Study of Factors Driving Pitch, Roll and Yaw Coupling in Bluff Body Aerodynamics

Transcription

1 Study of Factors Driving Pitch, Roll and Yaw Coupling in Bluff Body Aerodynamics Vrishank Raghav Ranjit Mantri Narayanan Komerath Marilyn J. Smith School of Aerospace Engineering, Georgia Institute of Technology Atlanta GA, USA. Helicopter sling loads exhibit departures from stable behavior at certain speeds posing certain safety concerns. Rolling due to pendulum motion about the sling attachment point may couple with yaw and pitch oscillations, amplifying the motion to dangerous levels at certain speeds. This is a case of coupling between the aerodynamic forces and the dynamics of the tethering system, and can affect the handling qualities of the vehicle as well. In this work the factors driving the pitch, roll and yaw coupling in bluff body aerodynamics are studied. The sensitivity of the side force and yawing moment to yaw angle is studied in a low speed wind tunnel, in steady-state load measurements simulating the effect of velocity induced by quasi-steady pendulum-type roll motion. While the side force and yawing moment appear to be generally stable to induced yaw, at some speeds there is a reversal of the stability derivative, partially explaining observed behavior in tethered tests. The time-averaged side force and yawing moment behavior with yaw angle generally agree with predictions made using unstructured-grid Navier-Stokes computations. While the time-averaged loads at small yaw angles are small, there are substantial unsteady oscillations of the loads about these values. A hot-film constant temperature anemometer probe is used to measure spectra of velocity fluctuations near the edge of the model and in the wake downstream. Spectral peaks of integrated loads observed in 2-D computations occur in the same frequency band as those seen in the measured velocity spectra. ρ Free Stream Density, kg/m 3 C D Coefficient of Drag Yaw Moment Coefficient C M Nomenclature Graduate Research Assistant, Ph.D. Candidate, AIAA Student Member. Graduate Research Assistant, AIAA Student Member. Professor, AIAA Associate Fellow. Associate Professor, AIAA Associate Fellow. 1 of 13

2 C Y F y Side Force Coefficient Side Force, N S ref Reference Area, m 2 V Free Stream Velocity, m/s AR Aspect Ratio CONEX Container Express D Drag, N T Torque, N-m I. Introduction Stability problems are encountered by helicopter operators in transporting a wide variety of loads slung under the vehicle. Loads of different types exhibit departures from stable behavior at certain speeds posing safety concerns. This is a problem where the aerodynamics of bluff bodies interact with the dynamics of the tethering system, and the handling qualities of the vehicle. As a result, the flight speed of the vehicle must often be limited by this dynamic behavior, even though the vehicle may have enough power to fly much faster. For instance, Raz et al. 1 cite that the maximum flight speed of a UH-60 with a CONEX container sling load is 60 kts., though the cruise speed of that particular vehicle configuration is nearly 110 kts. The focus in this paper is on the basic fluid dynamics/dynamic behavior of flows around rectangular and cylindrical objects in a steady freestream. Experimental evaluations have previously shown to match well with full-scale flight tests for modeling the dynamics of loads with fixed separation points, such as CONEX containers. 1 The CONEX is a rectangular, sharp-edged bluff body often used for cargo purposes. The yaw sensitivity of this bluff body directly impacts the forces during scaled testing. Deviations from zero yaw attitude cause side forces that lead to divergent behavior through coupled roll oscillations. Wall effects change the sensitivity factors for this bluff body in different sized wind tunnel facilities. Hence, there is interest in determining the reasoning behind the aerodynamic phenomenon causing this behavior. For other geometries, such as cylinders, the separation point is highly dependent on flow velocity and Reynolds number, as observed in flight tests of an engine canister. 2 Therefore, multiple representative configurations must be evaluated in order to obtain meaningful data. Current sling load prediction models of configurations with fixed separation points rely on static load estimates, 3 or dynamic loading with restricted degrees of freedom. 4 Other models for generic configurations rely on analytical approximations, 4 which do not have the fidelity that can be obtained from algorithms developed from wind tunnel data. The current focus is to examine the basic fluid dynamics/dynamic behavior of flows around rectangular and cylindrical objects in a steady free stream. Ongoing wind tunnel experiments at two tunnels at Georgia Tech, augmented by computational fluid dynamics (CFD) simulations, capture the flow behavior in detail. Specifically, the sensitivity of these bluff bodies to the side loading leading to yaw perturbations and the resulting initiation of pitch/yaw/roll oscillations that may be amplified by tunnel wall effects or forced by rotor wakes are examined. 2 of 13

