Near-wall Behavior Research Articles

Near-wall behavior of turbulent wall-bounded flows

A data base compiling a large number of results from direct numerical simulations and physical experiments is used to explore the properties of shear and normal Reynolds stresses very close to the wall of turbulent channel/pipe flows and boundary layers. Three types of scaling are mainly investigated, classical inner, standard mixed, and pure outer scaling. The study focuses on the wall behavior, the location and the value of the peak Reynolds shear stress and the three normal stresses. A primary observation is that all of these parameters show a significant Kármán number dependence. None of the scalings investigated works in an equal manner for all parameters. It is found that the respective first-order Taylor series expansion satisfactorily represents each stress only in a surprisingly thin layer very close to the wall. In some cases, a newly introduced scaling based on u τ 3 / 2 u e 1 / 2 offers a remedy.

Classification of shock wave reflections from a wedge. Part 2: Experimental and numerical simulations of different types of Mach reflections

Shadowgraph images of different types of irregular reflections that illustrate the suggested classification are presented. The complex forms of the Mach reflection are studied by numerical simulation at various initial parameters. Emphasis is on the near-wall behavior of the contact discontinuity in the main Mach configuration and on intersection between contact discontinuities. Analysis shows that, if an incident shock wave is strong, interaction of the shock wave with an infinite wedge is a nonstationary process.

A121 閉空間内の乱流予混合火炎の直接数値計算(燃焼科学と技術の新展開II)

Direct numerical simulations of turbulent premixed flame in confined vessel have been conducted to investigate heat losses and quenching mechanism of turbulent premixed flames near the wall. Near-wall behaviors of hydrogen/air premixed flames and heat transfer characteristic were investigated by considering detailed kinetic mechanism and temperature dependence of transport and thermal properties. In confined vessel, the frame is affected by the pressure wave which caused by the flame ignition and the flame propagation, and the flame displacement speed of the appearance decreases remarkably. However, the turbulent burning velocity at that time doesn't decrease because of an increase of fluid velocity normal to the flame.

Computational Investigation of Torque on Coaxial Rotating Cones

This article looks at a modification of Taylor–Couette flow, presenting a numerical investigation of the flow around a shrouded rotating cone, with and without throughflow, using the commercial computational fluid dynamics code FLUENT 6.2 and FLUENT 6.3. The effects of varying the cone vertex angle and the gap width on the torque seen by the rotating cone are considered, as well as the effect of a forced throughflow. The performance of various turbulence models are considered, as well as the ability of common wall treatments/functions to capture the near-wall behavior. Close agreement is found between the numerical predictions and previous experimental work, carried out by Yamada and Ito (1979, “Frictional Resistance of Enclosed Rotating Cones With Superposed Throughflow,” ASME J. Fluids Eng., 101, pp. 259–264; 1975, “On the Frictional Resistance of Enclosed Rotating Cones (1st Report, Frictional Moment and Observation of Flow With a Smooth Surface),” Bull. JSME, 18, pp. 1026–1034; 1976, “On the Frictional Resistance of Enclosed Rotating Cones (2nd Report, Effects of Surface Roughness),” Bull. JSME, 19, pp. 943–950). Limitations in the models are considered, and comparisons between two-dimensional axisymmetric models and three-dimensional models are made, with the three-dimensional models showing greater accuracy. The work leads to a methodology for modeling similar flow conditions to Taylor–Couette.

Evaluation of Extended Weak-Equilibrium Conditions for Fully Developed Rotating Channel Flow

The weak-equilibrium condition, which is the basis in the development of algebraic Reynolds stress models is assessed in the prediction of fully developed turbulent channel flow under the influence of system rotation. The budget of the various terms of the exact transport equation for the anisotropy tensor is evaluated by using a DNS database. Two diffusive transport constraints are evaluated by using the DNS data. The results show that neither of them can hold for the near-wall region. An asymptotic analysis of the near-wall behavior is performed and an alternative form of the diffusive transport constraint is proposed. The analysis shows that the proposed alternative diffusive transport constraint has the potential to improve the predictive ability of the resultant ARSM.

