scholarly journals MATHEMATICAL MODEL OF THE MULTI-CHANNEL SPIRAL CYCLONE / DAUGIAKANALIO SPIRALINIO CIKLONO ORO GREIČIŲ TYRIMAS

2013 ◽  
Vol 5 (4) ◽  
pp. 349-355
Author(s):  
Justina Danilenkaitė ◽  
Aleksandras Chlebnikovas ◽  
Petras Vaitiekūnas
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Differential Equations ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Cylindrical Part ◽  
Navier Stokes ◽  
Laminar And Turbulent Flow

The article deals with a problem of experimental investigation and numerical simulation of gas aerodynamics of a multi-channel spiral cyclone with a tangential inlet. The paper presents an overview of experimental and theoretical works on the cyclones having a particularly complex turbulent flow and focuses on three-dimensional transport differential equations for a non-compressible laminar and turbulent flow inside the cyclone. The equations have been solved applying the numerical finite volume method using the RNG (Re–Normalisation Group) k-ε turbulence model. The numerical simulation of the flow cyclone has been carried out. The height of the cyclone is 0.80 m with 0.33 m in diameter, the height of the spiral–cylindrical part – 0.098 meters and that of the cone – 0.45 m. Inlet dimensions (cylindrical part on the side), in accordance with drawings makes a×b = 28×95 mm. The mathematical model for the air traffic movement cyclone has accounted for Navier-Stokes (Reynolds) three-dimensional differential equations. The simulation results have been obtained with reference to the cyclone of tangential velocity profiles using RNG k-ε turbulence model. The inlet velocity of 5.1 m/s slightly differs from experimental results, thus making an error of 7%. Article in Lithuanian. Santrauka Nagrinėjama dujų aerodinamikos daugiakanaliame spiraliniame ciklone eksperimentinio tyrimo ir skaitinio modeliavimo problema. Apžvelgti eksperimentiniai ir teoriniai ciklonų, kuriuose susidaro ypač sudėtingas sūkurinis srautas, tyrimai. Pateiktos nespūdžiojo laminarinio ir turbulentinio srauto tekėjimo ciklono viduje diferencialinės trimatės pernašos lygtys. Jos skaitiškai spręstos baigtinių tūrių metodu taikant RNG (Re – Normalisation Group) k–ε turbulencijos modelį. Atliktas skaitinis oro srauto judėjimo ciklone modeliavimas. Ciklono aukštis 0,80 m, skersmuo 0,33 m, spiralinės-cilindrinės dalies aukštis 0,098 m, kūginės – 0,45 m, įtekėjimo angos matmenys (cilindrinės dalies šone) pagal brėžinius yra a×b = 28×95 mm. Oro srauto judėjimo ciklone matematinį modelį sudaro Navjė ir Stokso (Reinoldso) trimačių diferencialinių lygčių sistema. Modeliavimo rezultatai, t. y. taikant RNG k–ε turbulencijos modelį (įtekėjimo greitis 5,1 m/s) gauti tangentinio greičio ciklone kitimo duomenys, nežymiai (su 7 % paklaida) skyrėsi nuo eksperimentinių rezultatų.

scholarly journals AIR STREAM VELOCITY MODELLING IN MULTICHANNEL SPIRAL CYCLONE SEPARATOR

2014 ◽  
Vol 22 (3) ◽  
pp. 183-193 ◽  
Author(s):  
Petras Vaitiekūnas ◽  
Egidijus Petraitis ◽  
Albertas Venslovas ◽  
Aleksandras Chlebnikovas
Keyword(s):  
Turbulent Flow ◽  
Turbulence Model ◽  
Air Flow ◽  
Three Dimensional ◽  
Absolute Error ◽  
Equation System ◽  
Cylindrical Part ◽  
Stream Velocity ◽  
Cyclone Separator ◽  
Air Stream

Numerical modelling problem is investigated in a gas aerodynamics multichannel spiral cyclone separator with a tangential inflow. Experimental and theoretical papers analysing cyclone separator with particularly complex turbulent flow were reviewed. The three-dimensional transport differential equations for incompressible laminar and turbulent flow inside the cyclone separator were presented. They were numerically solved by finite volume method using the Re-Normalisation Group (hereinafter RNG) k-ε turbulence model. The numerical air flow movement was modelled in cyclone separator with the following dimensions: 0.95 m height, 0.330 m diameter, 0.88 m height of spiral-cylindrical part, 0.39 m height of conical part, inflow dimensions (on the side of cylindrical part) according to the drawings were a × b = 28 × 95 mm. The mathematical model of air flow movement in cyclone separator was composed by Navier-Stokes (Reynolds) as the three-dimensional differential equation system. The modelling results were obtained by the tangential and axial velocity profiles in cyclone separator using RNG k-ε turbulence model, the inflow velocity from 4.1 m/s to 15.4 m/s coincided well with the experimental results. This is the first article testing for multichannel cyclone and determined distributions of aerodynamic parameters. The absolute error between experimental and modelling results changed from 0.01 to 0.24 units.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

