Favre-averaged Navier-Stokes Equations Research Articles

Flow Performance Enhancement of a Fluidic Oscillator Through the Integration of Rectangular Ribs on Coanda Surface

Abstract Fluidic oscillators utilize internal flow dynamics to produce oscillatory fluid jets. The Coanda surface in the mixing chamber of a fluidic oscillator plays a critical role by facilitating controlled fluid manipulation through flow attachment and redirection. The mixing chamber pressure drop, jet oscillating frequency, and deflection angles are hence dependent on the geometry of the Coanda surface. In this study, the Coanda surface is modified by using rectangular ribs of different aspect ratios. The effects of ribbed Coanda surface on oscillating jet characteristics are computed numerically through two-dimensional unsteady Favre-averaged Navier–Stokes equations. The aspect ratio (ARribs), the ratio of rib height to rib base, is varied from 0.64 to 1.56 and air is used as a working fluid. An increase in the ARribs increases the jet oscillation frequency. The highest aspect ratio achieves an oscillation frequency of 820 Hz, contrasting with 355 Hz for the smooth case. On the other hand, the jet deflection angles are decreased as the aspect ratio increases. Interestingly the introduction of the ribs on the Coanda surface decreased the pressure drop in the oscillator. A decrease in pressure drop of 22% for an aspect ratio of 1.56 was achieved as compared to the smooth case. These results are attributed to the influence of the ribs on the formation of a separation bubble formed in the mixing chamber. The jet performance parameter, frequency-deflection-pressure ratio, was found to be 43% higher for ARribs of 1.56 as compared to the smooth case.

Numerical Simulation of a Sonic Jet Injected into a Supersonic Crossflow With K.(l) Turbulence Model

Numerical simulation of normal injection of a sonic jet into supersonic crossflows were performed with a k-ul turbulence model. Favre-averaged Navier-Stokes equations along with k-6p equations were solved in a coupled manner by calculating inviscidfluxes with Roe's flux-dffirence splitting, central dffirencing of derivatives in the viscous terms, and by performing Runge-Kutta time integration in a finite volume formuLation. Experiments of sLot injection at several freestream Mach numbers and injection pressure ratios were simulated. It was observed that simulations agreed well at low pressure ratios but departed with increasing pressure ratio as had been observed in other simulations. A qualitative difference in the structure of the jet was observed when explicit compressibility fficts were included. In turn, the agreement with experiment improves significantly. It was also observed that imposing a lower ReynoLds number in the caLculations than the value determined from reported experimental conditions resulted in solutions expected of transitional separation and vvhich then agreed more closely with experiment.

Control of Scramjet Inlet Recirculations Using Fuel Injection

A novel approach using ramp fuel injectors is here proposed to reduce or eliminate shock-induced recirculation regions in scramjet inlets. The study is performed using UArizona’s CFDWARP code solving the Favre-averaged Navier–Stokes equations closed by the revised Wilcox model with dilatational dissipation and rapid compression corrections. The results obtained are representative of hydrogen fuel injected after the second shock of a three-shock scramjet inlet at a flight Mach number of 7.5 and an altitude of 34 km. Injecting fuel in the inlet leads to particularly high values of the cross-stream velocities that reduce the size of the recirculation bubbles. This is attributed to be due to i) large cross-stream shearing created by the bow shock above the ramp injectors, to ii) the large density difference between the fuel and the air leading to baroclinicity, and to iii) the greater acceleration of the light fuel by the pressure gradients. As opposed to previous methods that achieved partial reduction of the separation region, fuel injection can lead to a complete elimination of the recirculation bubbles in scramjet inlets. To eliminate recirculations, only half of the fuel needs to be injected in the inlet with the rest injected in the combustor as usual.

