Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate

1996 ◽  
Vol 328 ◽  
pp. 177-227 ◽  
Author(s):  
P. Koumoutsakos ◽  
D. Shiels
Keyword(s):  
Flat Plate ◽  
Free Stream ◽  
Stokes Equations ◽  
The Body ◽  
Navier Stokes ◽  
Vorticity Field ◽  
Navier Stokes Equations ◽  
Unsteady Forces ◽  
Viscous Incompressible Flow ◽  
Experimental Works

The development of a two-dimensional viscous incompressible flow generated from an infinitesimally thin flat plate, impulsively started or uniformly accelerated normal to the free stream is studied computationally. An adaptive numerical scheme, based on vortex methods, is used to integrate the vorticity–velocity formulation of the Navier–Stokes equations. The results of the computations complement relevant experimental works while providing us with quantities such as the vorticity field and the unsteady forces experienced by the body. For the uniformly accelerated plate the present simulations capture the development of a number of centers of vorticity along the primary separating shear layer. This phenomenon has been observed in experimental works but has not been predicted by inviscid models. The present simulations suggest that this Kelvin–Helmholtz-type instability is driven by the interaction of primary and secondary vorticity near the tips of the plate and depends on the acceleration of the plate.

scholarly journals On the viscous hypersonic blunt body problem

1964 ◽  
Vol 20 (3) ◽  
pp. 353-367 ◽  
Author(s):  
William B. Bush
Keyword(s):  
Blunt Body ◽  
Free Stream ◽  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Absolute Temperature ◽  
The Body ◽  
Navier Stokes ◽  
Nose Radius ◽  
Navier Stokes Equations ◽  
Specific Heats

The viscous hypersonic flow past an axisymmetric blunt body is analysed based upon the Navier-Stokes equations. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number, P, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number, M, and the free-stream Reynolds number based on the body nose radius, R, go to infinity, and ε = (γ − 1)/(γ + 1), where γ is the ratio of the specific heats, and δ = 1/(γ − 1) M2 go to zero.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

Studies on Natural Convection Induced Flow and Thermal Behavior Inside Electronic Equipment Cabinet Model

2001 ◽  
Author(s):  
Masaru Ishizuka ◽  
Guoyi Peng ◽  
Shinji Hayama
Keyword(s):  
Natural Convection ◽  
Thermal Behavior ◽  
Body Surface ◽  
Stokes Equations ◽  
The Body ◽  
Electronic Equipment ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Induced Flow

Abstract In the present work, an important basic flow phenomena, the natural convection induced flow, is studied numerically. Three-dimensional Navier-Stokes equations along with the temperature equation are solved on the basis of finite difference method. Generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. Differential terms with respect to time are approximated by forward differences, diffusions terms are approximated by the implicit Euler form, convection terms in the Navier-Stokes equations are approximated by the third order upwind difference scheme. The heat flux at the body surface of heater is specified. The results of calculation showed a satisfactory agreement with the measured data and led to a good understanding of the overall flow and thermal behavior inside electronic equipment cabinet model which is very difficult, if not impossible, to gather by experiment.

Validation of a Numerical Method for Unsteady Flow Calculations

1993 ◽  
Vol 115 (1) ◽  
pp. 110-117 ◽  
Author(s):  
M. Giles ◽  
R. Haimes
Keyword(s):  
Heat Transfer ◽  
Flat Plate ◽  
Numerical Method ◽  
Stokes Equations ◽  
Companion Paper ◽  
Ideal Gas ◽  
Euler Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Loss Prediction

This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier–Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier–Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space–time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

CFD Analysis of Vortex Shedding in a Circular Cylinder: Flow Induced Vibration Design

2006 ◽  
Author(s):  
Nadeem Ahmed Sheikh ◽  
M. Afzaal Malik ◽  
Arshad Hussain Qureshi ◽  
M. Anwar Khan ◽  
Shahab Khushnood
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
The Body ◽  
Navier Stokes ◽  
Structural Vibrations ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Implicit Approach

Flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations. The effect of vibrating instability of a single cylinder is investigated in a uniform flow using the power of computational methods. Fluid structure coupling procedure predicts the fluid forces responsible for structural vibrations. An implicit approach to the solution of the unsteady two-dimensional Navier-Stokes equations is used for computation of flow parameters. Calculations are performed in parallel using a domain re-meshing/deforming technique with efficient communication requirements. Results for the unsteady shedding flow behind a circular cylinder are presented with experimental comparisons, showing the feasibility of accurate, efficient, time-dependent estimation of shedding frequency and resulting vibrations.

scholarly journals Physical and numerical analysis of the front of a gravity current on a horizontal bottom

1998 ◽  
Vol 26 ◽  
pp. 289-295
Author(s):  
Mohamed Naaim ◽  
Thierry Pellarin
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Gravity Current ◽  
Processing System ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Experimental Approaches ◽  
Two Parameters ◽  
Two Stages

In this paper, numerical and experimental approaches are applied to analyse the dynamics of the front of a gravity current. This study focused on two parameters: internal density and velocity fields. The salt concentration was determined by a potentiometric process. The internal velocities were determined using an optical device and an image-processing system. The structure of the head of the gravity current was analysed. Its density was measured and two stages of evolution were observed. This analysis allows us to coufirm the existence of two important stages. Forxf<xs, where the dynamics depend on the initial condition, the flow consists of a head and body and the front density is constant. Forxf>xs, we show that the density of the front decreases and evolves towards the Hallworth and others (1993) law. From a comparison between the experiments and the numerical model, we show that the numerical model, which is based on Navier–Stokes equations and on thek−Lturbulence model (whereLis the height of the gravity current), can predict well flow in the slump regime and in the inertia–buoyancy regime with smoothed results in the transition from the head to the body of the gravity current.

Similarity Solutions for the Interaction of a Potential Vortex With Free Stream Sink Flow and a Stationary Surface

1974 ◽  
Vol 96 (1) ◽  
pp. 49-54 ◽  
Author(s):  
J. A. Hoffmann
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Free Stream ◽  
Stokes Equations ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Surface ◽  
Direct Numerical Integration ◽  
Potential Vortex

Similarity equations, using an assumed transformation which reduces the partial differential equations to sets of ordinary differential equations, are obtained from the boundary layer and the complete Navier-Stokes equations for the interaction of vortex flows with free stream sink flows and a stationary surface. Solutions to the boundary layer equations for the case of the potential vortex that satisfy the prescribed boundary conditions are shown to be nonexistent using the assumed transformation. Direct numerical integration is used to obtain solutions to the complete Navier-Stokes equations under a potential vortex with equal values of tangential and radial free stream velocities. Solutions are found for Reynolds numbers up to 2.0.

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