Ulrich Rist

Direct numerical simulation of controlled transition in a flat-plate boundary layer

The three-dimensional development of controlled transition in a flat-plate boundary layer is investigated by direct numerical simulation (DNS) using the complete Navier-Stokes equations. The numerical investigations are based on the so-called spatial model, thus allowing realistic simulations of spatially developing transition phenomena as observed in laboratory experiments. For solving the Navier-Stokes equations, an efficient and accurate numerical method was developed employing fourth-order finite differences in the downstream and wall-normal directions and treating the spanwise direction pseudo-spectrally. The present paper focuses on direct simulations of the wind-tunnel experiments by Kachanov et al. (1984, 1985) of fundamental breakdown in controlled transition. The numerical results agreed very well with the experimental measurements up to the second spike stage, in spite of relatively coarse spanwise resolution. Detailed analysis of the numerical data allowed identification of the essential breakdown mechanisms. In particular, from our numerical data, we could identify the dominant shear layers and vortical structures that are associated with this breakdown process.

Numerical investigation of the three-dimensional development in boundary-layer transition

A numerical method for solving the complete Navier-Stokes equations for incompressible flows is introduced that is applicable for investigating three-dimensional transition phenomena in a spatially growing boundary layer. Results are discussed for a test case with small three-dimensional disturbances for which detailed comparison to linear stability theory is possible. The validity of our numerical model for investigating nonlinear transition phenomena is demonstrated by realistic spatial simulations of the experiments by Kachanov and Levchenko1 for a subharmonic resonance breakdown and of the experiments of Klebanoff et al.2 for a fundamental resonance breakdown.

Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation

The mechanism of turbulence development in periodic Klebano transition in a boundary layer has been studied experimentally and in a direct numerical simulation (DNS) with controlled disturbance excitation. In order to compare the results quantitatively, the flow parameters were matched in both methods, thus providing complementary data with which the origin of turbulence in the transition process could be explained. Good agreement was found for the development of the amplitude and shape of typical disturbance structures, the -vortices, including the development of ring-like vortices and spikes in the time traces. The origin and the spatial development of random velocity perturbations were measured in the experiment, and are shown together with the evolution of local high-shear layers. Since the DNS is capable of providing the complete velocity and vorticity elds, further conclusions are drawn based on the numerical data. The mechanisms involved in the flow randomization process are presented in detail. It is shown how the random perturbations which initially develop at the spike-positions in the outer part of the boundary layer influence the flow randomization process close to the wall. As an additional eect, the interaction of vortical structures and high-shear layers of dierent disturbance periods was found to be responsible for accelerating the transition to a fully developed turbulent flow. These interactions lead to a rapid intensication of a high-shear layer very close to the wall that quickly breaks down because of the modulation it experiences through interactions with vortex structures from the outer part of the boundary layer. The nal breakdown process will be shown to be dominated by locally appearing vortical structures and shear layers.

Investigations of time-growing instabilities in laminar separation bubbles

Abstract The occurrence of temporally growing unstable disturbances is investigated based on eigenvalues with zero group velocity from linear stability theory (LST) and compared with observations of upstream travelling disturbances obtained in a two-dimensional direct numerical simulation (DNS) of an unsteady laminar separation bubble. Numerical solutions of the Orr–Sommerfeld equation using analytically constructed base-flow velocity profiles modelled by a modified hyperbolic tangent function help to identify the role of parameters, such as maximum reverse flow, wall distance and intensity of the shear layer, as well as Reynolds number on the possibility that a true time-growing instability occurs. Then, the viscous or inviscid nature of the solutions found is classified on the basis of their eigenfunctions. For large wall distances two unstable modes are found. Apart from a low-frequency motion of the bubble the DNS exhibit high-frequency oscillations which periodically appear and disappear. Part of these disturbances travel upstream and amplify with respect to time. Their initial occurrence and their frequency are in excellent agreement with the results of the parameter study based on LST and a closer examination of the disturbances yields insight into their spatial structure.

A Combined Experimental/Numerical Study of Unsteady Phenomena in a Laminar Separation Bubble

A laminar boundary layer separates in a region of adverse pressure gradient on a flat plate and undergoes transition. Finally the turbulent boundary layer reattaches, forming a laminar separation bubble (LSB). Laminar-turbulent transition within such a LSB is investigated by means of Laser-Doppler-Anemometry (LDA), Particle Image Velocimetry (PIV), and direct numerical simulation (DNS). The transition mechanism occurring in the flow-field under consideration is discussed in detail. Observations for the development of small disturbances are compared to predictions from viscous linear instability theory (Tollmien–Schlichting instability). Non-linear development of these disturbances and their role in final breakdown to turbulence is analyzed.

