DIRECT NUMERICAL SIMULATION OF VIBRATIONINDUCED T-S WAVE ON BOUNDARY LAYER WALL

The spatial growth of the disturbance in the boundary layer is directly numerically simulated, and the receptivity of the Blasius basic flow to the local two-dimensional （2-D） sustainable micro-vibration is investigated. Results show that the disturbance velocity presents the sine vibration features with the change of time, and the vibration period is identical to the vibration of the local wall. The disturbance velocity presents the fluctuation feature downstream, and the streamwise wave length approximates to the results from the Orr-Sommerfeld equation （OSE）. The growth rate from direct numerical simulation（DNS） is a little greater than that from OSE, and their trends are almost consistent. Under the condition of Re= 2 800, the disturbance amplitude gradually grows in the given computational region with the period T=30. However, it firstly increases and then decreases with the period T= 20. The disturbance harmonic of the former is obviously larger than that of the latter. The maximum streamwise and vertical disturbance velocities from DNS do not fully coincide with those from OSE at the vicinity of the local vibration wall, but coincide well with the former when they travel downstream. The 2-D disturbance induced by the local micro-vibration represents the form of Tollmien-Schlichting （T-S） wave on the boundary layer.

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 Particle Dispersion in Gas-Solid Compressible Turbulent Jets

A numerical method was developed to directly simulate the compressible, particle-laden turbulent jets.The fourth order compact finite difference schemes were used to discretize the space derivatives. The Lagrangian method was adopted to simulate the particle motion based on one-way coupling. It is found that the turbulent intensity profiles attain self-similar status in the jet downstream regions. At the Stokes number of 1, particles are concentrated largely in the outer boundaries of the large-scale vortex structures with the most uneven distribution and the widest dispersion in the lateral direction. Particles at the much smaller Stokes numbers are distributed evenly in the flow field, and the lateral dispersion is also considerable. Distribution of particles at much larger Stokes numbers is more uniform and the lateral dispersion becomes small. In addition, the inflow conditions have different effects on the particle dispersion. The direct numerical simulation (DNS) results accord with the previous experiments and numerical studies.

AN ANALYSIS OF SUBGRID-RESOLVED SCALE INTERACTIONS WITH USE OF RESULTS FROM DIRECT NUMERICAL SIMULATIONS

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range. By decomposing the subgrid energy transfer and nonlinear interaction into ‘forward’ and ‘backward’ groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.

Direct numerical simulation of viscoelastic-fluid-based nanofluid turbulent channel flow with heat transfer

Our previous experimental studies have confirmed that viscoelastic-fluid-based nanofluid(VFBN) prepared by suspending nanoparticles in a viscoelastic base fluid(VBF, behaves drag reduction at turbulent flow state) can reduce turbulent flow resistance as compared with water and enhance heat transfer as compared with VBF. Direct numerical simulation(DNS) is performed in this study to explore the mechanisms of heat transfer enhancement(HTE) and flow drag reduction(DR) for the VFBN turbulent flow. The Giesekus model is used as the constitutive equation for VFBN. Our previously proposed thermal dispersion model is adopted to take into account the thermal dispersion effects of nanoparticles in the VFBN turbulent flow. The DNS results show similar behaviors for flow resistance and heat transfer to those obtained in our previous experiments. Detailed analyses are conducted for the turbulent velocity, temperature, and conformation fields obtained by DNSs for different fluid cases, and for the friction factor with viscous, turbulent, and elastic contributions and heat transfer rate with conductive, turbulent and thermal dispersion contributions of nanoparticles, respectively. The mechanisms of HTE and DR of VFBN turbulent flows are then discussed. Based on analogy theory, the ratios of Chilton–Colburn factor to friction factor for different fluid flow cases are investigated, which from another aspect show the significant enhancement in heat transfer performance for some cases of water-based nanofluid and VFBN turbulent flows.

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.

