Ideal Inviscid Fluid Research Articles

Bounds on the spreading radius in droplet impact: the inviscid case

We consider the classical problem of droplet impact and droplet spread on a smooth surface in the case of an ideal inviscid fluid. We revisit the rim–lamella model of Roisman et al. (Roisman et al . 2002 Proc. R. Soc. Lond. A 458 , 1411–1430 ( doi:10.1098/rspa.2001.0923 )). This model comprises a system of ordinary differential equations (ODEs); we present a rigorous theoretical analysis of these ODEs, and derive upper and lower bounds for the maximum spreading radius. Both bounds possess a W e 1 / 2 scaling behaviour, and by a sandwich result, the spreading radius itself also possesses this scaling. We demonstrate rigorously that the rim–lamella model is self-consistent: once a rim forms, its height will invariably exceed that of the lamella. We introduce a rational procedure to obtain initial conditions for the rim–lamella model. Our approach to solving the rim–lamella model gives predictions for the maximum droplet spread that are in close agreement with existing experimental studies and direct numerical simulations.

Port-Hamiltonian modeling of ideal fluid flow: Part I. Foundations and kinetic energy

In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie–Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac structures. The first novelty of the presented model is the inclusion of non-zero energy exchange through, and within, the spatial boundaries of the domain containing the fluid. The second novelty is that the port-Hamiltonian model is constructed as the interconnection of a small set of building blocks of open energetic subsystems. Depending only on the choice of subsystems one composes and their energy-aware interconnection, the geometric description of a wide range of fluid dynamical systems can be achieved. The constructed port-Hamiltonian models include a number of inviscid fluid dynamical systems with variable boundary conditions. Namely, compressible isentropic flow, compressible adiabatic flow, and incompressible flow. Furthermore, all the derived fluid flow models are valid covariantly and globally on n-dimensional Riemannian manifolds using differential geometric tools of exterior calculus.

Vortical Freak Waves in Water Under External Pressure Action

A vortical model for freak wave formation in water is presented. The wind action is simulated by nonuniform pressure on the free surface. The motion of the fluid is described by an exact solution of 2D hydrodynamic equations for ideal inviscid fluid in Lagrangian variables. Fluid particles rotate in circles of different radius. The model describes the appearance of a freak wave in the field of the Gerstner wave. The physical parameters of the wave and feasibility of the proposed scenario are discussed.

Radiation force on spheres in helicoidal Bessel beams modeled using finite elements.

Analysis of the scattering of sound by spheres centered on ordinary and helicoidal (higher-order) Bessel beams [P. L. Marston, J. Acoust. Soc. Am. 124, 2905–2910 (2008)] makes it possible to evaluate the radiation force on spheres centered on the beam in an ideal inviscid fluid. Potentially surprising results include cases where the radiation force is directed opposite the propagation direction of both types of beams [P. L. Marston (submitted for publication)]. For potential biomedical applications such as drug delivery, it would be necessary to know if a small transverse displacement of the sphere from the beam’s axis causes a radiation force that pushes the sphere toward (or away from) the axis of the beam. Three-dimensional finite elements were applied to that problem. To trust FEM calculations of the radiation force with helicoidal beams, it was first necessary to verify that analytical values for the axial force are recovered in the on-axis helicoidal case since only the zero-order beam had been previously studied [D. B. Thiessen and P. L. Marston, J. Acoust. Soc. Am. 122, 3025 (2007)]. Cases were found where displacement of a sphere from the beam axis causes a transverse restoring force. [Supported by ONR and NASA.]

Is the Kelvin Theorem Valid for High Reynolds Number Turbulence?

The Kelvin-Helmholtz theorem on conservation of circulation is supposed to hold for ideal inviscid fluids and is believed to be play a crucial role in turbulent phenomena. However, this expectation does not take into account singularities in turbulent velocity fields at infinite Reynolds number. We present evidence from numerical simulations for the breakdown of the classical Kelvin theorem in the three-dimensional turbulent energy cascade. Although violated in individual realizations, we find that circulation is still conserved in some average sense. For comparison, we show that Kelvin's theorem holds for individual realizations in the two-dimensional enstrophy cascade, in agreement with theory. The turbulent "cascade of circulations" is shown to be a classical analogue of phase slip due to quantized vortices in superfluids, and various applications in geophysics and astrophysics are outlined.

An infinitude of constant-energy flows of a gas

By converting the usual equations of motion for ideal inviscid fluids to Lagrangian form it is possible to exhibit infinitely many constant-energy flows of a compressible gas.

