Search results for "Boundary layer thickness"
showing 8 items of 8 documents
Breakdown of Burton-Prime-Slichter approach and lateral solute segregation in radially converging flows
2005
A theoretical study is presented of the effect of a radially converging melt flow, which is directed away from the solidification front, on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) solution describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for the flows converging along the solidification front. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. Although such a divergence can formally be avoided by restricting the axial extension of the melt to a layer of fi…
Experimental characterisation of the CIRA plasma wind tunnel SCIROCCO test section
2008
Abstract During the Validation Phase of the CIRA-PWT SCIROCCO Facility located at Capua (Italy), a test campaign has been carried out to verify the performances of the facility with the use of the two conical nozzle configurations “D” and “F” with exit diameters are, respectively of, 1150 and 1950 mm. For the first time the data results of the tests have been used to characterize the plasma flow in the test section of the facility. In particular, analytical relationships between the main thermo-fluid-dynamic parameters in the test section and the reservoir conditions of the facility have been found, and compared to the CFD prediction developed during the Design Phase of the facility. Very i…
A method to transform a nonlocal model into a gradient one within elasticity and plasticity
2014
Abstract A method based on the principle of the virtual power (PVP) is presented, by which a mechanical problem of nonlocal elasticity, or plasticity, is transformed into one of gradient nature. Different Taylor series expansion techniques are applied to the driving local strain fields of the nonlocal problem, either full spatial expansion within the bulk volume, or uni-directional expansion along the normal to the thin boundary layer. This, at the limit when the boundary layer thickness tends to zero, makes the PVP of the nonlocal model transform itself into one featuring a counterpart gradient model. Also, for a class of “associated” nonlocal and gradient elasticity models (i.e. the kerne…
A study of hydrothermal convection in saturated porous media
1993
Abstract Because of its relevance to many geological and technical problems, hydrothermal convection is investigated here mainly with the aid of numerical models by a systematic analysis of the properties of this type of convection for a range of super-critical Rayleigh numbers. Calculations were performed for two-dimensional models with constant properties in a region of aspect ratio 2. The principal results in the case of temperature fixed at the impermeable top and bottom are the following for the Nusselt number Nu, the cell aspect ratio a, and the boundary layer thickness δ: Nu ≈ 1.7 R0.5, a ≈ 1.3 R−0.4, δc ≈ 0.4 R−0.4 for 2.5 R = R f /R f ∗ and Rf and R f ∗ are the ambient and critical…
Existence and Singularities for the Prandtl Boundary Layer Equations
2000
Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.
On the Prandtl Boundary Layer Equations in Presence of Corner Singularities
2014
In this paper we prove the well-posedness of the Prandtl boundary layer equations on a periodic strip when the initial and the boundary data are not assigned to be compatible.
Group analysis and similarity solutions of the compressible boundary layer equations
1989
In this paper the application of Lie's methods to the equations of the laminar boundary layer is discussed. The momentum and energy equations in Prandtl's form are considered for a steady, viscous, compressible laminar flow with non zero pressure gradient, variable viscosity and thermal conductivity. Group analysis yields similarity solutions for given pressure distributions and particular values of the invariance group parameters (group classification). Crocco's transformation is obtained for the infinite-dimensional group of the Lie's algebra admitted by the equations.
Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method
1999
In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non…