Skip to main content
NCBI home page
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences logoLink to Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
. 2014 Aug 13;372(2022):20130326. doi: 10.1098/rsta.2013.0326

High-performance computing-based exploration of flow control with micro devices

Kozo Fujii 1,✉
PMCID: PMC4095902  PMID: 25024414

Abstract

The dielectric barrier discharge (DBD) plasma actuator that controls flow separation is one of the promising technologies to realize energy savings and noise reduction of fluid dynamic systems. However, the mechanism for controlling flow separation is not clearly defined, and this lack of knowledge prevents practical use of this technology. Therefore, large-scale computations for the study of the DBD plasma actuator have been conducted using the Japanese Petaflops supercomputer ‘K’ for three different Reynolds numbers. Numbers of new findings on the control of flow separation by the DBD plasma actuator have been obtained from the simulations, and some of them are presented in this study. Knowledge of suitable device parameters is also obtained. The DBD plasma actuator is clearly shown to be very effective for controlling flow separation at a Reynolds number of around 105, and several times larger lift-to-drag ratio can be achieved at higher angles of attack after stall. For higher Reynolds numbers, separated flow is partially controlled. Flow analysis shows key features towards better control. DBD plasma actuators are a promising technology, which could reduce fuel consumption and contribute to a green environment by achieving high aerodynamic performance. The knowledge described above can be obtained only with high-end computers such as the supercomputer ‘K’.

Keywords: flow control, micro device, large eddy simulation, computational fluid dynamics, dielectric barrier discharge plasma actuator

1. Introduction

With the progress in simulation methods and rapid progress of computing performance in the last 30 years, computational fluid dynamics (CFD) has become an important tool for fluid dynamic analysis and industrial design and is now used by researchers and engineers in both academia and industry [1,2]. However, compared to its use at present, CFD has much more inherent capabilities, which should be explored and used. One of the important benefits of CFD, which has not been well used, is its facility for creating and identifying innovative concepts because of the ease of experimentation. Although very few good examples can be found in the existing literature, such efforts may introduce industrial innovations or a paradigm shift in engineering.

Controlling flow separation has been one of the important research topics in fluid dynamics. Among the many types of flow control, considerable interest has been provided to the control of flow separation over an aerofoil at high angles of attack because such flow control would prevent aerodynamic stall and remarkably improve aerodynamic characteristics of aircraft, which could help realizing much more stable flights. This technology is also applicable to fluid machines such as turbines/fans and ground transportation systems, and performance could be drastically improved if a device for controlling flow separation is developed.

Controlling flow separation with relatively small energy input obviously requires newer ideas. Small changes of body geometry or flow conditions may introduce flow separation and completely change the aerodynamic characteristics because of nonlinearity. However, when considering this fact not as a deficiency but as a benefit, we may be able to control the flow only with a very small change of local flow by small or micro devices. With this concept as a background, micro and small devices, such as dielectric barrier discharge (DBD) plasma actuators and synthetic jets have been demonstrated to be very effective for the control of flow separation over an aerofoil. Both experiments and computations proved that these devices change separated flows to attached flows with very low power consumption, at least under relatively low Reynolds number conditions [3,4].

The technology using these devices may have a significant impact on improving the environment, because they may considerably improve fuel efficiency and reduce emissions as well as minimizing aerodynamic noise emanating from vortex motion in the separated shear layer. In addition, these devices have the potential to change the aircraft and/or fluid machinery design method from the currently practiced ‘geometry design’ to future ‘device design’. Even a flat plate wing with a series of these devices over the surfaces may achieve much higher aerodynamic performance than the well-designed wing geometry for any given flow conditions.

The attractiveness of these devices, especially DBD plasma actuators, has led to a number of studies with both experimental and computational approaches [5–20]. The results clearly demonstrated the capability of plasma actuators to control flow separation. The plasma actuator, as shown in figure 1, comprises two electrodes with a dielectric between them. When high alternating current voltage is applied on the electrodes, the plasma actuator induces weak flows because of the ion motion being generated in the region between the exposed electrode and dielectric. Electric consumption is very small (for example, a few watts in the laboratory experiment) because the phenomena used here is DBD.

Figure 1.

Figure 1.

