Direct numerical simulation of turbulent pipe flow

Fully developed turbulent pipe flow at low Re-number is studied by means of direct numerical simulation (DNS). In contrast to many previous DNS's of turbulent flows in rectangular geometries, the present DNS code, developed for a cylindrical geometry, is based on the finite volume technique rather than being based on a spectral method. The statistical results are compared with experimental data obtained with two different experimental techniques. The agreement between numerical and experimental results is found to be good which indicates that the present DNS code is suited for this kind of numerical simulations.     

Direct numerical simulation of turbulent flow in a spanwise rotating square duct at high rotation numbers

In this paper, direct numerical simulations have been performed to study the effects of Coriolis force on the turbulent flow field confined within a square duct subjected to spanwise system rotations at high rotation numbers. In response to the system rotation, secondary flows appear as large streamwise counter-rotating vortices, which interact intensely with the four boundary layers and have a significant impact on flow statistics, velocity spectra and coherent structures. It is observed that at sufficiently high rotation numbers, a Taylor–Proudman region appears and complete laminarization is almost reached near the top and side walls. The influence of large organized secondary flows on the production rate and re-distribution of turbulent kinetic energy has been investigated through a spectral analysis. It is observed that the Coriolis force dominates the transport of Reynolds stresses and turbulent kinetic energy, and forces the spectra of streamwise and vertical velocities to synchronize within a wide range of scales.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

Direct numerical simulation of a freely decaying turbulent interfacial flow

Whereas Large Eddy Simulation (LES) of single-phase flows is already widely used in the CFD world, even for industrial applications, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed data base from direct numerical simulation (DNS) of two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. This work is a first contribution in the study of the interface/turbulence interaction in the configuration where the interface is widely deformed and where both phases are resolved by DNS. To do this, the interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (HIT) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. Comparisons with existing theories built on wall-bounded or free-surface turbulence are carried out. To understand energy transfers between the interfacial energy and the turbulent one, PDFs of the droplet sizes distribution are calculated. An energy budget is carried out and turbulent statistics are performed including the distance to the interface as a parameter. A spectral analysis is achieved to highlight the energy transfer between turbulent scales of different sizes. The originality of this work is the study of the interface/turbulence interactions in the case of a widely deformed interface evolving in a turbulent flow.     

Direct numerical simulation of a turbulent plane Couette-Poiseuille flow with zero-mean shear

Direct numerical simulations of a turbulent Couette-Poiseuille flow with zero-mean-shear at the moving wall (SL-flow) is performed to examine flow features compared to those for a turbulent pure Poiseuille flow (P-flow). Profiles of the streamwise mean velocity, indicator function and ratio of production to dissipation show that the logarithmic region is significantly elongated for the SL-flow compared to that for the P-flow at a similar Reynolds number. In addition, the magnitudes of the Reynolds stresses are found to be larger in both inner and outer layers for the SL-flow than those for the P-flow. The spanwise spectra of the production term in the turbulent kinetic energy equation are examined to provide a structural basis for explaining the statistical behaviors. In addition, because the growth of the energy-containing motions extends to the outer layer further for the SL-flow due to the presence of a positive mean shear throughout the entire wall layer, the self-similar behavior of the energy balance between the production and transport terms with respect to the self-similar wavenumber is found far from the wall. We also find the increase in the number of uniform momentum zones in the SL-flow, revealing the hierarchical distribution of the energy-containing eddies which are composed of multiple uniform momentum zones. These coherent motions lead to the elongation of the logarithmic region for the SL-flow. Finally, investigation of the turbulent energy transfer process in a spectral domain for the SL-flow demonstrates importance of outer layer very-long structures, and these structures attribute to the energy transport process in an entire flow field.     

Direct numerical simulation of wall turbulent flows with microbubbles

The marker‐density‐function (MDF) method has been developed to conduct direct numerical simulation (DNS) for bubbly flows. The method is applied to turbulent bubbly channel flows to elucidate the interaction between bubbles and wall turbulence. The simulation is designed to clarify the structure of the turbulent boundary layer containing microbubbles and the mechanism of frictional drag reduction. It is deduced from the numerical tests that the interaction between bubbles and wall turbulence depends on the Weber and Froude numbers. The reduction of the frictional resistance on the wall is attained and its mechanism is explained from the modulation of the three‐dimensional structure of the turbulent flow. Copyright © 2001 John Wiley & Sons, Ltd.     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Direct numerical simulation of the turbulent flow in a pipe with annular cross section