Turbulent Separated Flows: Near-Wall Behavior and Heat and Mass Transfer

This paper was presented at the Eleventh Asian Congress of Fluid Mechanics as an invited/keynote lecture. The lecture summarizes development of physical model for transfer processes in turbulent separated flows. Attention is focused on the factors that have led to significant advances in understanding of the mechanisms of transfer processes in separated flows, which differs from those in traditional attached turbulent flows in channels and zero pressure gradient turbulent flows. The physical model of transfer processes in the near-wall region of turbulent separated and reattached flows based on the assumption of the governing role of generated local pressure gradient that takes place in the immediate vicinity of the wall in separated flow as a result of intense instantaneous accelerations induced by large-scale vortex flow structures is discussed. Similarity laws for mean velocity and temperature profiles and spectral characteristics of the transfer processes resulting in the physical model are confirmed by the available experimental data. The physical model has provided explanations of the well-known empirical heat and mass transfer correlations for turbulent separated flows and other types of flows close in their structure to those of turbulent separated flows.

Natural convection boundary layer in a 5:1 cavity

The natural convection boundary layer in a tall cavity with an aspect ratio of AR=5 is studied numerically. The Rayleigh number based on the width of the cavity is RaW=4.028×108. The large eddy simulation method together with different subgrid scale models are used to study the near-wall behavior of the boundary layer and the turbulence structure. It is found that the dynamic subgrid scale model is the most accurate model in terms of predicting the transition location. Results also indicate that the conventional grid resolutions expressed in viscous units that are used for forced convection flows are not appropriate in the case of the natural convection flows and higher grid resolutions are necessary. The turbulence statistics are studied in both the turbulent and the transition regions. Although the results of the fully turbulent region show no important grid dependency, it is found that the accuracy of the results in the transition region is highly grid dependent, suggesting that the subgrid scale fluctuations in the transition region are of different nature compared to the fully turbulent region. The budget of the momentum, temperature, and Reynolds stress transport equations are studied and the behavior of the important terms in the boundary layer is investigated.

분류유동이 있는 채널 난류유동의 LES 해석

Recent experimental data shows that the noticeable feature of irregular roughened spots on the fuel surface occurs during the combustion test with PMMA/GOX in the hybrid rocket motor. The generation of these unexpected patterns is likely to be resulted from the disturbed boundary layer due caused by wall blowing which is intented to simulate the process of fuel vaporization. LES technique was implemented to investigate both the flow characteristics near fuel surface and the subsequent evolution of turbulence modified by the wall blowing. Simple channel geometry instead of circular grain configuration was used for the investigation without chemical reactions in order to allow for a focused examination on the near-wall behavior at the Reynolds number of 22,500. It was shown that the wall blowing pushed turbulent structures upwards making them tilted and this skewed displacement, in effect, left the foot prints of the structures on the surface. This change of kinematics may explain the formation of irregular isolated spots on the fuel surface observed in the experiment.

Investigation of eddy-viscosity models modified using discrete filters: A simplified “regularized variational multiscale model” and an “enhanced field model”

