Development and applications of the efficient hybrid RANS/ILES approach for the calculation of complex turbulent jets

An efficient hybrid RANS/ILES approach is suggested for simultaneous calculation of flows in nozzles and jets of realistic configurations. The basic elements of the method are described, which permit of attaining a high accuracy of the results using relatively coarse grids. Results are given of calculations of the efflux of subsonic and supersonic jets from nozzles of different types. Good agreement between calculation results and experimental data is observed in the case of computational grids with 5.0 × 10⁵–1.2 × 10⁶ nodes. The level of turbulence intensity is predicted both on the axis and in the layers of mixing of jets. The impact of parameters at the nozzle exit section on the characteristics of turbulence in the mixing layer in the initial region of jets is investigated.     

A finite difference calculation procedure for three-dimensional turbulent separated flows

A general finite difference scheme has been proposed along with a three-dimensional co-ordinate transformation procedure for the prediction of three-dimensional fully elliptic flows. This numerical scheme has been successfully employed for the calculations of the three-dimensional turbulent separated flow in a rectangular diffuser. The complexity of the phenomena is seen to increase tremendously for the three-dimensional flows of this class.     

The application of hybrid RANS/ILES approach for the investigation of the effect of nozzle geometry and mode of efflux on the characteristics of turbulence of exhaust jets

The efficient hybrid RANS/ILES approach is used for the investigation of the effect of nozzle geometry and parameters of flow at the nozzle exit section on the characteristics of turbulence in the exhaust jet. The calculations are performed for nozzles of different types such as conical and chevron nozzles and the nozzle of double-flow turbojet engine (TJE) with chevrons on the core nozzle. The effect of the foregoing parameters on the level of fluctuations of velocity and pressure in the investigated jets is demonstrated. The effect of off-design mode of efflux on the parameters of turbulence in the jet is investigated under conditions of supersonic efflux of the jet. The effect of misalignment of the core and fan nozzles on the flow in the jet is considered for the nozzle of double-flow TJE. Grids containing about 10⁶ cells are used for the calculations. The accuracy of the results is confirmed by comparison with the known experimental data.     

Analysis of three-dimensional structures in complex turbulent flows

The basic integral relations used in analyzing various images of flows are given. The differences in the Abel transform for laminar and turbulent flows have been shown. The integral Uberoi–Kovasznay transform used in analyzing direct-shadow images of turbulent flows has been described. The present possibilities of digital laser speckle-photography for analyzing speckle-images of turbulent flows with the use of integral Erbeck–Merzkirch transforms have been analyzed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 1, pp. 8–17, January–February, 2009.     

A study of unsteady-state operating conditions of a supersonic inlet by the RANS/ILES method

Using the hybrid RANS/ILES method, a flow was investigated under unsteady-state conditions in a rectangular mixed-compression supersonic inlet at M_d = 2. The computations were made for Mach numbers of the incident flow M₀ = 1.8, 2, and 3. The geometry of two variants was investigated, viz., with the boundary layer bleed system and without it. Calculations were performed on the meshs containing (1.69–1.78) × 10⁶ cells. The flow rate through the supersonic inlet was varied within a wide range. Under most of the conditions investigated, the flow in the duct was unsteady as a consequence of separation of the boundary layer upon its interaction with the shock waves. For all geometric variants investigated and M₀, the throttle characteristics were constructed by the averaged flow parameters as well as the dependences of the flow rate through the boundary layer bleeding system and the static pressure pulsation level on the air inlet throttle ratio. Comparison of the computed results with the experimental data showed a good agreement in terms of both the averaged flow parameters and the pulsation characteristics.     

Mathematical models for the numerical study of turbulent flows

Abstract

This paper presents (1) a brief overview of the mathematical models used in the numerical study of turbulent flows; (2) a K‐? model of turbulence; and (3) extensions of the K‐? model to account for some of the effects of compressibility, low Reynolds number, streamline curvature, and preferential stress dissipation.     

