Internal Three-Dimensional Viscous Flow Solution Using the Streamlike Function

1986 ◽  
Vol 108 (3) ◽  
pp. 348-353 ◽  
Author(s):  
A. Hamed ◽  
S. Abdallah
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Streamwise Vorticity ◽  
Elliptic Solution ◽  
Inviscid Flows ◽  
Navier Stokes Equations ◽  
Curved Ducts

This paper presents a new method for the three-dimensional elliptic solution of the Navier–Stokes equations. It is based on the streamlike-function vorticity formulation which was developed by the authors to study the development of secondary velocities and streamwise vorticity for inviscid flows in curved ducts. This formulation is generalized for viscous flows and used to predict the development of internal three dimensional flow fields. The computed results are presented and compared with experimental measurements for the three-dimensional viscous flow in a straight duct.

Laminar Incompressible Viscous Flow in Curved Ducts of Regular Cross-Sections

1977 ◽  
Vol 99 (4) ◽  
pp. 640-648 ◽  
Author(s):  
K. N. Ghia ◽  
J. S. Sokhey
Keyword(s):  
Cross Sections ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Incompressible Viscous Flow ◽  
Square Ducts ◽  
Curved Ducts

The laminar three-dimensional flow in curved ducts has been analyzed for an incompressible viscous fluid. The mathematical model is formulated using three-dimensional parabolized Navier-Stokes equations. The equations are generalized using two indices which permit the choice of Cartesian or cylindrical coordinate systems and straight or curved ducts. The solutions are obtained numerically using an ADI method for a number of duct geometries and flow parameters. The study presents detailed results for developing laminar flow in rectangular curved ducts; also, the effect of longitudinal curvature on secondary flow is fully analyzed. An investigation is made of the occurrence of Dean’s instability and, for curved square ducts, it is found to first appear at Dean number ≃ 143.

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

2016 ◽  
Vol 8 (6) ◽  
pp. 887-910 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Strong Shock ◽  
Viscous Flows ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Inviscid Flows ◽  
Navier Stokes Equations ◽  
Viscous Compressible Flows

AbstractIn this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

scholarly journals An Accurate Cartesian Method for Incompressible Flows with Moving Boundaries

2014 ◽  
Vol 15 (5) ◽  
pp. 1266-1290 ◽  
Author(s):  
M. Bergmann ◽  
J. Hovnanian ◽  
A. Iollo
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Flows ◽  
The Body ◽  
Navier Stokes ◽  
Ghost Cell ◽  
Order Accuracy ◽  
Navier Stokes Equations ◽  
Moving Body

AbstractAn accurate cartesian method is devised to simulate incompressible viscous flows past an arbitrary moving body. The Navier-Stokes equations are spatially discretized onto a fixed Cartesian mesh. The body is taken into account via the ghost-cell method and the so-called penalty method, resulting in second-order accuracy in velocity. The accuracy and the efficiency of the solver are tested through two-dimensional reference simulations. To show the versatility of this scheme we simulate a three-dimensional self propelled jellyfish prototype.

Solutions of the Three-Dimensional Navier-Stokes Equations in Non-Orthogonal Coordinates to Calculate the Flow in a Log Spiral Impeller

1982 ◽  
Author(s):  
B. W. Swanson
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Elliptic Solution ◽  
Navier Stokes Equations ◽  
Orthogonal Grid ◽  
Good Agreement ◽  
Orthogonal Coordinates

A modification of Moore’s (12) method has been developed for solving the three-dimensional Navier Stokes equations to calculate the flow in a log spiral impeller. A complete mathematical development of this method is presented. The parabolic finite-difference marching code used to make the calculations is an extensive revision of a CATHY3 code obtained from D. B. Spalding. Calculations are made for Vr, Vθ and Vz on a non-orthogonal grid that is ideally suited for impellers with back-swept blades. An inviscid solution is in good agreement with the elliptic solution and validates the computational procedure. The method is applied to calculate the viscous three-dimensional flow in a log spiral impeller.

Series Solution of Three-Dimensional Unsteady Laminar Viscous Flow Due to a Stretching Surface in a Rotating Fluid

2007 ◽  
Vol 74 (5) ◽  
pp. 1011-1018 ◽  
Author(s):  
Yue Tan ◽  
Shi-Jun Liao
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Current Approach ◽  
Numerical Results ◽  
Navier Stokes ◽  
Rotating Fluid ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Time Region

An analytic technique, namely the homotopy analysis method, is applied to solve the Navier–Stokes equations governing unsteady viscous flows due to a suddenly stretching surface in a rotating fluid. Unlike perturbation methods, the current approach does not depend upon any small parameters at all. Besides contrary to all other analytic techniques, it provides us with a simple way to ensure the convergence of solution series. In contrast to perturbation approximations which have about 40% average errors for the considered problem, our series solutions agree well with numerical results in the whole time region 0⩽t<+∞. Explicit analytic expressions of the skin friction coefficients are given, which agree well with numerical results in the whole time region 0⩽t<+∞. This analytic approach can be applied to solve some complicated three-dimensional unsteady viscous flows governed by the Navier–Stokes equations.

Viscous Flow Analysis as a Design Tool for Hydraulic Turbine Components

1990 ◽  
Vol 112 (1) ◽  
pp. 5-11 ◽  
Author(s):  
T. C. Vu ◽  
W. Shyy
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Hydraulic Turbine ◽  
Design Tool ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Alternative Designs

Viscous flow analysis based on the full Reynolds-averaged Navier-Stokes equations is being applied to successfully predict turbulent flow characteristics and energy losses in different hydraulic turbine components. It allows the designer to evaluate the hydraulic performance of alternative designs before proceeding with laboratory testing or to perform elaborate parametric study to optimize the hydraulic design. In this paper, the applications of three-dimensional viscous flow analysis as an analytical design tool for elbow draft tube and spiral casing are presented and their impact on engineering design assessed.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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