Subgrid-scale (SGS) models for large-eddy simulation (LES) having the formalism of an effective eddy-viscosity model, but that operates on a modified velocity field, are further evaluated and new ones are proposed. The modified field is obtained using regular filtering of the LES field carried out in physical space. This is actually done by using a discrete and compact operator (only using nearest neighbors values), eventually iterated; this ensures that the proper filtering behavior is preserved, even for near wall points. The first model investigated here is inspired by the variational multiscale approach originally proposed by T. J. Hughes et al. [Phys. Fluids 13, 505 (2001)]. Here, the modelling is simplified, leading to a SGS viscosity effect operating on the “small-scale LES field” that is obtained by subtracting the LES field from its filtered counterpart. Such a model (here called RVMM for short) was already proposed and partially evaluated {e.g., see G. S. Winckelmans and H. Jeanmart [Direct and Large-Scale Eddy Simulation IV (Kluwer, Dordrecht, 2001)] and H. Jeanmart and G. S. Winckelmans (CTR Proceedings of the Summer Program, 2002), the “model M2” of A. W. Vreman [Phys. Fluids 15, L61 (2003)], the “high-pass filtered Smagorinsky model” of S. Stolz et al. [Direct and Large-Eddy Simulation V (Kluwer, Dordrecht, 2004) and S. Stolz et al., Phys. Fluids 17, 065103 (2005)]}. The other model investigated here is an “enhanced field model” (EFM). The SGS viscosity model then operates on a LES field that is artificially enhanced at the small scales; that obtained by adding to the LES field the small-scale field. The two model families are presented in a unified way; they have a behavior that combines viscous and hyperviscous effects, while remaining simple and practical. They however do not naturally have the proper y3 near wall behavior for the SGS dissipation; hence, they need some near wall damping. To ensure the proper near-wall behavior, we use here the dynamic procedure (self-consistent for each model). The performance of both models is compared to that of other models (also dynamic): the Smagorinsky model, hyperviscosity models, and a hybrid model combining explicitly a Smagorinsky term and a hyperviscosity term. The cases here investigated are LES of decaying isotropic turbulence starting at Reλ=90 and LES of turbulent channel flow at Reτ=395. A good behavior of the RVMM and EFM, as compared to the others, is observed in all cases. They constitute an easily implemented and better alternative than the dynamic Smagorinsky model.

Lagrangian dispersion in turbulent channel flow and its relationship to Eulerian statistics

Lagrangian and Eulerian statistics were obtained from the direct numerical simulation of a turbulent channel flow. The Eulerian integral time scales and time microscales were compared to their Lagrangian equivalents. It is found that the Lagrangian time scales equal the Eulerian time scales at the wall. Otherwise, these proved to be consistently larger than the Eulerian time scales, and the latter are also found to be scaled by the propagation velocity rather than the mean velocity. The near-wall behavior of the ratio of the Lagrangian to Eulerian integral time scales is explained by the difference between the mean velocity and the propagation velocity of the turbulent structure. The ratio is proportional to the inverse of the turbulence intensity ( T L/ T E = βU/ σ). β for the streamwise component is nearly a constant value of 0.6 (20 < y + < 70), in agreement with atmospheric data and analyses. The ratio of the Lagrangian to the Eulerian time microscales is fairly constant away from the wall ( y + > 40). After period over the integral time scale elapsed, the effect of shear on turbulent diffusion appears and the mean-square dispersion is almost proportional to t 3 in agreement with the predictions of Riley and Corrsin [The relation of turbulent diffusivities to Lagrangian velocity statistics for the simplest shear flow. J. Geophys. Res. 79 (1974) 1768–1771] for homogeneous shear flow. After particles are distributed fairly uniformly between two walls, the mean-square dispersion becomes proportional to t and in agreement with theory of Taylor’s longitudinal dispersion.

Testing of Reynolds-stress-transport closures by comparison with DNS of an idealized adverse-pressure-gradient boundary layer

Results are used from direct numerical simulation (DNS) of incompressible plane-channel flow subjected to a uniform straining field typical of a two-dimensional adverse pressure gradient (APG) to investigate the accuracy of three second-moment closures specially designed to account for wall-bounded turbulence. Since the DNS statistics satisfy a one-dimensional unsteady problem with rigorously defined boundary and initial conditions, and since the flow contains many of the essential features found in suddenly decelerated boundary layers, this allows an efficient and straightforward but non-trivial assessment of the closures. The Reynolds-stress budgets from the DNS are used to examine the individual production/dissipation/transport terms used by each closure. This reveals shortcomings in all three schemes, especially in the near-wall behavior of their pressure–strain models. One of the major findings of this study is the degree to which the individual modeling shortcomings are offset by the tendency for them to cancel each other. The Wilcox Stress- ω model best captures the cumulative effect of the APG straining, compared to the models of Launder and Shima and So et al., in terms of giving mean velocities and the time at which the surface shear stress reverses sign that most closely agree with the DNS. However, its prediction of the streamwise u ′ u ′ ¯ and wall-normal v ′ v ′ ¯ Reynolds stresses is much less accurate than that given by the other two schemes.

