Direct Numerical Analysis Research Articles

Effect of flame holder temperature on the instability modes of laminar premixed flames

Direct Numerical Simulations (DNS) and theoretical analysis of combustion instabilities in laminar premixed flames are performed to investigate the effect of flame holder temperature (Tc) on the self-excited instability modes. Four flames with different anchor positions and recirculation zones are triggered to be unstable by increasing acoustic losses at the boundaries. At Tc = 300 K and 773 K, intrinsic thermo-acoustic (ITA) modes dominate the oscillation frequencies both in anechoic and acoustic systems. The instability modes are mainly determined by the flame characteristics, and significantly affected by the recirculation zone and flame holder. At Tc = 400 K and 1500 K, the instability modes are mainly determined by the couplings between acoustic and ITA modes, and significantly affected by the flame characteristics and system acoustic modes. The dominant oscillation frequencies are closed to the acoustic modes at Tc = 400 K, but in low frequency ranges at Tc = 1500 K. These results indicate that the ITA modes affect the combustion instability in different ways with different flame characteristics. It may cause intrinsic instability or couple with acoustic modes to cause new instability modes. In realistic combustion systems, the ITA modes must be considered carefully in the analysis of combustion instability.

A novel model for incorporation of differential diffusion effects in PDF simulations of non-premixed turbulent flames based on reaction-diffusion manifolds (REDIM)

In this work, reaction-diffusion manifold (REDIM) reduced chemistry is used in the simulation of turbulent non-premixed flames based on a transported-probability density function model. Differential molecular diffusion is applied in the generation of the manifolds. This is the first work to consider the gradients of the reduced variables as additional parameters in the REDIM model, and one-directional gradients are utilized to generate the REDIM reduced chemistry. Hereby, the influence of turbulence on differential molecular diffusion is automatically considered in terms of reduced variable gradients, and the physical transport properties (e.g., diffusion coefficients) are used in a detailed way, without any additional modeling (e.g., unity-Lewis number assumption). Although the scalar gradients appear as multi-directional in a general turbulent reacting flow, previous direct numerical simulation analysis reveals that REDIMs generated from one-directional gradients can accurately describe the system featuring multi-directional gradients, if this one-directional gradient has a major effect on the chemistry. Here, it is proposed to obtain such gradients under the hypothesis that the flame structure is locally one-dimensional at each spatial position. In order to retrieve the gradients of the reduced variables for the interpolation of the thermo-kinetic states from the REDIM table, the sub-grid gradient is evaluated here from the particle fields. The well-known Sandia series of flames is selected to validate the proposed algorithm. The results show that the new algorithm can reproduce the thermo-kinetic quantities with high accuracy for all investigated flames.

Mechanical Characteristics of Steel Shear Keyed Joints in the Construction and Finished States

Joints that represent locations of discontinuity were the prominent factors affecting the overall behavior of precast segmental bridges. In this study, the steel shear key was designed, which was used to transmit the shear stress of the joints. To study the mechanical characteristics of the steel shear keyed joints in the construction and finished states, direct shear experiments and numerical analysis were carried out. The experimental results showed that the steel shear keyed joints had a high bearing capacity and good ductility. Under the action of confining stress, the joints relied on the mechanical occlusion between the steel keys to transmit the shear forces. When the load‐displacement curve entered the horizontal stage, it can still bore large relative deformation, and the bearing capacity did not decrease. In the construction state, the inelastic deformation of the steel shear key should be used to control the design value of the temporary load. In the finished state, the bearing capacity of joints should be controlled by the direct shear strength of the steel shear key, which can be calculated according to the shear formula. The shear strength of the material and size of the steel shear key are the main factors affecting the bearing capacity of steel shear keyed joints.

Direct numerical simulation and stability analysis of the transitional boundary layer on a marine propeller blade

It is generally assumed that the cross-flow instability exists on propeller blade boundary layers due to their similarity with the rotating disk flow. However, to the best of our knowledge, there is no experimental or numerical evidence that directly shows the existence of the cross-flow instability on propellers. In this paper, we present a direct numerical simulation of the boundary layer flow around a marine propeller blade. For the investigated case, the cross-flow velocity inside the attached laminar boundary layer is smaller than the rotating disk case, but it is large enough to lead to the cross-flow instability. The wave-numbers and wave-direction of the cross-flow vortices observed agree well with the prediction of linear stability theory. Linearized Navier–Stokes simulations show that the boundary layer is absolutely unstable in the radial direction but convectively unstable in the streamwise direction. A significant flow direction deviation between laminar and turbulent regions is also observed on the blade surface. In the separation bubble, there is an unusually large radial velocity (around 50% of the inviscid streamwise velocity). Both the flow direction deviation and the large radial velocity in the separation bubble can be explained by the relationship between Coriolis forces and circumferential velocities.

