CFD Background
• Purpose:
To provide more CFD background in Training / Demos
To be able to answer more of those difficult questions
To show industry standard or rule of thumb approaches to using CFD
To provide advice about what to do when things go wrong
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Theory:
Dynamic Thermal Model:
Each room has lumped air volume – single air temperature.
Apache uses algorithms to calculate surface heat transfer
coefficients for convective heat transfer from air volume to
fabric.
Unsteady one-dimensional heat transfer by conduction.
Apache uses finite difference numerical solution in one
dimension through fabric only. Simplified form of the Fourier
equation which is itself a simplified form of the general
energy equation used in MicroFlo
Apache employs shortwave and longwave surface radiation
heat transfer models.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Theory:
CFD Model:
Steady three-dimensional convection-conduction heat
transfer and fluid flow. MicroFlo uses finite volume
numerical solution throughout domain volume. MicroFlo
can be adapted to handle unsteady flows.
MicroFlo uses a turbulence model in conjunction with
wall functions. Wall functions are used to calculate the
flux of heat and momentum in the near-wall regions
and are analogous to surface heat transfer coefficients
used in conventional thermal modelling.
No radiation model – boundary conditions include the
radiation transfer from Dynamic Thermal Model
The grid employed by MicroFlo is a structured nonuniform rectilinear cartesian grid and in order to cater
for irregular spaces, obstructions, sloping surfaces,
etc. MicroFlo incorporates a ‘blocking-off’ procedure
whereby grid cells that are located within solid regions
in the flow domain are rendered inactive (i.e. setting
the velocity components to zero) .
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Flux Balance:
Change in
variable with
time
=
Net flux of
variable into
volume due
to convection
+
Net flux of
variable into
volume due
to diffusion
+
Amount of
variable
created in
volume
Where a variable is Mass, Energy, Momentum (x, y, z velocity)
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Flux Balance Rearranged:
Net flux of
variable into
+
volume due
to convection
Net flux of
variable into
volume due
to diffusion
Amount of
variable
+
created in
volume
=
0
This ONLY occurs when everything is balanced when a CFD
model is converging the equation looks like….
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CFD Background
• Flux Balance Residual Error:
Net flux of
variable into
+
volume due
to convection
Net flux of
variable into
volume due
to diffusion
Amount of
variable
+
created in
volume
=
Residual
Error
The closer the Error to Zero the closer to a balanced flux and the closer
to the TRUE answer.
CFD gets closer to the answer by iterating, that is having an initial guess
– supplied by the user – and the repeatedly changing the guess until the
error reduces to an acceptable level
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CFD Background
• Flux Balance Residual Error:
U – x velocity
V – y velocity
W – z velocity
T – temperature
K – creation of
turbulent energy
Ε – dissipation of
turbulent energy
M – mass continuity
The plotted value here is the maximum calculated residual, if the
value gets smaller during the iterations, as above, it is
approaching an acceptable solution or converging
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Flux Balance Residual Error:
U – x velocity
V – y velocity
W – z velocity
T – temperature
K – creation of
turbulent energy
Ε – dissipation of
turbulent energy
M – mass continuity
If the value gets larger, as above, it is NOT approaching an
acceptable solution i.e. diverging
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CFD Background
• Iterations – searching for the answer:
Three issues to consider:
• Converging to the correct answer
• Diverging
• Converging to the wrong answer
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CFD Background
• Iterations – converging to the right answer:
Consider that the flux balance in a volume is
represented by something simple like y = x2
(In reality the equations are much more complicated!)
The answer/solution for balance is 0 (02 = 0)
But if this wasn’t obvious a way to find the answer would have been to
guess a starting point (Initial Condition) and then iterate to find a solution:
Guess x=2
22=4 (residual error)
Too Big
Guess x=1
12=1
Too Big
etc etc…
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CFD Background
• Iterations – converging to the wrong answer:
2nd guess
1st guess
3rd guess
x2 - 1
Actual
answer
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Two possible answers – physical answer??
CFD Background
• Iterations
Problems in convergence are connected with deriving the pressure field.
