Favre-averaged Navier-Stokes Research Articles

Turbulence effects in the topology optimization of compressible subsonic flow

AbstractTurbulence significantly influences fluid flow topology optimization, and this has already been verified under the incompressible flow regime. However, the same cannot be said about the compressible flow regime, in which the density field now affects and couples all of the fluid flow and turbulence equations and makes obtaining the adjoint model, which is necessary for topology optimization, extremely difficult. Up to now, the turbulence phenomenon has still not been considered in compressible flow topology optimization, which is what is being proposed and analyzed here. Rather than being based in the Reynolds‐Averaged Navier–Stokes (RANS) equations which are defined only for incompressible flow, the equations are now based on the Favre‐Averaged Navier–Stokes (FANS) equations, which are the counterpart of the RANS equations for compressible flow and feature different dependencies and terms. The compressible turbulence model being considered is the compressible version of the Spalart–Allmaras model, which differs from the usual Spalart–Allmaras model, since now there are some new spatially varying density and specific heat terms that depend on the primal variables and that act over some of the turbulence terms of the overall model. The adjoint equations are obtained by using an automatic differentiation scheme through a coupled software platform. The optimization algorithm is IPOPT, and some examples are presented to show the effect of turbulence in the compressible flow topology optimization.

Finite-rate chemistry Favre-Averaged Navier-Stokes based simulation of a non-premixed SynGas/Air flame

Abstract The present paper is devoted to the study of the influence of chemical mechanisms, turbulence models and gas radiative properties models on the characteristics of a turbulent diffusion CO/H2/N2 -air flame, i.e., the so-called syngas flame in a Favre-averaged Navier-Stokes (FANS) environment. For this purpose, a transient FANS solver for combustion is used. The simulations are carried out using three distinct turbulence models, i.e., the standard k-ε (SKE), the renormalization group (RNG) k-ε, and the Shear Stress Transport (SST) models. The turbulence-chemistry interaction is modeled using the Partially Stired Reaction (PaSR) model. The chemical mechanisms used in the present study are: (i) a compact skeletal C2 mechanism, (ii) a mechanism developped by Frassoldati-Faravelli-Ranzi (FFR) containing 14 species and 33 reactions and (iii) the optimised syngas mechanism by Varga. Radiation heat transfer is handled by the P-1 method. In addition, the performances of two gas radiative properties models, i.e., the grey mean gas and the weighted-sum-of-gray-gases (WSGG) models, are assessed in radiative heat transfer modeling of the syngas flame. The predicted results reveal that the combination of the RNG turbulence model and the C2 skeletal mechanism shows the best agreement with measurements. The WSGG model used predicts results with the same level accuracy as the grey gas model in modeling of the syngas flame.

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.

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.

Effect of Mach number and plate thickness on the flow field and heat transfer characteristics of supersonic turbulent flow over a flat plate at different thermal boundary conditions

Conjugate heat transfer analysis of supersonic turbulent flow over a finite thickness flat plate is studied numerically. The flow field is modeled by employing the Favre averaged Navier–Stokes (FANS) equations. Turbulence is modeled with the Menter’s shear-stress-transport (SST) k−ω model. The comparison of NCHT (non-conjugate heat transfer) and CHT (conjugate heat transfer) analysis shows that the interface temperature and fluid temperature variation for the CHT analysis are lower compared to the NCHT analysis. The results indicate that the interface temperature is significantly increased for the low thermal conductivity plate material, due to the reduced rate of heat transfer. The effect of plate thickness on the flow field temperature variation is negligible. However, it is observed that the maximum interface temperature Ti,max increases with the increase in plate thickness. The values of maximum interface temperature difference between the 5 mm and 2 mm thick Steel-1006 plates at Mach numbers 2, 4, and 5 in non-dimensional (non-dimensionalized with free-stream temperature) form are 0.05594, 0.129, and 0.1816 respectively for the isothermal boundary condition. Results indicate that for Mach 2, the heated wall thermal boundary conditions acts like heat source, leading to the higher interface temperature, whereas for Mach 4, and 5 the heated wall thermal boundary conditions acts like heat sink, thus lowering the interface temperature. The results show that for NCHT analysis the leading edge shock strength, and mean pressure along the wall increases with an increase in Mach number. The non-conjugate results (flow and heat transfer characteristics) of the present numerical study is validated with the direct numerical simulation (DNS) results available in the literature.

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.

