Short Wave–Long Wave Interactions for Compressible Navier–Stokes Equations

2011 ◽  
Vol 43 (2) ◽  
pp. 764-787 ◽  
Author(s):  
João Paulo Dias ◽  
Hermano Frid
Keyword(s):  
Stokes Equations ◽  
Short Wave ◽  
Navier Stokes ◽  
Wave Interactions ◽  
Navier Stokes Equations ◽  
Long Wave

scholarly journals Study of the stability of a thin liquid layer in the Landau–Levich problem

2020 ◽  
pp. 48-55
Author(s):  
A. V. Lyushnin ◽  
◽  
K. A. Permyakova ◽  
Keyword(s):  
Liquid Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Liquid Layer ◽  
Wave Approximation ◽  
Long Wave ◽  
Interphase Boundaries ◽  
The Stability ◽  
Long Wave Approximation

The stability of the liquid layer in the Landay–Levich problem is theoretically investigated. The free energy of this layer is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of two electric layers at both interphase boundaries. In the framework of long-wave approximation, the stability of such a system with respect to perturbations is studied in the system of Navier–Stokes equations. A stability map is provided for different layer thicknesses.

A LATTICE BOLTZMANN METHOD FOR COMPUTATION OF AEROACOUSTIC INTERACTION

2007 ◽  
Vol 18 (04) ◽  
pp. 463-472 ◽  
Author(s):  
E. W. S. KAM ◽  
R. C. K. LEUNG ◽  
R. M. C. SO ◽  
X. M. LI
Keyword(s):  
Stokes Equations ◽  
Scattering Problem ◽  
Relaxation Times ◽  
Short Wave ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Bgk Model ◽  
Navier Stokes Equations ◽  
First Case ◽  
Boltzmann Method

This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.

scholarly journals The role of surfactants on the mechanism of the long-wave instability in liquid film flows

2014 ◽  
Vol 741 ◽  
pp. 139-155 ◽  
Author(s):  
George Karapetsas ◽  
Vasilis Bontozoglou
Keyword(s):  
Liquid Film ◽  
Concentration Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Instability ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Long Wave ◽  
Insoluble Surfactant ◽  
Interfacial Concentration

AbstractThe analysis for the physical mechanism of the long-wave instability in liquid film flow is extended to take into account the presence of a surfactant of arbitrary solubility. The Navier–Stokes equations are supplemented by mass balances for the concentrations at the interface and in the bulk, by a Langmuir model for adsorption kinetics at the interface, and are expanded in the limit of long-wave disturbances. The longitudinal flow perturbation, known to result from the perturbation shear stress which develops along the deformed interface, is shown to contribute a convective flux that triggers an interfacial concentration gradient. This gradient is, at leading order, in phase with the interfacial deformation, and as a result produces Marangoni stresses that stabilize the flow. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the spatial phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation and leads to the attenuation of Marangoni stresses. Higher-order terms are derived, which provide corrections for disturbances of finite wavelength.

scholarly journals Effect of the evaporation action on the stability of a thin liquid layer in the Landau–Levich problem

2021 ◽  
pp. 23-29
Author(s):  
A. V. Lyushnin ◽  
Keyword(s):  
Liquid Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensionless Number ◽  
Navier Stokes Equations ◽  
Wave Approximation ◽  
Long Wave ◽  
Interphase Boundaries ◽  
The Stability ◽  
Long Wave Approximation

The stability of the liquid layer in the Landau–Levich problem is theoretically investigated in the presence of the evaporation effect from the free surface. The free energy of a thin layer of an incompressible fluid is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of double electric layers at both interphase boundaries. The stability of such a system with respect to perturbations is studied in the framework of the long – wave approximation in the system of Navier-Stokes equations. A stability map is provided for different values of the evaporation parameter. It is established that the stability of the system increases with an increase in the dimensionless number of evaporation.

Nonlinear wave interactions in shear flows. Part 1. A variational formulation

1974 ◽  
Vol 66 (2) ◽  
pp. 209-221 ◽  
Author(s):  
J. R. Usher ◽  
A. D. D. Craik
Keyword(s):  
Variational Formulation ◽  
Stokes Equations ◽  
Direct Method ◽  
Substantial Reduction ◽  
Resonant Interaction ◽  
Navier Stokes ◽  
Algebraic Complexity ◽  
Wave Interactions ◽  
Navier Stokes Equations ◽  
Parallel Shear Flow

A modified version of Bateman's variational formulation of the incompressible Navier-Stokes equations and boundary conditions (see Dryden, Murnaghan & Bateman 1956) is introduced. This is employed to examine a particular nonlinear problem of hydrodynamic stability which was treated previously, using a ‘direct’ approach, by Craik (1971). This problem concerns the resonant interaction at second order of a triad of wave modes in a parallel shear flow.The present method is conceptually attractive; it also has the major advantage over the ‘direct’ method of a substantial reduction in algebraic complexity, which allows results to be derived far more readily. Also, some further improvements are made upon Craik's previous analysis. Such a variational approach may often be simpler than present conventional methods of tackling nonlinear viscous-flow problems. The present paper shows how other problems of nonlinear stability and wave interactions may be tackled in this way.

scholarly journals CALCULATIONS OF WAVES FORMED FROM SURFACE CAVITIES

1976 ◽  
Vol 1 (15) ◽  
pp. 63 ◽  
Author(s):  
Charles L. Mader
Keyword(s):  
Water Waves ◽  
Wave Motion ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Critical Depth ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Tsunami Waves ◽  
Long Wave

The wave motion resulting from cavities in the ocean surface was investigated using both the long wave, shallow water model and the incompressible Navier-Stokes equations. The fluid flow resulting from the calculated collapse of the cavities is significantly different for the two models. The experimentally observed flow resulting from explosively formed cavities is in better agreement with the flow calculated using the incompressible Navier-Stokes model. The resulting wave motions decay rapidly to deep water waves. Large cavities located under the surface of the ocean will be more likely to result in Tsunami waves than cavities on the surface. This is contrary to what has been suggested by the upper critical depth phenomenon.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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