Open in a new tab

DBD plasma actuator over the wing. (Online version in colour.)

Many studies have focused on the strength of the induced flows and the change of the lift coefficients. In these studies, continuous DC current was applied with different parameters such as DC voltage, frequencies and shape of the frequency waves. Some studies demonstrated that the so-called ‘burst mode’ (schematically shown in figure 2) with duty cycles has better capability to control flow separation with less energy consumption [4,6,7,10,14,16,18]. Here, the burst mode actuation indicates that the base high-frequency wave signals are periodically switched on and off with a low burst frequency. Non-dimensional burst-wave frequency, F+, is defined based on the burst frequency, freestream velocity and representative length scale. Figure 3 shows an example of the experiment for the burst mode actuation. Flow becomes attached when the DBD plasma actuator is on with the burst mode.

Figure 2.

Figure 2.

Open in a new tab

Schematic picture of duty cycles (burst mode).

Figure 3.

Figure 3.

Open in a new tab

Flow control with the DBD plasma actuator, NACA0015, α=12°. (a) OFF and (b) ON.

2. Basic equations, numerical approach and model configuration

Three-dimensional compressible Navier–Stokes equations in body-fitted coordinates, which are normalized by the freestream density, freestream velocity and the chord length of the aerofoil, are employed as the governing equations in this study. Body force terms that represent the effect of induced flows by the DBD plasma actuator are added to the original Navier–Stokes equations. The body force terms are the modified version of the model proposed by Suzen & Huang [20] so that they include unsteady features. They consist of the electric force multiplied by the non-dimensional coefficient, Dc, which translates the electromagnetic force to the magnitude of the body force in the flow field. Dc is the non-dimensional parameter that is defined as the electric body force divided by the freestream dynamic pressure. Therefore, the value of Dc under the same electric body force condition (same electric power) changes depending on the velocity and model scales (see [3] for more details about the formulation). Comparison of induced velocities for the flows over a flat plate with actuation in both the computation and experiment identifies Dc values for the condition of each velocity and model scale. For example, let us consider the DBD plasma actuator that creates maximum induced velocity of 2 m s−1, which is easily achieved by the DBD actuator system used in the experiment. For the Reynolds number 6.3×104 with a freestream velocity of 1 m s−1 and a representative model length of 1 m, the Dc value corresponding to maximum induced velocity of 2 m s−1 becomes 16.25. For the same Reynolds number, 6.3×104, but with a freestream velocity of 10 m s−1 and a representative model length of 0.1 m, the Dc value becomes 0.01625.

Simulations are conducted for separated flows over aerofoils of NACA0006, NACA0012 and NACA0015 at several angles of attack. The DBD plasma actuator is attached to the aerofoil parallel to the leading edge, as shown in figure 1. The design parameters of the DBD plasma actuator, such as Dc, non-dimensional burst frequency (F+), burst ratio (BR) and location of the DBD plasma actuator, are varied, and the effects of each parameter over the flow field and aerodynamic characteristics are discussed.

Preliminary studies indicated that the mechanism to control flow separation by the DBD plasma actuator depends on the velocity and body scales. Therefore, simulations were performed at three different Reynolds numbers: the lowest one is the case at Re=6.3×104, the middle one is the case at Re=2.6×105 and the highest one is the case at Re=1.6×106. The lowest Reynolds number corresponds to the experiment, which was performed in the laboratory, using a small, low-speed wind tunnel. Although limited, experimental data are also available for the middle Reynolds number. On the other hand, only the data without the DBD plasma actuator are available for the highest Reynolds number. Note that simulations at a one-order-higher Reynolds number require approximately 100-times-higher computational costs. Therefore, cases are carefully selected, and only limited results are available at the Reynolds number of the order of 106. In all the cases, computations start with the flow field with the DBD plasma actuator off. Once the flow structure is established, the DBD plasma actuator is turned on and induced flows are imposed.

