Numerical modelling of momentumless wakes using semiempirical turbulence models of second and third order

2007 ◽  
Vol 22 (1) ◽  
Author(s):  
O. F. Voropaeva
Keyword(s):  
Numerical Modelling ◽  
Turbulence Models ◽  
Third Order ◽  
Momentumless Wakes

scholarly journals ANALYSIS OF NUMERICAL MODELLING OF TURBULENCE IN A CONICAL REVERSE‐FLOW CYCLONE

2010 ◽  
Vol 18 (4) ◽  
pp. 321-328 ◽  
Author(s):  
Petras Vaitiekūnas ◽  
Inga Jakštonienė
Keyword(s):  
Numerical Modelling ◽  
Swirling Flow ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Equation System ◽  
Reynolds Stress Model ◽  
Cylindrical Part ◽  
Solid Particles ◽  
System Modelling

This paper aims to analyse the problem of numerical modelling of the airflow in a conical reverse‐flow (CRF) cyclone with tangential inlet (equipment for separation of solid particles from gaseous fluid flow). A review of experimental and theoretical papers that describe cyclones with very complex swirling flow is performed. Three‐dimensional transport differential equations for incompressible turbulent flow inside a cyclone are solved numerically using finite volume‐based turbulence models, namely, the Standard k–ϵ model, the RNG k–ϵ model and the Reynolds stress model (RSM). The paper describes the numerical modelling of the airflow in the CRF cyclone, the height of which is 0.75 m, diameter ‐ 0.17 m, height of cylindrical part ‐ 0.255 m, height of conical part ‐ 0.425 m, inlet area is 0.085×0.032 m2. Mathematical model of airflow in a cyclone consisted of Navier‐Stokes (Reynolds) three‐dimensional differential equation system. Modelling results, obtained from the numerical tests when inlet velocity is 4.64, 9.0 and 14.8 m/s and flow rate is, respectively, 0.0112, 0.0245 and 0.0408 (0.0388) m3/s, have demonstrated a reasonable agreement with other authors’ experimental and theoretical results. The average relative error was ± 7.5%. Santrauka Nagrinejama duju aerodinamikos kūginiame grižtamojo srauto (KGS) ciklone (irenginys kietosioms dalelems atskirti iš oro srauto) su tangentiniu srauto itekejimu skaitinio modeliavimo problema. Trimates nespūdžiojo turbulentinio srauto ciklono viduje pernašos diferencialines lygtys skaitiškai sprestos baigtiniu tūriu metodu taikant standartini k–ϵ, RNG k–ϵ ir Reinoldso itempiu (RIM) turbulencijos modelius. Atliktas skaitinis oro srauto judejimo KGS ciklone modeliavimas. Ciklono aukštis – 0,75 m, skersmuo ‐ 0,17 m, cilindrines dalies aukšti ‐ 0,255 m, kūgines ‐ 0,425 m, itekejimo angos plotas 0,085×0,032 m2. Oro srauto judejimo ciklone matematinis modelis – Navje ir Stokso (Reinoldso) trimačiu diferencialiniu lygčiu sistema. Modeliavimo rezultatai, kai itekejimo greitis 4,64, 9,0 bei 14,8 m/s ir debitas – 0,0112, 0,0245 ir 0,0408 (0,0388) m3/s, neblogai sutapo su kitu autoriu eksperimentiniais rezultatais. Vidutine santykine paklaida ‐ ± 8 proc. Резюме Анализируется проблема аэродинамики газового потока в коническом возвратного потока (КВП) циклоне (оборудование для отделения твердых частиц от газового потока) с тангенциальной подачей газа. Произведен обзор экспериментальных и теоретических работ в циклонах такого типа, в которых образуется сложное вихревое течение потока. Для моделирования использованы трехмерные дифференциальные уравнения переноса, численно решаемые методом конечных объемов с использованием следующих моделей: стaндартной k–e, RNG k–e и рейнольдсовой модели турбулентности напряжений. Произведено численное моделирование движения потока воздуха в циклоне КВП, высота которого 0,75 м, диаметр – 0,17 м, высота цилиндрической части – 0,255 м, конической части – 0,425 м, площадь входного отверстия – 0,085×0,032 м 2 . Математическую модель движения потока воздуха в циклоне составила система трехмерных дифференциальных уравнений Навье-Стокса и Рейнольдса. Анализ результатов, произведенный при скоростях втекания в циклон 4,64, 9,0 и 14,8 м/с (дебит – 0,0112, 0,0245 и 0,0408 м 3 /c) и для модели рейнольдсовых напряжений, показал приемлемую согласованность с результатами других исследователей – со средней относительной погрешностью ± 7,5 проц.

