Two-dimensional Direct Numerical Simulations Research Articles

Spatial linear disturbances in a plane wall jet

A two-dimensional direct numerical simulation study of the linear instability in a laminar plane wall jet is presented. The evolution of the wall jet disturbances is in reasonable agreement with predictions by spatial linear stability theory only with regard to the wavelength and the amplitude shape of the disturbance, whereas significant differences in the linear growth rate are noticed. As a consequence, the “stable island” on the instability map based on linear stability theory turns out to be connected with the outer stable region in the simulations, thus taking the form of a “stable peninsula”. The failure of the theory is attributed to the rapid streamwise spread and decay of the wall jet, which is incompatible with the assumption of parallel flow. We also assess the maximum possible transient linear amplification of two-dimensional disturbances in the plane wall jet, using the concept of optimal initial disturbances. The transient energy growth relies on the Orr mechanism, and the upper bound of the disturbance energy increases linearly in time for the present flow configuration. The optimal disturbances exhibit local maxima near the edge of the jet and close to the wall, where sites of effective receptivity are hence expected. We find that the outer region of the plane wall jet is more receptive to time periodic forcing than the inner region.

An extended multi-regime flamelet model for IC engines

Modeling internal combustion engines is challenging due to the various coupled multi-physics phenomena. With the advent of modern supercomputing and advanced modeling techniques, studying and designing these engines through detailed simulations is becoming tractable. Since the combustion process is the primary controlling feature in these engines, a high fidelity combustion model is essential. This model must be efficient and valid across different combustion regimes, since modern engines might operate in hybrid modes. The Representative Interactive Flamelet (RIF) combustion model is a possible choice. This model has been developed to describe ignition, combustion, and pollutant formation in direct-injected diesel engines. However, it has recently been shown that the model has the correct asymptotic behavior for both diesel and Homogeneous Charge Compression Ignition (HCCI) regimes, and the model has been applied successfully for HCCI type combustion. In this study, the model is validated against two-dimensional direct numerical simulation data with multi-step finite rate chemistry to evaluate model performance in the diesel, the HCCI, and hybrid regimes. A wide range of temperature and mixture fraction stratification cases are simulated to evaluate the model performance across different modes. The model performs well for all cases considered, even when high levels of concurrent thermal and charge stratification are present.

S053014 速度欠損領域の不安定波によって励起した圧縮性混合層のDNS

The spatial development of vortices in a subsonic mixing layer which have wake components is investigated numerically using two-dimensional direct numerical simulations (DNS). The mixing layer is formed by a thin flat plate and forced by normal velocity disturbances of various frequencies at the lower region of the flat plate trailing edge. The numerical results show that the growth of the disturbance induces the counter-rotating vortices in the wake like region of the mixing layer. It is found that the vortices caused by the disturbance of the frequency St=0.042 uppress development of the mixing layer. This frequency corresponds the dominant vortices period in the near downstream region of the trailing edge for non-disturbance case. This result suggests that the emission noise caused by vortex rollup or pairing in the mixing layer can be reduced by forcing with a disturbance at the lower region of the flat plate trailing edge.

Ghost Fluid法を用いた気液二相流での圧力波の伝播に関する二次元直接数値計算

Ghost Fluid法を用いた気液二相流での圧力波の伝播に関する二次元直接数値計算

Boundary-layer-separation-driven vortex shedding beneath internal solitary waves of depression

AbstractWe investigate global instability and vortex shedding in the separated laminar boundary layer beneath internal solitary waves (ISWs) of depression in a two-layer stratified fluid by performing high-resolution two-dimensional direct numerical simulations. The simulations were conducted with waves propagating over a flat bottom and shoaling over relatively mild $(S= 0. 05)$ and steep $(S= 0. 1)$ slopes. Over a flat bottom, the potential for vortex shedding is shown to be directly dependent on wave amplitude, for a particular stratification, owing to increase of the adverse pressure gradient ($\mathrm{d} P/ \mathrm{d} x\gt 0$ for leftward propagating waves) beneath the trailing edge of larger amplitude waves. The generated eddies can ascend from the bottom boundary to as high as 33 % of the total depth in two-dimensional simulations. Over sloping boundaries, global instability occurs beneath all waves as they steepen. For the slopes considered, vortex shedding begins before wave breaking and the vortices, shed from the bottom boundary, can reach the pycnocline, modifying the wave breaking mechanism. Combining the results over flat and sloping boundaries, a unified criterion for vortex shedding in arbitrary two-layer continuous stratifications is proposed, which depends on the momentum-thickness Reynolds number and the non-dimensionalized ISW-induced pressure gradient at the point of separation. The criterion is generalized to a form that may be readily computed from field data and compared to published laboratory experiments and field observations. During vortex shedding events, the bed shear stress, vertical velocity and near-bed Reynolds stress were elevated, in agreement with laboratory observations during re-suspension events, indicating that boundary layer instability is an important mechanism leading to sediment re-suspension.

