SONIC BOOM MINIMIZATION OF AIRFOILS THROUGH COMPUTATIONAL FLUID DYNAMICS AND COMPUTATIONAL ACOUSTICS

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1 SONIC BOOM MINIMIZATION OF AIRFOILS THROUGH COMPUTATIONAL FLUID DYNAMICS AND COMPUTATIONAL ACOUSTICS Michael P. Creaven * Virginia Tech, Blacksburg, Va, Advisor: Christopher J. Roy Virginia Tech, Blacksburg, Va, Abstract This project analyzes 2-D, inviscid, steady supersonic flow over different designs at Mach 2.2 while at 60,000ft. The s tested have sharp leading and trailing edges. The shapes range from diamond to convex to a combination of the two. A hybridization of Computational Fluid Dynamics (CFD) and Computational Acoustic simulations are used to obtain values for the lift coefficient, drag coefficient, and maximum overpressure. The trends obtained from this very specialized case show that flat bottomed s generate the smallest overpressures, and the highest lift to drag ratios. The reason for this is that the thinner shapes create smaller disturbances in the flow and thus generate smaller shock waves, which in turn reduce the drag, and the overpressure. This study does not take into consideration structural issues, viscosity, differing angles of attack, or 3-D effects. * Undergraduate Student, Aerospace and Ocean Engineering, 125 Lee Hall, mcreaven@vt.edu Associate Professor, Aerospace and Ocean Engineering, 330 Randolph Hall, cjroy@vt.edu Nomenclature L = chord length x = axial coordinate y u = maximum distance from the centerline to the upper surface of the with respect to L y l = maximum distance from the centerline to the lower surface of the x u = location of yu from the leading edge x l = location of yl from the leading edge δ = shape function of the P = free stream pressure δp = over pressure M = Mach number T = temperature I. Background The main challenges facing commercial supersonic flight are the increased drag due to shock waves and the resulting sonic boom. Both of these issues need to be addressed and overcome before supersonic commercial flight is considered a viable option. Current Federal Aviation Administration regulations prohibit commercial aircraft from reaching supersonic speeds over the United States. The reason for this ban is the loud boom that is generated by aircraft flying close to or faster than the speed of sound. As an aircraft flies through the atmosphere it creates pressure waves in the air which travel at the speed of sound and propagate away from the aircraft. As the speed of the aircraft increases the distance between waves becomes smaller. At supersonic speeds the plane is traveling faster than the pressure waves thus the pressure waves compress and form a thin shock wave. The sudden change from high pressure in front of the shock wave to low pressure behind the shock wave is what generates a sonic boom. 1 The pressure over 1

