Markus J. Kloker

Outflow Boundary Conditions for Spatial Navier-Stokes Simulations of Transition Boundary Layers

For numerical simulations of the spatially evolving laminar-turbulent transition process in boundary layers using the complete Navier-Stokes equations, the treatment of the outflow boundary requires special attention. The disturbances must pass through this boundary without causing reflections that would significantly alter the flow upstream. In this paper, we present various methods to influence the disturbed flow downstream of the region of interest, such that the disturbance level at the outflow boundary is significantly reduced, and hence the possibility of reflections is minimized. To demonstrate the effectiveness of the various techniques to alter the disturbance flow near the outflow boundary, the fundamental breakdown of a strongly decelerated boundary layer is simulated. Our results show that the most effective method is to spatially suppress the disturbance vorticity within a so-called relaminarization zone. The suppression of the disturbance vorticity is gradually imposed within this zone by means of a weighting function. The enforced decay of the disturbance vorticity leads to a practically complete dissipation of any fluctuating component. Most importantly, this technique causes only a negligible upstream effect. The relaminarized boundary-layer flow then passes through the outflow boundary without significant reflections.

A Robust High-Resolution Split-Type Compact FD Scheme for Spatial Direct Numerical Simulation of Boundary-Layer Transition

In this paper an efficient split-type Finite-Difference (FD) scheme with high modal resolu- tion - most important for the streamwise convection terms that cause wave transport and interaction - is derived for a mixed Fourier-spectral/FD method that is designed for the spatial direct numerical simulation (DNS) of boundary-layer transition and turbulence. Using a relatively simple but thor- ough and instructive modal analysis we discuss some principal trouble sources of the related FD discretization. The new scheme is based on a 6th-order compact FD discretization in streamwise and wall-normal direction and the classical 4th-order Runge-Kutta time-integration scheme with sym- metrical final corrector step. Exemplary results of a fundamental-(K-) type breakdown simulation of a strongly decelerated Falkner-Skan boundary layer (Hartree parameterH D 0.18) using 70 mega grid points in space are presented up to the early turbulent regime (Re;turb 820). The adverse pressure gradient gives rise to local separation zones during the breakdown stage and intensifies final breakdown by strong amplification of (background) disturbances thus enabling rapid transition at moderate Reynolds number. The appearance and dynamics of small-scale vortical structures in early turbulence basically similar to the large-scale structures at transition can be observed corroborating Kachanovs hypothesis on the importance of the K-regime of breakdown for coherent structures in turbulence.

Stabilisation of a three-dimensional boundary layer by base-flow manipulation using plasma actuators

The applicability of dielectric barrier discharge plasma actuators for controlling the crossflow-vortex-induced laminar breakdown in a three-dimensional swept-wing-type boundary-layer flow is investigated using direct numerical simulation. Similar to the classical application of suction at the wall the aim is to modify the quasi two-dimensional base flow and to weaken primary crossflow (CF) instability, mainly due to a reduction of the basic CF. Not only localised volumetric forcing by plasma actuators but also CF counter-blowing and spots with a moving wall are investigated to identify effective fundamental mechanisms. It is found that counter blowing always results in partial blockage of the flow and eventually increased CF velocity, whereas moving-wall spots can slightly reduce the CF and the amplitude of crossflow vortices. Using discrete volumetric forcing a significant attenuation even of finite-amplitude crossflow vortices and thus a distinct transition delay is achieved.

DNS of Laminar-Turbulent Transition In Separation Bubbles

A Laminar Separation Bubble (LSB) is created under the influence of an adverse (positive) pressure gradient along a wall by laminar separation, laminar-turbulent transition and turbulent re-attachment of the flow to the wall. Direct Numerical Simulations (DNS) of the flow in an airfoil boundary layer which are based on solving the full Navier-Stokes equations exhibit good quantitative agreement of the mean-flow data with wind-tunnel experiments, but only examinations of the unsteady results are able to reveal the underlying physics. Thus, a hitherto unknown temporal amplification of three-dimensional small-amplitude disturbances is observed and explained by the entrainment of three-dimensional fluctuations by the roll-up of the detached boundary layer. Once the three-dimensional disturbances become saturated this mechanism leads to a rapid breakdown of the laminar flow into regions of small-scale turbulence which are organized in a quasi two-dimensional coherent manner.

Numerical investigation of plasma-actuator force-term estimations from flow experiments

The accuracy of the experimental force-term estimation for cold, dielectric barrier discharge (DBD) plasma actuators based on fluid-velocity information is investigated by means of numerical simulations for cases without and with a laminar base flow. First, a wall jet induced by a steady planar body force similar to that induced by a plasma actuator under quiescent-air conditions is simulated. Second, the same steady force is applied to stabilise a laminar two-dimensional zero-pressure-gradient boundary-layer flow under the usual assumption of force independence. For both cases the force distribution is reconstructed applying two different methods to eliminate the pressure gradients unknown from experiments. The method based on the vorticity transport equation requires the force to be dominated by one component only. It is found that its accuracy is unaffected by a base flow but strongly dependent on the characteristics of the force distribution. The other method is based on the primitive-variable formulation of the Navier–Stokes equations, and the force components are assumed to dominate the pressure gradients, which are neglected. It is shown that this assumption is valid for the wall-parallel force component only, and in the case of a base flow the pressure gradients must not be neglected. The clarification of the accuracy of the different methods enables to evaluate the force-independence assumption in detail. For the case with base flow, the effect of force unsteadiness is investigated.

