CFD-Assignment_Ramji_Amit_10241445

CFD Practical Exercises
CFD Analysis for Aerospace Applications 7ENT1006
Amit Ramji
10241445
University of Hertfordshire - Aerospace Engineering
Year 5 – CFD for Aerospace Application – 7ENT1006
29th
April 2015

Amit Ramji - 10241445 – A5 – University of Hertfordshire
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Table
of
Contents

Introduction ...................................................................................................................................................1
1. Case 1 – Air Flow Within an Annulus ....................................................................................................1
1.1. Literature Review ............................................................................................................................1
1.2. Geometry ........................................................................................................................................1
1.3. Analytical Methods ..........................................................................................................................1
1.4. Numerical Methods - Computational Fluid Dynamics .....................................................................3
1.4.1. Modeling Geometry ..................................................................................................................3
1.4.2. Mesh Conditions and Substantiation ........................................................................................4
1.4.3. Physical and Boundary Conditions...........................................................................................5
1.4.4. Physics Models.........................................................................................................................5
1.4.5. Running the Solver ...................................................................................................................5
1.4.6. Post Processing........................................................................................................................6
1.4.7. Velocity Visualization................................................................................................................6
1.4.8. Pressure Visualization ..............................................................................................................6
1.4.9. Velocity Profile..........................................................................................................................7
1.4.10. Velocity Visualization..............................................................................................................8
1.5. Discussion and Analysis .................................................................................................................8
1.6. Conclusion for Annulus Case..........................................................................................................8
2. Case 2 – Supersonic Airflow over Airfoils..............................................................................................9
2.1. Diamond Wedge .............................................................................................................................9
2.1.1. Modeling Geometry ..................................................................................................................9
2.1.2. Mesh Conditions and Substantiation ........................................................................................9
2.1.3. Physical and Boundary Conditions.........................................................................................10
2.1.4. Physics Models.......................................................................................................................11
2.1.5. Running the Solver .................................................................................................................11
2.1.6. Post Processing......................................................................................................................11
2.1.7. Mach No Visualization ............................................................................................................12
2.1.8. Pressure Visualization ............................................................................................................13
2.1.9. Discussion and Analysis.........................................................................................................15
2.1.10. Conclusion for Diamond Wedge Airfoil Case .......................................................................15
2.2. Airfoil Section RAE2822 ...................................................................................................................15
2.2.1. Importing Geometry................................................................................................................15
2.2.2. Mesh Conditions and Substantiation ......................................................................................16
2.2.3. Physical and Boundary Conditions.........................................................................................16
2.2.4. Physics Models.......................................................................................................................16
2.2.5. Running the Solver .................................................................................................................16
2.2.6. Post Processing......................................................................................................................17
2.2.7. Mach No Visualization ............................................................................................................17
2.2.8. Pressure Visualization ............................................................................................................18
2.2.9. Velocity Visualization and Areas of concern...........................................................................20
2.2.10. Sample Lift and Drag Coefficient Monitor Plots....................................................................22
2.2.11. Discussion and Analysis.......................................................................................................22
2.2.12. Conclusion for RAE2822 Airfoil Case...................................................................................22
3. Case 3 – Convective Heat Transfer from a Heat Source within an Enclosed Room...........................23
3.1. Modeling Geometry.......................................................................................................................23
3.2. Mesh Conditions and Substantiation.............................................................................................23
3.3. Physical and Boundary Conditions ...............................................................................................24
3.4. Physics Models .............................................................................................................................24
3.5. Running the Solver........................................................................................................................25
3.6. Post Processing ............................................................................................................................25
3.7. Temperature Visualization ............................................................................................................25
3.8. Velocity Visualization ....................................................................................................................25
3.9. Density and Pressure Visualization...............................................................................................26
3.10. Vorticity and Enthalpy Visualization ............................................................................................26
3.11. Discussion and Analysis .............................................................................................................26
3.12. Conclusion for Thermal Convection Case...................................................................................27
References..................................................................................................................................................27

