COMPUTATIONAL STUDY OF THE SEPARATED FLOW STRUCTURE INDUCED BY THE SYNTHETIC JET ON A BACKWARD-FACING STEP

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1 COMPUTATIONAL STUDY OF THE SEPARATED FLOW STRUCTURE INDUCED BY THE SYNTHETIC JET ON A BACKWARD-FACING STEP Koichi Okada, Koo Fujii and Koji Miaji ABSTRACT In order to clarif the mechanism of the snthetic jet on the massivel separated flow appearing at the backward-facing step, flow-fields with/without the snthetic jet are numericall simulated. Implicit large edd simulation using high-order and high-resolution compact difference scheme is applied. A flow field without a snthetic jet, flow fields with the snthetic jet at non-dimensional frequencies of the wall oscillation, F + h =. and F + h=., are computed, where no-dimensional frequenc of F + h is normalied with the height of backward-facing step and free stream velocit. Although previous studies show that each F + h is good conditions, the present computation shows that length of the separation region onl at F + h =. become 5 percent shorter than that without snthetic jet. It seems that F + h =. is near shear laer instabilit frequenc without the snthetic jet. Strong two-dimensional vortices induced from the snthetic jet interact with the shear laer, which results in the increase of the Renolds stress. At F + h =., length of the separation region is almost same as that without snthetic jet. Miing is not enhanced in the shear laer because Renolds stress does not increase. Weak and short periodic vortices induced from the snthetic jet do not interacts with the shear laer ver much. Kewords: Active flow control, Backward-facing step, CFD, Separation flow, Snthetic jet INTRODUCTION Flow-control technolog has been widel researched to improve the aerodnamic performance of transportation sstems such as aircrafts and cars. The common objectives in man cases are to prevent massive flow separations for both the eternal and internal flows. Passive flow control devices such as a vorte generator and natural bleed have been mainl used for practical applications because of its simplicit and lightweight, while an active flow control using continuous blowing and suction has been also investigated (Okada and Hiraoka, ) due to rather large effects on the main stream. The drawbacks of such large jets are the comple duct sstems and heavweights. Therefore, in recent ears, man researchers have been studing active flow control methods based on micro scale devises. One of them is a snthetic jet. A tpical snthetic jet induces vortices at an orifice eit b oscillating the wall at Corresponding author: Yokohama National Universit, Department of Ocean and Space Engineering, okada@flab.isas.jaa.jp Japan Aerospace Eploration Agenc, Institute of Space and Astronautical Science fujii@flab.isas.jaa.jp Yokohama National Universit, Department of Ocean and Space Engineering, miaji-k@nu.ac.jp

2 the bottom of the cavit connected to the orifice (Fig. ). The snthetic jet has advantages over conventional flow control devises such as active flow control capabilit, light weight and compactness because it does not require an air-supplier sstems and the total mass flow of the jet is ero. It is suitable for man kinds of airplanes including UAVs/MAVs and helicopters. Dnamic control capabilit is favorable, too. Most of previous eperimental studies on the snthetic jet have been focused on demonstrating effects of the snthetic jet for flow control, or finding optimal conditions for the snthetic jet on an airfoil or backward facing step. In eperimental studies, Amita et al. () and Seifert and Darabi (996) parametricall studied in their eperiments the effects of the position of installation, non-dimensional jet frequenc (based on chord length or separation length and free stream velocit), and the jet mass flow on the flow separation control around an airfoil. Gleer et al. (5) researched especiall non-dimensional jet frequenc effects on the flow separation control around an airfoil. Previous research (Seifert; Darabi, 996) showed that good non-dimensional jet frequenc is (O) but the showed better non-dimensional jet frequenc is (O). On the other hand, Yoshioka et al. () studied eperimentall separation control of backward-facing step configuration using periodic ecitation and showed that better no-dimensional frequenc F + h (based on height of backward-facing step and free stream velocit) is.. Vukasinovic et al. (4) studied eperimentall separation control of backward-facing step configuration using snthetic jet and showed that F + h=(o) is effective value. However, the flow control mechanism of the snthetic jet has not been clear et. As for numerical studies, Kral et al. (998) compared snthetic jet and stead jet results on the flow separation control around an airfoil and show effectiveness of snthetic jet using two-dimensional RANS computation but flow control mechanism has not been clear et. Kral et al. (997) compared computed and eperimental results and found that flow computation with top-hat tpe velocit boundar condition agrees with eperimental time-mean vertical velocit in quiescent condition. Mittal et al. () has computationall shown that the orifice eit velocit in quiescent condition is different from that in the condition with eternal flow. Most of previous simulations do not consider effect of cavit flow on separation control. Therefore, it is necessar to research the optimal usage on flow control for improving performance and efficienc drasticall. The objective of the present stud is to understand mechanics of separation flow control. The snthetic jet in static air condition was analed as our preliminar stud (Okada et al., 8). The objective of the stud was to investigate effect of internal flows in snthetic jet cavit. First, three-dimensional computation solving both the orifice jet and internal flow in the cavit are compared with conventional simulation approaches. D vorte structure is captured in the cavit model. Then, the effects of dimensional parameters are researched to understand the flow induced b the snthetic jet. Different frequenc cases change three-dimensional flow fields. Different amplitude cases, changes three-dimensional flow fields and vorte intensit. Research with eternal flow is conducted as net step. A backward-facing step configuration is chosen for the first step of line of this research, because the flow field and geometr become simpler than those around an airfoil. In order to clarif the mechanism of the snthetic jet on the massivel separated flow appearing at the backward-facing step, flow-fields with/without the snthetic jet are numericall simulated. The present analsis is focused on the frequenc characteristics of the snthetic jet.

