Long-wave theory for a new convective instability with exponential growth normal to the wall

2005 ◽  
Vol 363 (1830) ◽  
pp. 1119-1130 ◽  
Author(s):  
J.J Healey
Keyword(s):  
Numerical Solutions ◽  
Flow Instability ◽  
Cross Flow ◽  
Wave Theory ◽  
Linear Stability Theory ◽  
Wave Regime ◽  
Long Wave ◽  
Point Analysis ◽  
New Type ◽  
Layer Flow

A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.

The long-time behaviour of incompressible swept-wing boundary layers subject to impulsive forcing

1998 ◽  
Vol 355 ◽  
pp. 359-381 ◽  
Author(s):  
M. J. TAYLOR ◽  
N. PEAKE
Keyword(s):  
Boundary Layer ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Leading Edge ◽  
Rotating Disk ◽  
Linear Stability Theory ◽  
Swept Wing ◽  
Long Time ◽  
Layer Flow

The long-time limit of the response of incompressible three-dimensional boundary layer flows on infinite swept wedges and infinite swept wings to impulsive forcing is examined using causal linear stability theory. Following the discovery by Lingwood (1995) of the presence of absolute instabilities caused by pinch points occurring in the radial direction in the boundary layer flow of a rotating disk, we search for pinch points in the cross flow direction for both the model Falkner–Skan–Cooke profile of a swept wedge and for a genuine swept-wing configuration. It is shown in both cases that, within a particular range of the parameter space, the boundary layer does indeed support pinch points in the wavenumber plane corresponding to the crossflow direction. These crossflow-induced pinch points do not constitute an absolute instability, as there is no simultaneous pinch occurring in the streamwise wavenumber plane, but nevertheless we show here how they can be used to find the maximum local growth rate contained in a wavepacket travelling in any given direction. Lingwood (1997) also found pinch points in the chordwise wavenumber plane in the boundary layer of the leading-edge region of a swept wing (i.e. at very high flow angles). The results presented in this paper, however, demonstrate the presence of pinch points for a much larger range of flow angles and pressure gradients than was found by Lingwood, and indeed describe the flow over a much greater, and practically significant, portion of the wing.

Control of the secondary cross-flow instability using localized suction

2012 ◽  
Vol 706 ◽  
pp. 470-495 ◽  
Author(s):  
Tillmann Friederich ◽  
Markus J. Kloker
Keyword(s):  
Flow Instability ◽  
Three Dimensional ◽  
Cross Flow ◽  
Base Flow ◽  
Transition To Turbulence ◽  
Significant Delay ◽  
Transition Control ◽  
Dimensional Boundary ◽  
Nonlinear Disturbance ◽  
Layer Flow

AbstractTransition control by suction in a three-dimensional boundary-layer flow subject to cross-flow instability is investigated using direct numerical simulation. Whereas the classical application of (homogeneous) suction at the wall is aimed at modifying the quasi-two-dimensional base flow to weaken primary cross-flow instability, here the three-dimensional nonlinear disturbance state with large-amplitude steady cross-flow vortices (CFVs) is controlled. Strong, localized ‘pinpoint’ suction is shown to be suitable for altering the CFVs and the associated flow field such that secondary instability is weakened or even completely suppressed. Thus significant delay of transition to turbulence can be achieved.

Nonlinear long-wave stability of superposed fluids in an inclined channel

1994 ◽  
Vol 277 ◽  
pp. 55-83 ◽  
Author(s):  
B. S. Tilley ◽  
S. H. Davis ◽  
S. G. Bankoff
Keyword(s):  
Nonlinear Analysis ◽  
Travelling Waves ◽  
Wave Theory ◽  
Cubic Nonlinearity ◽  
Weakly Nonlinear ◽  
Inclined Channel ◽  
Weakly Nonlinear Analysis ◽  
Long Wave ◽  
Layer Flow ◽  
Sivashinsky Equation

We consider the two-layer flow of immiscible, viscous, incompressible fluids in an inclined channel. We use long-wave theory to obtain a strongly nonlinear evolution equation which describes the motion of the interface. This equation includes the physical effects of viscosity stratification, density stratification, and shear. A weakly nonlinear analysis of this equation yields a Kuramoto–Sivashinsky equation, which possesses a quadratic nonlinearity. However, certain physical situations exist in two-layer flow for which modifications of the Kuramoto–Sivashinsky equation are physically pertinent. In particular, the presence of the second layer can mediate the wave-steepening instability found in single-phase falling films, requiring the inclusion of a cubic nonlinearity in the weakly nonlinear analysis. The introduction of the cubic nonlinearity destroys the symmetry-breaking bifurcations of the Kuramoto–Sivashinsky equation, and new isolated solution branches emerge as the strength of the cubic nonlinearity increases. Bistability between these new solutions and those associated with the Kuramoto–Sivashinsky equation is found, as well as the formation of a hysteresis loop from smaller-amplitude travelling waves to larger-amplitude travelling waves. The physical implications of these dynamics to the phenomenon of laminar flooding in a channel are discussed.