Numerical Optimization of Electromagnetic Performance and Aerodynamic Performance for Subsonic S-Duct Intake

In order to improve the performance of subsonic unmanned aerial vehicle (UAV), a knapsack S-duct intake has been designed. The influences of an S-bend diffuser on aerodynamic performance and electromagnetic performance were analyzed firstly. The viscous flow field has been simulated by solving Favre averaged Navier–Stokes equations using a shear stress transport (SST) k-ω turbulence model. The surface current has been simulated by solving Maxwell equations using a multi-level fast multipole method (MLFMM). The multi-objective optimization of the S-duct intake was studied by using the diffuser as the optimized object. The parametric expression of the diffuser model was realized using the fourth order function geometric representation technique. The efficient model based on the Kriging model and non-dominated sorting genetic algorithm-Ⅱ (NSGA-Ⅱ) were used to accelerate the optimization progress. By analyzing the results of an optimal intake chosen from the Pareto front, the total pressure distortion (TPD) index DC60 has decreased by 0.24 at the designed Mach number of 0.9, and the average Radar Cross Section (RCS) has decreased by 2db at the frequency of 3GHz. The optimized S-duct intake could have both excellent aerodynamic performance and electromagnetic performance at various complex conditions.

Decarbonization of a tissue paper plant: Advanced numerical simulations to assess the replacement of fossil fuels with a biomass-derived syngas

Numerical simulations based on Computational Fluid Dynamic techniques are performed to analyze the possibility of feeding a biomass-derived syngas into the combustion chamber upstream of the hoods for tissue-paper drying, to replace fossil fuels and thus decarbonize the plant. It was observed that, in the context of Favre-Averaged Navier–Stokes equations simulation, syngas requires detailed kinetics and finite-rate approaches, as the fast-chemistry ones, largely employed in the industrial practice for conventional fuels, lead to unreliable results. The actual chamber, originally designed to be fed with liquid petroleum gas, does not operate properly when fueled with syngas, with incomplete oxidation of carbon monoxide. Numerical simulations have proven how very few modifications of the chamber can be devised to permit feeding efficiently the syngas, obtaining low pollutant emissions and meeting the desired requirements in terms of flow and thermal uniformity for the drying process. The solution proposed in the present study, with the effective use of a biomass-derived syngas to feed the drying section of a tissue paper plant, will allow saving approximately 8500 ton/y of CO2 emissions in comparison with today’s fossil fuel carbon footprint.

Computation of viscous flow characteristics of a supersonic intake using eddy-viscosity turbulence models

Results of numerical investigation of flow and performance characteristics of a rectangular supersonic intake experimentally tested at Mach number of 4.03 are presented. The viscous flowfield has been obtained by solving Favre averaged Navier–Stokes equations with two eddy viscosity turbulence models, namely, Mentor’s baseline (BSL) k-ω and shear stress transport (SST) k-ω models. In addition, the effect of wall temperature conditions as well as several configurations of cowl and isolator are simulated to validate the computational methodology. The analysis has been carried out at a freestream Mach number of 4.03 and 0° angle-of-attack, corresponding to a unit Reynolds number of about 6.9×107 m−1. The predicted boundary-layer and the wall static pressure distribution using SST k-ω model shows better agreement with the experimental data compared to the BSL model and hence indicates superior capability to capture the onset and the amount of flow separation due to SWBLIs. Moreover, the terminal shock structure at different operating modes as well as the “unstart because of SWBLIs” is predicted quite accurately using the model. The wall temperature condition is found to have a strong effect on the amount of flow separation at the cowl and the subsequent interactions. Further, the results show that the sidewalls have a marginal effect on the centerline wall static pressure, though a three-dimensional flowfield with two stream-wise vortices are observed close to it as a result of the swept SWBLIs of the cowl shock with the sidewall boundary-layer leading to a higher loss in performance.

