Calculation of Turbulent Flows in a Hydraulic Turbine Draft Tube

1990 ◽  
Vol 112 (3) ◽  
pp. 257-263 ◽  
Author(s):  
M. Agouzoul ◽  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Draft Tube ◽  
Three Dimensional ◽  
Hydraulic Turbine ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
Conservative Form ◽  
Hydraulic Turbine Draft Tube

A numerical method to simulate three-dimensional incompressible turbulent flows has been developed and applied to the calculation of various flow situations in a draft tube. The conservative form of the primitive-variable formulation of the Reynolds averaged Navier-Stokes equations, written for a general curvilinear co-ordinate system, is employed. An overlapping grid combined with opposed differencing for mass and pressure gradients is used. All the properties are stored at the center of the same computational cell which is used for mass and transport balances. The k–ε model is used to describe the turbulent flow. The boundary conditions for the turbulent properties are treated with a particular attention.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

1997 ◽  
Vol 119 (4) ◽  
pp. 900-905 ◽  
Author(s):  
X. Zheng ◽  
C. Liao ◽  
C. Liu ◽  
C. H. Sung ◽  
T. T. Huang
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Grid Algorithm ◽  
High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

Flow Analysis of the M151 Aircraft Model Using the Academic CFD Code Galatea

2017 ◽  
Author(s):  
Dimitrios A. Inglezakis ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Research Association ◽  
Navier Stokes Equations ◽  
Aircraft Model ◽  
Short Period

CFD (Computational Fluid Dynamics) solvers have become nowadays an integral part of the aerospace manufacturing process and product design, as their implementation allows for the prediction of the aerodynamic behavior of an aircraft in a relatively short period of time. Such an in-house academic solver, named Galatea, is used in this study for the prediction of the flow over the ARA (Aircraft Research Association) M151/1 aircraft model. The proposed node-centered finite-volume solver employs the RANS (Reynolds-Averaged Navier-Stokes) equations, combined with appropriate turbulence models, to account for the simulation of compressible turbulent flows on three-dimensional hybrid unstructured grids, composed of tetrahedral, prisms, and pyramids. A brief description of Galatea’s methodology is included, while attention is mainly directed toward the accurate prediction of pressure distribution on the wings’ surfaces of the aforementioned airplane, an uncommon combat aircraft research model with forward swept wings and canards. In particular, two different configurations of M151/1 were examined, namely, with parallel and expanding fuselage, while the obtained results were compared with those extracted with the commercial CFD software ANSYS CFX. A very good agreement is reported, demonstrating the proposed solver’s potential to predict accurately such demanding flows over complex geometries.

scholarly journals Intermittency in solutions of the three-dimensional Navier–Stokes equations

2003 ◽  
Vol 478 ◽  
pp. 227-235 ◽  
Author(s):  
J. D. GIBBON ◽  
Charles R. DOERING
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Average Width ◽  
Binary Character ◽  
Spatio Temporal ◽  
High Reynolds

Dissipation-range intermittency was first observed by Batchelor & Townsend (1949) in high Reynolds number turbulent flows. It typically manifests itself in spatio-temporal binary behaviour which is characterized by long, quiescent periods in the signal which are interrupted by short, active ‘events’ during which there are large excursions away from the average. It is shown that Leray's weak solutions of the three-dimensional incompressible Navier–Stokes equations can have this binary character in time. An estimate is given for the widths of the short, active time intervals, which decreases with the Reynolds number. In these ‘bad’ intervals singularities are still possible. However, the average width of a ‘good’ interval, where no singularities are possible, increases with the Reynolds number relative to the average width of a bad interval.

