Two-dimensional Direct Numerical Simulations Research Articles

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.

Numerical investigation of spontaneous flame propagation under RCCI conditions

This paper presents results from one and two-dimensional direct numerical simulations under Reactivity Controlled Compression Ignition (RCCI) conditions of a primary reference fuel (PRF) mixture consisting of n-heptane and iso-octane. RCCI uses in-cylinder blending of two fuels with different autoignition characteristics to control combustion phasing and the rate of heat release. These simulations employ an improved model of compression heating through mass source/sink terms developed in a previous work by Bhagatwala et al. (2014), which incorporates feedback from the flow to follow a predetermined experimental pressure trace. Two-dimensional simulations explored parametric variations with respect to temperature stratification, pressure profiles and n-heptane concentration. Statistics derived from analysis of diffusion/reaction balances locally normal to the flame surface were used to elucidate combustion characteristics for the different cases. Both deflagration and spontaneous ignition fronts were observed to co-exist, however it was found that higher n-heptane concentration provided a greater degree of flame propagation, whereas lower n-heptane concentration (higher fraction of iso-octane) resulted in more spontaneous ignition fronts. A significant finding was that simulations initialized with a uniform initial temperature and a stratified n-heptane concentration field, resulted in a large fraction of combustion occurring through flame propagation. It was also found that the proportion of spontaneous ignition fronts increased at higher pressures due to shorter ignition delay when other factors were held constant. For the same pressure and fuel concentration, the contribution of flame propagation to the overall combustion was found to depend on the level of thermal stratification, with higher initial temperature gradients resulting in more deflagration and lower gradients generating more ignition fronts. Statistics of ignition delay are computed to assess the Zel’dovich (1980) theory for the mode of combustion propagation based on ignition delay gradients.

Impact of Forward-Facing Steps on Laminar-Turbulent Transition in Transonic Flows

The influence of forward-facing steps on the amplification of disturbances in transonic flows is studied numerically. The main goal is to find a function for an additional amplification factor that can be incorporated into the method. In the present study, both two-dimensional direct numerical simulation of disturbances as well as linear stability theory are used to gain detailed information on the flow. Good agreement between -factor results from direct numerical simulation and linear stability theory is obtained. Subsonic and slightly supersonic results show differences in the flow topology and in the shape of the -factor curve, but effective factors are in the same order of magnitude.

Dynamics of bluff-body-stabilized premixed hydrogen/air flames in a narrow channel

Two-dimensional direct numerical simulations were conducted for bluff-body stabilized flames of a lean hydrogen/air mixture at near-blowoff conditions in a meso-scale channel. Parametric simulations were conducted by incrementally varying the inflow velocity in the vicinity of the blowoff limit, and the corresponding flame response was monitored. The present study is a showcase of combustion DNS with embedded boundary representation, and full demonstration of the detailed visualization of the near-blowoff flame characteristics. As the inflow velocity approaches blowoff limit, the flame dynamics exhibit a complex sequence of events, such as periodic local extinction and recovery, and regrowth of the bulk flame by the flame segments attached behind the bluff-body. The total extinction is observed as the attached flames shrink down and are no longer able to regrow the bulk flames. Despite the disparity in the physical scale under study, the observed sequence of the extinction pathway shows a strong similarity with experimental observations at larger scale combustion systems.

Numerical Benchmark for High-Reynolds-Number Supercritical Flows with Large Density Gradients

Because of the extreme complexity of physical phenomena at high pressure, only limited data are available for solver validation at device-relevant conditions such as liquid rocket engines, gas turbines, or diesel engines. In the present study, a two-dimensional direct numerical simulation is used to establish a benchmark for supercritical flow at a high Reynolds number and high-density ratio at conditions typically encountered in liquid rocket engines. Emphasis has been placed on maintaining the flow characteristics of actual systems with simple boundary conditions, grid spacing, and geometry. Results from two different state-of-the-art codes, with markedly different numerical formalisms, are compared using this benchmark. The strong similarity between the two numerical predictions lends confidence to the physical accuracy of the results. The established database can be used for solver benchmarking and model development at conditions relevant to many propulsion and power systems.