The turbulent flow in a pipe of annular cross section is studied for the first time through a direct numerical simulation (DNS) using the Navier–Stokes equations written in cylindrical coordinates. To this aim a novel numerical method is developed, which extends to the cylindrical coordinate system an existing, efficient method designed for cartesian coordinates, and allows us to eliminate the pressure and formulate the problem in two scalar unknowns. The unnecessary increase of resolution at smaller radius typically brought about by polar coordinates, with its consequent stability limitations, is avoided by changing the number of azimuthal Fourier modes with the radial coordinate itself. In addition, the azimuthal extension of the computational domain is reduced, for the cases with lowest curvature, by considering only a part of the annulus, without loss of physical significance of the results. A computer code based on this method is run on a desktop PC for the simulation (with up to 16 million degrees of freedom) of the turbulent flow in a pipe with annular cross section, in a range of relatively low curvatures. This investigation highlights that curvature effects are already evident, even on first order turbulence statistics like the mean axial velocity distribution, in a low-curvature range where it is commonly believed that the flow should be hardly distinguishable from the flow over a plane surface.     

Direct numerical simulation of turbulent mixing of a passive scalar in pipe flow

Turbulent mixing of a passive scalar in fully developed turbulent pipe flow has been investigated by means of a Direct Numerical Simulation (DNS). The scalar is released from a point source located on the centreline of the pipe. The domain size of the concentration field has been chosen large enough to capture the different stages of turbulent mixing. Results are presented for mean concentration profiles, turbulent fluxes, concentration fluctuations, probability density functions and higher-order moments. To validate the numerical simulations the results are compared with experimental data on mixing in grid-turbulence that have been reported in the literature. The agreement between the experimental measurements and the computations is satisfactory. We have also considered the Probability Density Function (PDF). For small diffusion times and positions not on the plume centreline, our results lead to a PDF of an exponential form with a large peak at zero concentration. When the diffusion time increases, the PDF shifts from a exponential to a more Gaussian form.     

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

湍流横掠固定颗粒的全尺度直接数值模拟

气固两相流模拟中,当固相尺度接近或大于Kolmogorov尺度时,普通的点源模型将不再适用,固体相的体积效应和表面效应将对流体相产生显著的影响。通过采用直接数值模拟方法,结合内嵌边界方法对湍流中不同湍流强度流体横掠大于Kolmogorov尺度的固相颗粒进行了全尺度模拟,讨论分析了在两种湍流度下方形颗粒对湍流的调制影响以及颗粒的受力情况。     

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

We study compressible turbulent flow in a circular pipe at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies. Regarding velocity statistics, we find that Huang’s transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny (Re_τ ≈ 1000), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et al. (2014). The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear.     

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, cross-stream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.     

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.     

Direct numerical simulation of fluid flow laden with many particles

Two-dimensional channel flow of fluid laden with many particles is studied by direct numerical simulation using the Navier–Stokes equation coupled with the equation of motion for respective particles. Fractional four-step method with Crank–Nicolson scheme and ALE technique is adopted for P2P1 mixed finite element formulation of the governing equations for fluid motion. The motion and distribution of particles in the fluid is virtually described and the calculated relative viscosity is compared with previous results within the limits of possibility. The effect of the ratio of channel gap to particle diameter on the relative viscosity and the tubular pinch effect are also delineated.     

Direct numerical simulation of a turbulent Couette-Poiseuille flow,part 2: Large- and very-large-scale motions

A direct numerical simulation dataset of a fully developed turbulent Couette-Poiseuille flow is analyzed to investigate the spatial organization of streamwise velocity-fluctuating u-structures on large and very large scales. Instantaneous and statistical flow fields show that negative-u structures with a small scale on a stationary bottom wall grow throughout the centerline due to the continuous positive mean shear, and they penetrate to the opposite moving wall. The development of an initial vortical structure related to negative-u structures on the bottom wall into a large-scale hairpin vortex packet with new hairpin vortices, which are created upstream and close to the wall, is consistent with the auto-generation process in a Poiseuille flow (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). Although the initial vortical structure associated with positive-u structures on the top wall also grows toward the bottom wall, the spatial development of the structure is less coherent with weak strength due to the reduced mean shear near the top wall, resulting in less turbulent energy on the top wall. The continuous growth of the structures from a wall to the opposite wall explains the enhanced wall-normal transport of the streamwise turbulent kinetic energy near the centerline. Finally, an inspection of the time-evolving instantaneous fields and conditional averaged flow fields for the streamwise growth of a very long structure near the centerline exhibits that a streamwise concatenation of adjacent large-scale u-structures creates a very-large-scale structure near the channel centerline.     

二维槽道湍流数值模拟与白组织特性

从流体力学基本方程出发,讨论了二维槽道湍流的衰减特性,通过对流场施加合适的体积力,采用拟谱方法对二维槽道强制湍流进行了数值模拟.研究了二维槽道衰减湍流的自组织与逆能量级串特性,再现了二维槽道衰减湍流中湍涡的自组织过程,以及不同波数湍流结构所携能量在自组织过程中的变化,并解释了二维槽道湍流平均速度曲线特征以及海洋环流所特有的自然现象.