Dissipative instability of fluid flows with piecewise linear velocity profiles

1986 ◽  
Vol 21 (6) ◽  
pp. 854-860
Author(s):  
P. I. Kolykhalov
Keyword(s):  
Piecewise Linear ◽  
Fluid Flows ◽  
Velocity Profiles ◽  
Linear Velocity ◽  
Dissipative Instability

scholarly journals Suction Injection Induced MHD Flow through Vertical Narrow Porous Channel with Permeable Properties

2019 ◽  
Vol 8 (4) ◽  
pp. 121-126
Keyword(s):  
Transverse Velocity ◽  
Rectangular Channel ◽  
Fluid Flows ◽  
Mhd Flow ◽  
Research Problem ◽  
Velocity Profiles ◽  
Current Research Problem ◽  
Flow Equations ◽  
Electrically Conducting ◽  
Permeability Parameter

The current research problem deals with fluid flows that are electrically conducting known as Magnetohydrodynamic(MHD) flow, viscous oscillatory and stratified fluid in a vertical long small geometry rectangular channel that has permeable property with one side being porous and the other side being nonporous. Corresponding fluid flow equations are simplified and hence solved by applying Lubrication approximation by using similarity transformation. The interpretations of the influences of various quantities that are involved to the problem on velocity profiles, pressure and density distributions are explained in detail. The results of the research problem shows that the Magnetohydrodynamic parameter encourages backflow nearer to the boundaries of the channel while permeability parameter influences the flow differently for axial and transverse velocity profiles. The results for =0 reduces to the results that are already available in the literature.The current research problem deals with fluid flows that are electrically conducting known as Magnetohydrodynamic(MHD) flow, viscous oscillatory and stratified fluid in a vertical long small geometry rectangular channel that has permeable property with one side being porous and the other side being nonporous. Corresponding fluid flow equations are simplified and hence solved by applying Lubrication approximation by using similarity transformation. The interpretations of the influences of various quantities that are involved to the problem on velocity profiles, pressure and density distributions are explained in detail. The results of the research problem shows that the Magnetohydrodynamic parameter encourages backflow nearer to the boundaries of the channel while permeability parameter influences the flow differently for axial and transverse velocity profiles. The results for =0 reduces to the results that are already available in the literature.

scholarly journals Stability of an MHD shear flow with a piecewise linear velocity profile

2006 ◽  
Vol 448 (3) ◽  
pp. 1177-1184 ◽  
Author(s):  
M. S. Ruderman ◽  
L. Brevdo
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Piecewise Linear ◽  
Linear Velocity

Induced motions in shear flows with piecewise linear velocity profile

1983 ◽  
Vol 18 (1) ◽  
pp. 153-158
Author(s):  
A. B. Ezerskii
Keyword(s):  
Velocity Profile ◽  
Shear Flows ◽  
Piecewise Linear ◽  
Linear Velocity

scholarly journals On Bragg resonances and wave triad interactions in two-layered shear flows

2019 ◽  
Vol 867 ◽  
pp. 482-515 ◽  
Author(s):  
Raunak Raj ◽  
Anirban Guha
Keyword(s):  
Shear Flows ◽  
Resonance Condition ◽  
Piecewise Linear ◽  
Multiple Scale ◽  
Linear Velocity ◽  
Velocity Shear ◽  
Fredholm Alternative ◽  
Bragg Resonance ◽  
Weakly Nonlinear ◽  
Doppler Shifts