Our former simulations using a Reynolds-averaged Navier–Stokes model did not exhibit the effect of burst mode because small eddy motions play an important role in flow control. Therefore, the implicit large eddy simulation (iLES) method is used with a sixth-order compact differencing scheme. The compact differencing scheme has approximately 50–100 times higher spatial resolution than conventional second-order schemes, which save computer time and memory [21]. Such a scheme was necessary even with the world's leading-edge supercomputer because even specific cases require considerable time for computation. In this iLES method, 10th-order filtering acts as an alternative to the sub-grid model. For time integration, lower–upper symmetric, alternating-directional implicit symmetric Gauss-Seidel [22] methods are used. To ensure time accuracy, a backward second-order difference formula is used for time integration, and three to five sub-iterations [23] are adopted.

Computational grids are carefully prepared so that they are appropriate for iLES simulations at each Reynolds number. To enhance the grid resolution in the region where the body force is imposed, the overset zonal method [24] is employed. The body force is computed with the modified Suzen model in advance, and the resultant ‘push–push’ type sinusoidal body force changing in time is mapped on the grid for flow simulations. The total number of grid points is approximately 20 million for Re=6.3×104, 100 million for Re=2.6×105 and 1 billion for Re=1.6×106. As a computational region, span length of 20% of the chord is prepared for the lowest Reynolds number case and 10% for the middle Reynolds number case. A span length of only 5% of the chord is prepared for the high Reynolds number cases to save time for computation, although it may not be sufficient for quantitative discussions.

3. Results using the ‘K’ computer

With the Japanese 10 PFLOPS supercomputer ‘K’, more than 220 different cases of iLES simulations at the Reynolds number of 6.3×104 were conducted. The results were validated by the comparison with the wind-tunnel experiment conducted at the Institute of Space and Astronautical Science [16,18]. In addition to the analysis of the flow structures, the effects of device locations, input voltage, BR and other parameters are discussed based on the observations for future practical use.

Computed surface pressure distributions and the resultant lift and drag coefficients demonstrated a clear effect of the burst actuations. Figure 4 shows the pressure distributions over the aerofoil surface at α=12°. The solid line is the result of DBD-off condition (no actuation), and the short-dot chain line (almost overlapping the DBD-off result) is the result of continuous actuation with Dc=1.0. The long single-dot chain line is the result of F+=1 and the dash line is the result of F+=6, which are both in the burst mode. These two burst frequencies were chosen because previous experimental studies demonstrated that these two burst frequencies are effective for controlling flow separation. Note that the continuous mode fails to recover the suction peak near the leading edge, which indicates that the flow is still separated there. Both the burst modes, in contrast, show the suction peak and the pressure distributions indicate attached flows. Effect of the burst mode is clearly realized in the present iLES simulations and the advantage of the burst modes is observed. At this Reynolds number, the so-called laminar separation bubble appears. The flow separates slightly after the leading edge but is soon re-attached because of the laminar–turbulent transition. The plateau region observed in both F+=1 and F+=6 corresponds to this phenomenon. The longer bubble region usually has larger vortex structures in the separated shear layer. Table 1 shows a summary of the lift and drag coefficients of these cases. The computed lift-to-drag (L/D) ratio becomes more than four times higher in the burst mode. In addition, the result indicates that F+=6 works better than F+=1.

Figure 4.

Figure 4.

Open in a new tab

α=12°, Dc=1.0, 10% bursting. (Online version in colour.)

Table 1.

Summary of the lift and drag coefficients: α=12°, Dc=1.0.

CL CD L/D
off 0.472 0.151 2.822
F+=1 0.842 0.069 12.168
F+=6 0.895 0.058 15.495
normal 0.421 0.142 2.976
Open in a new tab

The analyses of the instantaneous flow fields, phase-averaged flow fields, frequency spectrum and linear stability were conducted. These analyses along with other post-processed data enabled us to identify a few different representative flow structures and classify the types of flow-control mechanisms. Figure 5 shows one of the results that were obtained. The horizontal axis is the rapidness of the turbulent kinetic energy (TKE) growth in the chordwise direction and the vertical axis is the L/D ratio. Details on the method used for computing the rapidness of TKE growth are discussed in Ref. [25]. Figure 5 clearly shows that all the results can be classified into three groups. The bottom-right one is the group, in which separation is not well controlled and the L/D is still low. The TKE develops slowly in this group. The top-left one is the group, in which separation is well controlled, and the L/D becomes high. The TKE develops rapidly in this group. The group present in the top-right area is the most interesting one because the TKE development is slow but high L/D is obtained. Analysis of the instantaneous flows shows that the two-dimensional spanwise vortex stays near the aerofoil surface until the middle-to-rear region of the aerofoil and then transition occurs, which maintains the lift coefficient to be high. The result indicates that the promotion of TKE energy and the resultant induction of laminar–turbulent transition is one of the key mechanisms for suppression of flow separation by the DBD plasma actuator. However, the existence of the third group indicates that another mechanism exists for flow control by the DBD plasma actuator.

