CFD Simulations and Wind Tunnel Experiments of a Generic Split-Canard Air-to-Air Missile at High Angles of Attack in Turbulent Subsonic Flow

Transcription

1 AIAA Atmospheric Flight Mechanics Conference August 2011, Portland, Oregon AIAA CFD Simulations and Wind Tunnel Experiments of a Generic Split-Canard Air-to-Air Missile at High Angles of Attack in Turbulent Subsonic Flow Tomi Honkanen 1, Tuomas Tuisku 2 and Antti Pankkonen 3 Aalto University School of Engineering, Espoo, Finland A generic split-canard air-to-air missile was simulated at angles of attack up to 60 degrees in turbulent subsonic flow using open source CFD software package OpenFOAM. The results were compared with aerodynamic data from wind tunnel experiments of the same geometry. The investigated missile represents typical modern canard-controlled shortrange infrared (IR) homing air-to-air missile (AAM). Main emphasis was on the longitudinal aerodynamic characteristics of the missile and the control-effect of the deflected canard fins in subsonic speed range. Motivation for the research was to get aerodynamic reference data for missile flight mechanics modeling. The presented results consist mainly of longitudinal aerodynamic force coefficients and center of pressure graphs at several angles of attack. The results of the CFD simulations are in good agreement with the experimental data. The results provide an excellent basis for expanding the scope of the investigation further. Nomenclature a = speed of sound C X = force coefficient in the x direction C Z = force coefficient in the z direction C M = pitching moment coefficient C = turbulence model coefficient D ref = reference diameter I = turbulence intensity k = turbulent kinetic energy Ma = Mach number U /a p, p = local and freestream static pressure c.p. = center of pressure q = dynamic pressure U 2 Re = Reynolds number U D ref / U, U = local and freestream velocity u = shear velocity w / u, v, w = velocity components in Cartesian coordinates y = distance from wall y + = nondimensional distance (yu )/ 1. Research Engineer, Department of Applied Mechanics, Aerodynamics Research Group, P.O. Box 14400, Sahkomiehentie 4, FI Aalto 2. Research Engineer, Department of Applied Mechanics, Aerodynamics Research Group 3. Research Engineer, Department of Applied Mechanics, Flight Mechanics Research Group x, y, z = coordinate system, x along the body axis, z up and y left when looking along positive x-axis t w = angle of attack = sideslip angle = canard deflection angle = turbulent dissipation rate = absolute viscosity = turbulent/eddy viscosity = kinematic viscosity = air density = shear stress on the wall = bank angle = specific turbulent dissipation rate AAM = air-to-air missile CFD = computational fluid dynamics IR = infrared MPI = message passing interface NV = normalized variable RANS = Reynolds Averaged Navier-Stokes SIMPLE = semi-implicit method for pressurelinked equations SST = shear stress transport TVD = total variation diminishing 1 Copyright 2011 by Tomi Honkanen. Published by the, Inc., with permission.

2 I. Introduction ncreased maneuverability of fighter aircraft has led to the introduction of agile 4 th generation short-range air-to-air Imissiles. These missiles allow wide off-boresight angle engagements to give the advantage of first launch. The missiles can experience high angles of attack and sideslip during the violent post-launch maneuvers. High turn rates are also required in the end-game to counter the evasive action of highly maneuverable modern fighter aircraft equipped with thrust vectoring. Typically air-to-air missiles fly at supersonic speeds. This is also the speed range which is the most emphasized during a missile design process. 1,2 The increased post-launch maneuvering capability of advanced missiles requires aerodynamic effectiveness also in the subsonic speed range. A series of subsonic CFD simulations and wind tunnel experiments on generic air-to-air missile geometry is described in this document. The motivation for the research was to get aerodynamic reference data for rapid modeling methods. The investigation began with thorough preparations and test runs that are described in detail in the master s theses 3,4 by the authors Honkanen and Tuisku. After the testing phase a final series of especially interesting configurations and flight states was planned and executed. This document covers the setup and results of this final series. II. Generic Missile Geometry The generic air-to-air missile of this investigation represents typical modern canard-controlled IR homing shortrange missile. The missile has a spherical tip and a conical nose section. The missile base does not have a boat tail shape so the body diameter is constant after the nose section. The delta-shaped canard fins are located immediately after the nose section in two sets of four. The root section of the first canard fins overlaps the conical nose section by 3.0 mm. Consecutive canard fins also have a 3.0 mm gap between them. The leading edge sweep angle of the canard fins is 45. The canard fins are set in-line with the four tail fins (cruciform configuration). The tail fins are tapered and they have straight leading and trailing edges. The second set of canard fins are movable control surfaces. The first set of canard fins and the tail fins are fixed surfaces. This type of canard fin configuration is called split-canard. Canard-controlled missiles have some notable advantages compared to other configurations. The lift generated by the canard fins produces lots of pitching moment which increases control effectiveness. The delta-shape of the canards is advantageous at high angles of attack because of good stall properties. The split-canard configuration enhances stall characteristics even more because the fixed front fins turn the flow and reduce the effective angle of attack of the second set of fins. 1,2 The main dimensions of the geometry and the coordinate system used in this document is presented in Fig 1. The total length of the missile body is meters and the body diameter is 150 mm. The length of the nose section including the tip is 250 mm. The radius of the spherical tip is 50 mm. The wing span is 510 mm. The cross section of the canard fins is double-wedge with rounded leading and trailing edges (radius is 0.5 mm at root). The chord at root and tip is 200 mm and 20 mm respectively. The maximum thickness is 10 mm for root and 1.0 mm for tip. The tail fins also have a double-wedge tip section but their root section has a constant thickness section between the wedges. The root chord is 350 mm and the tip chord is 170 mm. The maximum thickness is 10 mm for both root and tip sections. The rounded leading and trailing edges have a radius of 0.5 mm. Figure 1. Main dimensions of the missile geometry in mm and the coordinate axes. The origin is located at the center point. y-axis is directed inside the image. 2

