Control of flow deflection angle around the corner using microjet array

Abstract

In this study, a new technique for active control of the flow around a corner is proposed and a key parameter dominating the flow deflection angle is proposed. In the technique, a microjet array is used for controlling the deflection of the flow at 33 m/s ~ 54 m/s around the 25-degree corner with a small downstream-facing step, the surface of which is lined with the micro-orifices from which jets are injected into the flow. The flow velocities around the corner are measured using a PIV (particle image velocimetry) technique under each condition for injecting the microjets into the flow. The results reveal that a vortex is produced by the microjet array and the flow past the corner is pulled into the low-pressure region near the vortex core, i.e., the flow that has passed the corner deflects downward to the vortex. The results also reveal that the flow deflection angle increases with the supply pressure, i.e., the deflection angle increases with the jet Mach number. In addition, a parameter in the form of a momentum coefficient is introduced for data reduction by considering that the flow deflection is induced by a Rankine’s combined vortex. As a result, the relationship between the momentum coefficient and the streamline slope is expressed by a single linear relation regardless of the flow speed, which suggests that the flow deflection angle is controllable precisely by using the microjet array.

Introduction

The aerodynamic performance of vehicles (e.g., car, truck, bus, and train) depends strongly on the flow structures appearing behind them. Taking a car as an example, there are two representative types of flow structures causing the drag force of the car, i.e., separation bubbles developed along the slant rear surface of the car and a pair of counter-rotating streamwise vortices generated from both sides of the slant part. The sizes of these flow structures depend on the flow deflection angle at the corner between the roof and the slant surface of the car. According to the experimental results of Turney et al¹, when the angle of the corner between the roof and the slant surface of the car is small, the size of the separation region along the slant rear surface is relatively small, whereas the downward driving force becomes so strong as to generate a pair of counter-rotating streamwise vortices having a high vorticity. On the other hand, in the case of a large angle of the corner, the size of separation region is larger although the downward driving force to generate the vortex pair is smaller because the flow does not deflect much downward. These facts suggest that the deflection angle of the flow at the corner has an optimal value to minimize the drag force of the car. It is preferable for further optimization to control the flow deflection angles not only at the corner between the roof and slant rear surface but also at the other two corners which are formed between a side of the car and slant rear surface.

In general, the car shape is designed or body kits are attached on the car body in order to optimize the flow structures behind the car for the purpose of minimizing the drag force². However, these approaches limit the concepts of car design and comfortability in the car. In addition to such a problem, it is too difficult for these approaches to optimize the flow structures under each driving condition. These problems are solved by employing a technique of active flow control because this technique does not need to change remarkably a car shape, i.e., only small devices are mounted in or attached on the car. Such a technique also can respond to various driving conditions.

Several researchers tried to actively control the flows behind a vehicle model using steady microjets^3–5, fluidic oscillators⁶, pulsating jets⁷, synthetic jets⁸, or plasma actuators⁹. These techniques are based on the concept of enhancement in the momentum transfer from the main flow to the flow close to the wall in the boundary layers. Such a concept is also effective in boundary-layer flows besides the flows behind a vehicle model ranging from subsonic to supersonic flows^10–12.

The flow control method based on the momentum transfer enhancement might encounter the difficulty in optimizing the flow behind the vehicle to minimize the drag force according to various driving conditions because it is difficult to predict the flow deflection angle in this method. There are a few studies that the flow behind a car model is controlled by using a streamwise blowing technique, i.e., the concept of these studies is different from those of the abovementioned techniques based on the momentum transfer enhancement. These studies accomplished the reduction in the drag of the car model^13,14. However, the flow deflection angle was not discussed in these studies. If the flow deflection angles at individual corners can be controlled independently under each driving condition, it might be easy to optimize the flow structures behind the vehicle so that the drag force is minimized.

