Three-dimensional Direct Numerical Simulations Research Articles

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Pressure effects on flame structures and chemical pathways for lean premixed turbulent H2/air flames: Three-dimensional DNS studies

This paper presents three-dimensional direct numerical simulations of lean premixed turbulent H2/air flames over a range of pressures using a detailed chemical mechanism. Effects of pressure on flame front structures and heat release from pressure-dependent pathways are analysed. Under the same initial turbulence at different pressures, the Kolmogorov length scale and local flame thickness decrease with increasing pressure. Thinner and sharper structures are found on the flame front at elevated pressures. As the pressure is increased from 1 atm to 5 atm, heat release is greatly enhanced at convex regions but weakened at concave regions of the flame fronts, which indicates that the effect of Darrieus-Landau instability is becoming stronger. The correlation of heat release and fuel consumption is also strengthened as pressure is elevated. A main pressure-dependent heat release reaction, H + O2(+M) = HO2(+M), is found to contribute less to the total heat release with increasing pressure for turbulent flames, which is contrary to the trend in laminar flames. In the low temperature zones, this is due to the decreased H radical pool at elevated pressure. In the high temperature regions, the reaction is less competitive compared with H + OH+M = H2O+M, thereby reducing its contribution to the heat release.

Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads.

We propose a square cross-section microfluidic channel with an orthogonal side branch (asymmetric T-shaped bifurcation) for the separation of elastic capsules and soft beads suspended in a Newtonian liquid on the basis of their mechanical properties. The design is performed through three-dimensional direct numerical simulations. When suspended objects start near the inflow channel centerline and the carrier fluid is equally partitioned between the two outflow branches, particle separation can be achieved based on their deformability, with the stiffer ones going "straight" and the softer ones being deviated to the "side" branch. The effects of the geometrical and physical parameters of the system on the phenomenon are investigated. Since cell deformability can be significantly modified by pathology, we give a proof of concept on the possibility of separating diseased cells from healthy ones, thus leading to illness diagnosis.

Strouhal–Reynolds number relationship for flow past a circular cylinder

The Strouhal–Reynolds number ($St{-}Re$) relationship for flow past a circular cylinder in the low $Re$ range of $Re\leqslant 1000$ is investigated through two- (2D) and three-dimensional (3D) direct numerical simulations (DNS). An improved method is proposed for the determination of the separating velocity and the wake width to allow for a better estimation of the wake Strouhal number $St^{\ast }$. For $Re$ in the extended laminar regime calculated by 2D DNS, the $St^{\ast }$ values are found to be more uniform than the original $St$ for the 2D flow. It is also found that the $St^{\ast }$ values for the 2D and 3D flows agree well in the laminar regime of $Re$ up to approximately 270. In addition, uniform $St^{\ast }$ values are also obtained for different mode A and mode B flow structures triggered artificially by using different cylinder span lengths in DNS. It is demonstrated that the drop in $St$ (with respect to its 2D counterpart) with the development of different 3D wake structures is due to the decrease in the separating velocity and the increase in the wake width for a 3D flow, rather than the existence of a particular wake structure such as pure mode A or vortex dislocation. However, as the wake flow becomes increasingly turbulent with further increase in $Re$, the $St^{\ast }$ value for the 3D flow increases gradually and deviates from its 2D counterpart, since for turbulent 3D flows the vortex shedding frequency scales on a length smaller than the wake width.

Characterization of transition from Darcy to non-Darcy flow with 3D pore-level simulations

We characterize seepage flow in porous media via a series of three-dimensional (3D) direct numerical simulations (DNSs) of Navier-Stokes flows in representative volume elements (RVEs) at the pore level. The immersed boundary method with a fixed staggered grid is employed for calculations based on the finite difference method in the pore domain formed with spatially arranged rigid particles in RVEs. The numerical results of the DNSs with different particle sizes and different seepage flow velocities are volume-averaged over the RVEs to evaluate the permeability coefficients of the seepage flows and are ordered according to the Reynolds numbers for porous media. After the numerical scheme is validated with a simple RVE model, the transition from Darcy to non-Darcy flow, for which experimental results have reported in the literature, is demonstrated in terms of the calculated permeability coefficients and examined based on the pore-level flow characteristics to clarify the mechanism of the permeability change, i.e. the macroscopic behaviour of RVEs related to the Reynolds number.

