Impedance eduction in the presence of turbulent shear flow using the linearized Navier-Stokes equations

2017 ◽  
Author(s):  
Chenyang Weng ◽  
Anita Schulz ◽  
Dirk Ronneberger ◽  
Lars Enghardt ◽  
Friedrich Bake
Keyword(s):  
Shear Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations

Computations of Ship Stern and Wake Flow and Comparisons with Experiment

1990 ◽  
Vol 34 (03) ◽  
pp. 179-193
Author(s):  
V. C. Patel ◽  
H. C. Chen ◽  
S. Ju
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Numerical Method ◽  
Stokes Equations ◽  
Ship Hull ◽  
Wake Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations has been employed to study the turbulent shear flow over the stern and in the wake of a ship hull. Detailed comparisons are made between the numerical results and available experimental data to show that most of the important overall features of such flows can now be predicted with considerable accuracy.

Bounds for turbulent shear flow

1970 ◽  
Vol 41 (1) ◽  
pp. 219-240 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Shear Flow ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Experimental Values

Bounds on the transport of momentum in turbulent shear flow are derived by variational methods. In particular, variational problems for the turbulent regimes of plane Couette flow, channel flow, and pipe flow are considered. The Euler equations resemble the basic Navier–Stokes equations of motion in many respects and may serve as model equations for turbulence. Moreover, the comparison of the upper bound with the experimental values of turbulent momentum transport shows a rather close similarity. The same fact holds with respect to other properties when the observed turbulent flow is compared with the structure of the extremalizing solution of the variational problem. It is suggested that the instability of the sublayer adjacent to the walls is responsible for the tendency of the physically realized turbulent flow to approach the properties of the extremalizing vector field.

Large-scale instabilities of turbulent wakes

1972 ◽  
Vol 54 (3) ◽  
pp. 481-488 ◽  
Author(s):  
W. C. Reynolds
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Small Scale ◽  
General Interest ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Eddy Structures ◽  
The Stability

The equations describing the statistical features of small amplitude waves in a turbulent shear flow are derived from the Navier-Stokes equations. Closure is achieved through a postulated constitutive equation for the alteration of the statistical properties of the turbulence by the organized wave. The theory is applied in an examination of the stability of a hypothetical wake consisting of small-scale turbulence enclosed within a steady uncontorted superlayer. A set of superlayer jump conditions is derived from fundamental considerations, and these are of more general interest. For this hypothetical flow the analysis predicts largescale instabilities and superlayer contortions reminiscent of large-eddy structures observed in real flows. These instabilities therefore offer an explanation of the presence of large-scale organized motions in turbulent free shear flows.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

Lift, drag and added mass of a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2233-2248 ◽  
Author(s):  
Dominique Legendre ◽  
Catherine Colin ◽  
Typhaine Coquard
Keyword(s):  
Shear Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Added Mass ◽  
Unsteady Motion ◽  
Navier Stokes ◽  
Mass Force ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Linear Shear

The three-dimensional flow around a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations in a boundary-fitted domain. The main goal of the present study is to provide a complete description of the forces experienced by the bubble (drag, lift and added mass) over a wide range of sliding and shear Reynolds numbers (0.01≤ Re b , Re α ≤2000) and shear rate (0≤ Sr ≤5). The drag and lift forces are computed successively for the following situations: an immobile bubble in a linear shear flow; a bubble sliding on the wall in a fluid at rest; and a bubble sliding in a linear shear flow. The added-mass force is studied by considering an unsteady motion relative to the wall or a time-dependent radius.

The evolution of thermocline waves from an oscillatory disturbance

1993 ◽  
Vol 254 ◽  
pp. 401-416 ◽  
Author(s):  
D. Nicolaou ◽  
R. Liu ◽  
T. N. Stevenson
Keyword(s):  
Finite Difference ◽  
Shear Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Ray Theory ◽  
Navier Stokes Equations ◽  
Linear Shear ◽  
Wave Shapes ◽  
The Way

The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.

