Handbook of Turbomachinery Second Edition Revised - Ventech!

tends to be less satisfactory when three-dimensional flow, curvature,
rotation, and adverse pressure gradients are present. Clearly, these
conditions occur regularly in turbomachinery applications. Therefore,
although the zero-equation models are desirable because of their simplicity
and low impact on computation time, they are not sufficiently general to be
appropriate for turbomachinery flows.
Two-equation models offer a somewhat more representative picture of
the physics of turbulent flow, by utilizing two partial differential equations,
which govern the transport of selected turbulence properties. Typically,
those properties are turbulent kinetic energy and turbulent energy
dissipation, although other properties are occasionally used. Once the
turbulence properties are computed, by solving the transport equations,
they are then used in an algebraic model to obtain a turbulent viscosity, in a
similar manner to the zero-equation models. The two-equation model of
Lam and Bremhorst [44] is frequently used for turbomachinery applications.
The advantage of the two-equation models is found in their more
realistic modeling of turbulence properties, which imposes only a small
penalty in terms of computation time (due to the requirement of solving two
additional partial differential equations). However, the Reynolds stress terms
in the Navier–Stokes equations are still being modeled using a turbulent
viscosity. In addition, a set of constants must be specified in the transport
equations. These constants, which are determined from experimental data
for simple flows, actually vary from one flow regime to another and therefore
are not always calibrated to the particular flow being analyzed. Therefore,
although the two-equation models represent an improvement over the zeroequation
models, many of the same shortcomings are still present, because of
the basic assumption that the Reynolds stresses may be modeled through the
use of a turbulent viscosity. Thus, the two-equation models, in their basic
form, are still inadequate for flows with rotation, curvature, adverse pressure
gradients, and a high degree of three-dimensionality.
Some researchers have attempted to compensate for the shortcomings
of the turbulent-viscosity-based models by introducing modifications into
the transport equations to treat the more complex flows. For example, both
Hanjalic and Launder [45] and Nagano and Tagawa [46] have presented
two-equation models that attempt to deal with adverse pressure gradients.
Abid [47] has developed a version of the two-equation model that addresses
both pressure gradients and compressibility. Another approach that offers
greater accuracy is renormalization group theory [48, 49], which permits a
local analytical, rather than an empirical, representation of the constants in
the model. These techniques attempt to expand the range of application of
the two-equation models. However, the basic assumption remains, namely,
that the Reynolds stress terms may be modeled using a turbulent viscosity.
Copyright © 2003 Marcel Dekker, Inc.