Direct numerical simulation of turbulent channel-flow catalytic combustion: Effects of Reynolds number and catalytic reactivity

Three-dimensional direct numerical simulations of fuel-lean (equivalence ratio ϕ=0.24) hydrogen/air turbulent catalytic combustion were carried out in a platinum-coated planar channel with isothermal walls and an incoming fully-developed turbulent flow, at two inlet bulk Reynolds numbers (ReH=5700 and 12,360 based on the channel height H) and four global catalytic reaction rates. The turbulent flow laminarization due to heat transfer from the hot catalytic walls was appreciable, with turbulent intensities dropping by 37% and 25% at the channel outlet for the low and high ReH, respectively. The ratio of the local average turbulent hydrogen conversion rate to the corresponding local laminar conversion rate (〈s˙T〉/s˙L) was found to be a monotonically increasing function of streamwise distance, Reynolds number ReH, and catalytic reactivity. Despite the turbulent flow laminarization, 〈s˙T〉/s˙L ratios at the channel outlet reached values up to 170% for the highest ReH = 12,360 and for infinitely-fast catalytic chemistry. A correlation was further established for the ratio of the turbulent hydrogen conversion rate at finite-rate chemistry to the corresponding turbulent conversion rate at infinitely-fast chemistry. The instantaneous local catalytic reaction rates exhibited large fluctuations, which were up to 300% and 500% for the low and high ReH, respectively. Fourier analysis indicated that a diminishing catalytic reactivity acted as a low-pass frequency filter for the overlying fluctuations of the turbulent flow.

Floquet stability analysis in the wake of a NACA0015 airfoil at post-stall angles of attack

We perform a Floquet stability analysis in the wake of a NACA0015 airfoil, with four angles of attack, α=20°, 17.5°, 15°, and 12.5°, considered. The central aim is to predict the secondary instabilities at the fixed moderate angles of attack, which are sufficiently large for massive separation from the airfoil, while at the same time allowing the formation and travelling of surface vortex on the airfoil, differentiating from the cases with very large angles of attack. We divide the angles of attack into two groups. We report that mode C is the first unstable mode for both groups, and which is also the only unstable mode for the small angles of attack, i.e., α=15° and α=12.5°, while for the high angles of attack, i.e., α=20° and α=17.5°, four unstable modes are observed. They are mode A, mode quasi-periodic, mode SL, and mode SS. The modes SL and SS are both subharmonic but with different wave numbers. We conjecture that these two subharmonic modes are resulted from the splitting of mode C. A comparison in the base flow topologies between the two groups shows that the different instability behaviors are probably due to their different flow patterns of the base flows. Three-dimensional direct numerical simulations (DNSs) have also been employed to study the physical realizability of the dominant unstable modes. A good consistency between the Floquet analysis and the 3D DNS results is achieved, indicating that the dominance of the linear instability is responsible for such a three-dimensional flow as the Reynolds number is not far from the critical value. Moreover, we find that the critical Reynolds numbers for the onset of three-dimensional instability fall into the range of 159.7–234.2 by defining this new Reynolds number according to the width of the flow wake. These values are very close to that of a bluff body. Furthermore, we note that the corresponding Strouhal numbers are around 0.17 for all the angles of attack, implying the relevance of three-dimensional instabilities to the wake dynamics or more specifically the fluctuation in the wake.

Direct Numerical Simulation Study on the Stabilization Mechanism of a Turbulent Lifted Pulverized Coal Jet Flame in a Heated Coflow

The stabilization mechanism of a turbulent lifted pulverized coal jet flame in a heated coflow is investigated by means of three-dimensional direct numerical simulation. The coal particles are tracked in the Lagrangian frame with experience of moisture evaporation, volatile releasing, and carbon combustion. The devolatilization process is modeled with a competing two-step model, and the carbon reaction is described by a single-film model. It is found that the mean velocities for the gas-phase and particles can develop into self-similar profiles, while the fluctuation velocities have not achieved the self-similar status. The turbulence can be enhanced by ignition and combustion processes. By investigating the correlations among the temperatures, heat release rate, and devolatilization rate, it is found that autoignition of the volatile is the key mechanism responsible for coal flame stabilization under the present condition. The heating effects from the stripe flames in the shear layers, heated coflow, and...