Measurement and modelling of homogeneous axisymmetric turbulence

1998 ◽  
Vol 374 ◽  
pp. 59-90 ◽  
Author(s):  
TORBJÖRN SJÖGREN ◽  
ARNE V. JOHANSSON
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Theoretical Description ◽  
Wind Tunnel Experiments ◽  
Third Order ◽  
Point Velocity ◽  
First Time ◽  
Rapid Pressure

A new method for determining the slow and rapid pressure-strain rate terms directly from wind-tunnel experiments has been developed with the aid of a newly developed theoretical description of the kinematics of homogeneous axisymmetric turbulence. Both the straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. Direct experimental determination of the different terms in the transport equation for the Reynolds stress tensor plays a major role in the validation and development of turbulence models. For the first time it is shown that the pressure{strain correlation can be determined with good accuracy without balancing it out from the Reynolds stress transport equation (and without measuring the pressure). Instead it is determined through evaluation of integrals containing second- and third-order two-point velocity correlations. All the terms in the Reynolds stress equations are measured directly and balance is achieved.

Investigation and Modeling of the In-Tube Heat Transfer of Fluids at Supercritical Pressure During Heating

2017 ◽  
Author(s):  
Chen-Ru Zhao ◽  
Zhen Zhang ◽  
Han-Liang Bo ◽  
Pei-Xue Jiang
Keyword(s):  
Heat Transfer ◽  
Numerical Modelling ◽  
Convection Heat Transfer ◽  
Turbulence Models ◽  
Vertical Tube ◽  
Supercritical Pressure ◽  
Flow And Heat Transfer ◽  
Pressure Water ◽  
Predicted Values ◽  
Semi Empirical

Investigations and numerical modelling are performed on the heat transfer to CO2 at supercritical pressure under buoyancy affected conditions during heating in a vertical tube with inner diameter of 2 mm. Numerical modelling are carried out using several low Reynolds number (LRN) k-ε models, including the model due to Launder and Sharma (LS), Abe, Kondoh and Nagano (AKN), Myong and Kasagi (MK) models. The numerical results are compared with the corresponding experimental data and the predicted values using the semi-empirical correlation for convection heat transfer of supercritical fluids without deterioration. The abilities of various LRN models to predict the heat transfer to fluids at supercritical pressures under normal and buoyancy affected heat transfer conditions are evaluated. Detailed information related to the flow and turbulence is presented to get better understanding of the mechanism of the heat transfer deterioration due to buoyancy, as well as the different behavior of various LRN turbulence models in responding to the buoyancy effect, which gives clues in future model improvement and development to predict the buoyancy affected heat transfer more precisely and in a broader range of conditions as they come to be used to simulate the flow and heat transfer in various applications such as in the supercritical pressure water-cooled reactor (SCWR) and the supercritical pressure steam generator in the high temperature gas cooled reactor (HTR).

Numerical Modelling Techniques for Turbine Blade Internal Cooling Passages

2015 ◽  
Author(s):  
Priyanka Dhopade ◽  
Luigi Capone ◽  
Matthew McGilvray ◽  
David Gillespie ◽  
Peter Ireland
Keyword(s):  
Heat Transfer ◽  
Numerical Modelling ◽  
Secondary Flow ◽  
Mesh Generation ◽  
Fluid Dynamic ◽  
Turbine Blades ◽  
Turbulence Models ◽  
Secondary Flows ◽  
Internal Cooling ◽  
Modelling Techniques

Numerical modelling of internal cooling passages in gas turbine blades is a challenging task due to their physical characteristics, such as rounded duct corners, the presence of rib turbulators and their staggered locations between surfaces. This results in complex fluid dynamic phenomenon such as counter-rotating vortices and other secondary flow structures that can drive the heat transfer. Heat transfer mechanisms in such passages are inherently coupled with momentum transport and diffusion. Current industry practices for numerical modelling of such passages use unstructured mesh generation tools, steady Reynolds-averaged Navier-Stokes (RANS) equations and two-equation turbulence models such as k-ε and k-ω SST. This paper investigates two generic, engine-representative rib geometries using current numerical practices to determine their limitations. Three mesh generation tools and two turbulence models are compared across two rib geometries. The results are qualitatively and quantitatively compared to detailed experimental Nusselt numbers on the passage walls. It was found that as long as the rib geometry results in a secondary flow that directly impinges onto the wall, the meshing tools and turbulence models agree reasonably well with experiments. When the passage includes wall-wrapped ribs resulting in more complex secondary flows, this decreases the validity of the numerical tools, suggesting that more sophisticated modelling techniques are required as rib geometries continue to evolve.

scholarly journals Reynolds-Averaged Navier-Stokes Modeling of Turbulent Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz Mixing Using a Higher-Order Shock-Capturing Method

2019 ◽  
Author(s):  
Oleg Schilling
Keyword(s):  
Sulfur Hexafluoride ◽  
Mixing Layer ◽  
Turbulence Models ◽  
Shock Capturing ◽  
Navier Stokes ◽  
Weno Reconstruction ◽  
Third Order ◽  
Central Difference ◽  
Reynolds Averaged Navier Stokes ◽  
Good Agreement

