Experimental study on Ahmed's body drag coefficient for different yaw angles

J. Wind Eng. Ind. Aerodyn. 157 (2016) 140–144

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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Experimental study on Ahmed's body drag coefficient for different yaw angles F.J. Bello-Millán a, T. Mäkelä a, L. Parras b,n, C. del Pino b, C. Ferrera c a

Universidad de Granada, Instituto Interuniversitario de Investigación del Sistema Tierra en Andalucía (IISTA) Av. del Mediterráneo, 18006 Granada, España Universidad de Málaga, E.T.S. Ingeniería Industrial, Universidad de Málaga, 29071 Málaga, España c Universidad de Extremadura, Department of Mechanical, Energy and Materials Engineering, Badajoz, España b

art ic l e i nf o

a b s t r a c t

Article history: Received 19 September 2015 Received in revised form 16 June 2016 Accepted 7 August 2016

We present experiments conducted in a wind tunnel to characterize yaw angle effects on the drag force acting on the Ahmed body with slant angle of 25°. The main contribution of this experimental work is to create a reliable database of drag coefficients under yawed conditions. For zero yaw angle, we find a small variation in the drag coefficient, CD, for Reynolds number in the range 3 × 105 − 30 × 105, resulting in the known tendency of a drag coefficient decrement as the Reynolds number increases. This trend is in agreement with other experimental works but is 30% greater than the usual CD (Re) function. Secondly, the drag coefficient increases significantly with an increment in the yaw angle at a constant Reynolds number. Three distinctive regions for the drag coefficient as a function of the yaw angles are established from the experimental results: the drag coefficient increases for 0° ≲ β ≲ 60°, remains constant in the range 60° ≲ β ≲ 75° and finally, the drag coefficient grows again until β = 90°. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Ahmed body Aerodynamics Drag coefficient

1. Introduction The Ahmed vehicle model (Ahmed et al., 1984) is one of the most widely studied bluff bodies in the Aerodynamics Community due to the large number of published references (Han, 1989; Minguez et al., 2008), and reliable experimental databases. One can validate new experimental setups or wind tunnel measurements by comparing them with those obtained in other facilities. This is also the case of numerical simulations, where grid convergence or turbulent models are checked using values of the velocity field around or behind this body, or forces acting on it. Thus, a free turbulent stream acting on the Ahmed body is considered important from a fundamental point of view due to the flow separation, the unsteadiness of the drag forces or the vorticity generation over the surface (Chong et al., 1990; Serre et al., 2013). These findings can be later used to improve the design of real vehicles. Other reference models used in automotive aerodynamics, whose shapes are similar to real cars are discussed thoroughly in Le Good and Garry (2004). The classic Ahmed body design has three important parts (Ahmed et al., 1984) (see a sketch in Fig. 1). First, a windward face with rounded corners which adapts the flow in the inlet and allows the boundary layer to follow the body shape without n

Corresponding author. E-mail address: [email protected] (L. Parras).

http://dx.doi.org/10.1016/j.jweia.2016.08.005 0167-6105/& 2016 Elsevier Ltd. All rights reserved.

separations. Secondly, a rectangular shape to stabilize the flow. Finally, an area characterized by the slant angle, where the largest flow separation point is located. Originally, the Ahmed body was designed to study the slant angle effect on the drag force of vehicles and the presence of vortical structures extended downstream beyond the end of the bluff body, rather than the influence of yaw angles. Only small values of the yaw angle were tested in Ahmed et al. (1984) to ensure bluff body symmetry in the experimental configuration. In fact, significant variations have been observed when the slant angle was changed: from 2D attached wakes to massively separated 3D, counter-rotating trailing vortices. High drag forces are induced for slant angles between 12.5° and 30° due to the complex three dimensional wakes, which create strong low pressure conditions downwind of the body (Howard and Pourquie, 2002). However, the drag force for different yaw angles becomes a significant parameter to simulate the behavior of a vehicle taking a curve or exposed to cross wind configurations (which corresponds to yaw angles typically lower than 10°). The airflow around bodies under yawed conditions has been studied in other ground vehicles (Krajnović et al., 2011, 2012) though there is little or no information on the force exerted on the Ahmed body in this particular configuration. To that end, the behavior when the model is yawed becomes the motivation of this work. Numerically, the flow around the Ahmed body is a challenge in CFD. Different turbulent models have been tested, specifically Reynolds Averaged Navier Stokes (RANS) (Han, 1989; Guilmineau,

F.J. Bello-Millán et al. / J. Wind Eng. Ind. Aerodyn. 157 (2016) 140–144

Fig. 1. Schematic of the Ahmed's body shape, dimensions in millimeters (Ahmed et al., 1984). The flat plate used to attach the model to the force sensor to allow the rotation is shown in dashed line.