Numerical Simulation of the Relation between Plasma Reflection and Keyhole Dimension in the Keyhole PAW Process

2011 ◽  
Vol 399-401 ◽  
pp. 1812-1815
Author(s):  
Feng Liang Yin ◽  
Sheng Zhu ◽  
Sheng Sun Hu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Plasma Arc ◽  
The Status ◽  
Voltage Signal ◽  
Plasma Reflection

A three-dimensional mathematical model has been established to research the relation between the plasma reflection and status of keyhole during the keyhole PAW processing. It has been found that the strength of the plasma reflection is related to the keyhole dimension. Another condition to make the plasma refection appearance is that the keyhole or concave in the pool must be unsymmetrical about the axis of the plasma arc. The mechanism of detecting circuit designed based on the fact that the plasma refection is able to indicate the status of keyhole is mathematically studied. The result shows that the voltage signal in the detecting circuit can be used to indicate the status of keyhole.

Turbulent Flow Velocity Between Rotating Co-Axial Disks of Finite Radius

1989 ◽  
Vol 111 (3) ◽  
pp. 333-340 ◽  
Author(s):  
J. F. Louis ◽  
A. Salhi
Keyword(s):  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Finite Radius ◽  
Navier Stokes Equations ◽  
Rotating Cavity ◽  
Tangential Wall ◽  
Frictional Forces

The turbulent flow between two rotating co-axial disks is driven by frictional forces. The prediction of the velocity field can be expected to be very sensitive to the turbulence model used to describe the viscosity close to the walls. Numerical solutions of the Navier–Stokes equations, using a k–ε turbulence model derived from Lam and Bremhorst, are presented and compared with experimental results obtained in two different configurations: a rotating cavity and the outflow between a rotating and stationary disk. The comparison shows good overall agreement with the experimental data and substantial improvements over the results of other analyses using the k–ε models. Based on this validation, the model is applied to the flow between counterrotating disks and it gives the dependence of the radial variation of the tangential wall shear stress on Rossby number.

A Reynolds-Averaged Navier-Stokes Solver in a Turbomachinery Design System

2007 ◽  
Author(s):  
Fahua Gu ◽  
Mark R. Anderson
Keyword(s):  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Integrated Design ◽  
Navier Stokes ◽  
Design System ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Machine Performance ◽  
Reynolds Averaged Navier Stokes

The design of turbomachinery has been focusing on the improvement of the machine efficiency and the reduction of the design cost. This paper presents an integrated design system to create the machine geometry and to predict the machine performance at different levels of approximation, including one-dimensional design and analysis, quasi-three-dimensional-(blade-to-blade, throughflow) and full-three-dimensional-steady-state CFD analysis. One of the most important components, the Reynolds-averaged Navier-Stokes solver, is described in detail. It originated from the Dawes solver with numerous enhancements. They include the use of the low speed pre-conditioned full Navier-Stokes equations, the addition of the Spalart-Allmaras turbulence model and an improvement of wall functions related with the turbulence model. The latest upwind scheme, AUSM, has been implemented too. The Dawes code has been rewritten into a multi-block solver for O, C, and H grids. This paper provides some examples to evaluate the effect of grid topology on the machine performance prediction.

scholarly journals Unsteady Three-Dimensional MHD Non-Axisymmetric Homann Stagnation Point Flow of a Hybrid Nanofluid with Stability Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 784 ◽  
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Industrial Sector ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid

The hybrid nanofluid under the influence of magnetohydrodynamics (MHD) is a new interest in the industrial sector due to its applications, such as in solar water heating and scraped surface heat exchangers. Thus, the present study accentuates the analysis of an unsteady three-dimensional MHD non-axisymmetric Homann stagnation point flow of a hybrid Al2O3-Cu/H2O nanofluid with stability analysis. By employing suitable similarity transformations, the governing mathematical model in the form of the partial differential equations are simplified into a system of ordinary differential equations. The simplified mathematical model is then solved numerically by the Matlab solver bvp4c function. This solving approach was proficient in generating more than one solution when good initial guesses were provided. The numerical results presented significant influences on the rate of heat transfer and fluid flow characteristics of a hybrid nanofluid. The rate of heat transfer and the trend of the skin friction coefficient improve with the increment of the nanoparticles’ concentration and the magnetic parameter; however, they deteriorate when the unsteadiness parameter increases. In contrast, the ratio of the escalation of the ambient fluid strain rate to the plate was able to adjourn the boundary layer separation. The dual solutions (first and second solutions) are obtainable when the surface of the sheet shrunk. A stability analysis is carried out to justify the stability of the dual solutions, and hence the first solution is seen as physically reliable and stable, while the second solution is unstable.

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