Исследование акустических характеристик одиночной сверхзвуковой струи, истекающей в затопленное пространство

In this paper, the acoustic characteristics of a single supersonic jet flowing from a nozzle of a rocket engine into a flooded space at different pressure ratios are studied. A system of the Favre-averaged Navier-Stokes equations is used to describe the unsteady flow of a viscous compressible heat-conducting gas in a supersonic Laval nozzle and an outflowing jet. The system is enclosed by the ideal gas law. The implementation of the physical and mathematical model and the numerical studies are carried out using the OpenFOAM Extended open platform based on the modified dbnsTurbFoam solver. A conical nozzle with an opening angle of 45° at the Mach number of 3 at the nozzle exit is considered in this study. Air is used as the working gas. Amplitude-frequency spectra of acoustic radiation at the point located at a distance from the nozzle outlet are obtained at different pressure ratios of the outflowing supersonic jet. Analysis of the amplitude-frequency characteristics of the jet under study shows that the maxima occur mainly at low frequencies. The maximum oscillation amplitude for the considered jet configurations is revealed at a pressure ratio of 1 on a frequency of 787 Hz. The maximum sound pressure level is 149 dB.

Numerical investigation of impact of fixed-exit boundary-layer bleed on supersonic intake performance

Results of numerical investigation of flow and performance characteristics of a rectangular supersonic intake with boundary-layer bleed system are presented. The effects of several flush slot bleed geometric parameters including entrance and exit area, plenum size, rear edge vertical displacement and the position relative to the incident shock have been studied to clarify their effects on the compression performance. The viscous flowfield has been obtained by solving Favre averaged Navier-Stokes equations with shear stress transport (SST) k-ω turbulence model. Moreover, the numerical methodology deployed is validated with the experimental data from literature. The analysis has been carried out in the freestream Mach number range of 1.8-2.5 and at 00 angle-of-attack, corresponding to a unit Reynolds number of approximately 1.9−2.7×107 m−1. The results show that with the use of bleed, the exit flowfield uniformity as well as the critical and peak total pressure recovery (TPR) improves considerably at all operating conditions. Furthermore, the analysis indicates that the exit throat area of a slot bleed operating at a particular design condition can be increased up to a point such that it is just sufficient to eliminate the upstream boundary-layer at its peak operation. The variation in the bleed entrance area or its position relative to the throat entrance only alters the critical performance depending on the supercritical boundary-layer mass flow loss; however, the peak TPR or the sustainable backpressure remains the same at all upstream conditions, controlled by the fixed-exit throat area. Further, it is found that for the removal of comparable amount of boundary-layer mass flow, the effects of pure flush slot or of a configuration with slight vertical displacement at its rear edge, located at the same position are similar.

Numerical simulations of the 2D supersonic flow through the tip-section turbine blade cascade with a flat profile

Numerical simulations of 2D compressible flow through the tip-section turbine blade cascade with a flat profile and the supersonic inlet were carried out by the OpenFOAM code using the Favre-averaged Navier-Stokes equations completed by the γ-Re_θt bypass transition model with the SST turbulence model. Predictions completed for nominal regimes were concentrated particularly on the effect of the shock-wave/boundary layer interaction on the transition to turbulence. Further, the link between the inlet Mach number and the inlet flow angle i.e. the so called unique incidence rule was studied. Obtained numerical results were compared with experimental data covering optical and pressure measurements.

Characteristic Scales in Shock–Turbulence Interaction

A semi-empirical estimate of the time-averaged thickness of a planar shock embedded in a turbulent mean flow is presented in an effort to quantify the characteristic time and length scales for turbulence modeling. Simplified Favre-averaged Navier–Stokes equations are reformulated and combined with the Rankine–Hugoniot relations to obtain an equation that relates the shock structure and its characteristic thickness to the upstream turbulent and mean flow quantities. The only mean flow and turbulence quantities needed to compute the shock thickness or velocity profile through the shock are upstream Mach number , turbulent Mach number , and the Taylor-based Reynolds number . The accuracy of method for the shock structure is validated against direct numerical simulations of shock–turbulence interaction and shows a very good agreement over a wide range of Mach, Reynolds, and turbulent Mach numbers. Finally, the obtained ratio of characteristic shock time scale to the upstream turbulence time scale is shown to be proportional to the turbulent kinetic energy amplification through the shock and supported through direct numerical simulations.