Large eddy simulation subfilter modeling of soot-turbulence interactions

The small-scale interactions between turbulence, chemistry, and soot have a profound effect on the soot formation, growth, and destruction processes in turbulent reacting flows. In this work, the small-scale subfilter interactions between turbulence and soot are modeled using a presumed subfilter PDF for the statistical moments of the soot number density function. Due to a very large (infinite) Schmidt number, soot is confined to very thin structures. In addition, soot is formed initially from Polycyclic Aromatic Hydrocarbons, which exhibit a strong sensitivity to the local scalar dissipation rate in the flow field. These interactions of soot with the gas-phase chemistry, molecular transport, and turbulence result in very high spatial and temporal intermittency. Therefore, the soot subfilter PDF is presumed to be a pair of delta distributions with a sooting mode and a non-sooting mode. In addition to the mean values of the scalars, one additional parameter is needed to specify this distribution. The presumed soot subfilter PDF approach is evaluated a priori using a recent two-dimensional direct numerical simulation (DNS) database of soot evolution in a nonpremixed flame. The analysis shows that predictions of the soot intermittency as well as the soot source terms are improved with this presumed soot subfilter PDF approach compared to simply using the mean values of the soot scalars. Several choices for specifying the additional parameter of the PDF are also evaluated with the database. The results show that the parameter is best specified using the second moment of the soot number density. In addition, the transport equation for the second moment of the number density is briefly discussed. A model for the lone unclosed term is proposed and evaluated with the DNS data.

Effects of fuel droplet size on soot formation in spray flames formed in a laminar counterflow

The effects of fuel droplet size on soot formation in spray flames formed in a laminar counterflow are investigated experimentally and numerically. Sauter mean diameter (SMD) of quasi-monodispersed fuel spray ( n-decane) is carefully controlled independently from the other spray characteristics using a frequency-tunable vibratory orifice atomizer, and the two-dimensional spatial distributions of soot volume fraction and soot particle size are measured by laser induced incandescence (LII) and time resolved LII (TIRE-LII), respectively. In addition, the soot formation processes are examined in detail by a two-dimensional direct numerical simulation (DNS) employing a kinetically based soot model with flamelet model. The results show that the soot formation area and location are strongly affected by the SMD of the fuel spray. As the SMD of the fuel spray increases, the average soot formation area expands, whereas local suppression of soot formation is instantaneously observed in the spray flames because of the appearance of groups of unburned droplets. The size of soot particles tend to be larger in the outer part of the soot formation area compared to soot in the inner part. This is because the surface growth of soot particles markedly proceeds compared to the coagulation and oxidation.

A test of time-dependent theories of stellar convection

Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf's formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes.

Global linear and nonlinear stability of viscous confined plane wakes with co-flow

The global stability of confined uniform density wakes is studied numerically, using two-dimensional linear global modes and nonlinear direct numerical simulations. The wake inflow velocity is varied between different amounts of co-flow (base bleed). In accordance with previous studies, we find that the frequencies of both the most unstable linear and the saturated nonlinear global mode increase with confinement. For wake Reynolds number Re = 100 we find the confinement to be stabilising, decreasing the growth rate of the linear and the saturation amplitude of the nonlinear modes. The dampening effect is connected to the streamwise development of the base flow, and decreases for more parallel flows at higher Re. The linear analysis reveals that the critical wake velocities are almost identical for unconfined and confined wakes at Re ≈ 400. Further, the results are compared with literature data for an inviscid parallel wake. The confined wake is found to be more stable than its inviscid counterpart, whereas the unconfined wake is more unstable than the inviscid wake. The main reason for both is the base flow development. A detailed comparison of the linear and nonlinear results reveals that the most unstable linear global mode gives in all cases an excellent prediction of the initial nonlinear behaviour and therefore the stability boundary. However, the nonlinear saturated state is different, mainly for higher Re. For Re = 100, the saturated frequency differs less than 5% from the linear frequency, and trends regarding confinement observed in the linear analysis are confirmed.

