Finite element analysis of axisymmetric free jet impingement

Abstract

SUMMARYA numerical algorithm to determine the impingement of an axisymmetric free jet upon a curved deflector is presented. The problem is considered within the potential flow theory with the allowance of gravity and surface tension effects. The primary dependent variable is the Stokes streamfunction, which is approximated through finite elements using the isoparametric Hermite Zienkiewicz element. To find the correct position of the free boundaries, a trial-and-error method is employed which amounts to solving a boundary value problem (BVP) for the Stokes streamfunction at each iteration step. An efficient method is proposed to solve this BVP. The algorithm to find the correct position of the free boundaries is tested by computing the impingement upon an infinite disc and a hemispherical deflector. To confirm the correctness of the solution, each problem has been solved using several different mesh gradings. A comparison between the Zienkiewicz and the other standard Co finite elements is also given. KEY WORDS Free jet impingement Axisymmetric Finite element

Numerical solution of Bernoulli‐type free boundary value problems by variable domain method

“…Although for practical purposes one is interested in the computation of the impingement against a coaxially placed curved obstacle which results in two free surfaces we shall restrict our study to the impingement against an infinite wall. We note that supplementing the variable domain method with a similar approach as in References 10, 25 and 26 impingement against curved obstacles with two free surfaces can be successfully solved. Impingement against the infinite wall is modelled within a finite computational domain.…”

Curvilinear Composite Triangular Element of Class C

“…Nevertheless, both bases of the reduced and complete-HCT element are contained in the space generated by and thus from the computational point of view there is no need to consider rectilinear or curvilinear triangles separately. Note also that is a global basis function and thus no transformation of the local degrees of freedom into the global ones is necessary as is usual in the implementation of Hermite finite elements 17 .…”

Deformation of stream surfaces in steady axisymmetric flow

“…Axisymmetric flow has been examined in the groundwater field for inhomogeneity in hydraulic conductivity bounded by either a sphere [Dagan, 1979] or a spheroid [Fitts, 1991; Jankovi• and Barnes, 2000] and for flow produced by infiltration to a partially penetrating well [Muskat, 1932]. Analogous examples exist for electrical and thermal conductors with spheroidal geometry [Maxwell, [Gorokhov et al, 1996], flow past cavities formed downgradient of a disk [Wrobel, 1993], and flow through contractions and exits of a wind tunnel [Albayrak, 1991;Mejak, 1991 where use has been made of 0i00i q/ = 0 and where r•a and are defined as xP nor 0 are constant) are examined here to quantify how axisymmetric flow affects the relative position of a streamline with respect to neighboring streamlines. This is an important topic as the arrangement of neighboring streamlines in two-and three-dimensional nonaxisymmetric flows have been shown to differ [Steward, 1998]; threedimensional flow generates a persistent rearrangement of streamlines that cannot be reproduced using a two-dimensional model.…”

“…Analogous examples exist for electrical and thermal conductors with spheroidal geometry [Maxwell, 1881;Carslaw and Jaeger, 1959; Moon and Spencer, 1961]. Aeronautical engineers have examined transonic flow over axisymmetric bodies [Barron et al, 1990;Zhang et al, 1991], flow past bodies with surface injection [Gorokhov et al, 1996], flow past cavities formed downgradient of a disk [Wrobel, 1993], and flow through contractions and exits of a wind tunnel [Albayrak, 1991;Mejak, 1991]. Chemical and mechanical engineers have examined heat and mass transfer in cylindrical reactors [Bart and Weiss, 1992], material processing through converging and diverging ducts (e.g., injection moulding, glass moulding, and glass fiber drawing) [Lee and Jaluria, 1992;Manogg et al, 1995;Liu, 1994], and cusp formation in bubbles [Pozrikidis, 1998]…”