Lecture 05

Lecture 5: Finite Volume Methods from OpenFOAM Viewpoint: Part 1

V.Vuorinen  Aalto University School of Engineering  CFD Course, prin! "#1$

 January 30th 2017, Otaniemi  [email protected] 

Lecture 5: Finite Volume Methods from OpenFOAM Viewpoint 1%"

V.Vuorinen  Aalto University School of Engineering  CFD Course, prin! "#1$

 January 30th 2017, Otaniemi  [email protected] 

Objective to provide overview of: & Kinetic energy and dissipation – periodic flow as an example & “FOAM” – Field Operation  A nd Manipulation & Line by line look into an explicit OpenFOAM code

What happens to the kinetic energy of the flow if you stop stirring/pouring milk? tot 

dEkin =−χ tot < 0 d t   E kin=∫V  tot 

1 2

u

2

dV 

χ tot =∫V  ν | ∇ u |2 dV 

Note: equation is derived by u⋅ NS and volume integrating because

What happens to the kinetic energy of the flow if you stop stirring/pouring milk? tot 

dEkin =−χ tot < 0 d t   E kin=∫V  tot 

1 2

u

2

dV 

χ tot =∫V  ν | ∇ u |2 dV 

/* Code snapshot from the utility kinE calculating total kinetic energy */ scalar meshVol = gSum( mesh.V() ); scalar kinE = 0.5*(fvc::domainIntegrate(magSqr(U)).value())/meshVol;

Kinetic energy dissipates into heat as seen in this 2d uasi!turbulent case "periodic boundary conditions# t =10s

t =90s

t =30s

Kinetic energy dissipates into heat as seen in this 2d uasi!turbulent case "periodic boundary conditions# t =10s

t =90s

t =30s

2nd order FVM

Spectral method

$W2: %ou monitored/controlled the kinetic energy decay by numerics "numerical diffusion due to diffusive numerical scheme#

Numerics: tot 

dEkin tot  =−χ tot  visc −χnum d t  Note: the equation is derived by: u⋅( NS +ϵ ) + volume num integrating

ϵ num=ϵ dispersive +ϵ diffusive

Overview of Open&O'( )&* )ode +tructure "+ource: Open&O'( ,ser-s (anual#

Overview of Open&O'( )&* )ode +tructure "+ource: Open&O'( ,ser-s (anual#

 a n d  m  m  e c o   h  t  :  i li t y    t  u  p l e  y ”  m  a  x  E  i t  t i c  r  o  “ v

 r s i o n  e  v  o ! n  ”  r  u  o  g y  t s O w n  e  :  p l e  t u d e n  m  a  x  S  E  o a m  F  o  “ i c

 n d  a  m  m ”  m  a  o  o  c  F  c o  t h e  i  :  “   e  l  r  p  ”  l v e  o  s  e  E x a m i n e M e s h  : t h   e  l  f  p  e  “ r  E x a m

.ssentials of Open&O'( top!level solver  rk4projectionFoam Vuorinen et al "omputers # Fluids $2%&'( Vuorinen et al )dvances in *ngineering Sot!are $2%&,(

.ssentials of Open&O'( top!level solver  rk4projectionFoam Vuorinen et al "omputers # Fluids $2%&'( Vuorinen et al )dvances in *ngineering Sot!are $2%&,(

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'th order e-plicit .unge/0utta time integration 2nd order e-plicit inite volumes space 1roection method $3irsch( or pressure correction

.ssentials of Open&O'( top!level solver  rk4projectionFoam Vuorinen et al "omputers # Fluids $2%&'( Vuorinen et al )dvances in *ngineering Sot!are $2%&,(

.ssentials of Open&O'( top!level solver  rk4projectionFoam File name:rk4projectionFoam.C

Vuorinen et al "omputers # Fluids $2%&'( Vuorinen et al )dvances in *ngineering Sot!are $2%&,( ●

