Pseudospectral simulation of turbulent viscoelastic channel flow

The methodology and validation of direct numerical simulations of viscoelastic turbulent channel flow are presented here. Using differential constitutive models derived from kinetic and network theories, numerical simulations have demonstrated drag reduction for various values of the parameters, under conditions where there is a substantial increase in the extensional viscosity compared to the shear viscosity (Sureshkumar, Beris, Handler, Direct numerical simulation of turbulent channel flow of a polymer solution, Phys. Fluids 9 (1997) 743–755 and Dimitropoulos, Sureshkumar, Beris, Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: effect of the variation of rheological parameters, J. Non-Newtonian Fluid Mech. 79 (1998) 433–468). In this work, new results pertaining to the Reynolds stress and the pressure are presented, and the convergence of the pseudospectral algorithm utilized in the simulations, as well as its parallel implementation, are discussed in detail. It is shown that the lack of mesh refinement, or the use of a larger value for the artificial stress diffusivity used to stabilize the conformation tensor evolution equations, introduce small quantitative errors which qualitatively have the effect of lowering the drag reduction capability of the simulated fluid. However, an insufficient size of the periodic computational domain can also introduce errors in certain cases, which albeit usually small, can qualitatively alter various features of the solution.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

Unsteady turbulence in plane channel flow

Direct numerical simulations were conducted for oscillating flow with zero time mean (reciprocating flow) in a plane channel subject to a harmonic forcing term of varying amplitude and frequency. The results confirmed the existence of four flow regimes (laminar, “disturbed laminar”, intermittently turbulent, and fully turbulent) depending on the above parameters. The flow behaviour was found to depend on the complex interplay of mean and turbulence quantities, as described by the closed loop formed by the streamwise Reynolds-averaged momentum equation in conjunction with the exact transport equations for the turbulent (Reynolds) stresses. A crucial role in this loop appeared to be played by the different time response of the mean flow to the applied forcing at different cross-stream locations, due to the laminar and turbulent diffusion of momentum from the walls and causing characteristic distortions of the cross-stream mean velocity profiles at different phases (i.e. acceleration vs. deceleration). The intrinsic inertia of turbulence quantities themselves played only a minor role, as confirmed by the fact that, in a broad range of conditions, turbulent stresses were roughly in phase with the respective production and dissipation terms. The structure of turbulence was found to depend largely on the instantaneous mean velocity profile, as confirmed by “frozen velocity” simulations.     

Adaptive modeling of turbulent flow with residual based turbulent kinetic energy dissipation

In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier–Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error control based on the error in the functional output. We then derive a local energy estimate for a particular finite element method, which we connect to related work on dissipative weak Euler solutions with kinetic energy dissipation due to lack of local smoothness of the weak solutions. The ideas are illustrated by numerical results, where we observe a law of finite dissipation with respect to a decreasing mesh size.     

Benchmarks on tera-scalable models for DNS of turbulent channel flow

Due to the extensive requirements of memory and speed for direct numerical simulation (DNS) of channel turbulence, people could only perform DNS at moderate Reynolds number before. However, with the fast development of supercomputers, it has become more and more approachable for researchers to perform DNS of turbulence at high Reynolds number. This makes it imperative to consider the development of tera-scalable DNS codes that are capable of fully exploiting these massively parallel machines. In order to achieve this, three parallel models (1D, 2D and 3D decompositions) have been implemented and benchmarked. All these models have been successfully ported on BlueGene/L. We have benchmarked these models on BG/L at ANL and BGW at IBM Watson center. Details of these models have been described, discussed and presented in this paper. The optimized model can be used to perform DNS at high Reynolds number in the near future.     

Analysis of the energy budget in turbulent channel flow using orthogonal wavelets

The spatial and scale statistics of turbulence kinetic energy are examined in turbulent channel flow at Re_τ = 300 using the orthonormal wavelet transform. The behaviour of the production, viscous and transfer terms is examined in terms of their variation with both space and scale. All terms are numerically large at wavenumbers at which a −5/3 slope is apparent in the velocity spectra, and they all exhibit significant spatial variability as evidenced by large flatnesses which increase with decreasing scale size. The flatness of terms involving transfer are particularly large. Attention focusses primarily on the sublayer and local-equilibrium regions: in the former, scale-to-scale flux is large and negative and consistent with conventional “backscatter” in Fourier space. In the linear sublayer, the flux is positive, consistent with Couette-like vortex stretching. The present work paves the way for close scrutiny of those components of the subgrid-scale stress that contribute most to the subgrid energy flux in large-eddy simulation of near-wall turbulent flows.     

