DNS and Modelling of Passive Scalar Transport in Turbulent Channel Flow with a Focus on Scalar Dissipation Rate Modelling

A direct numerical simulation of turbulent channel flow with an imposed mean scalar gradient is analyzed with a focus on passive scalar flux modelling and in particular the treatment of the passive scalar dissipation equation. The Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half width is 265. Budgets are presented for the passive scalar variance and its dissipation rate, as well as for the individual scalar flux components. These form a basis for a discussion of modelling issues related to explicit algebraic scalar flux modelling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence structure in an annuli with strongly heated inner cylinder

This structure of turbulent flow in an annulus with strong inner cylinder wall heating has been studied in terms of velocity and temperature with wall temperatures up to 707 °C and a Reynolds number of 48,000. With increase in wall heating, the turbulence very close to the wall was suppressed due to an increase in the kinematic viscosity. In the inner region, the intermittent mixing became intensive and the turbulent intensity increased whereas, in the outer region, the turbulence was suppressed since intermittent mixing was no longer effective. The results show that the thermal structure can be considered in terms of a passive scalar for wall temperatures less then around 200 °C, except in the leading region of the heated area. Received: 2 March 1998/Accepted: 2 November 1998     

Effect of a moving wall on a fully developed, equilibrium turbulent boundary layer

Experiments were conducted in a wind tunnel to assess the effect of a moving wall on a fully developed, equilibrium turbulent boundary layer. Pitot-static and total head probes were used in conjunction with both single- and two-component hot-wire anemometer probes to quantify the effect of wall motion on the boundary layer velocity statistics. A variable speed, seamless belt formed the wind tunnel test section wall. When stationary, the belt was found to possess a fully developed, equilibrium turbulent boundary layer in excellent agreement with archival data. With the tunnel wall moving at the free-stream speed, and at a sufficient distance above the wall, the velocity statistics in the moving-wall boundary layer were found to collapse well when scaled as a self-preserving turbulent wake. The near-wall mean velocity profile of the moving wall was found to exhibit an extended region of linearity compared to canonical turbulent boundary layer and internal flows. This can be attributed to the reduced shear resulting from wall motion and the subsequent reduction in Reynolds stress. Received: 2 June 1999/Accepted: 8 August 2000     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Passive Scalar in a Turbulent Channel Flow with Wall Velocity Disturbances

Direct Numerical Simulations (DNS) of a passive scalar in a turbulent channel flow with a normal velocity disturbance on the lower wall are presented for high and low Reynolds numbers. The aim is to reproduce the complex physics of turbulent rough flows without dealing with the geometric complexity. In addition, isothermal walls that cannot be easily assigned in an experiment, are considered. The paper explains the increase of heat transfer through the changes of the velocity and thermal structures. As in real rough flows, the transpiration produces an isotropization of the turbulence near the wall.     

Structure of turbulent two-dimensional channel flow with strongly heated wall

A laser Doppler velocimeter and a resistance thermometer were used to study velocity and temperature statistics in a strongly heated turbulent two-dimensional channel flow, with the wall temperature up to 700 °C and a Reynolds number of 14,000. Normalized mean velocity and mean temperature profiles were not significantly affected by the wall heating. Turbulent intensities of temperature fluctuation were also insensitive to the heat flux. However, turbulent intensities of velocity fluctuation were suppressed in the region away from the wall, whereas those near the wall were not changed noticeably by the wall heating. This phenomenon was explained by the balance of three parameters: turbulent production, viscous dissipation and intermittency.     

锥体效应对超音速湍流边界层统计特性的影响

通过直接数值模拟,计算了空间模式下,来流马赫数为2.5, 半锥角为$5^{\circ}$, 零攻角的绝热钝锥湍流边界层,研究了湍流的统计特性,并把结果与超音速平板湍流边界层和马赫数为6的高超音速钝锥湍流边界层的结果进行了比较,重点定量地考察了锥体效应对边界层湍流统计特性的影响. 研究发现,锥体效应对平均温度剖面以及压缩性的影响是显著的;而其它统计量,比如速度壁面律、雷诺应力的分布和湍动能各项的贡献等,受锥体效应的影响很小.      