2 the ambient pressure is referred to as the overpressure. This loud boom can be intense enough to damage weak structures, as well as cause significant disturbances in human and animal populations. It is predicted that federal regulations will set the maximum allowable overpressure to 0.4 psf. The first country to produce an economically viable aircraft that meets federal regulations will be purchased by airlines from countries around the world. 2 The idea of minimizing a sonic boom has been around since the In fact even the idea of boomless supersonic flight has been mentioned. There has been much research done in the area recently, most notably the shaped nose cone configuration of the F-5E 3, and the Gulf Stream Quiet Spike. 4 Both of these were in conjunction with NASA Dryden, and demonstrated that the sonic boom could be shaped such that the intensity was significantly decreased. Experimental tests and demonstrations such as these are extremely expensive, and require a great deal of preparation. 3 The use of CFD is advantageous in many ways, but primarily due to its lower cost compared to experimental tests. Another benefit of CFD analysis is that it eliminates flow field disturbances as seen in wind tunnel testing, were pressure waves generated by the tunnel walls create an unrealistic and unfavorable test environment. The two main challenges in applying CFD to the sonic boom problem are the need for accurate prediction of the shock wave structure in the near-field region and the prevention of numerical (i.e. non-physical) dissipation of the sonic boom pressure wave in the far field. These challenges are addressed with a combination of careful numerical error estimation and comparison with existing experimental sonic boom data. II. Introduction This study uses commercially available computational software to approximate the propagation of pressure waves from an traveling at an assumed cruise of a supersonic transport of Mach number 2.2, at 60,000ft, and at a 0 o angle of attack. The purpose of this study is to analyze different supersonic configurations and their effects on lift, drag, and overpressure (δp). Airfoils were analyzed because they are the most essential aspect to an aircraft and have received much less attention in sonic boom studies than fuselages. Two shapes were analyzed on the upper surface, convex and diamond and these same two shapes were analyzed on the lower surface. A total of four different surface combinations were possible and thus 4 different shapes. The thicknesses (y u, y l ) and the thicknesses location (x u, x l ) were varied between each configuration. A mesh was created for each of these configurations, and a grid study was performed to ensure that the created grids were adequate resolved. The grids were run through a CFD simulation that returned the L/D ratio and the pressure profile at the end of the near-field, which in turn was input into an acoustics code which returned the sonic boom pressure footprint on the ground. The results show that thinner s with a flat lower surface have the highest L/D ratios and lowest peak overpressures. III. Airfoil Configurations Four different configurations were used. These configurations can be broken up into four surfaces, a round upper surface, a diamond upper surface, a round lower surface, and a diamond lower surface. The combination of these four surfaces results in the four different configurations or series: the 1 series has a round upper and lower surface, the 2 series has a diamond upper and lower surface, the 3 series has a round upper surface and a diamond lower surface, and the 4 series 2

3 has a diamond upper surface and a round lower surface. The different configurations can be seen in Figure 1. Each configuration is a function of the maximum thickness on the upper surface (y u ), the maximum thickness on the lower surfaces (y l ), and the location of these thicknesses x u, and x l respectively. Figure 2 shows an described by these parameters. The parameters have been grouped into a single number for convenience. An example is The format of the number is as follows: series number (3), y u (0.08c), y l (- 0.06c), x u (0.5c), x l (0.25c). If y l is negative the negative sign is placed in front of the entire number. The upper surface of the 1 and 3 series s are described by the piece-wise equation (1). y x = y u cos x + L 2 x u π 2x u y u cos x + L 2 x u π 2 L x u, x x u, x > x u (Eq 1) The lower surface of the 1 and 4 series s are described by equation (2). y x = y l cos x + L 2 x l π 2x l y l cos x + L 2 x l π 2 L x l, x x l, x > x l (Eq 2) The upper surface of the 2 and 4 series s are described by equation (3). y x = y u x u x, x x u y u (L x) L x u, x > x u (Eq 3) The lower surface of the 1 and 4 series s are described by equation (4). y x = y l x l x, x x l y l (L x) L x l, x > x l (Eq 4) The s used in this study have y u values that range from 0.02c to 0.08c, y l values that range from -0.04c to 0.04c. The x u and x l values range from 0.25c to 0.75c. IV. Setup The s that were designed and tested are designed for a supersonic transport similar to the Concorde. The flight altitude is at 60,000ft, and the cruise Mach number is 2.2, and the angle of attack is 0 o. In this project it is assumed that the wing is inside the Mach cone of the aircraft, and does not experience free stream conditions. The conditions inside of the Mach cone were estimated by solving a conical flow problem for the nose of the Concorde. The results were a Mach number of 2.15, pressure of Pa, and a temperature of 220.8K. The simulations also assumed that the flow was inviscid, and the fluid was an ideal gas. V. Grid Generation There were a total of 60 different designs. Each was imported into Gridgen, a commercial grid generation program. Two 321x129 node blocks were generated around the, one along the upper surface and the other along the lower surface, thus the final mesh for each configuration was a 321x257 node grid. The grid dimensions are 5 chord lengths above and below the, half a chord length in front of the and 11 chord lengths behind the. Figure 3 and 4 show one of the grids that was generated, and Figure 5 shows a schematic of the distribution of the nodes along the boundaries of the lower block. The dimensions are based on the height which extends 5 chord lengths above and below the. This is the distance were diffraction, or interaction between shock waves and expansion waves becomes negligible. 5 The length was then selected to make sure that the shocks were captured within the 5 chord height domain. 3

