Incompressible Turbulent Channel Flow Research Articles

J0550101 チャネル乱流におけるレイノルズ数効果に関する数値解析的研究

In the present study, the effect of the Reynolds number on the incompressible turbulent channel flow is investigated by means of the direct numerical simulation. In the large Reynolds number case, the turbulence energy, Reynolds shear stress and bulk mean velocity increase and the anisotropy of the Reynolds normal stresses near the wall is weakened in comparison with the low Reynolds number one. The large-scale structures appear in the visualization result of the large Reynolds number flow and this behavior corresponds to the dependency of the length scales obtained from the two-point correlation on the Reynolds number.

A subgrid-scale eddy-viscosity model based on the volumetric strain-stretching

We propose a novel subgrid-scale (SGS) eddy-viscosity model for large eddy simulation (LES) to accurately reproduce the effect of subgrid stresses on the resolved scales. The developed SGS model is based on the second-order volumetric strain-stretching (VSS) tensor, which is constructed by the multiplication of diagonal components of the strain-rate tensor with its off-diagonal components. The proposed VSS-model is validated in typical flow cases: freely decaying isotropic turbulence, incompressible turbulent channel flow at Reτ = 395, compressible turbulent channel flows at Ma = 1.5 and Reτ = 221, and Ma = 3.0 and Reτ = 556. LESs with the dynamic Smagorinsky model and the Vreman model are also performed to compare the performance of the VSS-model. The proposed model correctly recovers cubic wall behavior in the vicinity of solid boundaries in incompressible flow regime, and it has no limitation in its application to geometrically complex flows.

Velocity statistics in turbulent channel flow up to

AbstractThe high-Reynolds-number behaviour of the canonical incompressible turbulent channel flow is investigated through large-scale direct numerical simulation (DNS). A Reynolds number is achieved ($Re_{\tau } = h/\delta _v \approx 4000$, where $h$ is the channel half-height, and $\delta _v$ is the viscous length scale) at which theory predicts the onset of phenomena typical of the asymptotic Reynolds number regime, namely a sensible layer with logarithmic variation of the mean velocity profile, and Kolmogorov scaling of the velocity spectra. Although higher Reynolds numbers can be achieved in experiments, the main advantage of the present DNS study is access to the full three-dimensional flow field. Consistent with refined overlap arguments (Afzal & Yajnik, J. Fluid Mech. vol. 61, 1973, pp. 23–31; Jiménez & Moser, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007, pp. 715–732), our results suggest that the mean velocity profile never achieves a truly logarithmic profile, and the logarithmic diagnostic function instead exhibits a linear variation in the outer layer whose slope decreases with the Reynolds number. The extrapolated value of the von Kármán constant is $k \approx 0.41$. A near logarithmic layer is observed in the spanwise velocity variance, as predicted by Townsend’s attached eddy hypothesis, whereas the streamwise variance seems to exhibit a shoulder, perhaps being still affected by low-Reynolds-number effects. Comparison with previous DNS data at lower Reynolds number suggests enhancement of the imprinting effect of outer-layer eddies onto the near-wall region. This mechanisms is associated with excess turbulence kinetic energy production in the outer layer, and it reflects in flow visualizations and in the streamwise velocity spectra, which exhibit sharp peaks in the outer layer. Associated with the outer energy production site, we find evidence of a Kolmogorov-like inertial range, limited to the spanwise spectral density of $u$, whereas power laws with different exponents are found for the other spectra. Finally, arguments are given to explain the ‘odd’ scaling of the streamwise velocity variances, based on the analysis of the kinetic energy production term.

Towards CFD Modeling of Carbon Dioxide Turbulent Pipe Line Transportation

Safe and financially efficient pipeline transportation of carbon dioxide is a critical issue in the developing field of Carbon Capture and Storage (CCS) Technology. Presence of large and small scale structures and high Reynolds numbers in the pipeline, draw special attention to numerical simulation of turbulent material transport through the individual components of the carbon dioxide (CO2) chain process. In this study Large Eddy Simulation (LES) of incompressible turbulent channel flow and pipe flow has been performed using OpenFoam an open source CFD tool. The results are compared with those from Direct Numerical Simulation (DNS) and the existing experimental data.