An experimental study of turbulent boundary layers approaching separation

The present paper deals with the experimental analysis of a strong decelerated turbulent boundary layer developed on a flat plate. The aim of the study was to examine the effects of pressure gradient on a non-equilibrium boundary layer while indicating local areas of equilibrium flow. The effect of the Reynolds number on a turbulent boundary layer developed with matching the external pressure gradient conditions was also analysed. The emphasis was on the analysis of mean flow statistics i.e. mean velocity profiles, streamwise Reynolds stress and the effect of large- and small-scale interactions by analysing the skewness factor and energy isocontours maps. The comparative analysis of the external data indicated that the structure of the turbulent boundary layer depends not only on local effects of pressure gradient but also on the upstream history of the flow. For the same condition of pressure gradient, the increased momentum is observed near the wall with the increase of the Reynolds number at the Incipient Detachment, where increased turbulence production is also observed, leading to the failure of the outer scaling methods. Surprisingly, the effect of the Reynolds number decays at the intermittent transitory detachment where similar profiles were observed. The upper inflection point in the mean profile corresponded well with the outer maximum of the Reynolds stress and zero crossing of skewness factor. Position of this point occurs at different locations, depending on the flow history effects. The last observation demonstrates that the inflection points results from large- and small-scale interactions, which led to the increased convection velocity of small scales near the wall.     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Layered structure of turbulent plane wall jet

This paper investigates the layered structure of a turbulent plane wall jet at a distance from the nozzle exit. Based on the force balances in the mean momentum equation, the turbulent plane wall jet is divided into three regions: a boundary layer-like region (BLR) adjacent to the wall, a half free jet-like region (HJR) away from the wall, and a plug flow-like region (PFR) in between. In the PFR, the mean streamwise velocity is essentially the maximum velocity, and the simplified mean continuity and mean momentum equations result in a linear variation of the mean wall-normal velocity and Reynolds shear stress. In the HJR, as in a turbulent free jet, a proper scale for the mean wall-normal flow is the mean wall-normal velocity far from the wall and a proper scale for the Reynolds shear stress is the product of the maximum mean streamwise velocity and the velocity scale for the mean wall-normal flow. The BLR region can be divided into four sub-layers, similar to those in a canonical pressure-driven turbulent channel flow or shear-driven turbulent boundary layer flow. Building on the log-law for the mean streamwise velocity in the BLR, a new skin friction law is proposed for a turbulent wall jet. The new prediction agrees well with the correlation of Bradshaw and Gee (1960) over moderate Reynolds numbers, but gives larger skin frictions at higher Reynolds numbers.     

Structure of near wall turbulence downstream of a wall mounted protrusion: an interesting Reynolds stress suppression phenomena

A local suppression in the generation of near wall Reynolds stress is achieved by modifying the buffer region and sublayer (y ⁺ <30) of a turbulent pipe flow with a 16.4 wall unit high wall mounted protrusion. Multi-component, multi-point, time resolved laser Doppler velocimetry measurements are made in the undisturbed and modified ARL/PSU glycerin tunnel pipe flow at a Reynolds number of approximately 10000. A downstream converging flow field is produced by the divergence of the approaching mean flow around the protrusion. A pair of counter-rotating vortices, 15 wall units in diameter with common flow down, are generated by the protrusion and also contribute to the wall directed flow convergence. The convergence region is 15 wall units high and more than 100 wall units long and appears to decouple the near wall region from the outer turbulent wall layer. Locally, turbulent velocity fluctuations in the form of Reynolds stress producing events, sweeps and ejections, are retarded within this region. This results in a reduction in near wall uv Reynolds stress and local wall shear. Interestingly, the counter-rotating vortices act to increase turbulent diffusion in a manner which is uncorrelated with Reynolds stress generation.     

DNS of a spatially developing turbulent boundary layer with passive scalar transport

A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier–Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U_∞ and momentum thickness θ is Re_θ=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors’ knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.     

