Large Eddy Simulation of the Stable Boundary-Layer: A Retrospect to Nieuwstadt’s Early Work

Observations and theory presented in a paper by Nieuwstadt (J Atmos Sci 41:2202–2216, 1984) are reviewed and reconsidered. We have used a large eddy simulation (LES) model to make a 10-h rerun. Averaged results obtained for the last hour were considered to be representative for the wind-driven, quasi steady nocturnal boundary layer as reported in Nieuwstadt’s paper. The turbulence characteristics found with the LES model are in good to excellent agreement with the majority of the observations and confirms the uniqueness of the dataset, though the scatter in the data is (understandably) large. Laboratory experiments of the stable boundary layer might reduce the uncertainty in existing data and should be encouraged. The concept of local scaling, introduced by Nieuwstadt in 1984 was also confirmed by our simulations. Nieuwstadt’s experiment and local scaling theory of the SBL were a major achievement and an important contributions to our understanding of the SBL.     

Effect of Strong External Turbulence on a Wall Jet Boundary Layer

The initial stage of the development of a wall jet under the influence of strong external turbulence has been studied in a novel shear-flow mixing-box experiment. A fully developed channel flow of depth h (40 mm) enters along the top wall of a cuboidal box of height 11 h in which a combination of oscillatory and turbulent velocity fluctuations are generated by a vertical oscillating grid at the midplane 5 h below the wall. When the ratio of the rms grid-generated velocity fluctuations, , to the local mean velocity inside the wall jet layer, u, is greater than about 0.1, significant changes are observed in the mean shear profile and in the eddy structure of the wall jet. The wall jet thickness increases by approximately 25% but the maximum velocity decreases by less than 10% compared to the case without the external turbulence. Fluctuations of the streamwise velocity component increase as expected in the outer part of the wall jet, but the most significant result is the increase by 70% of the fluctuations in the boundary layer close to the wall. CFD simulations using the k-ɛ RNG of the FLUENT CFD Code do not properly model the effect of the large scale external turbulence in this experiment. However, an artificial method, which introduces a series of small inlet/outlet jets to represent external turbulence, approximately simulates the overall effects of the oscillating grid on the wall jet, but does not simulate the amplification of the near wall turbulence. F. T. M. Nieuwstadt: Rest in peace (1946–2005).     

Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows

A novel method is proposed that allows accurate estimates of the local wall shear stress from near-wall mean velocity data in fully developed pipe and channel flows. DNS databases are used to demonstrate the accuracy of the method and to provide the reliability requirements on the experimental data.To demonstrate the applicability of the method, near-wall LDA measurements in turbulent pipe and channel flows were performed. The estimated wall shear stress is shown to be accurate to within 1%. Streamwise mean velocity and turbulence intensity profiles normalized with the wall friction velocity at several Reynolds numbers are presented.The current research was funded in part by the European Community under the BRITE-EURAM program, Deutsche Forschungsgemeinschaft (Du 101/16-1,2) and Deutscher Akademischer Austauschdienst. The authors are also grateful to Professors F. Nieuwstadt, N. Kasagi, P. Moin and Drs. J. Kim and N. Gilbert for providing their direct simulation data.     

