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Flow over NACA Airfoil using Converge CFD

GGokula Krishnan A21 May 2020
CFD
  • Objective:
    • To simulate the flow over NACA 2412 airfoil for various Angles of Attack(AoA) and compare the results.
  • Theory:
    • Aero-foil or airfoil is a basic unit of an aircraft wing, whose characteristics are responsible for the creation of major part of the lift and drag of the aircraft as a whole. There are many aero-foil profiles available of-late, these are unique in characteristics. These characteristics are obtained by varying one or more parameters of the aerofoil shown in the below figure. Here, chord line is the line joining the leading and trailing edge of the airfoil profile; camber line is the curve formed by the locus of the points halfway between the upper and the lower surface.
    • The nomenclature of an aero-foil is done based on the following convention:
      • It may be of a four digit or five digit type, here four digit is used, i.e., NACA 2412.
      • The first digit represents the maximum camber in percentage of chord. Here, 2`=>` maximum camber is 2% of chord.
      • The second digit represents the position of maximum camber in tenths of chord. Here, 4`=>`position of maximum camber is 0.4 times the chord.
      • The third and fourth digits represent the maximum thickness in percentage of the chord. Here, 12`=>`maximum thickness is 12% of the chord.
    • The forces acting on the aero-foil are as follows:
      • Lift Force, the force acting along the Y-axis, i.e., perpendicular to the direction of flow. The formula is as follows:
        • `L=1/2*rho*A*v^2*C_l", where "L" - Lift force in N, "``rho " - Density of the fluid in kg/"m^3", "``A" - Wing area("m^2") = Chord length"(m)" * span"(m), "``v" - Velocity of the fluid in m/s, "``C_l" - Lift coefficient"`
      • Drag Force, the force acting along the X-axis, i.e., parallel to the direction of flow.The formula is as follows:
        • `D=1/2*rho*A*v^2*C_d", where "D" - Drag force in N, "``rho " - Density of the fluid in kg/"m^3", "``A" - Wing area("m^2") = Chord length"(m)" * span"(m), "``v" - Velocity of the fluid in m/s, "``C_d" - Drag coefficient"`
      • Thrust Force is the force that propels the aircraft or aero-foil forward. Weight is the downward force, due to gravity.
    • Note: The lift and drag coefficients are dimension-less parameters which varies based on the AoA of the aerofoil, Reynolds number of the flow and various other parameters.
  • Procedure:
    1. The NACA 2412 aero-foil based wing geometry is created in SolidWorks as shown in Fig. 1, using the NACA 2412 data available in "airfoil-tools" website, and saved as STL file.
    2. The STL file is imported into Converge Studio and the virtual wind tunnel is created as shown in Fig. 2 & 3 respectively. (Note: The dimensions of the wind tunnel are based on a convention that the length must be 50 times the characteristic or chord length of the aero-foil and the height 30 times. Here, the chord length is 0.1`m`, so the length of the wind tunnel is 5`m` and the height is 3`m`)
    3. Then the boundaries are flagged such as, inlet, outlet, top-bottom wall, front and back 2D boundaries, and most importantly the aerofoil profile.
    4. The inputs for simulation are given as follows:
      1. Materials, i.e. the fluid medium, here air is chosen.
      2. The type of the solver is density based solver with compressible flow and a transient one.
      3. The simulation time parameters are selected. The time for simulation is set as 0.5s based on the 'flow through time'.
        • `"Flow through time "= "Length of the tunnel" / "Velocity of the fluid"``=> "Flow through time"= 5/30.4=0.16s`(Note: The determination of velocity is discussed in the next point)
        • Generally, the time period for simulation is approximately three to four times that of the flow thru' time, so it is set to `~~`0.5s.
      4. The regions and initial conditions are specified as follows:
        • The velocity of the flow along the x-direction is given as 30.4 m/s in correspondance to Reynolds number value of 200000. `(Re=(v*l_c)/nu,"where "v" - Velocity of flow, "l_c" - chord or characteristic length, "nu" -Kinematic viscosity"``=> 200000=(v*0.1)/(1.52*10^-5) =>v=(200000*1.52*10^-5)/0.1=30.4m"/"s)`
        • The initial pressure is set to atmospheric pressure.
      5. The boundary conditions are specified for all the boundaries such as the fluid flow velocity for inlet, atmospheric pressure for outlet, 2D boundary condition for front and back, symmetric boundary for top-bottom walls and stationary wall boundary for aero-foil profile.
