Control of Laminar Separation Bubbles by Small-Amplitude 2 D and 3 D Boundary-Layer Disturbances

Laminar separation bubbles in a flat-plate boundary layer flow with a velocity drop of 10%, 20%, and 25% applied locally at the free-stream boundary of the integration domain have been investigated by means of direct numerical simulations. Different steady and unsteady boundary layer disturbances were introduced at a disturbance strip upstream of separation and their effects on the separation bubble have been studied in 2-d and 3-d simulations. Generally, the same phenomena appear in both cases, i.e. the size of the separated region can be controlled by initially small 2-d disturbances, which grow to large levels by the hydrodynamic instability of the flow. Such unsteady disturbances, have a stronger impact on the size of the bubble than steady disturbances. Without loosing much efficiency, the pure 2-d forcing can be replaced by a three-dimensional forcing that produces obliquely travelling waves. The decisive parameter to influence the size of the separation bubble is the location of non-linear saturation of the disturbance modes, which may, but doesn’t necessarily coincide with the location of transition to full turbulence. 1.0 INTRODUCTION A transitional laminar separation bubble (LSB) is characterized by laminar separation (S) because of an adverse pressure gradient, laminar-turbulent transition (T), and turbulent re-attachment (R). Despite the occurrence of negative skin friction within the bubble LSBs may cause an undesired drag rise because of a considerable influence on the global pressure distribution of the airfoil. Unfortunately, their spatial extent is difficult to predict by theory or in wind-tunnel experiments, because of their Reynolds-number dependence and their sensitivity to background disturbances which are difficult to take into account. Small environmental changes may have a sudden influence and operating an airfoil at “off-design conditions” can make it prone to LSBs. However, such considerations will become completely obsolete once a suitable separation-bubble control becomes available for operational use. The key of LSB control is to control laminar-turbulent transition since an earlier transition will move the re-attachment upstream. Existing systems to avoid the formation of LSBs involve the generation of turbulence upstream of the separation. Most often used turbulators apply zigzag or dimple tape mounted on the surface of the airfoil. Other devices use vortex generators [6] or constant blowing of air through holes in the surface of the airfoil [5] to generate-large scale streamwise vortices. For such active blowing devices a complicated system to provide the necessary bleed air might be necessary. All these systems have in common that they have to be developed for an optimum design point. Therefore, these systems cannot capture off-design conditions like different speed tasks of sail planes optimized for thermal flights. Active-blowing devices can be switched off at off-design conditions, but nevertheless additional disturbances may be generated by secondary flow through the holes in the presence of pressure gradients in the spanwise direction of the airfoil. Active systems which deform the surface of the airfoil to introduce disturbances into the flow Small-Amplitude Control of Laminar Separation Bubbles 6 2 RTO-MP-AVT-111 NATO UNCLASSIFIED NATO UNCLASSIFIED represent a solution to these problems. Switched off, these systems would no longer be a source of additional drag. As a drawback these systems only provide very small deformation amplitudes and imply electric driving and control devices. Moreover, a complex integrated sensor, controller and actuator system becomes desirable to become independent of any external interference with the system by the pilot. As maximum efficiency is the aim, according active turbulators have to be low-energy consuming and thin layered to fit into the limited space available on an airfoil besides the required supporting structural components. Nevertheless, such surface-mounted active devices can generate high-frequency perturbations which are necessary to introduce Tollmien-Schlichting-type boundary-layer disturbances into the flow. Due to hydrodynamic instability of the LSB flow, these boundary-layer disturbances become strongly amplified which leads to laminar-turbulent transition despite of their low initial disturbance amplitude. By introducing boundary-layer perturbations at a disturbance strip upstream of the separation into the laminar flow, transition can be triggered and therefore the size of the LSB be influenced. In the present work LSB flows are investigated in detail by means of linear stability theory [12] and direct numerical simulations (DNS) to evaluate methods using disturbance modes with different excitation parameters with respect to their impact on the size of typical mid-chord LSBs under different adverse pressure gradients. 