Validation of the RANS-SOM Combustion Model Using Direct Numerical Simulation of Incompressible Turbulent Reacting Flows

The second-order moment combustion model, proposed by the authors is validated using the direct numerical simulation （DNS） of incompressible turbulent reacting channel flows. The instantaneous DNS results show the near-wall strip structures of concentration and temperature fluctuations. The DNS statistical results give the budget of the terms in the correlation equations, showing that the production and dissipation terms are most important. The DNS statistical data are used to validate the closure model in RANS second-order moment （SOM） combustion model. It is found that the simulated diffusion and production terms are in agreement with the DNS data in most flow regions, except in the near-wall region, where the near-wall modification should be made, and the closure model for the dissipation term needs further improvement. The algebraic second-order moment （ASOM） combustion model is well validated by DNS.

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder:Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution

Three-dimensional direct numerical simulations of the wake flow downstream of a near-wall circular cylinder at different gap ratios and boundary layer thicknesses are carried out by using the iterative immersed boundary method.The non-dimensional gap between the cylinder and the wall,G/D=0.2,0.6 and 1.0,the non-dimensional boundary layer thickness,δ/D=0.0,0.7 and 1.6,the Reynolds number,Re=350,and the aspect ratio of the cylinder,L/D=25are adopted.High-resolution visualizations of the complex vortex structures at differentδ/D and G/D are presented.The transition of the streamwise vortex mode,the combined effects ofδ/D and G/D on the flow statistics,the pressure and shear stress distribution and the hydrodynamic forces are analyzed.Results show that with decreasing G/D and increasingδ/D,the gap flow and its vortex-shedding are significantly weakened,together with an elongated wake and an enlarged low-velocity area near the wall,leading to the wake mode transition from the two-sided to one-sided vortex-shedding.Different relative positions of the cylinder regarding the boundary layer alter the flow features of the shear layers.With an increase inδ/D,the front stagnation point shifts to the upper surface,and the distance between the flow divergence point and the maximum pressure position increases.The mean drag coefficient and r.m.s.values of drag and lift coefficients decrease with a decrease in G/D and an increase inδ/D,while the mean lift coefficient increases with decreasing G/D but decreases with increasingδ/D.

Direct numerical simulation of matrix diffusion across fracture/matrix interface

Accurate descriptions of matrix diffusion across the fracture/matrix interface are critical to assessing contaminant migration in fractured media. The classical transfer probability method is only applicable for relatively large diffusion coefficients and small fracture spacings, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks. Motivated and required by practical applications, we propose a direct numerical simulation （DNS） approach without any empirical assumptions. A three-step Lagrangian algorithm was developed and validated to directly track the particle dynamics across the fracture/matrix interface, where particle＇s diffusive displacement across the discontinuity is controlled by an analytical, one-side reflection probability. Numerical experiments show that the DNS approach is especially efficient for small diffusion coefficients and large fracture spacings, alleviating limitations of the classical modeling approach.

Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow

In this paper,we present a direct numerical simulation（DNS） of elastic turbulence of viscoelastic fluid at vanishingly low Reynolds number（Re = 1） in a three-dimensional straight channel flow for the first time,using the Giesekus constitutive model for the fluid.In order to generate and maintain the turbulent fluid motion in the straight channel,a sinusoidal force term is added to the momentum equation,and then the elastic turbulence is numerically realized with an initialized chaotic velocity field and a stretched conformation field.Statistical and structural characteristics of the elastic turbulence therein are analyzed based on the detailed information obtained from the DNS.The fluid mixing enhancement effect of elastic turbulence is also demonstrated for the potential applications of this phenomenon.

Characteristics and generation of elastic turbulence in a three-dimensional parallel plate channel using direct numerical simulation

Direct numerical simulations（DNSs） of purely elastic turbulence in rectilinear shear flows in a three-dimensional（3D） parallel plate channel were carried out,by which numerical databases were established.Based on the numerical databases,the present paper analyzed the structural and statistical characteristics of the elastic turbulence including flow patterns,the wall effect on the turbulent kinetic energy spectrum,and the local relationship between the flow motion and the microstructures＇ behavior.Moreover,to address the underlying physical mechanism of elastic turbulence,its generation was presented in terms of the global energy budget.The results showed that the flow structures in elastic turbulence were 3D with spatial scales on the order of the geometrical characteristic length,and vortex tubes were more likely to be embedded in the regions where the polymers were strongly stretched.In addition,the patterns of microstructures＇ elongation behave like a filament.From the results of the turbulent kinetic energy budget,it was found that the continuous energy releasing from the polymers into the main flow was the main source of the generation and maintenance of the elastic turbulent status.

