experimental and numerical aspects of simulating unsteady

3rd International Symposium on Integrating CFD and Experiments in Aerodynamics 20-21 June 2007 U.S. Air Force Academy, CO, USA

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Experimental and numerical aspects of simulating unsteady flows around the X-31 configuration Andreas Schütte1 Martin Rein2 Gebhard Höhler2 1German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology Lilienthalplatz 7, 38108 Braunschweig, Germany Email: [email protected] 2German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology Bunsenstrasse 10, 37073 Göttingen, Germany Email: Martin.Rein @dlr.de Email: Gebhard.Hoehler @dlr.de Abstract The procedure of realizing aerodynamic aspects of experimental and numerical maneuver simulations of a fighter aircraft will be presented. The work is part of the DLR Project SikMa-"Simulation of Complex Maneuvers". In this project the X-31 configuration is used as a target configuration for numerical and experimental maneuver simulations. The numerical aerodynamic investigations using the DLR TAU-Code are part of an objective to develop and validate a numerical tool for simulating the unsteady aerodynamics of a free flying aeroelastic combat aircraft, by use of coupled aerodynamic, flight mechanics and aeroelastic computations. In order to obtain a database for validation of the aerodynamic methods within the project, ground-based simulations of complex maneuvers of a model of the X-31 aircraft have been performed in the low-speed wind tunnel NWB of the German-Dutch Wind Tunnels DNW. In the wind tunnel tests a newly installed, novel test rig with six degrees of freedom (DOF) was used for the first time. The focus of the paper is on the validation process of steady and unsteady guided maneuver simulations of the X-31 configuration. Experimental and numerical requirements are discussed based on experimental and numerical results. Lessons learned and directions for future investigations are provided. Key words: X-31, TAU-Code, Maneuver, Chimera, Unsteady Aerodynamics, Wind Tunnel Techniques, Hexapod α = Angle of attack Δα = Amplitude, angle of attack a0 = Initial angle of attack β = Angle of side slip Δβ = Amplitude, angel of side slip Φ = Rolling angle Θ = Pitching angle Ψ = Yawing angle

η = Flap deflection angle F = Reference area li = Chord length of the model cp = (p-p∞)/q∞ = Pressure coefficient q∞ = ρ∞ ⋅V∞

2/2 = Dynamic pressure coefficient CL = L /(q∞⋅⋅F) = Lift coefficient CY= Y /(q∞⋅⋅F) = Side force coefficient CM = M/(q∞⋅F⋅lι) = Pitching moment coefficient


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Cl = l /(q∞⋅⋅F⋅ lι) = Rolling moment coefficient Cn = N /(q∞⋅⋅F⋅ lι) = Yawing moment coefficient Ma= V∝ /a = Mach number a = TR ⋅⋅κ = Velocity of sound V∝ = On flow velocity Re = V∝⋅li /ν = Reynolds number ν = Kinematic viscosity f = Frequency t = Time k = 2π f⋅li /V∝ = Reduced frequency Introduction The improvement of maneuverability and agility is a substantial requirement of modern fighter aircraft. Currently, roll-rates of 200º/s and more can be achieved, especially if the design of the aircraft is inherently unstable. Most of today's and probably future manned or unmanned fighter aircraft will be delta-wing-configurations. Already at medium angles of attack the flow field of such configurations is dominated by vortices developed by flow separation at the wings and the fuselage. A delay in time of vortex position and condition to changing on-flow conditions of the maneuvering aircraft can lead to significant phase shifts in the distribution of loads. In such a case, reliable results for the analysis of the flight properties can only be achieved by a combined non-linear integration of the unsteady aerodynamics, the actual flight motion, and the elastic deformation of the aircraft structure. A review of the overall numerical and experimental data from the DLR project SikMa can be found in various previous papers. The experimental setup and wind tunnel experiments are presented by Rein et al. [1]. The numerical simulation environment as well as steady and time accurate coupled numerical results of CFD, CSM and flight mechanics is described by Schütte et al. [2]. The main objective of this paper is focusing on the validation process of the RANS solver DLR-TAU for vortex dominated flow fields of real fighter aircraft configurations within maneuver flight. This concerns the description of the experimental environment, the set up of flight data for the experimental tests and the numerical simulation of a guided flight maneuver of the X-31 configuration taking several moving control surfaces into account. Numerical Approach The behavior of the fluid flow affecting the object of interest is simulated with the TAU-Code, a CFD tool developed by the DLR Institute of Aerodynamics and Flow Technology [3, 4, 5]. The TAU-Code solves the compressible, three-dimensional, time-accurate Reynolds-Averaged Navier-Stokes equations using a finite volume formulation. The TAU-Code is based on a hybrid unstructured-grid approach, which makes use of the advantages that prismatic grids offer in the resolution of viscous shear layers near walls, and the flexibility in grid generation offered by unstructured grids. The grids used for simulations in this paper were created with the hybrid grid generator Centaur, developed by Centaur Soft [6]. A dual-grid approach is used in order to make the flow solver independent from the cell types used in the initial grid. The unstructured grid approach is chosen due to its flexibility in creating grids for complex configurations, e.g. a fully-configured fighter aircraft with control surfaces and armament. The TAU-Code consists of several different modules, among which are:

• The Preprocessor module, which uses the information from the initial grid to create a dual-grid and the coarser grids for multigrid.

