Effect of large bulk viscosity on large-Reynolds-number flows

2014 ◽  
Vol 751 ◽  
pp. 142-163 ◽  
Author(s):  
M. S. Cramer ◽  
F. Bahmani
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Bulk Viscosity ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Large Reynolds Number ◽  
Steady Flows ◽  
Outer Flow ◽  
First Order ◽  
Large Bulk

AbstractWe examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of Emanuel (Phys. Fluids A, vol. 4, 1992, pp. 491–495).

On vortex boundary layers

1985 ◽  
Vol 400 (1819) ◽  
pp. 253-261 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Outer Flow ◽  
The Core ◽  
Dimensional Boundary ◽  
Radial Pressure Gradient ◽  
Potential Vortex ◽  
Vortex Axis

Flow visualization is used to study the flow that results when a potential vortex rotates normal to a stationary horizontal disc. Viscosity is seen to remove the singularity on the vortex axis and lead to the development of a three-dimensional boundary layer. The flow remains laminar below a Reynolds number, Re , of about 10 4 , where Re is based on radius and velocity at the disc edge. With further increases in Re the boundary layer becomes turbulent but relaminarizes as it is advected radially inwards by the highly favourable radial pressure gradient associated with the outer flow. The radius of the zone of relaminarized fluid decreases with increasing Re . Close to the axis the flow effuses vertically to form the core of the vortex which, for Re < 10 4 , is observed to undergo a massive disruption, either of the axisymmetric or helical form. The sense of the helix was observed on some occasions to be with that of the outer flow and on others to be opposite that of the outer flow.

The creation and evolution of coherent structures in plant canopy flows and their role in turbulent transport

2016 ◽  
Vol 789 ◽  
pp. 425-460 ◽  
Author(s):  
Brian N. Bailey ◽  
R. Stoll
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Conceptual Model ◽  
Coherent Structures ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Large Reynolds Number ◽  
Plant Canopy ◽  
Two Dimensional ◽  
The Creation

In this paper we used simulation tools to study turbulent boundary-layer structures in the roughness sublayer. Of particular interest is the case of a neutrally-stratified atmospheric boundary layer in which the lower boundary is covered by a homogeneous plant canopy. The goal of this study was to formulate a consistent conceptual model for the creation and evolution of the dominant coherent structures associated with canopy roughness and how they link with features observed in the overlying inertial sublayer. First, coherent structures were examined using temporally developing flow where the full range of turbulent scales had not yet developed, which allowed for instantaneous visualizations. These visualizations were used to formulate a conceptual model, which was then further tested using composite-averaged structure realizations from fully-developed flow with a very large Reynolds number. This study concluded that quasi two-dimensional mixing-layer-like roller structures exist in the developed flow and give the largest contributions to mean Reynolds stresses near the canopy. This work fully acknowledges the presence of highly three-dimensional and localized vortex pairing processes. The primary argument is that, as in a mixing layer, the smaller three-dimensional vortex interactions do not destroy the larger two-dimensional structure. Because the flow has a very large Reynolds number, the roller-like structures are not well-defined vortices but rather are a conglomerate of a large range of smaller-scale vortex structures that create irregularities. Because of this, the larger-scale structure is more difficult to detect in correlation or conditional sampling analyses. The frequently reported ‘scalar microfronts’ and associated spikes in pressure occur in the slip-like region between adjacent rollers. As smaller vortices within roller structures stretch, they evolve to form arch- and hairpin-shaped structures. Blocking by the low-flux canopy creates vertical asymmetry, and tends to impede the vertical progression of head-down structures. Head-up hairpins are allowed to continually stretch upward into the overlying inertial sublayer, where they evolve into the hairpin structures commonly reported to populate wall-bounded flows. This process is thought to be modulated by boundary-layer-scale secondary instability, which enhances head-up hairpin formation along quasi-streamwise transects.

