Search results for "Inviscid flow"
showing 10 items of 26 documents
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.
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array
2014
In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous int…
Efficient parallel computations of flows of arbitrary fluids for all regimes of Reynolds, Mach and Grashof numbers
2002
This paper presents a unified numerical method able to address a wide class of fluid flow problems of engineering interest. Arbitrary fluids are treated specifying totally arbitrary equations of state, either in analytical form or through look‐up tables. The most general system of the unsteady Navier–Stokes equations is integrated with a coupled implicit preconditioned method. The method can stand infinite CFL number and shows the efficiency of a quasi‐Newton method independent of the multi‐block partitioning on parallel machines. Computed test cases ranging from inviscid hydrodynamics, to natural convection loops of liquid metals, and to supersonic gasdynamics, show a solution efficiency i…
Conformation constraints for efficient viscoelastic fluid simulation
2017
The simulation of high viscoelasticity poses important computational challenges. One is the difficulty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high stiffness of the governing differential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables efficient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric fluids, which defines simple governing equations for a conformation tensor. The model can represent a diverse pa…
How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non-viscous SPH simulations
2009
Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations are performed, using the SPH method, to study the migration of one protopla…
On the induced drag reduction due to propeller-wing interaction
1995
AbstractThe aerodynamic interaction between a wing and a couple of propellers in tractor configuration is investigated by means of a model based on the lifting line concept and under the assumption of quasi-steady incompressible motion of inviscid fluid. The ways the propellers influence the wing performances, particularly the induced drag, are analysed. It turns out that the lift increase and the possible drag reduction depend strongly on the direction of the blade rotation and on the propeller distances from midspan, and result from two main effects: the direct propeller induction on the wing and the modification of the lift distribution along the span. An additional nonlinear (mixed) con…
On numerical simulation of electromagnetic field effects in the combustion process
2018
This paper deals with a simplified model taking into account the interplay of compressible, laminar, axisymmetric flow and the electrodynamical effects due to Lorentz force’s action on the combustion process in a cylindrical pipe. The combustion process with Arrhenius kinetics is modelled by a single step exothermic chemical reaction of fuel and oxidant. We analyze non-stationary PDEs with 6 unknown functions: the 3 components of velocity, density, concentration of fuel and temperature. For pressure the ideal gas law is used. For the inviscid flow approximation ADI method is used. Some numerical results are presented.
Periodic massloss from viscous accretion flows around black holes
2014
We investigate the behaviour of low angular momentum viscous accretion flows around black holes using Smooth Particle Hydrodynamics (SPH) method. Earlier, it has been observed that in a significant part of the energy and angular momentum parameter space, rotating transonic accretion flow undergoes shock transition before entering in to the black hole and a part of the post-shock matter is ejected as bipolar outflows, which are supposed to be the precursor of relativistic jets. In this work, we simulate accretion flows having injection parameters from the inviscid shock parameter space, and study the response of viscosity on them. With the increase of viscosity, shock becomes time dependent …
Lagrangian finite element modelling of dam–fluid interaction: Accurate absorbing boundary conditions
2007
The dynamic dam-fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under the assumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements, which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transient analysis of fluid-structure system. Comp Struct 1979;10:383-93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element for the dynamic analysis of fluid-solid system. Int J Numer Methods Eng 1983;19:1657-68]. The irrotational condition for inviscid fluids is imposed by the penalty method and con…