A direct numerical simulation analysis of coherent structures in bubble-laden channel flows

Abstract

Mechanical strength and microstructure of engineered cementitious composites: A new configuration for direct tensile strength, experimental and numerical analysis

The use of engineered cementitious composites (ECCs) have been gained wide attention considering their properties such as high values of tensile strength and ductility. However, the required methods to direct measurement of their tensile strength are not developed adequately. This study investigates some mechanical properties (compressive and flexural strengths) with more emphasis on the direct tensile strength as well as changes in the used raw materials. Therefore, the ground-granulated blast-furnace slag (GGBFS) and fly ash (FA) were used as cementitious materials and two types of silica and river aggregates for making cementitious mixtures. Moreover, the direct tensile strength of the specimens with two different configurations was evaluated. The composites' microstructure was analyzed by the images obtained from scanning electron microscopy (SEM) and X-ray energy diffraction spectroscopy (EDS). According to the results, though mixtures containing fly ash had significantly lower mechanical strength, they had significantly higher energy absorption and strain-hardening behavior than the slag. Furthermore, the direct tensile proposed model's results showed the ultimate strength and strain up to 56% and 21% higher than the model proposed by previous researchers. Consequently, parametric analysis and finite element modeling performed for the tensile model revealed acceptable model output compared to the experimental results.

A-Priori Validation of Scalar Dissipation Rate Models for Turbulent Non-Premixed Flames

The modelling of scalar dissipation rate in conditional methods for large-eddy simulations is investigated based on a priori direct numerical simulation analysis using a dataset representing an igniting non-premixed planar jet flame. The main objective is to provide a comprehensive assessment of models typically used for large-eddy simulations of non-premixed turbulent flames with the Conditional Moment Closure combustion model. The linear relaxation model gives a good estimate of the Favre-filtered scalar dissipation rate throughout the ignition with a value of the related constant close to the one deduced from theoretical arguments. Such value of the constant is one order of magnitude higher than typical values used in Reynolds-averaged approaches. The amplitude mapping closure model provides a satisfactory estimate of the conditionally filtered scalar dissipation rate even in flows characterised by shear driven turbulence and strong density variation.

Parallel direct numerical simulation and analysis of turbulent Rayleigh–Bénard convection at moderate Rayleigh numbers using an efficient algorithm

Direct numerical simulation of turbulent Rayleigh-Bénard convection up to Rayleigh number 108 is performed using a fully-implicit, non-dissipative, discrete kinetic energy-conserving algorithm and a parallel flow solver based on it. The algorithm is especially suitable for simulating low-Mach number, variable density/viscosity, transitional and turbulent flows with or without heat transfer. Furthermore, since it does not rely on the Boussinesq assumption, large temperature differences and high Rayleigh numbers can be handled without loss of accuracy, unlike the pure incompressible ones. It is first shown that the algorithm is able to predict the evolution of thermally-driven instability to turbulent regime and all the characteristics of turbulent convection accurately, using low- and high-order turbulent statistics and various secondary diagnostics derived. Then, effects of increasing Rayleigh numbers on the development of the instability are analyzed in detail. Additionally, Nusselt-Rayleigh scaling properties are studied and a scaling relation is provided. Results show that Rayleigh-Bénard convection at relatively high Rayleigh numbers, corresponding to a boundary layer-dominated regime and little beyond it to a bulk-dominated regime, is characterized by weakening thermal fluctuations, thinning thermal boundary layers, increasing vertical velocity fluctuations and decreasing skewness. It is also observed that the turbulent heat flux dominates the heat transfer. Finally, the corresponding Nusselt-Rayleigh scaling relation is predicted as Nu=0.132Ra0.297.

A direct numerical simulation analysis of turbulent V-shaped flames propagating into droplet-laden mixtures