Three-dimensional numerical investigation and modeling of binary alumina droplet collisions

The off-center collision of binary equal-sized alumina droplets has been investigated by employing a three-dimensional direct numerical simulation method which involves the volume of fluid (VOF) and adaptive mesh refinement method. The simulations of tetradecane droplet collision are carried out to validate the numerical method. The results show good agreement with experiments. The off-center collisions of alumina droplet with diameter 10μm are numerically investigated at various Weber numbers (30–400) and impact numbers (0.1–0.7). The Ohnesorge number is 0.1151. Four collision outcomes are obtained, coalescence after substantial deformation, reflexive separation, coalescence after long extension, and stretching separation, respectively. Bouncing is achieved by employing the double VOF functions method. In addition, as to the collision at various impact parameters, the critical Weber number of separation is obtained. And the collision regimes of alumina droplet are mapped out. Furthermore, alumina droplet collisions are modeled with the consideration of viscous dissipation, including the model of coalescence after minor deformation, bouncing model, reflexive separation model, stretching separation model, as well as the model for calculating the droplet parameters after separation. Bouncing model, reflexive separation model and stretching separation model are in good agreement with the present numerical results.

The K-type and H-type transitions of natural convection boundary layers

The K-type and H-type transitions of a natural convection boundary layer of a fluid of Prandtl number 7 adjacent to an isothermally heated vertical surface are investigated by means of three-dimensional direct numerical simulation (DNS). These two types of transitions refer to different flow features at the transitional stage from laminar to turbulence caused by two different types of perturbations. To excite the K-type transition, superimposed Tollmien–Schlichting (TS) and oblique waves of the same frequency are introduced into the boundary layer. It is found that a three-layer longitudinal vortex structure is present in the boundary layer undergoing the K-type transition. The typical aligned $\wedge$-shaped vortices characterizing the K-type transition are observed for the first time in pure natural convection boundary layers. For exciting the H-type transition, superimposed TS and oblique waves of different frequencies, with the frequency of the oblique waves being half of the frequency of the TS waves, are introduced into the boundary layer. Unlike the three-layer longitudinal vortex structure observed in the K-type transition, a double-layer longitudinal vortex structure is observed in the boundary layer undergoing the H-type transition. The successively staggered $\wedge$-shaped vortices characterizing the H-type transition are also observed in the downstream boundary layer. The staggered pattern of $\wedge$-shaped vortices is considered to be caused by temporal modulation of the TS and oblique waves. Interestingly the flow structures of both the K-type and H-type transitions observed in the natural convection boundary layer are qualitatively similar to those observed in Blasius boundary layers. However, an analysis of turbulence energy production suggests that the turbulence energy production by buoyancy rather than Reynolds stresses dominates the K-type and H-type transitions. In contrast, the turbulence energy production by Reynolds stresses is the only factor contributing to the transition in Blasius boundary layers.

Two-stage autoignition and edge flames in a high pressure turbulent jet

A three-dimensional direct numerical simulation is conducted for a temporally evolving planar jet of n-heptane at a pressure of 40 atmospheres and in a coflow of air at 1100 K. At these conditions, n-heptane exhibits a two-stage ignition due to low- and high-temperature chemistry, which is reproduced by the global chemical model used in this study. The results show that ignition occurs in several overlapping stages and multiple modes of combustion are present. Low-temperature chemistry precedes the formation of multiple spatially localised high-temperature chemistry autoignition events, referred to as ‘kernels’. These kernels form within the shear layer and core of the jet at compositions with short homogeneous ignition delay times and in locations experiencing low scalar dissipation rates. An analysis of the kernel histories shows that the ignition delay time is correlated with the mixing rate history and that the ignition kernels tend to form in vortically dominated regions of the domain, as corroborated by an analysis of the topology of the velocity gradient tensor. Once ignited, the kernels grow rapidly and establish edge flames where they envelop the stoichiometric isosurface. A combination of kernel formation (autoignition) and the growth of existing burning surface (via edge-flame propagation) contributes to the overall ignition process. An analysis of propagation speeds evaluated on the burning surface suggests that although the edge-flame speed is promoted by the autoignitive conditions due to an increase in the local laminar flame speed, edge-flame propagation of existing burning surfaces (triggered initially by isolated autoignition kernels) is the dominant ignition mode in the present configuration.

