On the Approximation of Two-Dimensional Transient Pipe Flow Using a Modified Wave Propagation Algorithm

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Hossein Mahdizadeh ◽  
Soroosh Sharifi ◽  
Pourya Omidvar
Keyword(s):  
Turbulence Models ◽  
Water Hammer ◽  
Test Cases ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Pressure Profiles ◽  
High Reynolds ◽  
Numerical Solver ◽  
Transient Pipe Flow ◽  
Volume Method

In this study, a second-order accurate Godunov-type finite volume method is used for the solution of the two-dimensional (2D) water hammer problem. The numerical scheme applied here is well balanced and is able to treat the unsteady friction terms, together with the convective terms, within the differences between fluxes of neighboring computational cells. In order to consider the effect of unsteady friction terms during the water hammer process, k−ε and k−ω turbulence models are employed. The performance of the proposed method with the choice of different turbulence models is evaluated using experimental data obtained from one low and one high Reynolds-number turbulent test cases. In addition to velocity and pressure distributions, the turbulence characteristics of each variant of the model, including eddy viscosity, dissipation rate, and turbulent kinetic energy during the water hammer process are fully analyzed. It is found that the inclusion of the convective inertia terms leads to more accurate pressure profiles. The results also show that using a relatively high Courant–Friedrichs–Lewy (CFL) number close to unity, the introduced numerical solver with both choices of turbulence models provides reasonable and acceptable predictions for the studied flows.

Turbulence Models Performance Assessment for Pressure Prediction during Cylinder Water Entry

2012 ◽  
Vol 224 ◽  
pp. 225-229 ◽  
Author(s):  
Bao Dong Guo ◽  
Pei Qing Liu ◽  
Qiu Lin Qu ◽  
Yue Li Cui
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Water Entry ◽  
Navier Stokes ◽  
Engineering Practice ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Dynamic Mesh Technique ◽  
Volume Method ◽  
Mesh Technique

Numerical simulations of two-dimensional cylinder free droping into water are presented based on volume of fluid (VOF) method and dynamic mesh technique. Solutions with a time-accurate finite-volume method (FVM) were generated based on the unsteady compressible ensemble averaged Navier-Stokes equations for the air and the unsteady incompressible ensemble averaged Navier-Stokes equations for the water. Computed pressure histories of the cylinder were compared with experimentally measured values. The performance of various turbulence models for pressure prediction was assessed. The results indicate that Realizable k-epsilon model with Enhanced Wall Treatment is the best choice for engineering practice.

Comparison of Various Turbulence Models in Respect to Their Suitability for CFD Calculations of Diffuser Flows

2006 ◽  
Author(s):  
Mauricio Co´rdova ◽  
Bernd Stoffel
Keyword(s):  
Boundary Layer ◽  
Turbulence Models ◽  
Test Cases ◽  
Two Dimensional ◽  
Air Flows

This paper presents results of a study conducted to determine which linear turbulence models are the most appropriate ones to predict the behaviour of air flows in channel diffusers. Due to the fact that the studied flows could be characterised as two-dimensional, the simulations were carried out with a 2D-CFD-Code. This work includes simulations of two test cases without and with boundary layer detachment, respectively. Moreover, the flows take place in diffusers with a symmetrical or an asymmetrical geometry.

A Comparison of a Cell-Centre Method and a Cell-Vertex Method for the Solution of the Two-Dimensional Unsteady Euler Equations on a Moving Grid

1995 ◽  
Vol 209 (3) ◽  
pp. 203-213 ◽  
Author(s):  
A L Gaitonde ◽  
S P Fiddes
Keyword(s):  
Euler Equations ◽  
Moving Mesh ◽  
Test Cases ◽  
Two Dimensional ◽  
Flow Solver ◽  
Transfinite Interpolation ◽  
Pressure Distributions ◽  
Flow Speeds ◽  
A Cell ◽  
Cell Centre