Two-dimensional direct numerical simulation of bubble cloud cavitation by front-tracking method

Unsteady bubble cloud cavitation phenomenon caused by negative pressure pulse has been treated numerically by applying a front tracking method. The behaviour of bubble cloud expanding and contracting is evaluated by tracking the motion of all bubble interfaces. Numerical investigation demonstrates that: (1) In the collapsing of bubble cloud micro liquid jets toward the inner bubbles are formed while the outer layer bubbles contract extremely, and then a high impact pressure is released when the inner central bubble contacts to its minimum. (2) The oscillation of bubble cloud depends upon the void fraction greatly. In the case of high void fraction, the frequency of cloud oscillation is lower than that of individual bubble and the decay of the oscillation becomes much slowly also.

Numerical simulation of flow dynamics in the periodic regime in an idealized thermoacoustic engine

Flow dynamics in the stack and heat exchangers of a standing wave thermoacoustic engine is studied using two-dimensional direct numerical simulations. The numerical approach is based on asymptotic coupling in the low Mach number limit of a nonlinear dynamic model in the active cell with linear acoustics in the resonator. Computed results of the initial amplification and of the periodic regime eventually reached are shown. For the former, results show the existence of a critical temperature for which the system becomes unstable so that the engine starts, which is strongly dependent upon the load. Analysis of the results in the periodic regime shows the importance of vortex dynamics and the role of vortex shedding at sharp heat exchanger corners.

Sediment Wave Formation Caused by Erosional and Depositional Turbidity Currents: A Numerical Investigation

Results are presented from two-dimensional direct numerical simulations of sediment wave formation via a succession of erosional and depositional turbidity currents. For currents propagating down a slope, we observe the formation of upstream migrating periodic sediment waves. The strength of the wave formation process is discussed as function of the governing dimensionless parameters.

Active control of vortex shedding: an explanation of the gain window.

This paper explains the gain window phenomenon seen in early experimental and computational studies on active, closed-loop control of vortex shedding, whereby shedding is completely suppressed only if the feedback gain lies within some narrow window of stabilizing gains. Using two-dimensional direct numerical simulations and reduced-order modeling techniques, a low-order, linear model of the cylinder wake is formed at a Reynolds number of 60. This model is used to reproduce and to explain the gain window seen in previous studies. It is shown that the gain window is not caused by the destabilization of a higher mode but rather is determined entirely by the behavior of the open-loop unstable mode under the action of the closed-loop controller. It is demonstrated that the time taken for actuated fluid to convect to the sensor location plays an important part in explaining this gain window. A similar analysis at a higher Reynolds number of 80 reveals that the wake remains unstable for all choices of the feedback gain. The study illustrates the limitations of closed-loop suppression of vortex shedding when a very simple control strategy is used.

A DNS study of the ignition of lean PRF/air mixtures with temperature inhomogeneities under high pressure and intermediate temperature

Two-dimensional direct numerical simulations (DNSs) of ignition of lean primary reference fuel (PRF)/air mixtures at high pressure and intermediate temperature near the negative temperature coefficient (NTC) regime were performed with a 116 species-reduced mechanism to elucidate the effects of fuel composition, thermal stratification, and turbulence on PRF homogeneous charge compression-ignition (HCCI) combustion. In the DNSs, temperature and velocity fluctuations are superimposed on the initial scalar fields with different PRF compositions. In general, it was found that the mean heat release rate increases slowly and the overall combustion occurs rapidly with increasing thermal stratification regardless of the fuel composition. In addition, the effect of the fuel composition on the ignition characteristics of PRF/air mixtures was found to be significantly reduced with increasing thermal stratification. Chemical explosive mode (CEM) and displacement speed analyses verified that nascent ignition kernels induced by hot spots due to a high degree of thermal stratification usually develop into deflagration waves rather than spontaneous auto-ignition at reaction fronts and as such, the mean heat release rate becomes more distributed over time. These analyses also revealed that the fuel composition effect vanishes as the degree of thermal stratification is increased because the deflagration mode of combustion, of which propagation characteristics are nearly identical for different PRF/air mixtures, becomes more prevailing with increasing degree of thermal stratification. Ignition Damköhler number was proposed to quantify the successful development of deflagration waves from nascent ignition kernels; for cases with large ignition Damköhler number, turbulence with high intensity and short timescale can advance the overall combustion by increasing the overall turbulent flame area instead of homogenizing initial mixture inhomogeneities.