Transition scenario and transition control of the flow over a semi-infinite square leading-edge plate

In recent investigations of the flow over a square leading-edge flat plate, elliptic instability and transient growth of perturbations are proposed to explain the turbulent transition mechanism of the separating and reattaching flow reported in early experimental visualizations. An original transition scenario as well as a transition control method is presented by a detailed numerical study in this paper. The transient growth of perturbations in the separation bubble induces the primary instability that causes the 2D unsteady flow consisting of Kelvin-Helmholtz (KH) vortices. The pairing instability of the KH vortices induces the subharmonic secondary instability, and then resonance transition occurs. The streamwise Lorentz force as the control input is applied in the recirculation region where the separation bubble generates. The maximum energy amplification magnitude of perturbations takes a linear attenuation with the interaction number; thus, the primary instability is reduced under control. The interaction number represents the strength of the streamwise Lorentz force relative to the inertial force of the fluid. The reduced primary instability is not strong enough to induce the secondary instability, so the flow is globally stable under control. Three-dimensional direct numerical simulation confirms the results of the linear stability analysis. Although the growth rate of the convectively unstable secondary instability is limited by the flow field scale, the feedback loop of the energy transfer promotes the resonance transition. However, as the separation bubble scale is reduced and the feedback loop is broken by the streamwise Lorentz force, the three-dimensional transition is suppressed and a skin-friction drag reduction is achieved.

Direct numerical simulation of near nozzle diesel jet evolution with full temporal-spatial turbulence inlet profile

Fuel atomization which begins with turbulence perturbation has a significant influence on engine performance. The effect of turbulence on near nozzle field characteristics under various liquid-gas density ratios is performed in present models. First, using three-dimensional DNS (3-D Direct Numerical Simulation) method, a time-varying single-phase fully developed turbulent pipe flow is generated to store time-varying outlet velocity databases which are then mapped as the two-phase jet inlet velocities. After that, the characteristics of near nozzle diesel jet evolution are studied by solving the two-phase turbulent flows and tracking the two-phase interfaces based on DNS and VOF (Volume of Fluid) methods. It shows that with fully developed turbulent inject velocities, the topology of the jet evolves gradually from violent wavy surface, ligaments, to droplet parcels with different dimensions and shapes, which are considered more realistic and different from uniform/sinusoidal perturbation inject velocities, especially in the near nozzle field. Jets surface distortion, stretched and sheared interface are captured. Three different separation processes in different downstream positions are detected. In the initial stage of the jet, long and narrow ligaments act as primary breakup. In the later stage, the whole breakup process evolves more disorderly and more intensively, so that flat and curly ligaments are observed. Also, higher gas densities and narrower nozzle sizes can accelerate the jet break-up process. Furthermore, the present work is reasonably compared with experimental and numerical modeling results.

Effect of Torsion on the Friction Factor of Helical Pipe Flow

Three-dimensional direct numerical simulations of a viscous incompressible fluid flow through a helical pipe with a circular cross section were conducted for three Reynolds numbers, Re (= 80, 300, and 1000), and two nondimensional curvatures, δ (= 0.1 and 0.05), over a wide range of torsion parameters, β (= nondimensional torsion/\(\sqrt{2\delta } \)), from 0.02 to 2.8. Well-developed axially invariant regions were obtained where the friction factors were calculated, in good agreement with the experimental data obtained by Yamamoto et al. [Fluid Dyn. Res. 16, 237 (1995)]. It was found that the friction factor sharply increases as β increases from zero, then decreases after taking a maximum, and finally slowly approaches that of a straight pipe when β tends to infinity. It is interesting that a peak of the friction factor exists in the region 0.2 ≤ β ≤ 0.3 for all the Reynolds numbers and curvatures studied in the present paper, which manifests the importance of the torsion parameter in helical pipe flow.

Laminar forced convective heat transfer in helical pipe flow

Laminar forced convective heat transfer in a helical pipe with circular cross section subjected to wall heating was investigated numerically by three-dimensional (3D) direct numerical simulations (DNS) comparing with the experimental data obtained by Shatat (2010). The study was performed for three Prandtl numbers, Pr = 8.5, 7.5 and 4.02, over the wide range of torsion. In 3D steady calculations, we found the appearance of fully-developed axially invariant flow regions, where the averaged Nusselt number (averaged over the peripheral of the pipe cross section) were calculated, being in good agreement with the experimental data. Because of the effect of torsion on the heat transfer characteristics, the averaged Nusselt number exhibits repetition of decrease and increases as torsion increases from zero for all Reynolds numbers. It was found that there exists two maximums and two minimums of the averaged Nusselt number. It is interesting that the global minimum of the Nusselt number occurs at β≅0.1 and the global maximum at β≅0.55.