A Treatment of wall boundaries for turbulent flows by the use of a transmission finite element method

A method to connect momentum Navier-Stokes equations with the universal law of the wall using the finite element method is developed for turbulent wall flows. This method is based on a domain decomposition of the fluid into subdomains near a solid boundary where the law of the wall is valid. A transmission formulation is introduced to match these regions and a new class of boundary finite element is used. This finite element takes into account the near-wall profile of the velocity and the transmission conditions. Computational results are presented for Poiseuille flow and flow over a backward-facing step.     

A hybrid stabilization approach for reduced-order models of compressible flows with shock-vortex interaction

Model order reduction approaches, such as proper orthogonal decomposition (POD)-Galerkin projection, provide a systematic manner to construct Reduced-Order Models (ROM) from pregenerated high-fidelity datasets. The current study focuses on the stabilization of ROMs built from high-fidelity simulation data of a supersonic flow passing a circular cylinder, which features strong interactions between shockwaves and vortices. As shown in previous literatures and the current study, an implicit subspace correction (ISC) method is efficient in the stabilization of similar problems, but its accuracy is not consistent when applied on different ROMs; on the other hand, an eigenvalue reassignment (ER) method delivers superb accuracy when the mode number is small, but becomes too expensive and less robust as the number increases. A Hybrid method is proposed here to balance the computational cost while improving the overall robustness/accuracy in ROM stabilization. The Hybrid method first handles the majority of the modes using the ISC method and then applies the ER method to fine tune a smaller number of modes under a constraint for accuracy. Furthermore, when the typical L2 inner product is changed to a symmetry inner product in both POD computation and Galerkin projection, the performance of the stabilized ROMs is substantially improved for all methods.     

On nonlinear models for the pressure-strain rate correlations in turbulent flows

Simple inequalities are obtained that can be used for direct verification of the adequacy of nonlinear models describing a rapid part of the pressure-strain rate correlation tensor. Analysis of a quadratic model shows that such models cannot be accepted in a most part of the physical domain because of violation of the condition of positive definiteness of the spectral matrix of two-point correlations of the pulsation velocity. The boundaries of such “forbidden” zones can be even wider than those for the classical linear models.     

An investigation of the Prandtl number effect on turbulent heat transfer in channel flows by large eddy simulation

Summary Fully developed turbulent channel flow with passive heat transfer has been calculated to investigate the turbulent heat transfer by use of the large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objectives of this study are to examine the effectiveness of the LES technique for predicting the turbulent heat transfer at high Prandtl numbers and the effects of the Prandtl number on the turbulent heat transfer in a fully developed turbulent channel flow. In the present study, the Prandtl number is chosen as 0.1 to 200, and the Reynolds number, based on the central mean velocity and the half-width of the channel, is 10⁴. Some typical cases are computed and compared with available data obtained by direct numerical simulation (DNS), theoretical analysis and experimental measurement, respectively, which confirm that the present approach can be used to predict the heat transfer satisfactorily, even at high Prandtl numbers. To depict the effect of the Prandtl number on turbulent heat transfer, the distributions of mean value and fluctuation of resolved flow temperatures, the heat transfer coefficient, turbulent heat fluxes, and some instantaneous iso-thermal sketches are analyzed.     

Computational techniques and validation of 3-dimensional viscous/turbulent codes for internal flows

Computational techniques and codes developed for the prediction of three-dimensional turbulent flows in internal configurations and rotor passages are described. Detailed calibration and validation of the flow fields in 90° curved ducts, cascades, end-wall flows and turbomachinery rotors are presented. Interpretation and comments on accuracy, level of agreement with various turbulence models and limitations of the codes are described. The single pass space-marching code is found to be efficient for curved duct and two-dimensional cascade flows. Multipass space-marching, time-marching and zonal methods are found to be accurate for complex situations. The efficiency and accuracy of a zonal technique, with considerable saving in computational time, is demonstrated. Paper presented atagard Symposium “Validation of Computational Fluid Dynamics,” May 2–5, 1988, Lisbon, Portugal The research work on computation was sponsored by the David Taylor Naval Ship Research and Development Center with Dr D Fuhs as the technical monitor, and NASA Lewis Research Center with Dr P Sockol as the technical monitor.     