An investigation of pulsating turbulent open channel flow by large eddy simulation

Pulsating turbulent open channel flow is investigated by use of large eddy simulation (LES) technique coupled with a dynamic subgrid-scale (SGS) model for turbulent SGS stress. The three-dimensional filtered Navier-Stokes equation is numerically solved by a fractional-step method. The objective of this study is to deal with the behaviors of pulsating turbulent open channel flow, in particular turbulence characteristics in the free surface-influenced layer, and to examine the reliability of the LES approach for predicting the pulsating turbulent flow with a free surface. In this study, the frequency of driving pressure gradient ranges low, medium and high value. The mean and phase-averaged statistical turbulence quantities, the resolved turbulent kinetic energy and Reynolds stresses budgets, and the flow structures are obtained and analyzed. With the increase of the driving frequency, the depth of the surface-influenced layer increases and the turbulent Stokes length near the bottom wall decreases. Different turbulence characteristics between the accelerating and decelerating phases are interpreted comprehensively. Turbulence intensities reveal that turbulent flow has a strong anisotropy in the free surface-influenced layer, in particular in the decelerating phases during the pulsating cycle. The budget terms of the resolved turbulent kinetic energy, the vertical and spanwise Reynolds stresses in the free surface region are analyzed. The flow structures clearly exhibit that bursting processes near the bottom wall are ejected toward the surface and the most surface renewal events are closely correlated with the bursting processes. These processes are strengthened during the decelerating period since strong turbulence intensities are generated.     

A DNS algorithm using B-spline collocation method for compressible turbulent channel flow

Direct numerical simulation (DNS) offers useful information about the understanding and modeling of turbulent flow. However, few DNSs of wall-bounded compressible turbulent flows have been performed. The objective of this paper is to construct a DNS algorithm which can simulate the compressible turbulent flow between the adiabatic and isothermal walls accurately and efficiently. Since this flow is the simplest turbulent flow with adiabatic and isothermal walls, it is ideal for the modeling of compressible turbulent flow near the adiabatic and isothermal walls. The present DNS algorithm for wall-bounded compressible turbulent flow is based on the B-spline collocation method in the wall-normal direction. In addition, the skew-symmetric form for convection term is used in the DNS algorithm to maintain numerical stability. The validity of the DNS algorithm is confirmed by comparing our results with those of an existing DNS of the compressible turbulent flow between isothermal walls [J. Fluid Mech. 305 (1995) 159]. The applicability and usefulness of the DNS algorithm are demonstrated by the stable computation of the DNS of compressible turbulent flow between adiabatic and isothermal walls.     

Identification of near-wall flow structures producing large wall transfer rates in turbulent mixed convection channel flow

In this paper, we analyze the influence of aiding and opposing buoyancy on the statistics of the wall transfer rates in a mixed convection turbulent flow at low Reynolds numbers in a vertical plane channel. The analysis is carried out using a database obtained from direct numerical simulations performed with a second-order finite volume code. The aiding/opposing buoyancy produces an overall decrease/increase of the intensities of the fluctuations of the wall shear stresses in comparison with the forced convection flow. The near wall structures responsible for the positive extreme values of the fluctuations of the wall shear stress, educed by a conditional sampling technique, consist in two quasi-parallel counterrotating streamwise vortices that convect high momentum fluid towards the wall in the region between them. Buoyancy produces an overall increase of the Reynolds stresses near the cold wall in comparison with the hot wall. This affects the streamwise length, the orientation, the velocity and the intensity of these flow structures near the two walls of the channel. It is found that the flow structures near the cold wall are shorter and produce more intense fluctuations than those near the hot wall.     

On restraining the production of small scales of motion in a turbulent channel flow

Since most turbulent flows cannot be computed directly from the incompressible Navier-Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and conservation properties. In particularly, the energy, enstrophy (in 2D) and helicity are conserved. The underlying idea is to restrain the convective production of small scales in an unconditional stable manner, meaning that the approximate solution cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The resulting simulation method is successfully tested for a turbulent channel flow (Re_τ = 180 and 395).     

