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1 MAGETOHYDRODYAMIC Vol. 37 (21), o. 1-2, pp BOUDARY LAYER COTROL BY MEA OF WALL PARALLEL LORETZ FORCE T. Weier 1, U. Fey 1, G. Gerbeth 1, G. Mutschke 1, O. Lielausis 2, E. Platacis 2 1 Forschungszentrum Rossendorf, P.O.Box , D-1314 Dresden, Germany 2 Institute of Physics, University of Latvia, alaspils 1, LV-2169, Latvia Lorentz forces can be used to control the near wall flow of low conducting liquids like sea-water. To achieve force densities strong enough to modify the flow, both magnetic and electric fields have to be applied to the fluid. Here, wall parallel Lorentz forces in the streamwise direction were used to influence the velocity profile of a flat plate boundary layer as well as the flow around a symmetric hydrofoil. Velocity measurements inside the boundary layer and direct force measurements are given for the flat plate. At moderate force strength, the mean velocity profile is characterized by a momentum thickness smaller than in the unforced case, whereas at high enough Hartmann numbers a wall jet develops. Additionally, a turbulent, but approximately non growing boundary layer has been observed. The effect of a suction-side, streamwise Lorentz force on a ACA- 17-like hydrofoil is quantified by means of force balance measurements. Depending on the angle of attack, two different effects are observed. (1) At small angles of incidence, a moderate increase in lift due to additional circulation is observed. imultaneously, a decrease in drag of the hydrofoil is caused by the momentum added. (2) At higher angles of attack, where the unforced hydrofoil would normally stall, a more pronounced lift increase and a corresponding drag reduction are observed due to separation prevention. Introduction. The application of electromagnetic forces to control boundary layer transition in a fluid of low electrical conductivity was proposed by Gailitis and Lielausis [1] in Only recently, the idea of using Lorentz forces for seawater flow control has attracted new attention [2] [4]. everal different force configurations have been investigated, mainly withthe aim of reducing turbulent boundary layer skin friction. osenchuckandcoworkers [5] studied experimentally the application of wall normal forces and found skin friction reductions of up to 5%. However, numerical simulations of comparable configurations by O'ullivan and Biringen [6] and experimental investigations by others [7] could not reproduce these strong reductions. Berger et al. [8] performed direct numerical simulations of a channel flow controlled by a Lorentz force oscillating in spanwise direction, a configuration somewhat similar to a spanwise oscillating wall. While the authors report successful skin friction reduction of up to 4%, the calculated power requirements exceed the gain. Experiments by Meng et al. [2], Henoch and tace [3], and direct numerical simulations by Crawford and Karniadakis [4] examined the influence of a streamwise Lorentz force on a turbulent boundary layer and channel flow, respectively. All authors report a reduction of the streamwise velocity fluctuations, but also an increase of the skin friction due to the force applied. The present paper is focused on utilizing the accelerating effect of a streamwise Lorentz force to control a flat plate boundary layer and flow separation on hydrofoils. 1. Background and parameters. Unlike typical MHD, electromagnetohydrodynamics (EMHD) [2] uses applied magnetic as well as applied electric fields to generate the Lorentz force. This is required due to the relatively low electrical 177

2 y x U z + + Fig. 1. Configuration of electrodes and permanent magnets to generate a wall parallel Lorentz force in streamwise direction. conductivity (ff = O(1)/m) of electrolytes like seawater. The current density j is given by Ohm'slaw: j = ff(e + u B) (1) with E denoting the electric field, u the velocity, andbthe magnetic induction, respectively. ince ff has such alowvalue, the currents generated by theu Bterm are very small as well. As a consequence, the Lorentz force f = j B due to such currents is almost undetectable. In order to obtain current densities large enough for flow control purposes it is therefore necessary to apply an external electric field of magnitude E with E =(U 1 B ) fl 1, where B denotes the applied magnetic field and U 1 the velocity ofthe outer flow. This implies that the force density distribution can be determined independently oftheflow field. A stripwise arrangement of electrodes and permanent magnets of alternating polarity and magnetization can be used to produce a streamwise Lorentz force. uch a geometry is sketched in Fig. 1. Apart from end effects, both electric and magnetic fields have only components in wall normal (y) and spanwise (z) direction. Consequently, the Lorentz force possesses only a streamwise component F [/m 3 ] F [/m 3] y/a Fig. 2. Lorentz force distribution in the y z plane (left) and mean Lorentz force density versus wall distance according to equation (2) (right). 178