Direct numerical simulation of particle interaction with ejections in turbulent channel flows

Direct numerical simulations (DNS) of incompressible turbulent channel flows coupled with Lagrangian particle tracking are performed to study the characteristics of ejections that surround solid particles. The behavior of particles in dilute turbulent channel flows, without particle collisions and without feedback of particles on the carrier fluid, is studied using high Reynolds number DNS ( Re = 12,500). The results show that particles moving away from the wall are surrounded by ejections, confirming previous studies on this issue. A threshold value separating ejections with only upward moving particles is established. When normalized by the square root of the Stokes number and the square of the friction velocity, the threshold profiles follow the same qualitative trends, for all the parameters tested in this study, in the range of the experiments. When compared to suspension thresholds proposed by other studies in the Shields diagram, our simulations predict a much larger value because of the measure used to characterize the fluid and the criterion chosen to decide whether particles are influenced by the surrounding fluid. However, for intermediate particle Reynolds numbers, the threshold proposed here is in fair agreement with the theoretical criterion proposed by Bagnold (1966) [Bagnold, R., 1966. Geological Survey Professional Paper, vol. 422-1]. Nevertheless, further studies will be conducted to understand the normalization of the threshold.

Steady and time-periodic blowing/suction perturbations in a turbulent channel flow

Direct Numerical Simulations (DNS) of an incompressible turbulent channel flow with given local perturbations at the walls are performed. Steady and time-periodic blowing/suction are applied by means of narrow spanwise slots located at the lower and upper walls. Our previous investigations on time-periodic blowing/suction (Araya et al. (2008) [13,14] and Araya (2008) [15]) have revealed the existence of a characteristic forcing frequency of f ¯ = 0.64 or f + = 0.044 . At this frequency, the largest local increases of the skin friction in the region downstream from the slots, followed by the highest augmentation of the Stanton number, were achieved. In this study, we seek to compare the different effects of constant blowing/suction with time-periodic blowing/suction on the flow and thermal fields. For the cyclical perturbation, the normal disturbing velocity is varied sinusoidally in time at the characteristic frequency of f ¯ = 0.64 . In both cases, the forcing amplitude, A o , is fixed to 0.025. The Reynolds number of the unperturbed case is Re τ = 394 and the molecular Prandtl number is Pr = 0.71 . Isothermal conditions are assumed for the lower wall (hot) and the upper wall (cold), respectively. For the forcing amplitude considered, steady disturbances induce higher modifications on the mean time quantities than time-periodic blowing/suction does. In addition, the effects of steady perturbations were observed to last longer downstream. However, time-periodic blowing/suction disturbances at the characteristic forcing frequency of f + = 0.044 have been demonstrated to be more effective in promoting local pressure fluctuations despite its short-distance influence. Furthermore, the energy spectra analysis of fluctuations indicates that time-periodic perturbations at this forcing frequency would be more efficient to excite the very small scales in a turbulent channel flow than by steady disturbances at the same forcing amplitude.

Helical-wave decomposition and applications to channel turbulence with streamwise rotation

Using helical-wave decomposition (HWD), a solenoidal vector field can be decomposed into helical modes with different wavenumbers and polarities. Here, we first review the general formulation of HWD in an arbitrary single-connected domain, along with some new development. We then apply the theory to a viscous incompressible turbulent channel flow with system rotation, including a derivation of helical bases for a channel domain. By these helical bases, we construct the inviscid inertial-wave (IW) solutions in a rotating channel and derive their existing condition. The condition determines the specific wavenumber and polarity of the IW. For a set of channel turbulent flows rotating about a streamwise axis, this channel-domain HWD is used to decompose the flow data obtained by direct numerical simulation. The numerical results indicate that the streamwise rotation induces a polarity-asymmetry and concentrates the fluctuating energy to particular helical modes. At large rotation rates, the energy spectra of opposite polarities exhibit different scaling laws. The nonlinear energy transfer between different helical modes is also discussed. Further investigation reveals that the IWs do exist when the streamwise rotation is strong enough, for which the theoretical predictions and numerical results are in perfect agreement in the core region. The wavenumber and polarity of the IW coincide with that of the most energetic helical modes in the energy spectra. The flow visualizations show that away from the channel walls, the small vortical structures are clustered to form very long columns, which move in the wall-parallel plane and serve as the carrier of the IW. These discoveries also help clarify certain puzzling problems raised in previous studies of streamwise-rotating channel turbulence.