The Use of the RANS/ILES Method to Study the Influence of Coflow Wind on the Flow in a Hot,Nonisobaric, Supersonic Airdrome Jet during Its Interaction with the Jet Blast Deflector

The influence of the coflow wind on the flow in a hot, nonisobaric, supersonic airdrome jet from a biconical nozzle and its interaction with a jet blast deflector (JBD) are studied by the RANS/ILES method. The conditions at the external boundary of the computational domain are formulated for the problem of jet interaction with the JBD. All calculations were performed at the Joint Supercomputer Center of the Russian Academy of Sciences with a MVS-10P supercomputer. The features of method parallelization for the supercomputer with modern architecture are described. The total temperature of the jet at the nozzle output is T₀ = 1050 K and π_с = 4. The wind velocity ranges from 0 to 20 m/s. Two JBD positions are examined: at distances of 5 and 15D_e of the nozzle cross section. The computation grids consist of (6.33–8.53) × 10⁶ cells. Fields of the flow parameters and of their turbulent pulsations near the jet are obtained. The dimensions of the “safety zone” for people and machinery is determined by the temperature, pressure pulsations, and velocity near the airdrome surface. The influence of wind velocity on the size and shape of the safety zone are revealed. The distributions of pressure and temperature and their pulsations over JBD altitude are presented as a function of JBD position and wind velocity.     

Calculation of separated flows within the framework of the model of an ideal fluid with allowance for a turbulent shear layer on the boundary of the separation region

Using the example of the problem of a supersonic flow about bodies with a forward separation zone, the authors propose a theoretical model based on the model of an ideal fluid with allowance for a turbulent shear layer on the boundary of the separation region.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 4, pp. 555–563, October, 1986.     

Problems in the study of electrical arcs with turbulent flows

The unique features of a dc electrical arc burning in a long cylindrical channel with an accompanying flow of plasma-forming gas are considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 57, No. 1, pp. 48–53, July, 1989.     

Numerical investigation of three-dimensional turbulent flow and endwall heat transfer in a large-scale cascade of turbine blades

Numerical simulation is performed of three-dimensional turbulent flow and heat transfer in a cascade of turbine blades (Langston cascade), for which numerous data are available in the literature. For closing the system of Reynolds-averaged Navier-Stokes equations, use is made of two-parameter models of turbulence of the k-ω family, low-Reynolds version of the Wilcox model, and the SST model of Menter. Numerical solutions are obtained in detailed grids (over a million cells) using the finite-volume code of second-order accuracy. It is demonstrated that the predicted structure of flow and local heat transfer on the end wall are very sensitive to the choice of model of turbulence, especially in the case of a thick boundary layer at the cascade inlet. By and large, the use of the Menter model enables one to well reproduce the complex vortex structures of flow in the cascade, as well as the local and integral characteristics of loss of total pressure. The local endwall heat transfer is predicted adequately.     

The kinetic model of particle transfer in turbulent flows with consideration of collisions

The work presents the kinetic model of particle dynamics in turbulent flows taking into consideration inelastic collisions. Transfer coefficients of the dispersed phase in constrained flows are found on the basis of this model.Krzhizhanovskii Moscow Power Engineering Institute. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 1,Krzhizhanovskii Moscow Power Engineering Institute. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 1,     

Application of the hybrid zone/Monte Carlo method to 3-D curvilinear grids in radiative heat transfer

The zone method is applied to non-orthogonal curvilinear grids for the computation of radiative heat transfer. The interchange areas are calculated by the Monte Carlo technique which has been fitted with a generalized ray tracing procedure. The method is applied to two complex three-dimensional (3-D) cases where in homogeneities are present in the radiation space (non-uniform gas properties and/or shadowing effects), and the gas is taken as gray. For comparison purposes, the same examples are worked out with the discrete transfer method. Very small discrepancies are found between the two methods for the surface heat fluxes, but the gas volumetric radiative sources are much more sensitive to inhomogeneities in the gas phase, resulting in higher discrepancies for these terms. The method can be readily extended to incorporate real gases and scattering effects.     

Interference of separated flows behind backward-facing step in the presence of passive control

The interaction of turbulent separated flows behind a backward-facing step in the presence of a passive miniturbulizer has been experimentally studied using digital particle-tracking velocimetry techniques. It is established that an obstacle placed in front of the step modifies the profiles of velocity and turbulent pulsation and significantly changes the length of a recirculation zone.