3 The resulting force distribution calculated with the finite element Maxwell solver OPERA" is given in the left part of Fig. 2. An exponential decay ofthe averaged force density withincreasing wall distance is clearly visible in the right part of Fig. 2. However, strong spanwise variations of the force density occur near the plate. Averaged over z, the mean force density is given as F = ß 8 j M e ß a y ; (2) with M denoting the magnetization of the permanent magnets. Electrodes and magnets have the same width a. As usual for EMHD flows, the influence of the Lorentz force on the flow can be characterized by two dimensionless parameters, scaling the electromagnetic forces to either the viscous or the inertia forces. For the first parameter we follow the approachof Tsinober and htern [9] taking: Z = 1 j M a 2 8ß ρu 1 ν ; (3) as a corresponding Hartmann number. The normalization of the full avier tokes equations withforce term using mean flow quantities leads to the interaction parameter = j B L ρu 2 1 (4) giving the ratio of electromagnetic to inertial forces. Here B is the magnetic induction at the surface of the permanent magnets and L is a characteristic length equal to the chord length c in the case of hydrofoils, ρ denotes the fluid density. In the case of a flat plate boundary layer without pressure gradient, one could balance the viscous losses with the Lorentz force (Z = 1) as proposed by Lielausis and Gailitis [1]. In consequence, a solution of the boundary layer equations is obtained, describing an exponential boundary layer profile u U 1 =1 e ß a y : (5) This velocity distribution is similar to the asymptotic suction profile. Linear stability analysis shows that the asymptotic suction profile has a two orders of magnitude higher critical Reynolds number than the Blasius profile [1]. Therefore, a considerable transition delay could be expected by applying a wall parallel Lorentz force in the streamwise direction. To prevent flow separation, the momentum deficit of the boundary layer has to be overcome and the pressure gradient of the outer flow has to be balanced. Experimental demonstration of separation prevention on a circular cylinder by means of a streamwise Lorentz force withaccompanying numerical simulations have been given in [11]. 2. Results Flat plate boundary layer. LDA and force balance measurements were carried out at the Hamburg hip Model Basin (HVA). A detailed description of the experimental equipment can be found in[12]. A plate witha rounded leading edge and an overall lengthof 59 mm has been used. The electrodes and magnets covered a region starting 1 mm behind the leading edge and extending 4 mm in streamwise direction. Bothelectrodes and magnets had a widthof a = 1 mm. The dfeb magnets generate an induction of.35 T at their surface. 179

4 y/δ Re= Z= Z= 1.2 Z=12.9 Border Z=12.9 Middle u/u Fig. 3. Profiles of the mean value of the streamwise velocity component forthe flat plate boundary layer at different Z for x =5mm. The effect of a streamwise Lorentz force on the profile of the streamwise mean velocity u and the rms value u of their fluctuating component isshown in Figs. 3 and 4. y/δ Re= Z= Z= 1.2 Z=12.9 Border Z=12.9 Middle u /U Fig. 4. Profiles of the rms value of the streamwise velocity component for the flat plate boundary layer at different Z for x = 5 mm. 18

