Mark P. Simens

Turbulent boundary layers and channels at moderate Reynolds numbers

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/δ =0 .3–0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reθ ≈ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

Characterization of near-wall turbulence in terms of equilibrium and “bursting” solutions

Near-wall turbulence in the buffer region of Couette and Poiseuille flows is characterized in terms of recently-found nonlinear three-dimensional solutions to the incompressible Navier–Stokes equations for wall-bounded shear flows. The data suggest that those solutions can be classified into two families, of which one is dominated by streamwise vortices, and the other one by streaks. They can be associated with the upper and lower branches of the equilibrium solutions for Couette flow found by Nagata [“Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity,” J. Fluid Mech. 217, 519 (1990)]. The quiescent structures of near-wall turbulence are shown to correspond to the vortex-dominated family, but evidence is presented that they burst intermittently both in minimal and in fully turbulent flows. The intensity and period of the bursts are Reynolds-number dependent, but they saturate at high enough Reynolds numbers. The time-periodic exact solution found for Couette flo...

Low-dimensional dynamics of a turbulent wall flow

(Received 1 December 2000 and in revised form 1 February 2001) The low-dimensional dynamics of the structures in a turbulent wall flow are studied by means of numerical simulations. These are made both ‘minimal’, in the sense that they contain a single copy of each relevant structure, and ‘autonomous’ in the sense that there is no outer turbulent flow with which they can interact. The interaction is prevented by a numerical mask that damps the flow above a given wall distance, and the flow behaviour is studied as a function of the mask height. The simplest case found is a streamwise wave that propagates without change. It takes the form of a single wavy low-velocity streak flanked by two counter-rotating staggered quasi-streamwise vortices, and is found when the height of the numerical masking function is less than + 1 50. As the mask height is increased, this solution bifurcates into an almost-perfect limit cycle, a two-frequency torus, weak chaos, and full-fledged bursting turbulence. The transition is essentially complete when + 1 70, even if the wall-parallel dimensions of the computational box are small enough for bursting turbulence to be metastable, lasting only for a few bursting cycles. Similar low-dimensional dynamics are found in somewhat larger boxes, containing two copies of the basic structures, in which the bursting turbulence is self-sustaining. The physical mechanisms of wall-bounded turbulent shear flows are considerably less well understood than those of most other ‘classical’ turbulent flows. There are two competing conceptual models. In the rst one, wall turbulence is just a modication of ordinary shear turbulence, occurring when the latter approaches a wall, and is therefore dependent on the prior existence of an outside turbulent flow. In the second, it is an independent phenomenon which coexists with the outer flow and merges into it when the distance from the wall is large enough. In this paper we present some evidence supporting the latter view, examining the dynamics of the structures of the viscous and buer layers in simplied situations in which their interactions with the outer flow are severely restricted. Even natural flows scale in this region approximately on wall units, dened in terms of the kinematic viscosity , and of the friction velocity u =( @yUw) 1=2 , where @yUw is the derivative at the wall of the mean velocity prole. In that approximation, and if we admit that near-wall turbulence is not just a modication by the wall of the outside turbulent flow, only local quantities such as the dimensionless distance to the wall, y + = uy=, should matter, while global parameters such as the Reynolds number of the outer flow should be irrelevant. In the reduced systems considered in this paper the outer

The Effect of Surface Roughness on Laminar Separated Boundary Layers

Roughness effects on a laminar separation bubble, formed on a flat plate boundary layer due to a strong adverse pressure gradient similar to those encountered on the suction side of typical low-pressure turbine blades, are studied by direct numerical simulation. The discrete roughness elements that have a uniform height in the spanwise direction and ones that have a height that is a function of the spanwise coordinate are modeled using the immersed boundary method. The location and the size of the roughness element are varied in order to study the effects on boundary development and turbulent transition; it was found that the size of the separation bubble can be controlled by positioning the roughness element away from the separation bubble. Roughnesses that have a height that varies in a periodic manner in the spanwise direction have a great influence on the separation bubble. The separation point is moved downstream due to the accelerated flow in the openings in the roughness element, which also prevents the formation of the recirculation region after the roughness element. The reattachment point is moved upstream, while the height of the separation bubble is reduced. These numerical experiments indicate that laminar separation and turbulent transition are mainly affected by the type, height, and location of the roughness element. Finally, a comparison between the individual influence of wakes and roughness on the separation is made. It is found that the transition of the separated boundary layer with wakes occurs at almost the same streamwise location as that induced by the three-dimensional roughness element. [DOI: 10.1115/1.4025200]

Analysis of a Turbulent Boundary Layer Subjected to a Strong Adverse Pressure Gradient

A strongly decelerated turbulent boundary layer is investigated by direct numerical simulation. Transition to turbulence is triggered by a trip wire which is modelled using the immersed boundary method. The Reynolds number close to the exit of the numerical domain is Reθ = 2175 and the shape-factor is H = 2.5. The analysis focuses on the latter portion of the flow with large velocity defect, at higher Reynolds numbers and further from the transition region. Mean velocity profiles do not reveal a logarithmic law. Departure from the law of the wall occurs throughout the inner region. The production and Reynolds stress peaks move to roughly the middle of the boundary layer. The profiles of the uv correlation factor reveal that u and v become less correlated throughout the boundary layer as the mean velocity defect increases, especially near the wall. The structure parameter is low in the present flow, similar to equilibrium APG flows and mixing layers, and decreases as the mean velocity defect increases. The statistics of the upper half of the boundary layer resemble those of a mixing layer. Furthermore, various two-dimensional two-point correlation maps are obtained. The Cvv and Cww correlations obtained far from the transition region at Reθ = 2175 and at y/δ = 0.4 coincide with results obtained for a ZPG boundary layer, implying that the structure of the v,w fluctuations is the same as in ZPG. However, Cuu indicates that the structure of the u fluctuation in this APG boundary layer is almost twice as short as the ZPG one. The APG structures are also less correlated with the flow at the wall. The near-wall structures are different from ZPG flow ones in that streaks are much shorter or absent.

