Biomedical Engineering Reference
In-Depth Information
Table 5.1  Summary of common RANS turbulence models
Turbulence model
Notes
Advantages
Disadvantages
mixing length
No additional equations,
but relies on a mixing
length theory to find the
Reynolds stress
Fast calculation times.
Good predictions for
simple flows where
experimental correla-
tions for the mixing
length exist
Cannot describe
flow separation or
recirculation where
the turbulent length
scale varies
Spalart-Allmaras
One additional equation
for the turbulent viscosity
Good for attached
wall-bounded flows,
and flows with
mild separation and
recirculation
Bad for large
separation, free shear
flows, and decaying
turbulence
k-ε models
Two additional equa-
tions one for k and ε
each. Most widely used
model along with the
k-ω. Assumes fluid flow
is fully turbulent. The
model leads to equal
normal stresses, and
isotropic turbulence
Stable calculations and
reasonable predictions
for many flows. Most
general turbulence of
all RANS models
Poor predictions for
swirling and rotating
flows, strong separa-
tion, severe pressure
gradient. Lack of
sensitivity to adverse
pressure gradients
k-ω models
Two additional equations one for k and ω each. Its numerical behaviour
is similar to the k - ε and suffers from similar disadvantages such as the
isotropic turbulence assumption. Allows for a more accurate turbulent
profile near the wall but requires a fine mesh to resolve the thin turbulent
boundary layer. Is generally superior to k - ε for wall-bounded, free shear.
and low Reynolds number flows, but separation is typically predicted to
be excessive and early
Reynolds Stress
Models
Seven additional equa-
tions, one each for the six
independent Reynolds
stresses, and one turbu-
lent dissipation. Unlike
other RANS model,
the isotropic turbulence
assumption is avoided
Accurately predicts
more complex flows,
accounting for stream-
line curvature, swirl,
rotation, high strain
rates, and separation
More equations con-
tain more unknown
terms that need to be
modeled. Requires
more computational
time due to addi-
tional equations
We summarise the more common turbulence models in Table 5.1 highlighting
the advantages, disadvantages, and notes.
5.3
Introduction to Solid Mechanics
5.3.1
Elasticity
A material is elastic if it deforms under an applied force, and returns to its origi-
nal position when the force is removed. Conceptually we consider an elastic body
subjected to a force, F sufficient to initiate deformation (Fig. 5.15 ). As a result of
 
Search WWH ::




Custom Search