Figure 5.

Figure 5.

Open in a new tab

Aerodynamic performance versus rapidness of turbulent energy promotion in the chordwise direction: α=12°. (Online version in colour.)

In this example, the third group might be missed if limited number of cases were only simulated. Here, we recognize the importance of simulating many cases with different parameters, which the supercomputer ‘K’ enabled us to perform. Leading-edge, high-performance computing infrastructures (HPCIs) such as the supercomputer ‘K’ allow large-scale computations that reveal details and key essence of flow structures. We have to remember that another important benefit of leading-edge HPCI use lies in their capability of performing numerous simulations.

Note that similar plots as figure 6 are also available for different angles of attack [25]. At higher angles of attack, controlling flow separation is difficult, even in cases with rapid TKE growth. Consequently, the group located in the upper-left region in figure 5 comes down to the lower-left region. The results at the angles of attack between them distribute in the region.

Figure 6.

Figure 6.

Open in a new tab

Effect of the plasma actuator location over the aerodynamic performance. (Online version in colour.)

As mentioned, the effects of device locations, input voltage, BR and other parameters were studied. Because of space limitations, only three of them are presented here. Details of the effect of other parameters can be found in [10]. Figure 6 shows the relationship between the locations of the DBD plasma actuator and the obtained L/D's. Dc (strength of the induced flow) and F+ (burst frequency) are the parameters as shown in the captions. The separation point over the aerofoil surface for the case without the actuator is also shown. It is clear that the DBD plasma actuator shows good performance when located near the separation point. The actuator location is rather insensitive for achieving a high L/D ratio when large Dc is applied, but it becomes sensitive for small Dc. The DBD plasma actuator should be located near the separation point especially for small Dc for achieving a high L/D ratio. Note that this is true for other aerofoils with different separation points [25]. Figure 7 shows the effect of the BR. The continuous mode does not work, but burst mode with less than 50% bursting works well. L/D ratios do not change much for the BRs less than 50%. This is another indication that transition is more important than induced momentum when burst mode is used. A 10% actuation is sufficient and preferable for saving input energy for industrial applications such as wind turbines. Figure 8 shows the effect of burst frequency. For this flow condition, the DBD plasma actuator works for a wide range of frequencies, but functions best near F+=5. All the simulations presented thus far are the results for a NACA0015 aerofoil at an angle of attack of 12° and Reynolds number of 6.3×104. As shown in figure 4, the aerofoil at this Reynolds number tends to have a laminar separation bubble. The fact that promotion of laminar-to-turbulent transition is the key feature may be associated with this flow structure.

Figure 7.

Figure 7.

Open in a new tab

Effect of BR over the aerodynamic performance. (Online version in colour.)

Figure 8.

Figure 8.

Open in a new tab

Effect of burst frequency over the aerodynamic performance: α=12°, Dc=1, actuator located at x/c=5%. (Online version in colour.)

Turbulent transition seems to be triggered by the linear unstable modes of inflection points in the hyperbolic tangent-like profile of the separation shear layer. The Rayleigh equation is adopted and unstable modes are estimated assuming incompressible, inviscid flows. The spatial developing modes are analysed, and spatial growth rates are investigated [25]. The most unstable frequency obtained is approximately St=15. As observed in the animation of flow structure development, a few two-dimensional vortices are created immediately after the end of every bursting. These vortices merge together and become a strong two-dimensional vortex with the same frequency as F+. Although further analysis is necessary, this may be the reason that actuation is most effective in the case of F+=5, which is three times lower than the unstable frequency, St=15 [23].