2008) and large-eddy simulations (LES) starting with Hinterberger et al. and Krajnović and Davidson (2005a,b). Recently, Minguez et al. (2008) solved the problem using a combination of high-order large-eddy simulations (LES) with a spectral vanishing viscosity (SVV) technique, resulting in the so-called LES-SVV method, where a pseudopenalization technique was required to model the bluff body accurately. An excellent review of different approaches to modeling turbulence for bluff body simulations was given in said research (see references therein) in which it is discussed the use of Reynolds Averaged Navier Stokes (RANS) models, and three more alternatives to be combined with LES simulations: detached eddy simulation (DES), subgrid scale (SGS) models or the more general implicit LES (ILES) method. Later, the same authors (two French groups) collaborated with two German teams resulting in a significant numerical benchmark (Serre et al., 2013). Chief attention was paid on the respective advantages and disadvantages of the several methods used (LES and DES). The reported results were achieved with one DES and three different LES methods developed in the four research teams. The so-called LES-NWM (LES combined with wall functions) was the numerical method that best predicted the drag coefficient for a given Reynolds number. Following this line of research, Franck et al. (2009) ran LES simulations for a slant angle of 12.5° with Subgrid Scale Modeling (SGM), and stabilized pressure and velocity fields using a combination of Streamline Upwind Petrov–Galerkin (SUPG) and Pressure Stabilizing Petrov–Galerkin (PSPG) schemes. A similar article has been published recently (Aljure et al., 2014), in which other LES models are used (e.g. VMS or SIGMA models), concluding that sigma models usually give the closest drag coefficient values to the experimental ones. The main conclusions of these numerical studies is that steady RANS is unable to accurately predict the structures formed in the flow around the Ahmed body. For this reason, LES is the preferred turbulence model to solve this problem numerically. Due to the lower cost of unsteady RANS simulations, authors (Mirzaei et al., 2015) proposed recently new methods called PANS (Partial Average Navier–Stokes equations) that provide flow structures quite similar to experiments and LES results. Finally, it is worth mentioning that there have been some numerical (Krajnović and Basara, 2010; Krajnović, 2013) and experimental (Thacker et al., 2012) efforts to control the 3D separation in Ahmed's body. CFD simulations described above might be compared with experimental measurements to determine their validity. The comparison of experimental and numerical velocity fields, flow visualizations and numerical streamlines, or drag coefficients obtained both experimentally and numerically should be within an acceptable range of error. To that end, Lienhart et al. (2002) provided velocity measurements using a LDA technique. Furthermore, Meile et al. (2011) reported experimental values of CD as a function of Reynolds number which were compared with the numerical

