1 x 2 array for mach, T, P, rho, velocity, P0, and fanno each. The elements of each array correspond to the inputs element-wise.
gamma = [1.3, 1.4]; V = [0.53, 0.49]; [MACH, T, P, RHO, V, P0, F] = flowfanno(gamma, V, 'velo')
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.
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