Thermal characteristics of the Airy wall jet for constant surface heat flux

The Airy jet is a wall-bounded flow belonging to the similarity class of the well known free jet but, in contrast to the latter, its far field behavior is an algebraically decaying rotational flow. The present paper investigates the thermal characteristics of the Airy jet over a wall with prescribed constant heat flux. The scaling behavior found for small and large values of the Prandtl number is compared to those obtained earlier for (a) the case of a wall with prescribed constant temperature and for (b) the case of a preheated Airy jet adjacent to an insulated wal

Heat transfer characteristics of the algebraically decaying Glauert jet

The classical exponentially decaying wall jet considered independently by Tetervin (NACA TN 1644 40pp, 1948), Akatnov (Leningrad Politek Inst Trudy 5:24-31, 1953) and Glauert (J Fluid Mech 1:625-643, 1956) as well as its algebraically decaying counterpart (which will be referred to hereafter as "algebraic Glauert Jet”, or AG-jet for short) belong to the same similarity class of solutions of the boundary layer equations. We investigate in this paper the thermal characteristics of a nonpreheated AG-jet over a permeable wall for prescribed constant wall temperature and prescribed constant heat flux. Their scaling behavior for small and large values of the Prandtl number is discussed in detail and compared to that of the classical Tetervin-Akatnov-Glauert wall je

The preheated Airy wall jet

The Airy jet is a wall-bounded flow belonging to the similarity class of the well known free jet but, in contrast to the latter, its far field behavior is an algebraically decaying rotational flow. The velocity and temperature distributions of a preheated Airy jet flowing over an insulated wall are investigated using both analytical and numerical methods, and are compared with those of the classical (preheated) exponentially decaying wall jet. For the same value of the dimensionless skin friction parameter, the maximum of the similar velocity profile of the Airy jet exceeds that of the classical wall jet by approximately 20%. The dimensionless temperature along the insulated wall scales for large values of the Prandtl number with Pr2/3 for both jets, while for small values of the Prandtl number the temperature scales with Pr1/3 for the Airy jet and goes to 1 for the classical wall je

On the drag of model dendrite fragments at low Reynolds number

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag vs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with primary dendrite arm aspect ratio and a second dimensionless shape paremeter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism

Off-Axis Drag of Dendrite Fragments at Low Reynolds Number

The aim of the present investigation is to characterize the motion of dendrite fragments falling under the influence of gravity in a uniform liquid medium at low Reynolds number. In an earlier study, Zakhem, Weidman and de Groh (1992) reported on the settling speed of model equiaxed dendrite grains released along their axis of symmetry. In this follow-up study uniaxial model dendrite grains were released off-axis to observe and document their motion at different orientations. It was hypothesized that the dendrite models might rotate when released off-axis in which case an attempt would be made to document the ensuing unsteady motion. This latter event turned out to be in fact true: at the small but finite Reynolds numbers that existed, each uniaxial dendrite slowly rotated towards its equilibrium orientation while failing under the influence of gravity. In addition to completing the original goal, we have made use of a beads-on-a shell Stokes flow code to numerically determine the drag coefficient for capsules, i.e.. uniaxial dendrites without arms. The drag on horizontally and vertically falling capsules are reported and compared with measurements

Origin of coherent structures in a discrete chaotic medium

Using as an example a large lattice of locally interacting Hindmarsh-Rose chaotic neurons, we disclose the origin of ordered structures in a discrete nonequilibrium medium with fast and slow chaotic oscillations. The origin of the ordering mechanism is related to the appearance of a periodic average dynamics in the group of chaotic neurons whose individual slow activity is significantly synchronized by the group mean field. Introducing the concept of a "coarse grain" as a cluster of neuron elements with periodic averaged behavior allows consideration of the dynamics of a medium composed of these clusters. A study of this medium reveals spatially ordered patterns in the periodic and slow dynamics of the coarse grains that are controlled by the average intensity of the fast chaotic pulsation

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

On super free fall.

Villermaux & Pomeau (J. Fluid Mech., vol. 642, 2010, p. 147) analysed the motion of the interface of an inviscid liquid column released from rest in a vertical tube whose area expands gradually downwards, with application to an inverted conical container for which experimental measurements were carried out. An error in the analysis is found and corrected in the present investigation, which provides the new governing equation for the super-accelerated interface motion down gradually varying tubes in general, and integrated results for interface trajectories, velocities and accelerations down a conical tube in particular. Interestingly, the error does not affect any of the conclusions given in the 2010 paper. Further new results are reported here such as the equation governing the centre of mass and proof that the end point acceleration is exactly that of gravit

Ariel - Volume 9 Number 4

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