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results given with Fluent© code. Conan et al. (2011) studied the drag of the Ahmed body with different slant angles and different measurement techniques. Thacker et al. (2012) eliminated experimentally the flow separation by means of a comparison between two model configurations: sharp and rounded edge at the connection between the roof and the rear slant. All these works were developed for a zero yaw angle. These researchers found a decrease in the drag coefficient as the Reynolds number increased, and some of them analyzed in detail the regions between subcritical or supercritical slant angles. There are also flow field experimental results performed using PIV but for Reynolds numbers one order of magnitude smaller than the commented studies (Wang et al., 2013). The structure of the wake is very important in the response of the drag force on the following vehicle. This has been studied experimentally for two Ahmed's bodies, changing the vehicle spacing (Watkins and Vino, 2008). For low vehicle spacing, the effect of the wake of the first vehicle increases the drag force on the second; whereas the increase of the spacing between vehicles reduces the drag force on the second. On the other hand, there are numerical results on transient aerodynamic phenomena induced by passing maneuvers (Uystepruyst and Krajnović, 2013), in which the wake structure of the first vehicle interacts with the second producing suction forces between them. Regarding the yaw angle effect on the Ahmed body, Bayraktar et al. (2001) reported novel results for vehicles under cross wind configuration, e.g. caused by topographic variations. The yaw angle was significant not only for experimental calibration to set the base yaw angle at zero but also to investigate the cross wind effect in the model. An increase of drag coefficient with yaw angle was confirmed in the range beyond ±3° and it also presented a small dispersion of values about the mean value of the drag coefficient. Recently, the effect of the yaw angle on the forces on other vehicle models has been studied in detail. In particular, for “Willy”, a new car model introduced by Chometon et al. (2004). Apart from drag reduction studies in the Ahmed body with passive or active strategies, Cary et al. (2006) analyzed yaw angles up to 12°. Golhke et al. (2007, 2009) also gave some new insight into the physical mechanisms responsible for the force increase in cross-wind situations using the Willy model, and identifying the presence of strong vortices on the rear side. Other cross wind simulations around the square-back Willy model for several yaw angles using ISIS-CFD solver have been carried out by Guilmineau et al. (2013). They also found an increase of drag with yaw angle from β = 0° to 30°. Finally, there are studies of the wake structure of a vehicle in sudden crosswind configuration (Volpe et al., 2014), in which the wake structure bends to one side due to the presence of the crosswind. This effect produces a large overshoot in the lateral force coefficient. In the present study, drag coefficients were obtained experimentally as a function of the yaw angle, β, from 0° to 90° for the Ahmed body. Experimental methodologies, together with the wind tunnel facility, are described in detail in Section 2. The main results in terms of drag coefficients and flow visualizations are shown in Section 3. In the final section the main conclusions are drawn.

2. Experimental approach 2.1. Experimental setup Fig. 1 is a schematic of the original Ahmed body, with actual dimensions in mm included and the frame of reference used. The model for this work was a 55% scale replica of the original body, and was built using expanded polystyrene (EPS). The model was

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machined using a CNC mill with a tolerance lower than 0.1 mm. Only one rear body slant angle (α = 25°) was considered. The roughness effect of the body surface is out of the scope of this work. Experimental tests were conducted in the Vehicle Aero-Hydrodynamics Laboratory (Universidad de Málaga) in a closed lowspeed wind tunnel with a 4 m × 1 m × 1 m test section. The symmetry plane of the Ahmed scale model was located at the center of the wind tunnel test section, reducing wall and roof effects on the body. Velocity and air temperature variations inside the wind tunnel were monitored digitally. A freestream velocity, U, ranging from U¼6.9 m/s to 24.5 m/s was used. The turbulence intensity level was lower than 1.0% in the worst case. The yaw angle, β, is formed between the airflow direction and the longitudinal axis of the Ahmed body. Thus, the blockage ratio of the scale body represents only 3% and 9% of the tunnel section for β = 0° and β = 90°, respectively. Positive yaw angles correspond to clockwise rotation. Drag forces, FD, were measured with a digital force balance mounted in a stepper motor controlled by a PC that allows variations in the yaw angle within ±0.05° (see MartinezAranda et al., 2016 or Fedoul et al., 2014 for equipment, details and calibration). A rectangular aluminum flat plate of dimensions 275 × 196 mm2 and 3 mm thickness was machined and used as a rotating bracket attached to the underside of the body and the digital force sensor. This flat plate was located under the four legs of the Ahmed body (see Fig. 1). Drag forces caused by this plate were subtracted from the real forces obtained for the system plateþbody as it will be described below. Flow visualizations were obtained using smoke produced with a 0.12 mm diameter Ni–Cr wire in a (x,z)-plane. One 500 mW continuous green laser and a high-speed camera were used (see Fig. 2). Flow visualizations were recorded at 500 frames per second and 1024  1024 pixels of spatial resolution. The laser plane was aligned to the symmetry plane of the Ahmed body at β = 0°, which was perpendicular to the field of view of the camera. The drag coefficient CD is the non-dimensional form of the force FD exerted on the Ahmed body in the streamwise direction, and defined as