The continuity based pressure correction equation and the resulting
outer iterative scheme involves the continuing re-calculation of
dependent variable coefficients. It’s this inter-linkage that causes
problems, i.e. each outer iteration involves the partial solution of all of
the equation sets (using inner iterative schemes) and the re-calculation
of the dependent variable coefficients using the most up-to-date
dependent variable values, the outer iterations being repeated until a
converged solution is achieved.
Numerical procedure is very robust and is unlikely to fail.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Good Answer?:
The results from a converged solution may not (it is unlikely) be the
correct physical results how do we know?
•
Check the results – hand calculations
•
Is the solution dependant upon the grid - Mesh Independence Study
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CFD Background
• Good Answer?:
Check the results:
•
High velocities
•
High/Low temperatures
•
Large pressure differences
•
Hand calc – x people @ 90W each gives a temperature rise of…
Refine the mesh in the area where there is a problem
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Good Answer?:
Grid dependant:
If a mesh/grid has non regular shapes, i.e. quite long and thin volumes, or is too
coarse around areas of interest it is possible that the answer is dependant upon
the ‘poorness’ of the mesh.
For example, in the case of a jet being directed at a floor standing obstacle, an
area of recirculation may well develop behind the obstacle but obviously this will
not be revealed if the grid is too coarse in that region.
The way to check that any mesh does not have this effect is checks before the
runs start (Cell Aspect Ratio) and also a grid independence study.
To do this the density of the mesh is increased globally i.e. add 20% more mesh.
Re-run the simulation and check the output is similar to the previous solution.
Practically there may not be the time!
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions:
What’s k-ε / constant viscosity method and when would I use one or the other?
What’s Upwind, Hybrid, and Power Law and when would I use one or the other?
What is the Maximum Cell Aspect Ratio all about then?
What’s the inner iterations/false time step and when should I change it?
What’s relaxation and when should I change it?
Termination residuals – what’s that?
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions:
What’s k-ε / constant viscosity method and when would I use one or the other?
k-ε (k epsilon) is a turbulence model that focuses upon the mechanisms
that effect turbulent kinetic energy: the production and dissipation
(destruction) of kinetic energy caused by turbulence. Calculates the
turbulent viscosity. (Actually has no physical manifestation). Only applicable
for fully turbulent flows
Constant viscosity method – assumes that the viscosity is constant
throughout the model
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions:
Turbulence? – fluid flows are categorised into three types of flow:
Laminar – adjacent layers of fluid slide easily over each other
Transitional – partially turbulent
Fully Turbulent – random and chaotic flows
Turbulent flows are used in processes to increase mixing i.e. addition of a
dye to a fluid.
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CFD Background
• Types of flow:
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CFD Background
• Questions:
RANS – k-ε model only fully applicable to fully turbulent flow. So
what happens near walls?
There are three main methods of dealing with the near-wall region:
Wall functions – the conventional k-ε model is used throughout the fully turbulent domain but the
flux of momentum and heat in the near-wall region is obtained from wall functions which are
derived using the logarithmic law of the wall. Wall functions for the momentum equations
have been found to provide good predictions although there is some documented evidence to
suggest that in some cases the conventional energy equation wall functions can underpredict rates of heat transfer.
Low Reynolds-number (low-Re) form of the k-ε model – the conventional k-ε model equations
are modified to incorporate damping terms in an attempt to ensure that viscous effects
dominate in the near-wall region. The approach has been used with some documented
success but requires a fine grid in the near-wall region.
Two-layer model - the conventional k-ε model is used throughout the fully turbulent domain but
an alternative one equation length-scale model is adopted for the near-wall region. There is
some documented evidence that the two-layer approach is found to improve the prediction of
flow separation and related suction pressure prediction when used in bluff body applications
(such as wind flow over buildings) when compared with the standard k-ε approach.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions:
Other turbulence models?
LES – Large eddy simulation.
There is documented evidence that the k-ε model can fail to accurately predict flow
separation and reattachment in impingement flow conditions over bluff bodies.