Direct Numerical Simulations of Wake-Perturbed Separated Boundary Layers

A wake-perturbed flat plate boundary layer with a streamwise pressure distribution similar to those encountered on the suction side of typical low-pressure turbine blades is investigated by direct numerical simulation. The laminar boundary layer separates due to a strong adverse pressure gradient induced by suction along the upper simulation boundary, transitions, and reattaches while still subject to the adverse pressure gradient. Various simulations are performed with different wake passing frequencies, corresponding to the Strouhal number 0.0043< fhb=DU <0.0496 and wake profiles. The wake profile is changed by varying its maximum velocity defect and its symmetry. Results indicate that the separation and reattachment points, as well as the subsequent boundary layer development, are mainly affected by the frequency, but that the wake shape and intensity have little effect, and that the forcing is effective as long as the wake-passing period is shorter than the bubble-regeneration time. Moreover, the effect of the different frequencies can be predicted from a single experiment in which the separation bubble is allowed to reform after having been reduced by wake perturbations. The stability characteristics of the mean flows resulting from the forcing at different frequencies are evaluated in terms of local linear stability analysis based on the Orr-Sommerfeld equation. [DOI: 10.1115/1.4004882]

Alternatives to Kelvin-Helmholtz Instabilities to Control Separation Bubbles

We study the control of two-dimensional laminar separation bubbles on a flat plate at low Reynolds numbers, using two-dimensional DNS. A range of steady separation bubbles is obtained varying the pressure gradient. They are forced by a zero-mass flow, oscillatory wall blowing with different perturbation amplitudes and frequencies. The reduction in bubble length as a function of frequency has two minima for sufficient high amplitudes. One of them is related to the Kelvin-Helmholtz instability of the separated boundary layer, while the other, most effective one, is here denoted as the low-frequency regime. In this regime large vortices are created which are not a consequence of an instability of the original bubble. On the contrary the forcing creates an unsteady separation bubble which evolves into a large vortex. These vortices have large radii and attach to the wall due to their self-induced pressure field while convecting across the adverse pressure gradient zone. Scaling relations for the effect of the forcing are proposed and tested.© 2006 ASME

Coherent structures in a zero-pressure-gradient and a strongly decelerated boundary layer

Coherent structures in a strongly decelerated large-velocity-defect turbulent boundary layer (TBL) and a zero pressure gradient (ZPG) boundary layer are analysed by direct numerical simulation (DNS). The characteristics of the one-point velocity stastistics are also considered. The adverse pressure gradient (APG) TBL simulation is a new one carried out by the present authors. The APG TBL begins as a zero pressure gradient boundary layer, decelerates under a strong adverse pressure gradient, and separates near the end of the domain in the form of a very thin separation bubble. The one-point velocity statistics in the outer region of this large-defect boundary layer are compared to those of two other large-velocity-defect APG TBLs (one in dynamic equilibrium, the other in disequilibrium) and a mixing layer. In the upper half of the large-defect boundary layers, the velocity statistics are similar to those of the mixing layer. The dominant peaks of turbulence production and Reynolds stresses are located in the middle of the boundary layers. Three-dimensional spatial correlations of (u, u) and (u, v) show that coherence is lost in the streamwise and spanwise directions as the velocity defect increases. Near-wall streaks tend to disappear in the large-defect zone of the flow to be replaced by more disorganized u motions. Near-wall sweeps and ejections are also less numerous. In the outer region, the u structures tend to be shorter, less streaky, and more inclined with respect to the wall than in the ZPG TBL. The sweeps and ejections are generally bigger with respect to the boundary layer thickness in the large-defect boundary layer, even if the biggest structures are found in the ZPG TBL. Large sweeps and ejections that reach the wall region (wall-attached) are less streamwise elongated and they occupy less space than in the ZPG boundary layer. The distinction between wall-attached and wall-detached structures is not as pronounced in the large-defect TBL.

The Structure of APG Turbulent Boundary Layers

The characteristics of three-dimensional intense uv-structures (Qs) in a strongly decelerated large-velocity-defect boundary layer are analyzed. The Q2 and Q4 structures are found to be different from those of turbulent channel flows studied by Lozano-Duran et al. (J Fluid Mech 694:100–130, 2012). They are less streamwise elongated, less present near the wall and wall-detached structures are more numerous. Moreover, contrary to channel flows, wall-detached Q2, and Q4 structures contribute significantly to the Reynolds shear stress.

Spanwise Spectra, Reynolds Stresses and Correlations From DNS of Turbine Like APG Boundary Layers

It is becoming more apparent that to be able to fully understand the adverse pressure gradient boundary flow in general or downstream of reattachment it is needed to understand the relation between the upstream flow structures and the downstream flow structures. In this work the results for three different direct numerical simulations (DNS) of adverse pressure gradient (APG) flows are presented. The three cases have the same overall characteristics with respect to the imposed APG and the Reynolds number Reδ099 at the inlet. However, the first case has no additional perturbations imposed, in the second case the flow is tripped by a trip wire and in the third case a periodic wake is superimposed on the flow. The main points that are discussed are the spanwise spectra, two-dimensional correlations, and Reynolds stress budgets for the three different flow cases. Attention is in particular directed to a comparison between the three different cases.The most important conclusion is that the flow downstream of reattachment is strongly correlated with the flow structures at transition for almost the whole numerical domain.Copyright