Global linear and nonlinear stability of viscous confined plane wakes with co-flow

The global stability of confined uniform density wakes is studied numerically, using two-dimensional linear global modes and nonlinear direct numerical simulations. The wake inflow velocity is varied between different amounts of co-flow (base bleed). In accordance with previous studies, we find that the frequencies of both the most unstable linear and the saturated nonlinear global mode increase with confinement. For wake Reynolds numberRe= 100 we find the confinement to be stabilising, decreasing the growth rate of the linear and the saturation amplitude of the nonlinear modes. The dampening effect is connected to the streamwise development of the base flow, and decreases for more parallel flows at higherRe. The linear analysis reveals that the critical wake velocities are almost identical for unconfined and confined wakes atRe≈ 400. Further, the results are compared with literature data for an inviscid parallel wake. The confined wake is found to be more stable than its inviscid counterpart, whereas the unconfined wake is more unstable than the inviscid wake. The main reason for both is the base flow development. A detailed comparison of the linear and nonlinear results reveals that the most unstable linear global mode gives in all cases an excellent prediction of the initial nonlinear behaviour and therefore the stability boundary. However, the nonlinear saturated state is different, mainly for higherRe. ForRe= 100, the saturated frequency differs less than 5% from the linear frequency, and trends regarding confinement observed in the linear analysis are confirmed.

Direct numerical simulations of ignition of a lean n-heptane/air mixture with temperature inhomogeneities at constant volume: Parametric study

The effect of thermal stratification on the ignition of a lean homogeneous n-heptane/air mixture at constant volume and high pressure is investigated by direct numerical simulations (DNS) with a new 58-species reduced kinetic mechanism developed for very lean mixtures from the detailed LLNL mechanism (H.J. Curran et al., Combust. Flame 129 (2002) 253–280). Two-dimensional DNS are performed in a fixed volume with a two-dimensional isotropic velocity spectrum and temperature fluctuations superimposed on the initial scalar fields. The influence of variations in the initial temperature field, imposed by changing the mean and variance of temperature, and the ratio of turbulence to ignition delay timescale on multi-stage ignition of a lean n-heptane/air mixture is studied. In general, the mean heat release rate increases more slowly with increasing thermal stratification regardless of the mean initial temperature. Ignition delay decreases with increasing thermal stratification for high mean initial temperature relative to the negative temperature coefficient (NTC) regime. It is, however, increased with increasing thermal fluctuations for relatively low mean initial temperature resulting from a longer overall ignition delay of the mixture. Displacement speed and Damköhler number analyses reveal that the high degree of thermal stratification induces deflagration rather than spontaneous ignition at the reaction fronts, and hence, the mean heat release rate is smoother subsequent to thermal runaway occurring at the highest temperature regions in the domain. Chemical explosive mode analysis (CEMA) also verifies that mixing counterbalances chemical explosion at the reaction fronts for cases with large temperature fluctuation. It is also found that if the ratio of turbulence to ignition delay timescale is short, resultant diminished scalar fluctuations cause the overall ignition to occur by spontaneous ignition. However, the overall effect of turbulence is small compared to the effect of thermal stratification. These results suggest that the critical degree of thermal stratification for smooth operation of homogeneous charge compression-ignition (HCCI) engines depends on both the mean and fluctuations in initial temperature which should be considered in controlling ignition timing and preventing an overly rapid increase in pressure in HCCI combustion.

Numerical simulations of premixed flame cellular instability for a simple chain-branching model

Two-dimensional direct numerical simulations are performed to investigate the non-linear dynamics of low Lewis number premixed flames, in the context of a two-step chain-branching chemistry model. This consists of a thermally-neutral, but temperature sensitive, chain-branching step which produces intermediates such as radicals and an exothermic, zero activation energy chain-completion step which converts the intermediates into products. Emphasis is on examining the role of intermediates in the flame structure on the cellular instability and in comparing and contrasting with previous one-step chemistry model solutions. When intermediates are present only in small concentrations in the underlying one-dimensional flame structure, the two-step cellular dynamics are qualitatively similar to those of the one-step model, including cell-splitting and re-merging, symmetry breaking bifurcations and formation of asymmetric cells, localized quenching of the flame front and a significant enhancement of the flame speed. However, a higher peak value of the intermediates concentration, corresponding to a more distributed heat release, is shown to have a significant stabilizing effect, e.g., in a domain of fixed transverse size, the fully developed cellular structure and flame speed remain closer to those of the one-dimensional flame.