• The Solver module, which performs the flow calculations on the dual-grid. • The Adaptation module, which refines and de-refines the grid in order to capture flow phenomena like

vortex structures and shear layers near viscous boundaries, among others. • The Deformation module, which propagates the deformation of surface-coordinates to the surrounding grid. • The Motion module, which is used to define the motion of the aircraft model and the relative motion of the

control devices.


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The main elements of the TAU-Code relevant for the SikMa Project, in this case the Solver, Preprocessor, Adaptation, Deformation, Chimera and Motion module, have all been designed to work efficiently on massively parallel Linux clusters. The Solver module contains several upwind schemes, as well as a central scheme with artificial dissipation, which are used for the spatial discretization. For simulations of turbulent flows, the one-equation Spalart-Allmaras and several two-equation turbulence models are implemented. For steady computations either an explicit Runge-Kutta type time-stepping or an implicit LU-SSOR-scheme [7] are used in combination with the multigrid technique. For time-accurate simulations an implicit dual-time stepping approach is used. The TAU-Code can handle simulations containing multiple bodies in relative motion to one another, e.g. motion of control surfaces with respect to the aircraft, by use of a hierarchical motion-node structure, and the overlapping-grid Chimera technique. The motion of each body can either be calculated internally by the TAU-Code, or supplied by an external program through a Python implemented external interface. 1. TAU-Code Module: Adaptation The Adaptation module refines and de-refines the primary grid using sensors and indicators that are based on flow-solution variables contained in the latest flow field solution from the Solver module. One of the sensors that have commonly been used in various flow simulations is the total pressure value; however, recently new sensors have been implemented specifically in order to address vortex-dominated flow simulations. These new sensors are the λ2 criteria and kinematic vortex-number, Nk criteria, which take into account the rotation and rate-of-strain of the velocity gradient, and the normalized helicity Hn, which takes into account the angle between the translational and rotational velocity vectors. The new sensors are currently being evaluated as to their effectiveness in capturing the relevant flow phenomena in a vortex-dominated flow field [8]. 2. TAU-Code Module: Motion The Motion module is not a stand-alone executable but a library of functions that handle the calculation of the rigid-body translational and rotational transformation matrix for the TAU-Code. The module is built to take advantage of naturally occurring hierarchical motion structures, where for example flaps and slats inherit the motion of the wing to which they are attached. Several modes of motion description are allowed, of which the most common are the following:

• periodic - which allows the user to enter a reduced frequency (usually obtained from experimental data), and describe the motion using a combination of Fourier and polynomial series. For periodic motions the user has to specify the number of time-steps per period, such that the Motion module can calculate the maximum time-step allowed, based on the specified reduced frequency.

• rigid - which allows the user to specify a physical time-step size while using the same type of motion description as for the periodic motion. For periodic motions the user has to calculate the appropriate time-step based on the desired number of time-steps per period. For non-periodic motions the user can select a time-step which sufficiently resolves the prescribed motion.

• rotate - which allows the user to specify a constant rotation around a given axis using a reduced frequency as input parameter. The user has to specify the number of time-steps per period, such that the Motion module can calculate the maximum time-step allowed, based on the specified reduced frequency.

• external - which allows the user to create motion parameters (angles, rates, translation, displacement) in an external program and send those to the TAU-Code through a Python interface to the Motion module.

The rotation of a body can be described around either the body-fixed coordinate axis (as defined by the DIN 9300 standard), or around a vector defined in space (a so-called hinge-line vector). The translation of a body is specified in the body-fixed reference frame of the parent-node in the motion hierarchy (the inertial reference frame being the parent-node for the entire simulation).


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Fig 1: X-31 remote control model mounted with a belly sting to the Model Positioning Mechanism MPM in the DNW-NWB.

