A comparative study of inflow conditions for two‐ and three‐dimensional spatially developing mixing layers using large eddy simulation

A series of spatially developing mixing layers are simulated using the large eddy simulation (LES) technique. A hyperbolic tangent function and data derived from boundary layer simulations are used to generate the inflow condition, and their effects on the flow are compared. The simulations are performed in both two and three dimensions. In two‐dimensional simulations, both types of inflow conditions produce a layer that grows through successive pairings of Kelvin–Helmholtz (K–H) vortices, but the composition ratio is lower for the hyperbolic tangent inflow simulations. The two‐dimensional simulations do not undergo a transition to turbulence. The three‐dimensional simulations produce a transition to turbulence, and coherent structures are found in the post‐transition region of the flow. The composition ratio of the three‐dimensional layers is reduced in comparison to the counterpart two‐dimensional runs. The mechanisms of growth are investigated in each type of simulation, and amalgamative pairing interactions are found in the pre‐transition region of the three‐dimensional simulations, and throughout the entire computational domain of those carried out in two‐dimensions. The structures beyond the post‐transition region of the three‐dimensional simulations appear to behave in a much different manner to their pre‐transition cousins, with no pairing‐type interactions observed in the turbulent flow. In order to accurately simulate spatially developing mixing layers, it is postulated that the inflow conditions must closely correspond to the conditions present in the reference experiment. Copyright © 2007 John Wiley & Sons, Ltd.     

Large eddy simulation on the effect of free-stream turbulence on bypass transition

The effect of free-stream turbulence (FST) on bypass transition in a zero-pressure-gradient boundary layer is investigated by means of Large Eddy Simulation (LES). The broadband turbulent inflow is synthesized to validate the feasibility of LES. Both a zero-thickness plate and one with super-ellipse leading-edge are addressed. The calculated Reynolds-averaged fields are compared with experimental data and decent agreement is achieved. Instantaneous fields show the instability occurs in the lifted low-speed streaks similar to earlier DNS results, which can be ascribed to outer mode. Various inflows with bi-/tri-mode interaction are specified to analyze effects of particular frequency mode on the instability pattern and multifarious transition or non-transition scenarios are obtained. Outer instability is observed in the cases with one low-frequency mode and one high-frequency mode inflow as reported by Zaki and Durbin (2005), and with one more high-frequency mode appended. Inner instability is observed in the case with a low-frequency dominant inflow, while the high-frequency mode is indispensable to induce the secondary instability. Furthermore, the results show that the transition onset is highly sensitive to low-frequency mode while the transition rate is highly sensitive to high-frequency mode. Finally, the formational frequency of turbulent spot (FFTS) is counted and the frequency of laminar streaks is demonstrated by spectral analysis.     

High-resolution measurements of two-dimensional instabilities and turbulence transition in plane mixing layers

 High-resolution two-dimensional (2D) measurements on a large plane mixing layer provide new quantitative information of its spatial and temporal evolution to turbulence. Periodic acoustic excitation with three frequencies was used to stabilize the fundamental instability of the mixing layer (roll-up) and its first and second subharmonics (vortex pairings). Phase-locked velocity measurements of the time evolution in 2D space (x, y, t) reveal accurate spatially resolved primary (2D) instabilities of the mixing layer and turbulence transition. The measurements unveil new quantitative details of the initial Kelvin–Helmholtz waves and their spatial and temporal evolution into vortex shedding and the effect of the second subharmonic on the first vortex pairing. The second-subharmonic effect hastens alternate first pairings of the rollers, with the result that pairing is completed at two downstream locations. The pairings that occur closer to the knife-edge are more organized (laminar) than those occurring farther downstream (transitional). This effect is corroborated using Taylor’s hypothesis to compute the vorticity distributions from the measured velocity field and a pseudo-spectral simulation of the temporal evolution of the mixing layer. Received: 26 March 1998/Accepted: 2 March 1999     

A dynamic eddy-viscosity closure model for large eddy simulations of two-dimensional decaying turbulence

This paper puts forth a simplified dynamic eddy-viscosity subgrid-scale model for the vorticity transport equation which is employed in a large eddy simulation study of freely evolving isotropic two-dimensional turbulent flows. The dynamic parameter is averaged in space, thereby retrieving a spatially constant value which only varies in time. The proposed dynamic model is applied to a two-dimensional decaying turbulence problem in a square periodic box, which is a standard prototype of more realistic turbulent flows in the atmosphere and oceans, in order to eliminate any possible errors associated with the boundary conditions or mesh non-uniformities. Compared with high-resolution direct numerical simulations, the performance of the dynamic model is systematically investigated considering various filtering strategies by means of test filters. The effects of the computational resolution and the filtering ratio between the test and the grid filters are also studied by using a huge set of parameters.     

