Advanced ESC Topics Y

1
Advanced ESC Topics - Y

• What is Y and why does it matter to me?
• What are Wall Functions?
• How does ESC implement Wall Functions?
• How do I interpret the Y diagnostic written to
  the message file?
• How should I set up my models to get the best
  results?

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What is Y and why does it matter to me?

• Y is used when modeling turbulent flows.
  Because it is impractical (expensive) to fully
  resolve the boundary layer or near-wall region in
  most turbulent flows, ESC uses a semi-analytical
  approach to determine near-wall effects (shear
  stress, convective heat transfer coefficient).
  These effects are modeled by near-wall relations
  or wall functions.
• These wall functions are based on the Law of the
  Wall
• The Law of the Wall (developed by Prandtl) states
  that in turbulent flow, the dimensionless
  velocity u is purely a function of the
  dimensionless wall distance y. This permits the
  computation of wall fluxes (e.g.wall shear) given
  certain flow information at a distance from the
  wall.

3
What are Wall Functions?

• Wall functions are used with the Fixed Turbulent
  Viscosity (FTV) and K-epsilon flow model options
  to determine near-wall effects as functions of
  the non-dimensional value Y, in contrast to
  laminar solutions which explicitly calculate
  shear stress from near-wall velocity gradients.
• Wall functions are derived from dimensional
  analysis of turbulent boundary layers, based on
  physical reasoning .
• Wall functions and the Law of the Wall are based
  on Prandtls work from the 1930s.

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Law of the Wall variables

• Turbulence effects vanish near the wall the
  viscous inner layer is very thin, so Prandtl
  assumed that the flow behaves as if it knew
  nothing about what was happening near the duct
  wall. He proposed the following
• Dimensional Analysis gives
• Prandtl then defined the following
  non-dimensional terms
• Substitution leads to the Law of the Wall

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Characterizing the Law of the Wall

• U has dimensions of velocity and is referred to
  as the friction velocity. It is a measure of the
  velocity gradient at the wall. U is the ratio of
  the local fluid velocity to the friction
  velocity. Finally, Y is a form of Reynolds
  number, evaluated at distance Y from the wall,
  using the friction velocity.
• For most turbulent flows, the functional
  relationship of the Law of the Wall is impossible
  to determine. Theoretical models or experimental
  data are needed. To simplify this determination,
  ESC assumes that the flow is fully developed.
• This assumption allows the use of widely accepted
  empirical turbulent formulations which describe
  the Law of the Wall for different regions in the
  turbulent boundary layer.
• In the viscous sub-layer, where y values are
  less than 5, the velocity profile is assumed to
  be linear

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The Law of the Wall

• For the fully turbulent portion of the boundary
  layer, where y is greater than 30, Prandtls
  mixing length hypothesis (as well as experimental
  data) shows that
• This region is called the logarithmic layer, and
  corresponds to the region where turbulent shear
  (mixing) predominates.
• Between these two regions lies the overlap layer,
  where both viscous and turbulent shear are
  present. ESC uses blending functions to connect
  these two regions.

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How does ESC implement Wall Functions?

• When either a FTV or k-epsilon solution is
  specified, ESC makes initial guesses for U, and
  wall shear , based on the local velocity U,
  derived either from fan definitions, or buoyancy
  terms. The conservation equations are then solved
  by iteration until a consistent relationship
  between the wall function variables is achieved.

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Interpreting Y Values

• When Y is greater than 30, you can be reasonably
  certain that the first near-wall node is in the
  fully turbulent region of the boundary layer.
  Wall shear results and convection coefficients
  should be accurate, as they are based on core
  flow velocity values.
• When Y is between 11.5 and 30, the first
  near-wall node is inside the overlap layer
  between the inner viscous wall layer, and the
  outer fully developed region. ESC will correct
  for these results, and accuracy should be
  reasonable. Consider improving Y values if
  possible.
• When Y is less than 11.5, the near-wall node is
  inside the so-called laminar sublayer. The
  results will not be very accurate because they
  are dependent on the assumption that the velocity
  profile is linear. Improving Y values is highly
  recommended.

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Setting Up Models For Best Results

• Try to establish the flow regime before beginning
  the meshing process. If you know that the model
  will be turbulent, avoid modeling very narrow
  passages that require very fine mesh. Most
  likely there will be insignificant flow through
  them anyway. Avoid very fine air meshes. Follow
  the default modeling guidelines using no more
  than 2 elements across a duct (between boards).
• If the model is laminar, use as fine a mesh for
  the air elements as you can manage given time
  constraints and resource limitations. Dont go
  overboard. Check results against the Convection
  Wizard at www.mayahtt.com. If the flow is in
  transition, you may have to do a laminar and a
  turbulent solve to establish the possible range
  of results. There are no miracles when it comes
  to transition flows.
• Remember This level of detail is only necessary
  for final performance evaluation, not for design
  trade-offs.