Magnitude Of Density Gradient Research Articles

Breakup Mechanism of a Jet in the L-Shape Crossflow of a Gas Turbine Combustor

Experimental investigations are conducted to determine the mechanism and characteristics of a jet in an L-shape crossflow simulating the radial swirl injector of a lean premixed-prevaporized (LPP) combustor. To simplify the radial flow of the actual injector while ignoring the centrifugal effect, the L-shaped 2D-channel is used for the crossflow, and water is used as a fuel simulant. The jet breakup is captured using a high-speed camera, and the density gradient magnitude is post-processed to clarify the spray. The Sauter mean diameter (SMD) of the spray is measured via a laser diffraction method with a helium–neon laser optical system (HELOS). The characteristics of the jet in the L-shape crossflow are compared with the characteristics of the jet in a typical crossflow through the flat channel. The results for different outlet heights of the L-shape channel (H/d0) and different injector positions (L/d0) are presented. A dimensionless number (τ) consisting of a time ratio is introduced to describe the jet characteristics. In a previous work, the spraying tendency was demonstrated for different injector positions. In addition, the effect of the recirculation area on H/d0 was empirically shown. H/d0 determines the size of the recirculation area, and the range of τ determines the jet breakup mechanism inside the L-shape channel. The results of this study present the breakup mechanism of the jet in the L-shape channel flow, which simulates a jet in a radial swirler injector for gas turbine engines. It is expected that these results can be used to assist in designing gas turbine engines with more combustion efficiency.

Turbulent chemical-species mixing in the Venus lower atmosphere at different altitudes: a direct numerical simulation study relevant to understanding species spatial distribution

To evaluate a recent hypothesis of species stratification in the Venus lower atmosphere, a time-dependent, three-dimensional model is proposed for studying turbulent mixing of many species in the Venus lower atmosphere. This model is based on fundamental physics embedding non-equilibrium thermodynamics, the Onsager classical relationship between fluxes and forces, high-pressure transport property calculation and a real-gas equation of state. The conservation equations are self-contained, with no need for coefficients based on parametrizations to match Venus observations. The rationale for solving these equations in relatively small spatial domains at different altitudes in the Venus lower atmosphere is presented. The equations are solved in a temporal mixing layer configuration that is eminently suited to investigate turbulent mixing between two streams of different composition. The adopted simulation method is Direct Numerical Simulation (DNS). A substantial database of DNS realizations is generated for mixtures of two and seven species, with different levels of initial stratification, and at the realistic conditions of pressures and temperatures in the Venus lower atmosphere at three altitudes. High density-gradient magnitude regions (HDGM) are shown to form under initial high stratification conditions, with larger gradient values obtained at low altitudes where supercritical conditions occur. Independent of the altitude lower than 50 km, under low stratification conditions, mixing produces a more uniform spatial distribution of the density than at higher initial stratification. Under low initial stratification conditions, the influence of the minor species on the global behavior of the flow seems to be negligible. At high initial stratification conditions, differences in diffusion of various species play an important role in determining the mixture characteristics. The hypothesis of chemical species separation is discussed in the light of the present results which do not support the existence of stable species separation in the lower Venus atmosphere, independent of the number of species or the altitude.

Cold Pool Characteristics of Tornadic Quasi-Linear Convective Systems and Other Convective Modes Observed during VORTEX-SE

AbstractMany numerical studies have focused on the importance of baroclinically generated vorticity at the edge of cold pools in supercellular tornadogenesis, and observational work has consistently found that strongly tornadic supercells have less dense, more buoyant cold pools than weakly or nontornadic supercells. However, there is a lack of observational studies that consider potential relationships between cold pool characteristics (e.g., density) and tornado production within linear systems, such as mesoscale convective system (MCS) or quasi-linear convective system (QLCS) events. This study presents two tornadic QLCS events that were observed during the Verification of the Origins of Rotation in Tornadoes Experiment-Southeast (VORTEX-SE) field project in 2016 and 2017. Supercell and hybrid modes were also observed and compared to the observations from the linear systems. No obvious differences in the thermodynamic deficits of the tornadic and nontornadic samples were found, likely due to the weakness of the produced tornadoes (≤EF1) and the small tornadic sample size (five cold pools). Comparison across storm mode did find some differences, with QLCS cold pools producing larger virtual potential temperature and psuedoequivalent potential temperature deficits than those observed in supercells. More importantly, our findings suggest that, in a QLCS, the magnitude of density gradients along the leading edge of the cold pool may be related to tornadogenesis by virtue of the implied baroclinic vorticity generation.