5 The boundary layer profiles were measured at x = 5 mm from the leading edge of the plate, where the magnet/electrode array ends. Wall distance and velocity have been normalized withthe boundary layer thickness in the unforced case, ffi, and with the velocity of the outer flow, U 1, respectively. Due to the relatively high turbulence level of 2% in the channel, the flow is not laminar, despite the relatively low Reynoldsnumber Re = U 1 x=ν =1: The mean velocity profile for Z = is an intermediate profile between a Blasius and a logarithmic one. For Z = 1:2 thelorentz force moderately accelerates the near wall fluid. Therefore the profile becomes fuller, but the evolution of an exponential profile shape is not apparent. There are 3 possible causes for this. First, in order to establish the asymptotic profile, a certain evolution length has to be covered. A rough estimate for this distance gives a dimensionless streamwise coordinate ο = (νß 2 x)=(u 1 a 2 ), where ν denotes the kinematic viscosity of the fluid. ο should at least be of the order of 1 to allow the asymptotic profile to develop. Integration of the boundary layer equations for the laminar case show that at ο = 7 the boundary layer profile for Z = 1 has still a mean deviation of 1% from the exponential shape. The profiles in Fig. 3 are taken at ο =:13, i.e. at a position far from that for whichexponential behavior is expected. econd, the early transition of the boundary layer causes conditions not considered in the theory, mainly a strongly increased energy dissipation. Third, the real force distribution differs from the ideal one. Their modulations in spanwise direction could have instead of the desired stabilizing effect a destabilizing one by possibly triggering transition due to three dimensional mechanisms. At Z = 12:9themeanvelocity profile has the shape of a wall jet, demonstrating the now strongly accelerating effect of the force. The spanwise modulation of the force density distribution is reflected in the velocity profiles. The flow acceleration is stronger at the force maxima (border of electrodes and magnets), than at the minima (middle of the magnets). Looking at the rms values u in Fig. 4, a damping near the wall can be found for Z =1:2 andz =12:9. This corresponds to the findings by Henochand tace [3]. imilar effects are known for boundary layers accelerated by strong favorable pressure gradients [13]. Due to the acceleration, dissipation in the near wall region is increased and turbulence production is suppressed. Unlike thefavorable pressure gradient, the Lorentz force acts mainly in the direct vicinity ofthewall. For high Z, i.e. in the case where a wall jet develops, additional velocity gradients appear away from the wall. The increase in the rms values at y=ffi > :8 mightbedueto these gradients, as it has been observed in turbulent wall jets [14], too. As shown in Fig. 5, a boundary layer of virtually constant thickness can also be achieved, although the necessary value of Z = 7:5 ismuchlarger than 1. This is due to the increased dissipation caused by turbulent structures in contrast to the laminar case considered in [1]. Due to the inhomogeneous force distribution, the local Hartmann number in the experiment is higher then their averaged value of 7.5. Therefore the experimental findings agree relatively well with Z ß 15 obtained by the approach of htern [15]. However, just as in the case of the laminar boundary layer, the limited evolution length of the flow has also to be taken into account. From the velocity profiles in Fig. 3 one can deduce an increase in the wall shear with increasing Z, even if the data points very near the wall are missing due to the high density of electrolytic bubbles. Increase in the wall shear stress has also been found in the experiments of Henochand tace [3] and the numerical simulations of Crawford and Karniadakis [4]. The total drag force on the plate is the sum of skin friction and form drag on the one hand and thrust generated by 181

6 12 x=1mm x=18mm x=26mm x=34mm x=42mm x=5mm 1 8 y [mm] u/u Fig. 5. Boundary layer growthatre=3:5 1 5 for Z =(ffi) and Z =7:5 (ffl). the Lorentz force on the other hand. Force balance measurements given in Fig. 6 demonstrate clearly that the momentum gain due to the Lorentz force dominates the skin friction increase. The same conclusion could be drawn from an integration of the velocity profiles in Fig. 3. In consequence one can find a maximum reduction Re= Re= Re= C D Z Fig. 6. Total drag of the flat plate versus Z at different Re. 182