3 The base wall of the geometry is flat since the nozzle is not modeled. However, this not the case for the wind tunnel model because of the strain-gauge balance assembly, as explained in section IV.B. This difference in the geometry of the CFD model and the wind tunnel model certainly has an effect on the base pressure drag. Four different configurations of the generic missile were used in the CFD simulations. These configurations are called A, B, C, and D and they are presented in Fig. 2 below. Configuration A is the basic configuration as described before. In configuration B the left and right movable control canard fins have been deflected 15 upwards. In configuration C the second set of canard fins has been removed altogether. Configuration D is similar to configuration C except that the left and right canard fins have been deflected 15 upwards The four configurations make it possible to evaluate the control effect of the canard fins at high angles of attack. It is also possible to compare the split-canard configuration with a more traditional configuration of only one set of canard fins in similar conditions. Wind tunnel measurement data was available for configurations A, B, and C. Figure 2. From left to right: missile configurations A, B, C, and D. III. Computational Approach Open source CFD software package OpenFOAM was used to perform the simulations. OpenFOAM was introduced in 2004 and since then there has been several improved versions with added functionality. 5 Version was used in this investigation. The software package has programs and libraries for wide variety of problems which are not limited to CFD alone. However surprisingly little reference grade public material was found on using OpenFOAM for aerodynamics applications. A. Solver and Turbulence Model Time-independent steady-state approach was chosen to simulate the missile in incompressible and turbulent flow. The practical choice for this problem is the simplefoam solver application of OpenFOAM. This solver was used to solve RANS (Reynolds-Averaged-Navier-Stokes) equations with the finite volume method. This approach is unable to capture the dynamic behavior caused by separating vortices off the sides of the missile body. The selected turbulence model was k- SST with wall-functions. This turbulence model was chosen based on evaluations of different models with simple flat plate and airfoil validation tests. 3 Turbulence models with wall-functions are used with grids of which near-wall cell height is at least y + = 60 (distance to the cell center is half of this). A wall-function based approach is known to have limitations on applications with a high degree of flow separation, which is the case in high angle of attack aerodynamics. In this investigation the computational results were found to be in very good agreement with the experimental data. B. Simulation parameters Simulation parameters were dictated by the properties of the Aerodynamics Research Group s subsonic wind tunnel. Theoretical maximum flow velocity in the tunnel is approximately 70 m/s. Due to detected model vibration at higher angle of attacks, the velocity was limited to U = 45 m/s (Ma = 0.13). The missile model for the wind tunnel experiments was constructed in scale 1:2.5. The Reynolds number referenced on the model s body diameter of 60 mm was approximately 185,000. The dimensions of the computational grids used in the simulations were scaled to match those of the wind tunnel model. In this way both the Reynolds number and the Mach number are close to each other in the simulations and the experiments. Standard sea level atmosphere values were used for the kinematic viscosity and the speed of sound ( = x 10-6 m 2 /s, a = m/s). 3

4 The turbulence intensity I in the wind tunnel was known to be about one percent. This value was also used to calculate the turbulent kinetic energy k used in the simulations as an initial value. The turbulent kinetic energy value of m 2 /s 2 was calculated with Eq. (1). k 3 U I 2 2 (1) The turbulent dissipation rate was calculated with Eq. (2) using the above mentioned value for the turbulent kinetic energy k. The eddy viscosity ratio t / in Eq. (2) was selected to be 100. The value of the turbulence model coefficient C is k t C Since k- SST turbulence model was used in the simulations, an initial value for the specific turbulent dissipation rate was needed instead of. The specific turbulent dissipation rate was calculated with Eq. (3) using the value = 5.68 m 2 /s 3 obtained from Eq. (2). The resulting value is = 208 1/s. 1 (3) C k Since the Mach number was kept constant, the angle of attack was the only parameter that was varied in the simulations. Only symmetrical flight states were studied, so bank angle and sideslip were zero. All four configurations were simulated at = 0, 5, 10, 15, 30, 45, and 60. Grid independency was studied at = 15 and 30 using a fifth grid, which is a coarser version of configuration A grid. Total number of simulations was 30. C. Computational Grids and Boundary Conditions Total of five three-dimensional grids were created using commercial grid generator Gridgen by Pointwise, Inc. Another grid generator called Pointwise from the same company was used to export the grids to OpenFOAM format. Four of the grids correspond to the four different configurations A, B, C, and D described in section II. The fifth grid is a coarser grid of configuration A for grid independency evaluation purposes. All the grids were generated with the wall-function usage in mind. For wall-function turbulence models the distance from the wall to the cell center of the first cell near the wall should be in the logarithmic sub-layer, where 30 < y + < 300. Based on information from multiple sources it was decided to set the distance to lower end of this region. Therefore the distance to the cell center was set to y + = 30 and the height of the first cell to y + = 60. The relation between the dimensional distance y and the nondimensional distance y + is described in Eq. (4). y y 2 y L (4) u Re c The latter form in Eq. (4) was obtained by using the definitions of the shear velocity u and the wall shear stress w. In this form L is a reference length and Re L is the Reynolds number referenced on this length. The reference length was set as the body diameter of the missile model L = D ref = 60 mm. The local friction coefficient c f was obtained with Eq. (5), which is the friction coefficient at the position x of a turbulent flat plate according to Ref 6. Again x = L = D ref was used to calculate c f. L f (2) c f x ln 0.06 Re 2 x (5) 4

