diff --git a/src/TurbulenceModels/compressible/turbulentFluidThermoModels/derivedFvPatchFields/outletMachNumberPressure/outletMachNumberPressureFvPatchScalarField.H b/src/TurbulenceModels/compressible/turbulentFluidThermoModels/derivedFvPatchFields/outletMachNumberPressure/outletMachNumberPressureFvPatchScalarField.H
index e3af95d7980f6a51d152cd5a590e9d1783b93c4a..eea811362eed4ec2e338565eff582b318f7c19ca 100644
--- a/src/TurbulenceModels/compressible/turbulentFluidThermoModels/derivedFvPatchFields/outletMachNumberPressure/outletMachNumberPressureFvPatchScalarField.H
+++ b/src/TurbulenceModels/compressible/turbulentFluidThermoModels/derivedFvPatchFields/outletMachNumberPressure/outletMachNumberPressureFvPatchScalarField.H
@@ -28,47 +28,84 @@ Group
grpOutletBoundaryConditions
Description
- This BC set the outlet pressure for compressible flows is such as a
- choked condition is achieved given an input Mach number.
- Optionally, if the BC is operated in a non-choked condition (choked false),
- the constants C1 and A1 are used to calculate the corresponding Mach number at
- the outlet.
-
- The static pressure is calculates as :
-
- p_s = p_tot / [1+(k-1)/2*M^2]^(k/(k-1))
-
- where
-
- p_tot: [Pa] mass averaged total pressure on outlet patch
- k: [-] mass averaged heat capacity ratio on outlet patch
- M: [-] target Mach number on the outlet patch defining as either choked or non-choked
-
- For choked conditions:
-
- M = constant defined in dict
-
- For non-choked conditions:
-
- M = A1/(C1*A_outlet)*sqrt(2/(k-1)*[r^(2/k)-r^((k+1)/k)], r=p_back/p_tot
-
- where
-
- A_outlet: [m2] area of outlet patch
- A1: [m2] constant defined in dict
- C1: [-] constant defined in dict
- p_back: [Pa] constant defined in dict
-
+ This boundary condition maintains a certain subsonic Mach number at an
+ outlet patch by dynamically adjusting the static outlet pressure. It makes
+ it possible, for example, to simulate the flow in a preturbine engine
+ exhaust manifold, without resolving details of the flow inside the turbine.
+ In general, the flow in a choked nozzle can be non-trivial and expensive
+ to simulate.
+
+
+ This formulation is derived from a simple model of the gas flow through
+ a nozzle with fixed geometry. The nozzle flow is assumed to be quasi-steady,
+ 1D, isentropic and compressible.
+
+ This gives the following general relationship between pressure ratio and Mach
+ number in any cross section inside the nozzle:
+
+ \f[
+ \frac{p_{tot}}{p}=\left[ 1+ \frac{k-1}{2}\;M^2 \right]^{\frac{k}{k-1}}
+ \f]
+
+ where the constant ratio of heat capacities is \f$k=c_p/c_v\f$.
+ The Mach number in the cross section is \f$M=V/c\f$, where \f$c\f$ is
+ the speed of sound and V is the uniform velocity in the streamwise
+ direction.
+
+ Overall pressure difference across the nozzle is
+ \f[
+ r = pBack/p_{tot}
+ \f]
+
+ When \f$k=1.4\f$, the flow in the nozzle throat becomes choked when
+ \f$ r<0.5\f$ and non-choked otherwise. This implementation is not applicable
+ when \f$ r>=1 \f$ where backflow would occur.
+
+ The nozzle model assumption locks the relationship between nozzle cross
+ sectional areas and Mach numbers. For a choked flow it is only the Mach number
+ on the outlet patch, \f$M_{outlet}\f$, that needs to be stated in the
+ boundary dictionary.
+
+ Care should be taken however to ensure that the entries in the input dictionary
+ and the CFD geometry satisfy the following equation
+ \f[
+ c1\frac{A_{outlet}}{A_1}=\frac{1}{M_{outlet}}\left[\frac{1+\frac{k-1}{2}
+ M_{outlet}^2}{1+\frac{k-1}{2}}\right]^{\frac{k+1}{2(k-1)}}
+ \f]
+ where \f$c1\f$ compensate for non-uniform outlet profiles, \f$A_{outlet}\f$
+ is geometrical outlet patch area and \f$A_1\f$ is assumed nozzle throat area.
+
+ In the non-choked case the outlet patch Mach number is calculated as
+ \f[
+ M_{outlet} =
+ \frac{A_1}
+ {c1\;A_{outlet}}
+ \sqrt{\frac{2}{k-1}\left[r^\frac{2}{k}-r^\frac{k+1}{k} \right]}
+ \f]
+
+ The accompaning boundary conditions for velocit should be
+ pressureInletOutletVelocity.
+
+ Author: Jens Dahl Kunoy
+
+ Reference:
+ \verbatim
+ Fox, R.W & McDonald, A. T. (1994).
+ Introduction to Fluid Mechanics (4ed SI).
+ Wiley
+ \endverbatim
Usage
+
\table
- Property | Description | Required | Default value
- pBack | Back pressure | yes
- M | Average desired mach number | no
- C1 | Model input | no | 0.0
- A1 | Model input | no | 0.0
- choked | The outlet is considered chocked | yes
- relax | relaxation factor (1 fully relax) | no | 0.0
+ Property | Description | Required | Default value
+ choked | Defines nozzle conditions| Yes | None
+ relax | underrelaxation of static pressure| Yes | 0.0
+ M | outlet Mach number | Yes (choked) | None
+ A1 | Nozzle throat area [m2] | Yes (non-choked) | 0.0
+ pBack | Pressure downstream of nozzle| Yes (non-choked) | None
+ c1 | Correction factor for non-uniform profiles
+ | No (non-choked) | 0.0
\endtable
Example of the boundary condition specification:
@@ -79,8 +116,9 @@ Usage
pBack 101325;
c1 1;
A1 0.008;
+ relax 0.1;
choked false;
- value uniform 101325;
+ value uniform 200000;
}
\endverbatim