7 of the total drag of more than 8% for Re =1:8 1 5 and Z =12:9. However, this drag reduction is indistinguishable from thrust and the energy expenditure necessary to feed the electrodes exceeds by far th e energy savings by the reduced drag eparation control. The wall jet in Fig. 3 indicates the strong momentum increase in the boundary layer due to the Lorentz force. ince boundary layer separation occurs owing to an energy deficit of the near wall fluid, the streamwise Lorentz force should principally be able to counteract separation. Actually, a streamwise Lorentz force has already been successfully applied to control the flow around a circular cylinder in [11]. eparation could be entirely suppressed, resulting in a complete elimination of form drag. In asymmetric configurations, like the flow around a hydrofoil, flow separation does not only cause form drag, but also a lift decrease. Force balance measurements on two PTL IV hydrofoils have been performed in HVA's arctic environmental test basin. The shape of these hydrofoils is relatively similar to a ACA 17 profile. For detailed information on geometry and experimental equipment see [12]. The hydrofoils span widthand chord length was s = 36 mm and c = 159 mm,respectively. The electromagnetic system of the profiles differ in terms of electrode width a, surface induction B and electrode material. In Fig. 7 the influence of a suction side Lorentz force on the drag is given in dependence on the angle of attack (ff). The chord length Reynolds number is Re = 4 1 4, and the ratio of electrode width a to chord length c amounts to = =.29 =.84 C D α [ ] Fig. 7. Drag coefficient versus angle of attack for Re = 4 1 4, a=c =:3 and different interaction parameters. 183

8 2 1.5 = =1.36 =2.67 C L α [ ] Fig. 8. Lift coefficient versus angle of attack for Re =2:9 1 4, a=c =:6 and different interaction parameters. The drag coefficient C D = F D 1=2ρU 2 1 cs (6) gives the drag force F D normalized by the dynamic pressure and the area of the hydrofoil cs. Already at a zero angle of attack, an applied Lorentz force results in a drag reduction, due to the momentum gain. However, this drag reduction is relatively moderate ( C D =:37 at =:84). A larger effect on the drag results from separation delay. Typically, at such a low Reynolds number as in the present experiment, even in the case of relatively thick airfoils, flow separation occurs directly at the leading edge. The accompanying sudden change of the flow structure results in an abrupt and considerable drag increase ( C D =:74 for =andff =13 ffi ). At =:288 separation is postponed to ff =14:7 ffi thereby C D is reduced by C D = :44. A further increase of the Lorentz force up to =:845 delays separation up to ff =16:6 ffi resulting in C D =:84. Although the separation angle is shifted to higher values due to the Lorentz force, all curves show the stepwise drag increase, characterizing leading edge stall. Especially on a hydrofoil, separation does not only influence the drag, but also the lift F L. Fig.8shows the lift coefficient C L versus the angle of attack for ahydrofoil with a=c =:6 at Re = 2:9 1 4 and different interaction parameters. The Lift coefficient is defined analogously to the drag coefficient as C L = F L 1=2ρU 2 1cs : (7) As in Fig. 7 the Lorentz force is applied at the suction side only. If the Lorentz force is switched on, a lift increase can be seen already at small angles of attack. It is due to the additional circulation caused by the acceleration of the suction side flow. imilar to the drag reduction at small ff, the lift increase is only moderate. evertheless it is possible to obtain a lift force even without an inclination of the 184

