Semi-empirical Turbulence Model Research Articles

Bayesian parameter estimation and evaluation of the K-ω shear stress transport model for plane impinging jets

Numerical simulations with semi-empirical turbulence models are commonly used to model impinging jets, often used for cooling solid surfaces. In this work, the constants in the k-ω shear stress transport model in ANSYS FLUENT are calibrated to experimental velocity and heat transfer data for a plane turbulent impinging air jet to determine if Kennedy-O’Hagan calibration (Kennedy and O’Hagan 2001 J. R. Stat. Soc. B 63 425–64) can improve predictions of near-surface velocities and surface Nusselt numbers for similar flows. Impinging jets have been proposed to cool the target plates of the divertor in future magnetic fusion energy reactors, where simulations are used to estimate divertor performance. The flat-plate divertor (Wang et al 2009 Fusion Sci. Technol. 56 1023–7) uses a plane jet of helium issuing from a B = 0.5 mm slot to cool a surface with radius of curvature of 44B at a distance 4B from the slot. Predictions from the calibrated numerical model are compared with independent experimental data at different flow conditions, as well as surface temperature data for a flat plate divertor test section. The contribution of this work is evaluation of the accuracy of a calibrated turbulence model for modest extrapolations in flow geometry and flow conditions for a plane impinging jet.

Влияние неравномерности потока за корпусом модели одновального судна на гидродинамические и кавитационные характеристики отдельной лопасти в составе гребного винта

Object and purpose of research. This paper investigates wake non-uniformity effect of single-shafter model upon local and integral hydrodynamic and cavitation parameters of separate blade of its propeller. The study was performed on propeller models KP505 and containership models KCS. Materials and methods. Local and integral hydrodynamic parameters of propeller and container ship were obtained as per CFD methods. Viscous flow parameters are obtained through finite volume (FVM) solution of unsteady Reynolds equations (URANS) closed by biparametric semi-empirical turbulence model. Main results. The paper demonstrates that local and integral parameters of separate blade in “hull-propeller” system are considerably different from those determined in the uniform wake at the speeds obtained for the nominal wake field in behindhull conditions. Conclusion. Krylov State Research Centre experience of numerical calculations shows that 1) in many aspects of marine hydrodynamics numerical techniques are more informative than model tests and 2) in a number of cases, conventional propeller design approach based on the nominal wake field data (calculated or experimental) might lead to somewhat incorrect technical solutions.

Bayesian Parameter Estimation of the k-ω Shear Stress Transport Model for Accurate Simulations of Impinging-Jet Heat Transfer

Given the lack of fusion-relevant component test facilities, current estimates of the thermo-fluid performance of plasma-facing components are based for the most part on numerical simulations. A major source of uncertainty in these simulations is the semiempirical turbulence (closure) models for the Reynolds stresses appearing in the governing Reynolds-averaged Navier-Stokes equations, which involve a set of constants that depend upon the flow. The objective of this study is to evaluate Bayesian parameter estimation of turbulence closure constants in ANSYS Fluent to model heat transfer in impinging jets. The Bayesian statistical calibration produces a probability distribution for these constants from experimental data; the maximum a posteriori estimates are then taken to be the calibrated constants, or parameters. The turbulence model constants are calibrated using an experimental study of a submerged jet of air impinging on a flat heated surface at Reynolds numbers Re = O(104) and impingement distance in jet diameters H/d = 2. Numerical predictions using the calibrated model parameters are then compared with those generated using the default constants. Predictions obtained with model parameters calibrated on datasets of two different sizes are compared to evaluate the effect of the number of calibration samples. Finally, the extrapolative ability of the calibrated model is examined by predictions at a Re beyond the calibration values.

Разработка математической модели акустического источника, сопровождающего распад кавитационной каверны на схлопывающиеся пузырьки

