4.16 Blended freestream condition

There is a class of problems in CFD that involve external flow around one or more solid bodies, e.g. a vehicle, wind turbine, buildings, etc.

PICT\relax \special {t4ht=

A solution domain is specified which includes the solid body and extends some distance to a free boundary in the far-field. A flow velocity eqnis specified which can be applied as a fixed value type at an inlet patch.

The far-field boundary requires attention. The robust conditions at a free boundary for eqn and eqn are inlet-outlet-velocity and total pressure described in Sec. 4.15 and Sec. 4.7 respectively.

PICT\relax \special {t4ht=

The inlet-outlet-velocity requires eqn to be prescribed for inflow which may differ significantly from a determined eqn when there is outflow. Solution accuracy depends on the suitability of the prescribed eqn.

The flow direction in the far-field can often be close to tangential to the boundary, especially with a box-shaped domain. If the flow at one face changes from outflow to inflow, eqn suddenly changes to the prescribed fixed value and eqn decreases by eqn. Sometimes a pattern of switching can occur in adjacent faces and repeated switching can slow the convergence of a solution.

PICT\relax \special {t4ht=

The blended freestream condition is a mixed type with zero reference gradient, eqn, which modifies the value fraction eqn as shown above. In the limit that the flow direction is normal to the boundary, the condition becomes the fundamental fixed value and zero gradient types for eqn and eqn.

Between these extremes, eqn is blended linearly, e.g. for eqn by

 1- n--u-- 1- v = 2 1 juj ; with v = 2 when juj = 0: \relax \special {t4ht=
This means eqn for both eqn and eqn for tangential flow.

At a boundary face, eqn may be directed normal-inward, causing eqn by Eq. (4.27 ). The condition can then “lock” at eqn, so to avoid this, the calculation can use a velocity equating to the mean of the face and neighbour cell value, i.e. eqn.

Note that for eqn, the value fraction is calculated changing the sign of the second term in Eq. (4.27 ) i.e. eqn

The freestream conditions overcome the problem of switching to improve the convergence of solutions. Boundary velocities are determined, not prescribed, which seems to improve accuracy, e.g. in force calculations described in Sec. 8.4 and Sec. 8.6 .

Notes on CFD: General Principles - 4.16 Blended freestream condition