A moving-mesh system for the solution of two-dimensional Euler equations describing the compressible flow about an aerofoil undergoing arbitrary motions and deformations is presented. A finite volume formulation is chosen, where the volumes distort as the aerofoil moves. Independent motion of the inner and outer boundaries is permitted. By using transfinite interpolation, a fast technique for generating the required sequence of grids has been developed. Furthermore, as the flow speeds of the grid at the vertices of the finite volumes are required by any flow solver, these are also obtained by transfinite interpolation of the boundary speeds. The moving mesh has been implemented using two flow solvers, one is a cell-centre method and the other is a cell-vertex method. The flow solvers have been used to calculate a series of test cases and have produced good results in terms of detailed pressure distributions and load loops.

Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity

2020 ◽  
Vol 14 (3) ◽  
pp. 7269-7281
Author(s):  
El Amin Azzouz ◽  
Samir Houat
Keyword(s):  
Velocity Ratio ◽  
Two Dimensional ◽  
Lower Side ◽  
Square Cavity ◽  
Driven Cavity ◽  
Parallel Motion ◽  
Bottom Cavity ◽  
Secondary Vortices ◽  
Volume Method ◽  
Fluid Characteristics

The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Numerical Analysis of the Turbulent Flow Field Applied to Thermal Spallation Drilling

2004 ◽  
Author(s):  
Angela O. Nieckele ◽  
Luis Fernando Figueira da Silva ◽  
Joa˜o Carlos R. Pla´cido
Keyword(s):  
Reynolds Number ◽  
Numerical Analysis ◽  
Flow Field ◽  
Gas Phase ◽  
Accurate Determination ◽  
Rock Surface ◽  
Drilling Technique ◽  
High Reynolds ◽  
Drilling Conditions ◽  
Volume Method

Thermal spallation is a possible drilling technique which consists of using hot supersonic jets as heat source to perforate hard rocks at high rates. This work presents a numerical analysis of a typical spallation drilling configuration, by the finite volume method. The time-averaged conservation equations of mass, momentum and energy are solved to determine the turbulent compressible gas phase flow field. Turbulence is predicted by the classical high Reynolds number κ-ε model, as well as with a low Reynolds number κ-ε model. The influence of the jet Reynolds number is investigated. Special attention is given to the rock surface temperature, since its accurate determination is required to predict spallation rates under field-drilling conditions.

POSITIVITY OF k-EPSILON TURBULENCE MODELS FOR INCOMPRESSIBLE FLOW

2002 ◽  
Vol 12 (03) ◽  
pp. 393-406 ◽  
Author(s):  
ZI-NIU WU ◽  
SONG FU
Keyword(s):  
Reynolds Number ◽  
Point Source ◽  
Incompressible Flow ◽  
Iterative Procedure ◽  
High Reynolds Number ◽  
Operator Splitting ◽  
Turbulence Models ◽  
Diffusion Equations ◽  
Advection Diffusion ◽  
High Reynolds

The k-epsilon turbulence model for incompressible flow involves two advection–diffusion equations plus point-source terms. We propose a new method for positivity analysis. This method uses an iterative procedure combined with an operator splitting. With this method we recover the well-known positivity result for the standard high Reynolds number model. Most importantly, we are able to prove the positivity result for general low Reynolds number k-epsilon models.

scholarly journals Discontinuous finite volume element method of two-dimensional unsaturated soil water movement problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fan Chen ◽  
Zhixiao Xu
Keyword(s):  
Soil Water ◽  
Finite Volume ◽  
Unsaturated Soil ◽  
Water Movement ◽  
Optimal Error Estimate ◽  
Two Dimensional ◽  
Fully Discrete ◽  
Volume Method ◽  
Movement Problem ◽  
Soil Water Movement

AbstractIn this paper, a numerical approximation method for the two-dimensional unsaturated soil water movement problem is established by using the discontinuous finite volume method. We prove the optimal error estimate for the fully discrete format. Finally, the reliability of the method is verified by numerical experiments. This method is not only simple to calculate, but also stable and reliable.

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