Handbook of Turbomachinery Second Edition Revised - Ventech!

passage to the next, assuming that the inlet and exit conditions are also
periodic. As in the case of inlet conditions, if for some reason the flow is not
periodic over a single blade passage, then multiple passages would have to
be modeled, representing a periodic set. Periodicity is enforced by setting the
dependent flow variables equal at equivalent positions on the periodic
boundaries.
Initial conditions for the dependent variables are also of concern, for
both unsteady flows and steady flows, which are solved using time-marching
techniques (described later in this chapter). The initial conditions differ from
boundary conditions, in that they are not held fixed throughout the
solution. Rather, they provide a starting point for the entire flow field, from
which the solution will migrate. Although the initialization can be somewhat
crude and still yield a successful solution, convergence can often be
accelerated if the initialized flow distribution is reasonably realistic. Often,
solutions from a preliminary design streamwise curvature program or a 3D
inviscid analysis can be adapted for use as a flow-field initialization for
steady flows. Similarly, unsteady flows are typically initialized using the
steady flow solution.
Having established a set of governing equations for the flow, and
having also identified the necessary boundary conditions that must be
specified in association with those equations, it remains to deal with the
turbulence closure by selecting an appropriate turbulence model. This issue
will be addressed in the next section.
Turbulence and Transition Modeling. A wide variety of turbulence models
is available to provide closure for the turbulent stress and heat-flux terms in
the Reynolds-averaged Navier–Stokes equations. These range from
relatively simple zero-equation models, which algebraically represent the
turbulent stresses in terms of an empirically derived turbulent, or eddy,
viscosity, through two-equation models, which utilize partial differential
equations for the transport of two turbulence properties that are then
related to turbulent viscosity, to more complex algebraic and full Reynolds
stress models, which, as the names suggest, treat each term of the Reynolds
stress tensor and turbulent heat-flux vector separately to obtain a more
realistic representation of three-dimensional turbulence. Models of greater
complexity, such as large eddy simulation or solutions of the full Navier–
Stokes equations, are not practical at this stage for use in turbomachinery
analysis tools, due to the large amounts of computation time required.
The simple zero-equation models, of which the Baldwin–Lomax model
[43] is perhaps the most prevalent, require only the solution of an algebraic
equation for turbulent viscosity. This type of model is adequate for the
prediction of 2D boundary-layer flows, without separation; however, it
Copyright © 2003 Marcel Dekker, Inc.