Nonlinear Wind-Tunnel Wall-Interference Corrections Using Data Assimilation

This paper presents a novel approach for correcting wind-tunnel wall interference in the nonlinear flow regime, that is, in the presence of phenomena such as flow separation and shocks. The methodology uses a gradient-based optimization to minimize the difference between experimental measurements and a Favre-averaged Navier–Stokes (FANS) simulation. The aim is to exploit the high-fidelity experimental data to correct turbulence-modeling errors in the FANS simulations, as well as to use the accurate angle of attack and Mach number from the FANS simulations to correct the in-tunnel flow conditions. The optimization is carried out directly in free air, thus avoiding the requirement to mesh the wind-tunnel walls and/or to model the ventilated-wall boundary condition. A byproduct of this method is the availability of flow information everywhere around the test object, which augments and complements the experimental data. The methodology is tested on two-dimensional and three-dimensional flow cases, demonstrating a significant improvement in the agreement between experimental and numerical data.

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.

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.

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.

A new correlation of average temperature and maximum heat flux for turbulent supersonic flow in a large size channel up to Mach 5

Supersonic compressible turbulent flow through a large size channel is studied numerically. The flow is modeled by the Favre averaged Navier-Stokes (FANS) equation with k−ω as turbulence model, the resulting governing equations are solved by employing an in-house unsteady state density based solver developed using sixth order accuracy compact finite difference schemes. The effect of Mach number and different wall thermal boundary conditions influencing, the variation of velocity, temperature and density across the channel height are reported in the present study. In the present study, the height of the channel is considered as 10 mm and the bulk Reynolds number is in the range of 3.42×105 to 1.14×106 which is higher compared to previous studies. Furthermore, the present Reynolds number represents a fully turbulent flow scenario, common in many aerospace applications. The results indicate that for an adiabatic wall with higher Mach number, there is a substantial increase in the wall temperature. The flow characteristics for a heated wall carried at low and medium Mach numbers indicate that for higher wall temperature, the behaviour of flow characteristics shifts towards that of the adiabatic wall behaviour. However, for higher Mach numbers the flow characteristics behaves like that of isothermal wall condition. In the present work, mathematical correlations for average temperature and maximum heat flux based on the Mach number are developed for adiabatic and isothermal wall conditions, respectively. The present results are validated with direct numerical simulation (DNS) results reported in the literature.

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.

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.

Influence of slit sizes on the interaction structure of supersonic turbulent air flow with a multi-component injection jet in a channel

The supersonic air flow in a flat channel with transverse injection of a turbulent hydrogen jet through a slit in the bottom wall is numerically simulated. The solution of the initial Favre-averaged Navier-Stokes equations closed by the k-ω turbulence model is performed using an algorithm built on the basis of the WENO scheme. The interaction of a shock-wave structure with boundary layers on the lower and upper walls under conditions of an internal turbulent flow is investigated, namely, the effect of the width of the jet slit is studied. It is found that, in addition to the known shock-wave structures arising from the interaction of the incident flow with the transverse jet and the interaction of the main shock wave with the boundary layers near the walls, there is an additional system of shock waves and separation of the flow on the bottom wall at some distance from the jet downwards flow. Comparison with experimental data showed satisfactory agreement. undefined undefined Звуковая функция ограничена 200 символами Настройки : История : Обратная связь : Donate Закрыть

Numerical simulations of shock-wave interaction with a boundary layer in the plane supersonic flows with jet injection

A supersonic air flow in a plane channel with a transverse turbulent jet of hydrogen injected through a slot on the bottom wall is simulated. The algorithm for solving the Favre-averaged Navier-Stokes equations for the flow of a perfect multispecies gas on the basis of the WENO scheme is proposed. The main attention is paid to the interaction of the shock-wave structure with the boundary layers on the upper and lower duct walls under the conditions of an internal turbulent flow. Namely, a detailed study of the structure of the flow is done, and separation and mixing depending on the jet slot width are investigated. It is found that in addition to well-known shock-wave structures produced by the interaction of the free stream with the transverse jet and the bow shock interaction with the boundary layers near the walls, an additional system of shock waves and the flow separation arise on the bottom wall downstream at some distance from the jet. The comparison with the experimental data is performed.

Aerodynamic Characteristics of Steam Turbine Prismatic Blade Section

For the needs of high-performance steam turbines producer the data of a blade section measurement have been analyzed in detail using an experimental and numerical approach. The blade section is used on prismatic blades in high and medium pressure steam turbine parts. The linear blade cascade was tested at four pitch/chord ratios at two different stagger angles. The blade cascade was tested under two levels of Reynolds number in the range of output izentropic Mach numbers from 0.4 to 0.9.The inlet of the test section was measured pitch-wise by five-hole probe to determine the inlet flow angle. The free stream turbulence of inlet flow was determined at 2.5% what is very close to the operating conditions on first high pressure stages. Two-dimensional flow field at the center of the blades was traversed pitch-wise downstream the cascade by means of a five-hole needle pressure probe to find out the overall integral characteristics. The blade loading was measured throughout surface pressure taps at the blade center. An in-house code based on a system of Favre-averaged Navier-Stokes equation closed by non-linear two-equation EARSM k-ω turbulence model was adopted for the predictions. The code utilizes an algebraic model of bypass transition valid for both attached and separated flows taking into account the effect of free-stream turbulence and pressure gradient. Results are presented by integral characteristic in means of kinetic energy loss coefficient and velocity or pressure distribution in the blade wakes or on the blade surface. In this article, the effect of investigated criteria and comparison of experimental and numerical approach are presented and discussed.

