Analysis of Turbulent Flow Past a Class of Semi-Infinite Bodies

1986 ◽  
Vol 108 (2) ◽  
pp. 157-165
Author(s):  
A. M. Abdelhalim ◽  
U. Ghia ◽  
K. N. Ghia
Keyword(s):  
Flat Plate ◽  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Analytical Data ◽  
Flow Region ◽  
Two Dimensional ◽  
Infinite Body ◽  
Similarity Type ◽  
Flow Past

This study was undertaken with the primary purpose of developing an analysis for flow past a class of two-dimensional and axisymmetric semi-infinite bodies. The time-averaged Navier-Stokes equations for these flows are derived in surface-oriented conformal coordinates (ξ, η) in terms of similarity-type vorticity and stream-function variables. Turbulence closure is achieved by means of a two-equation turbulence model utilizing the kinetic energy k and its dissipation rate ε which enable determination of the isotropic eddy viscosity. The coupled vorticity and stream-function equations are solved simultaneously using an incremental formulation of the factored alternating-direction implicit scheme. The turbulence equations for k and ε are solved by the standard ADI method. Numerical solutions are obtained for the thin flat plate and compared with available experimental and analytical data. Also, results are obtained for flow over a parabola and compared with the flat-plate results in order to assess the effects of longitudinal curvature on the flow results. Finally, solutions are obtained for flow past a two-dimensional semi-infinite body with a shoulder, at Red = 24,000. The computed results have the same general trend as the experimental data; possible causes for the differences within the separated-flow region are cited.

Numerical Solutions of a Viscous Uniform Approach Flow Past Square and Diamond Cylinders

2002 ◽  
Author(s):  
Charles Dalton ◽  
Wu Zheng
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Elliptic Partial Differential Equation ◽  
Navier Stokes ◽  
Central Difference ◽  
Uniform Approach ◽  
Flow Past ◽  
Line Force ◽  
Vorticity Transport

Numerical results are presented for a uniform approach flow past square and diamond cylinders, with and without rounded corners, at Reynolds numbers of 250 and 1000. This unsteady viscous flow problem is formulated by the 2-D Navier-Stokes equations in vorticity and stream-function form on body-fitted coordinates and solved by a finite-difference method. Second-order Adams-Bashforth and central-difference schemes are used to discretize the vorticity transport equation while a third-order upwinding scheme is incorporated to represent the nonlinear convective terms. A grid generation technique is applied to provide an efficient mesh system for the flow. The elliptic partial differential equation for stream-function and vorticity in the transformed plane is solved by the multigrid iteration method. The Strouhal number and the average in-line force coefficients agree very well with the experimental and previous numerical values. The vortex structures and the evolution of vortex shedding are illustrated by vorticity contours. Rounding the corners of the square and diamond cylinders produced a noticeable decrease on the calculated drag and lift coefficients.

Jet-to-Plate Distance Effect on Heat Transfer From a Flat Plate to an Impinging Jet at Various Reynolds Numbers

2012 ◽  
Author(s):  
Patricia Streufert ◽  
Terry X. Yan ◽  
Mahdi G. Baygloo
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Flat Plate ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Air Jet ◽  
Plate Distance

Local turbulent convective heat transfer from a flat plate to a circular impinging air jet is numerically investigated. The jet-to-plate distance (L/D) effect on local heat transfer is the main focus of this study. The eddy viscosity V2F turbulence model is used with a nonuniform structured mesh. Reynolds-Averaged Navier-Stokes equations (RANS) and the energy equation are solved for axisymmetric, three-dimensional flow. The numerical solutions obtained are compared with published experimental data. Four jet-to-plate distances, (L/D = 2, 4, 6 and 10) and seven Reynolds numbers (Re = 7,000, 15,000, 23,000, 50,000, 70,000, 100,000 and 120,000) were parametrically studied. Local and average heat transfer results are analyzed and correlated with Reynolds number and the jet-to-plate distance. Results show that the numerical solutions matched experimental data best at low jet-to-plate distances and lower Reynolds numbers, decreasing in ability to accurately predict the heat transfer as jet-to-plate distance and Reynolds number was increased.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

The structure of two-dimensional separation

1990 ◽  
Vol 220 ◽  
pp. 397-411 ◽  
Author(s):  
Laura L. Pauley ◽  
Parviz Moin ◽  
William C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Shedding Frequency

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

Viscous shear flow past small bluff bodies attached to a plane wall

1975 ◽  
Vol 69 (4) ◽  
pp. 803-823 ◽  
Author(s):  
Masaru Kiya ◽  
Mikio Arie
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Major Axis ◽  
Plane Wall ◽  
Local Boundary ◽  
Flow Past ◽  
Viscous Shear

Numerical solutions of the Navier-Stokes equations are presented for two-dimensional viscous flow past semicircular and semielliptical projections attached to a plane wall on which a laminar boundary layer has developed. Since the major axis is in the direction normal to the wall and is chosen to be twenty times as long as the minor axis in the present case, the flow around the semielliptical projection will approximately correspond to that around a normal flat plate. It is assumed that the height of each obstacle is so small in comparison with the local boundary-layer thickness that the approaching flow can be approximated by a uniform shear flow. Numerical solutions are obtained for the range 0·1-100 of the Reynolds number, which is defined in terms of the undisturbed approaching velocity at the top of the obstacle and its height. The geometrical shapes of the front and rear standing vortices, the drag coefficients and the pressure and shear-stress distributions are presented as functions of the Reynolds number. The computed results are discussed in connexion with the data already obtained in the other theoretical solutions and an experimental observation.