Numerical Investigation on the Effect of Vortex Generator on Axial Compressor Performance

2014 ◽  
Author(s):  
Ruchika Agarwal ◽  
Anand Dhamarla ◽  
Sridharan R. Narayanan ◽  
Shraman N. Goswami ◽  
Balamurugan Srinivasan
Keyword(s):  
Cross Flow ◽  
Axial Compressor ◽  
Vortex Generator ◽  
Side Surface ◽  
Suction Side ◽  
Test Case ◽  
Stall Margin ◽  
Layer Flow ◽  
Flow Effects ◽  
End Wall

The performance of the compressor blade is considerably influenced by secondary flow effects, like the cross flow on the end wall as well as corner flow separation between the wall and the blade. The present work is focused on the studying the effects of Vortex Generator (VG) on NASA Rotor 37 test case using Computational Fluid Dynamics (CFD). VG helps in controlling the inception of the stall by generating vortices and energizes the low momentum boundary layer flow which enhances the rotor performance. Three design configuration namely, Counter-rotating, Co-rotating and Plow configuration VG are selected based on the improved aerodynamic performance discussed in reference [1]. These VG are located at 90% span and 42% chord on suction side surface of the blade. Among the three configurations, the first configuration has greater impact on the end wall cross flow and flow deflection which resulted in enhanced numerical stall margin of 5.4% from baseline. The reasons for this numerical stall margin improvement are discussed in detail.

Transcritical two-layer flow over topography

1987 ◽  
Vol 178 ◽  
pp. 31-52 ◽  
Author(s):  
W. K. Melville ◽  
Karl R. Helfrich
Keyword(s):  
Steady Flow ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Single Layer ◽  
Cubic Nonlinearity ◽  
Arbitrary Length ◽  
Weakly Nonlinear ◽  
Flow Over Topography ◽  
Layer Flow

The evolution of weakly-nonlinear two-layer flow over topography is considered. The governing equations are formulated to consider the effects of quadratic and cubic nonlinearity in the transcritical regime of the internal mode. In the absence of cubic nonlinearity an inhomogeneous Korteweg-de Vries equation describes the interfacial displacement. Numerical solutions of this equation exhibit undular bores or sequences of Boussinesq solitary waves upstream in a transcritical regime. For sufficiently large supercritical Froude numbers, a locally steady flow is attained over the topography. In that regime in which both quadratic and cubic nonlinearity are comparable, the evolution of the interface is described by an inhomogeneous extended Kortewegde Vries (EKdV) equation. This equation displays undular bores upstream in a subcritical regime, but monotonic bores in a transcritical regime. The monotonic bores are solitary wave solutions of the corresponding homogeneous EKdV equation. Again, locally steady flow is attained for sufficiently large supercritical Froude numbers. The predictions of the numerical solutions are compared with laboratory experiments which show good agreement with the solutions of the forced EKdV equation for some range of parameters. It is shown that a recent result of Miles (1986), which predicts an unsteady transcritical regime for single-layer flows, may readily be extended to two-layer flows (described by the forced KdV equation) and is in agreement with the results presented here.Numerical experiments exploiting the symmetry of the homogeneous EKdV equation show that solitary waves of fixed amplitude but arbitrary length may be generated in systems described by the inhomogeneous EKdV equation.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

scholarly journals Physics and Modeling of Various Hazardous Landslides

Geosciences ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 108
Author(s):  
Jόnas Elíasson ◽  
Þorsteinn Sæmundsson
Keyword(s):  
Turbulent Flows ◽  
High Velocity ◽  
Wave Theory ◽  
Type I ◽  
Flow Paths ◽  
Stable Slope ◽  
Slope Factor ◽  
New Type ◽  
Flowing Material ◽  
Type Studies

In 2014, the Varnes classification system for landslides was updated. Complex landslides can still be a problem to classify as the classification does not include the flow type in the hydrodynamical sense. Three examples of Icelandic landslides are presented and later used as case studies in order to demonstrate the methods suggested to analyze the flow. The methods are based on the different physical properties of the flow types of the slides. Three different flow types are presented, named type (i), (ii), and (iii). Types (i) and (ii) do not include turbulent flows and their flow paths are sometimes independent of the velocity. Type (iii) include high velocity flows; they are treated with the translator wave theory, where a new type of a slope factor is used. It allows the slide to stop when the slope has flattened out to the value that corresponds to the stable slope property of the flowing material. The type studies are for a fast slide of this type, also a large slip circle slide that turns into a fast-flowing slide farther down the path and finally a large slide running so fast that it can run for a kilometer on flat land where it stops with a steep front.

Computational Fluid Dynamics Evaluation of Heat Transfer Correlations for Sodium Flows in a Heat Exchanger

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Seok-Ki Choi ◽  
Seong-O Kim ◽  
Hoon-Ki Choi
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Cross Flow ◽  
Turbulence Models ◽  
Parallel Flow ◽  
Sst Model ◽  
Heat Transfer Correlations

A numerical study for the evaluation of heat transfer correlations for sodium flows in a heat exchanger of a fast breeder nuclear reactor is performed. Three different types of flows such as parallel flow, cross flow, and two inclined flows are considered. Calculations are performed for these three typical flows in a heat exchanger changing turbulence models. The tested turbulence models are the shear stress transport (SST) model and the SSG-Reynolds stress turbulence model by Speziale, Sarkar, and Gaski (1991, “Modelling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical System Approach,” J. Fluid Mech., 227, pp. 245–272). The computational model for parallel flow is a flow past tubes inside a circular cylinder and those for the cross flow and inclined flows are flows past the perpendicular and inclined tube banks enclosed by a rectangular duct. The computational results show that the SST model produces the most reliable results that can distinguish the best heat transfer correlation from other correlations for the three different flows. It was also shown that the SSG-RSTM high-Reynolds number turbulence model does not deal with the low-Prandtl number effect properly when the Peclet number is small. According to the present calculations for a parallel flow, all the old correlations do not match with the present numerical solutions and a new correlation is proposed. The correlations by Dwyer (1966, “Recent Developments in Liquid-Metal Heat Transfer,” At. Energy Rev., 4, pp. 3–92) for a cross flow and its modified correlation that takes into account of flow inclination for inclined flows work best and are accurate enough to be used for the design of the heat exchanger.

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