Object and purpose of research. This paper is intended to develop a mathematical model of cavitation void fragmentation into separate collapsing bubbles as an acoustic source for further implementation in Logos software package. The study was performed on propeller models in cavitating environment. Subject matter and methods. Volume and quantity of bubbles appearing after fragmentation of a cavitation void on propellers, as well as amplitude and frequency properties of a single bubble collapse are studied as per CFD methods. Viscous flow properties are found from finite-volume (FVM) solution to unsteady Reynolds equations (RANS) closed by a biparametric semi-empirical turbulence model. The coefficients in the mathematical model of acoustic source thus obtained were calibrated through validation that included noise measurements at KSRC Cavitation Tunnel. Main results. This work included numerical simulation of collapse dynamics for a single cavitation bubble at different initial conditions, with approximation of the pressure impact created by bubble collapse in the infinite fluid and near a solid wall. The study estimated volume and quantity of the bubbles created by the fragmentation of cavitation void on propellers (3 propellers of different shape operating at different advance ratios and cavitation numbers). The mathematical model representing above-mentioned process could be further implemented in Logos software as a finite-volume algorithm with k-ω SST turbulence model. The study also created a validation base for further testing and calibration of the mathematical model thus developed. Conclusion. The study was performed as part of project Mathematical simulation on exa- and zetaflops class supercomputers launched by National Centre for Physics and Mathematics (Russia). The analysis of obtained results has shown that the mathematical model suggested in this paper does have practical potential, but it needs additional empirical data for greater flexibility and more accurate estimates. Without this model, these practical tasks still could be handled but at a cost of considerable and, most importantly, unnecessary increase in required hardware resources.

Research and Development of Criterial Correlations for the Optimal Grid Element Size Used for RANS Flow Simulation in Single and Compound Channels

At present, software products for numerical simulation of fluid dynamics problems (ANSYS Fluent, Ansys CFX, Star CCM, Comsol, etc.) problems are widely used. These software products are mainly based on the numerical solution of the Navier–Stokes equations, the most common and computationally easy method of solving, which is Reynolds averaging (RANS), and further closing the system using semi-empirical turbulence models. Currently, there are many modeling methods and turbulence models; however, there are no generalized recommendations for setting up grid models for modeling flows, while for practical use both the correct mathematical models and the setting of the computational grid are important. In particular, there are no generalized recommendations on the choice of scale of global elements of grid models for typical single channels. This work is devoted to the development and study of relations for a priori estimation of the parameters of a grid model in relation to solving hydrodynamic problems with fluid flow in channels. The paper proposes the introduction of a generalized grid convergence criterion for single channels at high Reynolds numbers. As single channels, a channel with a sudden expansion, a channel with a sudden contraction, and diffuser channels with different opening angles are considered. Based on the results of variant calculations of typical single channels at various Reynolds numbers and various geometric parameters, generalized criterion correlations were obtained to find dimensionless linear scales of grid elements relative to the hydrodynamic characteristics of the flow in the channel. Variant calculations of the compound channel were investigated, which showed the adequacy of correlations proposed.

Валидация технологии прогнозирования гидродинамических характеристик судовых движителей в пакете программ «ЛОГОС»

Object and purpose of research. The objects of research are models of propeller and impeller of a water jet. The purpose of the work is to validate the new calculation module LOGOS of domestic software complex for engineering analysis and the technology for its use in predicting the hydrodynamic performance of ship propulsion based on comparison with experimental research data and reference calculations in foreign commercial software. Materials and methods. Methods of computational fluid dynamics are used to determine the hydrodynamic performance of ship propulsion systems. The characteristics of the viscous fluid flow are obtained from the solution of non-stationary Reynolds equations (RANS (Reynolds averaged Navier-Stokes equations)) by control volume method. The Reynolds equations are closed by a two-parameter semi-empirical turbulence model. To validate the results of numerical modeling in the LOGOS software package, data from experimental studies and reference calculations performed at the Krylov Center are used. Main results. Validation of the new calculation module of LOGOS software complex, performed on the basis of comparison with the results of experimental studies and reference calculations, demonstrates the high accuracy of modern domestic software in the field of computational fluid dynamics in solving problems of determining the hydrodynamic performance of propellers. Conclusion. The paper shows that the determination of hydrodynamic performance of ship propulsion models in a uniform viscous fluid flow can be performed using the domestic software package LOGOS. The accuracy of predicting the hydrodynamic performance of propellers in the meantime compares favourably to leading foreign software products and is confirmed by the results of experimental studies carried out in the deepwater towing tank of Krylov Center. At the same time, further development of the LOGOS software package is required for the correct solution of more complex tasks related to ship propulsion.

Внедрение методов суперкомпьютерной оптимизации в процесс проектирования водометных движителей

Object and purpose of research. This study discusses fast boats and waterjet propulsors. The purpose is to design a waterjet impeller shape to required conditions by means of supercomputer-based optimization with further validation of results at sea trials. Materials and methods. The optimization process is governed by a Russian software package pSeven. The computation core is Star CCM+ (Siemens). Parametric 3D model of the impeller is generated in BladePlus software (in-house KSRC development). Hydrodynamic parameters of waterjet are calculated as per CFD methods. Viscous flow parameters are found through the control-volume solution of unsteady Reynolds equations (URANS) closed by the bi-parametric semi-empirical turbulence model. Main results. The optimization studies yielded new shapes for impellers, stators and flow parts of waterjets. These solu-tions are more efficient than the prototype thanks to greater thrust of the propulsion system and lower resistance of the flow part without prejudice to good cavitation performance. Calculated hydrodynamic parameters of waterjets and the estimates for achievable speed of fast boats have been confirmed by the sea trials. Conclusion. Supercomputer optimization ensured successful beginning of the development of Russian waterjet family for fast boats not inferior to universally recognized market leaders in terms of performance parameters.

