[mach, T, P, rho, velocity, T0, P0]
= flowrayleigh(gamma, rayleigh_flow, mtype) returns
an array for each Rayleigh line flow relation. This function calculates
these arrays for a given set of specific heat ratios (gamma),
and any one of the Rayleigh line flow types. You select the Rayleigh
flow type with mtype.
This function assumes that the medium is a calorically perfect
gas in a constant area duct. It assumes that the flow is steady, frictionless,
and one dimensional. It also assumes that the main mechanism for the
change of flow variables is heat transfer.
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, do
not assume constant specific heats. In this case, the medium ceases
to be a calorically perfect gas; you must then 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.
Input Arguments
gamma
Array of N specific heat ratios.
gamma must be either a scalar or an array
of N real numbers greater than 1. gamma must
be a real, finite scalar greater than 1 for the following input modes:
low speed temperature ratio, high speed temperature ratio, subsonic
total temperature, supersonic total temperature, subsonic total pressure,
and supersonic total pressure.
rayleigh_flow
Array of real numerical values for one Rayleigh line flow. This
argument can be one of the following:
Array of Mach numbers. This array must be a scalar
or an array of N real numbers greater than
or equal to 0. If rayleigh_flow and gamma are
arrays, they must be the same size.
Use rayleigh_flow with mtype
value 'mach'. Because 'mach' is
the default of mtype, mtype is
optional when this array is the input mode.
Scalar value of temperature ratio. The temperature
ratio is the local static temperature over the reference static temperature
for sonic flow. rayleigh_flow must be
a real scalar:
Greater than or equal to 0 (at the Mach number equal
0 for low speeds or as Mach number approaches infinity for high speeds)
Less than or equal to 1/4*(gamma+1/gamma)+1/2
(at mach = 1/sqrt(gamma))
Use rayleigh_flow with mtype values 'templo' and 'temphi'.
Array of pressure ratios. The pressure ratio is the
local static pressure over the reference static pressure for sonic
flow. rayleigh_flow must be a scalar or
array of real numbers less than or equal to gamma+1
(at the Mach number equal 0). If rayleigh_flow and gamma are
arrays, they must be the same size.
Use rayleigh_flow with mtype value 'pres'.
Array of density ratios. The density ratio is the
local density over the reference density for sonic flow. rayleigh_flow
must be a scalar or array of real numbers. These numbers must be greater
than or equal to:
gamma/(gamma+1)
(as Mach number approaches infinity)
If rayleigh_flow and gamma are
arrays, they must be the same size.
Use rayleigh_flow with mtype value 'dens'.
Array of velocity ratios. The velocity ratio is
the local velocity over the reference velocity for sonic flow. rayleigh_flow must
be a scalar or an array of N real numbers:
Greater than or equal to 0
Less than or equal to (gamma+1)/gamma (as
Mach number approaches infinity)
If rayleigh_flow and gamma are
both arrays, they must be the same size.
Use rayleigh_flow with mtype value 'velo'.
Scalar value of total temperature ratio. The total
temperature ratio is the local stagnation temperature over the reference
stagnation temperature for sonic flow. In subsonic mode, rayleigh_flow must
be a real scalar:
Greater than or equal to 0 (at the Mach number equal
0)
Less than or equal to 1 (at the Mach number equal
1)
In supersonic mode, rayleigh_flow must
be a real scalar:
Greater than or equal to (gamma+1)^2*(gamma-1)/2/(gamma^2*(1+(gamma-1)/2)))
(as Mach number approaches infinity)
Less than or equal to 1 (at the Mach number equal
1)
Use rayleigh_flow with the mtype values 'totaltsub' and 'totaltsup'.
Scalar value of total pressure ratio. The total pressure
ratio is the local stagnation pressure over the reference stagnation
pressure for sonic flow. In subsonic mode, rayleigh_flow must
be a real scalar.
Greater than or equal to 1 (at the Mach number equal
1)
Less than or equal to (1+gamma)*(1+(gamma-1)/2)^(-gamma/(gamma-1))
(at Mach number equal 0)
In supersonic mode, rayleigh_flow must
be a real scalar greater than or equal to 1.
Use rayleigh_flow with mtype values 'totalpsub' and 'totalpsup'.
mtype
A string that defines the input mode for the Rayleigh flow in rayleigh_flow.
Type
Description
'mach'
Default. Mach number.
'templo'
Low speed static temperature ratio. The low speed temperature
ratio is the local static temperature over the reference sonic temperature.
This ratio for when the Mach number of the upstream flow is less than
the critical Mach number of 1/sqrt(gamma).
'temphi'
High speed static temperature ratio. The high speed temperature
ratio is the local static temperature over the reference sonic temperature.
This ratio is for when the Mach number of the upstream flow is greater
than the critical Mach number of 1/sqrt(gamma).
'pres'
Pressure ratio.
'dens'
Density ratio.
'velo'
Velocity ratio.
'totaltsub'
Subsonic total temperature ratio.
'totaltsup'
Supersonic total temperature ratio.
'totalpsub'
Subsonic total pressure ratio.
'totalpsup'
Supersonic total pressure ratio.
Output Arguments
All output ratios are static conditions over the sonic conditions.
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.
T0
Array of total temperature ratios. The temperature ratio is
the local stagnation temperature over the reference stagnation temperature
for sonic flow.
P0
Array of total pressure ratios. The total pressure ratio is
the local stagnation pressure over the reference stagnation pressure
for sonic flow.