Bluff body drag manipulation using pulsed jets andCoanda effect

D. Barros∗1,2, J. Boree1, B.R. Noack1, A. Spohn1, and T. Ruiz2

1Institut Pprime UPR-3346, CNRS – Universite de Poitiers – ENSMA,Futuroscope Chasseneuil, France.

2PSA Peugeot Citroen, Centre Technique de Velizy, 78943Velizy-Villacoublay Cedex, France

March 4, 2022

Abstract

We analyze the effects of unsteady forcing on the wake and drag of a square backblunt body. In combination with a Coanda effect, shear-layer forcing by periodic blow-ing of wall bounded jets allows to recover over 30% of the base pressure. The actuationfrequency is an order of magnitude higher than the natural shear-layer instabilities.High frequency Coanda blowing leads to a thinner time-averaged wake. The effectof this form shaping is analyzed by pressure taps on the rear side of the model incombination with PIV measurements. Velocity components of the mean field indicatea pressure recovery and favorable mean curvature effects across the separated shearlayers in the region close to the rear end of the blunt body when actuation is applied.The wake dynamics further downstream, however, remains very similar to the unforcedoscillatory wake mode.

1 Introduction

Drag reduction of bluff bodies has become a major challenge for transport vehicles dueto increasing need for reducing fuel consumption and carbon pollution. For example, toovercome the aerodynamic drag of road vehicles on a highway, more than 50% of the enginepower is necessary (Hucho & Sovran, 1993). The aerodynamic drag of cars is principallydue to their shape, causing significant pressure differences between their front and rearsurfaces. In contrast to streamlined bodies, the flow massively separates leading to theformation of a wake with reduced pressure and recirculating flow. The wake flow of simplifiedsquare back road vehicles was extensively studied in the past (Ahmed et al., 1984) and

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reviewed, more recently, by Grandemange et al. (2013) and Choi et al. (2014), where detailedunsteady features of such wakes are described. The wake contains low energy recirculatingflow surrounded by free shear layers. According to Huerre & Monkewitz (1990), these shearlayers are convectively unstable and act as a noise amplifier while the absolute instability ofthe recirculating flow produces self-sustained large-scale oscillations.

In recent years flow control turned out to be an efficient way to modify bluff body wakeswith the aim to increase the baseline pressure (Choi et al., 2008). The goal is either toreduce turbulent entrainment to elongate the wake flow towards the Kirchhoff solution orto decrease the cross section of the wake in order to increase directly the pressure recoveryby slowing down the main flow. In the former case, this was achieved mainly for nominallytwo-dimensional flows either by passive devices (Park et al., 2006; Parezanovic & Cadot,2012) or by active actuators like pulsating and zero-net-mass-flux jets (Pastoor et al., 2008;Chaligne et al., 2013). In contrast, pressure recovery is obtained by boat-tailing of the bodyshape (Choi et al., 2014) or by producing a flow deflection through steady jets associatedor not with a Coanda effect (Englar, 2001; Littlewood & Passmore, 2012; Pfeiffer & King,2012) in fully three-dimensional flows. For practical applications, all so far tested controltechniques show limitations related to power cost and geometrical constraints. In this studywe explore the possibility to decrease both constraints by deviating the flow through anunsteady Coanda effect.

Unsteady high frequency actuation appears to be an interesting possibility for wakecontrol since it allows to act directly on the spreading rate of the shear layers, while theglobal instability modes of the wake flow are not amplified (Glezer et al., 2005). Recently,Barros et al. (2014) and Oxlade et al. (2015) respectively applied this actuation techniqueto reduce the pressure drag of square back and axisymmetric blunt bodies using pulsed andzero-net-mass-flux jets. The unsteady jets were released along the border of the back sidein the direction of the main flow. The time-averaged flow observed by Barros et al. (2014)appeared virtually shaped to reduce the cross section of the wake and thus the pressure drag.

In the present work, we complete the straight high frequency jet actuation in Barroset al. (2014) by the addition of an unsteady Coanda effect to investigate the impact on thepressure drag of a square back blunt body similar to that studied by Ahmed et al. (1984).By mounting small curved surfaces along the blowing slits for the pulsed jets (see detail infigure 1) the flow is deviated towards the center line of the model leading to an increaseof the static pressure on the rear side of more than 30%. The increase in flow deviationbecomes particularly clear when the velocity field is analyzed near the upper trailing-edgeof the model. In addition, velocity fields of the whole wake show a significant decrease offlow entrainment inside the recirculation zone. Finally, hot-wire measurements confirm theabsence of any measurable effect on the wake shedding frequency.