5 Based on the calculations, the dimensional height of the near wall cells was set to y 0.3 mm everywhere on the body and fin surfaces. This value was used in all five grids. The total cell count and the number of surface cells for each grid are shown in Table 1. All the grids are hybrid grids which have hexahedral and prism cells. Close-up views of the nose and tail sections of the surface grid of configuration A are shown in Fig. 3. The grid has 160 cells in circumferential direction and approximately 360 cells in axial direction. The canard fins have 40 cells on the chord and 56 cells in spanwise direction. The tail fins have 72 Table 1. The number of total and surface cells. Grid Total Cell Count Surface Cell Count Conf. A 13,007, ,960 Conf. B 14,012, ,144 Conf. C 12,548, ,240 Conf. D 12,551, ,752 Conf. A, 4M 4,275,600 69,056 cells on the root chord and 40 cells on the tip chord. This is due to the use of prism cells on the middle surface section of the tail fins. Several layers of prism cells are also used to coarsen the grid away from missile. These grid dimensions apply roughly to grids B, C, and D also, as can be seen from the total cell count in Table 1. Figure 3. Detail view of the surface grid of configuration A near the nose and tail sections. The quality of the configuration B grid can be considered inferior compared with the other grids due to more cell skewness around the deflected fins. This leaves room for some speculation of grid quality affecting the results. Another small difference in configuration B grid is a small gap (~1 mm) between the missile body and the second set of canard fins. The grid of configuration D also has a gap between the body and the fins. This difference is not considered crucial since the wind tunnel model has these gaps anyway due to the way the model is assembled. The outer boundary of all the grids is cylinder-shaped with a spherical front section. The back wall of the grid is flat. The missile geometry is located in the middle of the grid. The distance from the missile surface to the outer boundary is approximately twenty times the missile length. Cut-out of the grid, and the boundary patches are presented in Fig. 4. Using the k- SST turbulence model requires boundary and initial conditions to be set for the turbulence parameters k,, and t. Boundary and initial conditions are also needed for the pressure and velocity fields. The constant values described in section III.B were used as initial conditions for the entire flow field. The reference pressure p was set to zero. The angle of attack for each case was taken into account by inputting the velocity as three vector components to the boundaries and the internal field. Freestream boundary condition was applied to all outer boundaries. The wall Figure 4. Cut-out of the grid geometry used in the simulations. boundary had different boundary condition depending on the parameter. Velocity was set to zero on the wall (no-slip condition) and zero gradient was applied for pressure. The turbulence parameters were configured as required for the selected turbulence model and wall-functions. D. Solution Methodology Parallel processing was used in the calculations. A cluster network of two to four computers equipped with two quad-core processors each was used. Total number of processor cores for each simulation case varied between 16 5