Lagrangian Structure Function's Scaling Exponents in Turbulent Channel Flow

The Lagrangian structure function's scaling exponents and intermittency of three-dimensional incompressible turbulent channel flow are investigated by using direct numerical simulation. The intermittency in streamwise velocity increments is found to increase in the near-wall region, which can be attributed to the presence of strong mean shear and organized motions in the near-wall region. It is found that the intermittency of transverse velocity increments is weaker than that of longitudinal ones. The present ESS evaluation of ζL(q) for the structure function of the streamwise velocity component in the channel centre is fairly close to experimental estimates of isotropic turbulence.

The Effect of Near-Wall Vortices on Wall Shear Stress in Turbulent Boundary Layers

The objective of the present study is to explore the relation between the near-wall vortices and the shear stress on the wall in two-dimensional channel flows. A direct numerical simulation of an incompressible two-dimensional turbulent channel flow is performed with spectral method and the results are used to examine the relation between wall shear stress and near-wall vortices. The two-point correlation results indicate that the wall shear stress is associated with the vortices near the wall and the maximum correlation-value location of the near-wall vortices is obtained. The analysis of the instantaneous diagrams of fluctuation velocity vectors provides a further expression for the above conclusions. The results of this research provide a useful supplement for the control of turbulent boundary layers.

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.

Numerical assessment of local forcing on the heat transfer in a turbulent channel flow

The influence of local forcing on an incompressible turbulent channel flow is numerically investigated. The extensive information provided by the direct numerical simulations enables us to have a better understanding of the physical mechanism responsible for local heat transfer enhancement. Time-periodic blowing/suction is applied by means of thin spanwise slots located at the lower and upper walls. The molecular Prandtl number is 0.71 and the Reynolds number based on the wall friction velocity and the channel half-height, Reτ, is 394 for the unforced case. The normal perturbing velocity is varied sinusoidally in time at several perturbing frequencies between 0.16<f¯<1.6 or 0.011<f+<0.11 and at a fixed amplitude of Ao=0.2. A phase-averaging procedure is employed to discriminate between the coherent and incoherent fluctuating components. It is shown that coherent thermal fluctuations reach peak values near the forcing slot, then sharply decay and almost disappear in a short distance downstream. The incoherent thermal fluctuations also show peak values next the source; however, they decay downstream to resemble the incoherent fluctuations of the unperturbed channel. It was concluded that the forcing frequency of f¯=0.64 or f+=0.044 produced the largest local increase in the skin friction in the region 0.1<x/Lx<0.3 (where Lx is the channel length), followed by the highest augmentation of the Stanton number. It is found that augmentation of the wall shear stress fluctuations is the major cause of skin friction, wall heat flux, and Stanton number enhancement downstream from the local forcing source. On the other hand, local maxima of Reynolds shear stresses, wall-normal turbulent heat fluxes, and the incoherent component of streamwise vorticity fluctuations exhibited analogous behavior along the streamwise direction.