      6. Firstly, `RNG" "k-epsilon` turbulence model is used for one simulation and compared with `k-omega" "SST` turbulence model(as it is preferred for external flows - from theory). Then, the best one for this simulation is selected and the same is applied for the rest.
      7. Now, base mesh grid size of 0.05m is selected after various trials. In addition, the Adaptive Mesh Refinement(AMR) feature of Converge CFD is used to refine the cells satisfying SGS criterion of 0.009`m`/`s` with 5 levels of embeding, this is done in order to refine the cells near the aero-foil profile and the regions of interest.(Note: The velocity gradient change is anticipated near the aero-foil profile, windward side and leeward side, so this feature is used in order to refine the cells in these regions to get a clear picture, as the simulation progresses)
      8. In Outputs and post-processing, the wall-boundary outputs are included so that the lift and drag related forces can be recorded.
    5. Then the input files are exported to a folder and the converge executable file is run to generate the output files.
    6. The output files are post-processed and viewed thru' Paraview software.
    7. The same procedure is repeated for 5`deg`, 10`deg`, 15`deg` Angle of Attack and the results are compared.
  • Observations and inferences:
    • Effect of turbulance model:
      • Comparison of drag force for different turbulence models:
        • Observation:
          • Both possess some amount of instability(indicated by ups and downs in the graph as the simulation furthers), but it is quite less in case of `k-omega" "SST` model.
        • Inference:
          • This is because the near wall treatment is better in case of `k-omega" "SST` model. Hence, it produces better results as the requirement is a wall boundary based one, i.e. drag.(Note: Since it is a test run, it is run only for 0.18s)
      • Comparison of lift force for different turbulence models:
        • Observation:
          • The drag plot as in `k-omega" "SST` turbulence model is almost stable, whereas in case of `RNG" "k-epsilon` turbulence model there are a few ups and downs.
        • Inference:
          • This is again accorded to the better near wall treatment in `k-omega" "SST` model. Therfore, it produces better wall boundary based output, i.e. lift.
      • Note:
        • From the above inference, it is clear that the `k-omega" "SST` turbulence model produces better results as the wall treatment is better, i.e near the boundary.
        • Moreover, it is better for predicting the vortex and recirculation related flows.
        • Also that, this model behaves like `RNG" "k-epsilon` turbulence model when away from the boundary and like `Standard" "k-omega` turbulence model when near the boundary. Thus, the solution is better comparatively.
        • Hence it is chosen as the turbulence model for all the following cases.
    • Case 1: Angle of Attack=1`deg`
      • Velocity Contour:
        • Observation:
          • The velocity of air above the upper surface of the aero-foil is higher(indicated red) than that of the lower surface.
          • The velocity at the leading edge and the trailing edge are very low(indicated deep blue).
        • Inference:
          • The velocity increases near the upper surface as the air gets diverted from its path and goes along with the stream of air actually flowing in the upper surface. Hence leading to summing up of velocities.
          • The velocity is very much lower at the leading edge as some amount of air strikes the edge and looses its kinetic energy.
          • The velocity is little lesser in the trailing edge as a partial vacuum is created near it. This is accorded to the boundary layer formation in the aerofoil surface. Moreover, as the AoA is smaller the meeting of air, after being obstructed by the aerofoil, in the leeward side takes place at shorter distance itself. This causes a small dip in velocity in the leeward side(indicated light blue).
      • Pressure Contour:
        • Observation:
          • The pressure at the leading edge and the trailing edge is quite higher(indicated red).
          • The pressure of air above the upper surface of the aero-foil is lower(indicated blue) than that of the lower surface.
        • Inference:
          • Some amount of air strikes the leading edge as it approches the aero-foil, which causes the increase in pressure at this location.
          • As the velocity is higher in the upper surface there is a pressure drop in this region, accorded to the less accumulation of fluid near this surface.
      • Mesh:
        • Observation:
          • The mesh refinement is higher near the aero-foil and lower in other regions.
        • Inference:
          • As the AMR feature is used the refinement pattern is as shown above.
          • The change in velocity gradient is higher near the aero-foil surface and some regions near the leading and trailing edge. Hence, the refinement is higher in these places.
          • The level of embeding is 5, which has increased the clarity of information in the contours.
