WARSAW UNIVERSITY OF TECHNOLOGY FACULTY OF POWER AND AERONAUTICAL ENGINEERING
DEPARTMENT OF MACHINE DESIGN
Practical / Internship – Project Project Presented By: Emeka Chijioke St209323
Aerodynamic Characteristics Characteristics of a NACA 4412 Airfoil
Supervisor: dr inż. Sławomir Kubacki Warsaw, September 2010
1. Introduction Airfoil geometry can be characterized by the coordinates of the upper and lower surface. It is often summarized by a few parameters such as: maximum thickness, thickness, leading edge , trailing edge and nose radius as shown in figure 1. One can generate a reasonable airfoil section given these parameters.
Figure.1: Outline of an airfoil
2. Objectives
The objectives of this project was to study the pressures and performances of a NACA 4412 airfoil and compare it with its real experimental results (a flying hot- wire measurements). Determining the characteristics, like pressure coefficient and distributions along the airfoil.
3. Turbulence models fluid dynamics modeling where a Turbulence modeling is the area of fluid simpler mathematical mathematical model is used to predict the effects of turbulence. turbulence. There are various mathematical mathematical models used in flow modeling to understand turbulence.
The turbulence model I used was one equation Spalart Allmaras to predict boundary layer separation on a NACA 4412 airfoil at the position of maximum lift ( = 15°) and mach number (= 0.05). Flow conditions around the airfoil were built up by finite volume analysis using FLUENT 12 software by Fluent Inc. –
The free stream velocity was set to 18.4 m/sec for the turbulence models for direct comparison with the flying hot-wire measurements.
4. Geometry The geometry was done in Gambit software. I copied the airfoil data file NACA 4412 from the NACA website. The airfoil naca4412.dat file looks like this below:
Data file 61 2 0 . 0000000 0 . 0005000 0 . 0010000 0 . 0020000 0 . 0040000 0 . 0080000 0 . 0120000 0 . 0200000 0 . 0300000 0 . 0400000 0 . 0500000 0 . 0600000
0 . 0000000 0 . 0023390 0 . 0037271 0 . 0058025 0 . 0089238 0 . 0137350 0 . 0178581 0 . 0253735 0 . 0330215 0 . 0391283 0 . 0442753 0 . 0487571
0 0 0 0 0 0 0 0 0 0 0 0
Figure 2 below shows the airfoil as it was imported into Gambit software. How I did it? From Main Menu > File > Import > ICEM Input ...
Form File Name, browse and select the naca4412.dat file. Select both Vertices and Edges under Geometry to Create: since these are the geometric entities needed, deselect Face. Click Accept .
Figure.2: NACA 4412 geometry from Gambit
Coming to the data file above, the first line of the file represents the number of points on each edge (61) and the number of edges (2). The first 61 set of vertices are connected to form the edge corresponding to the upper surface; the next 61 are connected to form the edge for the lower surface.
The chord length, c for the geometry in naca4412.dat file is 1 m, so x varies between 0 and 1. NOTE: If
you are using a different airfoil geometry specification file, note the range of x values in the file and determine the chord length c. You will need this later on.
5. Far field Boundary Conditions The purpose of far field boundary conditions is to represent the state of flow at a large distances from the source of disturbance. However, large outer boundary distances are difficult to model. Either the number of grid point is too large resulting in an unacceptable increase in computing time or the grid cells are largely stretched reducing the accuracy of the computation.
In an external flow such as that over an airfoil, I defined a far field boundary and meshed the region between the airfoil geometry and the far field boundary. The far field boundary was well placed away from the airfoil and ambient conditions was used to define the boundary conditions at the far field. The farther we are from the airfoil, the less effect it has on the flow and so more accurate is the far field boundary condition. The far field boundary I used is the line ABCDEFA in figure 3 below. C is the chord length.
Figure.3: Far field boundary geometry
6. Computational Mesh I meshed each of the 3 faces separately to get a final mesh. Before the mesh face, I define the point distribution for each of the edges that form the face i.e. the edges was first meshed. The mesh stretching parameters and number of divisions for each edge was selected based on t hree criteria:
1. clustering points near the airfoil since this is where the flow is modified the most; the mesh resolution as we approach the far field boundaries can become progressively coarser since the flow gradients approach zero.
2. Close to the surface, most resolution is needed near the leading and trailing edges since these are critical areas with the steepest gradients.
3. Smoothening the transitions in mesh size; large, discontinuous changes in the mesh size significantly decrease the numerical accuracy. The edge mesh parameters I used for controlling the stretching are successive ratio, first length and last length. The successive ratio R is the ratio of the length of any two successive divisions in the arrow direction as shown below. Go to the index of the GAMBIT User Guide and look under Edge>Meshing for this figure and accompanying explanation.
F igur e. 4: T he fi nal r esul tant mesh of the geometr y
Separately I would like to state how I meshed the airfoil in particular: I split the top and bottom edges of the airfoil into two edges so that there will be better control of the mesh point distribution. Figure 5 below shows the splitting edges.
F igur e.5: Split edger of the air foil
I did this because a non-uniform grid spacing will be used for x<0.3c and a uniform grid spacing for x>0.3c. To split the top edge into HI and IG, select Operation Tool pad > Geometry Command Button > Edge Command Button > Split/Merge Edge
Make sure Point is selected next to Split Within the Split Edge window.
Select the top edge of the airfoil by Shift-clicking on it. You should see something similar to figure 6 below:
F igure 6
I used the point at x=0.3c on the upper surface to split this edge into HI and IG. To do this, enter 0.3 for x: under Global. If your c is not equal to one, enter the value of 0.3*c instead of just 0.3.For instance, if c=4, enter 1.2 You should see that the white circle has moved to the correct location o n the edge.