The standard resonance conditions for Bragg scattering as well as weakly nonlinear wave triads have been traditionally derived in the absence of any background velocity. In this paper, we have studied how these resonance conditions get modified when uniform, as well as various piecewise linear velocity profiles, are considered for two-layered shear flows. Background velocity can influence the resonance conditions in two ways: (i) by causing Doppler shifts, and (ii) by changing the intrinsic frequencies of the waves. For Bragg resonance, even a uniform velocity field changes the resonance condition. Velocity shear strongly influences the resonance conditions since, in addition to changing the intrinsic frequencies, it can cause unequal Doppler shifts between the surface, pycnocline and the bottom. Using multiple scale analysis and Fredholm alternative, we analytically obtain the equations governing both the Bragg resonance and the wave triads. We have also extended the higher-order spectral method, a highly efficient computational tool usually used to study triad and Bragg resonance problems, to incorporate the effect of piecewise linear velocity profile. A significant aspect, both on the theoretical and numerical fronts, has been extending the potential flow approximation, which is the basis of the study of these kinds of problems, to incorporate piecewise constant background shear.

Distortion of Velocity Profiles of Water Flow with Heavy Molecular Weight Polymers

2019 ◽  
Vol 392 ◽  
pp. 228-238 ◽  
Author(s):  
Lawrence C. Edomwonyi-Otu
Keyword(s):  
Molecular Weight ◽  
Pressure Drop ◽  
Water Flow ◽  
Fluid Flows ◽  
Velocity Profiles ◽  
Polymer Fibers ◽  
Molecular Weights ◽  
Frictional Pressure Drop ◽  
Hydrolyzed Polyacrylamide ◽  
Insight Into

Transportation of fluids in pipelines is common in many industrial processes. The energy requirements for this transport is high because of the need to overcome the occurring frictional pressure drop or drag. However, the addition of high molecular weight polymers to fluid flows has been known to cause a reduction in the frictional pressure drop. It has also been reported to cause other changes in the flow including changes in the turbulence characteristics, holdup as well as asymmetry of the velocity profiles. In this work some experimental results are presented in order to gain better insight into the deviations from axisymmetry of velocity profiles of water flow in pipes when drag reducing agents are added. Drag reduction studies were carried out in a horizontal 14mmID acrylic pipe with hydrolyzed polyacrylamide and different molecular weights polyethylene oxide used as additives in fully developed flows. Asymmetry was observed at both transitional and turbulent flow regimes for all tested polymer types and it increased with molecular weights. While the molecular weight and degree of formation of entanglements and aggregates of the polymer fibers are indicated as the causes of the observed profile asymmetry, the contribution of system/setup imperfections can be ruled out.

scholarly journals Breaking the Kolmogorov Barrier in Model Reduction of Fluid Flows

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 26 ◽  
Author(s):  
Shady E. Ahmed ◽  
Omer San
Keyword(s):  
Energy Spectrum ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Piecewise Linear ◽  
Fluid Flows ◽  
Reduced Order ◽  
Temporal Complexity ◽  
Comparable Accuracy ◽  
The Cost ◽  
Modal Truncation

Turbulence modeling has been always a challenge, given the degree of underlying spatial and temporal complexity. In this paper, we propose the use of a partitioned reduced order modeling (ROM) approach for efficient and effective approximation of turbulent flows. A piecewise linear subspace is tailored to capture the fine flow details in addition to the larger scales. We test the partitioned ROM for a decaying two-dimensional (2D) turbulent flow, known as 2D Kraichnan turbulence. The flow is initiated using an array of random vortices, corresponding to an arbitrary energy spectrum. We show that partitioning produces more accurate and stable results than standard ROM based on a global application of modal decomposition techniques. We also demonstrate the predictive capability of partitioned ROM through an energy spectrum analysis, where the recovered energy spectrum significantly converges to the full order model’s statistics with increased partitioning. Although the proposed approach incurs increased memory requirements to store the local basis functions for each partition, we emphasize that it permits the construction of more compact ROMs (i.e., of smaller dimension) with comparable accuracy, which in turn significantly reduces the online computational burden. Therefore, we consider that partitioning acts as a converter which reduces the cost of online deployment at the expense of offline and memory costs. Finally, we investigate the application of closure modeling to account for the effects of modal truncation on ROM dynamics. We illustrate that closure techniques can help to stabilize the results in the inertial range, but over-stabilization might take place in the dissipative range.

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