4 VI. Grid Study The grid is a simple rectangle for the reason that other shaped grids would not iteratively converge sufficiently. Grids that were directly lined up with the shock and expansion waves were tested, however these shaped grids only converged 3.5 orders of magnitude. It was determined that this lack of convergence was due to the cells being skewed, which was due to the steep angle of the domain. Before the majority of the simulations were run a grid study was performed to ensure that the generated grids were adequate. It was performed on the top block of the (2 series, with an xu value of 0.5c, a yu value of 0.02cand a flat lower surface) grid. The simulation conditions were set to the Mach cone conditions, and the simulation was run until the scaled residuals converged 13 orders of magnitude. A refinement factor of 2 was selected, thus a coarse mesh of 161x65, a medium mesh of 321x129, and a fine mesh of 641x257 were tested. Because the simulations were assumed to be inviscid, it was possible to calculate an exact solution. Figure 6 shows the regions were the exact solution was compared to the simulated result, and Figures 7 and 8 show the percent error between the exact and simulated results, H = 1 corresponds to the fine mesh, and H = 4 corresponds to the coarse mesh. The study shows that the medium mesh is accurate enough, and that the lift and drag coefficients stop oscillating after the residuals have been resolved 5 orders of magnitude. VII. Computational Fluid Dynamics The flow calculations were performed using Fluent, a finite volume solver. In this case Fluent was set to use an implicit method, second order upwind method, and a density based solver. The fluid was defined as an ideal gas with a molecular weight of kg/kmol, and a specific heat capacity of J/kg K. The within the grid was assigned a wall boundary condition, and the edge of the grid was assigned a pressure far-field boundary condition. The boundaries as well as the domain were initialized with the interior Mach cone values of M=2.15, P=7757.6Pa, and T= The CFL number is a parameter used to define the stability criteria for time marching processes. In this project a CFL number between 2 and 6 was used was used for each case. The case was run until the residuals converged at least 6 orders of magnitude, and took about 15 minutes per case. Figure 9 shows the convergence of one of the grids. The lift and drag coefficients of the were recorded, and the 1-D pressure distribution along the bottom of the grid was saved and used as the input for the acoustic code. VIII. Geometric Acoustics An acoustic wave propagation code was used to propagate the near-field pressure disturbances through the far-field to the ground. The solution to the near field problem is used as an input for the wave propagation code which solves for the sonic boom footprint on the ground. The wave propagation program used is PCBoom4. It is based on the original Thomas code and uses geometrical acoustics and ray tracing to propagate waves. 6 The program is initialized with a height of 60,000ft, and the atmospheric distribution of a standard day. The model length was set to 60.5ft which is the mean aerodynamic chord of the Concorde. The trajectory is a straight line as if cruising. The results from the program give the footprint of the sonic boom, and the maximum overpressure can then be recorded. A footprint of the can be seen in Figure 10. 4