3 Bod surface Orifice Fig.. Snthetic jet (Mallinson, 999) ANALYSIS MODELS A. Configuration of snthetic jet A geometric configuration of the snthetic jet in the reference (Rietta and Visbal, 999) is chosen in this stud (Fig. ). The non-dimensional orifice depth d is equal to the non-dimensional orifice width h. The cavit depth Z D is d and the cavit width X L is 5d. The cavit span length in the direction is treated to have infinite length in the simulation since this stud target two-dimensional configuration. Fig.. Snthetic jet configuration B. Modeling of the wall oscillation The oscillation of the cavit wall is defined b equation (). h (, t) = A sin( π F + t) () w h Here, amplitude of the wall oscillation A is constant value. F + h is no-dimensional frequenc of the wall oscillation. Input parameter value show at computational conditions.

4 C. Configuration of Backward-facing step The backward-facing step configuration and flow conditions are same of Jovic s stud (996) because this eperiment has various comparable data for validation of No-control case. Fig. show whole image of the eperiment. Unit is centimeter and the scale of this figure is not collect. Blue region is the computational region. D. Numerical method Three-dimensional compressible Navier-Stokes equations are emploed as the governing equations. These equations are solved in the generalied curvilinear coordinates. The spatial derivatives of convective terms and viscous terms, metrics, and Jacobian are evaluated b the sith-order compact difference scheme (Lele, 99) since an induced velocit b snthetic jet are ver small and the boundar laer is efficientl solved. Near the boundar, second-order eplicit difference schemes are used. The tenth-order filtering (Gaitonde and Visbal, ) is used with filtering coefficient of.45. Visbal and Gordnier s approach (Visbal and Gordnier, ) for computation of metrics and Jacobian on deforming and moving meshes is used for satisfing the computation the geometric conservation law. For time integration, regarding the characteristic of the computer, a kind of implicit method Lower-Upper Smmetric Alternating Direction Implicit and Smmetric Gauss-Seidel (ADI-SGS) is used for time integration. This algorithm uses same kind of idea of Four-Factored Smmetric Gauss-Seidel (FF-SGS) (Fujii, 999) which adopt both ideas of the Lower-Upper Smmetric Alternating Direction Implicit (LU-ADI) and the Lower-Upper Smmetric Gauss-Seidel (LU-SGS). To ensure the time accurac, backward second order difference formula is used for time integration whereas three sub-iterations (Chakravarth, 984) are adopted. The computational time step is. in non-dimensional time so that the maimum Courant-Friedrichs-Lev (CFL) number becomes approimatel.. In the standard LES approach, additional stress and heat flu terms are appended, but in ILES approach (Visbal and Rietta, ) the are not appended. Instead, a high-order low-pass filter selectivel damps onl the poorl resolved high-frequenc waves. This filtering regulariation procedure provides an attractive method to the use of standard sub-grid-scale (SGS) models. Turbulent inflow boundar conditions are generated b using rescaling method of Gerald Urbin et al. (). Rescaling domain is -. < /H < -.. Outflow boundaries are located awa from the bump b rapid stretching the mesh in the streamwise direction (Colonius et al., 99). At the outflow boundar, all variables are etrapolated etrapolated from one point front of the outflow boundar. On the lower surface, no-slip conditions are adopted along with a ero normal pressure gradient. Finall, the upper surface is treated as a slip wall (W = ) and the normal derivative of other variables is set to ero. Periodic boundar condition is applied to the spanwise boundaries. E. Computational grids Patched grids approach (Fujii, 995) is emploed to generate grids for cavit, orifice, and backward-facing step regions, as shown in Fig., 4 and 5. The grid deformation approach developed b Melville et al. (997) is applied to generate a time-varing fluid grid sstem for the cavit region. This algebraic method can maintain the grid qualit of the initial grid near the deforming surfaces under arbitrar, moderate deflections and rotations. The total number of the grid points is about 7,,. (See Table. ) Between each region, 6 grid points are overlapped to maintain the same accurac as the internal grid points. The minimum grid sie in each direction of all grids is d =.7, d =.4 and d =.7, respectivel. The length of the computational region in span direction (-direction) is 4h. A buffer region is configured (Colonius et al., 99) to avoid non-phsical reflection of acoustic wave as shown in Fig. 4