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Table
of
Figures

Figure 1 - Geometry of Annulus....................................................................................................................1
Figure 2 – Velocity Profile for Fully Developed Annular Flow (Fig 6.15 from White, F. M. (2003))...............2
Figure 3 – Analytical velocity profile..............................................................................................................3
Figure 4 - Star-CCM CAD Annular Pipe .......................................................................................................3
Figure 5 – Mesh A = 0.5mm Base Size and Mesh B = 0.25mm Base Size..................................................4
Figure 6 – Prism Layers for Mesh A at wall boundaries ...............................................................................4
Figure 7 - Residuals for solver convergence for Mesh A ..............................................................................5
Figure 8 – Inlet and Outlet Velocity Vectors for Mesh A with peak at 0.21527 m/s ......................................6
Figure 9 – Detail View showing Initiation of parabolic velocity profile from Figure 8 (a) ...............................6
Figure 10 - Inlet and Outlet Velocity Vectors for Mesh B with un-converged peak at 0.33590 m/s ..............6
Figure 11 – Relative Pressure Variation across the Annulus........................................................................6
Figure 12 - Velocity Profile after parabolic flow initiation (at Li from Figure 1) ..............................................7
Figure 13 - Velocity Profile at fully developed flow (at LD from Figure 1 and 0.75m from section 1.3) .........7
Figure 14 - Fully Developed 3D Velocity Profile with Double Parabola ........................................................7
Figure 15 – Scalar Velocity plot of Annulus with peak velocity of 0.21493 m/s ............................................8
Figure 16 – Diamond Wedge Geometry with Chord=0.5m and 10° Semi-Wedge........................................9
Figure 17 – Domain Size of L=2.8m & H=2.2m (a) and 3D view of domain (b)............................................9
Figure 18 - Mesh Visualization - Overview (a), Cone (b) and Block refinement (c) ....................................10
Figure 19 – Block Mesh Refinement (a) and Wedge Mesh Profile (b)........................................................10
Figure 20 - Residuals for solver convergence for Diamond Wedge at 0° Incidence...................................11
Figure 21 - Diamond Wedge Mach No peak at 1.79 for 0° Incidence.........................................................12
Figure 22 - Diamond Wedge Mach No peak at 1.9 for -5° (a) and +5° Incidence (b) .................................12
Figure 23 - Diamond Wedge Mach No peak at 2.08 for -10° (a) and +10° Incidence (b) ...........................12
Figure 24 - Diamond Wedge Mach No peak at 2.3 for -15° (a) and +15° Incidence (b) .............................13
Figure 25 - Diamond Wedge Mach No peak at 2.54 for -20° (a) and +20° Incidence (b) ...........................13
Figure 26 - Diamond Wedge Pressure peak at stagnation of 1.24E+5 Pa for 0° Incidence .......................13
Figure 27 - Diamond Wedge Pressure peak at stagnation of 1.9E+5 Pa for -5° & +5° Incidence..............14
Figure 28 - Diamond Wedge Pressure peak at stagnation of 2.0E+5 Pa for -10° & +10° Incidence..........14
Figure 29 - Diamond Wedge Pressure peak at stagnation of 2.05E+5 Pa for -15° & +15° Incidence........14
Figure 30 - Diamond Wedge Pressure peak at stagnation of 2.07E+5 Pa for -20° & +20° Incidence........15
Figure 31 – Importing RAE2822 Airfoil Geometry into STAR CCM ............................................................15
Figure 32 – Mesh Import into STAR CCM for RAE2822 Airfoil – Boundary (a) and Detail Mesh (b) .........16
Figure 33 – Detail View of RAE2822 Mesh showing Prism layers for boundary layer detail ......................16
Figure 34 -- Residuals for solver convergence for RAE2822 at 0° Incidence.............................................16
Figure 35 – RAE2822 Mach No peak at 1.75 for 0° Incidence ...................................................................17
Figure 36 – RAE2822 Mach No peak at 1.9 for -5° (a) and +5° Incidence (b)............................................17
Figure 37 – RAE2822 Mach No peak at 2.0 for -10° (a) and 2.1 for +10° Incidence (b) ............................17
Figure 38 – RAE2822 Mach No peak at 2.2 for -15° (a) and 2.3 for +15° Incidence (b) ............................18
Figure 39 – RAE2822 Mach No peak at 2.5 for -20° (a) and +20° Incidence (b)........................................18
Figure 40 – RAE2822 Pressure peak at stagnation of 2.1 E+5 Pa for 0° Incidence...................................18
Figure 41 – RAE2822 Pressure peak at stagnation of 2.1 E+5 Pa for -5° and +5° Incidence....................19
Figure 42 – RAE2822 Pressure peak at stagnation of 2.1 E+5 Pa for -10° and +10° Incidence................19
Figure 43 – RAE2822 Pressure peak at stagnation of 2.1 E+5 Pa for -15° and +15° Incidence...............19
Figure 44 – RAE2822 Pressure peak at stagnation of 2.0 E+5 Pa for -20° and +20° Incidence................20
Figure 45 – RAE2822 Velocity Vectors for +15° Incidence.........................................................................20
Figure 46 – RAE2822 Velocity Vectors for +15° Incidence – Stagnation point move.................................20
Figure 47 – RAE2822 Velocity Vectors for +15° Incidence – Flow Separation at Trailing Edge ................20
Figure 48 – RAE2822 Velocity Vectors for +15° Incidence - Acceleration to Leading Edge ......................21
Figure 49 – RAE2822 Velocity Vectors for -20° & +20° Incidence – Trailing Edge Flow Separation ........21
Figure 50 – RAE2822 Velocity Vectors for +20° Incidence – Reversing Flow and Eddy Initiation .............21
Figure 51 – RAE2822 Velocity Vectors for +20° Incidence - Reversing Flow and Eddy Initiation..............21
Figure 52 – Lift Coefficient (a) and Drag Coefficient (b) monitor plot for RAE2822 at 0° Incidence ...........22
Figure 53 - Input Geometry with Radiator of 0.2 x 0.5m and wall separation of 0.1m on each edge ........23
Figure 54 – Manual Mesh Refinement (a), 3D Refined Mesh (b) and 2D Output Mesh (c)........................24
Figure 55 - Residuals for solver convergence for Thermal Convection case .............................................25
Figure 56 – Temperature visualization with Ambient of 300 K and peak of 313.15 K ................................25
Figure 57 – Max Velocity of 0.227 m/s and relative difference of 0.158 m/s ..............................................25
Figure 58 – Density difference of 0.0768 kg/m3
(a) and Relative Pressure difference of 3.55 Pa (b) ........26
Figure 59 – Visualization for Vorticity peak of 5.8/s (a) and Enthalpy at Radiator of 3.143 J/kg (b) ...........26

