To simplify the 3-D unsteady compressible NS equations to axisymmetric 2-D steady Incompressible laminar flow equations. Ignore the effects of gravity.

General Assumptions:

Steady flow.

Incompressible fluid.

Laminar and fully developed flow in z direction.

2D flow.

First, for 3D unsteady compressible Mass Conservation-continuity equation:

Steady means no change with time,

Incompressible means constant density, .

Laminar and fully developed flow in z direction so flow is parallel to the walls sides.

Pipe walls are stationary and no slip constraint at the pipe walls, at pipe walls.

Velocity only function of r, varies only with r direction (fully developed flow).

2D means only in r and z plane and no variation in direction.

Since,

Second, for 3D unsteady compressible Momentum equations:

In r-momentum

In -momentum

In z-momentum

Shear stress constitutive equations:

Incompressible means, constant density.

Steady means flow parameters do not change with time.

Laminar and fully developed flow in z direction so flow is parallel to the walls sides.

Pipe walls are stationary and no slip constraint at the pipe walls, .

Velocity only function of r, varies only with r direction (fully developed flow).

2D means only in r and z plane and no variation in direction.

Ignoring the effect of gravity, Fz and Fr equal Zero.

Third, applying all the previous conditions on the Shear stress constitutive equations:

Fourth, applying all the previous conditions on the momentum equations only in r and z direction:
In r-momentum

In z-momentum

(1.b)

First, Boundary conditions

Incompressible means constant density.

Steady means flow parameters do not change with time.

Laminar and fully developed flow in z direction so flow is parallel to the walls sides.

Pipe walls are stationary and no slip constraint at the pipe walls, .

Velocity only function of r, varies only with the r (fully developed flow).

2D means only in r and z plane and no variation in direction.

Ignoring the effect of gravity Fz and Fr equal Zero.

Second, by using the equation in question (1.a) for 2D steady laminar incompressible Mass Conservation-continuity equation:

Since,

Third, by using the equation in question 1.a for 2D steady laminar incompressible Momentum equations

In r-momentum

In z-momentum

Fourth, at Boundary conditions

By double integration;

And

So the velocity equation at any point in r direction is;

The Graph shows the distribution of velocity through the circular pipe diameter 2R=2m. First, the flow is driven by a pressure gradient dp/dz=1, if dp/dz<0 the velocity profile will be in the negative direction and in case of zero pressure gradient the velocity will be zero at any point in r direction (no flow). Second, the velocity profile is only function of r in a parabolic velocity profile. Third, as there is no slip condition at the pipe walls, the velocity of fluid close to the pipe walls equal zero. However, the maximum velocity can be found at the centre line of the pipe.

Fifth, Volumetric flow rate Q

The volumetric flow rate can be calculated be integrating the velocity profile over the cross sectional area of the circular pipe.

…. for circular Pipe

at R

From the volumetric flow rate equation Q,

Q increases as the quadratic radius of the pipe increase.

Q decrease as the fluid viscosity increase.

Q is directly proportional to the pressure gradient.

Fifth, Average or mean velocity

For fully developed laminar flow means

Maximum velocity at the centreline at r=0, as discussed in figure 2.

Question 2

Using Cartesian coordinate, you are asked to simplify the full 3-D unsteady compressible NS to 1-D steady incompressible laminar flow equations. You should include key steps and reasons for simplifications

(2.a)

To simplify the 3-D unsteady compressible NS equations to 1-D steady Incompressible laminar flow equations. Ignore the effects of gravity;

General Assumptions:

Axis as in Figure 3, x-y-axis.

Steady flow.

Incompressible flow.

Laminar and fully developed flow.

1D means only in x.

First, for 3D unsteady compressible Mass Conservation-continuity equation:

Second, for 3D unsteady compressible Momentum equations:

In x-momentum

In -momentum

In z-momentum

Shear stress constitutive equations for 1D (only in x):

Incompressible means , constant density.

Steady no change with time.

Flow is infinite in the z-x plane and fully developed flow means only depend on y.

1D means only in x plane and no variation in direction, .

Ignoring the effect of gravity at Fx.

Third, Applying those condition on the Shear stress constitutive equations:

Fourth, applying those conditions on Mass Conservation-continuity equation only in x direction:

Fifth, applying those conditions on the momentum equations only in x direction:

As P only function of x

(2.b)

Considering the boundary conditions (fixed bottom plate/wall, moving upper plate at constant

Velocity V, zero pressure gradient along streamwise direction, dp/dx=0).