6 and 32 depending on their availability. The mesh decomposition method used was scotch, which applies a special algorithm to minimize the number of processor boundaries within the mesh. Since no time derivatives were present in the equations, there is no need to define the Courant number when simplefoam solver is used. Time steps are therefore interpreted as iteration cycles. Typically time steps were needed for each simulation case. The cases with high angle of attack demanded more steps before satisfactory convergence was reached. One step took seconds to complete. This time depended heavily on the applied settings and the number of processor cores used. The longest computation time for an individual case was approximately 10 days in one instance. Residuals and aerodynamic force coefficients were tracked during the calculations to determine convergence. The solution was deemed to be converged when the residuals had stabilized and the aerodynamic coefficients were changing less than 0.5 % during the last 500 steps. In cases with high angle of attack some fluctuation was left in the aerodynamic coefficients. This is related to the dynamic effects caused by unsymmetrical flow separation that the selected simulation method is unable to reproduce. The time steps include multiple iterations to solve the system of equations. The number of these internal iterations is controlled by residual tolerances and minimum and maximum limits. The discretization and interpolation schemes and the equation solver parameters must also be specified manually. About iterations were used for the pressure equation per time step using the PCG (preconditioned conjugate gradient) solver. No more than 4-5 iterations were used for the momentum and the turbulence equations. The calculations were started with simple first order upwind discretization schemes for divergence terms to ensure stability of the calculations. These were changed to second order NV/TVD schemes as the solution progressed. The semi-implicit SIMPLE algorithm was used in solving the pressure and momentum equations. Relaxation factors were kept low (lots of relaxation) in the beginning but the factors were increased until the upper limit for them was reached (above this limit the calculation would diverge). This limit was found to be 0.35 for pressure, 0.75 for velocity, and 0.45 for kinetic energy and specific turbulent dissipation rate. IV. Wind Tunnel Experiments The wind tunnel experiments were conducted in the Aerodynamics Research Group s low speed wind tunnel at the Aalto University campus in Espoo. The methods and equipment used in the experiments are detailed in this section. A 1:2.5 scale model of the generic missile was designed and built in-house. An internal 6-degree-offreedom strain-gauge balance was used to measure the aerodynamic forces and moments. The experiments included three configurations (A, B, and C) of the missile geometry described in section II. All configurations were measured at seven angles of attack. A. Properties of the Wind Tunnel The Aerodynamics Research Group s subsonic wind tunnel has a closed-loop. The total length of the loop is 61.4 meters at the center line. The air flow is generated with an electric powered fan. The fan is powered by a DC motor with shaft output of 275 kw. The theoretical maximum flow speed is 70 m/s with an empty test section. The cross section of the test section is square-shaped with clipped corners and its area is 3.67 m 2. The contraction ratio is 7.4:1. The wind tunnel has no cooling system so the energy from the fan increases the temperature. The temperature is also affected by the surrounding environment. B. The Missile Scale Model The geometry of the generic missile, as described in section II, was developed by the Aerodynamics Research Group. For the wind tunnel experiments a scale model was built in scale 1:2.5. The geometry is simplified since no minor details are included. The limitations of the test section size prohibited the use of 1:1 model. It would not have been possible to use higher angles of attack with a model of this size. The flow is not steady in the regions near the tunnel walls, so the practically usable part of the test section is smaller than the actual size. The body parts of the missile model were manufactured of nontreated aluminum (EN AW-6060 T6) pipe which had outer diameter of 65 mm and wall thickness of 10 mm. The pipe was machined until the correct diameter (60 mm) was reached within the desired tolerances. The body is constructed of two parts: the front section and the aft section. The nose section is machined of aluminum bar (EN AW-6063, diameter 65 mm) and joined to the front section of the body using a threaded joint. Two disk-shaped fixtures were manufactured for the installation of the canard fins. One of these fixtures is first installed inside the front section part. The canard fins have 20 mm long shafts at their root which are then inserted through holes on the body into sockets on the fixture part. The fins can be set at any deflection angle and they are tightened to the fixture inside the front section using small hex screws. The process is repeated for the second set of 6

7 canard fins and after this the nose section is screwed to the front section. Approximately 0.5 mm gap is left between the fins and the body surface. The configurations C and D without the second set of canard fins were realized by covering the extra holes on the body with thin aluminum tape. The tail fins are fixed with screws through the aft body section. The canard fins and the tail fins are all manufactured of austenitic stainless steel AISI 316L. This material was chosen due its hardness which should ensure low wear and tear during handling of the fins. Manufacturing of the fins was outsourced due to tight geometric tolerances. The rest of the components were manufactured in own workshop. C. The Measuring Equipment and Accuracy The main instrument in the measurements was a 6-degree-of-freedom strain-gauge balance Rollab I6B114. Small strain-gauges inside the balance measure forces in axial, normal, and side direction, and also pitching, roll, and yaw moments. In this investigation the interest is solely in axial and normal forces and pitching moment because only symmetrical flight states are studied. The limit loads for the balance are presented in Table 2. A calibration conducted prior to the measurements revealed a maximum error of about 1.2 % for the side force component. The error was smaller for the other components. The balance was installed with a fixture inside the aft body section. The support arm manufactured for the balance consists of three separate parts and includes a double swivel mechanism that allows measurement of flight states that have both angle of attack and sideslip. Only angle of attack was varied in this investigation. The support arm was connected to a fixed vertical strut made of steel and covered with streamlined aluminum fairing. The support arm itself acts as an extension to the missile body and definitely has some effect on the flow. At zero angle of attack the arm is completely behind the missile and prevents some of the pressure drop behind the missile and therefore decreases the base pressure drag. At higher angles of attack the arm is exposed in the flow and prohibits the flow from turning freely around the back edge of the missile body. The permanent instrumentation of the wind tunnel measures the impact pressure, the air temperature, and the relative humidity near the test section, and the static pressure in the tunnel room. A computer connected to the system calculates air density, flow velocity and dynamic pressure using the measured parameters. The properties of the sensors are listed in Table 3. The dynamic pressure q was calibrated using available calibration data for an empty test section. The angle of attack was measured using a clinometer. The accuracy of the clinometer is one minute of arc (1/60 of degree). The accuracy of the angle of attack setting is ±5 minutes of arc (1/12 of degree) due to the manual adjustment method. The bank angle was set to zero and checked with the clinometer on the surface of the tail fins. The strain-gauge balance is fixed to the missile body so it has equal bank angle. The canard fin deflection was also measured with the clinometer. A laser was used to verify the deflection angle. However the error in the deflection setting cannot be considered to be less than ±0.5 degrees. The accuracy of the parallelism of the missile body axis with the tunnel walls is also ±0.5 degrees. These inaccuracies combined with manufacturing tolerances inevitably lead to some asymmetry in the wind tunnel model setup. Table 2. The limit loads of the Rollab I6B114 straingauge balance. Component Load Axial force 100 N Roll moment 9 Nm Normal force 600 N Yaw moment 6 Nm Side force 300 N Pitching moment 12 Nm Table 3. Specifications of the wind tunnel sensors. Measured parameter Measuring range Measuring accuracy Impact 0-3,500 Pa ±0.7 Pa pressure Static pressure Relative humidity and temperature 500-1,100 hpa % RH, C ±0.2 hpa ±2 % RH, ±0.1 C D. Measurements Three configurations (A, B, and C) were measured at = 0, 5, 10, 15, 30, 45, and 60. Unfortunately there is no measurement data for the configuration D. The available data is considered sufficient to compare the results. The velocity of the experiments was intended to match that of the simulations. This was not possible at = 60 due to heavy vibration of the model in the tunnel. Instead a lower velocity U = m/s was used. The vibration seemed to be oscillatory and abated for short periods. 7