Numerical Analysis of Intermediate Species Diffusion Effect on Low Temperature Oxidation in a Homogeneous n-Heptane Mixture

Two-dimensional direct numerical simulation (DNS) was applied to auto-ignition of n-heptane/air mixture. The diffusion of intermediate species was studied in terms of the influence on the ignition delay. The chemical reaction process. The simplified reaction mechanism was used in this study. Likewise, the influence of turbulence was investigated by comparing the results of 0 dimensional simulation and two-dimensional direct simulation of non-turbulence condition. In conclusions, the ignition delay was strongly affected by the different diffusion speeds of intermediate species. It was shown that the outflow of OH radical having larger diffusion coefficient decreases the reaction rate at the high temperature point. On the contrary, the reaction rate was enhanced by the influx of OH radical at the low temperature point.

Numerical Simulation of Flow over an Airfoil with a Cavity

Two-dimensional direct numerical simulation of the flow over a NACA0018 airfoil with a cavity is presented. The low Reynolds number simulations are validated by means of flow visualizations carried out in a water channel. From the simulations, it follows that there are two main regimes of flow inside the cavity. Depending on the angle of attack, the first or the second shear-layer mode (Rossiter tone) is present. The global effect of the cavity on the flow around the airfoil is the generation of vortices that reduce flow separation downstream of the cavity. At high positive angles of attack, the flow separates in front of the cavity, and the separated flow interacts with the cavity, causing the generation of smaller-scale structures and a narrower wake compared with the case when no cavity is present. At certain angles of attack, the numerical results suggest the possibility of a higher lift-to-drag ratio for the airfoil with cavity compared with the airfoil without cavity.

Effects of burning on the development of 2D turbulence

We present the results of two-dimensional (2D) direct numerical simulations of a Boussinesq fluid in the presence of gravity. Our simulations compare the evolution of a burning interface between a denser fuel and less dense ashes to the evolution of a non-burning interface. Initially, a dense, cool fluid is placed over a light, hot fluid and the interface between the two fluids is perturbed. Because of the presence of gravity, the system is Rayleigh–Taylor unstable, and the two fluids mix. We compare this Rayleigh–Taylor mixing problem to that in the same setup but with premixed combustion occurring at the interface between the two fluids. In both cases, the boundary conditions are periodic in the horizontal direction. As the force of gravity is increased, the flow behind the flame transitions from an ordered, laminar state to a chaotic, turbulent state. Our simulations explore the effect of burning on the development of the turbulent state, especially the effect of burning on the energy and enstrophy cascades, the mixing of the temperature fields and the shape of the flame front.

Three-dimensional numerical simulation of stably stratified flows over a two-dimensional hill: effect of stratification on the non-periodic separation and reattachment of the flow

Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows on to our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill; slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.

Shallow-water analysis of gravity-current flows past isolated obstacles

The flow of a partial-depth lock-exchange gravity current past an isolated bottom-mounted obstacle is studied by means of two-dimensional direct numerical simulations and steady shallow-water theory. The simulations indicate that the flux of the current downstream of the obstacle is approximately constant in space and time. This information is employed to extend the shallow-water models of Rottman et al. (J. Hazard. Mater., vol. 11, 1985, pp. 325–340) and Lane-Serff, Beal & Hadfield (J. Fluid Mech., vol. 292, 1995, pp. 39–53), in order to predict the height and front speed of the downstream current as functions of the upstream Froude number and the ratio of obstacle to current height. The model predictions are found to agree closely with the simulation results. In addition, the shallow-water model provides an estimate for the maximum drag that lies within 10% of the simulation results for obstacles much larger than the boundary-layer thickness.