The Motion module uses the given input to create the transformation matrices required to determine the current position of the surface-grids relative to the inertial system, and the relative position of one grid with respect to another for multi-body simulations 3. TAU-Code Extension: Chimera Technique The Chimera technique provides the capability to perform calculations with systems of overlapping grids. By allowing large relative body movement without the need for local remeshing or grid deformation, the technique is invaluable for the simulation of maneuvering combat aircraft, where large-amplitude control surface deflections and/or store release are a standard part of the simulation. The current implementation can handle multi-body simulations where the overlapping grid boundaries have been predefined; a version that allows 'automatic-hole-cutting' is currently under development. The Chimera search algorithm, which is based on a state-of-the-art alternating digital tree (ADT), is available for both sequential and massively parallel architectures. A more detailed description of the Chimera approach is given by Madrane et al. [9]. Experimental Approach The objective of the experimental work within the DLR project SikMa is providing an environment that allows for simulating complex maneuvers of aircraft in a ground-based facility in order to collect data for validation purposes. This challenging task requires a wind tunnel with a support system that enables one to impose well-defined guided motions to models, a model that is equipped with remotely controlled control surfaces and instrumented with various measurement devices, and a sophisticated data control and acquisition system. These apparatuses and devices need to be well coordinated. In particular, the maneuver-like motion of a model in the wind tunnel and the corresponding motions of its control surfaces need to be synchronized. In the following sections first, the individual systems are introduced, then results of basic tests are discussed. Finally, the approach in defining and performing a wind tunnel maneuver is presented. 1. Low-speed wind tunnel and model positioning mechanism

Ground-based maneuvers of X-31 delta wing configurations have been realized in the low-speed wind tunnel NWB of the foundation German–Dutch Wind Tunnels DNW in Braunschweig. The NWB is a continuous atmospheric tunnel. In all tests reported in this paper it has been operated with an open jet. The contraction ratio is given by 1:5.6 and at the nozzle exit the cross sectional area equals S = 3.25 m x 2.80 m = 9.1m2. In the open test section the maximum flow velocity is 75m/s and the maximum Reynolds number formed with a characteristic length of 0.1 S1/2 is Re ≈ 1.8 x 106. The angle of flow divergence is less than 0.1° and on the axis the turbulence level equals about 0.15%. At the low-speed wind tunnel NWB a new support system, the so-called MPM-“Model Positioning Mechanism”, has been installed. The model positioning mechanism provides six degrees of freedom to move a model relatively to an arbitrary center of reference. The MPM that is based on a modified hexapod approach is described in detail in [10].

In the NWB the X-31 model has been mounted to a belly sting that is connected with the Steward platform of the MPM . The setup in the wind tunnel is shown in Fig. 1. For several steady state measurements a rear sting support setup has been used as shown in Fig. 2.


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Fig 3: Exploded view of the X-31 remote control model mounted on a belly sting with connecting rod.

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Fig 4: Absolute value and phase of transfer function of a pressure sensor assembled in a cavity under the wing.

Fig 2: X-31 remote control model mounted on a rear sting support in the DNW-NWB.

The MPM allows performing motions within a workspace which spans 1100mm in flow, 300mm in lateral and 500mm in heave direction. In the present tests only the rotational degrees of freedom have been used. The angles were varied within the following ranges: pitching angle Θ, -5° ≤ Θ ≤ 15°, yawing angle Ψ, -10° ≤ Ψ ≤ 10°, and rolling angle Φ, -3° ≤ Φ ≤ 3°. The range of motion in a certain angle can be increased by adding an additional connecting rod which is arranged behind the belly sting. In this manner pitching motions of amplitudes up to 15° have been performed. Depending on the model used the payload reached up to a quarter of the maximum payload (5000N) of the MPM.

2. Models of the X-31 and their instrumentation In order to enable both motions of control surfaces and high dynamics of the model itself, two models of the experimental aircraft X-31 have been built to a scale of 1:7.25. One version is a remote control (RC) model and the other a lightweight (LW) model. The air intakes of both models are closed by a streamlined cover. In this manner comparative numerical computations need not consider the internal flow through the engine. The wing and the lower part of the fuselage of the RC-model are made out of steel, and the upper part of the fuselage is constructed from carbon fiber reinforced plastic. The LW-model is fully made from carbon fiber reinforced plastic (CFRP) except for the leading edge flaps and strakes that are made from aluminum. In the case of the RC-model also the other control surfaces are made from aluminum, except for the rudder which is formed from CFRP. After completion the geometries of the models have been compared and were found to agree excellently. The RC-model is equipped with eight servo motors that serve for moving four leading edge flaps, trailing edge flaps, canard and rudder via a remote control system during a test. The location of the motors and balance is depicted in Fig. 3. The setting of flaps of the LW-model can be performed manually prior to a test. In all tests they were fixed in a zero position. The mass of the lightweight model was kept just below 10kg while the mass of the remote control model equipped with motors was about 110kg. Both models have been instrumented with miniature pressure sensors. Time signals were simultaneously obtained at up to 50 taps that are arranged along two sections in spanwise direction on both wings. The resolution in time of pressure measurements is mainly determined by the geometry of the assembly of the sensors in the cavity below the tap.

