DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.     

Effect of coarse particles on the heat transfer in a particle-laden turbulent boundary layer

The temperature distribution in particle-laden turbulent flow, in a flume, was investigated both by DNS and experimentally. Simulations were performed at Re=171 and Pr=5.4 in order to study the interaction between the particle motion and flow turbulence. Two-way coupling was used to obtain various turbulence statistics, the grid resolution was sufficiently fine to resolve all essential turbulent scales. The effect of particle diameter on momentum, heat transfer and particle deposition was considered. The details of particle-turbulence interaction depend on the particle Stokes number and the particle Reynolds number.

The spatial structures of instantaneous flow and temperature fields were visualized. Low frequency small oscillations of deposited particles were observed. It was found that these small deviations from the initial position, caused strong changes in the instantaneous temperature field near the particle.

The experiments provided details of the temperature field on the heated wall close to the particle. In the front of the particle, a sharp increase in heat transfer coefficient was observed. The experimental results agree well with the computational predictions.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

Hairpin vortices in the largest scale of turbulent boundary layers

We have conducted direct numerical simulations of a turbulent boundary layer for the momentum-thickness-based Reynolds number ${\mathit{Re}}_{\theta }$ = 180–4600. To extract the largest-scale vortices, we coarse-grain the fluctuating velocity fields by using a Gaussian filter with the filter width comparable to the boundary layer thickness. Most of the largest-scale vortices identified by isosurfaces of the second invariant of the coarse-grained velocity gradient tensor are similar to coherent vortices observed in low-Reynolds-number regions, that is, hairpin vortices or quasi-streamwise vortices inclined to the wall. We also develop a percolation analysis to investigate the threshold-dependence of the isosurfaces and objectively identify the largest-scale hairpin vortices in terms of the coarse-grained vorticity, which leads to the quantitative evidence that they never disappear even in fully developed turbulent regions. Hence, we conclude that hairpin vortices exist in the largest-scale structures irrespective of the Reynolds number.     

DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow

The Lie group, or symmetry approach, developed by Oberlack (see e.g. Oberlack [26] and references therein) is used to derive new scaling laws for various quantities of a zero pressure gradient turbulent boundary layer flow. The approach unifies and extends the work done by Oberlack for the mean velocity of stationary parallel turbulent shear flows. From the two-point correlation (TPC) equations the knowledge of the symmetries allows us to derive a variety of invariant solutions (scaling laws) for turbulent flows, one of which is the new exponential mean velocity profile that is found in the mid-wake region of flat-plate boundary layers. Further, a third scaling group was found in the TPC equations for the one-dimensional turbulent boundary layer. This is in contrast to the Navier–Stokes and Euler equations, which have one and two scaling groups, respectively. The present focus is on the exponential law in the outer region of turbulent boundary layer corresponding new scaling laws for one- and two-point correlation functions. A direct numerical simulation (DNS) of a flat plate turbulent boundary layer with zero pressure gradient was performed at two different Reynolds numbers Re=750,2240. The Navier–Stokes equations were numerically solved using a spectral method with up to 140 million grid points. The results of the numerical simulations are compared with the new scaling laws. TPC functions are presented. The numerical simulation shows good agreement with the theoretical results, however only for a limited range of applicability. PACS 02.20.-a, 47.11.+j, 47.27.Nz, 47.27.Eq     

Effects of the roughness height in turbulent boundary layers over rod- and cuboid-roughened walls

Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over two-dimensional (2D) rod-roughened walls and three-dimensional (3D) cuboid-roughened walls are conducted to investigate the effects of the roughness height on the flow characteristics in the outer layer. The rod elements are periodically aligned along the downstream direction with a pitch of p_x/θ_in = 12, and the cuboid elements are periodically staggered with a pitch of p_x/θ_in = 12 and p_z/θ_in = 3, where p_x and p_z are correspondingly the streamwise and spanwise pitches of the roughness and θ_in is the momentum thickness at the inlet. The first surface roughness is placed 80θ_in downstream from the inlet, leading to a step change from a smooth to rough surface. The rod and cuboid roughness height (k) is varied in the range of 0.1 ≤ k/θ_in ≤ 1.8 (13 ≤ δ/k ≤ 285), respectively (δ is the boundary layer thickness), and the Reynolds number based on the momentum thickness (θ) is varied in the range of Re_θ = 300 ~ 1400. For each case, the self-preservation form of the velocity-defect and the turbulent Reynolds stresses is achieved along the downstream direction. As the roughness height increases, the roughness function (ΔU⁺) extracted from the mean velocity profiles increases, although the velocity-defect profiles for the rough-wall cases show good agreement with the profile from the smooth-wall case. The magnitude of the Reynolds stresses in the outer layer increases with an increase of k/δ. The outer layer similarity between the flows over the rough and smooth-walls is found when δ/k ≥ 250 and 100 for the 2D rod and 3D cuboid, respectively. The continuous increase of the Reynolds stresses in the outer layer with an increase of k/δ is explained by a large population of very long structures over the rough-wall flows. Because the characteristic width of the structures increases continuously with an increase of k/δ for the rod and cuboid roughness, a wide width of the structures leads to frequent spanwise merging between adjacent structures. The active spanwise merging events with an increase of k/δ increase the streamwise coherence of the structures with the appearance of significant meandering.     