3 II. Experimental Configuration Wind tunnel testing for the different bluff body configurations was conducted in the 9 x 7 ft. John J. Harper wind tunnel at the School of Aerospace Engineering of the Georgia Institute of Technology. Initial experiments were designed to verify the present effort s capability to reproduce published experimental results from the Technion tunnel on scale models of the the basic CONEX container. This rectangular box model also served as an excellent reference bluff body configuration as its edges provide clear separation lines and thus reduce the number of variable parameters. The Technion experimental campaign had sought to understand and alleviate instabilities encountered on a CONEX sling load. 1 A 1/11 th scaled model of a CONEX container of approximately 6 x 6 x 8 ft. weighing 4352 lbs was examined. Linear dimensions were scaled proportional to the scaling factor n, the mass proportional to n 3, frequency proportional to 1/ n, and velocity proportional to n. The Ref. 1 test model neglected the corrugated walls, skids, and top edge indentations present on the full-scale CONEX (see (Fig. 1(b)), as they found those to not have a significant effect on the model dynamic behavior. Rectangular box models were constructed from various materials to reduce the shell mass and allow variation of the inertia. Initial tests used a box made of cardboard with a weight inside. Later versions used plywood of 12.5 mm and then 6.25 mm thickness, and finally a hollow Plexiglas shell. To modify the moment of inertia, three sets of two weights were placed in the center of each axis of the box. Along the shorter horizontal axis, masses of 140 g were placed 75 mm from the center. Along the longest axis, masses of 70 g each were placed 68 mm from the center. Along the vertical axis, masses of 60 g were placed 68 mm from the center. The calculated moment of inertia was verified using torsional pendulum measurements. The torsional pendulum method related the period of small oscillations to the moment of inertia through an equivalent spring constant. Reference rods and a flat plate were used to evaluate the spring constant over the expected range of the moment of inertia. The period of oscillation was averaged over 20 samples for each axis. Table 1 correlates the different configurations with the models in published experiments. 1 The values for the GT baseline rectangular box model are within 2.4% by dimension, 0.5% by mass, and 5.6% by moment of inertia with the prior model. (a) CONEX container (b) Rectangular box model Figure 1. Comparison of full-scale loads and corresponding wind tunnel models. 3 of 13

4 Table 1. Scaled parameters for rectangular box model Ref. GT Scaled Error % Low Mid 1 Mid 2 Length (m) Width (m) Height (m) Mass (kg) I xx (10 3 kgm 2 ) I yy (10 3 kgm 2 ) I zz (10 3 kgm 2 ) III. Results Experimental evaluation of sling load dynamics has been conducted on the CONEX container. The actual CONEX container modeled in this study is a box of approximately 6 by 6 by 8 ft. For wind tunnel testing, the full-scale container was approximated by a 1/11 th scale Plexiglas model. Foam inserts were used to enable weights to be positioned in different locations to test variation in moment of inertia. The corrugated walls, skids, and top edge indentations present on the actual CONEX were neglected, as it was found in previous studies to not have a significant effect on the model dynamic behavior. 1 Dynamic wind tunnel tests of the CONEX sling load configuration were conducted in the 7 ft. by 9 ft. test section of the John J. Harper wind tunnel at the Georgia Institute of Technology. These validated the repeatability of similar tests conducted by the Israeli Institute of Technology 1 using an identically scaled model and run conditions. The model was suspended from a gimbal mount, allowing it to rotate freely about all axes at the mounting point. The preliminary results are published in Mantri et al. 5 They demonstrated the influence of the moment of inertia of the CONEX container on stability. Fig. 2 illustrates the influence of free stream speed on yaw oscillations. Additional phenomena observed during these tests include the emergence of a stable spinning case at higher velocities even without the influence of a rotor wake. This spinning motion has also been observed in flight testing. 2 Such correlation between the two confirms that there may be a Reynolds number dependency on the dynamic response of the two flight cases, as suggested by the fixed nature of the flow separation about rectangular geometries. The CONEX model s side force was highly sensitive to yaw, and it was observed that wind tunnel wall effects greatly amplify the divergent behavior. The yaw sensitivity produces side forces on the model and drives roll oscillations. Studies have been conducted to understand 4 of 13