There were several important findings about the flow mechanism in addition to those discussed above. Firstly, three mechanisms seem to be responsible for the DBD plasma actuators reducing flow separation. One is the laminar-to-turbulent transition mentioned above, which is remarkable for F+=6. The second one is the occurrence of a series of rather strong two-dimensional vortices, which drag the separation shear layer towards the aerofoil surface. This is remarkable for F+=1. The last one is the induction effect due to strong chordwise and downward momentum created directly by the DBD plasma actuator. This is observed for continuous actuation. It is important that these three mechanisms always stay together and different ones become dominant depending on the actuator parameters and flow conditions. Secondly, when considering the phase-average, several vortices are located near the aerofoil surface after the reattachment. Note that the number of vortices corresponds to the burst frequencies. The time-averaged velocity profile is obviously turbulent, but certain coherent structures exist in the flows, unlike that of a regular turbulent boundary layer. Animation of the phase-averaged flows shows that the flow stays near the aerofoil surface because of the existence of a series of vortices.

Now, we discuss how the DBD plasma actuator works for higher Reynolds numbers. We cannot discuss the scale effect of the DBD plasma actuator simply by the Reynolds number because the situation is different for either higher velocity or larger model scale. For higher freestream velocity, relative region size of the induced velocity by the DBD plasma actuator is the same, but maximum induced velocity (relative to the freestream velocity) becomes smaller. For larger model scales, the relative region size of the induced velocity by the DBD plasma actuator becomes smaller, but the relative maximum induced velocity is the same.

With that in mind, we conducted a limited number of simulations for higher Reynolds numbers [26]. Only one result for the Reynolds number 1.6×106 with a larger model scale is presented here. The angle of attack is α=20.1°, which is post-stall. When without the DBD plasma actuator, a very small laminar separation bubble is created near the leading edge, and the flow becomes turbulent immediately after that at this Reynolds number. The turbulent boundary layer develops over the aerofoil surface and separates at the 14.5% chordwise location. The DBD plasma actuator is set at 14.5% chord, because the placement near the leading edge did not improve aerodynamic characteristics much, as expected. The comparison of the flow fields with and without the DBD plasma actuator is shown in figure 9. Location of the flow separation moves towards the trailing edge when the DBD plasma actuator is on. A strong two-dimensional vortex that is created immediately after actuation moves the separation shear layer towards the wing surface. As a result, 50% lift improvement and 20% drag reduction are obtained with F+=1 and Dc=4. It is interesting to note that F+=1 works best in the burst mode in the CL increase, and continuous mode is the best in the CD reduction. It has been shown that DBD actuators improve aerodynamic characteristics even at high Reynolds numbers with the appropriate choice of parameters. As reported in the previous section, it is important to recognize that the turbulent boundary layer once attached by the DBD plasma actuators has an inherent coherent structure with specific peaks in the power spectrum of the chordwise velocity, as shown in figure 10. These peaks are obviously associated with the actuation burst frequencies. Such flows may be controlled by an idea, which is different from the control of typical turbulent boundary layer separations. This fact may become the key factor for the control of separated flows at higher Reynolds numbers. Note that this study is ongoing and further analysis will reveal the mechanism for turbulent flow control by the DBD plasma actuators.

Figure 9.

Figure 9.

Open in a new tab

Effects of the DBD plasma actuator: instantaneous flow field: α= 20.1°, Re=106, Dc=4.0, actuator located at x/c=14.5%. (a) Actuator OFF, (b) continuous mode and (c) actuator ON (burst mode), F+=1. (Online version in colour.)

Figure 10.

Figure 10.

Open in a new tab

Power spectra of chordwise velocity fluctuation at several chordwise locations: α=20.1°, Re=106, actuator located at x/c=14.5% F+=1, Dc=4.0. (Online version in colour.)

For the flow analysis of each case at this Reynolds number, 12 flow-through simulations over the wing with 1 800 000 time steps were required. One simulation required almost 600 h of computer time using 1984 nodes of the supercomputer ‘K’, which has more than 80 000 nodes in total.