5 F. Computational conditions Inlet flow Mach number and Renolds number based on height of backward-facing step and free stream velocit are. and 5, respectivel. 99 percent boundar laer thickness is.h at =-.5. Inflow boundar laer is turbulent is boundar laer. Renolds number and boundar laer thickness are same as those of Jovic stud (994). Snthetic jet has two important input parameters that are commonl used to describe the operating conditions for flow control; no-dimensional frequenc and momentum coefficient. no-dimensional frequenc mean frequenc of the wall oscillation and no-dimensional momentum coefficient mean ratio of momentum of snthetic jet and free stream. F + h = fh u C μ ρud j = () ρuh where f, h, u, ρ, u j, d and h are the dimensional frequenc of the wall oscillation, height of backward-facing step, free stream velocit, densit, averaged maimum velocit at orifice eit and width of snthetic jet. The present analsis is focused on the frequenc characteristics of the snthetic jet. Three cases are selected, No-control (without snthetic jet), F + h =. and F + h =., where non-dimensional frequenc F + h is normalied with height of backward-facing step and free stream velocit. Previous studies around airfoil (Amita et al., ; Seifert and Darabi, 996; Gleer et al., 5) show that these values are optimal conditions using chord length or separation length as reference length. (See Table.) In this stud, momentum coefficient use same value (. percent) each cases since the present analsis is focused on the frequenc characteristics of the snthetic jet. The value is sufficient small for separation control using snthetic jet. The amplitude use different value of F + h =. and F + h =. because u j is proportional amplitude and frequenc as shown equation (). (See Table.) u = k A F + () j h Fig.. Wind tunnel schematic(jovic,994) 5

6 one one h h 5h h Fig.. Computational region one one one one one4 h 4h one.5h Fig. 4. Cavit grid Fig. 5. Computational grid Table. Grid points one name j k l Δ Δ Δ/h one Backstep one Backstep one orifice one4 cavit Table. No-dimensional Frequenc Backstep Airfoil F + h F + sep F + chord F + sep Refarence Height of Length of Chord length Length of length Backstep separation region of Airfoil separation region.. 6

7 RESULTS AND DISSCUSSION Table. Snthetic jet conditions F + h C μ Amp...%.4.%.4 Time averaged flow-fields Time averaged flow directional velocit and stream line of -constant plane for each three cases are shown in Fig. 6. The stream line means a recirculation region. At No-control case, the flow separate from edge of backward-facing step, configures the recirculation region and reattach the bottom of wall. A small recirculation region also eists after backward-facing step. At F + h =., the recirculation region is smaller than No-control case but at F + h =., the recirculation region is almost same of No-control case. Fig. 7 show skin frictional coefficient on the bottom wall (.<<.) for each three cases. At F + h =., reattached point is obviousl shorter than the No-control and F + h =.. Table 4 mean reattached location calculated form skin frictional coefficient and show that at F + h =., length of separation region is shorter 5 percent than the No-control case but at F + h =., length of separation region is almost same of No-control case. Fig. 8 shows Renolds stress distribution for each three cases. At the No-control case, strong Renolds stress regions eist from the shear laer region (.<<.) and the recirculation region (.<<6.). At F + h =., the Renolds stress distribution is wholl high. This enhances miing of shear laer and separated flow re-attach. At F + h =., the Renolds stress distribution is almost same as the No-control case.. No-control F+ h =. C f No control F + h =. F + h =. F+ h = ua/ Fig. 6. Flow direction velocit distribution and stream line Fig. 7. Skin frictional Coefficient Table 4. Reattached location 7