Turbulent boundary layer flow with a step change from smooth to rough surface

A direct numerical simulation (DNS) dataset of a turbulent boundary layer (TBL) with a step change from a smooth to a rough surface is analyzed to examine the characteristics of a spatially developing flow. The roughness elements are periodically arranged two-dimensional (2-D) spanwise rods, with the first rod placed 80θ_in downstream from the inlet, where θ_in denotes the inlet momentum thickness. Based on an accurate estimation of relevant parameters, clear evidence for mean flow universality is provided when scaled properly, even for the present roughness configuration, which is believed to have one of the strongest impacts on the flow. Compared to previous studies, it is shown that overshooting behavior is present in the first- and second-order statistics and is locally created either within the cavity or at the leading edge of the roughness depending on the type of statistics and the wall-normal measurement location. Inspection of spatial two-point correlations of the streamwise velocity fluctuations shows a continuous increase of spanwise length scales of structures over the rough wall after the step change at a greater growth rate than that over smooth wall TBL flow. This is expected because spanwise energy spectrum shows presence of much energetic wider structures over the rough wall. Full images of the DNS data are presented to describe not only predominance of hairpin vortices but also a possible spanwise scale growth mechanism via merging over the rough wall.     

Self-consistent parabolized stability equation (PSE) method for compressible boundary layer

The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.     

Finite element solution to passive scalar transport behind line sources under neutral and unstable stratification

This study employed a direct numerical simulation (DNS) technique to contrast the plume behaviours and mixing of passive scalar emitted from line sources (aligned with the spanwise direction) in neutrally and unstably stratified open‐channel flows. The DNS model was developed using the Galerkin finite element method (FEM) employing trilinear brick elements with equal‐order interpolating polynomials that solved the momentum and continuity equations, together with conservation of energy and mass equations in incompressible flow. The second‐order accurate fractional‐step method was used to handle the implicit velocity–pressure coupling in incompressible flow. It also segregated the solution to the advection and diffusion terms, which were then integrated in time, respectively, by the explicit third‐order accurate Runge–Kutta method and the implicit second‐order accurate Crank–Nicolson method. The buoyancy term under unstable stratification was integrated in time explicitly by the first‐order accurate Euler method. The DNS FEM model calculated the scalar‐plume development and the mean plume path. In particular, it calculated the plume meandering in the wall‐normal direction under unstable stratification that agreed well with the laboratory and field measurements, as well as previous modelling results available in literature. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of Reynolds number on boundary layer turbulence

A new facility for studying high Reynolds number incompressible turbulent boundary layer flows has been constructed. It consists of a moderately sized wind tunnel, completely enclosed by a pressure vessel, which can raise the ambient air pressure in and around the wind tunnel to 8 atmospheres. This results in a Reynolds number range of about 20:1, while maintaining incompressible flow. Results are presented for the zero pressure gradient flat plate boundary layer over a momentum thickness Reynolds number range 1500–15?000. Scaling issues for high Reynolds number non-equilibrium boundary layers are discussed, with data comparing the three-dimensional turbulent boundary layer flow over a swept bump at Reynolds numbers of 3800 and 8600. It is found that successful prediction of these types of flows must include length scales which do not scale on Reynolds number, but are inherent to the geometry of the flow.     

Direct numerical simulation of stable and unstable turbulent thermal boundary layers

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence.     