Passive scalar statistics in a turbulent channel with local time-periodic blowing/suction at walls

Direct Numerical Simulations (DNS) of an incompressible turbulent channel flow with local forcing at the walls are performed. Time-periodic blowing/suction is applied by means of narrow spanwise slots located at the lower and upper walls in x / L x = 0 (where L x is the channel length). The normal perturbing velocity is varied sinusoidailly in time at several perturbing frequencies between 0.16 < f ¯ < 1.6 and at a fixed amplitude of A o = 0.2 . The temperature field is also computed and assumed to be a passive scalar. The Reynolds number of the unperturbed case is R e τ = 394 and the Prandtl number is P r = 0.71 . It is concluded that the forcing frequency of f ¯ = 0.64 or f + = 0.044 produces the largest local increase of the skin friction in the region 0.1 < x / L x < 0.3 , followed by the highest augmentation of the Stanton number. Furthermore, budgets of the passive-scalar variance and wall-normal turbulent heat fluxes at this frequency demonstrate a significant enhancement of the molecular diffusion at the wall and pressure-related terms, respectively. The latter confirms the importance of pressure fluctuations on the transport of passive scalars and redistribution of energy.

New scaling of turbulence statistics for incompressible thermal channel flow with different total heat flux gradients

The scaling of turbulence statistics for wall-bounded thermal turbulent flow with different total heat flux gradients was investigated using direct numerical simulation (DNS) of an incompressible turbulent channel flow with passive scalar transport at the friction Reynolds number of 300 and the Prandtl number of 0.72. DNSs for four cases were performed, where the non-dimensional total heat flux gradients were −1, −0.5, 0 and +0.5. It was revealed that temperature variance and turbulent heat flux were well scaled by the local friction temperature. In addition, using the linear stress-heat flux model, it was shown that the appearance of the logarithmic temperature profile was attributed to the distribution of the turbulent Prandtl number.

High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow

Classical fixed-coefficient eddy-viscosity models for large-eddy simulations (LES), e.g., the Smagorinsky [Mon. Weather Rev. 93, 99 (1963)] and the structure-function model [Métais and Lesieur, J. Fluid Mech. 239, 157 (1992)], have deficiencies with accurately describing laminar flow regions and the viscous sublayer of near-wall turbulence. This is mainly due to unphysically large model contributions in such flow regions and is one main reason for the difficulty with correctly predicting laminar-turbulent transition using such models. For transitional flows, subgrid-scale (SGS) models must be able to properly deal with at least the two limits of the laminar and the turbulent fluid state. The dynamic Smagorinsky model [Germano et al., Phys. Fluids A 3, 1760 (1991)] alleviates this problem by dynamically computing a small, but not necessarily vanishing, value for the model coefficient in laminar regions and in the vicinity of the wall. In this contribution we analyze high-pass filtered (HPF) eddy-viscosity models which were proposed recently and independently by Vreman [Phys. Fluids 15, L61 (2003)] and Stolz et al. [Direct and Large-Eddy Simulation V (Kluwer, Dordrecht, 2004), pp. 81–88]. We investigate high-pass filtering suitable for such HPF eddy-viscosity models, e.g., the Smagorinsky or the (filtered) structure-function model. Furthermore, we suggest suitable high-pass filters and examine the influence of different high-pass filters on the results of LES of transitional and turbulent incompressible channel flow. Except for the filter shape, the cutoff wavenumber of the high-pass filter is the only parameter besides the eddy-viscosity model coefficient, and its influence can be minimized by a proposed adaptation of the model coefficient. We find that high-pass filtering employed to the computational quantities prior to the calculation of the eddy-viscosity and strain rate in the SGS model significantly improves the quality of the prediction of transitional and turbulent flows without using any ad-hoc adaptation or dynamic procedure. Of particular importance is that the sensitivity of the results to the model coefficient is considerably reduced by the high-pass filtering. Furthermore, the proposed high-pass filters enable the computation of the structure function in the filtered or HPF structure-function models in all spatial directions also for inhomogeneous flows and on non-equidistant grids, removing the arbitrariness of a special treatment of selected (e.g., wall-normal) directions. Simulation results are presented for incompressible turbulent channel flow at Reynolds numbers Reτ (based on the channel half-width and the friction velocity) of 180 and 590 and for forced laminar-turbulent transition in a plane channel, demonstrating the effectiveness of the proposed approach. The results are compared to data of direct numerical simulations and to data obtained using the dynamic Smagorinsky model with different test filters.