Large-eddy simulation of natural convection boundary layer on a vertical cylinder

Large-eddy simulation of natural convection boundary layer along a constant temperature vertical cylinder is studied and the results are compared with experimental data. The highest local Grashof number is Gr z = 5 × 10 11. Although there are some discrepancies between the results in the region close to the wall, there is qualitative agreement between them. Mean values of the temperature near the wall show that the conventional law of the wall is valid in this case. However, the region where 〈 v +〉 = r +, is much smaller than that of forced convection. With respect to turbulence production, the near-wall behavior of turbulent shear stress and normal stresses are investigated and compared with the experimental results. The existence of a negative shear stress region close to the wall in the simulations is confirmed and its influence on stream-wise normal stress is shown. The integral form of the momentum equation suggests that the buoyancy balances the combination of the turbulent stresses and the viscous term. The existence of a region where the energy spectra are proportional to κ −3 is verified.

LES, T-RANS and hybrid simulations of thermal convection at high Ra numbers

Abstract The paper reports on application of different approaches to the simulations of thermal convection at high Rayleigh ( Ra ) numbers. Based on new well-resolved LES in 10 7 ⩽ Ra ⩽ 10 9 range, the performance of a T-RANS (using a low- Re three-equation 〈 k 〉–〈 e 〉–〈 θ 2 〉 ASM/AFM subscale model) and a hybrid approach (utilizing the concept of “seamless” RANS/LES merging) have been compared. Targeting accurate predictions of heat transfer at very high Ra numbers, the near-wall behaviour of the subscale turbulence contributions is analyzed in details. Whilst the application of the conventional LES on a coarse grid resulted in huge underprediction of the Nusselt number (50% at Ra = 10 9 ), thanks to a well-tuned subscale model, the T-RANS results showed excellent agreement for heat transfer with both the fine-resolved LES (for Ra ⩽ 10 9 ) and experimental data for over a ten-decades range of Ra (10 6 ⩽ Ra ⩽ 2 × 10 16 ). The visible absence of the fine-scale motion in the T-RANS, however, means that the T-RANS will perform poorly in flows where there are no strong large-scale forcing, as, e.g., in a side-heated vertical channel. In order to sensitize the T-RANS approach to high-frequency instabilities, different ways of hybrid RANS/LES merging based on “seamless” approach have been investigated. It is demonstrated that the hybrid approach is capable of capturing a significantly larger portion of the fine-structure spectrum than is possible with T-RANS, whilst also returning accurate predictions of heat transfer and turbulence statistics.

Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient

High-resolution laser-Doppler anemometer measurements were acquired in a two-dimensional turbulent boundary layer over a ramp. The goals were to provide a detailed data set for an adverse pressure gradient boundary layer far from separation and to examine near-wall behaviour of the Reynolds stresses as compared to flat-plate boundary layers. The flow develops over a flat plate, reaching a momentum thickness Reynolds number of 3350 at an upstream reference location. The boundary layer is then subjected to a varying pressure gradient along the length of the ramp and partially redevelops on a downstream flat plate. Mean velocity measurements show a log law region in all velocity profiles, but the outer layer does not collapse in deficit coordinates indicating that the boundary layer is not in equilibrium. Measurements of non-dimensional stress ratios and quadrant analysis of the two-component data indicate relatively small changes to the turbulence structure. However, the streamwise normal stress has an extended outer layer plateau, and the shear stress and wall-normal stress have outer layer peaks. Near the wall, the streamwise normal stress and shear stress collapse with flat-plate data using standard scaling, but the wall normal stress is substantially larger than flat-plate cases.