First, Boundary conditions

Incompressible means , constant density.

Steady no change with time.

, flow is infinite in the z-x plane and fully developed flow means only depend on y.

The lower plat in fixed and no slipping condition at both plates/walls.

2D means flow only in x and y direction, .

dp/dx=0.

Ignoring the effect of gravity, Fy and Fx equal Zero.

(2.b.i)

Second, by using the equation in question (2.a) but for 2D steady laminar incompressible Mass Conservation-continuity equation

Since,

Third, by using the equations in question (2.a) but for 2D steady laminar incompressible Momentum equations

In x-momentum

Since

Therefore;

In y-momentum

Therefore P is only a function of x: = constant=0

Fourth, at Boundary conditions

By double integration;

Equation number 1:

Equation number 2:

By adding then subtracting equations 1 and 2 together,

The graph at figure 5 shows the flow velocity profile with the relation between the velocity in the x-axis and the distance between the two plates (2h). As there is zero pressure gradient along the stream wise direction, the velocity profile of Ux(y) is liner velocity profile. With no slipping condition, the maximum velocity of the fluid found at the moving upper plate however for the minimum velocity found at the fixed bottom plate. The velocity profile is mainly affected by the plate velocity and the distance between both plats.

Figure 1- Flow velocity profile and effect of moving upper plate with different velocities

The graph at figure 6, shows the effect of different velocity of the moving upper plate. First, with higher upper plate velocity as discussed in figure 5 the velocity profile still liner but with smaller slop value. Second, with negative velocity at the upper plate moving in the opposite direction the velocity profile still laminar but in the opposite negative direction. Third, at zero upper plate velocity and the pressure gradient is zero along the stream wise direction, there will not be any fluid motion as the flow is only driven by the upper moving plate.

(2.b.ii)

Fifth, Volumetric flow rate Q

……… dA=dydz

Q is directly proportional with the moving plate velocity and the distance between both plates.

Sixth, Mean velocity

Maximum velocity is at the upper moving plate =0.2m/s.

Seventh, Reynold number

Density of water at 20°c = 998.2

Dynamic viscosity of water at 20°c =

Re < 2300, therefore it’s a laminar flow

(2.c)

Considering the boundary conditions (fixed bottom plate/wall, moving upper plate at constant velocity V, and a constant pressure gradient along streamwise direction.

First, Boundary conditions

Incompressible means , constant density.

Steady no change with time.

, flow is infinite in the z-x plane and fully developed flow means only depend on y.

2D means only in x and y direction.

The lower plat in fixed and no slipping condition at both plates/walls.

Ignoring the effect of gravity Fy and Fx equal Zero.

dp/dx=-2.

Dynamic viscosity of water at 20°c =.

(2.c.i)

Second, by using the equation in question (2.a) but for 2D steady laminar incompressible Mass Conservation-continuity equation

Since

Third, by using the equations in question (2.a) but for 2D steady laminar incompressible Momentum equations

In x-momentum

In y-momentum

So P is only a function of x therefore,

Fourth, at Boundary conditions

By double integration;

Equation number 1:

Equation number 2:

Figure 8- Flow velocity profile between two parallel plates at dp/dx= -2 Pa/m

By adding then subtracting equations 1 and 2;

The graph at figure 8 shows the flow velocity profile with the relation between the velocity in the x-axis and the distance between the two plates (2h). At (-2 pressure gradient) along the stream wise direction with the same velocity direction of the upper moving plate. The fluid reach the maximum velocity 0.225 m/s slightly higher compared to the velocity of the moving plate 0.2 m/s at a location between the upper moving plate and half the distance between both plates. The velocity Ux(y) between the two plates will be positive velocity parabolic profile.