Simulation of Three-Dimensional Shear Flow Around a Nozzle-Afterbody at High Speeds

1992 ◽  
Vol 114 (2) ◽  
pp. 178-185 ◽  
Author(s):  
Oktay Baysal ◽  
Wendy B. Hoffman
Keyword(s):  
Shear Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Surface Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Duct Flow ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Pressure Distributions

Turbulent shear flows at supersonic and hypersonic speeds around a nozzle-afterbody are simulated. The three-dimensional, Reynolds-averaged Navier-Stokes equations are solved by a finite-volume and implicit method. The convective and the pressure terms are differenced by an upwind-biased algorithm. The effect of turbulence is incorporated by a modified Baldwin-Lomax eddy viscosity model. The success of the standard Baldwin-Lomax model for this flow type is shown by comparing it to a laminar case. These modifications made to the model are also shown to improve flow prediction when compared to the standard Baldwin-Lomax model. These modifications to the model reflect the effects of high compressibility, multiple walls, vortices near walls, and turbulent memory effects in the shear layer. This numerically simulated complex flowfield includes a supersonic duct flow, a hypersonic flow over an external double corner, a flow through a non-axisymmetric, internal-external nozzle, and a three-dimensional shear layer. The specific application is for the flow around the nozzle-afterbody of a generic hypersonic vehicle powered by a scramjet engine. The computed pressure distributions compared favorably with the experimentally obtained surface and off-surface flow surveys.

scholarly journals A streamwise constant model of turbulence in plane Couette flow

2010 ◽  
Vol 665 ◽  
pp. 99-119 ◽  
Author(s):  
D. F. GAYME ◽  
B. J. McKEON ◽  
A. PAPACHRISTODOULOU ◽  
B. BAMIEH ◽  
J. C. DOYLE
Keyword(s):  
Couette Flow ◽  
Small Amplitude ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Theoretic Approach ◽  
Plane Couette Flow ◽  
Navier Stokes Equations ◽  
Turbulent Plane ◽  
3C Model

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behaviour of fully turbulent plane Couette flow using a streamwise constant projection of the Navier–Stokes equations. This results in a two-dimensional three-velocity-component (2D/3C) model. We first use a steady-state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the 2D/3C model under small-amplitude Gaussian forcing of the cross-stream components are compared to direct numerical simulation (DNS) data. The results indicate that a streamwise constant projection of the Navier–Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A systems-theoretic approach is used to demonstrate the presence of large input–output amplification through the forced 2D/3C model. It is this amplification coupled with the appropriate nonlinearity that enables the 2D/3C model to generate turbulent behaviour under the small-amplitude forcing employed in this study.

The interaction of a diffusing line vortex and an aligned shear flow

1985 ◽  
Vol 399 (1817) ◽  
pp. 367-375 ◽  
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Kinematic Viscosity ◽  
Stokes Equations ◽  
Radial Distance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Line Vortex ◽  
Linear Shear

An exact solution of the Navier─Stokes equations of incompressible flow, which represents the interaction of a diffusing line vortex and a linear shear flow aligned so that initially the streamlines in the shear flow are parallel to the line vortex, is presented. If Γ is the circulation of the line vortex and v the kinematic viscosity then, when Re ═ Γ/2π v is large, the vorticity of the shear flow is expelled from the circular cylinder 0 < r ≪ ( vt ) 1/2 Re 1/3 , where r is the distance from the axis of the diffusing line vortex and t the time since initiation of the flow. At larger radii a peak vorticity 0.903Ω Re 1/3 is found at a radial distance 1.26( vt )1/2 Re 1/3 , where Ω is the initial uniform vorticity in the shear flow. The vortex filament is embedded in a growing cylinder from which vorticity has been expelled, the cylinder itself being bounded by an annular region of thickness of order Re 1/3 ( vt ) 1/2 in which the vorticity is of order Ω Re 1/3 .

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