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*g pimpleFoam or icoFoam are “top/level” solvers ) top/level solver $eg rk4projectionFoam( !ould

mean: storing rk4projectionFoam.C +

some other iles in older /rk4projectionFoam/

and compiling the solver into e-ecutable !ith wmake ●

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1art o top/level solver code can be appended to header iles $3 e-tension( 4mportant: conigure the /Make/ older accordingly

.ssentials of Open&O'( top!level solver  rk4projectionFoam Vuorinen et al "omputers # Fluids $2%&'( Vuorinen et al )dvances in *ngineering Sot!are $2%&,(

phi = fvc::interpolate(U) & mesh.Sf(); dU = dt*(fvc::laplacian(nu, U) – fvc::div(phi,U)); phi = fvc::interpolate(U) & mesh.Sf(); dU = dt*(fvc::laplacian(nu, U) – fvc::div(phi,U));

Vuorinen et al "omputers # Fluids $2%&'(

FOAM – OpenFOAM provides extremely handy data types for storing data 

Vuorinen et al "omputers # Fluids $2%&'(

FOAM – OpenFOAM provides extremely handy data types for storing data – Snapshots from CreateFields.H showing how fields p/U can e created

         

volScalarField p ( IOobject ( "p", runTime.timeName(), mesh, IOobject::MUST_READ, IOobject::NO_WRITE ), p );

volVectorField U  (   IOobject ( "U",   runTime.timeName(),   mesh,   IOobject::MUST_READ,   IOobject::AUTO_WRITE ),   mesh );

Vuorinen et al "omputers # Fluids $2%&'(

FOAM – Some possile examples of field operation and manipulation !field algera" P = rho*R*T; // ideal gas law at cell centers P = correctBoundaryConditions(); U = U + dU; // only update cell centers U.correctBoundaryConditions(); // read BC from /0/U U == U + dU; // also correct BC's P.boundaryField() = rho.boundaryField()*R.boundaryField()*T.boundaryField(); T = fvc::grad(U); // create a volTensorField

5he synta- above !or6s directly in parallel 7 the strength o  FOAM

Vuorinen et al "omputers # Fluids $2%&'(

#et us interpret the following lines from math viewpoint 8 control volume centroid 8 control volume ace center

dU is a volVectorField – “vol”  because it is deined at cell volume centers similar to U dU = dt*(fvc::laplacian(nu, U) – fvc::div(phi,U));

phi is a surfaceScalarField - “surface” because it

is deined at cell suraces phi = fvc::interpolate(U) & mesh.Sf();

Aout interpolation and flux limiting

5his interpolation can be carried out in various !ays:

5his interpolation is very commonly carried out by:

linear GammaV limitedLinearV vanLeer

linear

f  B f  C  f  A

f  C 

F9; 94M45*.S

F#$% #&M&'&N( is useul interpolation technique close to high oscillating parts: ho! !ould you numerically compute lu-

Vuorinen et al "omputers # Fluids $2%&'(

#et us interpret the following lines from math viewpoint 8 control volume centroid 8 control volume ace center

dU is a volVectorField – “vol”  because it is deined at cell volume centers similar to U dU = dt*(fvc::laplacian(nu, U) – fvc::div(phi,U));

phi is a surfaceScalarField - “surface” because it

is deined at cell suraces phi = fvc::interpolate(U) & mesh.Sf(); dot product

@uter normal vectors multiplied by surace area o ace in the mesh

(otivation for $W : &luid solid interfaces "boundary layers# are crucial in heat transfer0 flow friction0 turbulence production etc C f  =

Bynamic viscosity

μ=ρν

τs

Friction coeicient $local(

2

ρ U ∞ / 2

 τ s =μ

( ) ∂u ∂ y

Surace shear stress

 y =0

' ' 

q s = h (T s −T ∞ ) ' ' 

q s =−k T  k T 

ρ c p

( )

=ν T 

∂ T  ∂  y

 y =0

Ne!tonAs cooling la! FourierAs la!

Fluid thermal conductivity

Source for pictures from instructor resources: 4ncroperaC de DittC 3eat and Mass 5ranser

Examples on #ES*+NS simulations of flows with oundary layers

BNS o turbulent pipe lo! at riction .eynolds number E%

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