Formation of three-dimensional structures on the transition to turbulence in boundary layers

Experiments have established that there are two main qualitatively different regimes of the transition from laminar to turbulent flow and an intermediate regime which possesses the characteristic features of both. These regimes reflect the different ways in which a two-dimensional wave pattern can be transformed into a three-dimensional one; they must be a consequence of the initial conditions. The aim of the investigation reported in the present work was to analyze these regimes by systematically varying the initial data, to demonstrate the possibility of controlling the nature of the transition, to obtain some data to test theoretical models of the development of three-dimensional wave patterns on transition, and to make further experimental investigations of the transition mechanisms.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 42–50, November–December, 1984.We are grateful to N. N. Yanenko (deceased), P. Torgersen, and D. Frederick for supporting the work, and T. Herbert for helpful discussions.The work was done while the first two authors were at the Virginia Polytechnic Institute and University during November and December 1982.     

Spectral structure of stratified turbulence: direct numerical simulations and predictions by large eddy simulation

Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.     

Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.     

Time‐accurate intermediate boundary conditions for large eddy simulations based on projection methods

Projection methods are among the most adopted procedures for solving the Navier–Stokes equations system for incompressible flows. In order to simplify the numerical procedures, the pressure–velocity de‐coupling is often obtained by adopting a fractional time‐step method. In a specific formulation, suitable for the incompressible flows equations, it is based on a formal decomposition of the momentum equation, which is related to the Helmholtz–Hodge Decomposition theorem of a vector field in a finite domain. Owing to the continuity constraint also in large eddy simulation of turbulence, as happens for laminar solutions, the filtered pressure characterizes itself only as a Lagrange multiplier, not a thermodynamic state variable. The paper illustrates the implications of adopting such procedures when the decoupling is performed onto the filtered equations system. This task is particularly complicated by the discretization of the time integral of the sub‐grid scale tensor. A new proposal for developing time‐accurate and congruent intermediate boundary conditions is addressed. Several tests for periodic and non‐periodic channel flows are presented. This study follows and completes the previous ones reported in (Int. J. Numer. Methods Fluids 2003; 42, 43 ). Copyright © 2005 John Wiley & Sons, Ltd.     

Influence of mesh deformation on the quality of large eddy simulations

The influence of mesh motion on the quality of large eddy simulation (LES) was studied in the present article. A three‐dimensional, turbulent pipe flow (Re_τ=360) was considered as a test case. Simulations with both stretching and static meshes were carried out in order to understand how mesh motion affects the turbulence statistics. The spatial filtering of static and moving mesh direct numerical simulation (DNS) data showed how an ideal LES would perform, while the comparison of DNS cases with static and moving meshes revealed that no significant numerical errors arise from the mesh motion when the simulation is fully resolved. The comparison of the filtered fields of the DNS with a moving mesh with the corresponding LES fields revealed different responses to mesh motion from different numerical approaches. A straightforward test was applied in order to verify that the moving mesh works consistently in LES: when the mesh is stretched in the streamwise direction, the moving mesh results should be in between the two extremal resolutions between which the mesh is stretched. Numerical investigations using four different LES approaches were carried out. In addition to the Smagorinsky model, three implicit LES approaches were used: linear interpolation (non‐dissipative), the Gamma limiter (dissipative), and the scale‐selective discretisation (slightly dissipative). The results indicate that while the Smagorinsky and the scale‐selective discretisation approaches produce results consistent with the resolution of the non‐static mesh, the implicit LES with linear interpolation or the Gamma scheme do not. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulations of vortices in mixing layers and plane jets

Direct numerical simulations of two-dimensional mixing layers and jets are presented first within the temporal approximation, and then with spatial calculations. The evolution of a temperature field as a passive scalar is investigated simultaneously. Besides usual statistical quantities, the results are presented through visualisations of coloured vorticity- and temperature-contours in order to describe the evolutions of the fields with time. Concentrated vortices develop and the evolution of the layer is dominated by the interactions between these eddies which can be viewed as the coherent structures observed in laboratory experiments.     

Experimental study on the effect of pulsating inflow to an enclosure for improved mixing

Optimal control of inlet jet flows is of broad interest for enhanced mixing in ventilated rooms. The general approach in mechanical ventilation is forced convection by means of a constant flow rate supply. However, this type of ventilation may cause several problems such as draught and appearance of stagnation zones, which reduces the ventilation efficiency. A potential way to improve the ventilation quality is to apply a pulsating inflow, which has been hypothesised to reduce the stagnation zones due to enhanced mixing. The present study aims at testing this hypothesis, experimentally, in a small-scale two-dimensional water model using Particle Image Velocimetry with an in-house vortex detection program. We are able to show that for an increase in pulsation frequency or alternatively in the flow rate the stagnation zones are reduced in size and the distribution of vortices becomes more homogeneous over the considered domain. The number of vortices (all scales) increases by a factor of four and the swirl-strength by about 50% simply by turning on the inflow pulsation. Furthermore, the vortices are well balanced in terms of their rotational direction, which is validated by the symmetric Probability Density Functions of vortex circulation (Γ) around Γ = 0. There are two dominating vortex length scales in the flow, namely 0.6 and 0.8 inlet diameters and the spectrum of vortex diameters become broader by turning on the inflow pulsation. We conclude that the positive effect for enhanced mixing by increasing the flow rate can equally be accomplished by applying a pulsating inflow.     