8 No-control 6.h F + h =. 4.5h F + h =. 6.h No-control F + h = F + h = ' ' uw Fig. 8. Renolds stress distribution Instantaneous flow-fields Instantaneous iso-surfaces of the second invariant of the velocit gradient tensor Q and flow directional velocit distribution of each three cases are shown in Fig. 9, Fig. and Fig.. Q iso-surface is colored b -vorticit where red and blue colors respectivel show clock-wise and counter-clockwise rotating vortices in the -direction. This iso-surface indicates vorte structure in general. No-control case, the separated shear laer is induced from the edge of backward-facing step and the vortices are generated in the separated shear laer, then the flow split up and down, the upper flow throw and diffuse after recirculation region. On the other hand, the lower flow counterflow upward, make the recirculation region as shown in Fig. 6 and induce longitudinal vortices in.<<4.. At F + h =., There are totall a lot of vortices compared with No-control case for snthetic jet blowing. F + h =. show more three dimensional flow structure and the strong longitudinal vortices compared with other two cases in 4.<<8.. Fig., Fig. and Fig. present Instantaneous iso-surfaces of Q and pressure distribution of each three cases. Q iso-surface is colored b -vorticit where red and blue colors respectivel show clock-wise and counter-clockwise rotating vortices in the -direction. No-control case, vortices are generated in separated shear laer. Moreover, vortices turn to three-dimensional structure in.<<. b inflow turbulent boundar laer. At F + h =., Strong two-dimensional vortices induced from the snthetic jet interact with the shear laer, which results in the increase of the Renolds stress in the shear laer region. At F + h =., Weak and short periodic vortices induced from the snthetic jet because amplitude is small compared with F + h =. as shown in Table. Fig. 5, Fig. 6 and Fig. 7 show the time lines of static pressure and nd invariant of the velocit gradient tensor Q of each three cases. The Blue lines show same vorte structure. No-control case, vortices are periodicall generated in separated shear laer. At F + h =., Strong two-dimensional vortices induced from the snthetic jet interact with the shear laer. It seems that F + h =. is near shear laer instabilit frequenc of No-control case. These vortices turn to three-dimensional structure, which 8

9 possibl make Renolds stress stronger in the recirculation region. At F + h =., Weak and short periodic vortices induced from the snthetic jet do not interacts with the shear laer ver much and diffuse in the recirculation region. Separation shear laer Separation shear laer Longitudinal vortices Longitudinal vortices =. =4. =6. =8. =. =4. =6. =8. - ω -.5 u/a. - ω -.5 u/a. Fig. 9. Iso-surfaces of nd invariant of the velocit gradient tensor and Flow direction velocit distribution (Iso-surface is colored b -vorticit), (No-control) Fig.. Iso-surfaces of nd invariant of the velocit gradient tensor and Flow direction velocit distribution (Iso-surface is colored b -vorticit), (F + h =.) Vortices from turbulence boundar laer Separation shear laer Longitudinal vortices =. =4. =6. =8. - ω - ω -.5 u/a p static /p. Fig.. Iso-surfaces of nd invariant of the velocit gradient tensor and Flow direction velocit distribution (Iso-surface is colored b -vorticit), (F + h =.) Fig.. Iso-surfaces of nd invariant of the velocit gradient tensor and Static pressure (Iso-surface is colored b -vorticit), (No-control) 9

10 Sound wave -dimensional vortices Vortices from snthetic jet Vortices from snthetic jet - ω p static /p - ω p static /p Fig.. Iso-surfaces of nd invariant of the velocit gradient tensor and Static pressure (Iso-surface is colored b -vorticit), (F + h =.) Fig. 4. Iso-surfaces of nd invariant of the velocit gradient tensor and Static pressure (Iso-surface is colored b -vorticit), (F + h =.) Merge Diffuse Merge Merge Diffuse Merge p static /p p static /p Fig. 5. Static pressure and nd invariant of the velocit gradient tensor (black lines, contour range:.-. with lines), (No-control) Fig. 6. Static pressure and nd invariant of the velocit gradient tensor (black lines, contour range:.-. with lines), (F + h =.)