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Introduction

In this paper, numerical and analytical methods of analysis are employed for the study of airflow
within Annular Pipes (section 1), around a Diamond Wedge and aerofoil section RAE2822 (section
2), alongside a Thermal Convection investigation of a radiator within an enclosed room (section 3).
The numerical side of analysis is carried out on STAR-CCM+ for multi-physical finite element
analysis.
Aims
! To investigate the flow properties and generate velocity profiles of annular pipe flow using
analytical and numerical techniques.
! To simulate diamond wedge and conventional airfoils in the virtual wind tunnel at various
incidence angles.
! To simulate a heat source within a room and investigate the convective flow properties.
1. Case
1
–
Air
Flow
Within
an
Annulus

1.1. Literature
Review

The analytical method derived from the Navier-stokes equations is compared against numerical
methods in this section. Annular pipe flow has been ever increasing in interest due to its numerous
applications in oil & gas, aerospace propulsion, automotive fuel systems and chemical injection
systems. The correct investigation into fully developed laminar flow is of particular interest to
engineers due to investigating fundamental energy losses in such pipes. The performance and flow
efficiency of simple concentric tubes may not seem obvious, however numerous literature suggests
applications into studying annuli with axially moving or rotating cores. Such interest of moving cores
evolves from the injection ports of fuel systems used in aero-engines and other petro-chemical uses.
Initial studies carried out by Ogawa et al. (1980) who considered numerically equivalent studies using
parallel plates.
1.2. Geometry

The following geometry (Figure 1) has been used to model the annular pipe. The annulus consists of
an outer diameter of ∅0.02m with a solid concentric core of ∅0.01m in axial alignment.
Figure 1 - Geometry of Annulus
The velocity of air at 20°C of the pipe is uniform across the inlet and is to follow a laminar regime.
The pipe of length L has an Initiation length of Li and a fully Developed length of LD.
1.3. Analytical
Methods

The velocity profile of an annulus is of great engineering interest as mentioned previously.
Mathematical manipulation involving limit functions of parabolas have been identified from the
Navier-Stokes equations. Using this, the entry and development length can be calculated alongside
the velocity shape profile of the fully developed flow.
R
r
Rp
L
LD
Li

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For the velocity profile of airflow inside an annulus, the following calculation is carried out:
𝑈 𝑅 =
𝑃
4𝜂
−𝑅!
+
𝑏! − 𝑎!
𝐿𝑛
𝑏
𝑎
𝐿𝑛 𝑅 +
𝑎! 𝐿𝑛 𝑏 − 𝑏! 𝐿𝑛 𝑎
𝐿𝑛
𝑏
𝑎
Equation 1 -–Velocity Profile for Fully developed flow
Or similarly:
𝑢(𝑟) =
1
4𝜇
−
𝑑
𝑑𝑥
𝑝 + 𝜌𝑔𝑧 𝑎!
− 𝑟!
+
𝑎! − 𝑏!
𝐿𝑛
𝑏
𝑎
𝐿𝑛
𝑎
𝑟
Equation 2 – Velocity Profile variant (Eqn 9.81 from White, F. M. (2003))
Figure 2 – Velocity Profile for Fully Developed Annular Flow (Fig 6.15 from White, F. M. (2003))
Consequently from the Rheological model for power law in fluids, the frictional pressure drop:
ΔP =
2𝑓𝜌𝑈!
𝐷
Friction factor for Annuli for laminar flow using Reynolds Number:
𝑓 =
16
𝑅𝑒
=
16
150
= 0.10667
Reynolds Number:
𝑅𝑒 =
𝜌𝑈𝐷
𝜂
Velocity of the flow:
𝑈 =
𝑅𝑒 × 𝜂
𝜌 × 𝐷
=
150 × 1.82076 × 10!!
1.205 × (0.02 − 0.01)
= 0.22665 𝑚/𝑠
Frictional pressure drop:
ΔP =
2×0.10667×1.205×0.22665!
(0.02 − 0.01)
= 1.320605 𝑃𝑎
R
(m)
U(R)
(m/s)

0.005
0.00000

0.0051
0.02054

0.0052
0.03996

0.0053
0.05829

"
"

"
"

"
"

0.0097 0.04740
0.0098 0.03217
0.0099 0.01636
0.01 0.00000
Table 1 – Theoretical data to generate velocity profile.