Figure 2- Flow velocity profile between two parallel plates at different dp/dx

Figure 3- Flow velocity profile and effect of moving upper plate with different velocitiesFigure 4- Flow velocity profile between two parallel plates at different dp/dx

Figure 5- Flow velocity profile and effect of moving upper plate with different velocities

Figure 6 – Fluid domain geometryFigure 7- Flow velocity profile and effect of moving upper plate with different velocitiesFigure 8- Flow velocity profile between two parallel plates at different dp/dx

Figure 9- Flow velocity profile and effect of moving upper plate with different velocitiesFigure 10- Flow velocity profile between two parallel plates at different dp/dx

As discussed in figure 8 the flow velocity properties in case of (-2 pressure gradient) along the stream wise direction with the same velocity direction of the upper moving plate, on the other hand, figure 9 shows that at positive 2 pressure gradient a backflow will appear at a location between the lower fixed plate and half the distance between both plates that means that the velocity of the upper moving plate not high enough to overcome the opposite direction of the pressure gradient. The velocity between the two plates will be negative velocity parabolic profile of Ux(y). For zero pressure gradient will be as discussed at figure 5 flow will be only driven by the velocity of upper moving plate.

Figure10 – Flow velocity profile and effect of moving upper plate with different velocities

Figure 11 – Fluid domain geometryFigure 12- Flow velocity profile and effect of moving upper plate with different velocities

Figure 13 – Fluid domain geometry

Figure 14- First trial with default meshingFigure 15 – Fluid domain geometryFigure 16- Flow velocity profile and effect of moving upper plate with different velocities

Figure 17 – Fluid domain geometryFigure 18- Flow velocity profile and effect of moving upper plate with different velocities

The graph at figure 10 shows the flow velocity profile with the relation between the velocity in the x-axis and the distance between the two plates (2h). At (-2 pressure gradient) along the stream wise direction with the same velocity direction of the upper moving plate. At higher upper plate velocity the maximum flow velocity will occur at the upper moving plate. With opposite plate direction at the same velocity (-0.2 m/s), the velocity of the upper moving plate is not high enough to overcome the opposite direction of the pressure gradient as discussed at figure 6. In case of two fixed plate, the velocity Ux profile is only function of y in a parabolic velocity profile and for Minimum velocity as there is no slip condition at the plates/walls the velocity of fluid close to the two fixed plates equal zero. However, the maximum velocity can be found at half distance between both fixed plates.

Fifth, Volumetric flow rate Q

………..

(2.c.ii)

Fifth, Volumetric flow rate Q

Dynamic viscosity of water at 20°c =

From the volumetric flow rate equation Q the following have been recognized;

Q increases as the distance between two plates increase.

Q decrease as the fluid viscosity increase.

Q is directly proportional to the pressure gradient.

Q increase as the moving plate velocity increase.

Sixth, Mean velocity

Seventh, Reynold number

Density of water at 20°c = 998.2

Dynamic viscosity of water at 20°c =

4000> Re > 2300, therefore its transient flow

Question 3

Use the available meshing tools in ANSYS to generate mesh for the two-dimensional flow over an airfoil (either S814 or S815) at low-speed (i.e. no shock wave on airfoil surfaces).

The generated mesh should reflect the key physical flow features, e.g. viscous boundary layer, rapid changes in flow field, etc. Also discuss and comment on mesh quality.

Part 1

Task (3.1)

Assumption:

The Fluid medium is air

Temp 25c

At low-speed (Subsonic)

S814 airfoil, chord length equal 1m

Air flow speed:

At Mach number is < 1, the flow speed is subsonic.

At 25 °c

K=1.4

Molecular mass M= 28.966 g/mol

Gas constant R=8.314472

Absolute Temp. T=273+25=298k

Assumed flow speed (inlet velocity) equal 5m/s.

Task (3.2)

Reynolds number:

L = 1m, the chord length of the airfoil

Task (3.3)

Low Reynolds number rang from 10x to 5x, Critical Reynold value 50x greater than this value the flow start change to turbulent flow.

So the flow is laminar throughout.

Part 2, ANSYS CFX modelling

By using ANSYS CFX16.2 (Academic)

First, Geometry:

The geometry of the airfoil was created by forming a surface from points imported by the airfoil coordinates points file given in lecture for S814 airfoil, the number of points is 65. Those points are connected together forming a curve then forming one surface. After that the surface have been extruded with a small value 0.01m as a unit length in Z direction forming 1 frozen body.

The chord length of the airfoil equal 1m and located about 3m from the edge of the air foil to the left (inlet) side of the fluid domain which is in a rectangle shape domain with dimensions 12mx6m. The fluid domain dimension gives a sufficient domain size to study the behaviour of the flowing fluid and how it will behave just before, all over and after the airfoil, the length of the modelled fluid domain is longer in case of any long, turbulent waves and to show when the fluid we go back to it is stable state.