4. Practical applications

Industrial applications are ultimately important. Therefore, we discuss the mid-term results for engineering applications in addition to the basic flow analysis for the final goal of product innovation. We selected performance improvement of wind turbines, under the collaboration with a company that conducted the field experiment, where the company showed improvement in torque for the wind turbines actually in use. The computation is ongoing and only the preliminary results for a small test model have been obtained to date, which are presented in figure 11 [27]. Three simple wings of squire span having NACA0012 aerofoil sections rotate under the freestream having 40° yaw angle. The torque increase with the DBD plasma actuator agreed well with the experiment. Computations to be conducted soon will show the results for practical configurations. For the current preliminary simulation, one rotation of three blades required 50 h of computer time by using 2350 nodes of the supercomputer ‘K’.

Figure 11.

Figure 11.

Open in a new tab

Application of the DBD plasma actuator to rotating machinery. (Online version in colour.)

It has been shown that micro devices such as DBD plasma actuators are effective for flow control and aerodynamic characteristics are improved. For actual applications, it is important to consider how such benefits are used. First, these devices provide wings and fluid machinery with robustness because they avoid flow separations at off-nominal conditions. Next, safety and system efficiency are both improved as they keep a certain level of lift with low drag, even at high angles of attack.

At this stage, maximum L/D values are improved for simple symmetric wing sections at relatively low Reynolds numbers, but the value of the maximum L/D is no better than that of well-designed wing sections. However, future study of these actuator devices would improve the level of L/D values. Based on the well-known Breguet's equation, the flight range of aircraft directly reflects the improvement of the L/D ratio. If certain level of L/D improvement is obtained for well-designed wing sections with these flow control devices, the same level of reduction would appear in the fuel consumption for the same flight. This would be a remarkable contribution towards a cleaner environment. Note that these devices may allow the use of simpler and much thicker wing sections to achieve the specified L/D value than well-designed wing sections. This would relax structure restrictions and increase fuel volume, which could result in improvement of the flight range of the aircraft. Further studies are necessary to discover the benefits of these devices at nominal conditions.

Numerous application candidates exist in addition to the aircraft and wind turbines discussed in this paper. Examples under consideration include automobiles and their parts, trains, fan ducts and air conditioners. Several of these potential applications are under discussion with their respective industries. Among them, collaborative research has started with one company that manufactures small cooling fans. This could become a good application example because the Reynolds number is relatively low, where the DBD plasma actuator has shown high performance.

5. Remarks on computer resources

As mentioned above, 1984 nodes of the supercomputer ‘K’ were used for high Reynolds number simulations. Computations for approximately 500 000 grid points are allocated to each node. Such allocation is determined based on the computational speed of each node and the network speed among nodes. If computational load of each node is too small, data transfer at the interface of each computational region allocated to each node becomes apparent and a bottleneck for efficient computation. If overly large grid points are allocated to each node, the required memory might not fit into the hardware or one computation would become too time-consuming. The specified number of nodes to be used here reflected the balance of such considerations. Weak scaling is important for engineering applications because the number of grid points allocated to each node is determined by the above consideration. Obviously, discretization using the number of stencils used here would require high CPU performance with high byte-per-flop (B/F) ratio with balanced node network speed, although such hardware would require considerable electric power.

Basic turbulence research and practical engineering study seem to have progressed separately thus far. However, now seems to be the time to merge them together as the examples presented here have shown. There still remains restriction of the computer capability for still more practical applications, but computers with Exa or higher scales hopefully would remove the restriction soon.

6. Summary

Large-scale computations for the study of the use of DBD plasma actuators for controlling flow separation were conducted using the Japanese Petaflops supercomputer ‘K’. The results for the Reynolds number around 105 indicated that (i) lift coefficients are recovered mostly due to laminar-to-turbulent transition of the separated shear layers near the leading edge, (ii) duty cycles with small BR are effective for the transition and the recovery of lift, (iii) two other mechanisms exist that are associated with induced flow strength for the control, (iv) device location should be close to the separation point, and (v) location becomes sensitive when the input voltage is low and BR is small. Three mechanisms for the flow separation control coexist but one of them becomes important depending on the flow and actuator device parameters. Many papers have focused on the strength of the flows created by the DBD plasma actuators, but other parameters are important as well, at least for this Reynolds number flow regime. It should also be noted that future studies should focus on drag reduction in addition to lift recovery, although most of the studies to date have only focused on the lift characteristics. Of course, performance of the DBD plasma actuator depends on how it is used.