2 Experimental set-up

2.1 Wind-tunnel facility

The experiments were performed inside the working section of a low-speed wind tunnel with2.6× 2.4 m2 cross-sectional area. Figure 1 shows a schematic of the test configuration. The

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Figure 1: Experimental set-up details. a) Wind-tunnel, flat plate dimensions and modelpositioning. The PIV field of view is illustrated in the symmetry plane of the configuration.b) Model dimensions and detail describing the pulsed jet system with the Coanda surface.

blunt body model with height H = 0.297m, width W = 0.350m and length L = 0.893m isthe same as used by Osth et al. (2014). The leading edges of the model were rounded withradius R = 0.085m. To achieve an approach flow outside the ground boundary layer, themodel was mounted on a false floor (flat plate with an elliptical leading edge). Four profiledsupports fixed the geometric ground clearance G = 0.05m. The upstream velocity Uo waskept constant at 15 m/s throughout the experiments. Based on the height of the model, theReynolds number of this flow is ReH = 3 × 105 corresponding to Reθ = 6 × 103 based onthe measured momentum thickness θ of the turbulent boundary layer at the upper trailingedge. When the units are not specified, all quantities were normalized by Uo and H.

2.2 Pressure and velocity measurements

In order to evaluate the pressure drag changes of the model when control is applied, 17pressure taps were installed on its rear surface. The differential pressure sensors operateswith the upstream static pressure po as the reference and within a range of 250 Pa. Wenormalize the pressure by using the pressure coefficient Cp = p−po

qo, where qo is the upstream

dynamical pressure of the flow. We define < Cp > and Cp as the spatial and the timeaveraged pressure coefficient respectively taken over the rear surface of the model and during60 seconds of acquisition. The acquisition frequency of the measurements was set as 6.25kHz. The spatially averaged pressure coefficient for the natural (reference) flow is called< Cpn >. To quantify the changes of Cp when the pulsed jets are applied, we define the

parameter γ = <Cp>

<Cpn>: as Cp values are negatives in the wake, when γ < 1 (resp. γ > 1) the

base pressure of the model increases (resp. decreases).Particle Image Velocimetry (PIV) was performed in the wake of the model (see detail

in figure 1(a)) to capture the essential modifications of the forced wake. Streamwise and

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Figure 2: Effects of periodic shear layer forcing on the base pressure of the model. a)Variation of γ with the actuation frequency StH (or Stθ). b) Influence of the momentumcoefficient Cµ on the γ parameter. c) Hierarchy of drag modifications for different controlconfigurations: I) Low frequency forcing (StH ∼ 0.4); II) Optimal Steady jets actuation;III) Optimal Steady Coanda blowing; IV) Optimal High Frequency blowing and V) OptimalHigh Frequency Coanda blowing.

transverse (respectively x and y directions) velocity components (respectively u and v) of theflow were measured using two LaVision Imager pro X 4M cameras (resolution of 2000×2000pixels). A laser sheet was pulsed with time delays of 120 µs in the symmetry plane of theconfiguration and image pairs were acquired at a sampling frequency of 3.5 Hz. Velocityvector calculations are processed with an interrogation window of 32 × 32 pixels (with a50% overlap) resulting in a spatial resolution of approximately 1% of the model’s height.Ensembles of 1000-1500 independent velocity fields were used to compute first and secondorder statistics. In addition, another PIV set-up was used to perform a zoom near the uppertrailing edge of the model. The resulting spatial resolution is about 0.3% of the model’sheight.

Hot wire measurements using a single probe (55P11) were acquired by the use of aStreamlinePro Anemometer System (from Dantec Dynamics R©) to evaluate the unsteadyand the spectral behavior of the wake as well as to calibrate the pulsed jets velocity used forcontrol, as described in the next section. The probe was mounted inside a 55H21 support.The wake velocity measurements were sampled at a frequency of 6.25 kHz and the durationof each test was 120s.

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2.3 Pulsed jets parameters

Periodic wake forcing is performed through the blowing of jets along the four trailing edgesof the model, as shown in figure 1(b). The generation of pulsed jets with an exit velocity Vjis a result of a pressure difference between the external flow and an internal compressed airreservoir located inside the body. The mass flow is driven periodically by the use of solenoidvalves distributed homogeneously along the periphery of the trailing edges. The frequencyof the pulsed jets is defined by Fi and kept constant along the four trailing edges. Details ofthe internal control set up as well as the velocity signals and their spectral behavior can befound in (Barros et al., 2014). The exit cross-section of the jet slit has a height h of (1±0.1)mm. Additionally to the pulsed jet generation, a Coanda surface is localized just bellowthe jet exit. This surface, as shown in figure 1(b), is a quarter of a disk and was installedalong the four trailing edges. In the present study, the radius r of this geometry was keptconstant and equal to 9 mm (about 3% of the model’s height). By using the time-averagedjet velocity Vj in the center line of the exit slit, we define the momentum coefficient of the

jet as Cµ =sjVj

2

SUo2 , where sj and S are the jet slit cross-sectional area and the frontal area of

the model, respectively. For spectral analysis, we consider the actuation frequencies in nondimensional form by defining Strouhal numbers based on the model’s geometry StH = HFi