Direct numerical simulation of supercritical oxy-methane mixing layers with CO2 substituted counterparts

Direct numerical simulations of temporally developing, three-dimensional, CH4/CO2, CH4/O2, and CO2/O2 mixing layers are conducted at a supercritical pressure of 300 atm. To effectively model the supercritical regime, the employed formulation includes the compressible form of the governing equations, the cubic Peng–Robinson equation of state and a generalized formulation for heat and mass flux vectors derived from non-equilibrium thermodynamics and fluctuation theory. A linear inviscid stability analysis is also performed for each case, to determine its most unstable wavelength. Flow visualizations reveal the presence of high density gradient magnitude regions for all three mixing layers, with conditional averages indicating increased presence of heavier fluid species within these regions. No significant departures are observed from perfect gas behavior, with compressibility factors very close to unity for all three mixing cases. Applicability of presumed probability density function methods is examined for the three supercritical mixing layers. An a priori analysis is also conducted to investigate various simplifying assumptions employed in modeling various subgrid scale (SGS) flux models. Two additional terms are identified in the large eddy simulation equations, the gradient of SGS contribution of pressure in the momentum equation and the gradient of SGS contribution of heat flux in energy equation, whose magnitudes are similar and comparable with their respective resolved terms. The performance of the scale similarity model to represent these additional terms is investigated. Finally, the performance of Smagorinsky, gradient, and scale similarity models is also investigated.

A Computational Fluid Dynamic Investigation of Inhomogeneous Hydrogen Flame Acceleration and Transition to Detonation

Gas explosions in homogeneous reactive mixtures have been widely studied both experimentally and numerically. However, in practice and industrial applications, combustible mixtures are usually inhomogeneous and subject to vertical concentration gradients. Limited studies have been conducted in such context which resulted in limited understanding of the explosion characteristics in such situations. The present numerical investigation aims to study the dynamics of Deflagration to Detonation Transition (DDT) in inhomogeneous hydrogen/air mixtures and examine the effects of obstacle blockage ratio in DDT. VCEFoam, a reactive density-based solver recently assembled by the authors within the frame of OpenFOAM CFD toolbox has been used. VCEFoam uses the Harten–Lax–van Leer–Contact (HLLC) scheme fr the convective fluxes contribution and shock capturing. The solver has been verified by comparing its predictions with the analytical solutions of two classical test cases. For validation, the experimental data of Boeck et al. (1) is used. The experiments were conducted in a rectangular channel the three different blockage ratios and hydrogen concentrations. Comparison is presented between the predicted and measured flame tip velocities. The shaded contours of the predicted temperature and numerical Schlieren (magnitude of density gradient) will be analysed to examine the effects of the blockage ratio on flame acceleration and DDT.

Evaluation of mixture-fraction-based turbulent-reaction-rate model assumptions for high-pressure reactive flows

Several assumptions of atmospheric-pressure (atmospheric-p) single-phase turbulent reaction rate models are examined for high-p reactive flows having turbulent characteristics. The study uses a Direct Numerical Simulation (DNS) database described elsewhere (Bellan, 2017). This database was obtained with a model combining multi-species mixing under high- p conditions, a real-gas equation of state (EOS) and a single-step chemical reaction. The database, created in the configuration of a temporal mixing layer, probes the effect of the initial Reynolds number, Re0, of the initial pressure, p0, and of the initial composition of the two mixing-layer streams. The reaction is initiated in a turbulent flow and in each simulation the computations are pursued past a time when a maximum average-volumetric p is attained, tpp*. The examination of the vorticity and enstrophy equations at a time before reaction initiation and also at tpp* highlights the pivotal role of the high density-gradient magnitude regions (Bellan, 2017) in producing turbulence and the crucial role at tpp* of the baroclinic effect representing the misalignments of gradients of thermodynamic variables. Compared to the classical mixture fraction equation, the results show that the mixture fraction obeys an equation in which there is an additional diffusion term having a larger r.m.s. magnitude than that of the mixture-fraction typical diffusion term. An assessment of the Conditional Source-term Estimation (CSE) model assumptions found that, using an accurate mixture fraction probability density function (PDF), one can obtain a very good representation of the turbulent reaction rate in the most intense reaction regions, however the quality of the predictions of CSE deteriorated significantly when a common model for the PDF, the β -PDF, was used despite the β-PDF being constructed with the accurate moments extracted from the DNS. In the regions of minimal reaction, the CSE model using the exact PDF extracted from the DNS does not provide an accurate representation of the turbulent reaction rate, a fact which is attributed to the combined effect of lack of correlation between fluctuations of the reaction rate and of the mixture fraction, and to the strong correlation of the thermodynamic variables through the real-gas EOS in regions of colder and denser fluid.