Flow Structure of Lifted Swirling Jet Flames

Swirling combustion is widely applied in various applications such as gas turbines, utility boilersor waste incinerators. This article contributes to the ongoing research by providing experimentaldata that are gathered in the mixing zone of a lifted swirling premixed natural gas flame. Theobjective of this paper is fivefold: (1) to introduce the lifted swirling flame featuring lowNO _x emissions (2) to provide experimental data such as major species distributions, temperature and streamlines of the flow pattern, (3) to report on velocity bias in probability density function (PDF) distributions and to present PDF sequences of velocities in medium scale swirling flows, (4) to make an assessment on the local small-scale turbulence that is present in the swirling mixinglayer and (5) to provide new experimental data for model verification and development.The PDFs are corrected in order to compensate for the velocity bias phenomenon, which is typicalfor randomly sampled LDA data. Sequences of axial PDF data are presented and measurement locationsof interest are selected to look at the PDF characteristics of the internal and externalrecirculation zones, the mixing layer and the onset of the reacting flow into detail. The mixinglayer PDFs covered a wide velocity range and revealed bimodality; even the concept ofmulti-modality is suggested and explored. Analysis showed that a sum of two Gaussian distributionscan accurately envelop the experimental PDFs. The reason for this broadband turbulence behavior isto be found in combination of precessing and flapping motion of the flow structures, and also incombustion generated instabilities of the lifted flame. As a result, the flame brush is wide (largescale motion) and the mixing (small-scale turbulence) flattens any high temperatures in thecombustion process.The multi-scale turbulence concept is subsequently used to make anassessment of the local turbulence characteristics in the mixing layer.The idea is that the PDFs capture both contributions of the flow-inherent fine grain turbulence (u _l ) which is superposed on slowlarge scale fluctuating structures. It is this u _l that will be of interest in continued research on the classification of the lifted flame into acombustion regime diagram (e.g. Borghi diagram). Finally, the bimodalitycharacter in reacting flows and the prediction of large-scale structuresmay be a challenge for LES researchers.     

Parameter estimation of engineering turbulence model

A parameter estimation algorithm is introduced and used to determine the parameters in the standardk-∈ two equation turbulence model (SKE). It can be found from the estimation results that although the parameter estimation method is an effective method to determine model parameters, it is difficult to obtain a set of parameters for SKE to suit all kinds of separated flow and a modification of the turbulence model structure should be considered. So, a new nonlineark-∈ two-equation model (NNKE) is put forward in this paper and the corresponding parameter estimation technique is applied to determine the model parameters. By implementing the NNKE to solve some engineering turbulent flows, it is shown that NNKE is more accurate and versatile than SKE. Thus, the success of NNKE implies that the parameter estimation technique may have a bright prospect in engineering turbulence model research.     

Analysis of Streamwise Velocity Fluctuations in Turbulent Pipe Flow with the Use of an Ultrasonic Doppler Flowmeter

Data collected from several studies of experimental and numerical nature in wall-bounded turbulent flows and in particular in internal flows (channel and pipe flows, Mochizuki and Nieuwstadt [1]) at different Reynolds numbers R ⁺(Ru _*/ν), indicate that: (i) the peak of the rms-value (normalized by u _*) of the streamwise velocity fluctuations (σ _u ⁺|_peak) is essentially independent of the Reynolds number, (ii) the position of the rms peak value (y ⁺|_peak) is weakly dependent of the Reynolds number, (iii) the skewness of the streamwise velocity fluctuations (S _u ) is close to zero at the position in which the variance has its peak. A series of measurements of streamwise velocity fluctuations has been performed in turbulent pipe flow with the use of an Ultrasonic Doppler Velocimeter and our results support those reported in [1]. This revised version was published online in July 2006 with corrections to the Cover Date.     

KOLMOGOROV BEHAVIOR OF NEAR-WALL TURBULENCE AND ITS APPLICATION IN TURBULENCE MODELING

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder¹ and followers^2,3,4,5. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterised by Kolmogorov microscales. According t o this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become “Kolmogorov” eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As a n example, the concept is incorporated in the standard κ - εmodel which is then applied t o channel and boundary layer flows. Using appropriate boundary conditions (based on Kolmogorov behaviour of near-wall turbulence), there is no need for any wall-modification to the κ - ε equations (including model constants). Results compare very well with the DNS and experimental data.     