Uo

or based on the momentum thickness of the separating upper boundary layer Stθ = θFi

Uo, as

commonly defined in the literature (Ho & Huerre, 1984).

3 Results and discussion

3.1 Effects of control on the base pressure

The effects of the Coanda blowing actuation frequency StH (or Stθ) on the pressure dragparameter γ are shown in figure 2(a). Here, the momentum coefficient Cµ was kept constantand equal to 1.4 × 10−3. Several features of the evolution of γ should be noticed. Firstly,steady blowing increases base pressure very slightly (about 2%). Besides, a broadband rangeof frequencies (StH ∈ [0.2, 1.6]) is responsible for base pressure decrease corresponding to anincrease of total drag of the model. Interestingly, in this range, a sharp peak at StH ∼ 0.4(indicated by configuration I) corresponds to a decrease of base pressure by 27%. Thisincrease of drag was also observed in another wind-tunnel facility by the authors and wasseem to amplify considerably the oscillatory dynamics of the wake (Barros et al., 2014). ForStrouhal numbers in the range StH ∈ [2, 12.1], drag reduction (base pressure increase) indifferent levels is observed. Up to 20% of base pressure recovery was measured for StH ∼ 12(Stθ ∼ 0.25). This frequency corresponds to about 60 times the discrete oscillatory frequencyof the wake (Grandemange et al., 2013) and about 11 times the most amplified estimatedfrequency of the upper shear layer (Ho & Huerre, 1984). Hence, actuation in this frequencyis decoupled from the natural flow instabilities and is denominated high frequency (HF)actuation.

The influence of Cµ on the pressure recovery γ is shown in figure 2(b) for StH = 0(steady blowing) and StH = 12.1 (HF). As benchmark, the values for steady and periodicblowing without Coanda effect are shown as dashed lines in the graph. In all cases γ is based

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Table 1: Efficiency parameter ζ for optimal drag reduction configurations shown in figure 2.

Configuration Cµ(×10−3) ∆Cp(%) ζ

StH = 0 Steady blowing (II) 7.0 5 1.82StH = 0 Steady Coanda blowing (III) 13.0 13 1.91StH = 12.1 High Frequency blowing (IV) 3.3 17 8.70StH = 12.1 High Frequency Coanda blowing (V) 4.7 33 6.71

on the natural flow. Without Coanda effect, the pressure increase tends to saturate withincreasing Cµ for constant and periodic blowing (see configurations II and IV highlightedin the graph). The simple addition of the Coanda surface is responsible for a limited basepressure increase of 3%. In addition, the pressure recovery on the rear surface does notsaturate but increases monotonically with Cµ for both StH . Notably, the HF forcing allowshigher reductions of γ. We achieved in the present work the lowest value γ = 0.67 forStH = 12.1 at Cµ = 4.7 × 10−3 (configuration V), corresponding to 33% of base pressureincrease which is considerably smaller than γ = 0.87 for Cµ = 13 × 10−3 obtained fromsteady Coanda blowing (configuration III). The measured hierarchy of drag modificationsdue to periodic forcing is summarized in figure 2(c). For square back geometries such asin the present work, the base pressure is responsible for about 70% of the total drag of themodel (Ahmed et al., 1984; Krajnovic & Davidson, 2003; Grandemange et al., 2013). Fromthis aspect, HF Coanda blowing can be expected to produce drag reductions of the order of23%.

An energy analysis is performed by defining an efficiency parameter ζ as the ratio ofthe mechanical power recovered by the estimated drag reduction and the mechanical powerspent to create the flux of kinetic energy from the pulsed jets. We define this parameter as:

ζ =

∣∣∣∆Cx

Cxo

∣∣∣CxoSUo3

sjVj3

, (1)

where Cx is the drag coefficient. For this analysis, we use the relation∣∣∣∆Cx

Cxo

∣∣∣ = 0.7(1−γ),

which indicates that the rear pressure corresponds typically to 70% of the total drag ascommented in the last paragraph. Besides, we consider Cxo ∼ 0.3 as a mean value commonlyobserved in past studies (Grandemange et al., 2013).