Direct numerical simulation of a high-pressure turbulent reacting temporal mixing layer

Direct Numerical Simulation realizations were created of a temporal mixing layer in which combustion occurs under high-pressure (high-p) turbulent conditions. The model combines the formulation of Masi, et al. (2013) for describing multi-species mixing under high-p conditions and a single-step chemical reaction of rate consistent with ignition prediction (Borghesi, and Bellan, 2015). In each simulation the computations are pursued past a time at which a maximum average-volumetric p is attained; most analysis is performed at this time, tpp*. The ensemble of realizations explores the effect of the initial Reynolds number, Re0, of the initial pressure, p0, and of the initial composition of the two mixing-layer streams. The results show that the thermodynamic energy added by the reaction at the small scales is partially dissipated and partially backscattered. The formation of turbulent small scales is initiated by the morphological changes in the flow through stretching and twisting rather than vice versa. The reaction establishes primarily in the oxidizer stream and is preponderantly of diffusion type. Overwhelmingly, the higher reaction rates occur in the diffusion flame, particularly in regions of high density-gradient magnitude. At higher p0 the reaction rate reaches higher values and occurs in regions of higher density gradients. The range of reaction rates is independent of the Re0 value but the magnitude of the density gradients increases with Re0. When H2O and CO2 are initially present, uphill diffusion dominates over regular diffusion and occurs in regions of smaller density-gradient magnitude whereas regular diffusion occurs in regions of larger density-gradient magnitude where the reaction is more vigorous. H2O is more prone than CO2 to regular diffusion in the larger density-gradient magnitude regions. When H2O and CO2 only form in the flame, both H2O and CO2 are subject to regular diffusion over the entire range of density-gradient values. The dissipation probability density function is a log normal distribution at large dissipation values.

축소형 액체로켓엔진에서 기체산소/케로신 및 기체아산화질소/에탄올 연소 분무의 비교

초임계 연소에 대한 기초연구로써 축소형 액체 로켓 엔진에서 기체산소/케로신, 기체아산화질소/에탄올 추진제 조합의 정상상태 연소의 분무를 관찰하고 비교하였다. 분무의 가시화에는 shadowgraph 기법을 사용하였으며 실험결과를 분석하기 위해 shadowgraph를 후처리하여 밀도구배강도 이미지를 사용하였다. 정상상태 연소압력이 동일한 조건에서 기체산소/케로신 추진제의 액체 제트 표면의 굴곡이 심하고 분사기 팁 근처에서 급격한 밀도구배를 보이는 것이 관찰되었다. 밀도구배강도의 평균 이미지에서 분무 중심 길이를 도출하였으며 더 낮은 운동량 플럭스 비 조건에서도 기체산소/케로신의 분무중심 길이가 더 짧은 것으로 나타났다. Reactive sprays of two propellant combinations(GOx/kerosene and <TEX>$GN_2O$</TEX>/ethanol) were observed and compared with each other as a basic research of visualizing supercritical combustion. A shadowgraph imaging method was used to visualize the reactive sprays, and shadowgraph images were converted to density gradient magnitude images to analyse the structure of reactive sprays. The gas-liquid interface of GOx/kerosene spray showed rougher boundary and steeper density gradient near the injector face than the <TEX>$N_2O$</TEX>/ethanol at similar combustion chamber pressure. Spray core length was calculated from averaged density gradient magnitude images and it was revealed that spray core length of GOx/kerosene was shorter than that of <TEX>$GN_2O$</TEX>/ethanol, although momentum flux ratio of GOx/kerosene propellant combination was lower.