Navier-Stokes Simulation of Harmonic Point Disturbances in an Airfoil Boundary Layer

Laminar-turbulenttransitionmechanismsinducedbyaharmonicpointsourcedisturbanceinae at-plateboundary layerwithadversepressuregradientareinvestigated by fourth-orderaccuratespatialdirectnumericalsimulation based on the complete three-dimensional Navier ‐Stokes equations for incompressible e ow. The disturbance is introduced into thetwo-dimensionalbasee owbytime-periodicsimultaneousblowing andsuction within acircular spot at the wall to quietly mimic the momentum input by an active loudspeaker below a hole in the surface in respective experiments. Thus a wave train consisting of pure Tollmien ‐Schlichting waves of a singlefrequency and a large number of obliqueness angles is stimulated, and its downstream evolution in both physical and spectral space is investigated. A breakdown scenario dominated entirely by oblique modes is observed that shows a spanwise peak/valley amplitude splitting with the valley plane at the centerline of the wave train. Dominant vorticity structures develop off centerline, and a clear-cut -shaped structure is formed in e nal stages related to the wall shear being a footprint of a e rst pair of K -vortices in the e ow.

Numerical Simulation of Two- and Three-Dimensional Instability Waves in Two-Dimensional Boundary Layers with Streamwise Pressure Gradient

The spatial development of two- and three-dimensional disturbances in flat plate boundary layers with streamwise pressure gradient is investigated using a numerical method for solving the complete Navier-Stokes equations for incompressible flow. The validity of the method is demonstrated by test cases with small amplitude disturbances for which comparison with linear primary stability theory is possible. Calculations for subharmonic and fundamental resonance breakdown in a strongly decelerated boundary layer indicate that, in contrast to a zero pressure gradient Blasius flow, the fundamental mechanism results in a stronger growth of the three-dimensional disturbances than the subharmonic mechanism.

Direct Numerical Simulation of Boundary-Layer Transition with Strong Adverse Pressure Gradient

Fundamental breakdown of a strongly decelerated Falkner-Skan-type boundary layer (Hartree-Parameter βH=−0.18) is investigated up to late stages by direct numerical simulation using the complete Navier-Stokes equations for three-dimensional incompressible flow and the so-called spatial model. Transition is initiated by a timewise-periodic small amplitude 2-D wave and a pair of oblique 3-D waves with identical frequency. It is observed that the resulting breakdown process under adverse pressure gradient is dramatically more complex than the well-known K-breakdown in the Blasius flow: In addition to the (upper) high-shear layer on top of the lambda (Λ-) vortex, a (lower) characteristic high-shear layer is formed simultaneously in between neighbouring Λ-vortices. This shear layer, induced by a secondary vortex system close to the wall, precipitates ultimate breakdown to turbulence.

Direct Numerical Simulation of Foreign-Gas Film Cooling in Supersonic Boundary-Layer Flow

The cooling-film behavior in an adiabatic supersonic air main flow over a flat plate is investigated using direct numerical simulations. Air and helium are employed as cooling gases and are injected with a low rate in the wall-normal direction through a single infinite spanwise slit into the laminar or turbulent boundary-layer flow. The blowing is realized by prescribing a fixed distribution of the cooling-gas mass flux, mass fraction, and temperature at either the orifice location without the cooling-gas channel (modeled blowing) or at the lower end of the included blowing channel (simulated/interacting blowing), thus allowing for an interaction of the main and cooling-gas flows. The influence of the modeling, the main-flow boundary-layer state, and the cooling-gas type on the film-cooling effectiveness and the skin-friction alteration is scrutinized; and valuable data for the validation of less costly computational fluid dynamics methods employing turbulence models are gained from this fundamental study.

Effects of a Discrete Medium-Sized Roughness in a Laminar Swept-Wing Boundary Layer

Direct numerical simulations of the effects of a cylindrical roughness element in the laminar 3-d boundary layer on the upper surface of a swept wing are performed. The roughness element generates streamwise vortices, where one is persistently growing in streamwise direction due to crossflow instability. By varying the roughness height, the onset of secondary instability of this crossflow vortex and ultimate transition to turbulence varies also in streamwise direction. When reaching the “effective”, i.e. the flow-tripping roughness height, the linear crossflow-instability regime is bypassed and breakdown to turbulence occurs in close vicinity to the element due to a global instability.