The rectangle sketch have been extruded with dimension 0.01m that formed a frozen body after that the airfoil body is subtracted from the rectangular body (fluid domain) as shown in figure 11.

Second, Meshing:

Number of trials have been done during the creation of the last submitted mesh trial. Extra care have been taken to simulate the close area around the airfoil and the boundary layer by adding inflation layers and changing element size.

Starting from the default meshing by using all the default setting as in figure 12 and noticed how poor meshing can affect the final result as in figure 13.

Number of modifications have been done on the geometry to get finer element size at the interested area as shown in figure 14 for one of the trials. At the final modification, A circle shape geometry which reflect the airfoil curvature with diameter 3m from the assumed centre of the airfoil about 0.32m from the front edge of the airfoil and a rectangle geometry reflect the expecting the outlet stream line configuration starting almost after the end of the airfoil till the end of the domain with height 0.6 m, those two geometry sketches have been extruded with the same thickness 0.01m as shown in figure 15.

Figure 19- Meshing geometry trial

Figure 15- Final mesh geometry

Figure 20- First trial at orthogonal quality checkFigure 21- Final mesh geometry

Figure 22- First trial at orthogonal quality check

Figure 23- Final trial orthogonal quality checkFigure 24- First trial at orthogonal quality checkFigure 25- Final mesh geometry

Figure 26- First trial at orthogonal quality checkFigure 27- Final mesh geometry

Through all the attached meshing trials files, sizing function, inflation layers option and properties are what have been changed from one trial to another to reach better result and better quality mesh.

In the final mesh advanced size function have been used on curvature and specify the value of curvature normal angle that control the element edge how to span specially on the fine curvature part of the airfoil final angle was 8°. Span angle centre is fine (36° to 12°).

Max face size and max element size is 0.10m.

Meshing body size set to be automatic method.

For inflation layers position, trials have been done using smooth transition and first layer thickness. At the last mesh first layer thickness was used with thickness 0.004m. The inflation layers boundary all over the airfoil edge with number 11 layers.

The final mesh properties as shown in Table 1, 2 and 3.

Defaults
Physics Preference	CFD
Solver Preference	CFX
Relevance	0
Sizing
Use Advanced Size Function	On: Curvature
Relevance Center	Fine
Initial Size Seed	Active Assembly
Smoothing	High
Transition	Slow
Span Angle Center	Fine
Curvature Normal Angle	8.0 °
Min Size	Default (2.0138e-003 m)
Max Face Size	0.10 m
Max Size	0.10 m
Growth Rate	Default (1.20 )
Minimum Edge Length	3.9987e-003 m
Element Midside Nodes	Dropped
Straight Sided Elements
Number of Retries	0
Extra Retries For Assembly	Yes
Rigid Body Behavior	Dimensionally Reduced
Mesh Morphing	Disabled
Statistics
Nodes	50720
Elements	25193

Table 1-Final mesh properties

Object Name	Automatic Method	Body Sizing	Inflation
State	Fully Defined
Scope
Scoping Method	Geometry Selection
Geometry	1 Body		1 Face
Definition
Suppressed	No
Method	Automatic
Element Midside Nodes	Use Global Setting
Type		Body of Influence
Bodies of Influence		2 Bodies
Element Size		3.e-002 m
Growth Rate		1.20	1.2
Local Min Size		Default (2.0138e-003 m)
Boundary Scoping Method			Geometry Selection
Boundary			2 Edges
Inflation Option			First Layer Thickness
First Layer Height			4.e-003 m
Maximum Layers			11
Inflation Algorithm			Pre

Table 2-Mesh control

Object Name	inlet	wall	outlet		outlet2
State	Fully Defined
Scope
Scoping Method	Geometry Selection
Geometry	1 Face	2 Faces		1 Face
Definition
Send to Solver	Yes
Visible	Yes
Program Controlled Inflation	Exclude
Statistics
Type	Manual
Total Selection	1 Face	2 Faces		1 Face
Suppressed	0
Used by Mesh Worksheet	No

Table 3 – Mesh name selected

Meshing quality check

Mesh Information
Wedges	135
Hexahedra	25058

Quality check is very important for result accuracy. Table 4 shows the mesh information and the type of the type of used elements.

Table 4- Mesh information

First, at the orthogonal quality comparison between the last two meshing trials, Meshing Statistics at the first quality check trial as shown in Table 5.