CD =

FD , 1 ρ(T )U2A 2

(1)

where ρ(T ) is the density of the air at a given temperature, U is the

freestream velocity, and A is the cross section of the Ahmed body front face for null yaw angle. For different yaw angles we keep the same definition of CD based on the frontal cross section (for null yaw angle), to only analyze variations on the drag force. On the other hand, Reynolds number is expressed by the equation

Re =

UL , ν(T )

(2)

where L ¼574.2 mm (model's length along longitudinal axis direction) and ν(T ) is the air kinematic viscosity, which depends on the air temperature, T. The resulting Reynolds number has a standard deviation of 2%, resulting from the velocity fluctuation of the wind tunnel commented above. The error in the kinematic viscosity could be neglected, because of the variations in the air temperature were within ±0.5 K in each test. 2.2. Experimental procedure The methodology for a single experiment is as follows. Velocity was set to U, waiting an average of 3 min to reach a fully developed flow. This could also be ensured by observing the small temporal variations in the force signals which were monitored in a PC. Three tests were recorded during an average time of 20 s under the same conditions (velocity and constant yaw angle). The mean temperature inside the tunnel in each experiment was recorded to compute the correct values of the kinematic viscosity ν(T ) and the density ρ(T ) of the air. The digital force sensor measured forces in the three directions of space although only the drag force acting on the Ahmed body was of interest. Consequently, no attention was paid to lift or pitch yaw forces (see below). The measuring frequency and accuracy of the force balance were 2.5 kHz and 0.1%, respectively. Force errors were computed as the standard deviation of three tests. In this novel setup the system plate þbody was mounted on a controlled stepper motor that rotates the system changing the yaw angle. The axial Ahmed body direction was located along the stream direction of the balance sensor (x-axis), while spanwise and vertical directions were related to y- and z-axes, respectively. For each freestream velocity U, we have measured the force exerted by the set of the Ahmed body and the plate, FAhmed + plate , and also the force that the air exerted on the system when only the plate was mounted, Fplate. The tare drag was removed from each measurement. Finally, the resulting force can be obtained as

FAhmed = FAhmed + plate − Fplate. Due to the unstable behavior of the flow, the drag force was unsteady, having an oscillation of 10% around the average value. To improve the results, each test was repeated three times and the mean and the standard deviation was used as the final result. Both the Ahmed body and the force sensor had the same reference system with joint movements. The measured force vectors on the x- and y-axes were added to compute the drag force acting on the body in the flow direction:

( )

( )

FD = Fx sensor cos β + Fy sensorsin β ,

Fig. 2. Sketch of the experimental setup: continuous laser, digital camera, together with DC motor and force sensor controlled by a PC.

(3)

where FD is the resulting drag force, and Fx sensor and Fy sensor are the mean force values. Considering velocity, force and temperature variations, the final mean drag coefficient values have a standard deviation lower than 0.02%. In addition, several random tests were repeated different days to ensure reliable data. The drag force as a function of the yaw angle was computed for β = 0° to β = 90° in steps of 5°. Finally, symmetry was ensured within small yaw angles to detect β = 0° and same results were also obtained for counter clockwise β angles (not shown).

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3. Results 3.1. Flow visualization Smoke visualizations were performed in two different sections: front and rear sides (see in Fig. 2 only a sketch of the rear side configuration). The experiments were carried out at a Reynolds number of 6.96 × 105. The airflow was attached to the Ahmed body in the front side as it is shown in Fig. 3 (a) at 0° yaw angle. Due to the configuration of the flow and the structure of the front side of the Ahmed body, simulations predict that a very thin recirculation bubble will form and it can be observed in Fig. 3 (a) (marked by one white arrow). One can observe that the flow is attached to the body on the rear side for null yaw angle. 3.2. Drag coefficient versus Reynolds number Fig. 4 shows the average experimental values of drag coefficient as Reynolds number increases. Those results can be seen as an extension of Thacker's results (Thacker et al., 2012) for lower Reynolds numbers and we have proposed a fit for the drag coefficient, as

CD = 0.3849 + 0.0603 e−

Re 1e − 6 0.5217 .