Near-wall behavior of RANS turbulence models and implications for wall functions

The paper proposes a novel wall-function formulation applicable to any RANS turbulence model. It is based on the assumption of wall layer universality, applied to the entire model. The approach is implemented via tables for the turbulence quantities and the friction velocity u τ . The influence of numerical errors on the wall-function solution is investigated and improvements are proposed. Numerical results are presented for a flat plate boundary layer at zero pressure gradient and for a flow with pressure gradient driven separation. The behavior of RANS turbulence models in the near wall region is also analyzed. The models considered are: Spalart–Allmaras, k– ω, k– g and v 2– f. The analysis of the v 2– f model resulted in new analytical solutions in the viscous sublayer and logarithmic layer. The analytical solutions for the Spalart–Allmaras model can be used directly as a simple wall function.

A Turbulence Model for Pulsatile Arterial Flows

Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the "nonequilibrium" effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the prediction of arterial flows.

Subgrid-Scale Diffusivity: Wall Behavior and Dynamic Methods

Abstract This study concerns the near-wall behavior of the subgrid-scale diffusivity. This is shown to depend on the thermal boundary conditions. Therefore, the constant subgrid-scale Prandtl number hypothesis is questionable and a direct modeling of the subgrid-scale diffusivity is considered instead. Large-eddy simulations are carried out using the Trio U code in a turbulent channel flow configuration with the three classical thermal boundary conditions (constant temperature, constant heat flux, and adiabatic wall). Different dynamic methods are used to model the subgrid-scale diffusivity and results are compared with constant subgrid-scale Prandtl number large-eddy simulations and with direct numerical simulations.

Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls

In this paper, the effects of adiabatic and isothermal conditions on the statistics in compressible turbulent channel flow are investigated using direct numerical simulation (DNS). DNS of two compressible turbulent channel flows (Cases 1 and 2) are performed using a mixed Fourier Galerkin and B-spline collocation method. Case 1 is compressible turbulent channel flow between isothermal walls, which corresponds to DNS performed by Coleman et al. (1995). Case 2 is the flow between adiabatic and isothermal walls. The flow of Case 2 can be a very useful framework for the present objective, since it is the simplest turbulent channel flow with an adiabatic wall and provides ideal information for modelling the compressible turbulent flow near the adiabatic wall. Note that compressible turbulent channel flow between adiabatic walls is not stationary if there is no sink of heat. In Cases 1 and 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5, and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000.To compare compressible and incompressible turbulent flows, DNS of two incompressible turbulent channel flows with passive scalar transport (Cases A and B) are performed using a mixed Fourier Galerkin and Chebyshev tau method. The wall boundary conditions of Cases A and B correspond to those of Cases 1 and 2, respectively. Case A corresponds to the DNS of Kim & Moin (1989). In Cases A and B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150.The mean velocity and temperature near adiabatic and isothermal walls for compressible turbulent channel flow can be explained using the non-dimensional heat flux and the friction Mach number. It is found that Morkovin's hypothesis is not applicable to the near-wall asymptotic behaviour of the wall-normal turbulence intensity even if the variable property effect is taken into account. The mechanism of the energy transfers among the internal energy, mean and turbulent kinetic energiesis investigated, and the difference between the energy transfers near isothermal and adiabatic walls is revealed. Morkovin's hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall.

Effect of Roughness on Wall-Bounded Turbulence

Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h + = 5.4, 10.8, and 21.6 for Reτ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.

An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models

New closure approximations are proposed, within the framework of non-linear eddy-viscosity modeling, which aim specifically at an improved representation of near-wall anisotropy in both shear and stagnation flows. The main novel element is the introduction of tensorial terms, alongside strain and vorticity, which depend on wall-direction indicators and which procure the correct asymptotic near-wall behavior of the Reynolds stresses. The newly formulated non-linear constitutive equation for the Reynolds stresses is combined with low-Reynolds-number forms of equations for the rate of dissipation ε or the specific dissipation ω, the latter incorporating a number of new features into the established form of the equation. The predictive performance of three model variants is investigated by reference to three test flows: a plane channel flow, a separated flow in a channel with periodic hill-shaped obstacles on one wall and a plane impinging jet. It is shown that the new model elements result in a substantially improved representation of the Reynolds-stress field at the wall, especially in the wall-normal Reynolds stress. One of the variants includes the use of the modified ω-equation, and it is shown that this model performs especially well in the presence of separation.