Cfx12 09 turbulence_printing

Turbulence
9-1
ANSYS, Inc. Proprietary
© 2009 ANSYS, Inc. All rights reserved.
April 28, 2009
Inventory #002598
Training Manual
9-1
April 28, 2009
Inventory #002598
Chapter 9
Turbulence
Introduction to CFX

Turbulence
9-2
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Training ManualWhat is Turbulence?
• Unsteady, irregular (non-periodic) motion in which transported
quantities (mass, momentum, scalar species) fluctuate in time and
space
– Identifiable swirling patterns characterize turbulent eddies
– Enhanced mixing (matter, momentum, energy, etc.) results
• Fluid properties and velocity exhibit random variations
– Statistical averaging results in accountable, turbulence related transport
mechanisms
– This characteristic allows for turbulence modeling
• Contains a wide range of turbulent eddy sizes (scales spectrum)
– The size/velocity of large eddies is on the order of the mean flow
• Large eddies derive energy from the mean flow
– Energy is transferred from larger eddies to smaller eddies
• In the smallest eddies, turbulent energy is converted to internal energy by
viscous dissipation

Turbulence
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Training ManualIs the Flow Turbulent?
External Flows
Internal Flows
Natural Convection
000,500Re ≥x along a surface
around an obstacle
where
where
Other factors such as free-stream
turbulence, surface conditions, and
disturbances may cause transition
to turbulence at lower Reynolds
numbers,3002Re ≥hd
000,20Re ≥d
is the Rayleigh number
µ
ρ
=
LU
LRe
etc.,,, hddxL =
k
TLgCTLg p
µ
∆βρ
=
αν
∆β
=
323
Ra9
10
Pr
Ra
≥
k
Cpµ
=
α
ν
=Pr is the Prandtl number
• Flows can be characterized by the Reynolds Number, Re

Turbulence
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Training ManualObservation by O. Reynolds
Laminar
(Low Reynolds Number)
Transition
(Increasing Reynolds Number)
Turbulent
(Higher Reynolds Number)

Turbulence
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Training ManualTurbulent Flow Structures
Energy Cascade
Richardson (1922)
Small
structures
Large
structures

Turbulence
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Training ManualGoverning Equations
Conservation Equations
Continuity
Momentum
Energy
where
Note that there is no turbulence equation in the governing
Navier-Stokes equations!
0)( =
∂
∂
+
∂
∂
i
i
u
xt
ρ
ρ
j
ij
i
ji
j
i
xx
P
uu
x
u
t ∂
∂
+
∂
∂
−=
∂
∂
+
∂
∂ τ
ρρ )()(








∂
∂
+
∂
∂
+
∂
∂
=
j
i
ij
i
j
j
i
ij
x
u
x
u
x
u
δµτ
3
2 2
2
1
itot uhh +=
)()()(
j
iji
j
jtot
j
tot
x
T
u
xt
P
uh
x
h
t ∂
∂
+
∂
∂
+
∂
∂
=
∂
∂
+
∂
∂
λτρρ

Turbulence
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Training ManualOverview of Computational Approaches
• Direct Numerical Simulation (DNS)
– Theoretically, all turbulent (and laminar / transition) flows can be simulated by
numerically solving the full Navier-Stokes equations
– Resolves the whole spectrum of scales. No modeling is required
– But the cost is too prohibitive! Not practical for industrial flows
• Large Eddy Simulation (LES) type models
– Solves the spatially averaged N-S equations
– Large eddies are directly resolved, but eddies smaller than the mesh are modeled
– Less expensive than DNS, but the amount of computational resources and efforts
are still too large for most practical applications
• Reynolds-Averaged Navier-Stokes (RANS) models
– Solve time-averaged Navier-Stokes equations
– All turbulent length scales are modeled in RANS
• Various different models are available
– This is the most widely used approach for calculating industrial flows
• There is not yet a single, practical turbulence model that can reliably predict
all turbulent flows with sufficient accuracy