F igure 7
Figure 8
Figure 8 above shows the zoomed grid around the airfoil from fluent software.
7. Results and Discussion: The Meshed geometry was exported from Gambit and was read into the Fluent solver software. Calculations and observations was made. Computation was done both for higher and lower mach numbers . It was computed for in viscid case, and with turbulence Model (Spalart Allmaras).
RESULT FOR LOWER MACH NUMBER FLUENT: Run fluent with 2d option and read mesh created in GAMBIT. Solver settings: density based, implicit ,2D, steady.
DEFINE ► MODEL ► VISCOUS, INVISCID. DEFINE ► MATERIALS, Ideal gas. DEFINE ► OPERATING CONDITIONS, set OPERATING CONDITIONS = 101325 Pa Boundary Conditions: DEFINE ► BOUNDARY CONDITIONS
Set farfield1 , farfield2 and farfield3 to the Pressure far field type.
Pressure far field 1,2,3 : Gauge pressure =0pa, Mach number = 0.05 constant, X component of flow direction = 0,9659m/s constant Y component of flow direction = 0,2588m/s constant –
–
Modified turbulent viscosity = 0.001
.
Figure 9 below shows the convergence residuals plot for inviscid case at design incidence ( = 15°) and mach number (= 0.05).
18.4 m/s T = 298K Spallart allmaras vt= 17.29 m/s –
–
Figure. 9.
Figure 10 below shows the velocity contour of the airfoil at the leading edge , the velocity of the upper surface is faster than the velocity on the lower surface. On the leading edge. The fluid accelerates on the upper surface as can be seen from the change in colors of the vectors.
Figure. 10: Vector Plot of Velocity Magnitude at the leading edge
Figure 11. shows the velocity contour of the airfoil at the trailing edge . On the trailing edge, the flow on the upper surface decelerates and converge with the flow on the lower surface
Figure. 11: Vector Plot of Velocity Magnitude at the trailing edge
Figure 12 below shows the convergence residuals plot for Spalart Allmaras case for lower mach number 0.05
Figure. 12
Figure 13 below shows the velocity magnitude of the airfoil with lower mach number 0.05 for spalart Allmaras model. As we can see there is high velocity on the upper surface of the airfoil near the leading edge, this includes that there is low pressure at this region. At the lower surface near the leading edge we see the stagnation point at low velocity. At the upper surface of the airfoil near the trailing edge we can see a stall. A stall is a reduction in the lift coefficient generated by an airfoil as angle of attack increases. This occurs when the critical angle of attack of the airfoil is exceeded. The critical angle of attack is typically about 15 degrees which was used in this computation, but it may vary significantly depending on the airfoil.
Figure . 13: Contour Plot of Velocity Magnitude
Figure14 shows the wall pressure distribution (Cp) for NACA 4412, as computed by the Spalart Allmaras model, inviscid case and compared with the experimental results. Both case cases gives similar result on pressure coefficient as in figure 14. In general, the pressure on the surface of an aerofoil is not uniform. From Figure 14 for = 15° it is seen that at this angle the reduction in the pressure on the upper surface (suction side), in particular near the leading edge, is the primary cause of the lift created. From x/c = 0.4 to the trailing edge the value of Cp varies only slowly. As shown from the flying hot-wire results (Experimental result), in the rear position of the aerofoil between x/c = 0.7 to 1 there exists an intermittent low separation near the trailing edge region. From the foregoing, the following conclusions may be drawn: (i) At = 15° the lift is principally caused by the pressure reduction on the front part of the upper surface and to a smaller extent by a pressure increase on the lower surface. (ii) We can see that the S.A model and the inviscid case produces similar result to that of experiment result.
2 1 0 -0.2
0
0.2
0.4
0.6
0.8
1
1.2
-1
pressure coeff. For Spalart-Allmaras invincid case
-2
Pressure coeff. For Exp.
-3 -4 -5 -6
Figure . 14: Comparison of Pressure coefficients
8. RESULT FOR THE CASE OF HIGER MACH NUMBER(1.5) Here the grid around the wall of the airfoil was redefined. The data, properties and boundary conditions added is the same as in the case of lower mach number(0.05), the only change is the input of the value of the high mach number which is 1.5. This was inserted in fluent solver. By increasing the grid numbers and changing the type of arranging mesh, refining the mesh, around the wall of the airfoil a proper y+ value is obtained, and the following results was obtained for higher mach 1.5 with Spalart Allmaras model : The range of y+ if from 2 20 as seen in figure .15. –
Figure. 15: y+ range from 2 - 20
Figure.16: Redefined grid around the wall of the airfoil
Figure .17 : convergence residuals plot for Spalart Allmaras case for higher mach number 1.5. Figure. 18 below shows the contour plot of Mach number on the airfoil, as we see there a shock on the upper surface of the airfoil at about x/c 0.2. Stagnation point is at leading edge. ≈
Figure.18: Contour Plot of Mach Number
Figure.19: below shows the pressure distribution around the airfoil, the lower curve is the upper surface of the airfoil, while the upper curve is the lower surface of the airfoil. The lower curve have a negative pressure coefficient as the pressure is lower than the reference pressure.
Figure.19: Pressure distribution around the airfoil
9. Conclusion
Compressible flow past NACA 4412 has been studied in detail using a turbulence model computation(Spalart Allmaras). Computational results are found to agree reasonably well with available experimental data. Conclusion can be drawn from the convergence of both inviscid case and S.A model, for lower mach number 0.05 as shown in figures 9 and 12 respectively. It is observed that we have better convergence in the case of S.A model than that of inviscid case. The reason is that there is unsteady flow around the airfoil for inviscid case, whereby causing slow and bad convergence history.
