Aerodynamic drag of transiting objects by large-scale tomographic-piv

Transcription

1 Aerodynamic drag of transiting objects by large-scale tomographic-piv W. Terra 1,*, A. Sciacchitano 1, F. Scarano 1 1: Aerospace Engineering Department, TU Delft, The Netherlands * Correspondent author: w.terra@tudelft.nl Keywords: Tomographic PIV, aerodynamic drag, HFSB, large-scale measurements ABSTRACT Experiments are conducted that obtain the aerodynamic drag of a sphere towed within a rectangular duct from PIV. The drag force is obtained invoking the time-average momentum equation within a control volume in a frame of reference moving with the object. The sphere with 0.1 m diameter is towed at velocity of 1.5 m/s, corresponding to Re = 10,000. The tomographic PIV measurements are conducted at 500 Hz in a volume of approximately 3 x 40 x 40 cubic centimeters. The large-scale measurement is attained making use of neutrally buoyant Helium-filled soap bubbles of approximately 0.3 mm diameter as air-flow tracers, preluding to a potential upscale of the technique. The measured drag depends upon three terms, namely the flow momentum, the pressure and the velocity fluctuations. These individual terms vary largely at different distances behind the sphere, while the sum attains a relatively constant value. More than two diameters behind the object the drag only varies by about 1%, yielding a practical criterion for the drag evaluation of bluff objects with this technique. 1. Introduction Aerodynamic forces result from the interaction between an object and a fluid in relative motion. The aerodynamic drag is the component of the resulting aerodynamic force along the direction of motion. The determination of the aerodynamic drag is relevant for many engineering applications, e.g. to enhance the performance and reduce the fuel consumption of aircraft and road vehicles, as well as for more general applications as speed sports and biomechanics for the study of human and animal locomotion and flight. Among the different techniques existing to quantify the aerodynamic drag, some directly measure the force through a force balance connected to the object (Zdravkovich, 1990). Other methods infer it indirectly, either by measuring the deficit of momentum in the wake of the

2 object (Selig et al., 2011) or by integrating the distribution of the fluid flow pressure over the object surface (Neeteson, 2015). The latter approach only considers the pressure drag of an object, and does not include the friction drag, yielding an underestimate for the total aerodynamic drag. Another relevant distinction is based on applications featuring either a stationary object (e.g. immersed in a wind tunnel) or a moving one (catapult, towing tank). In the first case the model position and flow conditions can be controlled accurately resulting in well repeatable measurements. However, in some cases wind tunnel experiments are unsuited, for example due to the interference of model supports, large models causing blockage effects, vortex development hindered by wall interactions, impossibility of measuring the flow around an accelerating object. Moreover a moving floor is needed for accurate ground vehicle aerodynamics. Bouard and Coutenceau (1980) studied the early stage development of the wake behind an impulsively started cylinder by towing it through a water channel. A towing approach in a water channel was also selected to study the wing-tip vortices development of an Airbus A at large distances behind the airplane (Scarano et al., 2002). This approach is potentially attractive for measurements on objects that move autonomously, like transport vehicles, athletes of speed sports and animals. In the specific case of professional cycling, the drag is routinely estimated with the mechanical power generated by the rider, which however includes also the friction force between wheels and ground and other mechanical resistance. Assumptions are required to extract the aerodynamic resistance from the latter (Grappe et al. 2007). The same holds for the constant speed torque measurement (Fontaras and Dilara, 2014) and coast down test (Howell et al., 2002) on cars and trucks. A general approach for the determination of the drag of transiting objects in air is relevant to the above mentioned applications. The drag force can be obtained from non-intrusive measurements of the velocity field in the wake of the object. Phase-locked particle image velocimetry (PIV) measurements over propeller blades have demonstrated the principle for rotor aerodynamics (Ragni et al. 2011). More recently, Neeteson et al. (2015) have extended the approach to transiting objects for the estimation of the drag of a sphere freely falling in water. The latter approach,