A DNS study of self-accelerating cylindrical hydrogen–air flames with detailed chemistry

The self-accelerating expanding cylindrical stoichiometric hydrogen–air flames at eight atmospheres were studied via two-dimensional direct numerical simulation (DNS) of the full compressible Navier–Stokes equations with detailed chemistry. The flame morphology and propagation were finely resolved by the application of a time step of 2.5ns and a grid size of 4μm. Temporally, the intermittent propagation of the flame front is captured through examining its propagation velocity. Spatially, the flame front is found to be comprised of segments exhibiting similar propagation properties, i.e. the intermittent instantaneous propagation of the flame front is attributed to the development of cellular structures induced by hydrodynamic instability. The long-term average propagation velocity of the flame front is described by a power law, with a self-acceleration exponent of 1.22 for the flame radius with respect to time. The increase in the global flame velocity is shown to be primarily a consequence of increased flame surface area, with the local front propagation velocity remaining largely at the constant laminar flame speed for the near-unity Lewis number mixture studied herein.

Intrusion-generated waves in a linearly stratified fluid

AbstractWe present an experimental and numerical study of the upstream internal wavefield in a channel generated by constant density intrusions propagating into a linearly stratified ambient fluid during the initial phase of translation. Using synthetic schlieren imaging and two-dimensional direct numerical simulations, we quantify this wave motion within the ambient stratified fluid ahead of the advancing front. We show that the height of the neutral buoyancy surface in the ambient fluid determines the vertical modal response with the predominant waves being mode 2 for intrusions near the mid-depth of the channel and mode 1 waves being produced by intrusions nearer the top or bottom of the domain. All higher vertical modes travel slower than the intrusion and so do not appear upstream ahead of the intrusion front. We find the energy flux into this upstream wavefield to be approximately constant, and to be between 10 and 30 % of the rate of available potential energy transfer into the flow.

Kinetic studies of methyl acetate pyrolysis and oxidation in a flow reactor and a low-pressure flat flame using molecular-beam mass spectrometry

The combustion chemistry of methyl acetate (MA) pyrolysis and oxidation was studied experimentally in an atmospheric flow reactor and a low-pressure flat flame using molecular-beam mass spectrometry (MBMS). Rate constants such as H-abstraction of MA by O, H, OH, CH3, and HO2 radicals as well as MA radical decomposition were computed by high-level ab initio and RRKM master equation calculations. A new methyl acetate kinetic model was developed and compared to the experimental data along with other existing models. Two-dimensional direct numerical simulations were conducted and the results were used to validate the zero-dimensional prediction in a flow reactor. The MA pyrolysis results in the flow-reactor experiments showed that MA decomposition to CH3+CH3+CO2 and CH3OH+CH2CO are the dominant pathways, which is consistent with the theoretical prediction of the new model. In addition, a two-stage MA oxidation was observed between 800K and 1050K, suggesting the possible existence of low-temperature chemistry for MA oxidation. The low-pressure flame experiment at a rich condition suggested that MA has unique reaction pathways to form aldehydes, ketones, and acids. Comparison with previous kinetic models showed that the present model considerably improved the predictability of species-temperature histories in the flow reactor and successfully identifies the main reaction pathway of ketene and acetic acid in a low pressure flame for the first time.