5 IX. Results 60 s were tested at a simulated cruising condition at an altitude of 60,000ft and a Mach number of 2.2 (values from the interior of the Mach cone were used). CFD was used to compute the near-field solution and computational acoustics was used to compute the far-field solution. The computational near-field flow solution shows that there is an attached oblique shock wave at leading edge then a expansion waves at the points of maximum thickness(x u, x l ), and then another shock wave at the trailing edge. This is the general solution trend of all of the cases. Figure 11a and 12a show the Mach number contours and the pressure contours of a single solution in the extreme near field. These figures show that the Mach number drops and the pressure increases, through the first shock wave. Then the Mach number increases and the pressure decreases through the expansion wave. The Mach number then drops, and the pressure increases through the trailing edge shock wave. Figures 11b and 12b show the complete near field. These figures show that past 0.5 chord lengths away. The shock and expansion waves begin to interact. By 5 chord lengths away the interactions become negligible, and it is assumed there is no more diffraction. The pressure distribution from the edge of the grid is extracted and run through PCBoom4. Figure 10 shows a sonic boom footprint of an. The footprint of this is representative of the other footprints, in that the behavior is similar, the only differences are the peak δp and the time interval. The peak δp, is defined as the maximum overpressure, in a signature. Effect of Upper Thickness The effect of the upper surface on the L/D ratio and the maximum peak overpressure on the ground was evaluated. 16 s were tested varying the shape, thickness, and location of thickness of the upper surface while the lower surface was maintained flat and shapeless. The results show that thinner s with an x u value of 0.5c have higher L/D ratios, and lower peak δp as can be seen in Figure 13. The results also show that a diamond upper surface produces a higher L/D ratio than a convex upper surface, and that the upper surface shape is independent of the maximum overpressure. Effects of Lower Thickness The shape of the upper surface was varied between diamond and convex, however the y u and x u values were fixed at 0.08c and 0.5c respectively. The bottom of the was varied between shape, thickness (y l ), and thickness location (x l ). Figure 14 shows the L/D and peak δp values as functions of the lower surface thickness (y l ) and location of maximum thickness (x l ) for a 1 series. The behavior shown in this figure is very similar to the behavior of the 2, 3, and 4 series s. The results from all four series show that the maximum L/D is achieved when the lower surface is flat, and consequently the minimum overpressure also occurs when the lower surface is flat. However if the lower surface is not flat the results suggest that the location of thickness (x l ) should be at 0.5c because at 0.5c the L/D is maximized and the δp is minimized compared to the other xl locations. Figure 15 shows the L/D and δp values as functions of the shape, and thickness (y l ), while the thickness location (x l ) is kept constant at 0.5c. When the lower surface is flat the L/D is maximum, and the peak δp is minimum. The general trends in this figure show that a diamond upper surface (2 and 4 series) produces a higher L/D ratio, and that a convex lower surface (1 and 4 series) produce a lower peak δp. 5

6 Physics The above results suggest a general theory that a thinner produces a higher L/D and a lower peak δp. This makes sense because a thinner would generate weaker shocks. In supersonic flight the majority of drag is due to wave drag, 7 thus weaker shock waves translate to less drag and higher L/D ratios. Stronger shock waves also create a larger overpressure, and when propagated to the ground create a larger peak overpressure. Therefore a thinner is generates higher L/D ratios and lower peak δp because it generates weaker shock waves. X. Future work This was a very narrow and specialized project. The leading and trailing edges of the were sharp. This allowed the shocks in the near field solution to be perfectly attached. The shocks may have also been perfectly attached since the solution was calculated assuming inviscid flow. For a supersonic case inviscid flow is not a poor assumption, however it is still an assumption and thus may have affected the results. The structure of the was not considered, the optimum was a diamond shaped with a 0.02c maximum thickness( ). The L/D ratio of this at the specified conditions is 2.1, and the peak overpressure is 0.001psf. This shape has not been structurally analyzed, however it visually appears too thin to be a realistic /option along the entire span of the wing. Another aspect that was not considered was the effect of angle of attack. These cases were run at a cruise condition were it was assumed that the aircraft would be at 0 o angle of attack. In future work these limitations will be addressed. The leading and trailing edges will be rounded to represent an actual. Structural analysis will be preformed to evaluate how realistic an design is. The flow calculations will take viscous effects into consideration. The numeric results will be verified with wind tunnel tests. XI. Conclusion This project analyzed different supersonic s using computational methods. The s were tested at what is an assumed cruise for a supersonic transport (altitude = 60,000ft, M =2.2). The near-field is calculated using CFD, and the far field is calculated using a geometric acoustics code. The L/D ratio is taken from the near field solution, and the peak overpressure is taken from the farfield acoustics solution. The results show a general trend that thinner s produce weaker shocks which produce larger L/D ratios and smaller peak overpressures. More specifically the results show that a diamond shaped upper surface, with a flat lower surface produces the maximum L/D and minimum peak δp. The convex lower surface produces the maximum L/D and minimum peak δp after the flat lower surface configuration. These results appear to be correct for this limited case. Angles of attack other than zero were not tested, structural analysis was not performed to ensure that configurations were realistic, the s had unrealistic sharp edges, and the flow was assumed inviscid. These limitations will be considered in future work, and under these new conditions the conclusions may change. 6