11 Diffuse Merge Diffuse p static /p Fig. 7. Static pressure and nd invariant of the velocit gradient tensor (black lines, contour range:.-. with lines), (F + h=.) SUMMARY The present computation shows that at F + h =., length of separation region is 5 percent shorter than the No-control case. It seems that F + h =. is near shear laer instabilit frequenc of No-control case. Strong two-dimensional vortices induced from the snthetic jet interact with the shear laer, which results in the increase of the Renolds stress in the shear laer region. These vortices turn to three-dimensional structure, which make Renolds stress stronger in the recirculation region. At F + h =., length of the separation region is almost same as the No-control case because miing is not enhanced in the shear laer and recirculation region. Weak and short periodic vortices induced from the snthetic jet do not interacts with the shear laer ver much and diffuse in the recirculation region. REFERENCES Okada, S. and Hiraoka, K. (), Eperimental Studies of Reduction of the Wing Tip Vorte b Suction, AIAA Paper -5. Mallinson, H. (999), Some Characteristics of Snthetic Jets, AIAA Paper Amita, M. et al. (), Aerodnamic flow control over an unconventional airfoil using snthetic jet actuators, AIAA Journal, Vol.9, Seifert, A. and Darabi, A. (996), Dela of Airfoil Stall b Periodic Ecitation, Journal of Aircraft, Vol.,

12 Gleer A., Amita, M. et al. (5), Aspect of Low-and High-Frequenc Actuation for Aerodnamic Flow Control, AIAA Journal, Vol.4, 5-5. Kral, L.D. and Donovan J.F. et al. (999), Active Flow control Applied to an airfoil, AIAA Paper 98-. Kral, L.D. and Donovan J.F. et al. (997), Numerical Simulation of Snthetic Jet Actuator, AIAA Paper Mittal, R. and Ramgunggoon, P. et al. (), Interaction of a Snthetic Jet with a Flat Plate Boundar Laer, AIAA Paper -77. Okada, K., Fujii, K. and Miaji, K., (8), Effect of Internal Flows in Snthetic Jet Cavit, Fifth International Conference on Computational Fluid Dnamics Yoshioka, S., Obi, S. and Masuda, S. (), Turbulence Statistics of periodicall perturbed separated flow over backward-facing step, International Journal of Heat and Fluid Flow, vol., 9-4. Rietta, D. and Visbal, R.M. (999), Numerical Investigation of Snthetic Jet Flowfields, AIAA Journal, Vol.7, No.9, You, D., and Moin, P. (6), Larger-edd simulation of flow separation over an airfoil with snthetic jet control, Center for Turbulence Research Annual Research Briefs. Srba Jovic (996), Backward-Facing Step Measurements at Low Renolds Number, Reh=5, NASA TM -887 Lele, S.K. (99), Compact Finite Difference Scheme with Spectral-Like Resolution, Journal of Computational Phsics, Vol., 6-. Gaitonde, D.V. and Visbal, R.M. (), Pade Tpe Higher-Order Boundar Filters for the Navier-Stokes Equations, AIAA Journal, Vol.8, No., -. Visbal, R.M. and Gordnier, R.E. (), Higher-Order Flow Solver for Deforming and Moving Meshes, AIAA Paper -69. Fujii, K. (999), Efficienc Improvement of Unified Implicit Relaation/Time Integration Algorithms, AIAA Journal, Vol. 7, No., 5-8. Chakravarth, S. R. (984), Relaation Methods for Unfactored Implicit Upwind Schemes, AIAA Paper M. R. Visbal, and D. P. Rietta (), Large-edd simulation on general geometries using compact differencing and filtering schemes, AIAA Paper -88. Gerald Urbin and Dole Knight, () Large-Edd Simulation of a Supersonic Boundar Laer Using an Unstructured Grid, AIAA Journal vol.9 No.7, Fujii, K. (995), Unified Zonal Method Based on the Fortifies Solution Algorithm, Journal of Computational Phsics, Vol.8, 9-8. Melville R. B., Morton S. A. and Rietta D. P. (997), Implementation of a Full-Implicit, Aeroelastic Navier-Stokes Solver, AIAA Paper T, Colonius, S. K. Lele and P. Moin (99), Boundar Condition for Direct Computation of Aerodnamics Sound Generation, AIAA Journal, vol., No. 9.