Effects of physical properties on thermo-fluids cavitating flows

The aims of this paper are to study the thermo-fluid cavitating flows and to evaluate the effects of physical properties on cavitation behaviours. The Favre-averaged Navier-Stokes equations with the energy equation are applied to numerically investigate the liquid nitrogen cavitating flows around a NASA hydrofoil. Meanwhile, the thermodynamic parameter Σ is used to assess the thermodynamic effects on cavitating flows. The results indicate that the thermodynamic effects on the thermo-fluid cavitating flows significantly affect the cavitation behaviours, including pressure and temperature distribution, the variation of physical properties, and cavity structures. The thermodynamic effects can be evaluated by physical properties under the same free-stream conditions. The global sensitivity analysis of liquid nitrogen suggests that ρv, Cl and L significantly influence temperature drop and cavity structure in the existing numerical framework, while pv plays the dominant role when these properties vary with temperature. The liquid viscosity μl slightly affects the flow structure via changing the Reynolds number Re equivalently, however, it hardly affects the temperature distribution.

Investigation of Vortex Structures for Supersonic Jet Interaction Flowfield

The three-dimensional supersonic turbulent flow in presence of symmetric transverse injection of round jet is simulated numerically. The simulation is based on the Favre-averaged Navier-Stokes equations coupled with Wilcox’s turbulence model. The numerical solution is performed using ENO scheme and is validated with the experimental data that include the pressure distribution on the wall in front of the jet in the plane symmetry. The numerical simulation is used to investigate in detail the flow physics for a range of the pressure ratio . The well-known primary shock formations are observed (a barrel shock, a bow shock, and the system of λ-shock waves), and the vortices are identified (horseshoe vortex, an upper vortex, two trailing vortices formed in the separation region and aft of the bow shock wave, two trailing vortices that merge together into one single rotational motion). During the experiment the presence of the new vortices near the wall behind the jet for the pressure ratio is revealed.

Numerical Study of the Particle Dispersion on a Supersonic Shear Layer

The numerical study of the two-dimensional supersonic hydrogen-air mixing in the free shear layer is performed. The system of the Favre-Averaged Navier-Stokes equations for multispecies flow is solved using the ENO scheme of the third order accuracy. The k-ε two-equation turbulence models with compressibility correction are applied to calculate the eddy viscosity coefficient. The dispersion of the particles is studied by following their trajectories in the shear layer by Euler method. In order to produce the roll-up and pairing vortex rings, an unsteady boundary condition is applied at the inlet plane. At the outflow, the non-reflecting boundary condition is taken. The influence of different Mach numbers on the formation of vorticity structures and shear layer growth rate are studied. The obtained results are compared with the available experimental data and the numerical results of other authors. The numerical simulation of the particle dispersion in the shear layer with large scale vortical structure is conducted.

Effects of fluid thermophysical properties on cavitating flows

We studied the thermo-fluid cavitating flows and evaluated the effects of physical properties on cavitation behaviors. The thermo-fluid (including liquid nitrogen, liquid hydrogen and hot water) cavitating flows around a 2D hydrofoil were numerically investigated. The Favre-averaged Navier-Stokes equations with the enthalpy-based energy equation, transport equation-based cavitation model, and the k-ω SST turbulence model were applied. The thermodynamic parameter Σ, defined as \(\sum { = \left( {\rho _v ^2 L^2 } \right)/\left( {\rho _l ^2 C_v T_\infty \sqrt {\varepsilon _l } } \right)} \) was used to assess the thermodynamic effects on cavitating flows. The results manifest that the thermal energy solution case yields a substantially shorter and mushier cavity attached on the hydrofoil due to the thermodynamic effects, which shows better agreement with the experimental data. The temperature drop inside the cavity decreases the local saturated vapor pressure and hence increases the local cavitation number; it could delay or suppress the occurrence and development of the cavitation behavior. The thermodynamic effects can be evaluated by thermophysical properties under the same free-stream conditions; the thermodynamic parameter Σ is shown to be critical in accurately predicting the thermodynamic effects on cavitating flows. The surrogate-based global sensitivity analysis of liquid nitrogen cavitating flow suggests that ρv, Cl and L could significantly influence temperature drop and cavity structure in the existing numerical framework, while ρv plays the dominant role on temperature drop when properties vary with changing temperature. The liquid viscosity µl slightly affects the flow structure but hardly affects the temperature distribution.