A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow

This paper describes in detail a numerical scheme designed for direct numerical simulation (DNS) of turbulent drag reduction. The hybrid spatial scheme includes Fourier spectral accuracy in two directions and sixth-order compact finite differences for first and second-order wall-normal derivatives, while time marching can be up to fourth-order accurate. High-resolution and high-drag reduction viscoelastic DNS are made possible through domain decomposition with a two-dimensional MPI Cartesian grid alternatively splitting two directions of space (‘pencil’ decomposition). The resulting algorithm has been shown to scale properly up to 16384 cores on the Blue Gene/P at IDRIS–CNRS, France.Drag reduction is modeled for the three-dimensional wall-bounded channel flow of a FENE-P dilute polymer solution which mimics injection of heavy-weight flexible polymers in a Newtonian solvent. We present results for four high-drag reduction viscoelastic flows with friction Reynolds numbers Re_τ0 = 180, 395, 590 and 1000, all of them sharing the same friction Weissenberg number We_τ0 = 115 and the same rheological parameters. A primary analysis of the DNS database indicates that turbulence modification by the presence of polymers is Reynolds-number dependent. This translates into a smaller percent drag reduction with increasing Reynolds number, from 64% at Re_τ0 = 180 down to 59% at Re_τ0 = 1000, and a steeper mean current at small Reynolds number. The Reynolds number dependence is also visible in second-order statistics and in the vortex structures visualized with iso-surfaces of the Q-criterion.     

An investigation of turbulent open channel flow with heat transfer by large eddy simulation

Large eddy simulation of fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. Two typical temperature boundary conditions, i.e., constant temperature and constant heat flux being maintained at the free surface, respectively, are used. The objective of this study is to explore the behavior of heat transfer in the turbulent open channel flow for different temperature boundary conditions and to examine the reliability of the LES technique for predicting turbulent heat transfer at the free surface, in particular, for high Prandtl number. Calculated parameters are chosen as the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel depth. Some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures based on the velocity, vorticity and temperature fluctuations, are analyzed.     

Large eddy simulation of turbulent flow past a square cylinder confined in a channel

Turbulent flow past a square cylinder confined in a channel is numerically investigated by large eddy simulation (LES). The main objectives of this study are to extensively verify the experimental results of Nakagawa et al. [Exp. Fluids 27(3) (1999) 284] by LES and to identify the features of flows past a square cylinder confined in a channel in comparison with the conventional one in an infinite domain. The LES results obtained are in excellent agreement with the experiment both qualitatively and quantitatively. The well-known Kármán vortex shedding is observed. However, the vortices shed from the cylinder are significantly affected by the presence of the plates; mean drag and fluctuation of lift force increase significantly. Furthermore, periodic and alternating vortex-rollups are observed in the vicinity of the plates. The rolled-up vortex is convected downstream together with the corresponding Kármán vortex; they form a counter-rotating vortex pair. It is also revealed that the cylinder greatly enhances mixing process of the flow.     

Lattice BGK direct numerical simulation of fully developed turbulence in incompressible plane channel flow

Over the last decade, lattice Boltzmann methods have proven to be reliable and efficient tools for the numerical simulation of complex flows. The specifics of such methods as turbulence solvers, however, are not yet completely documented. This paper provides results of direct numerical simulations (DNS), by a lattice Boltzmann scheme, of fully developed, incompressible, pressure-driven turbulence between two parallel plates. These are validated against results from simulations using a standard Chebyshev pseudo-spectral method. Detailed comparisons, in terms of classical one-point turbulence statistics at moderate Reynolds number, with both numerical and experimental data show remarkable agreement.

Consequently, the choice of numerical method has, in sufficiently resolved DNS computations, no dominant effect at least on simple statistical quantities such as mean flow and Reynolds stresses. Since only the method-independent statistics can be credible, the choice of numerical method for DNS should be determined mainly through considerations of computational efficiency. The expected practical advantages of the lattice Boltzmann method, for instance against pseudo-spectral methods, are found to be significant even for the simple geometry and the moderate Reynolds number considered here. This permits the conclusion that the lattice Boltzmann approach is a promising DNS tool for incompressible turbulence.     

ODTLES: A multi-scale model for 3D turbulent flow based on one-dimensional turbulence modeling

A novel multi-scale approach for extending the one-dimensional turbulence (ODT) model of [A.R. Kerstein. One-dimensional turbulence: model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows, J. Fluid Mech. 392 (1999) 277] to treat turbulent flow in three-dimensional (3D) domains is described. In this model, here called ODTLES, 3D aspects of the flow are captured by embedding three, mutually orthogonal, one-dimensional ODT domain arrays within a coarser 3D mesh. The ODTLES model is obtained by developing a consistent approach for dynamically coupling the different ODT line sets to each other and to the large scale processes that are resolved on the 3D mesh. The model is implemented computationally and its performance is tested by performing simulations of decaying isotropic turbulence at two different Reynolds numbers and comparing to the experimental data of [H. Kang, S. Chester, C. Meneveau. Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulations, J. Fluid Mech. 480 (2003) 129; G. Comte-Bellot, S. Corrsin, Simple Eulerian correlation of full-and narrow band velocity signals in grid-generated ’isotropic’ turbulence, J. Fluid Mech. 48 (1971) 273].     