3D turbulent currents simulation in the coastal zone using the LES approach based on filtered ADCP data

The interest in turbulence in shallow waters, such as the Azov Sea, is caused by the fact that in the places of its existence there is an intensive transfer of the amount of motion and heat, the spread of passive impurities, the transfer of suspended particles. These processes significantly affect the formation and spatial structure of physical, chemical and biological fields of reservoirs and their spatial and temporal changes. Depending on the smoothing scale of the series of initial readings of the flow meters, the pulsation characteristics of the flow velocity were determined, which were processed in order to obtain data on turbulence and its scales. The research results provided empirical data on the conditions of generation and existence of small-scale turbulence. The collected empirical material is currently being processed to study the internal structure of the recorded disturbances of small-scale turbulence. In this paper, small-scale motion is excluded from the Navier-Stokes equations by applying the filtration operation and is modeled using subgrid models. To do this, in two-dimensional and three-dimensional cases, various types of filters are used: a box filter, a Gaussian filter and a Fourier filter, with a gradual decrease in the filter width, which allows you to reproduce a wider frequency range of fluctuations of the solution. The obtained data are planned to be used for numerical simulation of three-dimensional turbulent flows using the LES approach and comparison with the results of averaging by RANS. The article considers the possibilities of using various types of approximations for parametrization of vertical turbulent exchange. Algebraic models for calculating the coefficient of vertical turbulent exchange and semi-empirical turbulence models are compared.

Валидация методики оптимизации пропульсивного комплекса транспортного судна

Object and purpose of research. This research was intended to validate supercomputer-based optimization procedure for propulsion systems of carrier ships, with a case study of hull shape and propeller optimization for a Project 1594 vessel. Materials and methods. The optimization proceeds in Russian software package pSeven. The computation core is Siemens Star CCM+ software. Three-dimensional parametric model of the propeller is generated in KSRC-developed BladePlus software, whereas three-dimensional parametric model of the hull is generated in Siemens NX software package. Hydrodynamic parameters of the propulsion system are obtained as per CFD methods. Viscous flow parameters are obtained through control volume-based solution of unsteady Reynolds equations (URANS) closed by biparametric semi-empirical turbulence model. Main results. The study yielded a new bow shape offering lower wave-making resistance for the same overall dimensions. It also yielded a new shape of propeller offering higher efficiency than the initial one taking into account the limitations for available shaft torque. Design hydrodynamic parameters have been confirmed by the model test data obtained at KSRC Deepwater Test Tank. Propulsion performance calculation has shown a growth in the achievable speed of the optimized propulsion system in different running conditions. Conclusion. The optimization studies intended to improve propulsion efficiency of Project 1594 ships yielded new shapes for hull and propeller. The solution thus obtained features high propeller efficiency and low wave-making resistance of the hull. Numerical simulation results have been confirmed with experimental data.

VARIOUS APPROXIMATIONS OF VERTICAL TURBULENT EXCHANGE PARAMETERIZATION FOR THE ANALYSIS OF THE WAVES HYDRODYNAMIC IMPACT ON THE BOTTOM OF THE RESERVOIR

The article discusses the possibilities of using various types of approximations for parametrization of vertical turbulent exchange for calculating and evaluating the hydrophysical characteristics of the wave regime in the accumulative coastal zone of the southwestern corner of the Tsimlyansk reservoir. It is impossible to carry out these studies without using various types and classes of approximations for parametrization of vertical turbulent mixing. Algebraic models for calculating the coefficient of vertical turbulent exchange and semi-empirical turbulence models are compared. Using ADCP data on velocity pulsations for several stations to measure hydrological characteristics, the results of parameterization of the vertical turbulent exchange coefficient were analyzed. The developed numerical algorithms and the software package implementing them are used to study the pressure field, the velocity vector field of the aquatic environment and the prediction of the baric field for this section of the reservoir water area.