Study on the Numerical Model of Transonic Wind Tunnel Test Section

The authors consider numerical simulations of transonic flows through various turbine cascades in a confined channel which approximates boundaries of real wind tunnel. The boundaries of the wind tunnel are impermeable or there can be permeable tailboards to diminish shock wave reflections. The mathematical model is based on Favre-averaged Navier-Stokes equations closed by a turbulence model and model of transition to turbulence. The mathematical model is solved by an implicit finite volume method with multi-block grids. Several types of turbine blade cascades with subsonic or supersonic inlet are presented. The results are compared with optical measurements and simulations of periodic cascades. The validity of experimental reference flow parameters in relation to computed flow patterns is discussed.

A novel sharp interface immersed boundary framework for viscous flow simulations at arbitrary Mach number involving complex and moving boundaries

This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an in-house, parallel, multi-block structured finite volume flow solver, which employs a 3D unsteady Favre averaged Navier Stokes equations in a generalized curvilinear coordinate system; while we employ a combination of HCIB (Hybrid Cartesian Immersed boundary) method and GC(Ghost-cell) for solution reconstruction near immersed boundary interface. A significant difficulty for these sharp interface approaches is of handling sharp features/edges of complex geometries. In this study, we observe that apart from the need for robust node classification strategy and higher order boundary formulations, the direction in which the reconstruction procedures are performed plays an important role in handling sharp edges. Taking this into account we present a versatile interface tracking procedure based on ray tracing algorithm and a novel three step solution reconstruction procedure that computes pseudo-normals in the regions where the normal is not well-defined and reconstructs the flow field along those directions. We demonstrate that this procedure enables solver to efficiently handle and accurately represent sharp-edged regions. A fifth-order weighted essentially non-oscillatory (WENO) scheme is used for capturing shock-induced discontinuities and complex fluid-solid interactions with high resolution. The developed IBM framework is applied to a wide range of flow phenomena encompassing all-speed regimes (M=0.001 to M = 2.0). A total of seven benchmark cases (three stationary and four moving bodies) are presented involving various geometries (cylinder, airfoil, wedge) and the predictions are found to be in excellent agreement with the published results.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЗАИМОДЕЙСТВИЯ СОСТАВНОЙ СВЕРХЗВУКОВОЙ СТРУИ С ПРЕГРАДОЙ

The paper presents the results of the mathematical modeling of a supersonic twin jet interaction with an obstacle for the Mach number of 4.5 specified at the nozzle exit. Mathematical formulation of the problem includes a system of Favre-averaged Navier-Stokes equations and SST turbulence model for a viscous compressible ideal gas. The calculations are carried out using the free software OpenFOAM Extended with the Godunov method employed. The effect of the distance between nozzles on the shock-wave structure of the gas flow and on the force action of the plumes on the obstacle is studied. The distance between the nozzles varied in the range of 0.1−4. It is found that with an increase in the distance from 0.1 to 0.5, the flow structure is significantly rearranged, and two pressure maxima arise, which increase in comparison to the distance of 0.2. A decrease in pressure on the obstacle is observed at the distance over 1.0. For a distance of 4, two pressure maxima occur on the axis of each jet, while the force action of each jet is half as high as the resultant jet force action for a distance of 0.1. The transition from a stationary regime to a self-oscillating one is observed when the distance exceeds the value of 1.5.

