Bernhard Scheichl

Turbulent Marginal Separation and the Turbulent Goldstein Problem

A new rational theory of incompressible turbulent boundary-layer flows having a large velocity defect is presented on basis of the Reynolds-averaged Navier-Stokes equations in the limit of infinite Reynolds number. This wake-type formulation allows for, among others, the prediction of singular solutions of the boundary-layer equations under the action of a suitably controlled adverse pressure gradient, which are associated with the onset of marginally separated flows. Increasing the pressure gradient locally then transforms the marginal-separation singularity into a weak Goldstein-type singularity occurring in the slip velocity at the base of the outer wake layer. Interestingly, this behavior is seen to be closely related to (but differing in detail from) the counterpart of laminar marginal separation, in which the skin friction replaces the surface slip velocity. Most important, adopting the concept of locally interacting boundary layers results in a closure-free and uniformly valid asymptotic description of boundary layers that exhibit small, closed reverse-flow regimes. Numerical solutions of the underlying triple-deck problem are discussed.

Break-away separation for high turbulence intensity and large Reynolds number

Massive flow separation from the surface of a plane bluff obstacle in an incompressible uniform stream is addressed theoretically for large values of the global Reynolds number Re. The analysis is motivated by a conclusion drawn from recent theoretical results which is corroborated by experimental findings but apparently contrasts with common reasoning: the attached boundary layer extending from the front stagnation point to the position of separation never attains a fully developed turbulent state, even for arbitrarily large Re. Consequently, the boundary layer exhibits a certain level of turbulence intensity that is linked with the separation process, governed by local viscous-inviscid interaction. Eventually, the latter mechanism is expected to be associated with rapid change of the separating shear layer towards a fully developed turbulent one. A self-consistent flow description in the vicinity of separation is derived, where the present study includes the predominantly turbulent region. We establish a criterion that acts to select the position of separation. The basic analysis here, which appears physically feasible and rational, is carried out without needing to resort to a specific turbulence closure.

Asymptotic Theory of Turbulent Bluff-Body Separation: A Novel Shear Layer Scaling Deduced from an Investigation of the Unsteady Motion

A rational treatment of time-mean separation of a nominally steady turbulent boundary layer from a smooth surface in the limit Re → ∞, where Re denotes the globally defined Reynolds number, is presented. As a starting point, it is outlined why the ‘classical’ concept of a small streamwise velocity deficit in the main portion of the oncoming boundary layer does not provide an appropriate basis for constructing an asymptotic theory of separation. Amongst others, the suggestion that the separation points on a two-dimensional blunt body is shifted to the rear stagnation point of the impressed potential bulk flow as Re → ∞ — expressed in a previous related study — is found to be incompatible with a self-consistent flow description. In order to achieve such a description, a novel scaling of the flow is introduced, which satisfies the necessary requirements for formulating a self-consistent theory of the separation process that distinctly contrasts former investigations of this problem. As a rather fundamental finding, it is demonstrated how the underlying asymptotic splitting of the time-mean flow can be traced back to a minimum of physical assumptions and, to a remarkably large extent, be derived rigorously from the unsteady equations of motion. Furthermore, first analytical and numerical results displaying some essential properties of the local rotational/irrotational interaction process of the separating shear layer with the external inviscid bulk flow are presented.

On turbulent marginal boundary layer separation: how the half-power law supersedes the logarithmic law of the wall

As the authors have demonstrated recently, application of the method of matched asymptotic expansions allows for a self-consistent description of a Turbulent Boundary Layer (TBL) under the action of an adverse pressure gradient, where the latter is controlled such that it may undergo marginal separation. In that new theory, the basic limit process considered is provided by the experimentally observed slenderness of a turbulent shear layer, hence giving rise to an intrinsic perturbation parameter, say α, aside from the sufficiently high global Reynolds number Re. Physically motivated reasoning, supported by experimental evidence and the existing turbulence closures, then strongly suggests that α is indeed independent of Re as Re → ∞. Here, we show how the inclusion of effects due to high but finite values of Re clarifies a long-standing important question in hydrodynamics, namely, the gradual transformation of the asymptotic behaviour of the so-called wall functions, which characterises the flow in the overlap regime of its fully turbulent part and the viscous sublayer (and, consequently, its scaling in the whole shear layer), as separation is approached.

Experimental Validation of the Simulated Steady-State Behavior of Porous Journal Bearings

This study deals with a comparison between new experiments on the frictional behavior of porous journal bearings and its prediction by previous numerical simulations. The tests were carried out on bearings lubricated with polyalphaolefin-based oils of distinct viscosities. The theoretical model underlying the simulations includes the effects of cavitation by vaporization and accounts for the sinter flow by virtue of Darcys law. The effective eccentricity ratio corresponding to the experimentally imposed load is estimated by an accurate numerical interpolation scheme. The comparison focuses on the hydrodynamic branches of the Stribeck curve by dimensional analysis, where the variations of the lubricant viscosity with temperature are of main interest. The numerically calculated values of the coefficient of friction are found to reproduce the experimentally obtained ones satisfactorily well in terms of overall trends, yet the former lie predominantly below the measured ones, which results in a low-positive correlation between the two.