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Figure 3 – Analytical velocity profile
The Fully developed length is given by:
𝐿! = 0.05 × 𝑅𝑒 × 𝐷 = 0.05× 150 × (0.02 − 0.01) = 0.075𝑚
1.4. Numerical
Methods
-‐
Computational
Fluid
Dynamics

Further to carrying out an analytical method of determining the velocity profile and its fully developed
laminar length, a numerical analysis is carried out in STAR CCM using a medium and fine mesh for
flow investigation within the annulus.
1.4.1. Modeling
Geometry

The annular pipe with R=0.01m and r=0.005m (see Figure 1) has been modeled in the Star-CCM
CAD interface and extruded to L=0.1m. Inlet, outlet and wall boundaries have been applied to the
relevant surfaces for later use.
Figure 4 - Star-CCM CAD Annular Pipe
0

0.05

0.1

0.15

0.2

0.25

0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011

U(R)
m/s

R
(m)

Velocity
Pro3ile
for
Single
Annular
section

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1.4.2. Mesh
Conditions
and
Substantiation

Mesh Variable Mesh A Mesh B Rationale
Base Size 0.5mm 0.25mm Refined to investigate shear effects at
the walls and to refine the vector plots
to display the parabolic velocity profile
– see Figure 10b and Figure 14.
No of Prism
Layers
6 10 In order to investigate shear effects at
the wall boundaries – see Figure 6.
Prism Layer
stretching
1.5 1.5 Expansion ratio of prism layers.
Prism Layer 45% of base
(Abs size 0.225mm)
45% of base
(Abs size 0.1125mm)
Size of tube wall elements.
Surface Growth
Rate
1.3 1.3 Growth of surface elements not in
contact with wall face elements.
Surface Size 25% of base
(Abs size 0.125mm)
25% of base
(Abs size 0.0625mm)
General surface elements not in
Relative Target
Size
100% of base
(Abs size 0.5mm)
100% of base
(Abs size 0.25mm)
Aimed size of surface elements not in
Table 2 – Mesh Properties for Mesh A and B
Figure 5 – Mesh A = 0.5mm Base Size and Mesh B = 0.25mm Base Size
Figure 6 – Prism Layers for Mesh A at wall boundaries

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1.4.3. Physical
and
Boundary
Conditions

Initial and Flow
conditions
Value
Pressure 101325 Pa
Dynamic viscosity 1.85508 x10-5 Pa-s
Density (Air at 20°C) 1.205 kg/m^3
Velocity (Initial Conditions) [X0.0, Y0.0, Z0.22665] m/s
Velocity (Inlet) 0.22665 m/s
Pressure (Outlet) 0 Pa (Atmospheric reference pressure applies)
Gravity Neglected due to short distance of travel and horizontal orientation,
hence negligible effects of pressure head height.
Table 3 – Flow properties and Boundary Conditions for Annulus
1.4.4. Physics
Models

Model Rationale
Constant Density Low Reynolds number / low velocity hence considered incompressible.
Gas Properties of Air as per Table 3.
Gradients Faster solving method by use of gradient equation solvers.
Laminar Initial flow conditions for a laminar Reynolds number below 2000.
Segregated Flow Segregated solvers discretise the Jacobian matrix into smaller problems,
which in this case for annular pipe is a degree of freedom type. Although
coupled flows require less iterations, the segregated solver is more accurate
and appropriate for this type of short length scale analysis.
Steady Steady time simulation to observe the flow properties at a single steady state
time step.
Three
Dimensional
Conversion to 2D plane carried out later for visualisation (see Figure 8
through Figure 15).
Stopping Criteria 1500 Iterations (Actual Convergence in 150 for Mesh A – see Figure 7)
Table 4 – Physics solver models for Annulus
1.4.5. Running
the
Solver

Figure 7 - Residuals for solver convergence for Mesh A

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1.4.6. Post
Processing

Following the convergence of the solution of the annular pipe, some post processing was carried out
which involves visualization of the velocity profiles as vectors and relative scalars.
1.4.7. Velocity
Visualization

Figure 8 – Inlet (a) and Outlet (b) Velocity Vectors for Mesh A with peak at 0.21527 m/s
Figure 9 – Detail View showing Initiation of parabolic velocity profile from Figure 8 (a)
Figure 10 - Inlet (a) and Outlet (b) Velocity Vectors for Mesh B with un-converged peak at 0.33590 m/s
1.4.8. Pressure
Visualization

Figure 11 – Relative Pressure Variation across the Annulus

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1.4.9. Velocity
Profile

Figure 12 - Velocity Profile after parabolic flow initiation (at Li from Figure 1)
Figure 13 - Velocity Profile at fully developed flow (at LD from Figure 1 and 0.75m from section 1.3)
Figure 14 - Fully Developed 3D Velocity Profile with Double Parabola

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1.4.10. Velocity
Visualization

Figure 15 – Scalar Velocity plot of Annulus with peak velocity of 0.21493 m/s
1.5. Discussion
and
Analysis