3 however, relies upon the measurement of the surface pressure of a transparent object with index of refraction matched with that of the medium, making it unsuitable for experiments in air. An approach to measure the aerodynamic drag of transiting objects is currently missing. The present work discusses the use of large-scale tomographic PIV for the determination of the aerodynamic drag of transiting objects. The aerodynamic drag is evaluated by the application of a control volume approach from the flow velocity measured in the wake of the object. The approach is demonstrated by estimating the drag of a transiting object of moderate size (10 cm diameter). Helium filled soap bubbles (HFSB) are used as flow tracers, due to their high light scattering efficiency and tracing fidelity (Bosbach et al., 2009, and Scarano et al., 2015, among others). The drag force acting on a moving body is derived from the equations of conservation of momentum. Similar to Ragni et al. (2011), the time-average aerodynamic drag is expressed in terms of momentum deficit, fluctuating velocity and time-average pressure. The results are discussed in terms of these individual components computed at different distances behind the object. The discussion explains the contribution of the different terms to the aerodynamic drag and the change of contributions at increasing distances behind the model. Finally, the current work is intended as a milestone towards larger scale applications for the study of the aerodynamics of athletes in speed sports. 2. Working principle Drag from a control volume approach The integral drag force acting on a body can be derived through the application of the conservation of momentum in a control volume containing this body (Anderson, 1991), which is visualized in Fig. 1. For incompressible flow, the time dependent drag acting on the body can be written as D(t) = ρ u t V dv ρ (V n)u S ds ((pn τ n)ds) x S (1) where V is the velocity vector, ρ is the density, p pressure and τ the viscous stress. V is the control volume, with S its outer contour and n is the outward normal vector of S.

4 Fig. 1: Schematic description of the control volume approach. The viscous stress is negligible with respect to the other contributions when the control surface is sufficiently far away from the body surface (Kurtulus et al., 2007). Furthermore, the contour S is defined as the contour abcd, with segments ab and cd approximating streamlines. When the segments ab, cd and ad are taken sufficiently far away from the model, the expression of the drag becomes: D(t) = ρ u t dv + ρ (U u)u ds + (p p) ds (2) V S bc S bc The evaluation of the volume integral typically poses problems due to limited optical access all around the object. Evaluating this integral can be avoided by considering the time-average drag instead of the instantaneous one. When decomposing equation (2) into the Reynolds average components and averaging both sides of the equation, the time-average drag force is obtained: D = ρ (U u )u ds ρ u 2 ds + (p p ) ds (3) S bc S bc S bc where ū is the time-average streamwise velocity and u the fluctuating streamwise velocity. This expression allows us to derive the time-average drag of a model from the velocity and pressure statistics in a stationary wake volume. According to the principle of Galilean invariance, Equation (3) holds in any reference frame moving at constant velocity. Following Ragni et al. (2011), the following expression can be derived for the time-average drag acting on a model at constant speed UM:

5 D = ρ (U (u U M )(u U M )) S bc (t) ds ρ u 2 ds + S bc (t) S bc (t) (p p ) ds (4) where ū is the streamwise velocity measured in the stationary frame of reference and UM is the constant velocity at which the model moves. The time-average pressure on the right hand side of the equation is evaluated from the tomo-piv data solving the Poisson equation for pressure, according to van Oudheusden (2013). Appropriate boundary conditions must be prescribed to solve the Poisson equation for pressure. Finally, this approach allows to derive the time-average drag on a moving body at constant speed from the velocity statistics in a wake plane. However, instead of a plane, in this work a thin wake volume is considered for a more accurate reconstruction of the pressure. 3. Experimental apparatus and procedure Measurement system and conditions A schematic of the system devised for the experiments is shown in Fig. 2 and a picture taken of the setup in Fig. 3. The apparatus consists of a duct where a model is towed, 170 cm long with a squared cross section of 50x50 cm 2. The duct is closed in order to confine the seeding particles within a limited region and has transparent walls to allow access for illumination and imaging (Fig. 3). Fig. 2: Schematic views of the experimental setup.