Some effect on the lift recovery and drag reduction was observed at higher Reynolds numbers but benefits are yet limited compared with low Reynolds number flows. The flow simulations showed that specific spectra exist in the flow after the actuation, which may become a key issue for flow control. Based on this observation, future study, especially towards methods for avoiding turbulent separation, would improve the actuator performance for more practical applications. The results thus far indicate that the DBD plasma actuator in general might become a strong tool for controlling flow separation. It is true that this is still only a small step towards the final goal of this study to realize the revolutionary change from ‘geometry design’ to the future ‘device design’, as described in the Introduction to this paper. We believe, however, that future study with the help of HPCI would help accomplish this final goal.

The knowledge presented herein would not be obtainable without a Petaflops computer such as the ‘K’ computer. DBD plasma actuators are a promising technology for controlling flow separation and would reduce fuel consumption and contribute to a green environment by achieving high aerodynamic performance.

Acknowledgements

The computations presented in this paper are mostly conducted on the supercomputer ‘K’ at the Advanced Institute of Computational Science (AICS), Riken, and the Fujitsu FX10 at the Information Technology Center of University of Tokyo under the support of the Strategic Programs for Innovative Research (SPIRE) of the High Performance Computing Initiative in Japan. The members of this programme (Dr Taku Nonomura, Dr Hikaru Aono, Dr Makoto Sato and Dr Aiko Yakeno at JAXA/ISAS) are the contributors for this study.

Funding statement

This research was partly supported by the JSPS Grant-in-Aid for Scientific Research no. 24246141 in addition to the SPIRE program mentioned above.