A robust sharp interface based immersed boundary framework for moving body problems with applications to laminar incompressible flows

This study presents a robust, sharp interface immersed boundary (IBM) framework for moving body problems. The in-house solver makes use of a density-based finite volume framework for solving unsteady, 3D Favre averaged Navier Stokes equation in a generalized curvilinear coordinate system. The immersed boundary formulation is capable of handling arbitrarily complex three-dimensional bodies. The sharp interface approach allows for the exact imposition of boundary conditions at the immersed surface by reconstructing the flow field along its local normal. The implemented reconstruction schemes maintain second-order accuracy. The study focuses on issues of mass conservation and spurious temporal oscillations (pressure as well as force) that the sharp interface IBM approach typically faces when encountering moving body problems. A ghost node-based field extension technique provides an efficient way to improve mass conservation and as a result, reduces not only spurious oscillations but also increases temporal accuracy. Flow past both bluff body (triangular, circular and spherical), as well as streamlined body (airfoil), is presented here as validation studies. The ability of the present formulation to deal with moving body problems in the laminar incompressible flow regime is demonstrated by presenting cases that involve motions such as pitching and in-line oscillation. The predictions are found to be in good agreement with the published results and measurements as well.

Modelling of mixing and ignition of a cold hydrogen jet in a supersonic hot air flow

The paper presents the results of numerical studies of self-ignition and supersonic combustion of cold hydrogen jet supplied to the M=2 vitiated air flow. The calculations are carried out using the ANSYS Fluent on the basis of the full Favre-averaged Navier-Stokes equations supplemented by the κ–ω SST turbulence model and several kinetic mechanisms including 1, 16 and 38 reactions. The results of calculations of mixing of a cold hydrogen jet and a hot inert mixture are in good qualitative and quantitative agreement with experimental data. The results obtained for the reactive flow show that in the calculation the combustion layer is closer to the channel bottom wall than in the experiment, and the temperature of the reaction product is by 10 % lower.

Detailed Comparative Analysis of Interaction of a Supersonic Flow with a Transverse Gas Jet at High Pressure Ratios

The interaction of a 3D supersonic turbulent gas flow with a transverse sonic jet injected from the wall has been studied in detail both numerically and experimentally. However, the main drawback of such studies is the lack of detailed description of formation and propagation of vortex structures for moderate and large parameters n (ratio of pressure in the jet to pressure in the flow). Analysis performed in this study is aimed at revelation and detailed explanation of mechanisms of formation of vortices behind the injected sonic jet in a supersonic oncoming flow depending on n for improving the effectiveness of mixing of the jet with the flow. As initial equations, we have used 3D Favre-averaged Navier–Stokes equations closed by the k–ω model of turbulence; these equations are solved using the algorithm based on the essentially nonoscillatory scheme of the third approximation order. We have demonstrated the presence of the following vortex structures known from a number of theoretical publications: two oppositely rotating vortices in front of the jet, a horseshoe vortex; and two pairs formed in the mixing zone between the jet and the flow (one in the wake behind the jet and the other on the lateral line of the jet). We have determined the pressure ratios for which extra pairs of vortices appear (one pair emerges at the Mach disk edge as a result of interaction of a retarded flow of the jet behind the Mach disk with a high-velocity ascending flow behind the barrel and the other pair is formed due to the interaction of the ascending jet flow with the incoming main gas flow). As a result of comparative analysis, the pressure ratios for which a clear pattern of additional horn vortices is observed near the wall in the region behind the jet, have been determined. The dependence of the slope of the bow shock on the pressure ratio has been plotted. It is found that the pressure distribution at the wall in front of the jet in the symmetry plane is in satisfactory agreement with experimental data.

Numerical Solution of the Problem of Flow Past Projected Bodies for Determining Their Aerodynamic Coefficients

The method of solving the problem of external flow past a body for calculating the aerodynamic characteristics of projected bodies of complex geometrical shape is presented. Two approaches to the solution of the problem are considered: a numerical solution of the Favre-averaged Navier–Stokes equations with the use of the turbulence model and simulation of large vortices on the basis of the Navier–Stokes equations, in which numerical dissipation acts as a subgrid model of turbulence. Testing the results of calculations for the problem of flow past bodies by various methods showed their good correspondence to each other and with experimental data. For a projected body of a characteristic shape (missile) numerical simulation is made for a wide range of parameters: Mach numbers, angles of attack, and rotation speeds. Approximation dependences of the coefficients of aerodynamic forces and moments are constructed that can be used further for calculating the trajectories of projected bodies.

