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Determining Aerodynamic Drag of Transiting Objects by Time-Resolved 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016 Aerodynamic drag of transiting objects by large-scale tomographic-PIV W. Terra1,*, A. Sciacchitano1, F. Scarano1 1: Aerospace Engineering Department, TU Delft, The Netherlands * Correspondent author: [email protected] 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 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016 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 A340-300 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, 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016 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 휕푢 퐷(푡) = −휌 ∰ 푑푉 − 휌 ∯(푽 ∙ 풏)푢 푑푆 − ∯((푝풏 − 휏 ∙ 풏)푑푆)푥 (1) V 휕푡 S S 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. 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016 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: 휕푢 퐷(푡) = −휌 ∰ 푑V + 휌 ∬ (푈 − 푢)푢 푑S + ∬ (푝 − 푝) 푑S (2) 휕푡 ∞ ∞ V Sbc Sbc 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: ̅̅̅2̅ 퐷̅ = 휌 ∬ (푈∞ − 푢̅)푢̅ 푑S − 휌 ∬ 푢′ 푑S + ∬ (푝∞ − 푝̅) 푑S (3) Sbc Sbc Sbc 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: 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016 ̅̅̅2̅ 퐷̅ = 휌 ∬ (푈∞ − (푢̅ − 푈푀)(푢̅ − 푈푀)) 푑S − 휌 ∬ 푢′ 푑S + ∬ (푝∞ − 푝̅) 푑S (4) Sbc(푡) Sbc(푡) Sbc(푡) 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.
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