flowfanno

Fanno line flow relations

Syntax

[mach,T,P,rho,velocity,P0,fanno] = flowfanno(gamma,fanno_flow)

[mach,T,P,rho,velocity,P0,fanno] = flowfanno(___,mtype)

Description

Default Input Mode

[mach,T,P,rho,velocity,P0,fanno] = flowfanno(gamma,fanno_flow) returns an array for each Fanno line flow relation. This function calculates the arrays for a given set of specific heat ratios (gamma) for the Mach input mode.

Specify Input Mode

[mach,T,P,rho,velocity,P0,fanno] = flowfanno(___,mtype) uses any one of the Fanno flow types mtype. Specify mtype types after all other input arguments.

Examples

Calculate Fanno Line Flow Relations for Gases

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.

gamma = [1.3, 1.33, 1.4, 1.67];
[mach, T, P, rho, velocity, P0, fanno] = flowfanno(gamma, 0.5)

mach = 1×4

    0.5000    0.5000    0.5000    0.5000

T = 1×4

    1.1084    1.1188    1.1429    1.2318

P = 1×4

    2.1056    2.1155    2.1381    2.2198

rho = 1×4

    1.8997    1.8908    1.8708    1.8020

velocity = 1×4

    0.5264    0.5289    0.5345    0.5549

P0 = 1×4

    1.3479    1.3454    1.3398    1.3201

fanno = 1×4

    1.1724    1.1397    1.0691    0.8549

Calculate Fanno Line Flow Relations for Air

Calculate the Fanno line flow relations for air (gamma = 1.4) for subsonic Fanno parameter 1.2.

[mach, T, P, rho, velocity, P0, fanno] = flowfanno(1.4, 1.2, 'fannosub')

mach = 
0.4849

T = 
1.1461

P = 
2.2080

rho = 
1.9265

velocity = 
0.5191

P0 = 
1.3699

fanno = 
1.2000

Calculate Fanno Line Flow Relations for Specific Heat

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.

[mach, T, P, rho, velocity, P0, fanno] = flowfanno(1.4, [1.1 1.2], 'temp')

mach = 1×2

    0.6742         0

T = 1×2

    1.1000    1.2000

P = 1×2

    1.5556       Inf

rho = 1×2

    1.4142       Inf

velocity = 1×2

    0.7071         0

P0 = 1×2

    1.1144       Inf

fanno = 1×2

    0.2630       Inf

Calculate Fanno Line Flow Relations for Gases with Specific Heat Ratio and Velocity Ratio

Calculate the Fanno line flow relations for gases with specific heat ratio and velocity ratio combinations as shown.

gamma = [1.3, 1.4];
velocity = [0.53, 0.49];
[mach, T, P, rho, velocity, P0, fanno] = flowfanno(gamma, velocity, 'velo')

mach = 1×2

    0.5035    0.4565

T = 1×2

    1.1079    1.1520

P = 1×2

    2.0903    2.3510

rho = 1×2

    1.8868    2.0408

velocity = 1×2

    0.5300    0.4900

P0 = 1×2

    1.3410    1.4328

fanno = 1×2

    1.1414    1.4899

Input Arguments

gamma — Specific heat ratios

scalar | array | real numbers greater than 1

Specific heat ratios, specified as an array or scalar of N specific heat ratios.

Dependencies

gamma must be a real, finite scalar greater than 1 for these input modes:

• Subsonic total pressure ratio

• Supersonic total pressure ratio

• Subsonic Fanno parameter

• Supersonic Fanno parameter

Data Types: double

fanno_flow — One Fanno flow

array of real numerical values

One Fanno flow, specified as an array of real numerical values. This argument can be one of these types.