    • Case 2: Angle of Attack=5`deg`
      • Velocity Contour:
        • Observation:
          • The velocity of air is even higher than the previous case in the upper surface of the aero-foil(indicated red). Also that the region of high velocity is concentrated near the leading edge.
          • The thickness of the low velocity region(indicated light blue) behind the trailing edge has increased.
          • The velocity at the leading edge and the trailing edge are very low(indicated deep blue).
        • Inference:
          • The velocity is higher than the previous case because of the increase in AoA which diverts more amount of air towards the upper surface of the aero-foil.
          • The velocity is very much lower at the leading edge as some amount of air strikes the edge and looses its kinetic energy.
          • The velocity at the trailing edge and the region behind it are low, which depicts the formation of a considerable boundary layer thickness and hence a partial vacuum. As this thickness has increased,it leads to the increase in the thickness of low velocity region.
      • Pressure Contour:
        • Observation:
          • The pressure of air in the lower surface is far higher(indicated red) than that in the upper surface.
          • Pressure is very high at the leading edge(indicated deep red).
        • Inference:
          • As the air strikes the lower surface of the aero-foil, the kinetic energy of air is converted into pressure energy. Hence, as the air strikes the pressure on the lower surface increases leading to a positive pressure in the region.
          • As the velocity is higher in the upper surface, the pressure is lower, leading to a negative pressure. This combination of positive pressure in the lower surface and negative pressure in the upper surface leads to the production of lift.
          • Some amount of air strikes the leading edge as it approches the aero-foil, which causes the increase in pressure at this location.
      • Mesh Generation:
        • Observation:
          • Similar to the previous case, the mesh refinement is higher near the aero-foil and lower in other regions.
        • Inference:
          • The same reason is valid for this case too, i.e. the AMR feature used in refinement of the mesh.
          • The level of embeding is 5, which has increased the clarity of information in the contours.
    • Case 3: Angle of Attack=10`deg`
      • Velocity Contour:
        • Observation:
          • The maximum velocity has increased compared to the previous case.
          • The high velocity region is concentrated near upper part of the leading edge.
          • The velocity at the leading edge and the region of upper surface near the trailing edge are very low(indicated deep blue). Also that the thickness of this region has also increased.
        • Inference:
          • The maximum velocity has increased, which is accorded to the increase in AoA that obstructs air passing by and the air gets diverted to the upper part at higher velocities.
          • The boundary layer thickness has increased to a greater extent which leads to the concentration of high velocity region near the leading edge.
          • The negligible velocity near the upper surface of the trailing edge is also due to the increase in boundary layer thickness. This causes a scarce amount air to be present in this region, and also that a partial vacuum is created.
      • Pressure Contour:
        • Observation:
          • Similar to the previous case, the pressure of air in the lower surface is far higher(indicated red) than that in the upper surface.
          • Pressure is very high at the leading edge(indicated deep red).
        • Inference:
          • The same reason holds true for this case too, i.e., the air striking the lower surface causes the increase in pressure.
          • The pressure difference between the upper and the lower surface is higher, hence higher lift.
          • Some amount of air strikes the leading edge as it approches the aero-foil, which causes the increase in pressure at this location.
      • Mesh:
        • Observation:
          • Similar to the previous case, the mesh refinement is higher near the aero-foil and lower in other regions.
        • Inference:
          • The same reason is valid for this case too, i.e. the AMR feature used in refinement of the mesh.
          • The level of embeding is 5, which has increased the clarity of information in the contours.
    • Case 4: Angle of Attack=15`deg`
      • Velocity Contour:
        • Observation:
          • The velocity in the upper surface of the aero-foil is very low(negligible)-indicated blue.
          • The flow in the leeward side is uncertain.
          • High velocity can be found in some portions.
        • Inference:
          • The low velocity in the upper surface is due to the flow separation and recirculation of fluid as the AoA has increased.
          • Flow recirculation or reversal is a phenomenon in which the vortices(continuous rotating fluid or wakes) are formed. This happens as the contact of fluid with the upper surface is lost. Hence, this leads to the turbulence flow in the upper surface.
          • As this vortex moves in the direction of flow, it leads to formation of high velocities in some locations. This leads to a wave-like pattern in the leeward side.
          • Moreover, this flow separation leads to additional drag, called pressure drag and the lift decreases correspondingly. This condition when the flow separation takes place, the drag increases and the lift decreases is called as stalling condition.