Polybrachial structures in dimethyl ether edge-flames at negative temperature coefficient conditions

The structure and stabilisation mechanism of partially premixed, laminar, dimethyl ether (DME) flames are investigated using two-dimensional direct numerical simulation (DNS). The simulations are performed at a pressure of 40 atmospheres and at oxidiser temperatures of 700, 900, 1100, 1300, and 1500K, while keeping the lift-off length approximately fixed by varying the inlet velocity. At this pressure, DME exhibits two stage ignition below approximately 1100K and a negative temperature coefficient (NTC) regime from approximately 800–1100K. The DNS results are investigated by considering the thermochemical structure of the flames and by applying a transport budget analysis to key chemical species. The results show a transition from a lifted flame stabilised by conduction and diffusion-assisted flame propagation to a flame stabilised by autoignition with increasing temperature. At 700K, the flame has a classical tribrachial structure similar to freely propagating edge flames at non-autoignitive conditions. The intermediate temperature cases reveal a complex transition involving multiple heat release pathways upstream of the stabilisation point. At 900K, the flame consists of a main-tribrachial structure and an additional upstream branch due to low temperature chemistry: this is termed a tetrabrachial flame. At 1100 and 1300K, two upstream branches are observed in addition to the main tribrachial structure, one due to low temperature chemistry and the other due to high temperature chemistry, which initiates autoignition and stabilises the flame: these are termed pentabrachial flames. At 1500K, the low temperature upstream branch is suppressed, so there is only one upstream branch due to high temperature chemistry which proceeds to autoignition, this flame has a tetrabrachial structure, but one which is different from that observed in the 900K case.

Conditional moment closure modelling for HCCI with temperature inhomogeneities

This paper presents an approach for modelling combustion in homogeneous charge compression ignition (HCCI) conditions based on the first order conditional moment closure (CMC) method. The model is implemented into the open source C++ computational fluid dynamic (CFD) code known as OpenFOAM. Direct numerical simulations (DNSs) are used to evaluate the performance of the CFD-CMC solver. In the two-dimensional (2D) DNS cases, ignition of a lean n-heptane/air mixture with thermal inhomogeneities is simulated for nine cases, with two different mean temperatures and several different levels of thermal stratification. Results from the CFD-CMC solver are in excellent agreement with the DNS for cases which exhibit a spontaneous sequential ignition mode of combustion whereas for the cases in which a mixed mode of deflagration and spontaneous ignition exists, the CMC underpredicts the ignition delay. Further investigation using the DNS data demonstrates that this discrepancy is primarily attributed to the first order closure assumption. Conditional fluctuations are found to be more significant in the case with deflagrations. Further analysis of the DNS shows that scalar dissipation fluctuations are the cause of conditional fluctuations.

A shear instability mechanism for the pulsations of Rayleigh–Taylor unstable model flames

AbstractPrevious studies have shown that the behaviour of Rayleigh–Taylor (RT) unstable flames depends on the boundary conditions. If the boundary conditions at the domain walls are impermeable/adiabatic or reflecting then the flame assumes a stable parabolic shape. On the other hand, periodic boundary conditions can produce unstable pulsating solutions. In this paper, we explore why periodic boundary conditions allow unstable solutions by showing the results of two-dimensional direct numerical simulations of model flames. We show that RT unstable premixed model flames pulsate at low gravity because of a shear instability of the vorticity layers behind the flame front. The resulting vortex shedding is controlled by a region of absolute-like instability which moves closer to the flame front as gravity is increased, ultimately disturbing the flame and leading to pulsations. We demonstrate that this region is ‘absolutely unstable’ by showing that the wake is dominated by pure frequency oscillations. In addition, the shear instability can be described by the Landau equation and can be represented dynamically by a Hopf bifurcation. The applicability of the Landau equation allows the apparently complex spatio-temporal behaviour of the vortex shedding to be described by a simple temporal model with only a secondary spatial dependence. We show that the flame behaviour is analogous to the initial instability downstream of a circular cylinder, which leads to the von Kármán vortex street for large enough values of the Reynolds number.