Experimental and theoretical study of the flocculants mixing in water

The article discusses the process of high molecular weight flocculant particles dissolving in water during mechanical stirring. A procedure of mixer selection taking into account mixer geometry based on the Prandtl’s semi-empirical turbulence model was developed and described. It was found that the choice of the optimal rotation speed is related with the turbulent frictional stress generated by the impeller of the mixer. The results of experimental studies on the preparation of concentrated solutions of high molecular weight cationic flocculant MagnaflokМ 155 using various impeller types are shown. The efficiency of a conical mixer has been confirmed, which makes it possible prepare a flocculant solution 1.3 times faster due to the possibility of mixing at higher rotational speeds with lower power consumption

Analysis of the interaction of a supersonic gas flow with a solid low melting polymer as a ramjet engine propellant

The performance of ramjet engines with a supersonic combustion is one of the main directions of hypersonic aircraft development research is studied. Researchers around the world create special experimental facilities for testing engine models, investigate fuels for ramjet engines and classify new scientific data. Since the ambient temperature and the oxidizer flow temperature in engine air duct are low at the flight altitude of a hypersonic aircraft, low melting materials can be used as a fuel agent in a solid propellant. The main purpose of this work is analysis of heat and mass exchange processes associated with the motion of a supersonic gas flow in an axisymmetric duct described as a combustion chamber of a ramjet engine with a solid polymer. The mathematical model of the problem consists of the unsteady Reynolds-averaged Navier-Stokes equations and the equations of a semiempirical turbulence model. The stated problem was solved by the finite volume method. Initial and boundary conditions are identical to experimental conditions and this makes it possible to verify the results of the numerical solution directly during aerodynamic tests. Gas dynamic parameters for the gas flow in an air duct of a ramjet engine are described, pressure profiles at the gas-solid interface are plotted, and a transient pressure behavior is considered. The results of the solution of a coupled heat transfer problem allow analyzing a dynamic heat exchange pattern in a solid polymeric material (caprolone, polyethylene and polyoxymethylene). It has been found that the effect of a supersonic flow on the surface of a low melting material within one second leads to temperature changes in a solid to a depth of 20% of its total thickness.

Investigation of applicability area for turbulence models in the problems of mass transfer intensification by the control of a rotary divergent flow

The fundamental scientific problem of this kind arises in mechanics, chemistry and catalysis in the intensification of mass transfer. The turbulent mass transfer characteristics were analyzed experimentally in a controlled rotational-divergent flow. The laser Doppler anemometry was used for turbulent mass transfer diagnostic. The verification of numerical calculations by computational hydrodynamics has been carried out according to the results of experimental studies. Calculation of turbulent kinematic is build on solving of a system of continuity and the Navier-Stokes equations. The fluid is incompressible and isothermal. For averaged equations closure, semi-empirical turbulence models were used: the k-ε model of turbulence and the Reynolds stresses transfer model. The calculation has showed the existanceof a near-wall jet after a rotating device and the generation of reverse flow zones. Comparison with experimental data has shown that all models of turbulence adequately model the rotational-divergent flow only until the formation of flow gaps and the formation of reverse flow zones. The discrepancy with the experiment occurs while controlling the flow to equalize the velocity profiles.

SELECTION OF THE COMPUTATIONAL MODEL OF WIND FLOW IN THE PROBLEMS OF COMPUTATIONAL ARCHITECTURAL AND CIVIL ENGINEERING AERODYNAMICS IN ACCORDANSE WITH REGULATORY AND TECHNICAL DOCUMENTS

An overview of the main directions of numerical simulation of problems of architectural and civil engineering aerodynamics based on Computational Fluid Dynamics (CFD) is presented. The main advantages of numerical simulation in comparison with traditional methods of aero-physical modeling in wind tunnels are highlighted. The basic principles of numerical simulation of wind loads and actions on buildings and structures are outlined. In modern practice, numerical modeling by finite volume method is used with the decomposition of the velocity of the turbulent wind flow into the average and pulsation component within the averaged by Reynolds solution of Navier-Stokes equations using the semi-empirical turbulence model k-ш SST. In practice, the problem of the legitimate (in accordance with the requirements of building codes) selection of a computational model of wind flow is very important. This is equivalent to the assignment of boundary conditions within numerical simulation. The computational model of the wind, presented in the Russian building codes, requires additions to solve the problems of numerical simulation of architectural and civil engineering aerodynamics. A detailed comparison of the computational models of wind flow in Russian and foreign building codes is carried out. The following wind flow parameters are analyzed: the profile of the average wind speed, the profile of the intensity of turbulence, the profile of the scale of turbulence. A table of correspondence of terrain types according to the classification of Russian and foreign codes is proposed. The possibility of determining the parameters of the computational wind flow model based on the joint use of building codes in force in Russia and Belarus is shown. A set of measures is proposed with the goal of creating a regulatory and technical environment for the practical application of computational architectural and civil engineering aerodynamics in real design.

