cfd background

8/10/2019 CFD Background

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Integrated Environmental Solutions Ltd. 2004

CFD Background

Purpose:

To provide more CFD background in Training / Demos

To be able to answer more of those difficultquestionsTo show industry standardor rule of thumbapproaches to using CFD

To provide advice about what to do when things go wrong


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CFD Background

Theory:

Dynamic Thermal Model:

Each room has lumped air volumesingle air temperature.

Apache uses algorithms to calculate surface heat transfercoefficients 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 generalenergy equation used in MicroFlo

Apache employs shortwave and longwave surface radiation

heat transfer models.


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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 withwall 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 modelboundary conditions include the

radiation transfer from Dynamic Thermal Model

The grid employed by MicroFlo is a structured non-

uniform 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) .


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CFD Background

Flux Balance:

Change invariable 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)


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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

This ONLY occurs when everything is balanced when a CFD

model is converging the equation looks like.

0=


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CFD Background

Flux Balance Residual Error:

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

Ux velocity

Vy velocity

Wz velocity

Ttemperature

Kcreation of

turbulent energy

dissipation of

turbulent energy

Mmass continuity



CFD Background

Flux Balance Residual Error:

If the value gets larger, as above, it is NOT approaching an

acceptable solution i.e. diverging

Ux velocity

Vy velocity

Wz velocity

Ttemperature

Kcreation of

turbulent energy

dissipation of

turbulent energy

Mmass continuity



CFD Background

Iterations searching for the answer:

Three issues to consider:

Converging to the correct answer

Diverging

Converging to the wrong answer



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 wasnt 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



CFD Background

Iterations converging to the wrong answer:

Actual

answer

2ndguess

1stguess

3rdguess

x2- 1

Two possible answersphysical 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. Its this inter-linkage that causesproblems, 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.



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 resultshand calculations

Is the solution dependant upon the grid - Mesh Independence Study



CFD Background

Good Answer?:

Check the results:

High velocities

High/Low temperatures

Large pressure differences

Hand calcx people @ 90W each gives a temperature rise of

Refine the mesh in the area where there is a problem



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 theruns 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!


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CFD Background

Questions:

Whats k-/ constant viscosity method and when would I use one or the other?

Whats Upwind, Hybrid, and Power Law and when would I use one or the other?What is the Maximum Cell Aspect Ratio all about then?

Whats the inner iterations/false time step and when should I change it?

Whats relaxation and when should I change it?

Termination residualswhats that?


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CFD Background

Questions:

Whats k-/ constant viscosity method and when would I use one or the other?

k-(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 methodassumes that the viscosity is constantthroughout the model


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CFD Background

Questions:

Turbulence?fluid flows are categorised into three types of flow:

Laminaradjacent layers of fluid slide easily over each other

Transitionalpartially turbulent

Fully Turbulentrandom 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:RANSk-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 functionsthe conventional k- model is used throughout the fully turbulent domain but theflux 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 under-

predict rates of heat transfer.

Low Reynolds-number (low-Re) form of the k- modelthe conventional k- model equations

are modified to incorporate damping terms in an attempt to ensure that viscous effectsdominate 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- 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- approach.


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CFD Background

Questions:Other turbulence models?

LESLarge eddy simulation.

There is documented evidence that the k- 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- model and there is

very little documented work available on the application of LES to internal building

flow problems.


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CFD Background

Questions :

Whats Upwind, Hybrid, and Power Law and when would I use one or the other?

A B

Value at A Value at B

These are types of discretisation

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 isat A and B (influence) and how the

mass will move i.e. whether there is

convection (flow direction) or diffusion.

C

Value at C


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CFD Background

Questions :


Diffusion

tea bag in

water

Convection

paint brush

under tap


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CFD Background

Questions :


B

Effect of A Effect of C

B could be calculated by saying:

B = Effect of A + Effect of C

2

(Central differencing)


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CFD Background

Questions :


B

Effect of A Effect of C

If the direction is defined by convection:

B = Effect of A

This is the effect of the Upwind Method.

Means that solutions may be achieved

faster


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CFD Background

Questions :


Hybrid looks at the relative ratio of convection and diffusion (Pe) and chooses

an appropriate methodUpwind 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 convectiondominates.

Where diffusion dominates the Hybrid approach linearises the exact equations,

Power Law attempts to reproduce them.


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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 meshbut 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


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CFD Background

Questions :

What is the Maximum Cell Aspect Ratio all about then?

So we know that a large value of MCAR is badbut 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 over-

estimated.

Width

Height


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CFD Background

Questions :


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 22-1 = 3 Too BigGuess x=1 12-1 = 0


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CFD Background

Questions :


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 answerthe 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) 121 = 0


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CFD Background

Questions :


When should you change it?

When the residual convergence has flattened but hasnt 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 approachits the

text book approach to procuring convergence. Its really better to leave the relaxation factors set at

unity, i.e. dont touch them.

The equation sets within MicroFlo are set up in time dependent form. The temporal term has thesame 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, its the momentum equations that benefit most from relaxation because of the inter-

linked velocity dependent coefficients. In the case of a stubborn solution, its usually best to try

decreasing the velocity false time steps by consecutive factors of two.


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CFD Background

Questions :

Whats 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.


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CFD Background

Questions :

Termination residualswhats that?

Simply the point at when you consider that the solution total error is acceptably

lowthe default is 1 * e-005

The termination residual is the maximum calculated residual.


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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:If spaces were already joined by a hole in ModellIT and you didnt 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.

C


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CFD Background

Rules of Thumb:Keep walls in line with the axis.

Make sure when connecting spaces that they actually joinend 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.

CFD B k d


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CFD Background

When things go wrong:Problem

Residuals continuously

increasing

Residuals fail to reduce

Erratic convergence

Mass residual reduces

very slowly

Residuals all reducing

steadily but very slowly

Cause

False time steps set too high

Oscillating flow pattern

Unrealistic initial valuesInternal heat source without sink,

e.g. radiator in room with adiabatic

surfaces

Unstable flows, e.g. strong jets or

buoyancy driven plumes

Various causes

False time step set too low

Remedy

Reduce false time steps for velocities and

possibly temperature

Reduce false time steps for velocity

Check initial values under SettingsCheck that the problem is realistic.

Set cell monitor points and check for

continuously increasing/decreasing values,

which would indicate imbalance

Reduce false time steps for

velocity.

Increase number of inner iterations for

pressure

Increase false time steps

CFD B k d


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CFD Background

Put an initial course mesh ~ 0.10.2 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 arehappening and refine mesh if necessary

Change turbulence model to k-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 eitherrelaxation or false time steps to speed up convergence

Standard Approach:

CFD B k d


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CFD Background

Supply diffuser angle definition:

angle from a perpendicular line to the

diffuser i.e. 0straight down, 85alongthe ceiling (coander effect) along either

the x or the y direction

0 85

Supply Definition:

cfd background

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