      • Pressure Contour:
        • Observation:
          • The pressure at the leading edge is quite higher(indicated red).
          • The pressure of air above the upper surface and the regions near the trailing edge of the aero-foil are lower(indicated blue).
        • Inference:
          • Some amount of air strikes the leading edge as it approches the aero-foil, which causes the increase in pressure at this location.
          • The pressure in the upper surface and the regions near the trailing edge are low as the vortices are formed.
          • This leads to the increase in pressure drag on the aero-foil, which acts in the direction of flow of air as specified earlier.
      • Mesh:
        • Observation:
          • The mesh refinement is higher near the aero-foil and lower in other regions.
        • Inference:
          • The AMR feature is used, by the virtue of which the above refinement pattern is obtained.
          • The change in velocity gradient is higher near the aero-foil surface and some regions near the leading, trailing edge, and the regions of the wake. Hence, the refinement is higher in these places.
          • The level of embeding is 5, which has increased the clarity of information in the contours.
    • Comparison of various Parameters for different AoA:
      • YPlus Vs Time:
        • The Y+ value is a dimension-less parameter. It denotes the dimension-less distance between the node of the first cell and the boundary. It signifies where actually is the cell located in the boundary layer:
          • Viscous sub-layer if Y+ value is lesser than 10
          • Buffer layer if Y+ value is between 10 and 30
          • Turbulence layer or log-law region if Y+ value is between 30 and 300.
        • Here the Y+ value is in the range of 60 to 100, which comes under the turbulence or log law region of the boundary layer which is desirable. Thus, the mesh refinement is done optimally in order to capture the near wall phenomenon with clarity.
      • Lift Force Vs Time:
      • Angle of Attack Lift force (L) (Avg of last 0.2s) in N Lift Coefficient(`C_l= (2L)/(rho*A*v^2)`)
        1 18.1 0.668
        5 40.1 1.475
        10 46.0 1.692
        15 34.8 1.280
        The `C_l` for the first case is calculated as follows: `(2*18.1)/(1.1765*0.05*30.4^2)=0.668` (Note: Here, the area(A) is calculated using the formula: `"chordal length * span" = 0.1"*"0.5= 0.05m^2`).
      • Similarly, it is calculated for other cases and plotted as follows:
        • Lift Coefficient Vs Angle of Attack:
          • Observation:
            • The lift coefficient increases as the AoA increases to an extent(till 10 deg) then decreases(at 15 deg).
          • Inference:
            • The above pattern of increase and then decrease in lift coefficient after a certain degree is accorded to the stalling condition.
            • As the AoA increases the lift force increases due to the increase in pressure difference between the upper and the lower surface of the aero-foil(till 10 deg), which in turn increases the lift coefficient.
            • The dip in lift coefficient(after 10 deg) is due to the decrease in the lift force due to the vortex(wake) formation in the leeward side of the aero-foil . This is called the stalling of the air-foil. So, it can be concluded that this aero-foil reaches stalling condition at a particular angle between 10 deg to 15 deg.
      • Drag Force Vs Time:
      • Angle of Attack Drag force (D) (Avg of last 0.2s) in N Drag Coefficient(`C_d= (2D)/(rho*A*v^2)``
        1 0.616 0.023
        5 1.430 0.053
        10 3.830 0.141
        15 10.900 0.401
        The `C_d` for the first case is calculated as follows: `(2*0.616)/(1.1765*0.05*30.4^2)=0.023` (Note: Similar to the previous case, the area(A) is calculated using the formula: `"chordal length * span" = 0.1"*"0.5= 0.05m^2`).
      • Similarly, it is calculated for other cases and plotted as follows:
        • Drag Coefficient Vs Angle of Attack:
          • Observation:
            • The drag coefficient increases continually as the AoA increases.
            • The increase is very high(almost 2 to 3 times) between 10 deg and 15 deg AoA.
          • Inference:
            • As the angle of attack increases, the skin friction increases, which increases the drag force, which in turn leads to an optimal increase in drag coefficient(till 10 deg).
            • The increase in drag coefficient is very high between 10 and 15 deg as an additional drag force called the pressure drag increases due to the vortex formation in the leeward side of the aero-foil. Again, this is called the stalling condition. The plot suggests that the stalling takes place in between 10 and 15 deg.
  • Result:
    • Thus the flow over the NACA 2412 air-foil is simulated for various angles of attack and the comparative study done.
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