(4)

Fig. 4. CD as a function of Reynolds number for the present experimental results compared with other author's results.

On the other hand, Ahmed et al. (1984), Bayraktar et al. (2001) and Meile et al. (2011) results lay far below our experimental values. Thacker et al. (2012) stated that this difference can be due to the high sensitivity of the separation produced by the sharpness of the roof/rear window edge connection. Conan et al. (2011) results lay in an intermediate region between both fits. We have included in the same figure the results obtained by Serre et al. (2013), who performed very accurate LES simulations on the same problem. As it can be observed, some of their results are in agreement with the present experimental results. However, they are not able to estimate the real value of the drag coefficient provided by Thacker. We include the results that Thacker presented for a rounded edge which avoided the appearance of the recirculation bubble in the slant angle. Some of these results lay on those given in Serre et al. This leads the current authors to believe that the reason for the discrepancies is the impossibility of the numerical simulations to predict accurately the detached flow passing through the slant angle. 3.3. Drag force versus yaw angle Reynolds number of 6.96 × 105 was chosen to try out the novel experimental setup, so the yaw angle was changed from 0° to 90°. Drag coefficient measurements versus the yaw angle, β, are depicted in Fig. 5. Generically, the flow force Fx exerted on the

Fig. 3. Two different flow visualizations pictures with numerical streamlines for β = 0°: front side (a) and rear side (b). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 5. CD as a function of the yaw angle β for Re = 6.96 × 105.

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Ahmed body along the x-coordinate grows until β = 90°, due to the increment of area in the (y, z)-plane. Three regions were found experimentally: the drag coefficient increased for 60° ≳ β ≥ 0°, remained almost constant in the range 75° ≳ β ≳ 60° and finally, its value increased again for β up to 90°.

4. Conclusions Ahmed body aerodynamic has been a widely studied topic in the recent years. It has also been a benchmark for different numerical codes that try to model the experimental results. In the current study, a flat plate mounted on a digital force sensor in a wind tunnel was used as a rotating bracket for the Ahmed body to change the yaw angle. This technique allows the drag coefficient to be determined by means of a precise experimental procedure. The slant angle α was constant and equal to 25°. The resulting drag coefficient, CD, of the Ahmed body slightly decreases as the Reynolds number increases in the range of 3 × 105 − 30 × 105, for a null yaw angle, β = 0°. The experimental results obtained provide a different trend to Meile's fit, although there are other recent experiments that collapse with the current one, e.g. Thacker's experimental results with sharp edge. The experimental curve fitting, Eq. (4), presented here is as near to some of the newest numerical results as the one given by Meile. Also, Thacker's study on the rounded edge provides a drag coefficient that lies as near Serre et al. (2013) results. This leads the current authors to think that there is a huge influence on the connection between the roof and the rear slant surface, and that this small change in direction of the fluid is not well predicted by the numerical codes. This is a very interesting topic to pursue for future experimental and numerical investigations. In addition, it was found that the drag coefficient increases with the yaw angle. Three regions were reported: CD increases for 60° ≳ β ≥ 0°, remained almost constant in the range 75° ≳ β ≳ 60° and finally, it increased till β = 90°. Previous numerical studies reported the same increasing trend. Therefore, it can be concluded that reliable experimental data provided in the current research will help the appearance of future numerical work to study flow separation using turbulent models such as uRANS, LES or DES at yaw angles greater than 30°. Further study of the modification of the slant angle, α, which is also a parameter that strongly affects the wake behind this bluff body, is also needed to compute the surface CD(α , β ).

Acknowledgments The authors want to thank S. Pinazo-Ortega for his technical support building the experimental set-up and installing it in the wind tunnel. C.d.P. and L.P. would like to acknowledge also the support of the Ministerio de Ciencia e Innovación of Spain, Grant no. ENE2010-16851 and the grant Proyecto de Excelencia de la Junta de Andalucía number P11-TEP7776. F.J.B.M. wants to acknowledge the support from Abengoa Research under the cooperation framework program between said company and the Environmental Fluids Dynamics Research Group of the University of Granada. Also, authors thank A. Lira-Loarca and K.L. Rowe for the correction of the English style.

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