9 hydrofoil. At higher angles of attack, where the unforced hydrofoil would normally stall, a more pronounced lift increase is observed due to separation prevention. If a streamwise Lorentz force is applied, the lift coefficient increases further monotonically withgrowing angle of attack up to the point where the Lorentz force is no longer able to withstand the pressure gradient of the outer flow. From Fig. 8 one can infer that for the specified hydrofoil at Re = 2:9 1 4 and =2:67, stalling can be delayed up to 21 ffi, resulting in an increase in C L by 92% in comparison withthe unforced flow. 3. Conclusions. The influence of a streamwise Lorentz force on the flow along a flat plate has been studied in a saltwater flow. The experiments show a strong acceleration of the near wall flow if electromagnetic forces of sufficient strength are applied. A transitional boundary layer of approximately constant thickness was established, demonstrating the feasibility of balancing the friction losses of a boundary layer by a streamwise Lorentz force. The fluctuating streamwise velocity component is slightly damped due to the accelerating action of the Lorentz force. Force balance measurements on the controlled flat plate show a reduction of the total drag of up to 8% compared to the uncontrolled case. The sole reason for this dramatic drag reduction is the momentum gain caused by the Lorentz force. From the velocity profiles one can conclude that there is a skin friction increase in the forced cases. However, the momentum gain overcomes the skin friction increase for every Z value measured in the experiments. The control of flow separation on two hydrofoils by meansofasuction side streamwise Lorentz force has been successfully demonstrated. tall is delayed to higher angles of attack resulting in an increase in maximum lift and a decrease in total drag of the hydrofoils. Already at small angles of attack a small lift increase due to the applied Lorentz force has been measured caused by the asymmetric flow acceleration. Acknowledgements. Financial support from VDI under grant LD FKZ 13734/1 and DFG under grant IK 18/B1 1 is gratefully acknowledged. We are grateful to G. Lammers and G. Jensen from HVA for the fruitful cooperation. REFERECE 1. A. Gailitis and O. Lielausis. On a possibility to reduce the hydrodynamical resistance of a plate in an electrolyte. Applied Magnetohydrodynamics. Reports of the Physics Institute, vo1. 12 (1961), pp (in Russian). 2. J. C.. Meng, C. D. Henoch and J. D. Hrubes. eawater electromagnetohydrodynamics: a new frontier. Magnetohydrodynamics, vo1. 3 (1994), no. 4, pp C. Henoch and J. tace. Experimental investigation of a salt water turbulent boundary layer modified by an applied streamwise magnetohydrodynamic body force. Phys. Fluids, vol. 7 (1995), pp C. H. Crawford and G. E. Karniadakis. Reynolds stress analysis of EMHDcontrolled wall turbulence. Part I. treamwise forcing. Phys. Fluids, vol. 9 (1997), pp D. M. osenchucket al.. patial and temporal characteristics of boundary layers controlled with the Lorentz force. In 12th Australian Fluid Mechanics Conference (ydney, 1995). 6. P. O'ullivan and. Biringen. Direct numerical simulations of low Reynolds number turbulent channel flow with EMH D control. Phys. Fluids, vo1. 1 (1998), no. 5, pp J. Meng. Micro-electrode and magnet array for microturbulence control. U Patent U ,

10 8. T. W. Berger, J. Kim, C. Lee and J. Lim. Turbulent boundary layer control utilizing the Lorentz force. Phys. Fluids, vo1. 12 (2), no. 3, pp A. B. Tsinober and A. G. htern. On the possibility to increase the stability of the flow in the boundary layer by means of crossed electric and magnetic fields. Magnitnaya Gidrodinamika, vol. 3 (1967), no. 2, pp (in Russian). 1. P. G. Drazin and W. H. Reid. Hydrdodynamic tability (Cambridge University Press, Cambridge, 1981). 11. T. Weier et al.. Experiments on cylinder wake stabilization in an electrolyte solution by means of electromagnetic forces localized on the cylinder surface. Experimental Thermal and Fluid cience, vol. 16 (1998), pp. 8 l T. Weier et al.. Electromagnetic control of flow separation. In 2nd Int. Conf. on Marine Electromagnetics (Brest, France, 1999), pp K. reenivasan. Laminarescent, relaminarizing and retransitional flows. ActaMechanica, vol. 44 (1982), pp B. Launder and W. Rodi. The turbulent wall jet. Prog. Aerospace ci., vo1. 19 (1981), pp A. G. htern. Feasibility of modifying the boundary layer by crossed electric and magnetic fields. Magnitnaya Gidrodinamika, vo1. 6 (197), no. 3, pp (in Russian). Received

Boundary layer control by means of electromagnetic forces

ERCOFTAC Bulletin 44 2 pp.36 4 Boundary layer control by means of electromagnetic forces T. Weier, U. Fey, G. Gerbeth, G. Mutschke, V. Avilov Forschungszentrum Rossendorf P.O. Box 59, D 34 Dresden GERMAY