Turbulence
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Training ManualRANS Modeling – Time Averaging
• Ensemble (time) averaging may be used to extract the mean flow properties
from the instantaneous ones
– The instantaneous velocity, ui, is split into average and fluctuating components
• The Reynolds-averaged momentum equations are as follows
– The Reynolds stresses are additional unknowns introduced by the averaging
procedure, hence they must be modeled (related to the averaged flow quantities) in
order to close the system of governing equations
Fluctuating
component
Time-average
component
Example: Fully-Developed
Turbulent Pipe Flow
Velocity Profile
Instantaneous
component
jiij uuR ′′ρ−=
j
ij
j
i
jik
i
k
i
x
R
x
u
xx
p
x
u
u
t
u
∂
∂
+








∂
∂
µ
∂
∂
+
∂
∂
−=





∂
∂
+
∂
∂
ρ (Reynolds stress tensor)

Turbulence
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Training ManualRANS Modeling – The Closure Problem
• Closure problem: Relate the unknown Reynolds
Stresses to the known mean flow variables through new
equations
– The new equations are the turbulence model
• Equations can be:
– Algebraic
– Transport equations
• All turbulence models contain empiricism
– Equations cannot be derived from fundamental principles
– Some calibrating to observed solutions and “intelligent
guessing” is contained in the models

Turbulence
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Training ManualRANS Modeling – The Closure Problem
• The RANS models can be closed in one of the following ways
(1) Eddy Viscosity Models (via the Boussinesq hypothesis)
– Boussinesq hypothesis – Reynolds stresses are modeled using an eddy (or
turbulent) viscosity, μT. The hypothesis is reasonable for simple turbulent shear
flows: boundary layers, round jets, mixing layers, channel flows, etc.
(2) Reynolds-Stress Models (via transport equations for Reynolds stresses)
– Modeling is still required for many terms in the transport equations
– RSM is more advantageous in complex 3D turbulent flows with large streamline
curvature and swirl, but the model is more complex, computationally intensive,
more difficult to converge than eddy viscosity models
ijij
k
k
i
j
j
i
jiij k
x
u
x
u
x
u
uuR δρ−δ
∂
∂
µ−








∂
∂
+
∂
∂
µ=′′ρ−=
3
2
3
2
TT

Turbulence
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Training Manual
• A large number of turbulence models are available in CFX, some
have very specific applications while others can be applied to a
wider class of flows with a reasonable degree of confidence
RANS Eddy-viscosity Models:
1) Zero Equation model.
2) Standard k-ε model.
3) RNG k-ε model.
4) Standard k-ω model.
5) Baseline (BSL) zonal k-ω based model.
6) SST zonal k-ω based model.
7) (k-ε)1E model.
RANS Reynolds-Stress Models:
1) LRR Reynolds Stress
2) QI Reynolds Stress
3) Speziale, Sarkar and Gatski Reynolds Stress
4) SMC-ω model
5) Baseline (BSL) Reynolds' Stress model
Eddy Simulation Models:
1) Large Eddy Simulation (LES) [transient]
2) Detached Eddy Simulation (DES)* [transient]
3) Scale Adaptive Simulation SST (SAS)* [transient]
* Not available in the ANSYS CFD-Flo product
Available Turbulence Models

Turbulence
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Training Manual
• The velocity profile near the wall is
important:
– Pressure Drop
– Separation
– Shear Effects
– Recirculation
• Turbulence models are generally suited to
model the flow outside the boundary layer
• Examination of experimental data yields a
wide variety of results in the boundary
layer
The above graph shows non-
dimensional velocity versus non-
dimensional distance from the
wall. Different flows show
different boundary layer profiles.
Turbulence Near the Wall

Turbulence
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Training Manual
• By scaling the variables near the wall the velocity profile data takes
on a predictable form (transitioning from linear to logarithmic
behavior)
• Since near wall conditions are often predictable, functions can be
used to determine the near wall profiles rather than using a fine
mesh to actually resolve the profile
– These functions are called wall functions
Linear
Logarithmic
Scaling the non-dimensional
velocity and non-
dimensional distance from
the wall results in a
predictable boundary layer
profile for a wide range of
flows