2.0 NUMERICAL METHOD To study laminar separation bubbles multiple direct numerical simulations (DNS) of a flat-plate boundary layer have been performed. An adverse pressure gradient is applied locally at a given distance from the inflow at the free-stream boundary to force separation. The code used for the present DNS has been used in different research programs for the investigation of transitional boundary layers with or without separation, cf. [7][8][11][14][16][17]. Figure 1: Integration domain Figure 1 displays a sketch of the rectangular integration domain together with a definition of the coordinates and the respective velocity components. All variables are non-dimensionalized with respect to the free-stream velocity U∞ and a reference length L which leads to a reference Reynolds number Re = 100000. The complete Navier-Stokes equations for incompressible flows are solved in a vorticityvelocity formulation [16]. A fourth-order accurate numerical method is applied in time and space by finite differences in streamwise and wall-normal direction and by a four step explicit Runge-Kutta scheme in time. For the spanwise direction a spectral ansatz implying periodic boundary conditions in that direction is used. Due to this the Poisson equations for the streamwise and spanwise velocity reduce to ordinary differential equations. The remaining 2-d Poisson equation for the wall-normal velocity is solved by a line Small-Amplitude Control of Laminar Separation Bubbles RTO-MP-AVT-111 6 3 NATO UNCLASSIFIED NATO UNCLASSIFIED relaxation method accelerated by a non-linear multi-grid algorithm, once the vorticity-transport equations have been advanced to the next Runge-Kutta step. All equations can be solved separately for each spanwise spectral mode k allowing effective parallelization. At the inflow boundary a Blasius boundary layer solution with a momentum thickness Reynolds number Re* = U∞⋅δ/υ = 1722 is prescribed. At the surface of the plate the no-slip boundary condition is applied except for a disturbance strip upstream of the LSB where periodic 2-d and 3-d boundary layer disturbances are introduced into the flow by suction and blowing. The streamwise length of the disturbance strip has been set to one wavelength of the most amplified disturbance mode according to linear stability theory (LST) and the beginning is located approximately two wavelengths downstream of the inflow boundary. For the total streamwise length of the integration domain 18.41 wavelengths have been used, and the height of the domain corresponds to 16 boundary-layer displacement thicknesses at the inflow. To avoid non-physical reflections at the outflow boundary the disturbance amplitudes are artificially damped in a buffer domain by several orders of magnitude, using the method described in [8]. The laminar separation bubble is induced by a local deceleration of the ‘potential’ free-stream velocity imposed via the u-component at the upper boundary as in [13]. Because of Bernoulli’s equation this corresponds to imposing an adverse pressure gradient. The displacement effects of the LSB on the potential flow are captured by a viscous-inviscid boundary layer interaction model at every time step of the calculation (cf. [11] and [10]). Thus, the characteristic “pressure plateau” in the u-velocity distribution with a constant velocity in the upstream part of the separation bubble and a sharp velocity drop in the region of transition and re-attachment develops during the calculation (see next section). 3.0 NUMERICAL RESULTS Three different streamwise velocity drops have been used for the following investigations: one with 10%, one with 20%, and one with 25% reduction of free-stream velocity, where 10% means a reduction from U/U∞ = 1 to U/U∞ = 0.9, for instance. In the following, these will be denoted “case A”, “case B”, and “case C”, respectively. A comparison of the three is performed in Figure 2 in terms of the “potential velocity” UP, the resulting velocity UM at the free-stream boundary, and in terms of the separation streamline Ψ = 0. Clearly, a larger velocity drop leads to a larger adverse pressure gradient and hence earlier separation at the wall. Also, the height of the bubble increases with rising pressure gradient. In all cases the typical “pressure plateau” develops in the velocity UM (thick lines) as a result of the implemented viscous-inviscid interaction, as already anticipated above. Figure 2: Comparison of prescribed potential flow (thin lines) with resulting free-stream velocity (thick lines) and separation streamlines for the three base flows with 10% (A, ———), 20% (B, − ⋅ − ⋅ −) and 25% velocity drop (C, − − −) Small-Amplitude Control of Laminar Separation Bubbles 6 4 RTO-MP-AVT-111 NATO UNCLASSIFIED NATO UNCLASSIFIED The following sections are intended to demonstrate how the laminar separation bubble in these base flows react on different means of unsteady upstream forcing. The basic idea is to control laminar-turbulent transition by introducing small-amplitude disturbance waves upstream of the LSB. If these are in the unstabl