8 No filtering was done to any data but temporal mean of the measured forces was taken over a period of approximately one minute in all cases. The results presented in section V are based on these average values. The velocity was also slightly lower in the case of configuration C at = 60. The limit load of the pitching moment presented at Table 2 prohibited increasing the velocity beyond U = 44 m/s in this case. A list of the measurement cases is presented in Table 4. Table 4. List of the wind tunnel measurements. Case No. Configuration Angle of attack, deg Velocity, m/s Mach Reynolds number, ref. D ref 1 A ,000 2 A ,000 3 A ,000 4 A ,000 5 A ,000 6 A ,000 7 A ,000 8 B ,000 9 B , B , B , B , B , B , C , C , C , C , C , C , C ,000 Boundary layer transition posed some problems. A transition point cannot be fixed in OpenFOAM and the k- SST turbulence model does not include transition modeling. It was assumed that the boundary layer is always turbulent with this wall-function based model. Therefore it was decided to use boundary layer tripping on the wind tunnel model to ensure immediate turbulent transition. Fine grains of size mm were glued to the tip of the missile and the leading edges of all fins. The grain size was determined with methods described in Refs. 7 and 8. Flow separation scenarios and boundary layer properties of long axisymmetric bodies are explained in Refs. 9 and 10. A laminar boundary layer with separation followed by turbulent reattachment is to be expected at Reynolds numbers as low as the ones in this investigation, if no tripping is applied. 9 V. Results of the Simulations and Experiments The results of the CFD simulations and the wind tunnel experiments are presented in this section. The aerodynamic force and moment coefficients are the most interesting results and they are discussed in detail. Some consideration of possible error sources affecting the results is presented at the end of this section. A. Aerodynamic Force and Moment Coefficients The aerodynamic force and moment coefficients are presented in the coordinate axis system shown in Fig. 1. The mid-point of the missile body and the origin of the coordinate system is located 1,387.5 mm from the tip of the nose. For the scaled missile model this corresponds to 555 mm (total body length 1,110 mm). The strain-gauge balance inside the missile model body has a reference point which fixes its coordinate system location. This reference point is located at 581 mm from the nose and 26 mm aft of the mid-point. OpenFOAM outputs the computational results in its own coordinate system, where the axis orientations differ from the ones used in this document. Therefore separate coordinate system conversions were mandatory for both computational and experimental results to present them in the coordinate system chosen for this document. The aerodynamic forces were converted to nondimensional coefficients using body cross section area and diameter as reference area and length. 8

9 The presented measured results are temporal mean values over a period of approximately one minute. No wind tunnel corrections are applied to the results. 1. Pitching Moment and Pressure Center Location The pitching moment is defined as the moment around the y-axis with positive moment turning the missile nose upwards. Some manipulation of the measured results was necessary to eliminate the effect of the weight of the missile model. This was achieved by taking measurements of the forces and moments at zero velocity and later subtracting these zero values from the results. Because the horizontal distance between the center of gravity of the model and the balance s reference point changes as the angle of attack increases, these zero measurements were conducted before every case. Graphs of pitching moment coefficient vs. angle of attack are presented in Fig. 5. The results for configuration A are shown in graph a). The simulations cover the same range of angle of attack as the experiments. The computational results show good agreement with the experimental data. The only clear exception is at = 45 where the CFD predicts considerably more negative value. The pitching moment is positive until = and again after 55. Graph b) in Fig. 5 shows the results for configuration B. Agreement between the results is good except at = 30 where CFD predicts more negative value. a) b) c) d) Figure 5. Computed and measured pitching moment coefficient vs. angle of attack for configurations A, B, and C are presented in graphs a)-c). The computed result for configuration D is in graph d). The computational results for configuration B show slightly larger pitching moment at low angles of attack but after this the values are smaller than the measured ones. The pitching moment is approximately zero at = 60. The desired control effect of the deflected canard fins (positive pitching moment) is achieved until The effect of the canard fin deflection = +15 vanishes completely after approximately = 30. This can be seen when the results of configurations A and B are compared in graphs a) and b) in Fig. 6. 9