One can observe from Figure 8 through Figure 15 that the velocity profile and magnitudes are in
agreement with the analytical methods calculated in section 1.3. Figure 3 is an exact match to the
magnitude of 0.22 m/s and has the exact same profile as that displayed in Figure 13 and Figure 14.
Overall the benefits of having a finer mesh is not apparent until the section probe was used to
determine the velocity profile at 0.075m from the inlet. The velocity profile as shown in Figure 13 still
contains some stray vectors, this may be due to the planar section not being correctly aligned
perpendicular to the flow direction.
1.6. Conclusion
for
Annulus
Case

In order to verify the accuracy of the simulations, the mesh dependency tool has been utilized to
check if the mesh quality is suitable for this type of analysis. Considering that the converged
numerical results are in agreement with the analytical solutions, one can confidently say that the
outcomes of this investigation have been achieved.
As predicted during the start of this investigation, the velocity profile of the analytical solution and the
CFD simulation will resemble a parabola however with a bias towards one side. A skewed profile can
be observed in Figure 3, Figure 12 and Figure 13 and is due to the no slip condition being selected
for this model. The no-slip condition results in a velocity being zero through walls. When considering
pipe flow, the flow speed is at it’s highest at the center, hence a skewness cannot be observed and is
due to the logarithmic term in the annulus flow calculation. The fully developed flow will be parabolic
due to velocity decreasing near the boundary regions. The velocity at the boundary region is subject
to viscous shear stresses that will also be investigated for the airfoil analysis in section 2.2.9.

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2. Case
2
–
Supersonic
Airflow
over
Airfoils

In this section, two airfoils are considered for simulation in a virtual wind tunnel at supersonic
velocities. Various incidence angles are considered for the purpose of visualizing the flow around the
airfoils. The Diamond wedge (section 2.1) and the RAE2822 (section 2.2) airfoils are considered in
this investigation.
2.1. Diamond
Wedge

2.1.1. Modeling
Geometry

Figure 16 – Diamond Wedge Geometry with Chord=0.5m and 10° Semi-Wedge
Figure 17 – Domain Size of L=2.8m & H=2.2m (a) and 3D view of domain (b)
2.1.2. Mesh
Conditions
and
Substantiation

Mesh Variable Overset Mesh Rationale
Base Size 0.05m Refined to investigate shear effects at the walls and
the wedge boundary.
Minimum Proximity 0.05 The relative distance to the target surface, and is a
percentage of the base size.
Minimum Quality 0.01 Specifies the minimum allowable face quality as a
percentage to the base size.
No of Prism Layers 2 In order to investigate shear effects at the wedge
boundaries.
Prism Layer stretching 1.5 Expansion ratio of prism layers.
Prism layer 20% of base
(Abs size 0.01m)
In order to investigate shear effects at the wedge
boundaries.

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Surface Growth Rate 1.3 Growth of surface elements not in contact with wedge
face elements.
(Abs size 0.0125m)
General surface elements not in contact with wedge
face elements.
Relative Target Size 100% of base
(Abs size 0.05m)
Aimed size of surface elements not in contact with
wedge face elements.
Volumetric Control 1 Cone (Expansion) Overset mesh refinement of the trailing cone of the
blockage - see Figure 18b.
Volumetric Control 2 Block (Refinement) Mesh refinement localised around the blockage - see
Figure 18c and Figure 19.
Table 5 - Mesh Properties for Overset Mesh
Figure 18 - Mesh Visualization - Overview (a), Cone (b) and Block refinement (c)
Figure 19 – Block Mesh Refinement (a) and Wedge Mesh Profile (b)
2.1.3. Physical
and
Boundary
Conditions

Initial and Flow conditions Value
Pressure 101325pa
Thermal Conductivity 0.0260305W/m-k
Density (Air at 20°C) 1.205 kg/m^3
Turbulent Prandtl Number 0.9
Turbulence Intensity 0.01
Turbulence Viscosity Ratio 10
Velocity (Initial Conditions) [X478, Y0.0, Z0.0] m/s
Velocity 478 m/s = Mach 1.4
Table 6 – Flow properties and Boundary Conditions for Diamond Wedge

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2.1.4. Physics
Models

Model Rationale
Two-Layer All y+ Wall
Treatment
Selected automatically with K-Epsilon Turbulence models. When this option
is active the reference velocity is iteratively computed in accordance with the
wall and boundary stress consideration.
Realizable K-Epsilon
Two-Layer
Selected automatically with K-Epsilon Turbulence models.
K-Epsilon Turbulence Used for Turbulence modelling in STAR-CCM, could also use K-Omega,
Spalart-Allmaras, Boundary Layer transition or Large Eddy simulations.
Reynolds-Averaged
Nervier Stokes
For modelling viscous flows and viscous boundary layers.
Turbulent Turbulent Reynolds number, as flow is supersonic.
Coupled Energy The implicit unsteady approach used in Coupled flows is alternative to the
Explicit Unsteady flows. It offers an iteration approach using time-steps.
Ideal Gas A hypothetical gas whose molecules are assumed to occupy negligible
space and have zero interactions. A gas which obeys the gas laws precisely:
PV=nRT
Coupled Flow As with Coupled Energy.
Two Dimensional Conversion to 2D plane carried out (see Figure 21 through Figure 30).
Constant Density Low Reynolds number / low velocity hence considered incompressible.
Stopping Criteria 1500 Iterations (Actual convergence approx. 800 – see Figure 20)
Table 7 - Physics solver models for Diamond Wedge
2.1.5. Running
the
Solver

Figure 20 - Residuals for solver convergence for Diamond Wedge at 0° Incidence
2.1.6. Post
Processing

Once a converged solution is apparent, vector and scalar plots can be generated to show the Mach
number, velocity and pressure over and around the wedge airfoil. The solutions of the simulations
have been carried out for many angles of incidence (-20°, -15°, -10°, -5°, 0°, +5°, +10°, +15° and
+20°).