This study proposes a method for controlling the flow deflection angle at the corner by using the array of the microjets injected into the flow parallel to the slant wall surface. In the experiments, the microjets are acted on the flows around the corner of a model, the velocities of which range between 33 and 54 m/s. The speed of ~ 30 m/s (~ 110 km/h) corresponds to the speed of the car running on the expressway. It is expected that car’s speed is raised to ~ 55 m/s (~ 200 km/h) if autonomous driving technology is established, and there is a possibility that the technique of active flow control at this speed may become necessary. As a matter of fact, although the autonomous driving technology has not been established yet, cars have no speed limit in the German Autobahn.

The velocity fields around the corner of the model are measured by a PIV (particle image velocimetry) technique changing the condition for injecting the microjets into the flow. In addition, a key parameter for determining the flow deflection angle is suggested based on a simple flow analysis, and the appropriateness of the parameter is confirmed by the experimental results.

Experimental methods

The test model is shown schematically in Fig. 1. The flow created by a wind tunnel enters the test model as shown in Fig. 1a,b. The tunnel exit is open to the atmosphere, i.e., the flow enters the model at the atmospheric pressure. The model has a corner composed of the horizontal plate and the slant plate whose angle is 25 degrees to the horizontal plate as shown in Fig. 1a. The spanwise length of the model is 400 mm as shown in Fig. 1b. The incoming freestream velocities are set at U_∞ = 33 m/s, 43 m/s, and 54 m/s.

Fig. 1.

Test model.

The device for injecting the microjets into the corner flow is mounted into the model as shown in Fig. 1. The width of the device is 350 mm. The 43 orifices with a diameter of 0.4 mm are drilled into the device with a pitch of 7.0 mm along the spanwise direction so that the microjets are injected from the orifices into the flow parallel to the slant surface. The corner of the test model is magnified in Fig. 1c,d. Each orifice is drilled 1.5 mm below the surface of the slant wall upstream of the step. One of the orifice centers is placed in the central plane of the model, i.e., the arrangement of the orifices is symmetric with respect to the central plane of the model.

As mentioned later, the flow deflection angle is controllable by changing the pressure supplied to the stagnation chamber in the device. The pressures in the stagnation chamber (see Fig. 1b) range between p₀ = 120 kPa and p₀ = 240 kPa. In the same way as the studies about microjet^15–18, the jet Mach number M_j is defined as a Mach number of the jet that is fully expanded to the back pressure p_b. In general, pressure is uniform along the line across a subsonic shear layer. The subsonic shear layer is developed from the corner in the present flows. Therefore, the back pressure of the jet can be treated identically to the freestream pressure (i.e., atmospheric pressure). Thus, the jet Mach number M_j is defined as a Mach number of the jet that is isentropically expanded to the freestream pressure in the present study. The jet Mach numbers corresponding to the stagnation pressures stated above range between M_j = 0.52 and M_j = 1.19, and the mass flow rates per jet range between 2.73 × 10^–5 kg/s and 6.93 × 10^–5 kg/s. The coordinate system used to analyze the results is defined in Fig. 1c, where x and y are taken along the streamwise and height directions, respectively. The origin of the system is placed at the downstream end of the horizontal surface.

A PIV (particle image velocimetry) technique is used to clarify the effect of the microjet array on the corner flow. The laser is a double pulsed Nd:YAG laser (Litron Lasers, Nano PIV Series) operated with a second harmonic mode of 532 nm. The laser energy per pulse and pulse duration are 20 mJ and 6.5 ns, respectively. The interested region in the flow is illuminated from its upper part by the laser, which is shaped to a sheet by making the laser beam pass through the cylindrical lenses. The PIV measurements are performed on the two planes shown in Fig. 1d. One is contained in the central plane of the model, which is called plane I. The other denoted by plane II is placed between the centers of the two orifices adjacent to each other, one of which is on the central plane of the test model.

