Course outline 1 MM Introduction to applied CFD Review of the finite volume method Geometry creation and CAD import

FACE8 Applied CFD

2 MM Grid generation Grid quality Grid adaption static and dynamic Boundary conditions

3 MM Solution methods Solution quality

4 MM Advanced physical models

5 MM Post-processing Validation

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Literature

FACE8 Applied CFD

BPG 3.4 and 5.1 FLUENT Users Guide chapters 5 and 25 GAMBIT Users Guide chapter 3 p. 70-102

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FLUENT cell types

FACE8 Applied CFD

Choice is a trade-off Set-up time Computational expense Numerical diffusion

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FLUENT grid adaption

FACE8 Applied CFD4

Grid generation (1)Hex grids

FACE8 Applied CFD

Characteristics Simple in terms of numerical methods (easy to implement)

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Grid generation (2)non-uniform hex grids

CharacteristicsFACE8 Applied CFD

Still simple from numerical viewpoint Cells concentrated in regions of strong gradients

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Grid generation (3)tet grids

FACE8 Applied CFD

Characteristics Highly automated grid generation algorithmes applicable Local refinement easy In complex geometries flow pattern is not obvious

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mixed grids, boundary layers

Grid generation (4)

FACE8 Applied CFD

Characteristics Good grid quality in boundary layer flow aligned with surface Still flexible internally adaption to flow and geometry

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Unresolved details

FACE8 Applied CFD

In some cases it is prohibitively expensive to resolve all geometrical details Tube banks (pressure loss, heat transfer etc.) Packed beds ...

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Grid generation (1)quality and trust

FACE8 Applied CFD

Grid density is NOT the only parameter (grid analysis in Gambit): - skewness - aspect ratio - expansion ratio (between successive cells) Adaption of grid as solution proceeds (gradients etc.) The grid must be fine enough to capture features of interest Guidelines: - assess which geometrical detail can be omitted - avoid highly skewed cells (40 < < 140) - limit aspect ratio to around 20-100 - make use of grid adaption in regions of large errors or gradients - MAKE A GRID DEPENDENCY STUDY (AT LEAST 3 SIZES)10

quality and trust, geometrical uncertainties

Grid generation (2)

If used, check the CAD definition is sufficiently detailesFACE8 Applied CFD

Have all last minute changes been included in the CAD drawing Loads may cause deformation of the geometry The condition of surfaces may be affected by wear, erosion, fouling Guidelines: - check and document the correct geometry definition is used - check that CAD import has not caused a lack of accuracy - consider whether local detail can be omitted or require refinement

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Gambit grid quality analysis

Area Aspect ratio Diagonal ratio Edge ratio EquiAngle skew EquiSize skew MidAngle skew Stretch Taper Volume Warpage

FACE8 Applied CFD12

Aspect ratio

FACE8 Applied CFD

Quadrilateral and hexahedral

QAR

max[e1,e2,,,,en ] = min[e1,e2,,,,en ]

ei is the average edge length in a coordinate direction (i) local to the element, i.e. in 2D i=2.

a da +c 2 b+d e2 = 2 e1 =

b c

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Aspect ratio contd Triangular and tetrahedral elements

QARFACE8 Applied CFD

R =f r

QAR 1

f is a scaling factor and r and R represent the radii of the circles (2D) and spheres (3D) that inscribe and circumscribe the mesh element, respectively. For triangles f=1/2 and for tetrahedral f=1/3.

r

R14

Diagonal ratio

FACE8 Applied CFD

Quadrilateral and hexahedral elements

QDR

max [d1,d2,,,,,,dn ] = min[d1,d2,,,,,,dn ]

di are the lengths of the element diagonals QDR1

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Edge ratio

FACE8 Applied CFD

Definition

QER

max [s1,s2,,,,sn ] = min[s1,s2,,,,sn ]

si represents the length of the element edge i, and n is the total number of edges QER1 by definition

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EquiAngle skew The EquiAngle skew is a normalized measure of skewness defined as:

FACE8 Applied CFD

QEAS

max - q q - q eq min q = max , eq 180 - q q eq eq

mx and m are the maximum and minimum angles in a in degrees between the element edges and eq is a characteristic angle corresponding to an equilateral cell of similar form. For triangular and tetrahedral elements eq =60, and for quadrilateral and hexahedral elements eq =90. By definition 0QEAS 1 with 0 being optimal

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EquiAngle skew contd Relationship between QEAS and qualityQEAS Quality Perfect Excellent Good Fair Poor Very poor Degenerate

FACE8 Applied CFD

High quality mesh: 2D QEAS average 0.1 3D QEAS average 0.4

QEAS=0 0