Extending the strain path method analogy for modelling penetrometer installation

The Strain Path Method (SPM) is an approximate framework for simulating the disturbance caused by piles or penetrometers in soil. The key conceptual assumption of the SPM is that the deformation and strain fields caused during these penetration processes are strongly kinematically constrained (especially during undrained penetration of clays) and can be estimated independently from the actual constitutive properties of the surrounding soil. Previous applications of SPM have estimated strain fields for a variety of penetrometer geometries using velocity fields of ideal inviscid fluids. This paper refines the strain field for penetrometers with 60° conical tips using numerically computed velocity fields in viscous fluids with a variety of boundary conditions imposed on the penetrometer shaft. Following a parametric study, a set of flow conditions is selected which provides a best fit between computed soil deformations and physical displacement measurements made in three separate experiments. The approach is simple and rapid and, while highlighting some of the inaccuracies associated with the existing SPM solution, may also be used for comparative purposes to assist the development of other approaches to the deep penetration problem.

Shocks and energy dissipation in inviscid fluids: a question posed by Lord Rayleigh

Lord Rayleigh argued that after a discontinuity develops in a one-dimensional compression wave in an ideal inviscid fluid some sort of motion must continue. Arguments are given in support of this view and a suggestion is made as to what that motion might be. The relationship of this motion to that proposed by Onsager for incompressible inviscid turbulent flows is discussed.

Ray propagation in an inviscid fluid

There is a view in the scientific community that a luminiferous ether is not likely to be an ideal inviscid fluid, since the only known mode of wave propagation for such a fluid, the dilatation waves, cannot have the transverse properties exhibited by light. This view is apt to be changed by the findings in this paper, which show that a well-known ideal inviscid fluid can transmit rays with transverse properties. In this paper a ray is defined as a wave propagation phenomenon in a homogeneous and isotropic medium, where a given disturbance propagates without dispersion or change in characteristics along an axis and where all activities associated with the waves diminish rapidly to zero as one moves away from the axis. A characteristic feature of the rays found is a moving helical path on which the fluid velocity is singular and about which the irrotational fluid motion has a constant circulation. The fluid velocity diminishes as one moves away from this path and the velocity has longitudinal and transverse components. The speed of propagation of the rays is equal to that of dilatational waves. Two «companion» rays are found. In one ray the fluid circulation with respect to the direction of propagation and the helical path are both right handed. In the other, both are left handed. The solution for each ray is valid only when the ray is isolated, and the mathematical analysis in this paper deals only with the proof and the description of the two isolated rays. A brief discussion is given about the possible correspondence between the rays and actual physical phenomena. It appears that the infinitely long isolated ray described in this paper cannot correspond with an actual physical phenomenon, since both the angular and the linear momentum per unit length are infinite. It is possible that, when both companion rays are present and when each ray is of finite lenght, then such a solution may correspond to an actual physical phenomenon. However, such solutions involve ray interaction and end conditions that are likely impossible to deal with by exact mathematical means, and they are not dealt with in this paper.

Internal Aerodynamics Problems

SummaryThis paper defines Internal Aerodynamics and via similarity generalises the concept to include internal flows of fluids other than air.Variable area ducted flows are considered distinguishing one, two and three-dimensional treatments and the difference between accelerating and diffusing flows is stressed. The design of variable area ducts using ideal inviscid fluid theory, ideal fluid plus boundary layer theory and inviscid but rotational fluid theory is discussed. The success and limitations of these theories with reference to contractions and diffusers is surveyed The particular difficulty of a diffusing flow as affected by entry velocity profile and turbulence is considered.From the problem of simulating entry velocity profiles arises the need for the generation of required velocity profiles in duct systems. Examples of methods of generation and difficulties are discussed.Next follows a series of examples of internal flow problems.The radial flow diffuser is considered as an example of the interaction of viscous and inertia effects. An approximate theoretical treatment is given and the real flow, with the occurrence of reverse transition, is described.The deliberate production of a reversed flow regime for flame stabilisation is described with reference to a marine boiler register Aspects of pressure drop and stability are considered.Secondary flow is defined and the origin in the distortion of the upstream vorticity field is described. The case of a strut wall junction is given with details of the downstream flow where the secondary flow produces apparent multiple wakes from a single strut.Air flow excited vibration of heat exchanger tubes is described. Different mechanisms resulting in transverse or streamwise oscillations and the coupled modes of tube rows are discussed.Finally the paper emphasises the large available body of information in internal aerodynamics, largely of aeronautical origin, and considers its usefulness and limitations for the problems discussed.