Slides

Roman Thiele, KTH
Improved wall functions
in OpenFOAM
3rd Gothenburg Regional OpenFOAM User Group Meeting
Overview
• Introduction
• 2 Wall function sets
- UMISTA
- Laurien's thermal wall function
• Implementation of the two wall functions
• Status/Summary/Questions
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Heat transfer in SCW
• Strong variations
around pseudo critical
point
• Computationally
challenging
- LRN computations
- Thermal wall
functions
Source: Maria Jaromin, Lic. Thesis, 2012
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Heat transfer deterioration in SCW
• Work done by Maria Jaromin in CFX
• Deterioration observed under
strong heat flux
• Strong variations of thermophysical properties and buoyancy
effects close to the wall
Source: Maria Jaromin, Lic. Thesis, 2012
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UMISTA wall function
• How does it work
- Analytical integration of the boundary
layer equations through viscous and
logarithmic layer
• Several versions available
- Simplified version, give same results
as full temperature variation and is
simpler
- T varies linearly from wall to viscous
sublayer edge and from viscous
sublayer edge to opposite edge of cell
- Parabolic description of the molecular
viscosity in the viscous sublayer
• Inclusion of buoyancy terms and rapidly
changing properties
Source: Aleksey Gersimov, PhD Thesis, 2003
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UMISTA wall function
– Mixed Convection Results
Buoyancy aided
Buoyancy opposed
Source: Aleksey Gersimov, PhD Thesis, 2003
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Laurien's thermal wall function
• No separate wall function for the velocity as it is assumed that
temperature and velocity are decoupled
• Uses temperature varying thermo-physical properties
• Add's variation by probability density function to all variables
• Numerical integration through viscous and logarithmic layer
• Similar to Jayatilleke's wall function (based on turbulent logarithmic
layer)
Source: Laurien, Development of Numerical Wall-Functions to Model the Heat Transfer of Supercritical Fluids, 2010
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OpenFOAM framework for SCW
• Super critical water properties missing
• Need to be implemented
- Use libraries that exist and are based on different framework →
Freesteam and openfoam-ext project
• Employing solver buoyantPimple/SimpleFoam
- Buoyancy effect included in momentum equation
- Modified to write out property fields of use
- Modified to take SCW properties into account
• Work ongoing
Source: www.extend-project.de, http://freesteam.sourceforge.net/
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Implementation of UMISTA
• Original development for 2D staggered mesh with Cartesian coordinates
• OF is 3D, co-located mesh with curvilinear grid and possibility of
polyhedral cell
• Restrictions for mesh after implementation
- Cells must be hexahedral or prismatic at the boundary layer
• 3 boundary conditions necessary
-
(wall shear stress implementation)
(turbulent production and dissipation conditions)
(heat flux boundary condition)
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Pseudo algorithm UMISTA
– alphat based on q''
Iteration
1. Calculate to the edge of the cell, yn
2. Read Twall, if not present, use input
by user
3. Get initial Tv, by taking mean
between and TP and Twall
4. Calculate all value dependent on
Twall and Tv
5. Calculate Tvn
6. Calculate Twalln
7. Compare Twalln with Twalln-1
8. Calculate alphat
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Pseudo algorithm UMISTA
– μt wall function
• OF introduces wall shear stress
through turbulent viscosity at the
wall into the momentum equation
1. Calculate Twall and Tv as in
Iteration
temperature wall function
2. Calculate temperature dependent
thermophysical values
3. Calculate Un by interpolating the
velocity field to the cell surfaces and
project the velocity from the
opposite face into a parallel plane to
the patch face
4. Calculate
5. Calculate
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Implementation of Laurien's
– alphat based on q''
Iteration
1.Estimate Tcs through average between wall and first point temperature
2.Retrieve wall temperature from previous time step (pseudo time step) or
iteration or from the default value that is given to the wall when using the wall
heat flux boundary conditions
3.Calculate Tcs using equation (13)
4.Calculate temperature variation by equation (12)
5.Calculate the dimensionless temperature in point y +P using equation (1)
6.Calculate the variable friction velocity from equation (4)
7.Calculate the wall temperature from equation (7)
8.Compare the wall temperature to the previous wall temperature from previous
iteration, if relative difference is smaller than 10-6 then continue
9.Calculate the effective thermal diffusivity
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Status
• Status
- Completed implementation and mostly debugging
- Water properties
• Testing of different implementation strategies ongoing
• TODO:
- Testing against DNS/experimental data
• Problems
- SCW water properties in OpenFOAM
- Hard coded water properties (no low level access to thermal pysical
properties)
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Improved wall functions in OpenFOAM
Questions? Suggestions? Problem solved?