5 Figure 2. Yaw rates for CONEX configuration. the cause of this dynamic behavior. Simulations were conducted on these configurations using the NASA-developed unstructured CFD code FUN3D. 6 A series of static yaw angles were simulated at flight conditions. Due to the highly unsteady nature of the flow, overset feature-based grid adaption 7 was applied to the simulation. This utility improves the quality of the grid in the near- and far-field turbulent wake region of the bluff body, resulting in an improvement in the resolution of vorticity in the simulated flowfield and dynamic response of the body. The comparison of side force coefficient values over the yaw distribution can be seen in Fig. 3. The highly oscillatory nature of the flowfield can be observed with the use of the error bars, which denote the minimum and maximum values that were averaged to obtain the mean values. Figure 3. Side force coefficient at static rotation angles at 35 mph for the rectangular box with two-dimensional CFD simulations. To evaluate the ability of static aerodynamics to predict the stability of the dynamic system, a representative model was created using the simulation tool Simulink. 8 The sling load was modeled as a nonlinear rigid pendulum, with three degrees of rotational freedom about the pivot location. The tether (sling support)longitudinal elasticity and aerodynamic drag were neglected. Inertial properties were based on the scaled CONEX model from wind tunnel tests. Aerodynamic forcing of the pendulum was governed by aerodynamic 5 of 13

6 coefficients as a function of local yaw angle, obtained from wind tunnel tests, and the local relative velocity at a given point in the pendulum motion. Increasing the free stream velocity, modeled as the superposition of step functions, confirmed that a quasi-steady aerodynamic approximation is able to capture the wind tunnel-observed instability (Fig. 4(a)) in the roll mode, as also noted by Cicolani et al. 9 Additional validation of the model is shown in prediction of trail angle (Fig. 4(b)), which is closely approximated over the entire range of the flight speeds shown. (a) Quasi-steady simulation of scaled CONEX container using data from. 10 (b) Trail angle prediction of Simulink model. Figure 4. CONEX response predictions of Simulink model. It is necessary to note that although the two experimental curves in Fig. 4(b) represent the same model scale, they are of slightly different configurations. The trail angle results show that the model can predict steady behavior using both CFD and experimental data, but the quality of model predictions is highly dependent upon the accuracy of the aerodynamic loads provided to it. This supports the use of simplified aerodynamic experiments to assist in the prediction of complex dynamic motion, and the need for evaluation of static aerodynamic loads for additional geometries. To further understand the coupling between the various axes, quasi-steady measurements were collected using a load cell. The primary aerodynamic phenomenon associated with the rectangular bluff body is the formation of vortices shed from the edges of the rectangular body, even when the body is stationary, resulting in a quasi-steady flow field. The unsteady vortex shedding can act as an aerodynamic forcing function to induce vibration and torsional motion, as well as a turbulent wake. The drag is calculated from measurements as follows. The drag coefficient (C D ), the side force coefficient (C Y ) and yaw moment coefficient (C M ) is obtained by: D C D = 1 ρ 2 V 2 (1) S ref C Y = F y 1 ρ 2 V 2 (2) S ref T C M = 1 ρ 2 V 2 (3) S ref l ref 6 of 13

7 (a) Wind tunnel setup (b) Axial orientation Figure 5. Steady load cell setup for CONEX. where D is the drag, Sref is the reference area, lref is the reference length and ρ and V are the free stream density and velocity, respectively. The reference area for the box is m2 and the reference length for the box is m. The reference length for yaw moment of the rectangular box was 0.2 m. The pitching moment arms for the quasi-steady load measurement setup were m for the rectangular box. These data were compared to the theoretical drag coefficient values of 2.05 (2-dimensional flat plate) and 1.05 (3-dimensional rectangular box) from Hoerner.11 The quasi-static aerodynamic forces and moments on the bluff body models were measured using an ATI Gamma 6-degree-of-freedom load cell. The load cell was mounted below a pitch-yaw mount whose attitude could be set manually (Figure 5). Load cell data were acquired for 30 seconds at 1000 Hz for each test condition and averaged to determine the mean values. The yaw orientation were varied as shown in Figure 6 Figure 6. Definition of the orientation of the CONEX These experimental tests examined the aerodynamic forces and moments acting at different orientations for the bluff body models. The load cell measurements provide the effect of fixed yaw and pitch angle over an expanded speed range. The configurations focused on matching divergent conditions from wind tunnel testing. CFD simulations also were used to compare and validate the load measurements Figure 3. The results from these testing methods provide further understanding on the coupled behavior of the bluff body configuration. 7 of 13

8 A. Stability Analysis The stability of the CONEX is very essential to understanding the divergence behavior of the container. In particular, the yaw sensitivity to the aerodynamic forces is important in understanding the dynamic phenomenon that leads to the unsteady oscillations and steady rotation for the bluff bodies. Figure 7. angle Side Force coefficient between 0 and 90 degree yaw angle and at 0 degrees pitch Figure 8. Side Force Coefficient at various velocities at 0 degrees pitch angle The behavior of the side force is of particular interest with respect to the development of aerodynamic forcing functions that lead to instabilities. To establish this, fine resolution data 8 of 13

9 of side force and yawing moment has to be analyzed to determine whether a perturbation is stabilizing or destabilizing. This data has been shown to fit in with the previous data reported by Mantri 5 in Figure 7. The fine resolution data of side force coefficient is as shown in the Figure 8. Figure 9. Yaw Moment Coefficient at various velocities at 0 degrees pitch angle The Figure 10 shows a small roll perturbation introduced onto the CONEX. This in turn induces a side slip velocity as shown in the figure. The side slip velocity changes the induced angle of attack causing an effective yaw angle. It is observed that at certain yaw angles the new side force acts to augment the initial side force. But at the same time the yaw moment is acting to restore the CONEX to its original position. In other words the yaw moment has a stabilizing effect on the CONEX. The amplified side force increases the side slip velocity and creates a feedback loop, with an amplifying gain. The side force has a destabilizing effect on the CONEX. Hence it can be concluded that an initial roll displacement has a destabilizing effect on the CONEX container. The value of dc y /dβ for angles between 0 and 5 degrees is on an average 0.01 and the value of dc m /dβ for angles between 0 and 5 degrees is on an average Computational investigations indicate that the flow separation at these small yaw angles is dominated by two-dimensional phenomena, as illustrated in Figure 3 where two and three dimensional simulations are comparable. This conclusion is not valid at larger yaw angles, as the multiple separation/reattachment phenomena are clearly three-dimensional. 1. Sources of Error and CONEX Model Asymmetry It is observed that the side force values at 0 and 90 degree yaw (Figure 6 are not the expected zero value. Hence to carry out the stability analysis the side force was nulled at the 90 degree Yaw position and the same correction was applied throughout the azimuthal range. This spurious data maybe either due to the Loadcell measurements or the asymmetry of the CONEX model. The Load Cell has been calibrated multiple times to check for repeatability 9 of 13

10 Figure 10. Schematic of a small perturbation introduced on the CONEX container of results and does not seem to be the source of error. The asymmetry in the model causes a side force at zero yaw, which has been accounted for in the stability analysis and the the figures presented here. B. Frequency Spectra Hotwire anemometery was used to determine the frequency spectra in the wake of the CONEX, the results of the hotwire data are discussed here. Frequency spectra in the wake of a CONEX container is of great interest to study the unsteady forces causing the divergence. Figure 11 shows the points in the wake where the spectra was computed. The measurement was done at the center of the z-y plane. The frequency spectra of the sweep behind the CONEX container at 35 mph is shown in Figure 12. FFT analysis of CFD simulations at the same flight conditions and orientation confirm the findings of this approach. The first peak frequency identified by analysis of the CFD-predicted side force falls between Hz, which is also observed in Figure 12. This frequency corresponds to the frequency at which vorticity is shed from alternating sides of the rectangular body. The dominant frequency were further confirmed by performing the same experiment at a different velocity and checking for the linear scaling of the frequency. The coefficients from the frequency spectra can be used to reconstruct the unsteady forces in time as a Fourier series. This can be then implemented into the simulink model to improve the predictions of divergence in sling load dynamics. 10 of 13