10 The removal of the second set of canard fins has a considerable effect on the pressure distribution of the missile as expected. The pitching moment turns negative at = 5 because larger proportion of total lift is produced by the tail fins. At higher angles of attack the slope of the pitching moment curve changes to positive. Similar behavior is reported for a single canard missile in Ref. 11. The agreement between CFD and the measurements is very good for this configuration. The computational results for configuration D are shown in graph d). Wind tunnel measurements were not conducted for this configuration but the results can be compared to those of configurations B and C. The pitching moment coefficient is positive and the desired control effect is achieved until 11. The computational results of all four configurations are presented in graph a) in Fig 6. Similar presentation of measured data is in graph b). The most interesting fact in these graphs is how the pitching moment curves of configurations with the deflected fins join the curves of configurations with zero canard fin deflection. However there is some discrepancy between the CFD and the measured results of configurations A and B at = 30 and 45. In this case the author considers the measured results to be more accurate than CFD when the quality of the configuration B computational grid is taken into account. As stated before the effect of the canard deflection of configuration B vanishes near = 30. The same phenomenon is seen in the computational results for configuration D. The curve joins that of the configuration C at = 15. This leads to conclusion that with fin deflection of = +15 the split-canard configuration can produce pitching moment at higher angles of attack than the traditional single-canard configuration. The center of gravity (c.g.) of the generic missile is not fixed which prevents investigation of the missile stability with respect to a certain c.g. location. Instead, the location of the center of pressure was calculated. The resultant of the aerodynamic forces lies at the center of pressure (c.p). Even small changes in the c.p. location can have considerable effect on the pitching moment coefficient due to the high normal force values. The nondimensional distance from the moment reference point to the c.p. location X c.p. = x c.p. / D ref is calculated with Eq. (6) where C M is the pitching moment coefficient and C Z is the normal force coefficient. X cp.. a) b) Figure 6. Pitching moment coefficient vs. angle of attack. Results obtained from CFD are combined in graph a) and results from the measurements in graph b). CM (6) C Negative values mean the c.p. is located towards the nose from the reference point (the midpoint of the missile body in this case) and positive values mean the c.p. is located aft of the reference point. Graphs of c.p. location vs. angle of attack are presented in Fig. 7. Z 10

11 In graph a) in Fig. 7 it can be seen that the difference observed between the computed and measured pitching moment coefficient is also visible in the case of the c.p. The results of the normal force coefficient for configuration A in graph a) in Fig. 9 show that the agreement between the computed and measured force coefficient is very good. Therefore it seems that the difference between the CFD and experimental pitching moment is caused by differences in the c.p. location. The exception is point = 60 where the computed normal force is smaller than the measured one. The pitching moments are in good agreement despite of this because the center of pressure is located almost at the midpoint of the missile body at this angle of attack. a) b) c) d) Figure 7. Computed and measured center of pressure vs. angle of attack for configurations A, B, and C are presented in graphs a)-c). The computed result for configuration D is in graph d). Results at = 0 are omitted. In case of the configuration B the agreement between the CFD and measured results is fairly good as can be seen in graph b) in Fig 7. The canard fin deflection in configuration B naturally causes the c.p. to move towards the nose. The small difference on the c.p. location at = 30 explains the difference in pitching moment since the agreement with normal force is very good at this point in graph b) in Fig 9. The small difference in pitching moment between the computed and measured results at = 45 is on the other hand explained by the normal force since the c.p. locations match. It can be seen that the c.p. location is almost identical for configurations A and B beyond = 30. This is even more evident in graphs a) and b) in Fig. 8 where both the computed and measured c.p. curves are presented together. The c.p. locations predicted by CFD are in very good agreement with the measured results for configuration C. The differences between the pitching moments can be explained by looking at the normal forces in graph c) in Fig. 9. The c.p. is located aft of the midpoint for configuration C as predicted by the negative pitching moment. Again only computational data is available for configuration D. The c.p location moves expectedly towards the nose when compared to configuration C at low angles of attack but is identical after =

12 Graphs a) and b) in Fig. 8 show the same behavior described by the pitching moment curves. The c.p. location matches after certain angle of attack despite the canard fin deflection when configurations A and C are compared to configurations B and D respectively. a) b) Figure 8. Center of pressure vs. angle of attack. Results obtained from CFD are combined in graph a) and results from the measurements in graph b). 12