The wind tunnel is seeded with particles generated by a theatrical smoke generator. Scattered light from the particles is detected as an image by a camera (Seika Digital Image, PCM-4MT). The camera exposure is synchronized with each laser pulse using a pulse timing controller (Seika Digital Image, LC880). The time interval between two successive laser pulses is set at 7.0 μs. A pair of images is captured at a repetition rate of 5 Hz. One pixel on the digitized image corresponds to the physical size of 48 μm × 48 μm. Velocity vectors are calculated from each pair of the images by the recursive cross-correlation method using the open-source code of PIVlab in MATLAB¹⁹. The size of the final interrogation window is 8 × 8 pixels² with 50% overlap. Eight hundred pairs of images are captured per experimental run at each condition in the same setting of the measurement system. In order to estimate the uncertainties in the measured velocities, ten experimental runs are conducted in the selected cases of no jet and the microjet injections at p₀ = 240 kPa (M_j = 1.19) for U_∞ = 54 m/s, and then the standard deviations in the velocity data of ten experimental runs are calculated. The standard deviations are confirmed to be within 2 m/s.

The velocity profiles of the incoming flows at x = –20 mm are shown in Fig. 2 where the velocities are normalized by the freestream velocity U_∞. All the profiles are almost identical to one another and they are fitted reasonably well to the one-seventh power law, i.e., the boundary layers for all the freestream velocities, thicknesses of which are δ = 7 mm, are turbulent. The Reynolds numbers based on the boundary-layer thickness are 1.6 × 10⁴, 2.1 × 10⁴, and 3.1 × 10⁴ for U_∞ = 33 m/s, 43 m/s, and 54 m/s, respectively, which correspond to the unit Reynolds numbers of 2.3 × 10⁶ m⁻¹, 3.0 × 10⁶ m⁻¹, and 4.4 × 10⁶ m⁻¹, respectively.

Fig. 2.

Incoming velocity profiles (x = –20 mm).

Results and discussion

Effect of microjet array on corner flow

Figure 3 shows the streamlines around the corner for U_∞ = 33 m/s and U_∞ = 54 m/s without flow control. The streamlines are obtained from the averaged velocity vectors and superimposed on the map of x-component velocity normalized by the freestream velocity. There is no discernible difference in the normalized velocity and streamlines between both flows. The flow field for U_∞ = 43 m/s are also quite similar to those for U_∞ = 33 m/s and U_∞ = 54 m/s although it is not shown. The observations of Fig. 3 imply that the effect of the Reynolds number (unit Reynolds number) on the normalized velocity and streamlines is quite small in the flows around the corner under the condition of no jet.

Fig. 3.

Streamlines for no jet.

When the microjets are injected from the orifices into the flow, it deflected downward as shown in Fig. 4 (U_∞ = 33 m/s) and 5 (U_∞ = 54 m/s) that illustrate comparison between the streamlines with (solid lines) and without (broken lines) microjet injection, both of which are superimposed on the x-component velocity map. In all the velocity maps on plane I (Figs. 4a–c and 5a–c), the jet velocity measured by the PIV technique is quite lower than the jet velocity corresponding to the jet Mach number. This is because tracer particles are not seeded into the air in the stagnation chamber of the device, i.e., the jet issuing from the orifice does not contain the particles. Only the velocity of the air (containing the particles) entrained into the jet is measured on plane I. This is why the measured jet velocity is lower than the actual jet velocity.

Fig. 4.

Streamlines with jets for U_∞ = 33 m/s. Streamlines for microjets and no jet are depicted by solid and broken lines, respectively. Plane containing the orifice center is denoted by plane I. Plane between the centers of two orifices adjacent to each other is denoted by plane II.

Fig. 5.

Streamlines with jets for U_∞ = 54 m/s. Streamlines for microjets and no jet are depicted by solid and broken lines, respectively. Plane containing the orifice center is denoted by plane I. Plane between the centers of two orifices adjacent to each other is denoted by plane II.

The jet velocity measured on plane I becomes high in a region somewhat far from the orifice and the region shifts downstream as the jet Mach number becomes high as shown in Figs. 4a–c and 5a–c. In general, the microjet collapses abruptly at a certain location of the jet due to its unstable behavior^15,16,20 and the supersonic core in the supersonic jet becomes long with an increase of the jet Mach number^17,18. Air around the jet is unlikely to be entrained into the stable flow in the supersonic core. Using a small pitot tube, Aniskin et al.¹⁸ measured the supersonic core length of the nitrogen microjet discharged into the atmosphere from the convergent nozzle with its exit diameter of d = 340 μm. According to their experimental results, the supersonic core length for p₀ ~ 240 kPa (M_j ~ 1.2) is about 8d. This result is almost consistent with our results for M_j = 1.19 of Figs. 4c and 5c because the measured jet velocity (i.e., the velocity of air entrained into the jet) becomes remarkably high at ~ 4 mm (~ 10d) downstream from the orifice, i.e., the large amount of air containing the particles starts to be entrained into the jet in the vicinity of this location owing to the unstable behavior of the jet.