Motor

Balance

Motor


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y [mm]

c p

-400 -350 -300 -250 -200 -150 -100

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Fig 5: Pressure distribution on left wing in spanwise direction for two angles of attack. Solid lines: model mounted on rear sting (α ≈ -2° and α ≈ 16°), dashed lines: model mounted on belly sting (α ≈ -3° and α ≈ 15°).

Tests have shown that in the present case signals are not disturbed up to frequencies of 1kHz, as shown in Fig. 4. Integral quantities, i.e., forces and moments were determined by an internal six component strain gauge balance. In addition to these measurements the temperature and the angle of attack were controlled by two temperature sensors and an inclinometer, respectively. 3. Telemetric system for data acquisition Data are transferred from the moving model to an external data acquisition system by a multi-channel telemetric system. The system consists of eight modules located within the model and an external processor unit. Each module in the model contains eight independent supply units. These units are used for supplying the individual sensors with voltage. Furthermore, they contain remotely controlled amplifiers and 16bit A/D converters. Amplification and offset can be adjusted individually for each sensor from the external processor unit thus allowing for changing settings during measurements in the wind tunnel. The external processor unit is also used for online control of measured data, settings of amplification factors and supply of voltage to the modules and their supply units. Data are finally transferred from the processor to a data acquisition system via a digital interface at a rate of nearly 3kHz. 4. Static and dynamic tests The functionality of individual components of the experimental setup as well as their coaction has been carefully checked in a variety of static and dynamic wind tunnel tests. Furthermore, the symmetry of both models has been approved. In the following further examples that are of some importance for validating computational results by experimental data are discussed. In regard to the remote control model it is important to start motions of its control surfaces from a well-defined zero position. By purposely applying small changes to the zero position it has been shown that the flow around the X-31 configuration does not sensitively depend on the zero positions that are adjusted manually. Hence, slight inaccuracies in the adjustment need not be considered in numerical computations.

In a number of different static tests the physical features of the flow around the X-31 model, such as the onset of vortical flows and vortex breakdown, have been studied. In one of these tests the model was mounted on a rear sting, in all other tests a belly sting was used. In some of the latter cases an additional connecting rod was added for enhancing the range of either the angle of pitch or the angle of roll. It should be noted that already the different versions of mounting the model on a belly sting result in slightly different geometries. In Fig. 5 spanwise pressure distributions are compared that were obtained with the model mounted on a rear and belly sting (without connecting rod), respectively. The pressure distributions deviate from each other both qualitatively and quantitatively. When a rear sting is used three vortices are observable at the highest angle of attack shown in Fig. 5. With a belly sting one more vortex is present. Quantitatively, similar pressure distributions are obtained for different angles of attack. This is demonstrated in Fig. 5 where a pressure distribution at an angle of attack of α ≈ -3° is compared with α ≈ -2° and another distribution obtained α ≈ 15° with one at α ≈ 16°. Similar quantitative differences are also present when different versions of the belly sting are considered (belly sting, belly sting with connecting rod mounted to a pitch module, belly sting with connecting rod mounted to a roll module, see [11]).


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Figure 6a: Hysteresis during pitching oscillation (α0=15°, Δα=15°): unfiltered data of the lift coefficient versus angle of attack. Quasisteady motion (black) and dynamic oscillation (f=3Hz, red). Note the kink (marked by an arrow) in the red curve.

0 5 10 15 20 25 30-0.5

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Figure 6b: Hysteresis during pitching oscillation (α0=15°, Δα=15°): filtered data of the lift coefficient versus angle of attack. Quasisteady motion (black) and dynamic oscillation (f=3Hz, red). Note that in the red curve there is no longer a kink at the position of the arrow.

More importantly, characteristic angles of attack defined by the first appearance of vortex signatures in the pressure distributions also vary with the configuration of the mount. Differences are particularly important between rear and belly sting versions. Concludingly, the particular mount used in experimental work needs to be modeled in computations. In static tests only time-averages of pressures etc are recorded. This is no longer true for dynamic tests. In related experimental data there is always a certain degree of noise. When dynamic data are used for validating numerical results they are often filtered, for example, using a low pass filter, before comparison. This may lead to a loss of information as will be exemplified in the following example. Let us consider a pitching motion of the model at a high frequency. In the wind tunnel test the light weight model with all control surfaces in a zero position was used for enabling high dynamics. The oscillation considered is about αo = 15° at a frequency and amplitude of f = 3Hz (k = 0.16) and Δα = 15°, respectively. Under these conditions the angle of attack covers regimes without vortices up to the vortex breakdown regime during one cycle of the oscillation. As is well-known this can result in a hysteretic dependence of the flow on time.