Three-dimensional Direct Numerical Simulations (DNS) data has been used to analyse the gaseous phase combustion behaviour in a V-shaped flame configuration where fuel is supplied in the form of droplets such that an overall (i.e. liquid+gaseous) equivalence ratio of unity is maintained in the unburned gas. The analysis has been carried out for different initially mono-sized droplet diameters. A gaseous premixed V-shaped flame with the same flow conditions has been utilised to compare the flame propagation in V-shaped spray flames with a corresponding gaseous premixed flame case. It has been found that combustion in the gaseous phase mainly takes place under fuel-lean mode and the probability of finding fuel-lean burning increases with increasing droplet diameter. However, the mean equivalence ratio of the predominantly fuel-lean mixture increases with increasing axial distance from the flame holder. The presence of droplets has been found to give rise to dimples on the reaction progress variable isosurfaces, and the effects of droplet–induced flame wrinkling are reflected by the widening of the curvature probability density functions for large droplets. The heat release has been found to arise mainly from the premixed mode of combustion. Detailed analysis of reaction progress variable transport has been used to explain the mean variations of consumption speed and density-weighted displacement speed with the axial distance from the flame holder. The mean values of consumption speed, density-weighted displacement speed and turbulent burning velocity have been found to decrease with increasing droplet diameter. The flame speed statistics have been utilised to explain that the enhancement of the burning rate cannot be equated to the enhancement of the flame surface area in turbulent droplet-laden V-shaped flames.

On the receptivity of surface plasma actuation in high-speed boundary layers

Significant amounts of work have been conducted in the area of plasma flow control, while the receptivity of plasma actuation in high-speed boundary layers has not had much attention over the last two decades. In the present study, the receptivity of a Mach 4.5 flat-plate boundary layer to plasma heating actuation produced by pulsed-DC surface dielectric barrier discharge (SDBD) has been studied by direct numerical simulation (DNS) and stability analysis. With the help of multimode decomposition technology, the amplitude of normal modes can be obtained. The results show that both fast and slow modes can be excited by plasma actuation, and the receptivity maximum is observed near the lower neutral branch. Because the pulsed-DC SDBD actuation is typical periodic pulse signals, when the total power remains constant, the Fourier components with multiples of actuation frequency have the same energy, regardless of the waveform, period, and width of the actuation signal. Such characteristics benefit the robustness of the pulsed-DC SDBD actuator. A theoretical prediction method by combining the receptivity model and linear parabolized stability equations is considered in the present study, and good agreement with the DNS results is achieved.

Two-temperature Navier-Stokes equations for a polyatomic gas derived from kinetic theory.

A polyatomic gas with slow relaxation of the internal modes is considered, and the Navier-Stokes equations with two temperatures, the translational and internal temperatures, are derived for such a gas on the basis of the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas, proposed by Andries etal. [Eur. J. Mech. B, Fluids 19, 813 (2000)10.1016/S0997-7546(00)01103-1], by the Chapman-Enskog procedure. Then, the derived equations are applied to numerically investigate the structure of a plane shock wave in CO_{2} gas, which is known to have slowly relaxing internal modes. The results show good agreement with those obtained by the direct numerical analysis of the ES model for moderately strong shock waves. In particular, the results perfectly reproduce the double-layer structure of the shock profiles consisting of a thin front layer with rapid change and a thick rear layer with slow relaxation of the internal modes.

On the origin of drag increase in varying-phase opposition control

This study investigates the physics underlying the drag increase in a low Reynolds number turbulent channel flow due to varying-phase opposition control by means of direct numerical simulation and modal analysis. The drag increase occurs for an extended region of the parameter space and we consider a controller with a positive phase shift in Fourier domain between sensor measurement and actuator response as a representative example for this regime. Analyses of instantaneous flow fields as well as spatial power spectra show that the structure of drag-increased flows is remarkably different from that of drag-reduced and canonical flows. In particular, the near-wall region is dominated by structures of short streamwise and large spanwise extent. Isolation of a representative control scale shows that these energetic structures can be characterized as spanwise rollers, which induce strong ejection and sweep motions and lead to drag increase. The presence of rollers, and therefore drag increase, in the full nonlinear system correlates well with the presence of an amplified eigenvalue in the eigenspectrum of the linearized Navier–Stokes operator. It is further shown that the scales responsible for drag increase at positive phase shifts are inactive at negative phase shifts and do not contribute to drag reduction. These scales can therefore be excluded from a controller aimed at drag reduction, which relaxes the spatial resolution requirements on the control hardware. The eigenspectrum may be used as a computationally cheap tool to identify such detrimental scales during an early design stage.

Novel method of thermal behavior prediction of evacuated tube solar collector

Heat pipe evacuated tube solar collectors (HPETCs) are a type of solar collectors with appealing characteristics for the application in solar water heating (SWH) technologies. In order to better understand the heat transfer phenomena in HPETCs and improve their efficiency, there is a need for a fast and robust numerical tool. Due to the complexity of the heat transfer processes involved in modeling a collector’s performance, direct numerical analysis solutions (DNS) are computationally cumbersome. Recent studies have shown that resistance network (RN) models are suitable tools for studying the performance and thermal behavior of HPETCs. In this work, a novel method of resistance network based proper orthogonal decomposition (RNPOD) is presented which can not only consider the geographical and meteorological characteristics of the ambient surroundings, but also take into account the peripheral temperature distribution of a single HPETCs. Once the temperatures at each instance in time have been calculated, a POD method is used to predict the thermal behavior of the collector with desired temporal accuracy. The obtained results of this study are cross-validated with the previous experimental work of the authors, illustrating that the model is able to predict the peripheral temperature distribution with a maximum error of 10%.