3D Unsteady Turbulent Simulation of the Runaway Transient of the Francis Turbine

2007 ◽  
Author(s):  
Jinwei Li ◽  
Yulin Wu ◽  
Shuhong Liu ◽  
Yuliang Zhu
Keyword(s):  
Transient Process ◽  
Stokes Equations ◽  
Draft Tube ◽  
Guide Vane ◽  
Hydraulic Turbine ◽  
Moment Equation ◽  
Francis Turbine ◽  
Navier Stokes ◽  
Volume Discharge ◽  
Navier Stokes Equations

Based on Reynolds-averaged continuity and Navier-Stokes equations, and moment equation of the rotational system in the accelerated rotational relative coordinate, the governing equations of the runner region are obtained. The runaway transient simulation of the Francis turbine based on HL220 is made with RNG k-ε turbulence model under 9 guide vane openings. The variation diagrams of volume discharge, moment, rotational speed, and efficiency with respect to time are gained. Through further analysis of simulation results the transient process curve as well as the flow pattern under 9 guide vane openings are obtained, and detailed analysis is focused on flow in the draft tube to obtain variation of pressure distribution on symmetry surface of the draft tube with respect to time and pressure fluctuation of all test points in the turbine. Comparison between simulation and experiment results shows that they both are in good agreement, and it demonstrates that variation of all the parameters of the hydraulic turbine can be forecast accurately during the transient process.

Numerical Analysis of Turbulent Flow in Fluid Couplings

1997 ◽  
Vol 119 (3) ◽  
pp. 569-576 ◽  
Author(s):  
L. Bai ◽  
M. Fiebig ◽  
N. K. Mitra
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Flow Structures ◽  
Finite Volume Scheme ◽  
Vortex Generation ◽  
Navier Stokes Equations ◽  
Torque Transmission ◽  
Basic Equations

Numerical simulation of three-dimensional unsteady turbulent flows in fluid couplings was carried out by numerically solving Navier-Stokes equations in a rotating coordinate system. The standard k-ε model was used to take turbulence into account. A finite volume scheme with colocated body-fitted grids was used to solve the basic equations. Computed flow structures show the vortex generation and its effect on the torque transmission. Computed local velocity and torque flow compare well with measurements.

scholarly journals Numerical Research on Flow Characteristics around a Hydraulic Turbine Runner at Small Opening of Cylindrical Valve

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Zhenwei Mo ◽  
Juliang Xiao ◽  
Gang Wang
Keyword(s):  
Flow Velocity ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Hydraulic Turbine ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Small Opening ◽  
Turbine Runner ◽  
Computational Fluid Dynamics Cfd

We use the continuity equation and the Reynolds averaged Navier-Stokes equations to study the flow-pattern characteristics around a turbine runner for the small-opening cylindrical valve of a hydraulic turbine. For closure, we adopt the renormalization-groupk-εtwo-equation turbulence model and use the computational fluid dynamics (CFD) software FLUENT to numerically simulate the three-dimensional unsteady turbulent flow through the entire passage of the hydraulic turbine. The results show that a low-pressure zone develops around the runner blades when the cylindrical valve is closed in a small opening; cavitation occurs at the blades, and a vortex appears at the outlet of the runner. As the cylindrical valve is gradually closed, the flow velocity over the runner area increases, and the pressure gradient becomes more significant as the discharge decreases. In addition, the fluid flow velocity is relatively high between the lower end of the cylindrical valve and the base, so that a high-velocity jet is easily induced. The calculation and analysis provide a theoretical basis for improving the performance of cylindrical-valve operating systems.

Low Reynolds-Number Pipe Flow in the Vicinity of Three-Dimensional Obstacles

1979 ◽  
Vol 21 (5) ◽  
pp. 335-343 ◽  
Author(s):  
A. D. Gosman ◽  
N. S. Vlachos ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Recirculating Flow ◽  
Local Shear ◽  
Sector Angle

Numerical solutions of the three-dimensional Navier-Stokes equations are presented for boundary conditions corresponding to the laminar flow of Newtonian and non-Newtonian fluids in a round pipe with truncated sector-shaped obstacles. The influences of Reynolds number and sector angle on the velocity distributions, local shear stress and pressure drop are quantified and shown to be large. The results are complementary to those previously reported by Vlachos and Whitelaw (1)§ for axisymmetric obstacles, where related two-dimensional effects were quantified. They provide new information on three-dimensional, recirculating flow in ducts and form a basis for future calculations of corresponding turbulent flows.

Sign in / Sign up

Export Citation Format

Share Document