Fanno Flow Type	Description
Mach numbers	Mach numbers, specified as a scalar or array of N real numbers greater than or equal to 0. If flow_fanno and gamma are arrays, they must be the same size. Use flow_fanno with the mtype value 'mach'. Because 'mach' is the default of mtype, mtype is optional when this array is the input mode.
Temperature ratios	Temperature ratios, specified as an array or scalar of N real numbers: Greater than or equal to 0 (as the Mach number approaches infinity) Less than or equal to (gamma+1)/2 (at Mach number equal 0) Use flow_fanno with mtype value 'temp'.
Pressure ratios	Pressure ratios, specified as an array or scalar of real numbers greater than or equal to 0. If flow_fanno and gamma are arrays, they must be the same size. Use flow_fanno with mtype value 'pres'.
Density ratios	Density ratios, specified as an array or scalar of real numbers. These numbers must be greater than or equal to: sqrt((gamma-1)/(gamma+1)) (as the Mach number approaches infinity). If flow_fanno and gamma are arrays, they must be the same size. Use flow_fanno with mtype value 'dens'.
Velocity ratios	Velocity ratios, specified as an array or scalar of N real numbers: Greater than or equal to 0 Less than or equal to sqrt((gamma+1)/(gamma-1)) (as the Mach number approaches infinity) If flow_fanno and gamma are both arrays, they must be the same size. Use flow_fanno with mtype value 'velo'.
Total pressure ratio	Total pressure ratio, specified as a scalar greater than or equal to 1. Use flow_fanno with mtype values 'totalp' and 'totalpsup'.
Fanno parameter scalar	Fanno Parameter, specified as a scalar. In subsonic mode, flow_fanno must be greater than or equal to 0. In supersonic mode, flow_fanno must be: Greater than or equal to 0 (at Mach number equal 1) Less than or equal to (gamma+1)/(2*gamma)*log((gamma+1)/(gamma-1))-1/gamma (as Mach number approaches infinity) Use flow_fanno with mtype values 'fannosub' and 'fannosup'.

Data Types: double

mtype — Input mode of Fanno flow

'mach' (default) | 'temp' | 'pres' | 'dens' | 'velo' | 'totalpsub' | 'totalpsup' | 'fannosub' | 'fannosup'

Input mode of Fanno flow, specified as one of these values.

Type	Description
'mach'	Default Mach number
'temp'	Temperature ratio
'pres'	Pressure ratio
'dens'	Density ratio
'velo'	Velocity ratio
'totalpsub'	Subsonic total pressure ratio
'totalpsup'	Supersonic total pressure ratio
'fannosub'	Subsonic Fanno parameter
'fannosup'	Supersonic Fanno parameter

Data Types: double

Output Arguments

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

mach — Mach numbers

array

Mach numbers, returned as an array.

T — Temperature ratios

array

Temperature ratios, returned as an array.

P — Pressure ratios

array

Pressure ratios, returned as an array.

rho — Density ratios

array

Density ratios, returned as an array.

velocity — Velocity ratios

array

Velocity ratios, returned as an array.

P0 — Stagnation pressure ratios

array

Stagnation (total) pressure ratios, returned as an array.

fanno — Fanno parameters

array

Fanno parameters, returned as an array.

Limitations

• This function assumes that variables vary only in one dimension. 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. For thermally perfect gas correction factors, see [2]. If the temperature is so high that molecules dissociate and ionize (static temperature 5000 K for air), you cannot assume a perfect gas.

More About

Pressure Ratio

Calculated as local static pressure over the reference static pressure for sonic flow.

Temperature Ratio

Calculated as local static temperature over the reference static temperature for sonic flow.

Density Ratio

Calculated as local density over the reference density for sonic flow.

Velocity Ratio

Calculated as local velocity over the reference velocity for sonic flow.

Total Pressure Ratio

Calculated as local total pressure over the reference total pressure for sonic flow.

Fanno Parameter

This function uses Fanno variables given by the equation: F = f*L/D, where:

• F is the Fanno parameter.

• 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.

References

[1] James, John E. A. Gas Dynamics. 2nd ed. Boston: Allyn and Bacon 1984.

[2] Ames Research Staff. NACA Technical Report 1135. Moffett Field, CA: National Advisory Committee on Aeronautics, 1953. 667–671.

Version History

Introduced in R2010a