Investigation of a hypersonic crossing shock wave/turbulent boundary layer interaction

A combined theoretical and experimental study is presented for the interaction between crossing shock waves generated by (10°, 10°) sharp fins and a flat plate turbulent boundary layer at Mach 8.3. The theoretical model is the full 3-D mean compressible Reynolds-averaged Navier-Stokes RANS) equations incorporating the algebraic turbulent eddy viscosity model of Baldwin and Lomax. A grid refinement study indicated that adequate resolution of the flowfield has been achieved. Computed results agree well with experiment for surface pressure and surface flow patterns and for pitot pressure and yaw angle profiles in the flowfield. The computations, however, significantly overpredict surface heat transfer. Analysis of the computed flowfield results indicates the formation of complex streamline and wave structures within the interaction region.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Numerical prediction of locally forced turbulent boundary layer

An unsteady numerical simulation was performed to analyze flow structure behind a local suction/blowing in a flat-plate turbulent boundary layer. The local forcing was given to the boundary layer flow by means of a sinusoidally oscillating jet. A version of the unsteady k––f_μ model [Fluid Dyn. Res. 26 (6) (2000) 421] was employed. The Reynolds number based on the momentum thickness was about Re_θ=1700. The forcing frequency was varied in the range 0.011f⁺0.044 with a fixed forcing amplitude A_o=0.4. The predicted results were compared and validated with the experimental data. It was shown that the unsteady locally forced boundary layer flow is predicted well by the k––f_μ model. The time-dependent numerical flow visualizations were demonstrated during one period of the local forcing. The effect of the pitch angle of local forcing on the reduction of skin friction was examined.     

Large-eddy simulation of a turbulent boundary layer with blowing

The modifications of a turbulent boundary layer induced by blowing through a porous plate were investigated using large-eddy simulation. The Reynolds number (based on the length of the plate) of the main flow was about 850000. Large-eddy simulations of such a boundary layer needs a turbulent inflow condition. After a review of available turbulent inflow, we describe in details the condition we developed, which consisted of recycling the velocity fluctuations. Then we show the necessity for this inflow to be non-stationary and to be three dimensional with respect to the mass conservation equation. If these properties are not achieved, we found that the velocity fluctuations do not grow as expected along the domain. Finally, the results of simulations of the boundary layer submitted to blowing are compared with experimental measurements. The good agreement obtained validate our turbulent inflow conditions and also the blowing model used. PACS 47.27.Eq, 47.27.Te, 44.20.+b     

Effect of particles on turbulent thermal field of channel flow with different Prandtl numbers

The direct numerical simulation(DNS) of heat transfer in a fully developed non-isothermal particle-laden turbulent channel flow is performed.The focus of this paper is on the modulation of the particles on turbulent thermal statistics in the particle-laden flow with three Prandtl numbers(P r = 0.71,1.5,and 3.0) and a shear Reynolds number(Reτ = 180).Some typical thermal statistics,including normalized mean temperature and their fluctuations,turbulent heat fluxes,Nusselt number and so on,are analyzed.The results show that the particles have less effects on turbulent thermal fields with the increase of Prandtl number.Two reasons can explain this.First,the correlation between fluid thermal field and velocity field decreases as the Prandtl number increases,and the modulation of turbulent velocity field induced by the particles has less influence on the turbulent thermal field.Second,the heat exchange between turbulence and particles decreases for the particle-laden flow with the larger Prandtl number,and the thermal feedback of the particles to turbulence becomes weak.     

On near-wall turbulence-generating events in a turbulent boundary layer on a riblet surface

The boundary layer over a drag reducing riblet surface is investigated using hot-wire anemometry and flow visualisation. The concept of a riblet sublayer is introduced, and a definition is proposed in terms of a region of reduced turbulence energy production formed near the wall by the addition of riblets. The hot wire records are examined using a modified form of quadrant analysis, and results obtained over plain and riblet surfaces are compared. Close to the wall, the addition of riblets produces a marked reduction in the occurrence of ejection (2nd quadrant) events. A corresponding increase in the incidence of sweep (4th quadrant) events is accompanied by the development of a strong tendency toward a preferred event duration, and a preferred interval between events. These changes diminish rapidly with distance from the surface, becoming almost undetectable beyondy ⁺=40. They are discussed in the light of flow visualisation results, and interpreted in terms of mechanisms associated with the interaction between the riblets and the inner boundary layer flow structures. A conceptual model of the flow mechanisms in the riblet sublayer is proposed.