7 Percent Error XII. Figures Figure 1. Different Airfoil Series Figure 4. View of the grid around the (Flow is to the left) Figure 2. Airfoil Schematic Figure 5. Schematic of the node distribution along the boundaries of the lower face Figure 6. Schematic of the Tested Regions around the 10-2 Pressure Figure 3. The 321x257 node grid that was used to run the simulation P2 P3 P H Figure 7. Percent Error in the Pressure 7

8 Percent Error 10-1 Mach Number M2 M3 M H Figure 8. Percent Error in Mach number Figure 11a. Mach Contours around Figure 11b. Mach contours around Figure 9. Iterative convergence Figure 12a. Pressure contours around Figure 10. Sonic Boom Footprint of

9 δp and L/D δp and L/D Effects on δp and L/D for different Lower Surface Thicknesses L/D T Location at 0.25c L/D T Location at 0.5c Figure 12b. Pressure contours around Effects on δp and L/D for Different Upper Surfaces L/D T Location at 0.75c at 0.25c at 0.5c L/D T Location 0.25c (1 series) L/D T Location 0.5c (1 series) L/D T Location 0.25c (2 series) L/D T Location 0.5c (2 series) 0.25c (1 series) 0.5c (1 series) 0.25c (2 series) 0.5c (2 series) Lower Thickness (percent chord) at 0.75c Figure 14. L/D ratios and δp values, for a 1 series with varying lower thicknesses (y l ) and thickness locations (x l ). The upper surface is kept at y u = 0.08c, and x u = 0.5c Upper Thickness (percent chord) Figure 13. L/D ratios and δp values, for 1 and 2 series s with varying upper surface thicknesses (y u ) and thickness locations (x u ). The lower surface is kept at y u = 0, and x u = 0.5c. 9

10 δp and L/D Effects on δp and L/D for Different Configurations on the Lower Surface L/D 1 series L/D 2 series L/D 3 series L/D 4 series δp 1 series δp 2 series δp 3 series δp 4 series 4 Donald C. Howe, Kenrick A. Waithe, Edward A. Haering. Jr. Quiet Spike TM Near Field Flight Test Pressure Measurements with Computational Fluid Dynamics Comparisons, AIAA paper , January Laflin, K.R., Klausmeyer, S.M., Chaffin M., A Hybrid Computational Fluid Dynamics Procedure for Sonic Boom Prediction. AIAA Plotkin, K.J., and Grandi, F., Computer Models for Sonic Boom Analysis: PCBoom4, CABoom, BooMap, CORBoom. Wyle Report WR 02-11, June Bertin J.J., Cummings R.M. Aerodynamics For Engineers 5 th edition. Pearson Prentice Hall, Upper Saddle River NJ Lower Thickness (percent chord) Figure 15. L/D ratios and δp values, for different series with varying lower thicknesses (y l ). The upper surface is kept at y u = 0.08c, x u = 0.5c, the lower surface thickness is kept at x l =0.5c. XIII. References 1 John D. Anderson. Modern Compressible Flow 3 rd edition. New York NY, National Research Council. Commercial SUPERSONIC Technology The Way Ahead. Washington D.C Joseph W. Pawlowski, David H. Graham, Charles H. Boccadoro, Peter G. Coen, Domenic J. Maglieri Origins and Overview of the Shaped Sonic Boom Demonstration Program, AIAA paper , January