Quantitative colour schlieren development

This work evaluates the potential for producing quantitative data of the density field using a two-dimensional colour schlieren system within the test section of a shock tube. Density gradient components, magnitude and direction, form the basis of the quantitative evaluation. These are encoded onto an imaging plane by means of a colour-coded source mask placed along the optical axis of the schlieren system. Direction is indicated by the relative ratios of the three primary colours: red, green and blue (RGB). Magnitude is indicated by the relative intensities of the RGB values. Sensitivity of the system is adjusted by an iris diaphragm placed in the cutoff plane. The method described is applied to the focusing of a shock wave in a parabolic cavity. The experimental results of the schlieren technique are compared to computational simulations with synthetic two-dimensional colour and magnitude coding applied to the results. The source masks designed and used proved to require a greater intensity light source and thus the design of an LED light source was developed. The CFD solutions were converted into an image format directly comparable to the photographic images obtained. Image processing techniques have been employed to deconstruct photographs to allow for quantitative comparisons with a calibration lens. Density gradient direction has been conclusive; however, density gradient magnitude is not yet accurately determined due to light source constraints.

A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen

A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a ‘pressure correction’ (p correction) in the momentum equation. This additional term results from filtering the Navier–Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.In the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS p-correction term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and ‘mixed’ models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even better predictions in capturing vortical features are obtained with the GRD model. The GRD predictions improve when LES is initiated at a time past the initial range in which the p-correction term rivals in magnitude the leading-order term in the momentum equation. Finally, the ability of the LES to predict the FC-DNS irreversible entropy production is assessed. It is shown that the SSCP model is the best at recovering the domain-averaged irreversible entropy production. The sensitivity of the predictions to the initial conditions and grid size is also investigated.

Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.

Remeshing Strategy of the Supersonic Flow Over a Backward-Facing Step

AbstractA modified error indicator and an extended locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh are developed to study the supersonic flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Euler equations are solved. The modified error indicator, in which the unified magnitude of density gradient and unified magnitude of gradient of vorticity magnitude are incorporated, is utilized to treat the new node spacing of mesh remeshing. To assess the accuracy of the extended locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, two flow calculations which include the oblique-shock reflection at a wall and transonic flow around an NACA 0012 airfoil are performed. Based on the comparison with the related numerical and experimental data, the accuracy of the present approach is confirmed. According to the high-resolutional result on the adaptive mesh, the structure of backstep corner vortex, expansion wave and oblique shock wave is distinctly captured.

Direct numerical simulation of a transitional supercritical binary mixing layer: heptane and nitrogen

Direct numerical simulations (DNS) of a supercritical temporal mixing layer are conducted for the purpose of exploring the characteristics of high-pressure transitional mixing behaviour. The conservation equations are formulated according to fluctuation-dissipation (FD) theory, which is consistent with non-equilibrium thermodynamics and converges to kinetic theory in the low-pressure limit. According to FD theory, complementing the low-pressure typical transport properties (viscosity, diffusivity and thermal conductivity), the thermal diffusion factor is an additional transport property which may play an increasingly important role with increasing pressure. The Peng–Robinson equation of state with appropriate mixing rules is coupled to the dynamic conservation equations to obtain a closed system. The boundary conditions are periodic in the streamwise and spanwise directions, and of non-reflecting outflow type in the cross-stream direction. Due to the strong density stratification, the layer is considerably more difficult to entrain than equivalent gaseous or droplet-laden layers, and exhibits regions of high density gradient magnitude that become very convoluted at the transitional state. Conditional averages demonstrate that these regions contain predominantly the higher-density, entrained fluid, with small amounts of the lighter, entraining fluid, and that in these regions the mixing is hindered by the thermodynamic properties of the fluids. During the entire evolution of the layer, the dissipation is overwhelmingly due to species mass flux followed by heat flux effects with minimal viscous contribution, and there is a considerable amount of backscatter in the flow. Most of the species mass flux dissipation is due to the molecular diffusion term with significant contributions from the cross-term proportional to molecular and thermal diffusion. These results indicate that turbulence models for supercritical fluids should primarily focus on duplicating the species mass flux rather than the typical momentum flux, which constitutes the governing dissipation in atmospheric mixing layers. Examination of the passive-scalar probability density functions (PDFs) indicates that neither the Gaussian, nor the beta PDFs are able to approximate the evolution of the DNS-extracted PDF from its inception through transition. Furthermore, the temperature–species PDFs are well correlated, meaning that their joint PDF is not properly approximated by the product of their marginal PDFs; this indicates that the traditional reactive flow modelling based on replacing the joint PDF representing the reaction rate by the product of the marginal PDFs is not appropriate. Finally, the subgrid-scale temperature–species PDFs are also well correlated, and the species PDF exhibits important departures from the Gaussian. These results suggest that classic PDFs used in atmospheric pressure flows would not capture the physics of this supercritical mixing layer, either in an assumed PDF model at the larger scale, or at the subgrid scale.