MASS [FLOW] {RATE [ACTUAL | CORRECTED] | RATIO} value \
   [PRESSURE | DIRECT [RELAXER rlxr]] [ORDER {ZERO|0|ONE|1}] \
   [ZONE] range1[,range2[, ... rangen]]

This keyword allows the user to specify mass flow at outflow boundaries in the flowfield. The specified value must be positive.

	RATE		value represents the mass flow rate in lbm/sec, and may be actual (the default) or corrected, as specified by the ACTUAL or CORRECTED keyword. The corrected air flow is defined as Wc = Wactual thetax0.5 / deltax where deltax = Px / P0      thetax = Tx / T0 and Px and Tx are the total pressure and temperature at the duct exit, and P0 and T0 are equal to 14.7 psi and 520 °R, respectively.
	RATIO		value represents the mass flow ratio. The actual mass flow is computed as mass flow = (value) rhoinf Uinf Acap where Acap is the capture area found in the .cgd file zonal parameters.
	PRESSURE		A spatially-constant pressure is set at the boundary, and modified as the solution proceeds until the desired mass flow is achieved. This is the default.
	DIRECT		The momentum, and thus the mass flow, is modified directly, and the pressure adjusts as the solution proceeds.
	RELAXER		The specified mass-flow rate will be relaxed using the relaxtion factor rlxr. This option only applies when DIRECT is specified. The default value for rlxr is 1.0 (i.e., no relaxation).
	ORDER		Either zeroth- or first-order extrapolation will be used, as specified. The default is zeroth-order.

In the zone specification, the range parameter(s) must be one of the following forms:

	zonenum		Selects zone zonenum
	begzone:endzone		Selects all zones from begzone to endzone
	ALL		Selects all zones

Note that if multiple zones are listed, the specified mass flow will be applied in each zone.

With the PRESSURE option, the pressure will be constant over the entire outflow boundary, resulting in poor solutions for flows that should have cross-flow pressure gradients in that region. With the DIRECT option, cross-flow pressure gradients may be present at the outflow boundary, and the mass flow will be equal to the user-specified value (for rlxr = 1) for all iterations.

For flows with negligible cross-flow pressure gradients, the results and convergence rates using the PRESSURE and DIRECT options are nearly the same. For a test case with a significant cross-flow pressure gradient near the outflow boundary, the computed pressures using the two options differed by as much as 10%. The PRESSURE option, although non-physical for this case, had a slightly better convergence rate.

Internally, to apply this boundary condition WIND does the following:

1. At all the boundary points, the density, momentum, and energy are extrapolated from the interior to the boundary using either zeroth- or first-order extrapolation, as specified.
   
   
2. The mass flow at the boundary is computed by numerical integration.
   
   
3. If PRESSURE was specified, a new downstream pressure is computed based on the difference between the computed and specified mass flow rates.
   
   
4. If DIRECT was specified, a mass flow correction factor is computed as
   f_corr = 1 + r (m_spec / m_int - 1)
   
   where r is the input relaxation factor rlxr, and m_spec and m_int are the user-specified and integrated mass flow rates, respectively.
   
   
5. For each boundary point, the density and momentum, plus the pressure, effective gamma, compressibility factor, and speed of sound, are extrapolated from the interior to the boundary using either zeroth- or first-order extrapolation, as specified.
   
   
6. If DIRECT was specified, the extrapolated momentum values at the outflow boundary are modified using
   (rho u) = f_corr (rho u)_ext
   (rho v) = f_corr (rho v)_ext
   (rho w) = f_corr (rho w)_ext
   
   
7. If PRESSURE was specified, the energy at each boundary point is computed, consistent with the downstream pressure value from step 3 and the extrapolated values of density, etc., from step 5.
   
   
8. If DIRECT was specified, the energy at each boundary point is computed, consistent with the momentum values from step 6 and the extrapolated values of density, pressure, etc., from step 5.

The default for all extrapolation is zeroth-order (i.e., conditions at the boundary are set to the values at the computational plane adjacent to the boundary). This results in a discontinuous slope in flow values near the outflow boundary, which may be important for flows with significant streamwise pressure gradients. First-order extrapolation yields smoother results.

For flows with little or no streamwise pressure gradient near the outflow boundary, the results using zeroth- and first-order extrapolation are essentially identical. Convergence rates and the final residual values are generally better with zeroth-order extrapolation, however, so the default zeroth-order extrapolation is recommended.

For flows with significant streamwise pressure gradients near outflow boundaries, zeroth-order extrapolation can give poor results at the outflow boundary, and in some cases these can affect values at the inflow boundary. First-order extrapolation is thus recommended for these flows.

Examples

   MASS FLOW RATIO           0.95 ZONE 2
   MASS FLOW RATE  ACTUAL    180. ZONE 3
   MASS FLOW RATE  CORRECTED 220. ZONE 4