The Inviscid Limit for the Navier–Stokes Equations with Slip Condition on Permeable Walls

2013 ◽  
Vol 23 (5) ◽  
pp. 731-750 ◽  
Author(s):  
N. V. Chemetov ◽  
F. Cipriano
Keyword(s):  
Stokes Equations ◽  
Slip Condition ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Permeable Walls

Flow induced by jets and plumes

1981 ◽  
Vol 108 ◽  
pp. 55-65 ◽  
Author(s):  
W. Schneider
Keyword(s):  
Stokes Equations ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Slip Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Jet ◽  
Order Of Magnitude ◽  
Valid Solution ◽  
Solid Walls

The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular-conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls.

Transonic nozzle flow of dense gases

1993 ◽  
Vol 247 ◽  
pp. 661-688 ◽  
Author(s):  
A. Kluwick
Keyword(s):  
Stokes Equations ◽  
Equations Of State ◽  
Weak Shock ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Perturbation Equation ◽  
Navier Stokes Equations ◽  
Sonic Point ◽  
Specific Heats ◽  
Dense Gases

The paper deals with the flow properties of dense gases in the throat area of slender nozzles. Starting from the Navier–Stokes equations supplemented with realistic equations of state for gases which have relatively large specific heats a novel form of the viscous transonic small-perturbation equation is derived. Evaluation of the inviscid limit of this equation shows that three sonic points rather than a single sonic point may occur during isentropic expansion of such media, in contrast to the case of perfect gases. As a consequence, a shock-free transition from subsonic to supersonic speeds cannot, in general, be achieved by means of a conventional converging–diverging nozzle. Nozzles leading to shock-free flow fields must have an unusual shape consisting of two throats and an intervening antithroat. Additional new results include the computation of the internal thermoviscous structure of weak shock waves and a phenomenon referred to as impending shock splitting. Finally, the relevance of these results to the description of external transonic flows is discussed briefly.

scholarly journals Steady streaming in a channel with permeable walls

2013 ◽  
Vol 25 (1) ◽  
pp. 65-82
Author(s):  
KONSTANTIN ILIN
Keyword(s):  
Asymptotic Expansion ◽  
Viscous Fluid ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Stokes Layer ◽  
Permeable Walls ◽  
Time Injection

We study steady streaming in a channel between two parallel permeable walls induced by oscillating (in time) injection/suction of a viscous fluid at the walls. We obtain an asymptotic expansion of the solution of the Navier–Stokes equations in the limit when the amplitude of normal displacements of fluid particles near the walls is much smaller than both the width of the channel and the thickness of the Stokes layer. It is shown that the steady part of the flow in this problem is much stronger than the steady flow produced by vibrations of impermeable boundaries. Another interesting feature of this problem is that the direction of the steady flow is opposite to what one would expect if the flow was produced by vibrations of impermeable walls.

Numerical Simulation of Heat Distribution with Temperature-Dependent Thermal Conductivity in a Two-Dimensional Liquid Flow

2017 ◽  
Vol 18 (6) ◽  
pp. 507-513 ◽  
Author(s):  
Valjacques Nyemb Nsoga ◽  
Jacques Hona ◽  
Elkana Pemha
Keyword(s):  
Boundary Layers ◽  
Peclet Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Navier Stokes Equations ◽  
Péclet Number ◽  
Permeable Walls ◽  
Different Temperatures ◽  
Thermal Boundary Layers

AbstractThis paper is a contribution to a better understanding of heat transfer through porous channels used for mechanical sieving and filtration of liquids. The problem modeled by means of the Navier–Stokes equations and the energy equation is similar to a viscous flow between two uniformly permeable walls fixed at different temperatures. Thermal behaviors are determined through three branches denoted solutions of types I, II and III of a diagram of bifurcations presenting the values of the wall shear stress as the Reynolds number varies. We found that the distribution of temperature is similar through branches I and II where a large horizontal inflection area is observed as the Péclet number increases. This large horizontal inflection area inside the channel denotes the presence of thermal boundary layers which more precisely occur across branches I and II when the Péclet number approaches the value of 10. On the other hand, along branch III, thermal boundary layers do not exist and temperature presents a different behavior compared to those of branches I and II.

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