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2.1.7. Mach
No
Visualization

Figure 21 - Diamond Wedge Mach No peak at 1.79 for 0° Incidence
Figure 22 - Diamond Wedge Mach No peak at 1.9 for -5° (a) and +5° Incidence (b)
Shock Wave
Expansion Fan

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One can observe from Figure 21 though Figure 25 that the angle of incidence is of great significance
to the flow speeds around the wedge airfoil. It can also be observed that due to the symmetry of the
airfoil, the negative angles of attack have very similar flow properties to those with positive incidence.
2.1.8. Pressure
Visualization

Figure 26 - Diamond Wedge Pressure peak at stagnation of 1.24 E+5 Pa for 0° Incidence
Stagnation

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Figure 27 - Diamond Wedge Pressure peak at stagnation of 1.9 E+5 Pa for -5° (a) and +5° Incidence (b)

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2.1.9. Discussion
and
Analysis

One can observe from the pressure profiles of the various incidence angles in Figure 26 through
Figure 30 that the stagnation will always remain at the leading point of the diamond wedge due to its
geometry. As will be later observed, a rounded leading edge will result in the stagnation point moving
to the most frontal region of the airfoil. Furthermore, the pressure variation around the airfoil will
result in a lower lift coefficient compared to the chambered RAE2822 that is later described. Another
observation worth noting is the pressure at the stagnation point is almost twice that of the reference
atmospheric pressure. Symmetry of pressure distribution between negative and positive incidence is
once again followed due to the airfoil symmetry across the chord-wise plane.
2.1.10. Conclusion
for
Diamond
Wedge
Airfoil
Case

Overall the outcomes of this investigation are conclusively valuable as it demonstrates the variation
of velocity and pressure surrounding the diamond wedge airfoil at many incidence angles. The aims
set out during the start of this paper have been achieved and a thorough understanding of numerical
modeling has been established. By simulating the diamond wedge airfoil in many orientations, one
can simply use this technique on any airfoils of subject matter. The RAE2822 airfoil is considered in
the subsequent section where a similar approach and modeling techniques are used to investigate
the flow properties of the airfoil at various incidence angles.
2.2. Airfoil
Section
RAE2822

2.2.1. Importing
Geometry

Figure 31 – Importing RAE2822 Airfoil Geometry into STAR CCM

P a g e | 16
2.2.2. Mesh
Conditions
and
Substantiation

Figure 32 – Mesh Import into STAR CCM for RAE2822 Airfoil – Boundary (a) and Detail Mesh (b)
Figure 33 – Detail View of RAE2822 Mesh showing Prism layers for boundary layer detail
2.2.3. Physical
and
Boundary
Conditions

As per Table 6 in section 2.1.3.
2.2.4. Physics
Models

As per Table 7 in section 2.1.4.
2.2.5. Running
the
Solver

Figure 34 -- Residuals for solver convergence for RAE2822 at 0° Incidence

P a g e | 17
2.2.6. Post
Processing

Once a converged solution is apparent, vector and scalar plots can be generated to show the Mach
number, velocity and pressure over and around the wedge airfoil. The solutions of the simulations
have been carried out for many angles of incidence (-20°, -15°, -10°, -5°, 0°, +5°, +10°, +15° and
+20°).
2.2.7. Mach
No
Visualization

Figure 35 – RAE2822 Mach No peak at 1.75 for 0° Incidence
Figure 36 – RAE2822 Mach No peak at 1.9 for -5° (a) and +5° Incidence (b)
Figure 37 – RAE2822 Mach No peak at 2.0 for -10° (a) and 2.1 for +10° Incidence (b)
Stagnation Expansion fan

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Figure 38 – RAE2822 Mach No peak at 2.2 for -15° (a) and 2.3 for +15° Incidence (b)
Figure 39 – RAE2822 Mach No peak at 2.5 for -20° (a) and +20° Incidence (b)
One can observe from Figure 35 though Figure 39 that the angle of incidence is of great significance
to the flow speeds around the RAE2822 airfoil. Increasing speeds can be observed where the flow is
forced across the expansion regions of the airfoil. These expansion fans are a series of waves that
cause the flow to form around the airfoil and speed up. Flow separation can also be predicted in
Figure 38b and Figure 39b and is further investigated in section 2.2.9.
2.2.8. Pressure
Visualization