Direct numerical simulation of shock wave/boundary layer interaction controlled by steady microjet in a compression ramp

Shock wave/boundary layer interaction in a 24°turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation.Three different jet spacings which are termed as sparse,moderate and dense are considered,and the induced vortex system and shock structures are compared.A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation,reducing the separation region.The dense jet spacing configuration creates a larger momentum deficit region,reducing the friction downstream of the corner.Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock.The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation.Furthermore,the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods,revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.

DIRECT NUMERICAL SIMULATION OF TURBULENT FLOW IN A STRAIGHT SQUARE DUCT AT REYNOLDS NUMBER 600

This article presents the direct numerical simulation results of the turbulent flow in a straight square duct at a Reynolds number of 600, based on the duct width and the mean wall-shear velocity. The turbulence statistics along the wall bisector is examined with the turbulent flow field properties given by streamwise velocity and vorticity fields in the duct cross section. It was found that the solutions of the turbulent duct flow obtained in a spatial resolution with 1.2×10^6 grid points are satisfactory as compared to the existing numerical and experimental results. The results indicate that it is reasonable to neglect the sub-grid scale models in this spatial resolution level for the duct flow at the particular friction Reynolds number.

Direct numerical simulation of impinging shock wave and turbulent boundary layer interaction over a wavy-wall

The interaction of an impinging oblique shock wave with an angle of 30°and a supersonic turbulent boundary layer at Ma_(∞)=2.9 and Re_(θ)=2400 over a wavy-wall is investigated through direct numerical simulation and compared with the interaction on a flat-plate under the same flow conditions.A sinusoidal wave with amplitude to wavelength ratio of 0.26 moves in the streamwise direction and is uniformly distributed across the spanwise direction.The influences of the wavy-wall on the interaction,including the characterization of the flow field,the skin-friction,pressure and the budget of turbulence kinetic energy,are systematically studied.The region of separation grows slightly and decomposes into four bubbles.Local peaks of skin-friction are observed at the rear part of the interaction region.The low-frequency shock motion can be seen in the wall pressure spectra.Analyses of the turbulence kinetic energy budget indicate that both diffusion and transport significantly increase near the crests,balanced by an amplified dissipation in the near-wall region.Proper orthogonal decomposition analyses show that the most energetic structures are associated with the separated shock and the shear layer over the bubbles.Only the bubbles in the first two troughs are dominated by a low-frequency enlargement or shrinkage.

DIRECT NUMERICAL SIMULATION OF TURBULENT HEAT TRANSFER IN A WALL-NORMAL ROTATING CHANNEL FLOW

Direct Nmerical Simulation （DNS） of turbulent heat transfer in a wall-normal rotating channel flow has been carried out for the rotation number Nr from 0 to 0.1, the Reynolds number 194 based on the friction velocity of non ro taring case and the half-height of the channel, and the Prandtl number 1. The objective of this study is to reveal the effects of rotation on the characteristics of turbulent flow and heat transfer. Based on the present calculated results, two typical rotation regimes are identified. When 0 〈 Nr 〈 0.06, turbu lence and thermal statistics correlated with the spanwise veloc ity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. When Nr 〉 0.06, turbulence and thermal statistics are suppressed significantly because the Coriolis force effect plays as a dominated role in the rotating flow. Remarkable change of the direction of near wall streak structures based on the velocity and temperature fluctuations is identified.

Unified stability condition for particulate and aggregative fluidization—Exploring energy dissipation with direct numerical simulation

Fully resolved simulations of particulate and aggregative fluidization systems are performed suc-cessfully with the so-called combined lattice Boltzmann method and time-driven hard-sphere model （LBM-TDHS）. In this method, the discrete particle phase is described by time-driven hard-sphere model, and the governing equations of the continuous fluid phase are solved with lattice Boltz-mann method. Particle-fluid coupling is implemented by immersed moving boundary method. Time averaged flow structure of the simulated results show the formation of core-annulus structure and sigmoid distribution of voidage in the axial direction, which are typical phenomena in fluidization systems. Combining the results of the simulation, the energy consumption Nst for suspending and transporting solids is calculated from the direct numerical simulation （DNS） of fluidization, and the stability criterion Nst/NT = rain proposed in EMMS/bubbling model is verified numerically. Further-more the numerical results show that the value of Nst/NT in particulate fiuidization is much higher than that in aggregative fluidization, but Nst/NT = rain is effective for both particulate and aggregative fluidization.