It is found from Figs. 4a–c and 5a–c (streamlines on plane I) that the flow deflection angle becomes large as the jet Mach-number M_j increases (the pressure ratio p₀/p_b increases). It is also found that the flow deflection angle for U_∞ = 33 m/s is larger than that for U_∞ = 54 m/s under the same jet Mach-number. In addition, the flow deflection angle for U_∞ = 43 m/s is between the angles for U_∞ = 33 m/s and U_∞ = 54 m/s although the streamlines for U_∞ = 43 m/s are not shown.

In the case of M_j = 1.19, the streamlines on plane I are compared with those on plane II as shown in Fig. 4c,d for U_∞ = 33 m/s and Fig. 5c,d for U_∞ = 54 m/s. No remarkable difference is observed in streamlines between the two planes for both freestream velocities although a high velocity region resulting from the microjet injection is observed in plane I. This finding implies that the microjets affect the flow almost uniformly along the spanwise direction.

Figure 6 displays the velocity vectors on plane I and II for representative jet Mach-numbers in the case of U_∞ = 43 m/s. In this figure, color of each vector represents the absolute value of the normalized flow velocity, u_abs/U_∞. A counter-clockwise vortex appears just above the slant wall surface at each jet Mach-number on both planes. This vortex is driven by the shearing force caused by the microjets. Therefore, the circumferential velocity in the vortex becomes high as the jet Mach-number M_j (the pressure ratio p₀/p_b) increases, i.e., the velocity of the reversed flow above the jets becomes high with the jet Mach-number.

Fig. 6.

Velocity vectors for U_∞ = 43 m/s. Plane containing the orifice center is denoted by plane I. Plane between the centers of two orifices adjacent to each other is denoted by plane II. Color of each vector represents the absolute value of the flow velocity.

In general, a low-pressure region is produced around the vortex core. Therefore, the flow that has passed the corner (x = 0) is sucked toward the low-pressure region, which causes the downward deflection of the flow. It is considered that pressure in the vicinity of the vortex core becomes low as the circumferential velocity increases (i.e., the jet velocity increases). This is the reason why the flow deflection angle becomes high with the jet Mach number as shown in Figs. 4 and 5.

Analysis of flow deflection angle

The above discussion suggests that the deflection angle of the flow around the corner can be increased by injecting the microjets into the flow because the flow is sucked toward the low-pressure region of a vortex which is driven by the microjets. Assuming the vortex to be a Rankine’s combined vortex, the pressure at the vortex center p becomes low as the circumferential velocity u_θ increases. This velocity is regarded in this study as the velocity at the boundary between the forced and free vortices, as expressed by the following relation,

1

Here, p_∞ is the pressure at a place located sufficiently far from the vortex, which corresponds to the freestream pressure (i.e., atmospheric pressure), and ρ is the density. The circumferential velocity u_θ is assumed to be proportional to the jet velocity U_jet because the inside part of the vortex is forced by the jet. Equation (1) is thus written using constant C as,

2

Putting a cube above the vortex center as a control volume, the pressures at the upper and lower surface of which are p_∞ and p, respectively, the vertical velocity component v is caused in the flow inside the cube by the difference in pressure p_∞ − p. The momentum equation provides the following relation,

3

Equations (2) and (3) provides the following relation,

4

Using the above relation, the angle of the flow deflection θ occurring in the cube is given by,

5

Equation (5) suggests that the slope of a streamline is linearly proportional to the ratio of the jet momentum to the dynamic pressure of the primary flow , i.e., the slope of a streamline varies linearly to a parameter in the form of momentum coefficient expressed by,