A model of micro lubrication between two walls with an arbitrary temperature difference based on kinetic theory

Micro lubrication of a gas between two walls with an arbitrary temperature difference is studied on the basis of the Bhatnagar–Gross–Krook–Welander model of the Boltzmann equation. Applying the slowly varying approximation, the kinetic equation is studied analytically when the Knudsen number based on the gap size is large. The leading order approximation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by its free molecular solution. Due to this crude approximation, a macroscopic lubrication model of Reynolds-type equation is derived in a closed form. For an assessment of the model, a direct numerical analysis of the kinetic equation is also conducted. The lift calculated using our model approximates that of the direct numerical analysis within the error of 4% uniformly in the range of the temperature ratio between 0.75 and 2 and the Knudsen number Kn between 0.1 and 10. A heating of the moving wall reduces the lift acting on the other wall when Kn is sufficiently large, whereas it is enhanced when Kn is sufficiently small.

Modeling of Thermodynamic Fluctuations in Canonical Shock–Turbulence Interaction

Interaction of a shock wave with turbulence can generate large thermodynamic fluctuations in a flow. This can lead to enhanced mixing, peak heat transfer, and high sound level. The canonical interaction of homogeneous isotropic turbulence with a nominally normal shock wave acts as a model problem to investigate physics and develop predictive models. The case of purely vortical turbulence upstream of the shock is arguably the most fundamental case, and it is the focus of the current work. Direct numerical simulation (DNS) data and linear interaction analysis (LIA) are used to develop a predictive model for the thermodynamic field. Specifically, transport-equation-based models are proposed for the variances in temperature, pressure, density, and entropy. The jump in the thermodynamic variances is modeled in terms of the mean compression at the shock, and the closure coefficients are obtained via Kovásznay mode decomposition. By comparison, the downstream decay is modeled in a phenomenological way in terms of acoustic transient near the shock and a far-field decay due to viscous dissipation. The model predictions are found to match well with available DNS data for a range of shock strengths. In addition, the closed-form solution of the model equations gives the scaling of the thermodynamic fluctuations with mean flow Mach number.

Effect of turbulent Mach number on the thermodynamic fluctuations in canonical shock-turbulence interaction

Shock waves can generate high levels of turbulent fluctuations in temperature, pressure and other thermodynamic properties. These have significant role in turbulent mixing, heat transfer and acoustic noise in high-speed flows. The thermodynamic fluctuations generated by canonical shock-turbulence interaction are strong functions of the shock strength and the upstream turbulence intensity. For a fixed shock Mach number, the downstream thermodynamic variances, normalized by the upstream turbulence kinetic energy, are found to increase with the incoming turbulent Mach number (Mt). This is in contrast to the trend observed for Reynolds stresses and the turbulent dissipation rate. We use direct numerical simulations and linear interaction analysis to investigate the effect of Mt on the post-shock thermodynamic field. It is found that the presence of small amount of acoustic and entropy fluctuations in the incoming flow can explain the high intensity of the post shock thermodynamic variances in the high Mt cases.

Direct numerical simulation and statistical analysis of stress-driven turbulent Couette flow with a free-slip boundary

The effects of free-slip boundary on shear turbulence are studied numerically using the direct numerical simulation (DNS) approach. The flow considered in this study is a stress-driven turbulent Couette flow between two flat boundaries. The top boundary has an imposed shear stress in the streamwise direction and a free-slip condition for the streamwise velocity fluctuation and the spanwise velocity, and the bottom boundary satisfies the no-slip condition. This type of flow has a mean flow pattern similar to the turbulent plane Couette flow between a stationary flat plate and a moving flat plate but exhibits considerable differences in turbulence statistics due to the effects of the free-slip boundary. Statistical analysis based on the DNS data and theoretical derivation based on Taylor series expansion show that near the free-slip surface the turbulence variances of the three velocity components vary as quadratic functions of the vertical distance from the boundary while the Reynolds shear stress exhibits a linear behavior, which are very different from the counterparts near the no-slip boundary. The free-slip surface condition also leads to zero horizontal vorticities at the surface but allows nonzero vertical vorticity in the meantime, leading to considerable differences in the near-boundary statistics of vorticities and coherent vortex structures. Comparison of three DNS runs with different grid resolutions shows that smoothly resolving the more energetic turbulent flow structures near the free-slip boundary requires a higher horizontal grid resolution than that used for resolving the structures near the no-slip boundary.