Mesh statistics
Nodes	91172
Elements	45456
Mesh Metric	Orthogonal Quality
Min	2.428E-02
Max	0.999
Average	0.986

Table 5- First trial meshing statistics

Figure 16- First trial at orthogonal quality check

The orthogonal quality is ranged from 0 to 1. Value of 1 is the best orthogonal quality and it is advised to keep Min Orthogonal quality above 0.05. The minimum orthogonal quality 0.024 less than 0.05 as shown in the Table 5. At figure 16, the poor quality mesh have been identified almost at the inflation layers.

To achieving minimum orthogonal quality >0.05, some modification have been done. First layer thickness at the inflation layer changed from to 0.04m. Number of Inflation layers changed from 12 to 11.Curvature normal angel decreased to 8° which increase the refinement around the curved edge of the airfoil.

Mesh Statistics
Nodes	50720
Elements	25193
Mesh Metric	Orthogonal Quality
Min	8.018E-02
Max	0.999
Average	0.9776

Figure 17 and Table 6 shows the final meshing statistics, the min orthogonal quality above 0.05.

Table 6- Final trial meshing statistics and orthogonal quality

Figure 17- Final trial orthogonal quality check

Second, at skewness check table 7, shows mesh statistics.

Mesh Statistics
Nodes	50720
Elements	25193
Mesh Metric	Skewness
Min	2.6026e-003
Max	0.95426
Average	0.12941

Table 7- Final trial meshing statistics and Skewness

The average value is in the excellent range but on the other hand, the Max value is 0.95 which is considered as a poor quality. As shown in figure 18, only two element had been identified with this value.

Figure 18- Skewness quality check

Third at smoothness and aspect ratio, almost all changes in mesh sizes were gradual and the aspect ratio of the longest edge length to the shortest edge length not greater than 20% as shown in table 9

Mesh Statistics
Min edge length ratio	1.1335
Max edge length ratio	19.4501

Table 8- Aspect ratio

Third, Setup and Boundaries:

As shown at figure19,

At the default domain: Domain type is fluid (air), incompressible at fixed temperature 25 °c with pressure 1 atm. Using Turbulence model shear stress transport (SST) gives highly accurate result near walls and prediction of any flow separation, wall function set to be automatic.

Inlet domain: the inlet left side face of the rectangular fluid domain.

Subsonic flow with velocity components u=5m/s, v=w=0 m/s

Turbulence medium intensity = 5% as there is no information about the inlet turbulence.

Outlet domain: Opening type – the open three sides of the rectangular fluid domain.

Walls: symmetry type – two symmetry walls side of the rectangular fluid domain.

Domain – Default Domain
Type	Fluid
Location	B22
Materials
Air at 25 C
Fluid Definition	Material Library
Morphology	Continuous Fluid
Settings
Buoyancy Model	Non Buoyant
Domain Motion	Stationary
Reference Pressure	1.0000e+00 [atm]
Heat Transfer Model	Isothermal
Fluid Temperature	2.5000e+01 [C]
Turbulence Model	SST
Turbulent Wall Functions	Automatic

Table 9-Domain

Domain	Boundaries
Default Domain	Boundary – inlet
	Type	INLET
	Location	inlet
	Settings
	Flow Regime	Subsonic
	Mass And Momentum	Cartesian Velocity Components
	U	5.0000e+00 [m s^-1]
	V	0.0000e+00 [m s^-1]
	W	0.0000e+00 [m s^-1]
	Turbulence	Medium Intensity and Eddy Viscosity Ratio
	Boundary – opening
	Type	OPENING
	Location	opening
	Settings
	Flow Regime	Subsonic
	Mass And Momentum	Entrainment
	Relative Pressure	0.0000e+00 [Pa]
	Turbulence	Zero Gradient
	Boundary – wall
	Type	SYMMETRY
	Location	wall
	Settings
	Boundary – Default Domain Default
	Type	WALL
	Location	F26.22, F29.22, F30.22
	Settings
	Mass And Momentum	No Slip Wall
	Wall Roughness	Smooth Wall

Table 10- Boundary physics

Task (3.4), (3.5)

Fourth, Results:

Boundary layer thickness and near wall spacing calculation

According to the calculated low Reynold number, the flow was classified as a laminar flow. In Laminar flow viscous forces are effective, velocity streamlines are regular and move smoothly all over the airfoil as shown in figure 20.

Boundary layer is laminar as it depend on Reynold number and started to form because of the effect of viscosity.

