## 7.23.2 General Non-Reflecting Boundary Conditions

Overview

The general non-reflecting boundary conditions in FLUENT are based on characteristic wave relations derived from the Euler equations, and applied only on pressure-outlet boundary conditions. To obtain the primitive flow quantities ( ) on the pressure-outlet, reformulated Euler equations are solved on the boundary of the domain in an algorithm similar to the flow equations applied to the interior of the domain.

Unlike the turbo-specific NRBC method presented in the previous section, the General NRBC method is not restricted by geometric constraints or mesh type. However, good cell skewness near the boundaries where the NRBC will be applied is advisable for a more stable, converged solution. In addition, the General NRBCs can be applied to steady or transient flows as long as the compressible ideal-gas law is used.

Restrictions and Limitations

Note the following restrictions and limitations on the general NRBCs:

• The general NRBC is available only with the density-based solvers.

• The general NRBC is available only with compressible flow while using the ideal-gas law.

 The general NRBC should not be used with the wet steam or real gas models.

• The general NRBC is not available if the target mass flow rate is activated in the pressure-outlet panel.

• The general NRBC should not be used if the turbo-specific NRBC is activated.

 If you switch from Turbo-specific NRBC to general NRBC or vice versa, then make sure you switch off one NRBC model before turning on the next. You cannot use both NRBC models at the same time.

• NRBCs are not compatible with species transport models. They are mainly used to solve ideal-gas single-specie flow.

Theory

General NRBCs are derived by first recasting the Euler equations in an orthogonal coordinate system ( ) such that one of the coordinates, , is normal to the boundary Figure  7.23.5. The characteristic analysis [ 374, 375] is then used to modify terms corresponding to waves propagating in the normal direction. When doing so, a system of equations can be written to describe the wave propagation as follows:

 (7.23-43)

Where , and and , and are the velocity components in the coordinate system ( , , ). The equations above are solved on pressure-outlet boundaries, along with the interior governing flow equations, using similar time stepping algorithms to obtain the values of the primitive flow variables ( ).

 Note that a transformation between the local orthogonal coordinate system ( , , ) and the global Cartesian system (X, Y, Z) must be defined on each face on the boundary to obtain the velocity components ( , , ) in a global Cartesian system.

The terms in the transformed Euler equations contain the outgoing and incoming characteristic wave amplitudes, , and are defined as follows:

 (7.23-44)

From characteristic analyses, the wave amplitudes, , are given by:

 (7.23-45)

The outgoing and incoming characteristic waves are associated with the characteristic velocities of the system (i.e eigenvalues), , as seen in Figure  7.23.6. These eigenvalues are given by:

 (7.23-46)

For subsonic flow leaving a pressure-outlet boundary, four waves leave the domain (associated with positive eigenvalues , , , and ) and one enters the domain (associated with negative eigenvalue ).

To solve Equations  7.23-44 on a pressure-outlet boundary, the values of , , and must be first determined from Equations  7.23-46 by using extrapolated values of , , , and from inside the domain. Then, for the lone incoming wave, the Linear Relaxation Method (LRM) of Poinsot [ 287, 288] is used to determine the value of the wave amplitude. The LRM method sets the value of the incoming wave amplitude to be proportional to the differences between the local pressure on a boundary face and the imposed exit pressure. Therefore, is given by

 (7.23-47)

where is the imposed pressure at the exit boundary, is the relaxation factor, and is the local pressure value at the boundary.

In general, the desirable average pressure on a non-reflecting boundary can be either relaxed toward a pressure value at infinity or enforced to be equivalent to some desired pressure at the exit of the boundary.

If you want the average pressure at the boundary to relax toward at infinity (i.e. ), the suggested factor is given by:

 (7.23-48)

where is the acoustic speed , is the domain size, is the maximum Mach number in the domain, and is the under-relaxation factor (default value is 0.15) . On the other hand, if the desired average pressure at the boundary is to approach a specific imposed value at the boundary, then the factor is given by:

 (7.23-49)

where the default value for is 5.0

Using General Non-Reflecting Boundary Conditions

The General NRBC is available for use in the Pressure Outlet panel when either the density-based explicit or the density-based implicit solvers are activated to solve for compressible flows using the ideal-gas law.

To activate the general NRBC

1.   Select pressure-outlet from the Boundary Conditions Panel and click the Set... button.

2.   In the Pressure Outlet panel, enable the Non-Reflecting Boundary option.

3.   Select one of the two NRBC Pressure Specification options: Exit pressure is at infinity or Exit pressure is average pressure.

(a)   The Exit pressure is at infinity boundary is typically used in unsteady calculations or when the exit pressure value is imposed at infinity. The boundary is designed so that the pressure at the boundary relaxes toward the imposed pressure at infinity. The speed at which this relaxation takes place is controlled by the parameter, sigma, which can be adjusted in the TUI:

define boundary-conditions non-reflecting-bc

general-nrbc set

In the set/ submenu, you can set the sigma value. The default value for sigma is 0.15.

(b)   The Exit pressure is average pressure boundary specification is usually used in steady-state calculations when you want to force the average pressure on the boundary to approach the exit pressure value. The matching of average exit pressure to the imposed average pressure is controlled by parameter sigma2 which can be adjusted in the TUI:

define boundary-conditions non-reflecting-bc

general-nrbc set

In the set/ submenu, you can set the sigma2 value. The default value for sigma2 is 5.0 .

 There is no guarantee that the sigma2 value of 5.0 will force the average boundary pressure to match the specified exit pressure in all flow situations. In the case where the desired average boundary pressure has not been achieved, the user can intervene to adjust the sigma2 value so that the desired average pressure on the boundary is approached.

Usually, the solver can operate at higher CFL values without the NRBCs being turned on. Therefore, for steady-state solutions the best practice is to first achieve a good stable solution (not necessarily converged) before activating the non-reflecting boundary condition. In many flow situations, the CFL value must be reduced from the normal operation to keep the solution stable. This is particularly true with the density-based implicit solver since the boundary update is done in an explicit manner. A typical CFL value in the density-based implicit solver, with the NRBC activated, is 2.0.

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