6 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics LISBON PORTUGAL JULY 4 7, 2016 The model is a sphere of 10 cm diameter, which is towed through the tunnel at a constant speed of 1.5 m/s. The model is supported by an aerodynamic strut, which has a thickness to chord ratio of 15%, is 3 mm thick, 20 cm long and is mounted on a carriage moving on a rail beneath the bottom wall of the duct. The carriage is mounted to the shaft of a motor, which is digitally operated allowing to accurately control the speed of the model. The sphere is marked to track its position during the transit. During each experiment, the sphere begins its motion at a distance of about 25 diameters from the entrance to the duct to ensure a fully developed wake flow regime past the sphere within the measurement domain. Fig. 3: Overview of the developed system. Tomographic system The time-resolved tomo-piv measurements are conducted using HFSB as tracer particles (diameter ~ 300 μm). The HFSB are introduced into the tunnel by a rake of ten nozzles that generate about 30,000 particles per second each. The seeding system (nozzles and a control panel that regulates the air, helium and soap fluid flow rates) is provided by LaVision GmbH.

7 The illumination is provided by a Quantronix Darwin Duo Nd:YAG laser (nominal pulse energy of 25 mj at 1 KHz). The laser beam is diverged by spherical and cylindrical lenses. The oval cross section is cut into a rectangular one via light stops (Fig. 3). The size of the measurement volume is about 3 cm x 35 cm x 35 cm in x, y and z direction, respectively. The imaging system consists of three Photron Fast CAM SA1 cameras (CMOS, resolution of 1024 x 1024 pixels, pixel pitch of 20 μm, 12 bit). Each camera is equipped with a 60 mm Nikkor lens set to f/8. The magnification is approximately In the present conditions the seeding density is approximately 3 particles/cm 3 and 0.04 particles/pixel. PIV acquisition is performed within LaVision Davis 8.3 at a frequency of 500 Hz. Measurement procedure The tunnel entrance and exit are closed to contain the HFSB seeding before the spheroid transits through the tunnel. The door of the tunnel exit is of porous material to prevent creating overpressure in the container. The HFSB nozzles are operated until the concentration within the measurement volume reaches steady-state conditions (typically two minutes). Then they are switched off for the medium to become quiescent (typically 30 seconds). The tunnel entrance and exit walls are opened, the model is put in motion through the tunnel and data is acquired. Fig. 4- left depicts a sequence of the three raw images, separated by 30 ms, taken during a transit of the model through the measurement domain. The black silhouette of the sphere is clearly visible against a background of illuminated particles.

8 Fig. 4: (left) A sequence of three raw images of the sphere passing the measurement domain separated by a time increment of 30 ms; (righttop) Illumination distribution along the measurement depth in an area of 25 x 25 cm 2 ; (right-bottom) Illustration of the reconstruction of the time-average velocity from sequential phase-average velocity fields. Data reduction The tomo-piv data analysis is performed in LaVision Davis 8.3 and consists of standard image pre-processing and a velocity reconstruction by sequential MTE-MART (Lynch and Scarano, 2014). Volume reconstruction is performed on a discretized domain of 1074 x 1050 x 72 voxels and correlation volumes of 32 x 32 x 32 voxels with an overlap of 75% are used. This results in a sequence of instantaneous velocity vector fields with a density of 3 vectors/cm. Fig. 4 (right-top) presents the averaged distribution of particles over 100 reconstructed objects, showing the excellent signal-to-noise ratio of the reconstruction. A Galilean transformation of the instantaneous velocity data is performed in order to reduce the data in a frame of reference consistent with the moving object. In this frame of reference, phase-

9 average velocity fields are obtained by averaging the data acquired at different transits of the model. Afterwards, the phase-average velocity fields at the different time increments are combined, constructing a time-average velocity field that is elongated in streamwise direction. This approach is illustrated in Fig. 4 (bottom-right). To reconstruct time-average pressure from the measured velocity, Dirichlet boundary conditions are prescribed, which are derived from the isentropic flow relation. 4. Results Instantaneous flow field Fig. 5 shows the instantaneous velocity field in the center YZ-plane at four consecutive time instants. Non-dimensional time is defined as t = t U D, where D is the diameter of the sphere. At t * = 0 the back of the sphere is located at x = 0. Each increment in time corresponds to a translation in space of one sphere diameter in negative x-direction. A peak of negative streamwise velocity is clearly present in the near wake of the sphere at t * = 0. Furthermore, an area of accelerated flow is visible at the periphery of the wake. When time evolves, the sphere moves further along the negative x-direction and the velocity deficit in the measurement region becomes less pronounced. This is consistent with the characteristics of the mean flow past a sphere (Jang and Lee, 2008, Constantinescu and Squires, 2003). The wake of the supporting strut is also visible in the different velocity fields as a negative streamwise velocity below the sphere (z~0, y<0). Its effect on the drag estimate is discussed in the later sections.