First, The calculation of boundary layer thickness for laminar all over the airfoil based on laminar flow over a plate equation.

Boundary layer thickness:

For incompressible flow,

Coefficient of friction

Surface shear stress

Second, determination of near wall spacing and boundary layer calculation, by estimating value. As the flow on laminar flow and value mainly effective in case of turbulent flow, we will focuses on the effect of different first layer thickness and the inflation layers all around the airfoil and how that effect the value.

According to ANSYS CFX Solver Modelling Guide, starting with estimating the value of Y+. After that, by using the following formula we can calculate the first layer thickness or the near wall meshing spacing.

And for boundary layer thickness,

The following table 11 shows the effect of the inflation first layer thickness selection in three different meshing trials on the y+ value at maximum layers number 11, 12 and growth rate 1.2. The used first inflation layer thickness is at the second trial equal 0.004mm. Also illustrate at figure 22, the flow of velocity profile starting from the air foil surface passing by the boundary layer till the free stream. The boundary layer start to reduce the velocity gradually until it reach zero velocity at the airfoil surface, the boundary layer thickness can be calculated from the airfoil surface or starting from zero velocity till the velocity reach 99% of the main stream velocity and gives a parabolic velocity profile. Figure 24 shows the velocity vectors.

	At first layer thicken=0.001m	At first layer thickens =0.004m- (used)	At first layer thickens =0.01m
Min. Value	3	5.5	3.56
Max. Value	26	88.6	182.57
Velocity profile (boundary layer velocity profile)	Figure 21- velocity profile for trial 1 Figure 21- velocity profile for trial 1 Figure 21- velocity profile for trial 1 Figure 21- velocity profile for trial 1	Figure 22- velocity profile for trial 2 Figure 22- velocity profile for trial 2 Figure 22- velocity profile for trial 2 Figure 22- velocity profile for trial 2	Figure 23- velocity profile for trial 3 Figure 28- Velocity stream vectorFigure 23- velocity profile for trial 3 Figure 29- Velocity stream vector Figure 30- Y+ contourFigure 31- Velocity stream vectorFigure 23- velocity profile for trial 3 Figure 32- Velocity stream vectorFigure 23- velocity profile for trial 3

Table 11- comparison of different first layer thickness and velocity profile

Figure 24- Velocity stream vector

Figure 25, Shows Y+ values contour over the airfoil surface.

Pressure and velocity

Figure 26 and 27 shows the pressure distribution around the airfoil. It shows the max pressure point at the edge of the airfoil with attacking angel equal 0°. Starting from the Max pressure point in x direction, pressure start to decrease reaching the minimum pressure point after that pressure start to raise.

Figure 26- Pressure distribution contour

Figure 27- Pressure distribution graph

Figure 28 and 29 shows the pressure distribution around the airfoil. It shows zero velocity point at the edge of the airfoil with attacking angel equal 0°. Starting from the zero velocity point in x direction velocity start to increase reaching the maximum velocity after that velocity slightly start to decrease.

Figure 28- Velocity distribution contour

Figure 29- Velocity distribution graph

References:

[1]	K. Volkov, “Governing Equations,” Lecture Notes, 2015.
[2]	S. Demble, “Fluid Mechanics & Thermodynamic Principles,” Lecture Notes, 2015.
[3]	S. Dembele, “Turbulance Modelling,” Lecture Notes, 2015.
[4]	A. Heidari, “Domain Meshing,” Lecture Notes, 2015.
[5]	B. Massey, Mechanics of Fluids, 8th ed., LONDON AND NEW YORK: Taylor & Francis, 2006.
[6]	H.Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, 2nd Ed., Prentice Hall, 2007.
[7]	ANSYS, “Tetradedral Meshing with Inflation . Introduction to ANSYS Meshing,” ANSYS Customer Training Material, 2010.
[8]	ANSYS, “ANSYS CFX-Solver Modeling Guide,” 2015-Release 16.2.

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Table of Contents

Question 1

(1.a)

(1.b)

Question 2

(2.a)

(2.b)

(2.b.i)

(2.b.ii)

(2.c)

(2.c.i)

(2.c.ii)

Question 3

Part 1

Task (3.1)

Task (3.2)

Task (3.3)

Part 2, ANSYS CFX modelling

First, Geometry:

Second, Meshing:

Third, Setup and Boundaries:

Task (3.4), (3.5)

Fourth, Results: