Plane Channel Flow Research Articles

Polymer Melt Flow in Plane Channels: Effects of the Viscous Dissipation and Axial Heat Conduction

ABSTRACT The plastic transforming industry has shown considerable growth in the last years. In this context, commercial simulators have been developed, some of which combine simplified mathematical models with rheological properties of commercial polymers. In spite of the successes, these approximations are not able to capture important details of the flow behavior. The present work addresses some aspects of the polymer melt flow in plane channels using a more elaborate mathematical formulation based on the full momentum and energy conservation laws. The physical equations are discretized using finite differences based on a collocated mesh and second-order spatial accuracy formulas. Solutions featuring the development of hydrodynamic and thermal boundary layers are presented for a commercial polymer.

Large-eddy simulation of spatial transition in plane channel flow

Spatial large-eddy simulations (LES) of forced transition in plane incompressible channel flow are presented and compared to temporal simulations. Using the fringe method, spectral Fourier discretization is employed also in the streamwise, spatially evolving flow direction. Various subgrid-scale (SGS) models are examined including the dynamic Smagorinsky model, high-pass filtered (HPF) eddy-viscosity models and the relaxation-term model (ADM-RT). The applicability of the fringe method in conjunction with SGS models is demonstrated. Good results are obtained even at rather low LES resolution at which a coarse-grid no-model calculation is inaccurate. The most accurate prediction of transitional flow structures is obtained using the ADM-RT model. For this model, a detailed comparison between spatial and temporal simulation results is given. A clear representation of the transitional flow structures by LES up to the multi-spike stage could be established. Our results also show that the SGS models behave similarly in temporal and spatial simulations, thus allowing us to perform SGS model testing with the more straightforward and inexpensive temporal approach. The same SGS models work well without any change also in the fully developed turbulent flow.

Numerical Simulations of Circular Particles in Parallel Plate Channel Flow Using Lattice Boltzmann Method

Simulations with Lattice Boltzmann method are conducted for particulate suspension in a plane channel flow at low and moderate Reynolds numbers to investigate blood cell behavior in microvascular flows. The simulation results for three kinds of hematocrit indicate existence of an important relationship between the Reynolds number and the variance of the particles. When the hematocrit is small, it is found that the particles are concentrated between the centerline and the wall, that is, Segre-Silberberg effect appears. As the hematocrit becomes larger, on the other hand, this effect disappears and the variance of the particles is increased. In the case of an inelastic collision, the particles which flow near the wall are increased in comparison with the case of the elastic collision.

A Hybrid LES/RANS Approach Using Anisotropy-Resolving Algebraic Turbulence Models for Predicting Turbulent Heat Transfer

In order to derive a possible path for developing a large eddy simulation (LES) applicable to high Reynolds-number turbulent flows with heat transfer, a hybrid approach connecting LES with the Reynolds-averaged Navier-Stokes (RANS) modeling in the near-wall region is studied. In this study, an advanced non-linear eddy-viscosity model and a higher-order extension of the generalized gradient diffusion hypothesis model are introduced to resolve the near-wall turbulence and turbulent heat transfer more correctly. To investigate the model performance in detail, the proposed model is applied to fully developed plane channel flows with various grid resolutions. The present model provides encouraging results for further development of this kind of hybrid LES/RANS model.

Mean Velocity Profile in Recovery Region of Pure Poiseuille, Pure Couette and Couette-Poiseuille Type Turbulent Flows over a Backward-Facing Step

Mean velocity profiles in velocity recovery region of pure Poiseuille, pure Couette and Couette-Poiseuille type turbulent channel flows over a backward-facing step are measured and investigated experimentally. The flows are turbulent channel flows between moving and step-side stationary walls with different non-dimensional upstream pressure gradients β0 (flow type parameter). The channel expansion ratio is 1.50. The upstream flows are fully developed pure Poiseuille (β0=-1), pure Couette (β0=0) and Couette-Poiseuille (β0=-0.5) turbulence plane channel flows. The reattachment region is specified by tuft visualization method. The central point of the reattachment region is less dependent on β0. Velocity profiles are measured by hot-wire anemometry for the flows at Reτ0=300, where Reτ0 is the Reynolds number based on the friction velocity and channel half width at the upstream flow. The logarithmic law of velocity is observed even for sections just after the reattachment region. The additive constant appeared in the logarithmic law decreases with increase of β0. The half power law is formed at the beginning of the recovery region for the flows with β0=-0.5 and 0, while it is not observed for the flow with β0=-1.

Numerical experiments on wall turbulence at low Reynolds number

A direct numerical simulation of a turbulent channel flow, with regularly spaced two-dimensional roughness elements mounted at the wall and perpendicular to the flow direction, was performed at a very low Reynolds number of Re
940 based on the centerline velocity and the full channel height. Using the lattice Boltzmann numerical algorithm, all essential scales were resolved with about 19·106 grid points (1155 x 129 x 128 in the x1, x2 and x3 directions). The computed results confirm the existence of turbulence at such a low Reynolds number. Turbulence persisted over the entire computation time, which was sufficiently long to prove its self-maintenance. By examination of statistical features of the flow across the anisotropy-in variant map, it was found that these coincide with conclusions emerging from the analysis of transition and breakdown to turbulence in a laminar boundary layer exposed to small, statistically stationary, neutrally stable axisymmetric disturbances with the stream wise intensity component ( u'1) lower than the intensities in the normal ( u'1) and span wise directions u'1< u'2 = u'3. To further support the concept and the results of
theoretical considerations of the laminar to turbulent transition process in wall-bounded flows using statistical techniques and to demonstrate its great potential for engineering, an additional simulation was performed of a plane channel flow with regularly spaced riblet elements mounted at the wall and aligned parallel with the flow direction. The supplementary simulation was done at a Reynolds number of Re = 6584 using about 250·106 grid points (4096 x 257 x 240). Analysis of the simulation results carried out across the flow region located in the mid plane between the riblet elements confirms the central result which lies in the root of the statistical dynamics of the velocity fluctuations in wall-bounded flows: when the velocity fluctuations close to the wall tend towards the one-component state, so that the stream wise intensity component is much larger than the intensities in the normal and span wise directions, u'1< u'2 = u'3, the turbulent dissipation rate vanishes at the wall, leading to a significant reduction of the wall shear stress. For the simulated flow case the local value of wall shear stress reduction was found to exceed the wall shear stress reduction SR
92% which corresponds to a fully developed laminar channel flow with smooth walls at the same Reynolds number.

422 圧縮性平面チャネル流れの遷移機構に対するマッハ数の影響(流体工学VIII)

422 圧縮性平面チャネル流れの遷移機構に対するマッハ数の影響(流体工学VIII)

Nonlinear stochastic estimation of wall models for LES

A key technology for large eddy simulation (LES) of complex flows is an appropriate wall modeling strategy. In this paper we apply for the first time a fully nonparametric procedure for the estimation of generalized additive models (GAM) by conditional statistics. As a database, we use DNS and wall-resolved LES data of plane channel flow for Reynolds numbers, Re = 2800, 4000 (DNS) and 10,935, 22,776 (LES). The statistical method applied is a quantitative tool for the identification of important model terms, allowing for an identification of some of the near-wall physics. The results are given as nonparametric functions which cannot be attained by other methods. We investigated a generalized model which includes Schumann’s and Piomelli et al.’s model. A strong influence of the pressure gradient in the viscous sublayer is found; for larger wall distances the spanwise pressure gradient even dominates the τ w, zy component. The first a posteriori LES results are given.

Heat transfer enhancement in grooved channels due to flow bifurcations

The flow bifurcation scenario and heat transfer characteristics in grooved channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element methods for increasing Reynolds numbers in the laminar and transitional regimes. The Eulerian flow characteristics show a transition scenario of two Hopf bifurcations when the flow evolves from a laminar to a time-dependent periodic and then to a quasi-periodic flow. The first Hopf bifurcation occurs to a critical Reynolds number Rec1 that is significantly lower than the critical Reynolds number for a plane-channel flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω1 and m· ω1+n·ω2, respectively, with m and n integers. Friction factor and pumping power evaluations demonstrate that these parameters are much higher than the plane channel values. The time-average mean Nusselt number remains mostly constant in the laminar regime and continuously increases in the transitional regime. The rate of increase of this Nusselt number is higher for a quasi-periodic than for a periodic flow regime. This higher rate originates because better flow mixing develops in quasi-periodic flow regimes. The flow bifurcation scenario occurring in grooved channels is similar to the Ruelle-Takens-Newhouse transition scenario of Eulerian chaos, observed in symmetric and asymmetric wavy channels.

Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD)

The streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) methods are among the most popular stabilized formulations in finite element computation of flow problems. The discontinuity-capturing directional dissipation (DCDD) was first introduced as a complement to the SUPG and PSPG stabilizations for the computation of incompressible flows in the presence of sharp solution gradients. The DCDD stabilization takes effect where there is a sharp gradient in the velocity field and introduces dissipation in the direction of that gradient. The length scale used in defining the DCDD stabilization is based on the solution gradient. Here we describe how the DCDD stabilization, in combination with the SUPG and PSPG stabilizations, can be applied to computation of turbulent flows. We examine the similarity between the DCDD stabilization and a purely dissipative energy cascade model. To evaluate the performance of the DCDD stabilization, we compute as test problem a plane channel flow at friction Reynolds number Re τ = 180.

회전하는 원형단면 실린더 주위의 저 레이놀즈수 난류유동에 대한 직접수치모사

Turbulent flow around a rotating circular cylinder is investigated by Direct Numerical Simulation. The calculation is performed at three cases of low Reynolds number, Re=161, 348 and 623, based on the cylinder radius and friction velocity. Statistically strong similarities with fully developed channel flow are observed. Instantaneous flow visualization reveals that the turbulence length scale typically decreases as Reynolds number increases. Some insight into the spacial characteristics in conjunction with wave number is provided by wavelet analysis. The budget of dissipation rate as well as turbulent kinetic energy is computed and particular attention is given to the comparison with plane channel flow.

Viscous heating effects in fluids with temperature-dependent viscosity: triggering of secondary flows

Viscous heating can play an important role in the dynamics of fluids with a strongly temperature-dependent viscosity because of the coupling between the energy and momentum equations. The heat generated by viscous friction produces a local increase in temperature near the tube walls with a consequent decrease of the viscosity and a strong stratification in the viscosity profile which can trigger instabilities and a transition to secondary flows.In this paper we present two separate theoretical models: a linear stability analysis and a direct numerical simulation (DNS) of a plane channel flow. In particular DNS shows that, in certain regimes, viscous heating can trigger and sustain a particular class of secondary rotational flows which appear organized into coherent structures similar to roller vortices. This phenomenon can play a very important role in the dynamics of magma flows and, to our knowledge, it is the first time that it has been investigated by a direct numerical simulation.

RANS/LES coupling for unsteady turbulent flow simulation at high Reynolds number on coarse meshes

Industrial flow simulation usually concerns high Reynolds number and wall-bounded configuration. Unfortunately, large-eddy simulation (even with wall models) needs a great wall refinement to handle this kind of flows. This increases drastically the simulation computational cost up to become prohibitive. This study has two major objectives. To begin with, main drawbacks of large-eddy simulation for isothermal situation with usual wall models in coarse grids for high friction Reynolds number up to 2 × 10 4 in a plane channel flow configuration are highlighted using the Trio_U code developed at CEA Grenoble. Then, two strategies to improve the simulations results are proposed. First, a sophisticated wall model (called TBLE wall model) was tested and provided some improved results in low Reynolds number cases. However, shortcomings observed for large-eddy simulations with usual wall models seem to continue with the use of TBLE wall model. Then, a RANS/LES coupling approach relying on a forcing term was investigated and provided some promising results.

Nonclassical Solutions of the Classical Problem of Viscous Incompressible Flow in a Plane Channel

This article describes a procedure for numerical analysis of the dynamics of viscous incompressible fluids in the framework of the classical Navier-Stokes model using a system of equations that preserve the reciprocal relationship between the dynamic equations and the energy equation and ensure that the law of mass conservation is satisfied with fairly high accuracy in numerical work. We report the results of numerical analysis of time-dependent flows in sufficiently long channels with various boundary and initial conditions. The existence of nonclassical solution structures is demonstrated.

The Development Lengths of Laminar Pipe and Channel Flows

Abstract The authors’ research work into fully developed pulsating and oscillating laminar pipe and channel flows raised questions regarding the development length of the corresponding steady flow. For this development length, i.e., the distance from the entrance of the pipe to the axial position where the flow reaches the parabolic velocity profile of the Hagen-Poiseuille flow, a wide range of contradictory data exists. This is shown through a short review of the existing literature. Superimposed diffusion and convection, together with order of magnitude considerations, suggest that the normalized development length can be expressed as L∕D=C0+C1Re and for Re→0 one obtains C0=0.619, whereas for Re→∞ one obtains C1=0.0567. This relationship is given only once in the literature and it is presumed to be valid for all Reynolds numbers. Numerical studies show that it is only valid for Re→0 and Re→∞. The development length of laminar, plane channel flow was also investigated. The authors obtained similar results to those for the pipe flow: L∕D=C0′+C1′; Re, where C0′=0.631 and C1′=0.044. Finally, correlations are given to express L∕D analytically for the entire Re range for both laminar pipe and channel flows.

LES of Turbulent Separated Flow and Heat Transfer in a Symmetric Expansion Plane Channel

The LES method was applied to analyze numerically an unsteady turbulent separated and reattached flow and heat transfer in a symmetric expansion plane channel of expansion ratio 2.0. The Smagorinsky model was used in the analysis and fundamental equations were discretized by means of the finite difference method, and their resulting finite difference equations were solved using the SMAC method. The calculations were conducted for Re=15,000. It is found that the present numerical results, in general, agree well with the previous experimental ones. The complicated vortical flow structures in the channel and their correlations with heat transfer characteristics are visualized through various fields of flow quantities.

Two-equation modeling of turbulent rotating flows

The possibility to take into account the effects of the Coriolis acceleration on turbulence is examined in the framework of two-equation eddy-viscosity models. General results on the physical consistency of such turbulence models are derived from a dynamical-system approach to situations of time-evolving homogeneous turbulence in a rotating frame. Application of this analysis to a (k,ϵ) model fitted with an existing Coriolis correction [J. H. G. Howard, S. V. Patankar, and R. M. Bordynuik, “Flow prediction in rotating ducts using Coriolis-modified turbulence models,” ASME Trans. J. Fluids Eng. 102, 456 (1980)] is performed. Full analytical solutions are given for the flow predicted with this model in the situation of homogeneously sheared turbulence subject to rotation. The existence of an unphysical phenomenon of blowup at finite time is demonstrated in some range of the rotation-to-shear ratio. A direct connection is made between the slope of the mean-velocity profile in the plane-channel flow with spanwise rotation, and a particular fixed point of the dynamical system in homogeneously sheared turbulence subject to rotation. The general analysis, and the understanding of typical inaccuracies and misbehavior observed with the existing model, are then used to design a new model which is free from the phenomenon of blowup at finite time and able to account for both of the main influences of rotation on turbulence: the inhibition of the spectral transfer to high wave numbers and the shear/Coriolis instability.

Structure of Time-Dependent Transonic Flows in Plane Channels

The evolution and interaction of supersonic zones and the shock waves closing them are considered on the basis of the Lin-Reissner-Tsien equation for flow in plane channels with a local bottleneck.

Reduced-basis modeling of turbulent plane channel flow

Very-large-eddy simulations of turbulent plane channel flow of various Reynolds numbers have been performed. The simulations are based on relatively small sets of modes from a proper orthogonal decomposition (POD) of a direct numerical simulation or large-eddy simulation of the same flow. The intention is to investigate how these reduced basis simulations respond to change in Reynolds number and geometry. We find that the dynamical systems are able to reproduce the mean velocity and Reynolds stress profiles as long as the aspect ratio of the channel or the Reynolds number does not increase or decrease from the original setting with more than 50% or 30%, respectively. When the objective is a coarse description of the flow dynamics, significant savings in terms of computational cost are achieved by deriving the dynamical systems from the POD-basis. One possible application of such reduced basis simulations can be to efficiently generate turbulent inlet boundary conditions for direct numerical simulations.

Stability characteristics of suspension flow through wavy-walled channels

A numerical study of the linear temporal stability characteristics of particulate suspension flow through a converging-diverging symmetric wavy-walled channel is considered. The basic flow is a superposition of plane channel flow of particulate suspension and periodic flow components arising due to the small amplitude sinusoidal waviness of the channel walls. The disturbance equations are derived within the framework of Floquet theory and solved using the spectral collocation method. The effects of small amplitude sinusoidal waviness of the channel walls and those of the presence of particles on the initial growth of the disturbances are examined. Two-dimensional stability calculations for particulate suspensions indicate the presence of fast growing unstable modes that arise due to the waviness of the walls. Neutral stability calculations are performed in the disturbances wavenumber-Reynolds number (αs−Re) plane, for the wavy channel with representative values of wavenumber (λ) and the wall amplitude to semi-channel height ratio (∈w) for different values of volume fraction density of the particles (C). It is observed that the critical Reynolds number for transition decreases with increase of ∈w and C. However, the flow can be modulated by suitable wall excitation which in turn can stabilize the flow.