10 Fig. 5: Instantaneous streamwise velocity u in the YZ-plane at four time instants, t * = 0, t * = 1, t * = 2 and t * = 3 for a sphere velocity of 1.5 m/s Time-average flow field In the next sections the time-average velocity, fluctuating velocity and time-average pressure fields are presented and compared to literature to understand how the individual terms from Equation (4) contribute to the aerodynamic drag. Twenty instantaneous velocity fields, obtained from twenty different passages of the sphere through the measurement volume, are used to estimate the statistical average. The time-average data is presented in the reference frame of the

11 sphere in non-dimensional variables. Fig. 6 presents The streamwise velocity distribution in the central XY-plane (left), the central XZ-plane (middle) and Fig. 7 shows this velocity distribution in the YZ-plane (right) at x/d = The velocity field is rather axis-symmetric, which is to be expected for the flow past a sphere. The circular shape of the wake is altered only at the bottom of the measurement domain due to the presence of the supporting strut. From the streamlines in the wake of the sphere it is observed that the reattachment point is located at about x/d = 1.3, which is consistent with values from literature. Table 1 lists the results of four other works: Jang and Lee report a recirculation length, L/D, of 1.05 (Re = 11,000), Ozgoren et al. (2011) a value of about 1.4 (Re = 10,000) and Yun et al. (2006) and Constantinescu and Squires (2003) report 1.86 (Re = 10,000) and 2.2 (Re = 10,000), respectively. The wide range of values can be ascribed to differences in the experimental setup, and, in the case of numerical simulations, differences in turbulence models. The maximum reverse flow velocity is about -0.5 occurring at x/d = 0.6 and y/d ~ 0 (Fig. 6-top), which compares fairly well to the value of -0.4 reported by Constantinescu and Squires. The location of maximum reverse flow differs from the results of Constantinescu and Squires: x/d = 1.41 and y/d = 0. This, however, is consistent with the larger recirculation length that they report. In general the location of the maximum reverse flow compares well to that of the other authors listed in Table 1. Finally, the recirculation vortices show rather clearly in the central vertical plane (Fig. 6 bottomleft) and are located at about x/d = 0.75 and y/d = ±0.45. This again is consistent with literature. The presence of these vortices is less obvious from the horizontal center plane (Fig. 6 bottomright), which is most likely caused by a lack of statistical convergence.

12 Fig. 6: Non-dimensional time-average streamwise velocity in the wake of the sphere in the center XY-plane (left) and the center XZ-plane (right); contours (top) and streamlines (bottom)

13 Fig. 7: Non-dimensional time-average streamwise velocity in the wake of the sphere in the YZ-plane at x/d = 0.75; contours (left) and vectors (right). Present data and literature center of recirculation max reverse velocity (u U ) max( u 2 U ) Re L/D Position (x/d, y/d) value Position (x/d, y/d) value Position (x/d, y/d) Present work 10, ± ±0.4 Jang and Lee (2008) (PIV) Ozgoren et al. (2011) (PIV) Constantinescu et al. (2003) (LES) Yun et al. (2006) (LES) 11, ± * 1.0 * ±0.3 * 10, * 0.7 * ±0.4 * 10, , * 1.5 * 0.45 * Table 1: Comparison between present experimental results and those of Jang and Lee and Ozgoren and numerical results of Constantinescu and Yun. * Value is an estimation from presented figures in literature