Effect of Spanwise-Modulated Disturbances on Transition in a Separated Boundary Layer

A laminar boundary layer separates in a region of adverse pressure gradient on a flat plate and undergoes transition. The detached shear layer rolls up into spanwise vortices that rapidly break down into small-scale turbulence. Finally, the turbulent boundary layer reattaches, forming a laminar separation bubble. Development and role of three-dimensional disturbances for transition in such a separation bubble are studied by means of direct numerical simulation with controlled disturbance input. In the present case, the level of incoming three-dimensional perturbations is not relevant due to an absolute secondary instability of these disturbances in the region of convective two-dimensional shear layer rollup. In particular, this is true for steady perturbations up to moderate amplitudes. Following their generation by nonlinear interaction of disturbance waves in the region of favorable pressure gradient, these steady disturbances develop as streaks. Their downstream evolution can be first attributed to transient behavior, depending on initial excitation, followed by a universal state with characteristics of a modal instability. Numerical results are confirmed by a comparison with experimental data.

Opening the can of worms: an exploration tool for vortical flows

Gaining a comprehensive understanding of turbulent flows still poses one of the great challenges in fluid dynamics. A well-established approach to advance this research is the analysis of the vortex structures contained in the flow. In order to be able to perform this analysis efficiently, supporting visualization tools with clearly defined requirements are needed. In this paper, we present a visualization system which matches these requirements to a large extent. The system consists of two components. The first component analyzes the flow by means of a novel combination of vortex core line detection and the /spl lambda//sub 2/ method. The second component is a vortex browser which allows for an interactive exploration and manipulation of the vortices detected and separated during the first phase. Our system improves the reliability and applicability of existing vortex detection methods and allows for a more efficient study of vortical flows which is demonstrated in an evaluation performed by experts.

Mean flow deformation in a laminar separation bubble: separation and stability characteristics

The mutual interaction of laminar-turbulent transition and mean flow evolution is studied in a pressure-induced laminar separation bubble on a flat plate. The flat-plate boundary layer is subjected to a sufficiently strong adverse pressure gradient that a separation bubble develops. Upstream of the bubble a small-amplitude disturbance is introduced which causes transition. Downstream of transition, the mean flow strongly changes and, due to viscous-inviscid interaction, the overall pressure distribution is changed as well. As a consequence, the mean flow also changes upstream of the transition location. The difference in the mean flow between the forced and the unforced flows is denoted the mean flow deformation. Two different effects are caused by the mean flow deformation in the upstream, laminar part: a reduction of the size of the separation region and a stabilization of the flow with respect to small, linear perturbations. By carrying out numerical simulations based on the original base flow and the time-averaged deformed base flow, we are able to distinguish between direct and indirect nonlinear effects. Direct effects are caused by the quadratic nonlinearity of the Navier-Stokes equations, are associated with the generation of higher harmonics and are predominantly local. In contrast, the stabilization of the flow is an indirect effect, because it is independent of the Reynolds stress terms in the laminar region and is solely governed by the non-local alteration of the mean flow via the pressure.

Control of Laminar Separation Bubbles Using Instability Waves

This paper presents detailed investigations related to active transition control in laminar separation bubbles. The investigations rely on direct numerical simulations based on the complete Navier-Stokes equations for a flat-plate boundary layer. A laminar separation bubble is created by imposing a streamwise adverse pressure gradient at the freestream boundary of the integration domain. Different steady and unsteady boundary layer disturbances are then introduced at a disturbance strip upstream of separation and their effects on the separation bubble are studied. It is shown that the size of the separated region can be controlled most efficiently by very small periodic oscillations, which lead to traveling instability waves that grow to large levels by the hydrodynamic instability of the flow. Indications for the preferred frequency of these waves can be obtained from linear stability theory, but since the problem is nonlinear, only direct numerical simulations can really qualify or disqualify the predictions. Overall, it turns out that unsteady two- or three-dimensional disturbances have a stronger impact on the size of the bubble than steady disturbances, because they directly provide initial amplitudes for the laminar-turbulent transition mechanism.

Spatial resolution enhancement/smoothing of stereo-particle-image-velocimetry data using proper-orthogonal-decomposition-based and Kriging interpolation methods

Methods for data reconstruction and spatial enhancement of experimental data for a transitional boundary layer with laminar separation bubble are investigated. Particularly, proper orthogonal decomposition (POD) is applied to direct numerical simulation (DNS) data to extract the DNS-based POD modes, which are projected onto the experimental data (via a least-squares procedure) in order to obtain model coefficients. These model coefficients are then used to reconstruct, “interpolate,” and smooth the experimental data based on the DNS modes. In addition, in order to compare and assess the effectiveness of the present DNS-based procedure, Kriging interpolation is performed on the experimental (as well as numerical) data. These procedures are applied to time periodic (experimental) instantaneous spanwise vorticity (ωz) at a constant spanwise location. We have demonstrated that particle-image-velocimetry (PIV)-based POD modes can be smoothed by Kriging interpolation, thus a noise-free reconstruction of PIV dat...