A general theory for the dynamics of thin viscous sheets

2002 ◽  
Vol 457 ◽  
pp. 255-283 ◽  
Author(s):  
N. M. RIBE
Keyword(s):  
Evolution Equations ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Extensional Flow ◽  
Constant Thickness ◽  
Scaling Analysis ◽  
Two Dimensional ◽  
Principal Curvatures ◽  
Kinematic Evolution ◽  
Starting Point

A model for the deformation of thin viscous sheets of arbitrary shape subject to arbitrary loading is presented. The starting point is a scaling analysis based on an analytical solution of the Stokes equations for the flow in a shallow (nearly planar) sheet with constant thickness T0 and principal curvatures k1 and k2, loaded by an harmonic normal stress with wavenumbers q1 and q2 in the directions of principal curvature. Two distinct types of deformation can occur: an ‘inextensional’ (bending) mode when [mid ]L3(k1q22 + k2q21)[mid ] [Lt ] ε, and a ‘membrane’ (stretching) mode when [mid ]L3(k1q22 + k2q21)[mid ] [Gt ] ε, where L ≡ (q21 + q22)−1/2 and ε = T0/L [Lt ] 1. The scales revealed by the shallow-sheet solution together with asympotic expansions in powers of ε are used to reduce the three-dimensional equations for the flow in the sheet to a set of equivalent two-dimensional equations, valid in both the inextensional and membrane limits, for the velocity U of the sheet midsurface. Finally, kinematic evolution equations for the sheet shape (metric and curvature tensors) and thickness are derived. Illustrative numerical solutions of the equations are presented for a variety of buoyancy-driven deformations that exhibit buckling instabilities. A collapsing hemispherical dome with radius L deforms initially in a compressional membrane mode, except in bending boundary layers of width ∼ (εL)1/2 near a clamped equatorial edge, and is unstable to a buckling mode which propagates into the dome from that edge. Buckling instabilities are suppressed by the extensional flow in a sagging inverted dome (pendant drop), which consequently evolves entirely in the membrane mode. A two-dimensional viscous jet falling onto a rigid plate exhibits steady periodic folding, the frequency of which varies with the jet height and extrusion rate in a way similar to that observed experimentally.

Applying Ensemble Kalman Filter to Transonic Flows Through a Two-Dimensional Turbine Cascade

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Sasuga Ito ◽  
Masato Furukawa ◽  
Kazutoyo Yamada ◽  
Kaito Manabe
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Optimization Approach ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Eddy Simulation

Abstract Turbulence is one of the most important phenomena in fluid dynamics. Large eddy simulation (LES) generally allows us to analyze smaller eddies than when using simulations based on unsteady Reynolds-averaged Navier–Stokes equations (URANS). In addition, the numerical solutions of LES show good agreements with experiments and numerical solutions based on direct numerical simulation. URANS simulations are, however, frequently used in academia and industry because LES computations are much more expensive compared with URANS simulations. In this investigation, an optimization of unsolved coefficients of the k–ω two equations model is performed on the transonic flow around T106A low-pressure turbine cascade to improve the accuracy of turbulence prediction with URANS. For the optimization approach, two-dimensional URANS is combined with ensemble Kalman filter which is one of the data assimilation techniques. In the assimilation process, a time- and spanwise-averaged LES result is used as pseudo-experimental data. Three-dimensional URANS simulations are performed for the evaluation of the optimization effect. URANS simulations are also applied to a different turbine cascade flow for the evaluation of the robustness of the optimized coefficients. These URANS results confirmed that the optimized coefficients improve the accuracy of turbulence prediction.

Optimized Accelerating Parameters of Convergence for the Navier-Stokes Equations

1992 ◽  
Author(s):  
Bashar S. AbdulNour
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Reynolds Numbers ◽  
Computer Time ◽  
Navier Stokes ◽  
Computational Time ◽  
Navier Stokes Equations ◽  
Successive Over Relaxation

Abstract An over-relaxation procedure, that includes weighing factors, is applied to the steady, two-dimensional Navier-Stokes equations in order to reduce the computational time. The benefits obtained from this strategy are illustrated by the problem of viscous flow in the entrance region of an unconstricted and a constricted channel. The describing equations are expressed in terms of the stream function and vorticity. The convergence domain for the Successive Over-Relaxation method and the optimum values of the accelerating parameters, which consist of the over-relaxation and weighting factors for both the stream function and vorticity, are discussed. Numerical solutions are obtained for Reynolds numbers ranging from 20 to 2000. The computer time is reduced by as much as a factor of six using the optimum values of the accelerating parameters.

Sign in / Sign up

Export Citation Format

Share Document