Simulations of confined turbulent vortex flow

Large-eddy simulations (LES) of the turbulent flow in a swirl tube with a tangential inlet have been performed. The geometry, and flow conditions were chosen according to an experimental study by [Escudier MP, Bornstein J, Zehnder N. Observations and LDA measurements of confined turbulent vortex flow. J Fluid Mech 1980;98:49-63]. Lattice-Boltzmann discretization was used to numerically solve the Navier-Stokes equations in the incompressible limit. Effects of spatial resolution and choices in subgrid-scale modeling were explicitly investigated with the experimental data set as the testing ground. Experimentally observed flow features, such as vortex breakdown and laminarization of the vortex core were well represented by the LES. The simulations confirmed the experimental observations that the average velocity profiles in the entire vortex tube are extremely sensitivity to the exit pipe diameter. For the narrowest exit pipe considered in the simulations, very high average velocity gradients are encountered. In this situation, the LES shows the most pronounced effects of spatial resolution and subgrid-scale modeling.     

Numerical analysis of confined turbulent flow

This work outlines a second order accurate, coupled, conservative new numerical scheme for solving a two dimensional incompressible turbulent flow filed. Mean vorticity, ω, and mean stream function, ψ, are used as the mean flow dependent variables. The turbulent kinetic energy $\text{k}$ and the turbulent energy decay rate, ?, are used to define the turbulent state. In the present computational scheme two systems of equations and variables are considered: the mean flow system, ψ-ω, and the turbulent state system, $\text{k-?}$. Every system is solved implicity in a coupled double loop manner, and all the flow equations are solved iteratively in the global sense. Since the turbulence boundary conditions have a non-regular variation near a solid wall, they are coupled to the equations implicitly in both systems. In this way the numerical instabilities due to the irregular form of the equations near the solid walls are suppressed. The rate of convergence of the new numerical scheme of the coupled systems ψ-ω and $\text{k-?}$ is twice that realized when solving these equations separately. The necessary conditions for convergence of the numerical equations are investigated as well as the rate of convergence features. The detailed stability conditions are derived. As an example, the axisymmetric mixing of two confined jets with an internal heat source is considered with this numerical scheme.     

Massive MIMO信道建模

大规模多输入多输出(Massive MIMO)作为一个有发展前景的空中接口技术,指的是为蜂窝基站(BSs)配备大量的蜂窝基站天线元件。由于Massive MIMO天线具有非常大的尺寸,阴影衰落是可以在这些阵列的不同元件上看到的显著现象。这种现象需要被建模以具有准确的Massive MIMO信道模型。文章研究了在均匀线性Massive MIMO阵列下阴影衰落所带来的影响。应用阴影衰落的自相关模型从不相关的衰落系数产生相关的衰落系数,应用这些相关的衰落系数来获得修改的信道矩阵。并提出一些数值模拟以研究Massive MIMO阵列的阴影衰落是如何影响系统的信道容量的。     

Transient response analysis and modeling of near wall flow conditions in a micro channel: evidence of slip flow

An experimental tool for determination of the near wall transport parameters in a micro channel, supported by flow simulation, is presented. The method is based on the transient flow response due to convective diffusion, in absence of specific adsorption. An approximately step-function type temporal solute concentration variation serves as the input signal. The associated response signal of a surface plasmon resonance sensor, acting as an integral part of a micro channel, has been taken as the output signal. It provides the flow-dependent change of the NaOH solute concentration in the channel within the optical detection and near wall distance interval 0 < d < 0.5 μm. The temporal signal evolution and response time, until an initially plain aqueous solution is replaced by the solute, varies inversely with solute concentration and flow rate. In the asymptotic limits, the near wall forced convective and diffusive channel transit times, along with the associated velocities, can be extracted and separated. A low convective near wall flow speed would account for 100% adsorption efficiency. The validity of the scaling relation for Fickian diffusive transport has been confirmed by experiments. Convective near wall flow reveals a distorted parabolic flow profile. This indicates relaxation of the no-slip condition, and presence of slip flow. Neither boundary layer formation, nor near wall micro turbulences have been observed. Eventually, a compact mathematical transient flow model, outlined in the Laplace domain for the electrical equivalent analogue circuit and applicable to the convective diffusion equation, has been developed for the flow transients.