Abstract A numerical implementation of a large number of Reynolds-averaged Navier–Stokes (RANS) models based on two-, three-, four-equation, and Reynolds stress turbulence models (using either the turbulent kinetic energy dissipation rate or the turbulent lengthscale) in an Eulerian, finite-difference shock-capturing code is described. The code uses third-order weighted essentially nonoscillatory (WENO) reconstruction of the advective fluxes, and second- or fourth-order central difference derivatives for the computation of spatial gradients. A third-order TVD Runge–Kutta time-evolution scheme is used to evolve the fields in time. Improved closures for the turbulence production terms, compressibility corrections, mixture transport coefficients, and a consistent initialization methodology for the turbulent fields are briefly summarized. The code framework allows for systematic comparisons of detailed predictions from a variety of turbulence models of increasing complexity. Applications of the code with selected K–ε based models are illustrated for each of the three instabilities. Simulations of Rayleigh–Taylor unstable flows for Atwood numbers 0.1–0.9 are shown to be consistent with previous implicit LES (ILES) results and with the expectation of increased asymmetry in the mixing layer characteristics with increasing stratification. Simulations of reshocked Richtmyer–Meshkov turbulent mixing corresponding to experiments with light-to-heavy transition in air/sulfur hexafluoride and incident shock Mach number Mas = 1.50, and heavy-to-light transition in sulfur hexafluoride/air with Mas = 1.45 are shown to be in generally good agreement with both pre- and post-reshock mixing layer widths. Finally, simulations of the seven Brown–Roshko Kelvin–Helmholtz experiments with various velocity and density ratios using nitrogen, helium, and air are shown to give mixing layer predictions in good agreement with data. The results indicate that the numerical algorithms and turbulence models are suitable for simulating these classes of inhomogeneous turbulent flows.

scholarly journals Results of Numerical Modeling of Combustion Processes in a Vortex Chamber

2018 ◽  
Vol 209 ◽  
pp. 00023
Author(s):  
Artem V. Badernikov ◽  
Shota A. Piralishvily ◽  
Alexander I. Guryanov
Keyword(s):  
Numerical Modeling ◽  
Temperature Field ◽  
Numerical Modelling ◽  
Velocity Component ◽  
Burning Velocity ◽  
Turbulence Models ◽  
Velocity Model ◽  
Vortex Chamber ◽  
Curvature Correction ◽  
Combustion Processes

The results of numerical modelling of combustion in a vortex chamber are presented. The calculations are performed using k-ε and k-ε with curvature correction of streamlines turbulence models. Upon combustion calculation of the well mixed mixture the Burning Velocity Model (BVM) was applied. The usage of the streamlines curvature correction allows to increase the accuracy of the prediction of the circumferential velocity component and the temperature field in the vortex chamber.

Nonlocal Convective PBL Model Based on New Third- and Fourth-Order Moments

2005 ◽  
Vol 62 (7) ◽  
pp. 2189-2204 ◽  
Author(s):  
Y. Cheng ◽  
V. M. Canuto ◽  
A. M. Howard
Keyword(s):  
Fourth Order ◽  
Potential Temperature ◽  
Turbulence Models ◽  
Second Order ◽  
Order Moment ◽  
Third Order ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Analytic Expressions ◽  
Aircraft Data

Abstract The standard approach to studying the planetary boundary layer (PBL) via turbulence models begins with the first-moment equations for temperature, moisture, and mean velocity. These equations entail second-order moments that are solutions of dynamic equations, which in turn entail third-order moments, and so on. How and where to terminate (close) the moments equations has not been a generally agreed upon procedure and a variety of models differ precisely in the way they terminate the sequence. This can be viewed as a bottom-up approach. In this paper, a top-down procedure is suggested, worked out, and justified, in which a new closure model is proposed for the fourth-order moments (FOMs). The key reason for this consideration is the availability of new aircraft data that provide for the first time the z profile of several FOMs. The new FOM expressions have nonzero cumulants that the model relates to the z integrals of the third-order moments (TOMs), giving rise to a nonlocal model for the FOMs. The new FOM model is based on an analysis of the TOM equations with the aid of large-eddy simulation (LES) data, and is verified by comparison with the aircraft data. Use of the new FOMs in the equations for the TOMs yields a new TOM model, in which the TOMs are damped more realistically than in previous models. Surprisingly, the new FOMs with nonzero cumulants simplify, rather than complicate, the TOM model as compared with the quasi-normal (QN) approximation, since the resulting analytic expressions for the TOMs are considerably simpler than those of previous models and are free of algebraic singularities. The new TOMs are employed in a second-order moment (SOM) model, a numerical simulation of a convective PBL is run, and the resulting mean potential temperature T, the SOMs, and the TOMs are compared with several LES data. As a final consistency check, T, SOMs, and TOMs are substituted from the PBL run back into the FOMs, which are again compared with the aircraft data.

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