This is shown in Fig. 6a in which the lift coefficient is plotted versus the angle of attack. For comparison, also the corresponding results of a quasi steady motion are depicted which show a reduction of lift increase due to vortex breakdown for α > 22°. At the frequency f = 3Hz the lift coefficient assumes in a clockwise manner different values during upstroke and downstroke. In the curve representing the unsteady case a kink can be observed which represents vortex stabilization. This kink is smoothed out in the low pass filtered data that are plotted in Fig. 6b. Of course, in a careful analysis of experimental data including unfiltered signals, such a loss of information will be detected. and a more appropriate cut-off frequency may be used in filtering the data. But in some cases a trade-off between noise suppression and information about fast changes of the flow field is impossible. On the numerical side one should keep in mind that wind tunnel data may have been processed quasi-automatically using the same cut-off frequency for all data. Therefore a loss of information cannot be excluded. In certain cases this may explain differences between numerical and experimental results.


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Figure 7b: SHSS maneuver: smoothed symmetrised data for maneuver simulation in a wind tunnel.

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Figure 7a: SHSS maneuver: slightly smoothed data obtained from flight tests.

5. Wind tunnel maneuvers In wind tunnel maneuvers both model and control surfaces need to be moved simultaneously in a synchronized manner. It is difficult to predict the reaction of aircraft to changes in the angles of its control surfaces in the case of complex maneuvers. Actually, achieving this shall be the result of numerical computations to be performed after validation of the numerical approach by the results of ground-based maneuvers. Therefore, in the present case the dependence on time of the motion of the model and its control surfaces is based on real flight tests. The original flight data are noisy, the geometry of the experimental X-31 aircraft is not necessarily as symmetric as that of the models and, finally, the Reynolds number in flight tests differs from that in the wind tunnel tests. Therefore, data collected during flight tests have been smoothed and adjusted before being used for defining wind tunnel maneuvers. In the following this will be shown for the example of a steady-heading sideslip maneuver.

In Fig. 7a slightly smoothed data of the angles of the aircraft and its control surfaces are plotted versus time. Note that the time scale has already been adjusted according to the wind tunnel velocity and the scale of the model. As can be seen, the yawing motion of the aircraft to the left and right is not symmetric. Slightly random oscillations of leading edge flaps (not shown in Fig. 7a/b) are hardly important for the maneuver. Furthermore, the data are still too noisy for providing a useful input in a computation. Therefore, the data have been further smoothed and artificially symmetrized by hand. In this the angle of attack is held at a constant value and the canard is aligned in the flow direction at all times. The result is shown in Fig. 7b. In this maneuver the rudder performs large motions and the trailing-edge flaps are acting as ailerons opposing the rolling and yawing moment resulting from the motion of the rudder. Experimental results displayed in Fig 21 in the next section, show that the coefficients of the lateral force and the rolling and yawing moment remain quite small during the whole maneuver. This shows that the manual adjustments to the flight data of the maneuver have been successful. A more detailed description of the experimental approach and further examples are given in [11].

β Trailing-edge Flap left Trailing-edge Flap right Ruder

β Trailing-edge Flap left Trailing-edge Flap right Ruder


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Figure 9: Slice through pre-refined unstructured hybrid mesh of the X-31 configuration.

Figure 8: X-31 model topology for the computa-tional simulation with belly sting support.

Figure 10: 3D flow field over the X-31 conf. at 18º angle-of-attack. Clean-wing configuration.

Comparison of Experimental and Numerical Results In Fig. 8 the topology of the computational model for the simulation of the X-31 configuration is shown. All control devices are taken into account and two different setups are simulated. The first setup is simulated with a rear sting support as depicted before in Fig. 2. For the second a belly sting support is mounted on the lower side of the model for the unsteady calculations as it is usually configured in the experiments.

In Fig. 9 the hybrid mesh topology is depicted. A pre-refined mesh is used for both steady and unsteady simulations. To cover a certain range of pitching and yawing angle the pre-refinement is adapted to the areas where the vortices are assumed to be formed during the simulation. The steady

state results are simulated with no sting, while the unsteady simulations are simulated by taking a belly sting support into account, resembling the configuration in the experiments. The effect of the support is discussed later on. Fig. 10 shows the numerically simulated 3D flow field over the X-31 configuration, and gives a good indication of the complexity of the vortex flow topology over the wing and fuselage. In Fig. 11a an oil flow picture of the X-31 clean-wing from low speed experiments is shown. The experimental results are achieved from test done with a 1:14 X-31 model with a clean wing without control devices. The angle-of-attack is α = 18° at a Reynolds number of 0.7Mio. The attachment line of the strake vortex and the main wing vortex as well as the separation line of the main wing vortex near the leading-edge are emphasized. In Fig. 11b the results of the corresponding CFD calculation are depicted. It is seen that the flow topology from the calculation fits quite well with that of the experiment. In all further calculations presented here all control devices will be taken into account.


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Figure 13: Lift and pitching moment coefficient verses angle of attack. Steady state simulation. Comparison of TAU calculations with experimental data. Rear sting support. Ma = 0.12, Re = 2.07Mio.