14 Reynolds stress field Fig. 8 shows the contour plots of streamwise normal Reynolds stress, Rxx, in the center XY-plane (left) and the center XZ-plane (right). It is observed that the field of the normal Reynolds stress is rather symmetric in both planes. The distribution in the XZ-plane compares rather well to literature (Jang and Lee, 2008; Constantinescu et al., 2003; Yun et al., 2006), with maxima around x/d = 1 and z/d = ±0.4 and the presences of two branches of high local normal Reynolds stress, diverging from the streamwise axis and decreasing in strength for x/d > 1. The distribution in the XY-plane shows less similarity, likely due to the disturbance of the supporting strut. The local maxima of Rxx are between 0.35 and 0.4, which is within the range that is listed in literature (Table 1). Further statistical convergence of the results most likely allows pinpointing the location of the peaks of the Reynolds stresses more accurately. Fig. 8: Contours of the normal Reynold stress in the center XY-plane (left) and the center XZ-(right) Pressure reconstruction Fig. 9 depicts the distribution of the mean pressure coefficient in the center plane XY-plane (left) and the center XZ-plane (right). The general distribution of the pressure coefficient is as expected: The location of the pressure coefficient minima corresponds to the location of the recirculation vortices (Fig. 6 bottom-left) and a peak of high CP is observed right after the

15 reattachment point. The distribution of pressure shows a slight asymmetry in the XY-plane, which originates from similar asymmetries in the velocity statistics presented in Fig. 6 (left) and Fig. 8 (left). To the best knowledge of the authors, no reference exists that shows the pressure field in the wake of a sphere. For a comparison with literature only the base pressure coefficient can be evaluated, which is about -0.5 in the present work. Yun et al. (2006) and Constantinescu and Squires (2003) report a value of and Bakic et al. (2006) a value of -0.3 at Re = 50,000. With respect to these values we overestimate the base pressure. This work, however, does not aim to accurately measure the base pressure. The next section will discuss how the integral values of time-average velocity and pressure and the velocity fluctuations evolve in the wake of the sphere. This will provide more insight into the reliability of the reconstructed pressure. Fig. 9: Distribution of time-average pressure coefficient in the center XZ-plane (left) and the YZ-plane at x/d = 0.75 (right) Aerodynamic drag The time-average aerodynamic drag, derived from the velocity statistics measured in the wake of the model, is expected to be independent of the distance of the measurement plane behind the sphere. Therefore, the sum of the three right hand side terms from the drag Equation (4) is expected to yield a constant value, while these terms individually are expected to vary with x/d based on the results of time-average velocity, velocity fluctuations and time-average pressure

16 depicted in Fig. 7, Fig. 8 and Fig. 9, respectively. Fig. 10-left presents the drag coefficient computed in the wake of the model from YZ-planes between x/d = 0.5 and x/d = 3.5 including the three right hand side terms in the drag equation. As expected, the physical location at which the drag is computed does hardly affect the resulting drag coefficient value, which confirms the good quality of the data. The momentum term is strongly negative close to the sphere, with a peak at x/d = 0.6, and increases quickly afterwards to reach a relatively constant value after x/d = 2. The negative contribution of the momentum deficit at small x/d is mostly compensated by the pressure term, which is large close to the sphere. The pressure term is expected to reach zero value at large distance behind the model. It is observed that, instead, it reaches small negative values. Measurement errors of the velocity may be the reason for this behavior. These errors in the velocity are amplified in the velocity gradients, through which they propagate into the reconstructed pressure, making the pressure relatively sensitive to these measurement errors. The Reynolds stress term contributes negatively to the drag by definition. A negative peak is located at x/d = 1, which corresponds to the location of the peaks of Rxx in Fig. 8. As expected, this term slowly increases towards small values close to zero. Fig. 10-right presents the drag coefficient in the wake of the sphere together with a range of values reported in literature. The lower bound of this range is 0.39 reported by Yun et al. (2006) and Constantinescu and Squires (2003) and the upper bound is 0.44 from Achenbach (1972) (Re = 20,000). The drag coefficient of the present work varies by 0.17, from 0.33 at x/d = 0.95 and 0.5 at x/d = 0.5. However, both extrema are located close to the sphere. Considering only the region of x/d > 2, the computed drag is relatively constant and fluctuates between 0.47 at x/d = 2 and 0.48 at x/d = 2.6, which is about 1% of the average of A CD of overestimates the values in literature by 8 20%. This is, at least partly, caused by the supporting strut of the sphere. The contours of streamwise velocity in Fig. 6, show the effect of the strut on the flow in the wake, contributing to an increase in momentum deficit and, therefore, drag. Finally, a practical criterion is proposed to measure the aerodynamic drag of a transiting bluff body by the presented approach: the drag should be measured at least two diameters behind the model.