Table 1 summarizes the mechanical efficiency for the optimal drag configurations dis-cussed before with or without the use of the Coanda surface. For these actuation frequencies,the recovery of mechanical energy from drag reduction is greater than the power spent due tothe kinetic energy of the jets. The mechanical energy efficiency can reach important valuesof the order of 6-8 for StH = 12.1 representing considerable reduction of total energy costs.The efficiency is clearly greater for HF forcing when compared to steady blowing, highlight-ing the importance of the high-frequency actuation on the drag recovery of the model whencompared to the steady Coanda jets.

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Figure 3: Time-averaged near wake flow. Contours of streamwise velocity in the wakesymmetry plane and velocity vectors: (a) Natural flow with curved surface and (b) HFCoanda blowing. The dashed lines correspond to iso-contour of streamwise velocity u = 0.25.

3.2 Statistics of the near wake flow

To identify the modifications that occur inside the flow with the best drag reduction, wecompare the natural flow without forcing to the flow of configuration V with high frequencyCoanda blowing (StH = 12.1 at Cµ = 4.7 × 10−3). Figure 3 presents for both cases thecontour-plots of the time-averaged nondimensional streamwise velocity (u) with superim-posed velocity vectors at several selected streamwise locations. The wake extensions aremarked by the dashed lines which indicate the iso-contour of u equal to 0.25. Clearly thecontrolled wake appears to be thinner and more symmetric with respect to the centerline ofthe blunt body. Along the lower part of the forced wake, the maximal streamwise velocityincreased over more than 10%. Inside the recirculation zone, the entrained mass flux atx/H = 0.25 and x/H = 0.5 decreases about 30% with HF actuation (Gerrard, 1966). Fig-ure 4 illustrates the rapid evolution of the forced wake near the rear side of the model withthe help of the downstream evolution of the vorticity inside the shear layers. For the forcedcase, the maximum in vorticity rapidly moves towards the centerline of the model. At thesame time, the thickness of the shear layers becomes larger while the peak value of vorticitydecreases over more than 15% between x/H = 0.08 and x/H = 0.16. Both observationssuggest less entrainment for the recirculating flow of the forced wake. Finally, although allthese differences lead to up to 30% pressure recovery, the global time-averaged topology ofthe wake flow remains qualitatively the same.

The velocity fluctuations and spectral content of both wakes are now described. Fig-

ure 5(a) presents contour maps of the transverse velocity fluctuations v′2 in the wake. We

note that these fluctuations are damped for x/H > 0.2. At x/H = 0.2, v′2max reduced by16% and at x/H = 0.5 the reduction is even increased to 26% in both shear layers, suggestinga modified development of shear flow instabilities. The distribution of these fluctuations,however, remains quite similar along the wake for both natural and forced cases, indicatingthat wake dynamics is not strongly affected spatially in the near wake flow. Another in-dication of this statement is confirmed by means of the power spectral density (PSD) of avelocity signal taken at (x/H = 2.1, y/H = 0.9) by a single probe hot-wire. The spectralproperties are given in figure 5(b). The reference (natural Coanda) flow exhibits a discretepeak at the normalized frequency fH = Hf

Uo∼ 0.2, an oscillatory mode commonly observed

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Figure 4: Left: iso-contour lines of streamwise velocity u = 0.25. Right: vorticity profiles forthree streamwise positions (x/H=0.08, 0.12 and 0.16) in the upper and lower shear layers.

for this square back geometry (Grandemange et al., 2013). Interestingly, the high frequencyforced wake shows the same mode, indicating similar global oscillatory shedding for bothflows at the same frequency.

3.3 Mean pressure field

Recently, Barros et al. (2014) found that even without Coanda effect, high frequency blowingforces the separating streamline to bend. Since this change is reinforced by the Coanda effect,we expect an even stronger back pressure recovery due to the reinforced convex streamlinecurvature near the rear end of the blunt body. For the determination of the base pressuredistribution, we use the mean transverse momentum equation in combination with meanvelocity gradients and Reynolds stresses obtained from PIV data. The analysis is restrictedto the symmetry plane of the model and to regions very close the rear side of the model,where according to numerical simulations of (Osth et al., 2014) the flow remains highly two-dimensional due to negligible gradients in z. Besides, the vorticity thickness of the meanflow at the integration streamwise position (x/H = 0.08) is smaller than 5% of the widthof the model, enforcing the 2D character of the initially separated mean shear layer in thesymmetry plane.