Gas–solid interaction force from direct numerical simulation (DNS) of binary systems with extreme diameter ratios

Fluid-particle systems as commonly encountered in chemical, metallurgical and petroleum industries are mostly polydisperse in nature. However, the relations used to describe fluid-particle interactions are originally derived from monodisperse systems, with ad hoc modifications to account for polydispersity. In previous work it was shown that for bidisperse systems with moderate diameter ratios of 1：2 to 1：4, this approach leads to discrepancies, and a correction factor is needed. In this work we demonstrate that this correction factor also holds for more extreme diameter ratios of 1：5, 1：7 and 1： 10, although the force on the large particles is slightly overestimated when using the correction factor. The main origin of the correction is that the void surrounding the large particles becomes less in case ofa bidisperse mixture, as compared to a monodisperse system with the same volume fraction. We further investigated this discrepancy by calculating the volume per particle by means of Voronoi tessellation.

Direct numerical simulation of hypersonic boundary layer transition over a liftingbody model HyTRV

Direct numerical simulation(DNS)of transition over a hypersonic lifting body model HyTRV developed by China Aerodynamics Research and Development Center is performed.The free-stream parameters are:the free-stream Mach number is 6,the unit Reynolds number is 10000/mm,the free-stream temperature is 79 K,the angle of attack is 0,and the wall temperature is 300 K.Weak random blowing-and-suction perturbations in the leading range are used to trigger the transition.A high order finite-difference code OpenCFD developed by the authors is used for the simulation,and grid convergence test shows that the transition locations are grid-convergence.DNS results show that transition occurs in central area of the lower surface and the concaved region of the upper surface,and the transition regions are also the streamline convergence regions.The transition mechanisms in different regions are investigated by using the spectrum and POD analysis.

Direct Numerical Simulation of the Pulsed Arc Discharge in Supersonic Compression Ramp Flow

Direct numerical simulation(DNS)of shock wave/turbulent boundary layer interaction(SWTBLI)with pulsed arc discharge is carried out in this paper.The subject in the study is a Ma=2.9 compression flow over a 24-degree ramp.The numerical approaches were validated by the experimental results in the same flow conditions.The heat source model was added to the Navier-Stokes equation to serve as the energy deposition of the pulsed arc discharge.Four streamwise locations are selected to apply energy deposition.The effect of the pulsed arc discharge on the ramp-induced flow separation has been studied in depth.The DNS results demonstrate the incentive locations play a dominant role in suppressing the separated flow.Results show that pulsed heating is characterized by a thermal blockage,which leads to streamwise deflection.The incentive locations upstream the interaction zone of the base flow have a better control effect.The separation bubble shape shows as"spikes",and the downstream flow of the heated region is accelerated due to the momentum exchange between the upper boundary layer and the bottom boundary layer.The high-speed upper fluid is transferred to the bottom,and thus enhances its ability to resist the flow separation.More stripe vortex structures are also generated at the edge of the flat-plate.Furthermore,the turbulent kinetic disturbance energy is increased in the flow filed.The disturbances that originate from the pulsed heating are capable of increasing the turbulent intensity and then diminishing the trend of flow separation.

Direct numerical simulation of particle-fluid systems by combining time-driven hard-sphere model and lattice Boltzmann method

A coupled numerical method for the direct numerical simulation of particle-fluid systems is formulated and implemented, resolving an order of magnitude smaller than particle size. The particle motion is described by the time-driven hard-sphere model, while the hydrodynamic equations governing fluid flow are solved by the lattice Boltzmann method （LBM）, Particle-fluid coupling is realized by an immersed boundary method （IBM）, which considers the effect of boundary on surrounding fluid as a restoring force added to the governing equations of the fluid. The proposed scheme is validated in the classical flow-around-cylinder simulations, and preliminary application of this scheme to fluidization is reported, demonstrating it to be a promising computational strategy for better understanding complex behavior in particle-fluid systems.