11 Figure 11. Hotwire Data Points Figure 12. Frequency Spectra in the wake of the CONEX at shown measurement points (Figure 11) at 35mph IV. Conclusions 1. Scaled wind tunnel testing, augmented by numerical experiments is used to investigate the origins of the oscillations that develop in the behavior of bluff body loads slung below rotorcraft. 2. Dynamic wind tunnel testing of a tethered rectangular box reveals a sudden shift from 11 of 13

12 an orientation with the narrow side facing the wind, to the broad side facing the wind, at a specific speed. At other speeds the model remains stable. 3. Time-averaged load measurements using a 6-axis load cell reveal that the yaw-roll coupling behavior is generally stable to small yaw or roll perturbations, but exhibits instability at certain speeds, corresponding to the observed switching mentioned above. 4. Computational fluid dynamics analysis using the FUN3D Navier Stokes code shows good agreement with the time-averaged side force and yawing moment measurements. 5. Spectra of unsteady loads at quasi-steady conditions determined from computations under a 2D assumption, show peaks corresponding to periodic phenomena 6. Spectra of velocity fluctuations in the flow near the edge of the model obtained using hot-film anemometry in the wind tunnel also show peaks in the same band as the computational results. V. Acknowledgments This research has been supported by the U.S. Army via the Georgia Tech Vertical Lift Rotorcraft Center of Excellence. Dr. Michael Rutkowski of NRTC is the technical monitor. Computational support was provided through the DoD High Performance Computing Centers at ERDC through an HPC grant from the U.S. Army (S/AAA Dr. Roger Strawn). The authors would like to thank Dr. Tom Thompson and Dr. Marvin Moulton of the U.S. Army Aeroflightdynamics Directorate (AMRDEC) at Huntsville, AL, who provided valuable discussion and direction for the project. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. Army or the NRTC. Several students assisted in the measurements and computations. Rajiv Shenoy and Benjamin Koukol of the Georgia Tech Nonlinear Computational Aeroelasticity Lab (NCAL) helped with the CFD grid adaptation and CFD runs, including post-processing, respectively. References 1 Raz, R., Rosen, A., Carmeli, A., Lusardi, J., Cicolani, L., and Robinson, D., Wind Tunnel and Flight Evaluation of Passive Stabilization of a Cargo Container Slung Load, Journal of the American Helicopter Society, Vol. 55, 2010, pp Cicolani, L., Lusardi, J., Greaves, L., Robinson, D., Rosen, A., and Raz, R., Flight Test Results for the Motions and Aerodynamics of a Cargo Container and a Cylindrical Slung Load, NASA/TP , ARMY/TR-RDMR-AF-10-01, Tyson, P., Cicolani, L., Tischler, M., Rosen, A., Levine, D., and Dearing, M., Simulation Prediction and Flight Validation of the UH-60A Black Hawk Slung Load Characteristics, Annual Forum Proceedings of the American Helicopter Society, Vol. 55, 1999, pp Reddy, K., Truong, T., Stuckey, R., and Bourne, K., Dynamic Simulation of a Helicopter Carrying a Slung Load, Defence Science and Technology Organisation, Australian Department of Defence. 5 R Mantri, V Raghav, N. and Smith, M., Stability Prediction of Sling Load Dynamics Using Wind Tunnel Models, Proceedings of AHS Forum 67, Bonhaus, D., An Upwind Multigrid Method For Solving Viscous Flows On Unstructured Triangular Meshes, Master s thesis, George Washington University, of 13

13 7 Shenoy, R. and Smith, M. J., Unstructured Overset Grid Adaptation for Rotorcraft Aerodynamic Interactions, 67th Annual Forum Proceedings of the American Helicopter Society, Virginia Beach, VA, May 3 5, Simulink - Simulation and Model-Based Design, 9 Cicolani, L., Raz, R., Rosen, A., Gordon, R., Cone, A., Theron, J., Lusardi, J., Tischler, M., and Robinson, D., Flight Test, Simulation and Passive Stabilization of a Cargo Container Slung Load in Forward Flight, Annual Forum Proceedings of the American Helicopter Society, Vol. 63, 2007, p Rosen, A., Cecutta, S., and Yaffe, R., Wind Tunnel Tests of Cube and CONEX Models, Technion Institute of Technology, Dept. of Aerospace Engineering, TAE, Vol. 844, Hoerner, S., Fluid-Dynamic Drag, Hoerner Fluid Dynamics, Brick Town, NJ, of 13