Study on Differences in Turbulence Statistics between Compressible and Incompressible Low-Reynolds Number Turbulent Channel Flows Using Semi-Local Scaling

The differences in turbulence statistics between compressible and incompressible turbulent channel flows are investigated at low-Reynolds numbers using semi-local scaling. DNS of the compressible turbulent channel flow between isothermal walls at low-Mach numbers and DNS of the incompressible flow are performed. It is revealed that the reduction in the pressure-strain correlation term is due to the reductions in RMS velocity-derivative fluctuations and in the absolute correlations between pressure and velocity-derivative fluctuations in the compressible turbulent channel flow at low-Mach and Reynolds numbers.

Evaluation of high-pass filtered eddy-viscosity models for large-eddy simulation of turbulent flows

Large-eddy simulations (LES) of incompressible homogeneous isotropic turbulence and turbulent channel flow are performed at moderate Reynolds numbers using high-pass filtered (HPF) eddy-viscosity models. This family of models computes the subgrid-scale (SGS) terms from a high-pass filtered velocity field using classical closure relations, e.g. the Smagorinsky or the structure–function model closure. Unlike the classical fixed-coefficient eddy-viscosity models, the HPF models are able to accurately describe the viscous sublayer of near-wall turbulence. Moreover, it has been shown recently that the HPF models are also capable of predicting transitional flows. Detailed results of energy and dissipation spectra are given for forced isotropic turbulence at microscale Reynolds number up to Re λ≈5500. For turbulent channel flow at friction Reynolds number Re τ≈590, results are presented for first- and second-order statistics as well as for the energy budget including the SGS terms. The overall performance of the HPF eddy-viscosity models is very good for both flow cases using a constant model coefficient. An empirical adaptation of the model coefficient to the cutoff wavenumber of the chosen high-pass filter is given. In contrast to classical eddy-viscosity models, the HPF models allow the prediction of backscatter effects, which are important for wall-bounded flows close to the walls.

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

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

Response to “Comment on ‘Inapplicability of the dynamic Clark model to the large eddy simulation of incompressible turbulent channel flows’ ” [Phys. Fluids 16, 490 (2004)

Response to “Comment on ‘Inapplicability of the dynamic Clark model to the large eddy simulation of incompressible turbulent channel flows’ ” [Phys. Fluids <b>16</b>, 490 (2004)

Comment on “Inapplicability of the dynamic Clark model to the large eddy simulation of incompressible turbulent channel flows” [Phys. Fluids 15, L29 (2003)

Abstract

Numerical Analysis of Compressible Turbulent Channel Flow with Wall-Temperature Difference

The objective of this study is to clarify the effect of different thermal wall boundary conditions on turbulence statistics and structures in the compressible turbulent flow. We performed direct numerical simulation (DNS) of the compressible turbulent channel flow between isothermal walls with temperature difference (Case C1). The DNS data was compared with that of the compressible turbulent channel flow between adiabatic and isothermal walls (Case C2), and that of the incompressible turbulent channel flow between isothermal walls with temperature difference (Case I). The main results are as follows : (1) The mean velocity in the logarithmic region and the maximum of the RMS streamwise velocity fluctuation in wall units are smaller than those of Case I near the high temperature isothermal wall, while they are larger than those of Case I near the adiabatic wall. (2) Near the high temperature isothermal wall, the mean temperature profile has an additional maximum due to the friction work, and the RMS temperature fluctuation has the corresponding maximum. This is consistent with the fact the production term of temperature variance has the additional maximum in the region very close to the high temperature isothermal wall. (3) The correlation coefficient between streamwise velocity and temperature fluctuations of Case C1 is significantly different from those of Cases C2 and I in the region very close to the high temperature wall. (4) The direction of energy transfer due to pressure work near the high temperature isothermal wall is the same as that of near the adiabatic wall. (5) The compressible terms of the temperature variance transport equation are not negligible near the low temperature isothermal wall.