13 2. Normal Force Graphs of normal force coefficient are presented in Fig. 9. The curves of the normal force coefficient are slightly nonlinear up until = 30 for all configurations. After this the measured results still exhibit a positive slope, but the CFD results of configurations A and B clearly have a maximum value somewhere between = It is also possible that the configuration C has such a maximum value in the same range. The measured results of configurations A, B, and C, and the CFD results of configuration D exhibit different behavior. The values of the normal force coefficient increase all the way up to = 60. In this aspect the computational results of configuration D show clearly different behavior to configurations A, B, and C. The known differences between the measured and computational cases at = 60 are the slightly different Reynolds and Mach numbers. a) b) c) d) Figure 9. Computed and measured normal force coefficient vs. angle of attack for configurations A, B, and C are presented in graphs a)-c). The computed result for configuration D is in graph d). In general the agreement between the computational and the measured normal force results seem good but even small differences on the normal force have a great effect on the pitching moment if the change in the c.p. location does not cancel this effect. The computational and experimental normal force coefficient results are shown in their own curve groups in graphs a) and b) in Fig. 10. According to the graphs the normal force values are higher for the split-canard configurations A and B throughout the angle of attack range. The difference to the single-canard configurations C and D stabilizes after = 30. After the same point the effect of the canard deflection of configuration B vanishes and the results for A and B are identical when looking at the measured data. However CFD predicts that normal force of configuration A is larger at high angles of attack. This explains the differences in the pitching moment curves. Similar behavior is seen between the CFD results of configurations C and D. The normal force coefficient of configuration C is larger at = 30 and = 45.but at = 60.the configuration D wins out. It is also possible that if the perceived trend continues, similar reversal happens between configurations A and B soon after =

14 At low angles of attack the results of all configurations are very much as expected. Clearly the configurations with fin deflection provide more normal force than their clean counterparts. At = 0 CFD predicts approximately the same normal force coefficient for configurations B and D so the split-canard is of no benefit yet. This changes immediately at = 5 and at = 10 the difference is clear. At this point the results of configurations A and D are almost equal. At = 15 the effect of the fin deflection of configuration D has vanished compared to configuration C as stated before. The advantage of the split-canard configuration towards the single-canard configuration seems clear especially at high angles of attack. Interestingly this difference seems to become a bit smaller again at = 60. a) b) Figure 10. Normal force coefficient vs. angle of attack. Results obtained from CFD are combined in graph a) and results from the measurements in graph b). 14

15 3. Axial Force The agreement between the computed and measured axial force is not as good as with the pitching moment and normal force. This was expected to some degree due to the differences in the geometry especially at the base of the missile body. The boundary layer transition and flow separation are also probable causes for the differences. Despite these problems the similar trend between CFD and experimental results can clearly be seen in graphs a) and c) in Fig. 11. The axial force coefficient for configurations A and C decreases roughly linearly throughout the angle of attack range. The results predicted by CFD are higher than the measured ones for configurations A and C with the exception of = 45 for configuration A. The base pressure drag is a probable factor here. The CFD prediction of the axial force coefficient for configuration B was dissatisfactory. The axial force is clearly different from the measured values even at = The agreement is better at = 15, 30, and 60 but off almost 20 % at = 45. Since the pitching moment and normal force are in general in fairly good agreement between the computations and measurements, despite the above mentioned differences in geometry, there seems to be a conflict. One possible cause is the viscous part of the CFD solution, but it probably cannot be the only explaining factor. Measured data for configuration D is not available but it can be noted that the axial force coefficient does not change as much throughout the angle of attack range as in case of the other configurations. There is also an unexplained bump in the curve between = 0 and 15. a) b) c) d) Figure 11. Computed and measured axial force coefficient vs. angle of attack for configurations A, B, and C are presented in graphs a)-c). The computed result for configuration D is in graph d). 15

16 The computational and measured results are combined in their respective graphs a) and b) in Fig. 12. The difference in axial force coefficient between the measured results of configurations A and C is quite small. The slightly higher values for configuration A compared to configuration C at smaller angles of attack are partly due to larger wet surface area (greater skin friction) of configuration A. The difference is larger in the CFD results when compared to the measured results. The axial force coefficient is higher for the single-canard configurations at high angles of attack when comparing configurations C and D to A and B. The computational and experimental results both confirm this for configurations A and C, even if differences are small. The curves for configurations B and D are more difficult to analyze due to the lack of experimental data for configuration D and possible quality issues with the configuration B computational grid. a) b) Figure 12. Axial force coefficient vs. angle of attack. Results obtained from CFD are combined in graph a) and results from the measurements in graph b). 16

