Instabilities and inertial waves generated in a librating cylinder

2011 ◽  
Vol 687 ◽  
pp. 171-193 ◽  
Author(s):  
J. M. Lopez ◽  
F. Marques
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Boundary Layer Flows ◽  
Viscous Boundary Layer ◽  
Navier Stokes Equations ◽  
Damping Rate ◽  
Layer Flow ◽  
Viscous Boundary

AbstractA librating cylinder consists of a rotating cylinder whose rate of rotation is modulated. When the mean rotation rate is large compared with the viscous damping rate, the flow may support inertial waves, depending on the frequency of the modulation. The modulation also produces time-dependent boundary layers on the cylinder endwalls and sidewall, and the sidewall boundary layer flow in particular is susceptible to instabilities which can introduce additional forcing on the interior flow with time scales different from the modulation period. These instabilities may also drive and/or modify the inertial waves. In this paper, we explore such flows numerically using a spectral-collocation code solving the Navier–Stokes equations in order to capture the dynamics involved in the interactions between the inertial waves and the viscous boundary layer flows.

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.

scholarly journals Derivation of a Viscous Serre–Green–Naghdi Equation: An Impasse?

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 135
Author(s):  
Denys Dutykh ◽  
Hervé V.J. Le Meur
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Euler Equations ◽  
Stokes Equations ◽  
Current Status ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Bottom Region ◽  
Flow Domain ◽  
Layer Flow

In this article, we present the current status of the derivation of a viscous Serre–Green–Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom region (the so-called boundary layer) is described by Navier–Stokes equations. We consider a particular regime binding the Reynolds number and the shallowness parameter. The computations presented in this article are performed in the fully nonlinear regime. The boundary layer flow reduces to a Prandtl-like equation that we claim to be irreducible. Further approximations are necessary to obtain a tractable model.

Mixed Convective Heat Transfer From Rotating Spheres

1998 ◽  
Author(s):  
Ali Heydari ◽  
Bahar Firoozabadi ◽  
Hamid Fazelli
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Transfer Coefficients ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Layer Flow

Abstract This paper presents an analysis of flow and heat transfer over a rotating axsisymmetric body of revolution in a mixed convective heat transfer along with surface conditions of heating or cooling as well as surface transpriation. Boundary-layer approximation reduces the elliptic Navier-Stokes equations to parabolic equations, where the Keller-Cebeci method of finite-difference solution is used to solve the resulting system of partial-differential equations. Comparison of the calculated values of the velocity and temperature profiles as well as the shear and the heat transfer coefficients at the surface for the case of a sphere with the available literature data indicate the model well predicts the boundary-layer flow and heat transfer over a rotating axsisymmetric body.

scholarly journals A CFD Tutorial in Julia: Introduction to Compressible Laminar Boundary-Layer Flows

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 400
Author(s):  
Furkan Oz ◽  
Kursat Kara
Keyword(s):  
Boundary Layer ◽  
Programming Language ◽  
Laminar Boundary Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Navier Stokes ◽  
Aerodynamic Heating ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Navier Stokes Equations

A boundary-layer is a thin fluid layer near a solid surface, and viscous effects dominate it. The laminar boundary-layer calculations appear in many aerodynamics problems, including skin friction drag, flow separation, and aerodynamic heating. A student must understand the flow physics and the numerical implementation to conduct successful simulations in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. Numerical simulations require writing computer codes. Therefore, choosing a fast and user-friendly programming language is essential to reduce code development and simulation times. Julia is a new programming language that combines performance and productivity. The present study derived the compressible Blasius equations from Navier–Stokes equations and numerically solved the resulting equations using the Julia programming language. The fourth-order Runge–Kutta method is used for the numerical discretization, and Newton’s iteration method is employed to calculate the missing boundary condition. In addition, Burgers’, heat, and compressible Blasius equations are solved both in Julia and MATLAB. The runtime comparison showed that Julia with for loops is 2.5 to 120 times faster than MATLAB. We also released the Julia codes on our GitHub page to shorten the learning curve for interested readers.

scholarly journals Boundary Layer Flow due to the Vibration of a Sphere

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Muhammad Adil Sadiq
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
High Frequency ◽  
Stokes Equations ◽  
Outer Sphere ◽  
Stokes Drift ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Frequency Vibrations ◽  
Layer Flow

Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number ofO(1). The effect of the Stokes drift of fluid particles is also considered.

The Laminar Boundary Layer of a Source and Vortex Flow

1971 ◽  
Vol 22 (2) ◽  
pp. 196-206 ◽  
Author(s):  
T. S. Cham
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Large Pressure ◽  
Layer Flow ◽  
Special Case ◽  
Source Flow

SummaryA study is made of the interaction of a combination of free-vortex and source flow with a stationary surface. The laminar boundary layer flow can be expressed in ordinary differential equations by choosing suitable similarity transforms for the Navier-Stokes equations. When simplifying boundary-layer approximations are included, the equations do not yield any unique solution. Solutions to the complete equations are calculated numerically for the special case of equal source and vortex strengths for a limited range of Reynolds number. The results show the presence of “super” velocities and large pressure variations within the viscous layer.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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