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 =𝑃4𝜂

−𝑅! +𝑏! − 𝑎!

𝐿𝑛 𝑏𝑎

𝐿𝑛 𝑅 +𝑎!𝐿𝑛 𝑏 − 𝑏!𝐿𝑛 𝑎

𝐿𝑛 𝑏𝑎

Equation 1 -–Velocity Profile for Fully developed flow

Or similarly:

𝑢(𝑟) =14𝜇

−𝑑𝑑𝑥

𝑝 + 𝜌𝑔𝑧 𝑎! − 𝑟! +𝑎! − 𝑏!

𝐿𝑛 𝑏𝑎

𝐿𝑛𝑎𝑟

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 =16𝑅𝑒

=16150

= 0.10667

Reynolds Number:

𝑅𝑒 =𝜌𝑈𝐷𝜂

Velocity of the flow:

𝑈 =𝑅𝑒 × 𝜂𝜌 × 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)


General surface elements not in contact with wall face elements.

Relative Target Size



Aimed size of surface elements not in contact with wall face elements.

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.

Surface Size 25% of base (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


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.


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


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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.


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


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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.


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)




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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


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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.


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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 radiator boundaries.

Surface Growth Rate 1.3 Growth of surface elements not in contact with wall elements.

Surface Size 25% of base (Abs size 0.0125m)

In order to investigate shear effects at the wall and radiator boundaries.

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.


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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


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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)


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3.9. Density and Pressure Visualization

Figure 58 – Visualization for Density difference of 0.0768 kg/m3 (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.


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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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