Figure 6(a) compares the measured pressure distribution as well as pressure profilesdeduced from averaged PIV data for the reference and actuated flow. Since these profilesresult from integration of the vertical momentum equation along y at constantx/H = 0.08very close the rear side of the model, the first pressure tap on the upper part of the back sidehas been used as reference pressure to adjust the integration constant. Although fitted only

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Figure 5: Velocity fluctuations in the near wake. a) Contour maps of v′2. b) Power spectraldensity (PSD) of a velocity signal at the marked point (x/H = 2.1,y/H = 0.9). The HFspectra was shifted of one decade for clarity.

to one pressure tap, the curve progression accurately describes the distribution of Cp valuesmeasured by the remaining taps. The pressure increase obtained with HF Coanda blowing isdemonstrated by the shift of the Cp profile towards higher values, although as shown above,the global wake dimensions remain quite similar in both cases. However, across the shearlayers, a sharp increase of Cp is visible in case of actuation. From the averaged velocity fields,it becomes clear that inside the shear layer u ∂v

∂xand v ∂v

∂yundergo strong variations. The sign

of these terms is mostly determined by changes of the vertical velocity component v, whichcome along with curvature changes of the time-averaged streamlines. The resulting sharppressure gradients are shown in figure 6(b). The highest pressure recovery is thus related tochanges of curvature caused by the combined action of HF blowing and flow deviation bythe Coanda effect.

3.4 Shear-layer deviation

The changes in flow curvature are particularly visible in a zoomed view near the uppertrailing edge of the model. We compare the natural Coanda flow (i.e. no blowing) to HFCoanda blowing (config. V) and we add the optimal steady Coanda blowing (config. III) forcompleteness. Figure 7 shows the mean transverse velocity contours and velocity vectors nearthe flow separation at the upper shear layer. With actuated flow the downward deflection infigures 7(b,c) is clearly visible. The streamline originating from the middle of the blowing slitindicates that HF frequency forcing leads to the highest flow deflection. Unsteady Coandaforcing produces flow attachment all along the curved surface, while for steady blowing theflow already separates at about the middle of the rounded surface. The resulting increase ofconvex streamline curvature is accompanied by an increase of the pressure gradients acrossthe separating shear layer. This implies a higher base pressure recovery for the HF Coandablowing in accordance to the measured pressure increase presented in the last paragraph.

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Figure 6: Pressure distribution on the model’s base. a) Integrated Cp for natural Coandaflow and HF actuation with Coanda effect. The symbols correspond to values measuredby the pressure taps on the rear side. Cp contours highlight the different intensities of themeasured pressure distributions in both cases. b) Mean pressure gradient distribution.

Figure 7: Transverse velocity contours and velocity vectors near the upper trailing-edge. a)Natural Coanda, b) Optimal Steady Coanda blowing (config. III) and c) HF Coanda blowing(config. V). The dots represent the streamline originated from the exit slit of the pulsed jets.

4 Concluding remarks

In the present work, we combined periodic wake forcing and flow deflection by the Coandaeffect to increase the base pressure of a square back blunt body. Base pressure increasesof more than 30% can be achieved by this combination. Two main reasons were observed:first simple high frequency forcing reduces, in agreement with (Oxlade et al., 2015), velocityfluctuations along the shear layer development and diminishes the entrained flow within thewake. The obtained pressure recoveries remain restricted to several per cent. In addition,the unsteady Coanda effect produces flow deflections near the base of the blunt body. Thesedeflections cause the formation of convex curved mean streamlines with strong transversepressure gradients, which finally lead to a significant increase of base pressure. This contri-bution to the pressure recovery is most significant. Hence, the HF Coanda actuation workslike aerodynamic form shaping, but in contrast to modifications of the body shape, as for ex-ample discussed by (Choi et al., 2014), it needs minimal geometrical modifications to achievesubstantial pressure recovery.

Finally the Coanda effect appears to play an intriguing role in drag reduction. Low

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frequency Coanda blowing even decreases the base pressure while classical steady Coandablowing and in particular HF Coanda blowing increase the base pressure. Further studies areunder way to unravel the dynamics responsible for the performance of HF Coanda blowingon the drag reduction mechanisms observed.

5 Acknowledgements

The authors acknowledge the support during the experiments by J.M. Breux, P. Braud andR. Bellanger. The thesis of D.B is supported financially by PSA - Peugeot Citroen andANRT in the context of the OpenLab Fluidics between PSA - Peugeot Citroen and InstitutePprime (fluidics@poitiers). The authors acknowledge the funding of the Chair of Excellence- Closed-loop control of turbulent shear flows using reduced-order models (TUCOROM)-supported by the French Agence Nationale de la Recherche (ANR).

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