All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence

As a type of shock-capturing scheme, the traditional Roe scheme fails in large eddy simulation (LES) because it cannot reproduce important turbulent characteristics, such as the famous k^?5/3 spectral law, as a consequence of the large numerical dissipation. In this work, the Roe scheme is divided into five parts, namely, ξ, δU_p, δp_p, δU_u, and δp_u, which denote basic upwind dissipation, pressure difference-driven modification of interface fluxes, pressure difference-driven modification of pressure, velocity difference-driven modification of interface fluxes, and velocity difference-driven modification of pressure, respectively. Then, the role of each part in the LES of homogeneous decaying turbulence with a low Mach number is investigated. Results show that the parts δU_u, δp_p, and δU_p have little effect on LES. Such minimal effect is integral to computational stability, especially for δU_p. The large numerical dissipation is due to ξ and δp_u, each of which features a larger dissipation than the sub-grid scale model. On the basis of these conditions, an improved all-speed Roe scheme for LES is proposed. This scheme can provide satisfactory LES results even for coarse grid resolutions with usually adopted second-order reconstructions for the finite volume method.     

On the evolution of large scale structures in three-dimensional mixing layers

In this paper, several mathematical models for the large scale structures in some special kinds of mixing layers, which might be practically useful for enhancing the mixing, are proposed. First, the linear growth rate of the large scale structures in the mixing layers was calculated. Then, using the much improved weakly non-linear theory, combined with the energy method, the non-linear evolution of large scale structures in two special mixing layer configurations is calculated. One of the mixing layers has equal magnitudes of the upstream velocity vectors, while the angles between the velocity vectors and the trailing edge were π/2-φ and π/2+φ, respectively. The other mixing layer was generated by a splitter-plate with a 45-degree-sweep trailing edge. The project supported by the National Natural Science Foundation of China (19642001) and Deutsche Forschungsgemeinschaft (DFG)     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a ‘high-lift’ and an ‘ultra high-lift’ turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in ‘ultra high-lift’ design when compared to the ‘high-lift’ design. Stronger ‘Klebanoff streaks’ are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The ‘part-span’ Kelvin–Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging.     

Large eddy simulations on the effect of the irregular roughness shape on turbulent channel flows

Large Eddy Simulations (LES) are carried out to investigate on the mean flow in turbulent channel flows over irregular rough surfaces. Here the attention is focused to selectively investigate on the effect induced by crests or cavities of the roughness. The irregular shape is generated through the super-imposition of sinusoidal functions having random amplitude and four different wave-lengths. The irregular roughness profile is reproduced along the spanwise direction in order to obtain a 2D rough shape. The analysis of the mean velocity profiles shows that roughness crests induce higher effect in the outer-region whereas roughness cavities cause the highest effects in the inner-region with a reduced effect in the external region. The numerical simulations have been carried out at friction Reynolds number Re_τ=395. Similar results have been found for the higher order statistics: turbulence intensities or shear stresses. The analysis of the Reynolds stress anisotropy tensor confirms the existence of specific roles of cavities and crests in the turbulence modulation.     

Investigation of turbulence development in incompressible jets with zonal detached eddy simulation (ZDES) and synthetic turbulent inflow

Hybrid RANS/LES simulations of two incompressible jets are performed with the Zonal Detached Eddy Simulation (ZDES). Two functioning modes of the ZDES for the selection of RANS and DES areas are evaluated, namely the user-defined mode (mode 1) and the global- or automatic- mode (mode 2). The RANS-to-LES transition occurs quickly downstream of the nozzle exit and is found to involve the same physics as a laminar to turbulent transition with vortex pairing near the nozzle exit. The effect of the delay in the RANS-to-LES transition on the jet flow development is analyzed. In particular, the delay in the formation of small-scale turbulent structures results in too high turbulence levels in the mixing layers. Furthermore, it is shown, for two cases, that the injection of synthetic turbulence at the nozzle inlet, originally targeted at reproducing the experimental turbulence level in the jet core, has a significant impact on the mixing layer as it accelerates the RANS-to-LES transition, reduces the spatial wavelength of the vortex pairing and promotes the production of fine-scale turbulence which leads to a better agreement with experiments.