On the rapid rotation of a massive sphere in a monatomic gas

1974 ◽  
Vol 64 (1) ◽  
pp. 17-31
Author(s):  
M. R. Foster
Keyword(s):  
Boundary Layer ◽  
Prandtl Number ◽  
Solid Sphere ◽  
Large Reynolds Number ◽  
Thin Boundary Layer ◽  
Order Unity ◽  
Outer Flow ◽  
Rapid Rotation ◽  
First Order ◽  
Monatomic Gas

We consider the rapid rotation, in the sense of large Reynolds number ε−1, of a gravitating solid sphere in a monatomic gas. The flow is characterized by a thin boundary layer on the sphere and a thin, swirling, buoyant, radial jet in the equatorial plane. When the Prandtl number σ is of order unity, the boundary layer and jet are to first order uncoupled from the outer flow. For sufficiently small Prandtl number (which may be interpreted as approximating an optically thick radiating gas), the outer flowisboundary-layer driven. The parameter boundary between these two dissimilar steady states is σ =O(ε⅙).

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

The boundary layer in crossed-fields m.h.d.

1966 ◽  
Vol 25 (2) ◽  
pp. 229-240 ◽  
Author(s):  
W. R. Sears
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flat Plate ◽  
Flow Problem ◽  
Inviscid Flow ◽  
Magnetic Reynolds Number ◽  
Large Reynolds Number ◽  
Zero Values ◽  
Plate Solution ◽  
A Current

This study of the boundary layer of steady, incompressible, plane, crossed-fields m.h.d. flow at large Reynolds numberReand magnetic Reynolds numberRmbegins with a review of Hartmann's case, where a boundary layer occurs whose thickness is proportional to (Re Rm)−½. Following this clue, it is shown that in general the boundary layer is a ‘local Hartmann boundary layer’. Its profiles are always exponential and it is determined completely by local quantities. The skin friction and the total electric current in the layer are proportional to the square root of the magnetic Prandtl number, i.e. to (Rm/Re)½. Thus the exterior-flow problem, the solution of which precedes a boundary-layer solution, generally involves a current sheet at the fluid-solid interface.This inviscid-flow problem becomes tractable if (Rm/Re)½is small enough to permit a linearized solution. The flow field about a flat plate at zero incidence is calculated in this approximation. It is pointed out that the thin-cylinder solutions of Sears & Resler (1959), which pertain toRm/Re= 0, can immediately be extended to small, non-zero values of this parameter by linear combination with this flat-plate solution.

Darryl E. Metzger Memorial Session Paper: Comparison of Calculated and Measured Heat Transfer Coefficients for Transonic and Supersonic Boundary-Layer Flows

1995 ◽  
Vol 117 (2) ◽  
pp. 248-254 ◽  
Author(s):  
C. Hu¨rst ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Supersonic Boundary Layer ◽  
Nozzle Wall ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Three Dimensional Finite Element

The present study compares measured and computed heat transfer coefficients for high-speed boundary layer nozzle flows under engine Reynolds number conditions (U∞=230 ÷ 880 m/s, Re* = 0.37 ÷ 1.07 × 106). Experimental data have been obtained by heat transfer measurements in a two-dimensional, nonsymmetric, convergent–divergent nozzle. The nozzle wall is convectively cooled using water passages. The coolant heat transfer data and nozzle surface temperatures are used as boundary conditions for a three-dimensional finite-element code, which is employed to calculate the temperature distribution inside the nozzle wall. Heat transfer coefficients along the hot gas nozzle wall are derived from the temperature gradients normal to the surface. The results are compared with numerical heat transfer predictions using the low-Reynolds-number k–ε turbulence model by Lam and Bremhorst. Influence of compressibility in the transport equations for the turbulence properties is taken into account by using the local averaged density. The results confirm that this simplification leads to good results for transonic and low supersonic flows.

Secondary instability and subcritical transition of the leading-edge boundary layer

2016 ◽  
Vol 792 ◽  
pp. 682-711 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Bypass Transition ◽  
Wall Suction ◽  
Transition Mechanism

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as$Re\approx 175$, i.e. far below the linear critical Reynolds number$Re_{crit}\approx 583$of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above$Re_{tr}\approx 250$. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number$Re_{tr}\approx 250$at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

Sign in / Sign up

Export Citation Format

Share Document