Turbulence
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Training Manual
• Fewer nodes are needed normal to the wall when wall functions
are used
u
y
u
y
Boundary layer
Wall functions used to
resolve boundary layer
Wall functions not used to
resolve boundary layer

Turbulence
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Training ManualTurbulence Near The Wall
• y+
is the non-dimensional distance from the wall
– It is used to measure the distance of the first node away from the wall
u
y
Boundary layer
y+
• Wall functions are only valid within specific y+
values
• If y+
is too high the first node is outside the boundary layer and wall
functions will be imposed too far into the domain
• If y+
is too low the first node will lie in the laminar (viscous) part of the
boundary layer where wall functions are not valid

Turbulence
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Training Manual
• In some situations, such as boundary layer separation, wall
functions do not correctly predict the boundary layer profile
• In these cases wall functions should not be used
• Instead, directly resolving the boundary layer can provide accurate
results
• Not all turbulence models allow the wall functions to be turned off
Wall functions applicable Wall functions not applicable

Turbulence
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Training Manual
• Standard k-ε Model
– The “industrial CFD” standard since it offer a good compromise between
numerical effort and computational accuracy
– Wall functions are always used
– y+
should typically be < 300 for the wall functions to be valid
– There is no lower limit on y+
• CFX uses Scalable wall functions
• If your mesh results in y+
values below the valid range of the wall functions, the
nodes nearest the wall are effectively ignored
• This ensures valid results, within the model limitations, but is a waste of mesh
– Known limitations:
• Separation generally under predicted since wall functions are used
• Inaccuracies with swirling flows and flows with strong streamline curvature
k-epsilon Model

Turbulence
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Training Manual
• k-ω Model
– One of the advantages of the k-ω formulation is the near wall treatment
for low-Reynolds number computations
• Here “low-Reynolds” refers to the turbulent Reynolds number, which is low in
the viscous sub-layer, not the device Reynolds number
• In other words “low-Reynolds number computations” means the near wall
mesh is fine enough to resolve the laminar (viscous) part of the boundary layer
which is very close to the wall
– A low-Reynolds number k-ω model only requires y+
<= 2
• If a low-Re k-ε model were available, it would require a much small y+
– In industrial flows, even y+
<= 2 cannot be guaranteed in most
applications and for this reason, a new automatic near wall treatment
was developed for the k-ω models
k-omega Model

Turbulence
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Training Manualk-omega Model
• k-ω Model (continued)
– The Automatic wall treatment for the k-ω models switches between a low-
Reynolds number formulation (i.e. direct resolution of the boundary
layer) at low y+
values and a wall function approach at higher y+
values
– This lets you take advantage of a fine near-wall mesh when present
Airfoil at Mach 0.5 showing the mesh and y+ values.
y+ values are >2. A finer near wall mesh is required
to achieve y+ < 2.

Turbulence
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Training Manual
• Shear Stress Transport (SST) Model
– The SST model is based on the k-ω model and has the same automatic
wall treatment
– It accounts for the transport of the turbulent shear stress and gives
highly accurate predictions of the onset and the amount of flow
separation
– This is a good default choice
SST result and experiment
k-ε fails to predict separation
Experiment Gersten et al.
SST Model

Turbulence
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Training Manualy+
for the SST and k-omega Models
• When using the SST or k-ω models y+
should be < 300 so that the wall
function approach is valid
• This will not take advantage of the low-Reynolds formulation, which is necessary
for accurate separation prediction
• However, the model can still be used on these coarser near-wall mesh and produce
valid results, within the limitations of the wall functions
• To take full advantage of the low-Reynolds formulation y+
should be < 2

Turbulence
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Training ManualEstimating y+
• It is useful to estimate y+
before obtaining a solution
– Saves time!
• Use the following formula based on flow over a flat plate:
– ∆y is the actual distance between the wall and first node
– L is a flow length scale
– y+
is the desired y+
value
– ReL is the Reynolds Number based on the length scale L
• See the documentation for a derivation of this formula
– ANSYS CFX-Solver Modeling Guide >> Turbulence and Near-Wall
Modeling >> Modeling Flow Near the Wall >> Guidelines for Mesh
Generation
14/13
Re74 −+
=∆ LyLy