Modelling the Doctor Blade-Roller Tribosystem for Improving the Cleaning Performance During Paper Production

Doctor blades are commonly used in paper machines to keep the surface of rollers clean. Due to higher demanding conditions, the requirements for doctor blades have steadily increased. The wear rates must remain low, while simultaneously their cleaning function has to be ensured. For this reason, the paper industry has developed a high degree of empirical knowledge concerning the cleaning of roller surfaces. However, up to now, no systematic approach has been successfully applied to optimize the cleaning performance of the doctor blade-roller tribosystem. This study presents an attempt to model the system based on the force equilibrium conditions at the blade tip between hydrodynamic and contact forces. The change of the blade geometry due to wear is also taken into account. By these means, a non-dimensional group involving the key parameters is obtained. This allows for a systematic improvement of the cleaning efficiency, by targeted changes of the process parameters.

Evolution of a Boundary Layer from Laminar Stagnation-Point Flow towards Turbulent Separation

We present the most relevant recent findings that allow for a rational timeaveraged description of laminar-turbulent transition of an incompressible nominally two-dimensional and steady boundary layer along the impermeable surface of a rigid blunt body. Rigorous application of matched asymptotic expansions for sufficiently high values of both the Reynolds number and a turbulence-level gauge parameter shows that the presence of a leading-edge stagnation point is associated with the generation of a turbulent shear layer that exhibits an asymptotically small streamwise velocity deficit. Remarkably, however, the turbulence intensity never reaches its theoretically possible maximum that conforms to fully developed turbulent flow.

Gross separation approaching a blunt trailing edge as the turbulence intensity increases.

A novel rational description of incompressible two-dimensional time-mean turbulent boundary layer (BL) flow separating from a bluff body at an arbitrarily large globally formed Reynolds number, Re, is devised. Partly in contrast to and partly complementing previous approaches, it predicts a pronounced delay of massive separation as the turbulence intensity level increases. This is bounded from above by a weakly decaying Re-dependent gauge function (hence, the BL approximation stays intact locally), and thus the finite intensity level characterizing fully developed turbulence. However, it by far exceeds the moderate level found in a preceding study which copes with the associated moderate delay of separation. Thus, the present analysis bridges this self-consistent and another forerunner theory, proposing extremely retarded separation by anticipating a fully attached external potential flow. Specifically, it is shown upon formulation of a respective distinguished limit at which rate the separation point and the attached-flow trailing edge collapse as and how on a short streamwise scale the typical small velocity deficit in the core region of the incident BL evolves to a large one. Hence, at its base, the separating velocity profile varies generically with the one-third power of the wall distance, and the classical triple-deck problem describing local viscous–inviscid interaction crucial for moderately retarded separation is superseded by a Rayleigh problem, governing separation of that core layer. Its targeted solution proves vital for understanding the separation process more close to the wall. Most importantly, the analysis does not resort to any specific turbulence closure. A first comparison with the available experimentally found positions of separation for the canonical flow past a circular cylinder is encouraging.

A Uniformly Valid Theory of Turbulent Separation

The contribution deals with recent theoretical results concerning separation of a turbulent boundary layer from a blunt solid object in a uniform stream, accompanied by a numerical study. The investigation is restricted to incompressible nominally steady two-dimensional flow past an impervious obstacle surface. Then the global Reynolds number represents the only parameter entering the description of the Reynolds-averaged flow. It shall be large enough to ensure that laminar–turbulent transition takes place in a correspondingly small region encompassing the stagnation point. Consequently, the concomitant asymptotic hierarchy starts with the external Helmholtz–Kirchhoff potential flow, which detaches at an initially unknown point Open image in new window from the body, driving the turbulent boundary layer. It is found that the separation mechanism is inherently reminiscent of the transition process. The local analysis of separation not only fixes the actual scaling of the entire boundary layer but is also expected to eventually predict the position of Open image in new window in a rational way.

Modern Aspects of High-Reynolds-Number Asymptotics of Turbulent Boundary Layers

This contribution reports on recent efforts with the ultimate goal to obtain a fully self-consistent picture of turbulent boundary layer separation. To this end, it is shown first how the classical theory of turbulent boundary layers having an asymptotically small streamwise velocity deficit can be generalised rigorously to boundary layers with a slightly larger, i.e. moderately large, velocity defect and, finally, to situations where the velocity defect is of O(1). In the latter case, the formation of short recirculation zones describing marginally separated flows is found possible, as described in a rational manner.