Comparative analysis of transition models in prediction of flow over NACA-0012 airfoils in tandem

Comparative analysis of several semi-empirical turbulence models taking into account laminar-turbulent transition (γ-Reθt SST, γ-SST, γ-SA and eN-SA) was carried out for flow around an airfoil in the wake generated by another upstream airfoil for different Reynolds numbers and distances between airfoils. Two dimensional Reynolds-averaged Navier Stokes equations were solved in different CFD codes on unstructured and chimera-type structured grids. Results of the considered transition models are virtually independent of the computational code. Results of the SST-based transition models are in reasonable agreement with experimental data while SA-based models predict too early transition.

Estimating of turbulent velocity fluctuations in boundary layer with pressure gradient by Smoke Image Velocimetry

The results of the experimental estimating of the velocity profiles and turbulent pulsations in the boundary layer for adverse and favorable pressure gradients are presented. The profiles of characteristics based on the dynamics of two-component instantaneous velocity vector fields measured by the field optical method of Smoke Image Velocimetry are estimated. The measurements are performed with a large spatial and temporal resolution, the measurement results are relevant for estimating the terms of the conservation equation of turbulent energy in the boundary layer and for improving semiempirical turbulence models.

The Choice of Turbulence Models for Steam Jets

The noise from the steam dumping is a serious problem for many industries. For example, the popping of pressure relief valves of power boilers causes a temporal sound level overshoot over the admissible one up to 30-40 dBA in a radius of several kilometers. Mathematical modeling is an important tool for studying the outflow steam jets. Knowing processes of steam efflux into the atmosphere allows us correctly to calculate noise levels at a distance from them on the one hand and on the other hand to realize measures for sound attenuation. The study of mechanisms of noise generation by jets had begun in the end of 1940s and had been generally related to investigations of air jets and exhaust gas jets of aircrafts. The choice of turbulence models for steam jets has been studied insufficiently until recently. The significant subject of the steam jet simulation is the choice of the turbulence model. There are about a dozen mathematical models of turbulence, which are implemented in different software packages. In the case of simulation of turbulent flows with transient large scale vortex structures, it is ineffective and impossible to solve Reynolds averaged Navier-Stokes equations closed using semi empirical turbulence model or by means of the direct numerical simulation (DNS). Simulation of three dimensional and nonstationary vortices is carried out using a Large Eddy Simulation (LES) method in which the idea of the formal mathematical differentiation of coarse and fine structures by means of either operation, for example the filtration operation, is recommended. It is noted that, based on the LES method, it is possible to compute the coherent vortex structures, and the applicability of the model for prediction of noise generated by steam jets. LES model describes noise generation processes from steam jet more correct.

Numerical simulation of momentumless turbulent wake dynamics in linearly stratified medium

This paper presents comparison of two numerical models of the momentumless turbulent wake dynamics behind a body of revolution in a linearly stratified medium, namely, the model based on direct (DNS) numerical integration of Navier–Stokes equations in the Oberbeck–Boussinesq approximation and the mathematical model with application of a semi-empirical turbulence model of the third order. The results of calculations by these two models agree with the known experimental data.

Method of near-wall conditions for investigating flows and heat transfer at high turbulence intensity

The dynamic and thermal characteristics of steady near-wall boundary layers are studied under the conditions of highly intense freestream turbulence on the basis of semi-empirical differential turbulence models. The method of the boundary condition transfer from the wall in the flow is tested against flows with laminar-turbulent transition. At low Reynolds numbers the modified turbulence models are applied to investigate the influence of the highly turbulent freestream parameters on the development of the dynamic and thermal processes in boundary layers in the transitional regime and at developed turbulence. The calculated profiles of the velocity, the kinetic energy of the turbulence, the temperature, and the friction and heat transfer coefficients are compared with the experimental data in the cases in which the boundary conditions are imposed on the wall or are specified in the flow. A possible range of the intermediate boundary positions is established.

Numerical simulation of gas flows around aircraft with allowance for the flow/exhaust jet interaction

Three-dimensional steady gas flow around aircraft in the presence of an exhaust jet are considered. The mathematical flow model is based on the Reynolds-averaged Navier-Stokes equations for a two-component equilibrium turbulent medium and a two-parameter semiempirical turbulence model. A numerical implementation of the model is described. Numerical examples are given.