17 B. Consideration of Error Sources Grid independency was studied briefly by conducting simulations at = 15 and 30 with configuration A. A coarser grid with approximately 4 million cells was generated for this purpose. A thorough grid convergence study was not performed, but instead the results were simply compared to each to other. Table 5 shows the differences between the computed aerodynamic coefficients in percentage points. The prediction of the pitching moment coefficient proved to be most challenging. The normal force coefficients are very close to each other but even Table 5. Differences on the results obtained with grids Conf. A and Conf. A, 4M. C X C Z C M X c.p % -0.1 % +88 % +0.6 mm % 2.2 % -24 % -6.7 mm small differences on the pressure center location lead to noticeable differences on the pitching moment coefficient. On the other hand the absolute value of the pitching moment coefficient is only ~0.15 at = 15 so small variations lead to high difference in percentage points. If the differences on the results between the finer and coarser grid are compared to the differences between the computed and experimental results, it can be seen that on some occasions the results of the coarser grid are in better agreement with the experimental results but on some other points the opposite is true. The grid quality is considered good in general. The checkmesh utility of OpenFOAM reported only small number of minor cell geometry errors. The configuration B grid is inferior to the other grids due to more cells with poor geometry around the deflected canard fins. This is not an issue with the configuration D grid since there is only one set of canard fins. The choice for the first cell height is always difficult when wall functions are used. Variation of the cell height was not possible in the time frame of this investigation. A low-reynolds number turbulence model might perform better with cases which have large scale flow separation. These models would require finer mesh in the boundary layer region which leads to very high cell count if similar surface grid resolution is maintained. The missile scale model and the assembly include several sources for inaccuracies in the experimental results. As explained in section IV.C, setting of the deflection of the canard fins, the angle of attack and bank angle were all verified with a clinometer. This inevitably leads to some asymmetry in the model. The leading and trailing edges of the fins are so thin that rounding is not reproduced exactly. Boundary layer tripping was used on the leading edges of the fins, but OpenFOAM does not provide a method to fix the transition at the exactly same location for the simulations. In fact the effect of the tripping was not verified at all. The strain-gauge balance used in the measurements is quite light compared to the weight of the missile model. Theoretically, the balance itself can bend slightly under load and cause error to the measurements. The error due to bending is not thought to be significant within the limit loads listed in Table 2. The greater problem was the lack of rigidity of the missile-balance joint. This caused the oscillatory vibration effect which prohibited the use of intended velocity at high angles of attack. Despite the fact that the presented results are temporal mean values over a relatively long time period, the effect of the vibration to the results cannot be neglected. The detected vibration had maximum amplitude of about ±1 at = 60. The Reynolds number of the CFD simulations is also different from the experimental cases where the velocity was lower. The support arm and the support structure behind the missile also have an effect on the flow field and possibly even on the tail fins. A separate study of this effect was not conducted. VI. Conclusion A series of CFD simulations and wind tunnel measurements was conducted in order to determine the longitudinal aerodynamic characteristics of an air-to-air missile at high angles of attack in subsonic turbulent flow. Four different missile configurations were studied. The basic configuration, called configuration A, represents a typical modern split-canard short range air-to-air missile. The two side fins of the second set of canards have been deflected 15 upwards in configuration B. Configuration C represents a traditional single-canard missile where the second set of canard fins has been completely removed. The two side fins of the single-canard configuration have been deflected 15 upwards in configuration D. Main emphasis in the investigation was to evaluate the control effectiveness of the deflected canard fins and compare the split-canard and single-canard configurations. Thirty cases were simulated using CFD software OpenFOAM and 21 cases were measured in the wind tunnel. The series consisted of seven angles of attack in the range Experimental data is not available for comparison in case of configuration D, but the agreement between the results is generally good for the other configurations. The differences in pitching moment and normal force curves between the split-canard and single-canard configuration are clear especially at high angles of attack. The pitching moment effect of the canard deflection of 15 seems to 17

18 vanish completely after = 30 in case of the split-canard configuration and already after = 15 in case of the single-canard configuration. Simulation of only one deflection angle is insufficient for making any definitive conclusion on the control effectiveness, but the results are encouraging to expand the scope of the investigation further. This could include variation of the bank angle and other nonsymmetrical flight states. The center of gravity of the generic missile is not defined, so stability was not discussed in this investigation. 18

19 Appendix Tables of results Table 6. Pitching moment coefficient results of the CFD simulations and the wind tunnel experiments. = 0 = 5 = 10 = 15 = 30 = 45 = 60 Conf. A CFD Conf. A EXP Conf. B CFD Conf. B EXP Conf. C CFD Conf. C EXP Conf. D CFD Conf. D EXP n/a n/a n/a n/a n/a n/a n/a Table 7. Center of pressure results of the CFD simulations and the wind tunnel experiments. = 0 = 5 = 10 = 15 = 30 = 45 = 60 Conf. A CFD n/a , , Conf. A EXP n/a Conf. B CFD n/a Conf. B EXP n/a Conf. C CFD n/a Conf. C EXP n/a Conf. D CFD n/a Conf. D EXP n/a n/a n/a n/a n/a n/a n/a Table 8. Normal force coefficient results of the CFD simulations and the wind tunnel experiments. = 0 = 5 = 10 = 15 = 30 = 45 = 60 Conf. A CFD Conf. A EXP Conf. B CFD Conf. B EXP Conf. C CFD Conf. C EXP Conf. D CFD Conf. D EXP n/a n/a n/a n/a n/a n/a n/a Table 9. Axial force coefficient results of the CFD simulations and the wind tunnel experiments. = 0 = 5 = 10 = 15 = 30 = 45 = 60 Conf. A CFD Conf. A EXP Conf. B CFD Conf. B EXP Conf. C CFD Conf. C EXP Conf. D CFD Conf. D EXP n/a n/a n/a n/a n/a n/a n/a 19