17 Fig. 10: Mean drag coefficient computed at different distances behind the sphere; C D and the individual momentum, pressure and Re stress term (left), and, the present result relative to the range of values reported in literature (right). 5. Conclusions A control volume approach is applied to determine the aerodynamic drag of transiting objects by means of tomo-piv measurements in the wake of the model. The concept is demonstrated using a newly developed system to measure the flow over a sphere with a diameter of 10 cm moving at 1.5 m/s. Velocity statistics in the wake of the sphere have been obtained from a set of twenty model transits and the obtained time-average velocity, fluctuating velocities and timeaverage pressure compare well to literature. The aerodynamic drag is computed as the sum of these three components at different distances behind the sphere. As expected, the resulting drag is relatively constant. Relatively large variations of 0.17 are observed at x/d < 2. However, measuring the drag between x/d = 2 and x/d = 3.5, the results vary only about 1% from an average of This provides a practical criterion to evaluate the drag of bluff bodies with the presented approach.

18 Acknowledgements This work is partly funded by the TU Delft Sports Engineering Institute and the European Research Council Proof of Concept Grant Flow Visualization Based Pressure (no ). Andrea Rubino is kindly acknowledged for the support on the experiments. References o Achenbach (1972), Experiments on the flow past spheres at very high Reynolds numbers, J Fluid Mech, vol. 54, part 3, pp o Anderson jr. JD (1991), Fundamentals of aerodynamics, McGraw-Hill International editions o Bakic V, Schmid M, Stankovic BF (2006), Experimental investigation of turbulent structures of flow around a sphere, Thermal Sci, Vol. 10, No. 2, pp o Bouard R, Coutanceau M (1980), The early stage of development of the wake behind an impulsively started cylinder for 40<Re<10 4, J. Fluid Mech, vol. 101, part 3, pp o Constantinescu GS, Squires KD (2003), LES and DES Investigations of Turbulent Flow over a Sphere at Re=10000, Flow, Turb and Comb 70: o Fontaras G, Dilara P (2014), An Experimental Methodology for Measuring of Aerodynamic Resistances of Heavy Duty Vehicles in the Framework of European CO2 Emissions Monitoring Scheme, SAE int. J. Commer. Veh. 7 o Grappe F, Candau R, Belli A, Rouillon JD (1997), Aerodynamic drag in field cycling with special reference to Obree s position, Ergonomics, Vol. 40, No. 12, pp o Howell J, Sherwin C, Passmore M, Le Good, G (2002), Aerodynamic Drag of a Compact SUV as Measured On-Road and in the wind tunnel, SAE Transactions. J Passenger Cars - Mech Sys, SAE Paper No , pp o Jang YI, Lee SJ (2008), PIV analysis of near-wake behind a sphere at a subcritical conditions, Exp Fluids, 44: DOI /s o Kurtulus DF, Scarano F, David L (2007), Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV, Exp Fluids, 42: DOI /s o Lauder GV, Madden PGA (200&), Fish locomotion: kinematics and hydrodynamics of flexible foil-like fins, Exp Fluids, 43: DOI /s o Neeteson NJ, Bhattacharya S, Rival DE, Michaelis D, Schanz D, Schröder A (2015), Pressure- Field Extraction from Lagrangian Flow Measurements, 11th international symposium on particle image velocimetry, Santa Barbara, California o Ozgoren M, Okbaz A, Kahraman A, Hassanzadeh R, Sahin B, Akilli H, Dogan S (2011), Experimental Investigation of the Flow structure around a sphere and its control with jet flow via PIV, 6th International Advanced Technologies Symposium, Elazığ, Turkey o Ragni D, van Oudheusden BW, Scarano F (2011), Non-intrusive aerodynamic loads analysis of an aircraft propeller blade, Exp Fluids, 51: DOI /s

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