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence.

A three-dimensional (3D) direct numerical simulation (DNS) study of the propagation of a reaction wave in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is performed by solving Navier-Stokes and reaction-diffusion equations at various (from 0.5 to 10) ratios of the rms turbulent velocity U^{'} to the laminar wave speed, various (from 2.1 to 12.5) ratios of an integral length scale of the turbulence to the laminar wave thickness, and two Zeldovich numbers Ze=6.0 and 17.1. Accordingly, the Damköhler and Karlovitz numbers are varied from 0.2 to 25.1 and from 0.4 to 36.2, respectively. Contrary to an earlier DNS study of self-propagation of an infinitely thin front in statistically the same turbulence, the bending of dependencies of the mean wave speed on U^{'} is simulated in the case of a nonzero thickness of the local reaction wave. The bending effect is argued to be controlled by inefficiency of the smallest scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles are rapidly smoothed out by molecular transport within the local reaction wave.

On the energization of charged particles by fast magnetic reconnection

We study the role of turbulence in magnetic reconnection, within the framework of magneto-hydrodynamics, using three-dimensional direct numerical simulations. For small turbulent intensity we find that the reconnection rate obeys Sweet-Parker scaling. For large enough turbulent intensity reconnection rate departs significantly from Sweet-Parker behaviour, becomes almost a constant as a function of the Lundquist number. We further study energisation of test-particles in the same setup. We find that the speed of the energised particles obeys a Maxwellian distribution, whose variance also obeys Sweet-Parker scaling for small turbulent intensity but depends weakly on the Lundquist number for large turbulent intensity. Furthermore, the variance is found to increase with the strength of the reconnecting magnetic field.

Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model.

The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.

Disturbance Development in an Obstacle Wake in a Reacting Hypersonic Boundary Layer

The presented work is a continuation of the investigation of the influence of an isolated roughness on the laminar-turbulent transition for hypersonic boundary-layer flows. The first part of the investigation describing the steady flow around a cuboid obstacle as it was flown in the Hypersonic Boundary-Layer Transition experiment was described by Stemmer et al. [“Hypersonic Boundary-Layer Flow with an Obstacle in Thermochemical Equilibrium and Nonequilibrium,” Journal of Spacecraft and Rockets (in print)]. In the second part, stability investigations reveal odd and even instability modes being unstable in the wake. Direct numerical simulations are used to investigate the disturbance development of high-frequency velocity disturbances. The unsteady, fully three-dimensional direct numerical simulations under consideration of chemical equilibrium and nonequilibrium effects shed light on the role of the chemical models on the disturbance development. The chemical equilibrium case shows less damping of the disturbances in the integration domain compared to the perfect gas case. For the chemical nonequilibrium simulations, the disturbances are initially damped but experience amplification further downstream. Detailed investigations of the disturbance development in the wake flow are presented. The current results underline the necessity of the consideration of chemical nonequilibrium effects in direct numerical simulations of high-temperature boundary-layer transition from laminar to turbulent, even for moderate temperature and dissociation levels.

Dual Fuel Combustion of N-heptane/methanol-air-EGR Mixtures

Numerical simulations are performed to study the combustion processes of n-heptane and methanol/air/EGR under high-temperature and high-pressure conditions relevant to a dual-fuel compression-ignition engine. Detailed chemical kinetic mechanism and transport properties are considered in the simulation. The simulations are carried out by performing three-dimensional (3D) direct numerical simulation (DNS) in a cuboid constant volume enclosure and two-dimensional (2D) DNS in a constant volume domain corresponding to the 3D domain. The results reveal three combustion modes involved in dual fuel engines, the ignition of the n-heptane jet, the propagation of thin reaction fronts in the methanol/air/EGR mixture, and finally the onset of ignition of the entire mixture. In dual-fuel combustion under high initial temperature conditions (1000K or higher) the three different combustion modes occur rather quickly with two distinct peaks of heat release corresponding to the two ignition modes. At low temperatures (800K or lower) the ignition delay time of the mixture is longer and more complete mixing is achieved before the onset of a single ignition of the n-heptane/methanol mixture.