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By Terence James Haydock

Fluid AnalysisA simulated response in ANSYS

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Overview

• Introduction

• Background

o Density and pressure

o Example and Problem

• ANSYS Tutorial

• Summary

• References

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Introduction

Aim: To calculate a fluid analysis problem via analytical methods

and compare such results with a numerical analysis with ANSYS

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Background

A fluid is a material that offers no permanent resistance to change of shape i.e. its flow matches the shape of the vessel to which its found.

The general laws of mechanics for solids apply equally to fluids. Acting force, equilibrium, momentum and energy all have the same meaning, hence, Newton’s law are just as valid for solids and fluids.

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Density and Pressure

Density (ƿ) is found by dividing mass by volume and its SI units are kg/m^3. For example, water has a density of 1000kg/m^3. The density of other liquids are defined as a ratio of water (relative density or specific gravity) e.g. oil has a

relative density of 0.9.

When a fluids is not in motion is exerts pressure in all directions. The unit of pressure is N/m^2, though it is usually quoted in bar e.g. 100kN/m^2 which equals

10^5N/m^2 or 10^5Pa. Consider a vertical tube of water, at a height h, if the density of a liquid is ƿ and the cross sectional area is A, then the volume of liquid

is Ah and its mass is ƿAh. The weight of the liquid is ƿgAh. The pressure at any cross section due to liquid is:

P = force / area = ƿgAh / A

= ƿgh

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Cont.

The height h is also known as the pressure head, thus, pressure maybe given in terms of head. All liquids have the same pressure at the same level (2 & 3) and as

such, the required pressure is given by the column of liquid above 2. If the column is sealed (vacuum above liquid) the value is known as absolute pressure,

if open, then the liquid gives a gauge value, both are related by:

Absolute pressure = gauge pressure + atmospheric pressure

The stresses in the walls of a pressure vessel rely on the difference between external and internal pressures, with external pressure been atmospheric, thus, gauge pressure must also be used. In fluid mechanics the changein pressure is required whether the separate values are gaugeor absolute.

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Example

The pressure at the top of a mountain is found to be 0.7bar. Express this in metres of water. What would be the reading of a mercury barometer at this

point? Relative density of mercury, 13.6

Solution: The density of water maybe taken as 1000kg/m^3. Working in SI units, the equivalent head h is given by:

pgh = 0.7 x 10^5 or

h = = = 7.14m

The corresponding head for mercury is thus:

7.14 / 13.6 = 0.525m or525mm

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Problem

The cross section of a circular pipe is occupied by a constant flow of water. The water gradually expands due to varied diameters at either end, with one end been 0.2m diameter and the other with a 0.3m diameter. If the velocity at

the first section is 5m/s, find:

a) The volume flow rate,

b) The velocity at the second section,

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Area A1 Area A2

v1v2

Use subscripts for the two sections

a) The volume flow rate Q is:

smAvQ /1571.02.0*4

*5 3211

b) The equation of continuity is:

So the second velocity, after transposition is:

smA

Avv /222.2

3.0*)4/(

2.0*)4/(*5*

2

2

2

112

2211 AvAvQ

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If the question was further expanded and we were to describe the second area of 0.3m as been 2m above the first area of 0.2m, then what would the pressure

head be?

Tip: Bernoulli's equation would be used, as follows: pg

pvz

pg

pvz

gg

22

22

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11 22

Area A1

Area A2

z1

z2

v1

v2

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Transpose the equation and note the level difference ( z2 – z1 ), is 2m pressure difference and expressed as the head is as follows:

mg

v

g

vzz

pg

p

pg

p977.0

81.9*2

5222.22

22

2221

22

1221

The pressure difference is 0.977m of water greater at the first section.

In N/m^2 this becomes:

977.0*81.9*1000977.0*21 pgpp

2

2

/5.9

/3^10*5.9

mkNor

mN

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ANSYS TutorialGeometry

We start of with our first sketch, apply the correct dimensions of 0.2m and 0.3m, to represent the inlet and outlet. The distance in-between is set at 0.5m

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Mesh

As shown, the mesh has been applied using the advanced size function, on: proximity and curvature, with the rest of the options left at default. The result can be seen in a well

structured mesh.

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Right-click on Default Domain in

the Outline treeSelect Rename

The domain name can now be edited. Change the domain

name to Pipe

Set the Material to Water.The available materials can

be found in the drop-down menu

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Click the Boundary Details tab. Enter a value of 5 for Normal Speed. The default

units are [m s^-1]

Set Relative Pressure to 0 [Pa]. This is relative to the domain Reference Pressure,

which is 1 [atm]

Our next aim is to define the inlet an outlet of the pipe. By right clicking on pipe, going to inset and then boundary, we are given the options to do so. There are other variables to

choose from however, this options are for more complicated examples.

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The Solver Control options set various parameters that are used by the solver and can affect the accuracy of the results. The default settings are reasonable, but will not be correct for all simulations. In this case the default settings will be used, but you will still look at what those defaults are.

An expression will be used to define the monitor point. 7. Set Option to Expression Enter the expression: areaAve(Pressure)@inlety in the Expression Value field The expression calculates the area weighted average of pressure at the boundary inlet.

Click Start Run to begin the solution process. 45 iterations are required to reduce the RMS residuals to below the target of 1.0x10-4. The pressure monitor points

approach steady values

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When the results are loaded, CFD-Post displays the outline (wireframe) of the model. The icons on the viewer toolbar control how the mouse

manipulates the view

You can create many different objects in CFD-Post. The Insert menu shows a

full list, but there are toolbar

shortcuts for all items.

Such as: Location: Points, Lines, Planes, Surfaces, Volumes

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Summary

The results shown in ANSYS are very accurate when compared to the analytical

method we applied earlier. As such, we have proved the correct results for both

analytical and numerical application. Learning objectives covered in this

workshop relate to fluid analysis, with knowledge gained in density and

pressure when applied to real world application, furthermore the use of ANSYS

for verification has also proven to be a small example its potential.

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References

Norman. E. et al. Advanced Design and Technology. 1995Longman Group UK Limited, ISBN 0 582 014638

ANSYS 13.0 Help files