Polymer-induced turbulence modifications in an impinging jet

This effort explores the impact of dilute polymer solutions on the turbulence characteristics in a submerged liquid impinging-jet configuration. Turbulent impinging jets are commonly used in technological applications such as drying, scouring, cooling, or heating due to an enhancement in transport characteristics in the impingement region under certain nozzle-to-wall configurations. Previous efforts have identified significant turbulence modifications in the presence of dilute concentrations of polymer in both bounded and unbounded flows, though the former has received considerably more attention. To this end, particle-image velocimetry measurements were taken for an axisymmetric turbulent impinging jet with a nozzle-to-wall distance H/D = 6.8 and nominal Reynolds number of 26,000. Measurements were performed for both plain water and dilute polymer solutions of polyethylene oxide at concentrations of 50 and 100 ppm. The mean and turbulence characteristics of these three flows are contrasted and it is observed that the two polymer solutions modify both the mean and turbulent characteristics of the jet in all three regions of interest (the free-jet, impingement, and wall-jet regions). Of interest, the 50 ppm case yielded a slight suppression of the turbulence in the free-jet region accompanied by a longer axial length of the potential core compared to the case of plain water. In contrast, the 100 ppm case exhibits clear enhancement of the turbulence in the free-jet region and a shortening of the potential core length. The effect of polymer was opposite in the impingement and wall-jet regions wherein the turbulence was slightly suppressed in the 100 ppm case in a manner consistent with the onset of the Toms effect in this wall-bounded region of the flow.     

Measuring turbulence energy with PIV in a backward-facing step flow

Turbulence energy is estimated in a backward-facing step flow with three-component (3C, stereo) particle image velocimetry (PIV). Estimates of turbulence energy transport equation for convection, turbulence transport, turbulence production, viscous diffusion, and viscous dissipation in addition to Reynolds stresses are computed directly from PIV data. Almost all the turbulence energy terms in the backward-facing step case can be measured with 3C PIV, except the pressure-transport term, which is obtained by difference of the other turbulence energy terms. The effect of the velocity spatial sampling resolution in derivative estimations is investigated with four two-dimensional PIV measurement sets. This sampling resolution information is used to calibrate the turbulence energies estimated by 3C PIV measurements. The focus of this study is on the separated shear layer of the backward-facing step. The measurements with 3C PIV are carried out in a turbulent water flow at Reynolds number of about 15,000, based on the step height h and the inlet streamwise maximum mean velocity U₀. The expansion ratio (ER) is 1.5. Turbulence energy budget profiles in locations x/h=4, x/h=6, and x/h=10 are compared with DNS data of a turbulent flow. The shapes of profiles agree well with each other. Different ERs between the PIV case (1.5) and the DNS case (1.2) cause higher values for the turbulence energies measured by PIV than the energies by DNS when x/h=10 is approached. PIV results also show that the turbulence energy level in these experiments is generally higher than that of the DNS data.     

Time evolution of structures in rotating and stratified turbulence

Rotating and stably stratified turbulence exhibit not only significant anisotropies but also dynamics, which are qualitatively different from purely rotating or stratified turbulence. Furthermore, the different time scales due to rotation, stratification and the turbulence one open up a wide field of possibilities for the temporal evolution of rotating and stratified turbulence.We analyze results from DNS with different parameters α = f/N by visualizing iso-enstrophy surfaces, the temporal evolution of velocity correlation length scales and angular energy spectra.We retrieve standard results, such as a large anisotropy for small scales in rotating turbulence and a large anisotropy for intermediate scales in the vortex mode of stratified turbulence. Furthermore, at large times we find qualitatively different phenomena for cases α = 10 and α = 0.1 such as modified cascades due to the existence of potential energy or small scale vorticity production respectively.     

Towards better uncertainty estimates for turbulence statistics

 Methods for calculating the statistical uncertainty associated with the sampling of random processes such as those which occur in turbulence research are given. In particular, formulas based on normal distribution assumptions and on any general distribution shape are given for means, variances, Reynolds stresses, correlation coefficients, homogeneous and mixed turbulent triple products and fourth order turbulence moments. In addition, two resampling algorithms, the “bootstrap” and “jackknife”, are presented and compared using actual turbulence data. The availability of these methods will allow turbulence data to be presented with statistical uncertainty error bars on all turbulence quantities. Received: 11 December 1995 / Accepted: 12 April 1996     