Large eddy simulation of compressible channel flow

Astract The present study is a contribution to the analysis of wall-bounded compressible flows, including a special focus on wall modeling for compressible turbulent boundary layer in a plane channel. large eddy simulation (LES) of fully developed isothermal channel flows at Re = 3,000 and Re = 4,880 with a sufficient mesh refinement at the wall are carried out in the Mach number range 0.3 ≤ M ≤ 3 for two different source term formulations: first the classical extension of the incompressible configuration by Coleman et al. (J. Fluid Mech. 305:159–183, 1995), second a formulation presently derived to model both streamwise pressure drop and streamwise internal energy loss in a spatially developed compressible channel flow. It is shown that the second formulation is consistent with the spatial problem and yields a much stronger cooling effect at the wall than the classical formulation. Based on the present LES data bank, compressibility and low Reynolds number effects are analysed in terms of coherent structure and statistics. A study of the universality of the structure of the turbulence in non-hypersonic compressible boundary layers (M≤5) is performed in reference to Bradshaw (Annu. Rev. Fluid. Mech. 9:33–54, 1977). An improvement of the van Driest transformation is proposed; it accounts for both density and viscosity changes in the wall layer. Consistently, a new integral wall scaling (y ^c+) which accounts for strong temperature gradients at the wall is developed for the present non-adiabatic compressible flow. The modification of the strong Reynolds analogy proposed by Huang et al. (J. Fluid Mech. 305:185–218, 1995) to model the correlation between velocity and temperature for non-adiabatic wall layers is assessed on the basis of a Crocco–Busemann relation specific to channel flow. The key role of the mixing turbulent Prandtl number Pr _m is pointed out. Results show very good agreement for both source formulations although each of them involve a very different amount of energy transfer at the wall. The present work was performed within the framework of the French–German research initiative “large eddy simulation of complex flows’ (UR 507). The computing resources were provided by IDRIS-France. The authors gratefully acknowledge the financial support from the Centre National de la Recherche Scientifique (CNRS), the Centre d’été Mathématique de Recherche Avancée en Calcul Scientifique (CEMRACS) and the Direction Générale de l’Armement (DGA/D4S).     

Vortex-In-Cell and Probability Density Function Approach for a Passive Scalar Field in a Mixing Layer

A Reynolds-averaged simulation based on the vortex-in-cell (VIC) and the transport equation for the probability density function (PDF) of a scalar has been developed to predict the passive scalar field in a two-dimensional spatially growing mixing layer. The VIC computes the instantaneous velocity and vorticity fields. Then the mean-flow properties, i.e. the mean velocity, the root-mean-square (rms) longitudinal and lateral velocity fluctuations, the Reynolds shear stress, and the rms vorticity fluctuations are computed and used as input to the PDF equation. The PDF transport equation is solved using the Monte Carlo technique. The convection term uses the mean velocities from the VIC. The turbulent diffusion term is modeled using the gradient transport model, in which the eddy diffusivity, computed via the Boussinesq's postulate, uses the Reynolds shear stress and gradients of mean velocities from the VIC. The molecular mixing term is closed by the modified Curl model.

The computational results were compared with two-dimensional experimental results for passive scalar. The predicted turbulent flow characteristics, i.e. mean velocity and rms longitudinal fluctuations in the self-preserving region, show good agreement with the experimental measurements. The profiles of the mean scalar and the rms scalar fluctuations are also in reasonable agreement with the experimental measurements. Comparison between the mean scalar and the mean velocity profiles shows that the scalar mixing region extends further into the free stream than does the momentum mixing region, indicating enhanced transport of scalar over momentum. The rms scalar profiles exhibit an asymmetry relative to the concentration centerline, and indicate that the fluid on the high-speed side mixes at a faster rate than the fluid on the low-speed side. The asymmetry is due to the asymmetry in the mixing frequency cross-stream profiles. Also, the PDFs have peaks biased toward the high-speed side.     

The influence of flow-induced non-Newtonian fluid properties on turbulent drag reduction

Friction factors and velocity profiles in turbulent drag reduction can be compared to Newtonian fluid turbulence when the shear viscosity at the wall shear rate is used for the Reynolds number and the local shear viscosity is used for the non-dimensional wall distance. On this basis, an apparent maximum drag reduction asymptote is found which is independent of Reynolds number and type of drag reducing additive. However, no shear viscosity is able to account for the difference between the measured Reynolds stress and the Reynolds stress calculated from the mean velocity profile (the Reynolds stress deficit). If the appropriate local viscosity to use with the velocity fluctuation correlations includes an elongational component, the problem can be resolved. Taking the maximum drag reduction asymptote as a non-Newtonian flow, with this effective viscosity, leads to agreement with the concept of an asymptote only when the solvent viscosity is used in the non-dimensional wall distance.     

Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

Heat transfer in turbulent pipe flow based on a new mixing length model

A new model for the heat transfer in turbulent pipe flow is presented based on a modified form of the mixing length theory developed by Cebeci [1] for boundary layer flow problems. The model predicts the velocity and temperature distributions and the Nusselt number for fluids with low, medium and high Prandtl numbers (Pr=.02 to 15) and fits the available experimental data very accurately for values of Reynolds number exceeding 10⁴. Expressions for the eddy conductivity and for the turbulent Prandtl number are presented and shown to be dependent upon the Reynolds number, the Prandtl number, and the distance from the tube wall.     

Development of a Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow

The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stress-modelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.     

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.