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flowfanno

Fanno line flow relations

Description

Default Input Mode

example

[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

example

[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

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Calculate the Fanno line flow relations for air (gamma = 1.4) for subsonic Fanno parameter 1.2. This example 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')
mach =
    0.4849

T =
    1.1461

P =
    2.2080

rho =
    1.9265

velocity =
    0.5191

P0 =
    1.3699

fanno =
    1.2000

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. This example 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)
mach =

    0.5000    0.5000    0.5000    0.5000


T =

    1.1084    1.1188    1.1429    1.2318


P =

    2.1056    2.1155    2.1381    2.2198


rho =

    1.8997    1.8908    1.8708    1.8020


velocity =

    0.5264    0.5289    0.5345    0.5549


P0 =

    1.3479    1.3454    1.3398    1.3201


fanno =

    1.1724    1.1397    1.0691    0.8549

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. This example 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')
mach =
    0.6742         0

T =
    1.1000    1.2000

P =
    1.5556       Inf

rho =
    1.4142       Inf

velocity =
    0.7071         0

P0 =
    1.1144       Inf

fanno =
    0.2630       Inf

Input Arguments

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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

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

Fanno Flow TypeDescription
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

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

TypeDescription
'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

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

Mach numbers, returned as an array.

Temperature ratios, returned as an array.

Pressure ratios, returned as an array.

Density ratios, returned as an array.

Velocity ratios, returned as an array.

Stagnation (total) pressure ratios, returned as an 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

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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.

Introduced in R2010a