6

The numerator of the right-hand side of the above equation corresponds to the momentum per jet, which is expressed by the product of the mass flow rate per jet and the fully expanded jet velocity U_jet. The mass flow rate is calculated assuming that the air accelerates isentropically. The parameter w in the denominator of Eq. (6) is taken as the distance between the centers of the orifices adjacent to each other, i.e., w = 7 mm. In conclusion, the slope of a streamline, tan θ, varies linearly to the parameter C_μ and written using two constants C₁ and C₂ as,

7

The streamline slopes are estimated from the PIV data and plotted against the parameter C_μ for all the incoming velocities as shown in Fig. 7. The variable θ is defined as the angle of the streamline at x = 5δ which has passed the point of (x, y) = (− 3δ, δ) (see the schematic diagram in the upper part of Fig. 7). The streamlines above the selected streamline are almost parallel to one another as shown in the Figs. 4 and 5. In addition, the location at x = 5δ corresponds to the location where the main flow has finished turning around the corner. These mean that the parameter θ corresponds to the deflection angle of the main flow with large momentum. The pair of counter-rotating streamwise vortices behind the car is driven by the main flow deflecting downward. This is why the parameter θ is an appropriate measure for evaluating the effect of the present method.

Fig. 7.

Plots of streamline slope versus parameter C_μ.

It is clear from Fig. 7 that the data for all the incoming velocities are fitted well into a single linear line as suggested by the above discussion. The intercept of the linear line on the vertical axis corresponds to the slope of the streamline without microjet injection. The result shown in Fig. 7 reveals that the angle θ increases from 3° (no microjet) to 16° with the parameter C_μ in the range of 0 ≤ C_μ ≤ 0.8. The result also warrants that the flow deflection angle can be set at an intended value by adjusting the jet momentum (i.e., the supply pressure). That is to say, the flow deflection angle is precisely controllable.

Comparison of Figs. 4 and 5 reveals that the deflection angle of the flow for U_∞ = 33 m/s is larger than that for U_∞ = 54 m/s under the same jet Mach number (i.e., the same jet velocity). This can be explained from the Eqs. (6) and (7). Equation (7) reveals that the deflection angle θ increases as the value of C_μ increases. This suggests that the deflection angle increases with a decrease in the freestream velocity U_∞ as long as the jet velocity U_jet remains constant. This is because the value of C_μ increases with a decrease in U_∞ under the constant jet velocity as expressed by Eq. (6). In this way, the downward flow deflection around the corner is explained well by Eqs. (6) and (7) derived by considering that a Rankine’s combined vortex is created by the microjets.

Conclusions

In this study, a new technique for actively controlling the flow around the corner has been proposed. In this technique, the microjet array is used for controlling the deflection angle of the flow around the corner whose incoming speed is set at 33 m/s, 43 m/s, and 54 m/s. The flow velocities around the corner have been measured using a PIV (particle image velocimetry) technique under each condition of microjet injection. The experimental results reveal that the flow around the corner is effectively controlled to deflect downward by injecting the microjets into the flow and the flow deflection angle increases with the jet Mach number under the same freestream velocity.

It is observed in the PIV results that a vortex is produced owing to the shearing force caused by the microjets and the flow is pulled toward the low-pressure region around the core of the vortex. Based on this observation, a parameter in the form of momentum coefficient is introduced for data reduction with respect to the flow deflection angle by considering that the flow deflection is induced by a Rankine’s combined vortex. It is found through such data reduction that the relationship between the introduced parameter and the streamline slope is expressed by a single linear relation regardless of the freestream velocity. This finding suggests that the flow deflection angle is precisely controllable by adjusting the momentum of microjets (i.e., by adjusting the pressure supplying to the microjets).

Author contributions

Y.N. conducted the experiments and analyzed the experimental results. Y.S. constructed the measurement system and conducted the experiments. T.K. operates the wind tunnel and conducted the experiments. A.U. guided the research and edited the manuscript. T.H. guided the research and wrote the main manuscript text. All authors reviewed the manuscript.

Data availability

Data is provided within the manuscript.

Declarations

Competing interests

The authors declare no competing interests.