Figure 40 – RAE2822 Pressure peak at stagnation of 2.1 E+5 Pa for 0° Incidence
Stagnation

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Figure 41 – RAE2822 Pressure peak at stagnation of 2.1 E+5 Pa for -5° (a) and +5° Incidence (b)

P a g e | 20
2.2.9. Velocity
Visualization
and
Areas
of
concern

Figure 45 – RAE2822 Velocity Vectors for +15° Incidence
Figure 46 – RAE2822 Velocity Vectors for +15° Incidence – Stagnation point move
Figure 47 – RAE2822 Velocity Vectors for +15° Incidence – Initiation of Flow Separation at Trailing Edge

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Figure 48 – RAE2822 Velocity Vectors for +15° Incidence - Acceleration from 0.09m/s to 530m/s at Leading Edge
Figure 49 – RAE2822 Velocity Vectors for -20° (a) and +20° (b) Incidence – Flow Separation at trailing Edge
Figure 50 – RAE2822 Velocity Vectors for +20° Incidence – Reversing Flow and Eddy Initiation
Figure 51 – RAE2822 Velocity Vectors for +20° Incidence - Reversing Flow and Eddy Initiation

P a g e | 22
2.2.10. Sample
Lift
and
Drag
Coefficient
Monitor
Plots

Figure 52 – Lift Coefficient (a) and Drag Coefficient (b) monitor plot for RAE2822 at 0° Incidence
2.2.11. Discussion
and
Analysis

One can observe from the pressure profiles of the various incidence angles in Figure 40 through
Figure 44 that the stagnation will always remain at the leading edge of the RAE2822 airfoil. The
rounded leading edge results in the stagnation point moving to the most frontal region of the airfoil
when the incidence angle is at its extremes. Furthermore, the pressure variation around the airfoil is
designed for continual lift even when at low incidence angles and is due to the chambered shape of
the RAE2822 airfoil. Another observation worth noting is the pressure at the stagnation point is
almost twice that of the reference atmospheric pressure.
The velocity vector profiles for the +15° and +20° incidence angles as observed in Figure 45 through
Figure 51 show the gradual separation of the airflow at the trailing edge. The shear stress interaction
can be clearly observed in Figure 51, where any further increase in incidence angle will result in
complete flow separation, trailing edge vortices and reduced lift capability.
2.2.12. Conclusion
for
RAE2822
Airfoil
Case

Overall the outcomes of this investigation are conclusively valuable as it demonstrates the variation
of velocity, pressure and flow direction surrounding the RAE2822 airfoil at many incidence angles.
The aims set out during the start of this paper have been achieved and a thorough understanding of
numerical modeling has been established. By simulating the diamond wedge airfoil in many airfoils,
one can simply use this technique on any airfoils of subject matter. The RAE2822 airfoil is stimulating
to study due to its traditional chambered shape; its shape allows one to ponder on the flow properties
surrounding the entire airfoil. The velocity vector simulations carried out highlight the importance of
boundary layers, shear stresses in proximity to airfoils and the velocity variation when approaching
flow separation.

P a g e | 23
3. Case
3
–
Convective
Heat
Transfer
from
a
Heat
Source
of
a
Radiator

within
an
Enclosed
Room

A room with a radiator is simplified as two-dimensional, in a plane that is parallel to the gravity
direction and within which the flow is anisotropic. In the 3D direction, the geometry and flow are
assumed as isotropic and therefore 3D effects are ignored.
3.1. Modeling
Geometry

Figure 53 - Input Geometry into STAR CCM with Radiator of 0.2 x 0.5m and a wall separation of 0.1m on each edge
3.2. Mesh
Conditions
and
Substantiation

Mesh Variable Mesh Value Rationale
Base Size 0.05m Large element size to allow for faster computing
and convergence.
Radiator Proximity
Size
0.025m Manual refinement of the mesh near radiator
boundary to accurately determine the thermal
convection flows – see Figure 54
No of Prism Layers 6 In order to investigate shear effects at the wall and
radiator boundaries.
Prism Layer stretching 1.8 Expansion ratio of prism layers.
Prism layer 20% of base
(Abs size 0.01m)
In order to investigate shear effects at the wall and
Surface Growth Rate 1.3 Growth of surface elements not in contact with wall
elements.
(Abs size 0.0125m)
In order to investigate shear effects at the wall and
Relative Target Size 100% of base
(Abs size 0.05m)
Aimed size of surface elements not in contact with
radiator elements.
Table 8 - Mesh Properties for Thermal Convection case.