Specifically, turbulent intensity and suction pressure conditions over right-angled
surfaces causing flow separation are not well accounted for. This failing applies to
problems involving wind flow around buildings These failings have prompted interest
in a new approach to turbulence modelling based on segregating the treatment of the
turbulent flow into large scale and sub-grid scale. These techniques generally fall into
a category of turbulence modelling called large eddy simulation (LES).
Although this method has exhibited some promise in dealing with wind flow around
buildings, it is computationally much more expensive than the k-ε model and there is
very little documented work available on the application of LES to internal building
flow problems.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
What’s Upwind, Hybrid, and Power Law and when would I use one or the other?
These are types of discretisation
A
Value at A
B
Value at B
© Integrated Environmental Solutions Ltd. 2004
C
Value at C
or “how do I decide during the iterations
how much mass etc goes from A to B or
B to A”
This depends on how much mass etc is
at A and B (influence) and how the
mass will move i.e. whether there is
convection (flow direction) or diffusion.
CFD Background
• Questions :
What’s Upwind, Hybrid, and Power Law and when would I use one or the other?
Diffusion –
tea bag in
water
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Convection –
paint brush
under tap
CFD Background
• Questions :
What’s Upwind, Hybrid, and Power Law and when would I use one or the other?
Effect of A
Effect of C
B could be calculated by saying:
B
B = Effect of A + Effect of C
2
(Central differencing)
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
What’s Upwind, Hybrid, and Power Law and when would I use one or the other?
Effect of A
Effect of C
If the direction is defined by convection:
B = Effect of A
B
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This is the effect of the Upwind Method.
Means that solutions may be achieved
faster
CFD Background
• Questions :
What’s Upwind, Hybrid, and Power Law and when would I use one or the other?
Hybrid looks at the relative ratio of convection and diffusion (Pe) and chooses
an appropriate method – Upwind or Central differencing.
Power Law looks around at more volume before and after the volume currently
being assessed and apportions the influence of each using a power law
relationship.
Both Hybrid and Power Law resort to Upwind methods when convection
dominates.
Where diffusion dominates the Hybrid approach linearises the exact equations,
Power Law attempts to reproduce them.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
What is the Maximum Cell Aspect Ratio all about then?
Well we all know it is a check of the quality of the mesh – but what does it
mean and what simple things can we do to improve it, without adding too
many more grid points, when the checker throws up an error?
In any one of the three different directions, aspect ratio is computed by
dividing the cell face area by the height squared. The value of the measure is
always greater than one.
Width
Height
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
What is the Maximum Cell Aspect Ratio all about then?
So we know that a large value of MCAR is bad – but why? A large MCAR is
when the width is much greater than the height. This means long thin volumes.
The knock on effect of this is that the effect of a change in one or more of the
variables will propagate faster in one direction than the other direction. This
could mean for example that the effective ‘throw’ of a window will be overestimated.
Width
Height
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
What’s relaxation and when should I change it?
Relaxation reduces the amount the current value of a solution will be altered
by to the next “guessed” value.
Remember our x2 - 1 equation: starting point 2, difference between guesses 1
Guess x=2
Guess x=1
© Integrated Environmental Solutions Ltd. 2004
22 -1 = 3
12 -1 = 0
Too Big
CFD Background
• Questions :
What’s relaxation and when should I change it?
What if we had started from 1.5, difference 1?
Guess x=1.5
1.52 -1 =1.25
Too Big
Guess x=0.5
0.52 -1 =-0.75
Too Small
Guess x=1.5
1.52 -1 =1.25
Too Big
Here we would be oscillating around the answer – the relaxation factor alters the step
change between guesses.
i.e. an obvious relaxation here would be 0.5
New Difference between guesses = (Relaxation Factor)*(Original Difference) = 0.5 * 1
Therefore new guess x=1 (1.5-0.5)
© Integrated Environmental Solutions Ltd. 2004
12 – 1 = 0
CFD Background
• Questions :
What’s relaxation and when should I change it?
When should you change it?
When the residual convergence has flattened but hasn’t yet converged.
All relaxation really does is slow down the solution, hence “relaxes” it!
If you use relaxation too early it can mean that your solution will take longer to reach the answer.
Relaxation factors have only been included to satisfy practitioners who prefer this approach – it’s the
‘text book’ approach to procuring convergence. It’s really better to leave the relaxation factors set at
unity, i.e. don’t touch them.
The equation sets within MicroFlo are set up in time dependent form. The temporal term has the
same effect as an inertial relaxation. The false time steps are analogous to conventional time steps,
they may be increased or decreased to speed up or slow down convergence.
In both cases, it’s the momentum equations that benefit most from relaxation because of the interlinked velocity dependent coefficients. In the case of a stubborn solution, it’s usually best to try
decreasing the velocity false time steps by consecutive factors of two.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
What’s the inner iterations/false time step and when should I change it?
Inner Iterations: number of iterations performed on each variable
independently of the main iterations.
False time step: the parameter that fixes the difference in values between
each iterative guess.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Questions :
Termination residuals – what’s that?
Simply the point at when you consider that the solution total error is acceptably
low – the default is 1 * e-005
The termination residual is the maximum calculated residual.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Rules of Thumb:
Keep components in line in x and y and z if at all possible
Use power-law mesh spacing to increase density at areas of interest and less so in
open areas.
Increase mesh in areas where there is likely to be direction changes in the flow
Sufficient mesh density in between obstacles
Avoidance of high aspect ratio
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CFD Background
• Rules of Thumb:
Supply diffusers provide sufficient mesh density
Supply diffusers – model the actual free-area – jetting in centre of large diffuser
Check wake behind building
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CFD Background
• Rules of Thumb:
If spaces were already joined by a hole in ModellIT and you didn’t model then the
hole is counted as a wall. Remodel this using windows and Macroflo so the flow
rates can be established.
Go for as regular a grid as possible.
If a solution is diverging, reduce the velocity false time steps by a factor of two and
try again.
The mass residual is perhaps the best indication of convergence.
Use the cell monitor to get a better idea of convergence.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Rules of Thumb:
Keep walls in line with the axis.
Make sure when connecting spaces that they actually join – end points
Check inlets/outlets are performing as anticipated early in the solution process to
avoid wasting time converging an incorrect solution.
If possible align the predominant flow direction along one of the major grid axes.
False diffusion is increased with increasingly acute angles of cell attack.
Try to ensure that the first grid point from a wall is at least 0.1-0.2m from the wall.
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• When things go wrong:
Problem
Residuals continuously
increasing
Cause
False time steps set too high
Remedy
Reduce false time steps for velocities and
possibly temperature
Residuals fail to reduce
Oscillating flow pattern
Unrealistic initial values
Internal heat source without sink,
e.g. radiator in room with adiabatic
surfaces
Reduce false time steps for velocity
Check initial values under Settings
Check that the problem is realistic.
Set cell monitor points and check for
continuously increasing/decreasing values,
which would indicate imbalance
Erratic convergence
Unstable flows, e.g. strong jets or
buoyancy driven plumes
Reduce false time steps for
velocity.
Mass residual reduces
very slowly
Various causes
Increase number of inner iterations for
pressure
Residuals all reducing
steadily but very slowly
False time step set too low
Increase false time steps
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Standard Approach:
•
•
•
•
•
•
•
•
•
Put an initial course mesh ~ 0.1 – 0.2 grid size everywhere
Use constant viscosity method
Run for 10 iterations check the flows and all heat sources
Run for a further 100 iterations check the solution for areas where lots of things are
happening and refine mesh if necessary
Change turbulence model to k-ε method
Refine mesh by increasing local mesh density and overall density by ~ 10 -20%
Refine mesh until solution is independent of mesh (given available time)
Use a grid of 3*3*3 cell monitors to check independence
If cell monitors are levelling out and the convergence is flattening use either
relaxation or false time steps to speed up convergence
© Integrated Environmental Solutions Ltd. 2004
CFD Background
• Supply Definition:
Supply diffuser angle definition:
angle from a perpendicular line to the
diffuser i.e. 0° straight down, 85° along
the ceiling (coander effect) along either
the x or the y direction
0°
© Integrated Environmental Solutions Ltd. 2004
85°