Figure 14: Comparison of the pressure distribution at an angle of attack of α=12°. Rear sting support. Ma = 0.12, Re = 2.07Mio.

In Fig. 12a the results of a measurement with PSP- “Pressure Sensitive Paint” [12] obtained at an angle of attack of α = 16° at a Reynolds number of 2.07Mio are shown. Comparing the pressure distribution from the PSP measurement with the CFD calculation in Fig. 12b it is seen that the main footprints of the vortices as well as the location are accurately captured by CFD. The calculations were done using the Spalart-Allmaras turbulence model with vortex correction. The main difference with respect to the clean-wing configuration is the separated vortex shear layer, which occurs due to the gaps between the leading edge control-devices. This leads to a more complex vortex topology, with three vortices. Most inboard the suction peak of occurring from the strake in front of the wing can be observed. The first wing vortex comes from the inner wing, the second and third from the inner and outer leading-edge flap, respectively. The suction-strength of the vortex at the inner leading edge flap is predicted to be stronger and the outer vortex starting at the kink of the wing where the outer flap starts is predicted weaker than in the experiment.

Figure 11: a) Oil flow visualization of the X-31 clean wing at α = 18º. b) TAU calculation: Visualization of surface streamlines at α = 18º.

Figure 12: Left: Steady-state PSP measurement of the pressure distribution over the X-31 wing. Right: Steady TAU RANS calculation. Rear sting support.

TAU Calculation Ma = 0.12 Re = 0.7Mio α = 18°

Oil flow picture Ma = 0.12 Re = 0.7Mio α = 18°

PSP MeasurementMa = 0.12 Re = 2.07Mio α = 16°

TAU Calculation Ma = 0.12 Re = 2.07Mio α = 16°


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Figure 16: Guided pitching motion of the X-31 configuration. Comparison of TAU calculations with experimental data. Belly sting support.

Figure 15: Guided yawing motion of the X-31 configuration. Comparison of TAU calculations with experimental data. Belly sting support.

In Fig. 13 the lift and pitching moment coefficient is plotted verses the angle of attack. For all calculations of angles of attack at α = 10°, 12°, 14° and 16° a higher front loading pitching moment is predicted by the numerics, while the overall lift is fairly well predicted by the CFD calculation. One reason for the differences in suction peak is that the suction peak over the canard is predicted to be too low as seen in the pressure distribution in Fig. 14 at an angel of attack of α = 12°. Beside numerical influences like grid quality and grid refinement the flow over the canard is influenced by the flow over the wing. If the flow over the wing is not predicted correctly the effective angle of attack for the canard can’t be correct as well. The canard is accordingly a critical element within the validation process predicting the pitching moment correctly for this configuration.

Fig. 15 shows the result of a guided yawing motion maneuver. The initial pitching angle is α0 = 10° and the side slip amplitude is Δβ = 5°. The maneuver is done with a frequency of 1Hz. In this scenario the model is mounted on the belly sting support described above, see Fig. 1+8. The overall aerodynamic behavior is captured by the numerical simulation, although the pitching moment is under-predicted. The gradient of the rolling moment is predicted to be higher than in the experiment and the hysteresis shown in the experiment is predicted to be smaller by the calculation. Comparing the steady state pitching moment in Fig. 15 at α = 10° in comparison to the steady state results in Fig. 13 it is seen that the pitching moment in case of the belly sting is more than twice that without the sting. The reason for this is that the belly sting is shifting the local angle of attack of the inner wing to higher values. This causes a higher suction and a corresponding higher front loading on the wing. Furthermore, the induced angle of attack of the canard is rising, which leads to a higher lift on the canard and a higher rear loading pitching moment. Fig. 16 shows the result of a guided pitching motion maneuver. In this case the initial pitching angle is again α0 = 10° with an amplitude of Δα = 4°. The maneuver is again done with a frequency of 1Hz. As in case of a yawing motion the lift is predicted to be higher than in the experiment. The gradient is predicted correctly. The characteristic of the dynamic pitching moment is not given correctly by the numerical simulation. The reason is the same as described in the steady state case before.

X-31 yawing motion: α = 10°; ΔΨ = 5°; f = 1Hz X-31 pitching motion: α = 10°; Δα = 4°; f = 1Hz


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Figure 17: Flow topology during pitching maneuver at α=6°. Streamlines and surface pressure distribution.

Figure 18: Flow topology during pitching maneuver at α=14°. Streamlines and surface pressure distribution.

Figure 19: Overlapping chimera-grid of the right canard and trailing-edge flap.