References

  • 1.Shang JS. 2003. A glance back and outlook of computational fluid dynamics. ASME FEDSM 2003-45420. [Google Scholar]
  • 2.Fujii K. 2005. Progress and future prospects of CFD in aerospace-wind tunnel and beyond. Prog. Aerosp. Sci. 41, 455–470. ( 10.1016/j.paerosci.2005.09.001) [DOI] [Google Scholar]
  • 3.Corke TC, Post ML, Orlov DM. 2007. SDBD plasma enhanced aerodynamics: concepts, optimization and applications. Prog. Aerosp. Sci. 43, 193–217. ( 10.1016/j.paerosci.2007.06.001) [DOI] [Google Scholar]
  • 4.Glezer A, Amitay M. 2002. Synthetic jets. Annu. Rev. Fluid Mech. 34, 503–529. ( 10.1146/annurev.fluid.34.090501.094913) [DOI] [Google Scholar]
  • 5.Visbal MR, Gaitonde DV, Roy S. 2006. Control of transitional and turbulent flows using plasma-based actuators. AIAA 2006-3230 Reston, VA: AIAA. [Google Scholar]
  • 6.Rizzetta DP, Visbal MR. 2009. Large eddy simulation of plasma-based control strategies for bluff body flow. AIAA J. 47, 717–729. ( 10.2514/1.39168) [DOI] [Google Scholar]
  • 7.Kaneda I, Sekimoto S, Nonomura T, Asada K, Oyama A, Fujii K. 2012. An effective three-dimensional layout of actuation body force for separation control. Int. J. Aerosp. Eng. 2012( 10.1155/2012/786960) [DOI] [Google Scholar]
  • 8.Patel MP, Ng TT, Vasudevan S, Corke TC, Post ML, McLaughlin TE, Suchomel CF. 2007. Scaling effects of an aerodynamic plasma actuator. AIAA 2007-635 Reston, VA: AIAA. [Google Scholar]
  • 9.Sidorenko AA, et al. 2007. Pulsed discharge actuators for rectangular wings separation control. AIAA 2007-941 Reston, VA: AIAA. [Google Scholar]
  • 10.Asada K, Fujii K. 2010. Computational analysis of unsteady flow-field induced by plasma actuator in burst mode. AIAA 2010-5090. [Google Scholar]
  • 11.Greenblatt D, Wygnanski IJ. 2000. The control of flow separation by periodic excitation. Prog. Aerosp. Sci. 36, 487–545. ( 10.1016/S0376-0421(00)00008-7) [DOI] [Google Scholar]
  • 12.Greenblatt D, Schuele CY. 2012. Mechanism of flow separation control using plasma actuation. Phys. Fluids 24, 077102 ( 10.1063/1.4733399) [DOI] [Google Scholar]
  • 13.Sattari P, Rival DE, Martinuzzi RJ, Tropea C. 2012. Growth and separation of a start-up vortex from a two dimensional shear layer. Phys. Fluids 24, 107102 ( 10.1063/1.4758793) [DOI] [Google Scholar]
  • 14.Tsubakino D, Tanaka Y, Fujii K. 2007. Effective layout of plasma actuators for a flow separation control on a wing. AIAA 2007-474 Reston, VA: AIAA. [Google Scholar]
  • 15.Goksel B, Greenblatt D, Rechenberg I, Nayeri CN, Paschereit CO. 2006. Steady and unsteady plasma wall jets for separation and circulation control. AIAA 2006-3686 Reston, VA: AIAA. [Google Scholar]
  • 16.Asada K, Ninomiya Y, Oyama A, Fujii K. 2009. Airfoil flow experiment on the duty cycle of DBD plasma actuator. AIAA 2009-531 Reston, VA: AIAA. [Google Scholar]
  • 17.Poggie J, Tilmann CP, Flick PM, Silkey JS, Osborne BA, Ervin G, Maric D, Mangalam S, Mangalam A. 2010. Closed-loop stall control on a morphing airfoil using hot-film sensors and DBD actuators. AIAA 2010-547 Reston, VA: AIAA. [Google Scholar]
  • 18.Sekimoto S, Asada K, Anyoji M, Nonomura T, Fujii K. 2012. Comparative study of co-flow and counter blowing DBD plasma actuators for separated flow over an airfoil. AIAA 2012-1137 Reston, VA: AIAA. [Google Scholar]
  • 19.Enloe CL, McLaughlin TE, Font GI, Baughn JW. 2009. Plasma-induced force and self-induced drag in the dielectric barrier discharge aerodynamic plasma actuator. AIAA 2009-1622 Reston, VA: AIAA. [Google Scholar]
  • 20.Suzen YB, Huang PG. 2006. Simulations of flow separation contorl using plasma actuator. AIAA 2006-877 Reston, VA: AIAA. [Google Scholar]
  • 21.Fujii K. 2008. CFD contributions to high-speed shock-related problems. Shock Waves 18, 145–154. ( 10.1007/s00193-008-0146-x) [DOI] [Google Scholar]
  • 22.Fujii K. 1999. Efficiency improvement of unified implicit relaxation/time integration algorithms. AIAA J. 37, 125–128. ( 10.2514/2.676) [DOI] [Google Scholar]
  • 23.Nonomura T, Aono H, Sato M, Yakeno A, Okada K, Abe Y, Fujii K. 2013. Control mechanism of plasma actuator for separated flow around NACA0015 at Reynolds number 63 000: separation bubble related mechanisms. AIAA 2013-0853 Reston, VA: AIAA. [Google Scholar]
  • 24.Fujii K. 1995. Unified zonal method based on the fortified solution algorithm. J. Comput. Phys. 118, 92–108. ( 10.1006/jcph.1995.1082) [DOI] [Google Scholar]
  • 25.Sato M, Okada K, Nonomura T, Aono H, Yakeno A, Asada K, Abe Y, Fujii K. 2013. Massive parametric study by LES on separated-flow control around airfoil using DBD plasma actuator at Reynolds number 63 000. AIAA 2013-2750 Reston, VA: AIAA. [Google Scholar]
  • 26.Sato M, Okada K, Nonomura T, Aono H, Fujii K. 2013. LES of turbulent separated flow over NACA0015 at Reynolds number 1 600 000: toward the separation control by a DBD plasma actuator. In. 66th Ann. Meeting of the APS Division of Fluid Dynamics. R16.08 College Park, MD: American Physical Society. [Google Scholar]
  • 27.Aono H, Nonomura T, Sato M, Yakeno A, Okada K, Abe Y, Fujii K. 2014. Flow control using a DBD plasma actuator for horizontal-axis wind turbine blades of simple experimental model. In The 11th World Congress on Computational Mechanics (WCCM XI). Paper Ref: 2935. [Google Scholar]

Articles from Philosophical transactions. Series A, Mathematical, physical, and engineering sciences are provided here courtesy of The Royal Society

RESOURCES