Dynamics of passive scalars and tracers advected by a two-dimensional tripolar vortex

The dynamics of passive scalars and tracers during the formation and subsequent persistence of a laminar tripolar vortex, obtained through an unstable monopolar vortex seeded with a k = 2 azimuthal perturbation, is investigated. Two-dimensional direct numerical simulations of passive scalars with Schmidt numbers Sc = 0.1, 1, 10 and 100 are performed. The scalar variance for the four cases is analysed, as well as the different dispersion patterns up to 10 times greater than the time for formation of the tripolar vortex. During the formation of the tripole, an accelerated scalar dissipation is observed. That dissipation is connected to the advection-dominated processes associated with the growth of the perturbation mode. During that process, the patterns of mixing of the different passive scalars are very much the same as for vorticity. This stage of accelerated dissipation is preceded and followed by stages of diffusion-dominated scalar dissipation. Passive Lagrangian tracers are used to explore the transport of fluid elements during the evolution, and to provide a detailed view of the tripolar vortex formation and behaviour for longer times. Chaotic mixing was studied by examining patterns of spatial variation of finite-time Lyapunov exponents. As the perturbation grows and the tripolar vortex is formed, two large regions of regular flow, divided by a region of chaotic flow, form for each satellite. When the tripole is fully formed, it is composed of three distinct regular regions, corresponding to the core of negative vorticity and the two satellites of positive vorticity. The comparison between the evolution for vorticity, concentration, randomly distributed particles and Lyapunov exponents shows that transport occurs mainly in the regions of chaotic flow that surround the tripolar vortex after its formation. For longer times, both the chaotic/regular flow interfaces and the vorticity gradients are responsible for the integrity of the tripolar system.

Unsteady PTV velocity field past an airfoil solved with DNS: Part 2. Validation and application at Reynolds numbers up to Re ≤ 104

Hybrid unsteady-flow simulation combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) is introduced in the series of two papers. Particle velocities on a laser-light sheet acquired with time-resolved PTV in a water tunnel are supplied to two-dimensional DNS with time intervals corresponding to the frame rate of the PTV. Hybrid velocity fields then approach those representing the PTV data in the course of time, and the reconstructed velocity fields satisfy the governing equations with the resolution comparable to numerical simulation. In part 2, by extending the capabilities of the hybrid simulation to higher Reynolds numbers, we simulate flows past the NACA0012 airfoil over ranges of Reynolds numbers (Re ≤ 104) and angles of attack (−5° ≤ α ≤ 20°) and validate the proposed technique by comparing with experimental results in terms of the lift and drag coefficients. We also compare the results with unsteady Reynolds-averaged Navier–Stokes (URANS) simulation in two-dimensions and show the advantages of the hybrid simulation against two-dimensional URANS.

Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. Algorithm of hybrid simulation and hybrid velocity field at Re ≈ 103

We develop a hybrid unsteady-flow simulation technique combining direct numerical simulation (DNS) and particle tracking velocimetry (PTV) and demonstrate its capabilities by investigating flows past an airfoil. We rectify instantaneous PTV velocity fields in a least-squares sense so that they satisfy the equation of continuity, and feed them to the DNS by equating the computational time step with the frame rate of the time-resolved PTV system. As a result, we can reconstruct unsteady velocity fields that satisfy the governing equations based on experimental data, with the resolution comparable to numerical simulation. In addition, unsteady pressure distribution can be solved simultaneously. In this study, particle velocities are acquired on a laser-light sheet in a water tunnel, and unsteady flow fields are reconstructed with the hybrid algorithm solving the incompressible Navier–Stokes equations in two dimensions. By performing the hybrid simulation, we investigate nominally two-dimensional flows past the NACA0012 airfoil at low Reynolds numbers. In part 1, we introduce the algorithm of the proposed technique and discuss the characteristics of hybrid velocity fields. In particular, we focus on a vortex shedding phenomenon under a deep stall condition (α = 15°) at Reynolds numbers of Re = 1000 and 1300, and compare the hybrid velocity fields with those computed with two-dimensional DNS. In part 2, the extension to higher Reynolds numbers is considered. The accuracy of the hybrid simulation is evaluated by comparing with independent experimental results at various angles of attack and Reynolds numbers up to Re = 104. The capabilities of the hybrid simulation are also compared with two-dimensional unsteady Reynolds-Averaged Navier–Stokes (URANS) solutions in part 2. In the first part of these twin papers, we demonstrate that the hybrid velocity field approaches the PTV velocity field over time. We find that intensive alternate vortex shedding past the airfoil, which is predicted by the two-dimensional DNS, is substantially suppressed in the hybrid simulation and the resultant flow field is similar to the PTV velocity field, which is projection of the three-dimensional velocity field on the streamwise plane. We attempt to identify the motion that originates three-dimensional flow patterns by highlighting the deviation of the PTV velocity field from the two-dimensional governing equations at each snapshot. The results indicate that the intensive spots of the deviation appear in the regions in which three-dimensional instabilities are induced in the shear layer separated from the pressure side.