Детально-сравнительный анализ взаимодействия сверхзвукового потока с поперечной газовой струей при больших параметрах нерасчетности

The interaction of the spatial supersonic turbulent gas flow with a sound jet injected perpendicularly was widely studied both numerically and experimentally. However, there are only a few studies of the detail analysis of the formation and distribution of vortex structures from moderate till high pressure ratio (the ratio of pressure in the jet to pressure in the main flow).The aim of this paper is the study and identify the system of the vortex forming behind the injected sound jet in a transverse supersonic flow from the point of view of the mixing efficiency. For that the three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The presence of well known vortex structures are shown: two oppositely rotating vortices in front of the jet; horseshoe vortex; two pairs of the vortex in the mixing zone of the jet and the main flow, where one of them is located in the wake behind the jet and other in the lateral line of the jet. Also, the pressure ratio parameters are determined at which the additional pairs of vortices appear. Where, the first of them is formed on the edge of the Mach disk as a result of the interaction of the decelerated jet flow behind the Mach disk with the high-speed ascending flow behind the barrel. And, the second is due to the interaction of the ascending jet flow with the main gas flow. As a result of comparative analysis the criterion of the pressure ratio parameters are found under which a clear picture of additional horn vortices is observed near the wall in the region behind the jet. The graph of the dependence of the angle of inclination of the bow shock wave on the parameter of pressure ratio is obtained. Satisfactory agreement of the pressure distribution on the wall in front of the jet in the symmetry plane with experimental data is established.

Investigation of the Ways of Increasing the Shooting Range of the Barrel Artillery

Проанализированы основные способы повышения дальности стрельбы из артиллерийского орудия. Исследования проведены на основе разработанной методики расчета траектории движения снаряда. Аэродинамические коэффициенты сил и моментов, действующих на снаряд, определялись путем численного моделирования обтекания снаряда. Применен подход, основанный на численном решении уравнений движения сплошной среды Навье - Стокса, осредненных по Фавру с использованием k-ε-модели турбулентности с учетом эффекта сжимаемости. Сформулирована задача оптимизации коэффициента лобового сопротивления осколочно-фугасного снаряда классической формы от основных геометрических размеров. Проведены параметрические исследования зависимости коэффициента сопротивления снаряда от его геометрических размеров. Исследована зависимость дальности стрельбы от баллистических условий: массы снаряда, начальной скорости, угла стрельбы. Определено оптимальное сочетание массы и начальной скорости снаряда с учетом решения задачи внутренней баллистики. Рассмотрен способ повышения дальности стрельбы за счет использования реактивного двигателя в конструкции артиллерийского снаряда. Исследована зависимость дальности стрельбы от времени старта реактивного двигателя. Определены углы стрельбы, обеспечивающие максимальную дальность полета снаряда.

Buoyancy driven turbulent plume induced by protruding heat source in vented enclosure

The buoyancy driven thermal plume behavior inside a partial square enclosure with protruding isothermal heat source block is numerically investigated. The turbulent flow is modeled by using unsteady Favre-averaged Navier-Stokes (UFANS) equation with buoyancy modified Lam Bremhorst low Reynolds number k−ϵ model. A Simplified Marker and Cell algorithm (SMAC) is used to solve the governing equations and the computations are performed using an in-house code based on Finite difference method. The heat transfer characteristics and the bidirectional exchange across the vent are analyzed for different Grashof number 108 ≤ Gr ≤ 1011. Further, the thermal plume patterns are investigated by mounting the heat source block at five different locations δ = 0.25 H, 0.35 H, 0.5 H, 0.65 H and 0.75 H. A significant enhancement in the net mass flow rate and average Nusselt number is observed by increasing the Grashof number. It is found that the heat source location has strong influence on the vent bidirectional exchange rate, thermal mixing and heat transfer characteristics inside the enclosure. The present model is validated with the experimental and numerical benchmark results available in literature.