Numerical simulation of the effect of local volume energy supply on high-speed boundary layer stability

Two-dimensional direct numerical simulations and the linear stability analysis are performed for a flat-plate boundary layer in the Mach 6 free stream with the presence of local volume energy supply. It is expected that this technique can be used for the laminar flow control at high speeds where the second mode waves dominate. It is shown that the heat source produces different effects depending on its streamwise distance from the plate leading edge and its wall-normal distance. If the source is located upstream from the neutral point and its center is close to the boundary-layer edge, it reduces the second-mode growth rates and thereby diminishes the maximum amplitude of instability. If the source is shifted downstream from the neutral point and its center is within the boundary layer, the stabilization effect becomes weaker while the scattering of unstable waves by the source-induced non-uniformity of the mean flow comes into play. By variations of the wall-normal distance of the heat source located near the neutral point it was found that the maximal stabilization effect is achieved if the source center is near the critical layer.

Effects of ambient pressure and precursors on soot formation in spray flames

The effects of ambient pressure on soot formation in spray jet flames are investigated by means of a two-dimensional direct numerical simulation (DNS). In addition, the effects of precursors on soot formation are also discussed. The inception models considering acetylene and polycyclic aromatic hydrocarbon (PAH) precursors are employed and compared in this study. The extended flamelet/progress-variable approach (EFPV) in which heat transfer between a droplet and the surrounding fluid can be considered is employed as a combustion model. Jet A is used as a liquid fuel with considering the detailed chemistry including 274 chemical species and 1537 elemental reactions by the flamelet library. The evaporating droplets’ motions are tracked by the Lagrangian method and the non-equilibrium Langmuir–Knudsen model is used as an evaporation model. Results show that the spray jet flame structure and the soot formation characteristics are considerably affected by the ambient pressure condition. The soot volume fraction increases with increasing the ambient pressure. It is also revealed that the dominant process to promote the soot formation is different between the acetylene and PAH precursor models. It is essential to model a soot inception process with appropriate precursors in order to understand a detail mechanism of soot formation, since the precursor which plays the important role depends on the type of fuel and the combustion conditions.

Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

AbstractIn a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus onto particular structures known as wave attractors. These attractors are likely to appear in fluid containers with at least one boundary that is neither parallel nor normal to the rotation axis. A closely related process also applies to internal gravity waves in a stably stratified fluid. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. By varying the amplitude at which the system is forced periodically, we are able to describe the transition between the linear and nonlinear regimes as well as the characteristic properties of the two situations. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.

The evolution of large and small-scale structures in Kelvin–Helmholtz instabilities

To better understand the dynamics of Kelvin–Helmholtz instabilities in environmental flows, their evolution is investigated using direct numerical simulations (DNS). Two-dimensional DNS is used to examine the large-scale and small-scale structures of the instability at high Reynolds and Prandtl numbers that represent real environmental flows. The semi-analytical model of Corcos and Sherman (J Fluid Mech 73:241–264, 1976) is used to explain the physics of these simulations prior to saturation of the KH billow, and also provide a computationally efficient prediction of the vortex dynamics of the instability. The DNS results show that the large-scale structure of the billow does not depend on the Reynolds number for sufficiently high Reynolds numbers. The billow structure reveals a less straightforward dependence on the Prandtl number. Predictions of the model of Corcos and Sherman (J Fluid Mech 73:241–264, 1976) improve as Reynolds number and Prandtl number increase. The small-scale structure of the vorticity and density fields vary with both Reynolds and Prandtl numbers. Three-dimensional DNS of KH flows and their transition to turbulence are used to study small length scales. Based on the thickness of the braid, a simple method is introduced to estimate the Batchelor scale, which can be used as a guide for the resolution required for the direct numerical simulation of two and three-dimensional Kelvin–Helmholtz flow fields.