Handbook of Turbomachinery Second Edition Revised - Ventech!

The next step in modeling accuracy is taken with the algebraic
Reynolds stress model. Once again, partial differential equations are solved
for the transport of two turbulence properties. However, in this type of
model, these variables are not used to compute turbulent viscosity, but
rather are used in individual algebraic equations for each of the Reynolds
stress and turbulent heat-flux terms. In this way, more of the physics of the
turbulent flow is preserved, and complex three-dimensional flows including
curvature and rotation may be predicted accurately. The impact on
computation time is not substantially higher than that for a two-equation
model, however, because of the simplicity of the algebraic equations used to
model the Reynolds stress tensor and turbulent heat-flux vector.
Examples of algebraic Reynolds stress models may be found in Rodi
and Scheuerer [50] and also Zhang and Lakshminarayana [51]. The latter
presents a successful application of the model to a compressor rotor flow
prediction.
The next level of sophistication in turbulence modeling, the full
Reynolds stress model, offers a much more realistic representation of
turbulent flow. However, this accuracy comes at the price of significantly
greater modeling complexity. The complete set of Reynolds stress transport
equations must be solved, which approximately doubles the number of
partial differential equations in the governing equation set. This imposes
such a substantial computational penalty that the application of this model
is presently outside the realm of practicality for turbomachinery flow
analysis tools.
Therefore, based on the computing power available today, the twoequation
models, with complex flow enhancements, would represent a
minimum desired level of turbulence modeling capability for turbomachinery
analyses, with the algebraic Reynolds stress models being preferred for
additional accuracy.
The field of turbulence modeling is very active, and much current
literature exists on specific models. Patel et al. [52] reviewed a variety of
models for near-wall flows, and a comprehensive review paper by
Lakshminarayana [53] provides many references to models being used in
turbomachinery applications. In addition, Speziale [54] has produced a
detailed examination of recent developments in Reynolds stress modeling.
Transition modeling, to predict the transition from laminar to
turbulent flow, has received less attention for turbomachinery applications.
However, a recent study by Mayle [55] provides an extensive look at the
current status of this field. Among Mayle’s conclusions are that transition in
gas turbines is largely influenced by free-stream turbulence, pressure
gradient, and the periodic, unsteady passing of wakes; in contrast, surface
roughness, surface curvature, compressibility, and heat transfer have only a
Copyright © 2003 Marcel Dekker, Inc.