P a g e | 24
Figure 54 – Manual Radiator Region Mesh Refinement (a), 3D Refined Mesh (b) and 2D Output Mesh (c)
3.3. Physical
and
Boundary
Conditions

Initial conditions and
material properties.
Value
Pressure 101325pa
Thermal Conductivity 0.0260305W/m-k
Specific Heat (Air) 1003.62 J/kg-k
Radiator Temperature 40°C = 313.15 K
Room Boundary Temperature 20°C =293.15 K
Table 9 - Air properties and Temperature Conditions for Thermal Convection case
3.4. Physics
Models

Model Rationale
Coupled Energy The implicit unsteady approach used in coupled flows is alternative to the
Explicit Unsteady flows. It offers an iteration approach using time-steps.
Ideal Gas A hypothetical gas whose molecules are assumed to occupy negligible
space and have zero interactions. A gas which obeys the gas laws precisely:
PV=nRT
Coupled Flow As with Coupled Energy.
Two Dimensional Conversion to 2D plane carried out (see Figure 56 through Figure 59).
Gravity [X0.0, Y-9.81, Z0.0] m/s2
. Without consideration of gravitational effects, the
pressure variance between floor to ceiling cannot be modeled and is deems
an essential part of convection hear flow.
Laminar Convection with such small temperature gradients are considered highly
laminar, the velocity of convection flow is generally within the single digit
magnitude in m/s.
Steady Steady time simulation to observe the flow properties at a single steady state
time step.
Stopping Criteria 25000 Iterations (Actual convergence approx. 3000 – see Figure 55)
Table 10 - Physics solver models for Thermal Convection case

P a g e | 25
3.5. Running
the
Solver

Figure 55 - Residuals for solver convergence for Thermal Convection case
3.6. Post
Processing

Once a converged solution is apparent, velocity vectors, scalar temperature plots among others can
be generated to show the convective heat flow within the room and its flux properties.
3.7. Temperature
Visualization

Figure 56 – Temperature visualization showing Ambient of 300 K = 26.85°C (a) and peak at Radiator of 313.15 K
3.8. Velocity
Visualization

Figure 57 – Velocity visualization showing Max Velocity of 0.227 m/s (a) and relative difference of 0.158 m/s (b)

P a g e | 26
3.9. Density
and
Pressure
Visualization

Figure 58 – Visualization for Density difference of 0.0768 kg/m
3
(a) and Relative Pressure difference of 3.55 Pa (b)
3.10. Vorticity
and
Enthalpy
Visualization

Figure 59 – Visualization for Vorticity peak of 5.8/s (a) and Enthalpy at Radiator of 3.143 J/kg (b)
3.11. Discussion
and
Analysis

One can observe from Figure 56, that the constant temperatures set at the radiator and wall is stable
as initially set. It is worth noting that the velocity of 0.227 m/s in Figure 57a is very small and is a
result of the convective flow being laminar due to very small temperature gradients. If the
temperature difference between wall and radiator were increased, the flow velocity would increase.
Based on the above analysis, one can conclude that this type of analysis can be used in thermal
engineering applications, weather forecasting and component design involving sources and sinks of
thermal energy.
The density variation observed in Figure 58a is a direct result of the temperature difference observed
in Figure 56. The higher temperature regions near the radiator has a lower density than its
surroundings; for this reason the localized pressure is higher, hence the out-flow of thermal energy is
apparent. Using the 2nd
law of thermodynamics as a principal argument, one can justify the
increasing entropy in the room as a result of the thermodynamic arrow of time. In addition, the
temperature of the radiator and room will equalize if the temperatures were set to initial and non-
constant as in the above case.
Overall the heat flux in the room is of a circulation type as justified by the Vorticity plot in Figure 59a.
If this scenario was set up in 3-dimensions, the heat flux and vectors would be of a more complex
type spanning in x, y and z components. To improve the heat flow within the room, the radiator can
be oriented in a way where the surface area in vertical direction is larger. Increasing surface area of
radiators has been around for many years, with applications ranging from vehicle cooling, to
domestic radiators designed with complex fins. Additionally as convection is the primary source of
heat transfer throughout the room when compared with molecular interaction and radiation, a small
fan heater would be much more efficient at maintaining the room temperature by creating active
flows.

P a g e | 27
3.12. Conclusion
for
Thermal
Convection
Case

One can observe from the simulated data for the Thermal Convection case how the general flow
inside the room is of a rotating type and is due to the location of the radiator, temperature difference
between ambient conditions and it’s size. The flow follows a clockwise rotation as observed in Figure
57 and is due to the rising of hot air from the radiator, contacting the ceiling and flowing across the
right-hand side of the room where it slowly cools and falls due to an increase in density while cooling.
The air flow cycle repeats with the above clock-wise description; if this case were to be set up in 3-
dimensions, a more complex and intuitive observation can be observed where the same effects will
now be in 3 directions. The complexity of rotating flows due to the rising of hot air and falling of cool
air would require a significant increase in computing power and would take a long time to converge.
The industrial applications of such thermal analysis can be used in geological weather studies,
thermal engineering for engines, HVAC (Heating, Ventilation and Cooling), in civil engineering for
improving building efficiency and a significant use in aircraft and spacecraft cabin ventilation where
weight and energy are of great importance.
References

Ogawa, K., Ito, S., and Kuroda, C. (1980). "Laminar-Turbulent Velocity Profile Transition for Flows in
Concentric Annuli, Parallel Plates and Pipes." Journal of Chemical Engineering of Japan, Vol. 13, pp.
183-188.
White, F.M. Fluid Mechanics. Boston: McGraw-Hill, 2003. Print.

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