Turbulence
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Training ManualOther Turbulence Models
• When RANS models are not adequate, Eddy Simulation models can
be used
– As already mentioned, these are more computationally expensive
• Large Eddy Simulation (LES)
– Resolves the large eddies, models the small eddies
– Problem: Requires a very fine boundary layer mesh, making it
impractical for most flows
• Detached Eddy Simulation (DES)
– Uses a RANS model in the boundary layer, switches over to LES in the
bulk flow
– A “standard” boundary layer mesh can be used
– Problem: the RANS to LES switch depends on the mesh, which can
give unphysical results on the “wrong” mesh
• Scale-Adaptive Simulation (SAS)
– Like DES, but without the mesh dependency problems

Turbulence
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Training ManualInlet Turbulence Conditions
• Unless turbulence is being directly simulated, it is accounted for by
modeling the transport of turbulence properties, for example k and ε
• Similar to mass and momentum, turbulence variables require
boundary condition specifications
– Several options exist for the specification of turbulence quantities at inlets
(details on next slide)
• Unless you have absolutely no idea of the turbulence levels in your
simulation (in which case, you can use the Medium (Intensity = 5%)
option), you should use well chosen values of turbulence intensities
and length scales
– Nominal turbulence intensities range from 1% to 5% but will depend on
your specific application
• The default turbulence intensity value of 0.037 (that is, 3.7%) is
sufficient for nominal turbulence through a circular inlet, and is a good
estimate in the absence of experimental data

Turbulence
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Training ManualInlet Turbulence Conditions
• Default Intensity and Autocompute Length Scale
– The default turbulence intensity of 0.037 (3.7%) is used together with a computed length scale to
approximate inlet values of k and ε. The length scale is calculated to take into account varying levels of
turbulence. In general, the autocomputed length scale is not suitable for external flows
• Intensity and Autocompute Length Scale
– This option allows you to specify a value of turbulence intensity but the length scale is still automatically
computed. The allowable range of turbulence intensities is restricted to 0.1%-10.0% to correspond to very
low and very high levels of turbulence accordingly. In general, the autocomputed length scale is not
suitable for external flows
• Intensity and Length Scale
– You can specify the turbulence intensity and length scale directly, from which values of k and ε are
calculated
• Low (Intensity = 1%)
– This defines a 1% intensity and a viscosity ratio equal to 1
• Medium (Intensity = 5%)
– This is the recommended option if you do not have any information about the inlet turbulence
• High (Intensity = 10%)
• Specified Intensity and Eddy Viscosity Ratio
– Use this feature if you wish to enter your own values for intensity and viscosity ratio
• k and Epsilon
– Specify the values of k and ε directly
• Zero Gradient
– Use this setting for fully developed turbulence conditions

Turbulence
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Training ManualExample: Pipe Expansion with Heat Transfer
q=const
.
Outlet
axis
H
H 40 x H
Inlet
q=0
.
d
D
• Reynolds Number ReD= 40750
• Fully Developed Turbulent Flow at Inlet
• Experiments by Baughn et al. (1984)

Turbulence
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Training Manual
• Plot shows dimensionless distance versus Nusselt Number
• Best agreement is with SST and k-omega models which do a better job of
capturing flow recirculation zones accurately
Example: Pipe Expansion with Heat Transfer

Turbulence
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Training ManualSummary: Turbulence Modeling Guidelines
• Successful turbulence modeling requires engineering judgment of:
– Flow physics
– Computer resources available
– Project requirements
• Accuracy
• Turnaround time
– Near-wall treatments
• Modeling procedure
– Calculate characteristic Re and determine whether the flow is turbulent
– Estimate y+
before generating the mesh
– The SST model is good choice for most flows
– Use the Reynolds Stress Model or the SST model with Curvature
Correction (see documentation) for highly swirling, 3-D, rotating flows

Cfx12 09 turbulence_printing

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