Fig. 17 and 18 show the flow topology at the lower and upper points of the dynamic loop of the pitching maneuver. Fig. 17 shows that at α = 6° the flow is attached over the wing and even the flow around the canard is attached. Only a small vortex is generated at the strake in front of the inner wing. In Fig. 18, i.e., at α = 14° the flow topology has completely changed. Over the wing a vortex structure of four vortices starting from the wing strake, at the inner, from the inner and outer leading edge flap, has developed. The inner wing vortex and the vortex from the inner leading edge flap unify at approximately 70% chord length. Over the canard a strong vortex is generated which is not interacting with the wing vortices. The small strakes at the nose of the fuselage prevent the occurrence of rolling instabilities caused by time dependant flow separations. The final simulation which will be presented here is a guided SHSS-“Steady Heading Side Slip” Maneuver which has been simulated in the wind tunnel. As described above the guided wind tunnel maneuver is based on a flight experiment. During this maneuver the deflection of the ruder is initiating the side slip whereas the deflection of the Canard is held constant at ηCanard = 12° as well the aircraft at Θ = 12° pitching angle. The trailing edge flap deflection depends on the angle of side slip and is thus changing with time in order to compensate the rolling moment to get a roll angle of Φ = 0°. For tracking the movable control devices the Chimera technique is used in the computations. Fig. 19 is showing the Chimera mesh of the right canard and the right trailing edge flap. Currently a Chimera technique with predefined holes in the background mesh is available. An automatic hole-cutting procedure is under investigation. For enabling the capability of movable flaps the gap between the fuselage and the canard as well as the gap between wing and trailing edge flaps were larger than in the experiment. The effect of this modification will be discussed as well.

Red – flap grid Blue – back ground cut out


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Figure 21: Side slip angle and integral coefficients verses time of the experiment. SHSS maneuver. Belly sting support.

Figure 20: Side slip angle and integral coefficients verses time of the TAU calculation. SHSS maneuver. Belly sting support.

Figure 22: Complete time history of the SHSS maneuver from the experimental data.

Fig. 20 and 21 show the angle of side slip and the aerodynamic coefficients of forces and moments during the initial time period of the simulated SHSS maneuver. The flow conditions are Re = 2.07Mio, Ma = 0.12 and the angle of attack is constant at α = 12°. Due to huge time requirements of the computational simulation only the initial time history of the maneuver can be presented up to know. The whole time history of the experimental data is shown in Fig. 22.

The black lines representing the side-slip angle β. The lifting and side force coefficients are represented well by the calculation as can be seen by comparing the red and magenta lines in Fig. 20 and Fig 21. The overall yawing moment coefficient is predicted by the simulation in the same margin as seen in the experimental data in Fig. 21 and 22, the orange lines. This can be observed in the simulation in Fig. 20, but no conclusion can be made so far. Comparing the predicted pitching moment with the experiment the same effect occurs as in the steady state and unsteady results discussed before. The pitching moment is too small in the simulation. Because of necessary changes in the geometry within the numerical model the gap between the canard and the fuselage is larger as in the experiment. This causes a lower effective surface area of the canard in the experiment and delivers a lower rear loading pitching moment. Finally the rolling moment coefficient is about zero in the simulation where as in the experiment a weak damping rolling moment occurs.


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Figure 23: Pressure distribution at t = 0.4s and side-slip angle β ≈ 0°.

Figure 24: Pressure distribution at t = 0.84s and side slip angle β ≈ 0.75°.

Fig. 23 and 24 are showing the pressure distribution on the X-31 configuration at two different time steps of the simulation depicted in Fig. 20. Fig. 23 is showing the initial status of the flow at t = 0.4s where the side-slip angle β is approximately zero. The pressure distribution is symmetric over the wing. The footprints of the strake vortex and the inner wing vortex can be observed.

In Fig. 24 the pressure distribution at t = 0.84s is shown. Although the motions of the maneuver are right at the beginning and the side-slip angle of β ≈ 0.75° is rather small the yawing motion of the model leads to an asymmetric pressure distribution. Due to a positive side slip angle the suction peak of the inner vortex on the right side of the wing expands less down stream than on the left hand side. The side slip angle reduces the effective sweep angle on the luff side of the wing and adjusts the vortex breakdown to a lower angle of attack. On the lee side the effecting suction peak is further downstream due to the opposite effect described before. The results from the numerical simulation show the general capability of the numerical approach to simulate time accurate maneuvers of a complex fighter aircraft configuration with several moving control devices. However further investigations are necessary to validate the numerical method for configurations with vortex dominated flow fields. Reducing the differences between the numerical results in comparison to the experimental data within the validation process several investigation have to be done concerning the computational grid, the turbulence model and the capability to set up the geometry more accurately using an advanced Chimera approach. Finally an overall improvement of the efficiency of the TAU-Code within unsteady simulations is necessary.