Suitability of the k–ω turbulence model for scramjet flowfield simulations

The suitability of Wilcox's 2006 k– ω turbulence model for scramjet flowfield simulations is demonstrated by validation against five test cases that have flowfields representative of those to be expected in scramjets. The five test cases include a 2D flat plate, an axisymmetric cylinder, a backward‐facing step, the mixing of a pair of coaxial jets and the interaction between a shock wave and turbulent boundary layer. A generally good agreement between the numerical and experimental results is obtained for all test cases. These tests reveal that despite the turbulence model's sensitivity to freestream turbulence properties, the numerically predicted skin friction agrees with experimental data and theoretical correlations to their degree of uncertainty. The tests also confirm the importance of using a y⁺ value of less than 1 in getting accurate surface heat transfer distributions. In the coaxial jets case, the importance of matching the turbulence intensities at the inflow plane in improving the predictions of the turbulent mixing phenomena is also shown. A review of guidelines with regard to the setting up of grids and specification of freestream turbulence properties for turbulent Reynolds‐averaged Navier–Stokes CFD simulations is also included in this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

On a Generalized Nonlinear K–ε Model and the Use of Extended Thermodynamics in Turbulence

A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow – the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed. Received 19 February 1998 and accepted 23 October 1998     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M _t ² ), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.     

A LOCAL MESH REFINEMENT ALGORITHM APPLIED TO TURBULENT FLOW

This paper presents a local mesh refinement procedure based on a discretization over internal interfaces where the averaging is performed on the coarse side. It is implemented in a multigrid environment but can optionally be used without it. The discretization for the convective terms in the velocity and the temperature equation is the QUICK scheme, while the HYBRID-UPWIND scheme is used in the turbulence equations. The turbulence model used is a two-layer k–ϵ model. We have applied this formulation on a backward-facing step at Re=800 and on a three-dimensional turbulent ventilated enclosure, where we have resolved a geometrically complex inlet consisting of 84 nozzles. In both cases the concept of local mesh refinements was found to be an efficient and accurate solution strategy. © 1997 by John Wiley & Sons, Ltd.     

Possibility of drag reduction usingd-type roughness

An experiment was carried out in a low-speed wind tunnel to study the turbulence structure of the boundary layer over a two-dimensional square cavity on a flat plate. The main purpose of this investigation is to examine the way a square cavity modifies the near-wall structure of the turbulent boundary layer leading to a possible drag reduction overd-type roughness. The experimental results on pressure coefficient and friction coefficient indicated a small reduction in total drag in this configuration. This seems to be due to the stable vortex flow observed within the cavity which absorbs and reorganizes the incoming turbulence in the cavity, thereby modifying the near-wall turbulence structure of the boundary layer. The resultant turbulence structure was very similar to that over drag-reducing riblets surface.     

Numerical simulation of turbulent flow through series stenoses

The flow fields in the neighbourhoods of series vascular stenoses are studied numerically for the Reynolds numbers from 100 to 4000, diameter constriction ratios of 0.2–0.6 and spacing ratios of 1, 2, 3, 4 and ∞. In this study, it has been further verified that in the laminar flow region, the numerical predictions by k–ω turbulence model matched those by the laminar‐flow modelling very well. This suggests that the k–ω turbulence model is capable of the prediction of the laminar flow as well as the prediction of the turbulent stenotic flow with good accuracy. The extent of the spreading of the recirculation region from the first stenosis and its effects on the flow field downstream of the second stenosis depend on the stenosis spacing ratio, constriction ratio and the Reynolds number. For c₁ = 0.5 with c₂ ≤ c₁, the peak value of wall vorticity generated by the second stenosis is always less than that generated by the first stenosis. However, the maximum centreline velocity and turbulence intensity at the second stenosis are higher than those at the first stenosis. In contrast, for c₁ = 0.5 with c₂ = 0.6, the maximum values at the second stenosis are much higher than those at the first stenosis whether for centreline velocity and turbulence intensity or for wall vorticity. The peak values of the wall vorticity and the centreline disturbance intensity both grow up with the Reynolds number increasing. The present study shows that the more stenoses can result in a lower critical Reynolds number that means an earlier occurrence of turbulence for the stenotic flows. Copyright © 2003 John Wiley & Sons, Ltd.     

Simulation and Modelling of Turbulent Trailing-Edge Flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–ε) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Kármán vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.