Structure of strongly turbulent premixed n-dodecane–air flames: Direct numerical simulations and chemical explosive mode analysis

Structure of strongly turbulent premixed n-dodecane/air flames with high Karlovitz numbers (Ka) is studied based on three-dimensional (3D) direct numerical simulation (DNS) datasets. Heat release and fuel consumption rates in these flames are observed to be enhanced compared to what can be conventionally described as increases in flame surface area. To explain the cause for the burning rate enhancement, temperature and species mass fractions are first investigated to reveal the overall flame structure. The chemical explosive mode analysis (CEMA) is then employed to identify local combustion modes, including local assisted ignition, auto-ignition, and extinction, each of which is found to play a role in the overall burning rates. The spatial distribution of the local modes is found to be drastically different from that in comparable laminar flames where the local extinction mode is mostly absent. For the high-Ka cases (Ka = 103 and 104), the extinction mode is shown to be comparable to or more important than the auto-ignition mode for heat release and fuel consumption rates. In contrast, the auto-ignition mode plays a more important role in heat release than the extinction mode in laminar and the relatively low-Ka flames (Ka = 102). In addition, two types of mixture pockets are identified by CEMA: pockets of reactants in bulk products and pockets of hot products in bulk reactants. The dynamics of these pockets are strongly affected by the local modes of the spatially adjacent mixtures. While the pockets of reactants in bulk products are almost always consumed by auto-ignition and/or inward flame propagation, the pockets of products in bulk reactants may either grow themselves due to outward flame propagation or contract volumetrically due to local extinction. In contrast to the conventional understanding, local extinction can promote the overall burning process, as it enables mixing of the radicals and sensible energy from the product pockets into the surrounding reactants, thus facilitating their ignition. Clearly, such effects must be considered in order to closely model these flames.

Shock–turbulence interactions at high turbulence intensities

Shock–turbulence interactions are investigated using well-resolved direct numerical simulations (DNS) and analysis at a range of Reynolds, mean and turbulent Mach numbers ($R_{\unicode[STIX]{x1D706}}$, $M$ and $M_{t}$, respectively). The simulations are shock and turbulence resolving with $R_{\unicode[STIX]{x1D706}}$ up to 65, $M_{t}$ up to 0.54 and $M$ up to 1.4. The focus is on the effect of strong turbulence on the jumps of mean thermodynamic variables across the shock, the shock structure and the amplification of turbulence as it moves through the shock. Theoretical results under the so-called quasi-equilibrium (QE) assumption provide explicit laws for a number of statistics of interests which are in agreement with the new DNS data presented here as well as all the data available in the literature. While in previous studies turbulence was found to weaken jumps, it is shown here that stronger jumps are also observed depending on the regime of the interaction. Statistics of the dilatation at the shock are also investigated and found to be well represented by QE for weak turbulence but saturate at high turbulence intensities with a Reynolds number dependence also captured by the analysis. Finally, amplification factors are found to present a universal behaviour with two limiting asymptotic regimes governed by $(M-1)$ and $K=M_{t}/R_{\unicode[STIX]{x1D706}}^{1/2}(M-1)$, for weak and strong turbulence, respectively. Effect of anisotropy in the incoming flow is also assessed by utilizing two different forcing mechanisms to generate turbulence.

단원자 희박기체에서의 열전달 해석을 위한 모델 카이네틱 방정식의 직접 해석 기법

In the present study, the heat conduction process in a monatomic rarefied gas was investigated based on the solution of the kinetic relaxation models for various Knudsen numbers. Generalization of the equilibrium distribution function in the model kinetic equation allows the correct estimation of the heat flux for arbitrary Prandtl numbers. The kinetic model equations in terms of newly defined density distribution functions are used to investigate two-dimensional heat transfer flows between two infinite walls of constant temperature ratio. The macroscopic flow variables were recovered by the integration of the resultant distribution functions with respect to longitudinal velocities. The steady solutions obtained by means of the current methodology are in good agreement with the solutions of the direct numerical analysis for the full Boltzmann equation. The temperature jumps at the solid surfaces were successfully evaluated from the deviation of the resultant distribution functions from local equilibrium states. It is concluded that the temperature jumps near the solid boundaries increase as the parameter for the rarefaction of the flow increases. This paper deals with the numerical simulation of the natural convection in a two-dimensional square filled with a monatomic gas. It is clearly shown that increasing the Knudsen number of the flow results in the increment of the relative jumps at the solid wall boundary.