V∝ V∝


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Conclusion Results of the DLR-Project SikMa have been presented and discussed. The objective in SikMa was to develop new experimental and numerical capabilities for simulating unsteady aerodynamic behaviors of a fully configured fighter aircraft configuration. This was the topic of the present paper. As a target configuration the X-31 aircraft with movable control devices has been considered performing maneuver flight. In order to achieve the new testing capabilities a unique experimental setup was developed including a newly developed dynamic wind tunnel testing facility, wind-tunnel models and sophisticated data measurement equipment. On the numerical side a Chimera technique has been added to the TAU Code in order to realize relative motions between fuselage and control devices within a computational simulation. Furthermore an extended motion module was developed and the grid adaptation approach has been extended especially for vortex dominated flow fields. By using the unsteady RANS capability of the DLR-TAU-Code these extensions to the code resulted in improved investigations of steady and unsteady flows around the X-31 configuration. Particularly in the case of unsteady flows a detailed comparison of experimental and numerical results reveals some differences the origin of which has been addressed. On the experimental side it turned out that it is sometimes difficult to define wind tunnel maneuver by using data from flight tests. The latter are typically noisy and not necessarily as generic as one would like for a validation experiment. A remedy suggested in [1] would be to perform real wind tunnel maneuvers, i.e., to start with deflections of the control surfaces, measure the resulting forces and moments by the balance, and then determine by real-time flight mechanics calculations the corresponding motions of the model that are finally performed by the MPM. On the numerical side a simulation of a complete complex maneuver is as yet quite time demanding. Nonetheless, it has been shown that the extensions to the TAU-Code such as the Chimera technique and the motion module function very well. Improvements concerning unsteady flow calculations, and also mesh generation by means of better pre-refinement or using the mesh adaptation approach will finally enable standard computations of complex unsteady flows. Furthermore an improved Chimera approach will be established to handle all kind of complex control device geometries. Finally improvements in the physical modeling are required as well as investigations increasing the unsteady solver efficiency for maneuver flight simulations. References [1] Rein, M., Höhler, G., Schütte, A., Bergmann, A., Löser, T.: Ground-based simulation of complex maneuvers

of a delta wing aircraft. AIAA Paper 2006-3149, 2006. [2] Schütte, A.; Einarsson, G.; Schöning, B.; Raichle, A.; Mönnich, W.; Neumann, J.; Arnold, J; Orlt, M.;

Forkert, T.: Numerical Simulation of Maneuvering Aircraft by Aerodynamic, Flight Mechanics and Structural Mechanics Coupling. AIAA, 45th AIAA Aerospace Sciences Meeting and Exhibit. 8 - 11 Jan 2007, Reno, Nevada, USA, AIAA Paper 2007-1070, 2007.

[3] Galle, M.; Gerhold, T.; Evans, J.: Technical Documentation of the DLR TAU-Code. DLR Report No. IB 233-97/A43 1997.

[4] Gerhold, T.; Galle, M.; Friedrich, O.; Evans, J.: Calculation of Complex Three-Dimensional Configurations employing the DLR TAU-Code. AIAA-97-0167 1997.

[5] Gerhold, T: Overview of the Hybrid RANS Code TAU, in N. Kroll, J. Fassbender (Eds.) MEGAFLOW – Numerical Flow Simulations for Aircraft, NNFM Vol. 89, Berlin, 2005, pp. 81-92.

[6] Centaur Soft: http://www.Centaursoft.com [7] Dwight, R.P.: Time-Accurate Navier-Stokes Calculations with Approximately Factored Implicit Schemes.

Proceedings of the ICCFD3 Conference Toronto, Springer, 2004. [8] Widhalm, M.; Schütte, A.; Alrutz, T.; Orlt, M.: Improvement of the Automatic Grid Adaptation for Vortex

dominated Flows using advanced Vortex Indicators with the DLR-TAU Code. STAB-Symposium 2007, Göttingen, Germany. Announced to: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 96; C. Tropea, S. Jakirlic, H.-J. Heinemann, R. Henke, H. Hönlinger; Springer, Berlin Heidelberg New York, 2007


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[9] Madrane, A.; Raichle, A.; Stürmer, A.: Parallel implementation of a dynamic overset unstructured grid approach. ECCOMAS Conference Jyväskylä Finland, 24.-28. July 2004.

[10] Bergmann, A., Hübner, A.: Integrated Experimental and Numerical Research on the Aerodynamics of Unsteady Moving Aircraft. 3rd International Symposium on Integrating CFD and Experiments in Aerodynamics, 20-21 June 2007, U.S. Air Force Academy, CO, USA.

[11] Rein, M. and Höhler, G.: Vergleichende Untersuchungen zum Einfluss des Supports bei statischen Messungen an X-31 Modellen im DNW-NWB. DLR Report No. IB 224-2007 A35, Göttingen 2007.

[12] Engler, R.H., Klein, Chr., Trinks, O.: Pressure sensitive paint systems for pressure distribution measurements in wind tunnels and turbomachines. Meas. Sci. Techn. 11 (2000) 1077-1085.

experimental and numerical aspects of simulating unsteady

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