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Turbulent Jet Setup and Solution
Background
As stated in the Pre-Analysis section, the k-ε model solves the Reynolds equations, which are time-averaged Navier Stokes equations with additional velocity fluctuation terms. This model provides closure needed for these equations with additional model specific transport equations for k and ε that account for the turbulent properties.
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While k and ε can be specified, they can also be related to more physically understandable parameters I and d. I is the turbulent intensity,
Latex |
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\large $$d_H$$ |
...
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and
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d
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is
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the
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jet
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diameter.
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Latex |
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\large
$$
{I} = {0.16Re^{-1/8}}
$$
|
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Latex |
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\large
$$
{d_H} = {d}
$$
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Latex |
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\large
$$
{l} = {0.07d}
$$
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Note:
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for
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further
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understanding
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of
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model
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specifications,
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Fluent
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specifies
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certain
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constants
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as
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in
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the
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equations
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below.
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However,
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while
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these
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constants
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can
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be
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changed,
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Fluent
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initializes
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them
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at
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their
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standard
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values.
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Latex |
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\large
$$
{\epsilon} = {C_\mu^{3/4}k^{3/2} \over l}
$$
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Latex |
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\large
$$
{k} = {3 \over 2 (UI)^2}
$$
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Setup
Use the same case and data files as you downloaded and checked in the Laminar setup for the geometry and mesh, but save this case as 'Turbulent Jet'.
Set up the k-ε model for turbulence. In Solution Setup-Models, double click the previous "Viscous-Laminar"
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option
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to
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open
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the
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dialogue.
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Select
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the
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"k-epsilon
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(2eqn)"
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model
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for
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turbulence.
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Leave
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the
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model
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constants
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the
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same
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as
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defined
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in
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the
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dialogue
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below;
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these
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values
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have
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been
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refined
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to
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constraints
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of
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the
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model
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and
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are
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typically
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not
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varied
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as
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mentioned
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above.
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Press
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OK.
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Note
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that
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wall
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functions
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are
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not
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required
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for
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this
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case
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unlike
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the
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turbulent
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pipe
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flow
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solution,
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as
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there
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are
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no
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wall
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boundary
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viscous
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effects
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to
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account for.
In the Materials dialogue. change the viscosity for a higher Reynolds number:
Latex |
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for. !tmodel.png|border=1! \\ In the Materials dialogue. change the viscosity for a higher Reynolds number: {latex} \large $$ {Re} = {Ud \over \nu} = {10^5} $${latex} |
The
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inlet
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jet
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velocity
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will
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remain
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at
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1m/s;
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the
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inlet
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diameter
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is
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still
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0.01m
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from
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the
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geometry
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(ignoring
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the
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larger
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diameter
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with
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0m/s
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velocity
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inflow),
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so
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enter
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the
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viscosity
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for
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air as ν = 1E-7.
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Select
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Change/Create
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and
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then
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Close.
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The k-ε
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terms
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must
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be
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specified
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on
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all
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boundaries.
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Go
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to
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Solution
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Setup
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-
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Boundary
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Conditions
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and
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edit
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both
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Farfield
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and
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Inlet
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boundaries
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.
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Select
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"Intensity
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and
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Hydraulic
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Diameter"
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as
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the
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turbulence
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specification
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method.
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At
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Inlet
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1,
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from
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the
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specified
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Reynolds
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number
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and
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above
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equations,
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the
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intensity
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should
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be
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I=0.037942,
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and
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the
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hydraulic
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diameter
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should
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be
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0.01m
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(twice
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the
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measured
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inlet
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height).
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The other Inlet and both Farfield boundaries should have turbulent kinetic energy and dissipation rates set to zero, because there is no inlet velocity or turbulence associated with them. Press OK for all boundaries to save the inputs.
To initialize the solution, go to Solution Initialization. Select "Inlet 1" to initialize the domain, and press "Initialize".
Go to Monitors and edit the residual monitors. Note that both k and ε both have residual criteria; change it to 1E-06 for both.
Now go to Run Calculation. Run the solution until it all residuals appear to reach a steady state value. This should take a bit more than 5000 iterations, and you should end up with a residuals plot somewhat like the plot below. Note the fluctuations present in this plot.