Slot jet impingement heat transfer in the presence of jet-axis switching

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Abstract

Jet-axis switching is an established phenomenon whereby a non-circular, three-dimensional free jet undergoes a major change in cross-sectional shape with increasing downstream distance from the jet origin. This phenomenon has been demonstrated here to also occur for impinging jets. The focus of the present work is to investigate the heat transfer and fluid flow characteristics of rectangular slot jets which experience jet-axis switching. The jets in question have initial cross-sectional aspect ratios of 5:1 and 10:1. The jet cross sections, although highly skewed at first, evolve through near circularity and subsequently become skewed in the direction perpendicular to that of the initial skewness. In addition to the two initial aspect ratios, parametric variations were made of the Reynolds number, the distance of the impingement plate from the jet origin, and the contraction experienced by the flow passing through the aperture of the jet-forming orifice (i.e., the blockage ratio). The investigation was implemented by means of numerical simulation from which local and average Nusselt numbers were determined as functions of the foregoing parameters. Higher Reynolds numbers, greater downstream distances of the impingement plate, and greater blockages served to enhance the Nusselt number values. It remains to be seen whether there is an initial jet aspect ratio that is large enough to preclude axis switching and thereby allow two-dimensional modeling.

Introduction

It is widely accepted that jet impingement provides the highest local heat transfer coefficients among all forced convection fluid flows. This realization has motivated a steady stream of relevant research which has been well summarized and correlated [1], [2], [3], [4], [5], [6], [7]. A different stream of jet-related research has focused on the fluid mechanics of free jets. That research stream has discovered a flow transformative phenomenon termed axis switching [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. This phenomenon is encountered for free jets of non-circular cross section. In particular, it is found that a rectangular jet whose initial configuration is defined by a horizontal long dimension and a vertical short dimension undergoes a metamorphosis so that its downstream configuration is characterized by a horizontal short dimension and a vertical long dimension. This fluid flow phenomenon has been extensively investigated to reveal complex and esoteric structures, but it appears that no consideration has been given to the possible practical implications of axis switching.

The focus of the present investigation is to definitively determine the response of jet-impingement heat transfer to the axis-switching phenomenon. A necessary first step in the research is to demonstrate that axis switching continues to exist in the presence of jet impingement, the phenomenon having been previously observed only for free jets. Subsequent to that demonstration, the focus of the work is directed to the identification of jet axis switching as a heat transfer controlling mechanism for impinging jets.

The physical situation to be considered encompasses the creation of rectangular jets of different aspect ratio as the result of flow passing through and subsequently emerging from an orifice-capped rectangular duct into an expansion space. Axis-switching transitions are experienced by the jet as it passes through the expansion space. These transitions may be affected by the presence of impingement surfaces. The differences between the nature of jet switching for a free jet and an impinging jet must be recognized as a factor in the analysis of jet impingement heat transfer.

The analysis tool to be employed in the investigation is numerical simulation. Whereas the flow in the jet-creating duct is modeled as laminar, the emerging jet may be either laminar or turbulent. A metric is defined to quantify the regime of the flow.

Section snippets

Physical situation

The description of the physical model is facilitated by reference to Fig. 1. That figure is a perspective view of a rectangular duct of constant cross section through which a fluid passes in laminar flow. The exit cross section of the duct may be partially blocked by an orifice plate or may otherwise be unobstructed. In either situation, the exiting fluid expands into a large open space. The fluid entering the space may flow either freely without blockage or may impinge on a flat surface where

Governing equations

The solution of the physical problem defined in the preceding section was achieved by means of numerical simulation. The simulation model was developed to take account of the possible change in the flow regime that may occur in the duct proper and in the downstream expansion space. To accommodate such an event, the governing equations are written for turbulent flow, and a turbulence model that reduces to the laminar regime, when appropriate, is selected. The relevant physical principles that

Solution domain and discretization

A necessary prerequisite for the numerical simulation is the selection of the space in which the solution is to be sought. That space is normally referred to as the solution domain. In the present instance, the chosen domain is illustrated in Fig. 3. The domain encompasses the entirety of the rectangular duct and the downstream expansion space. For those cases in which fluid flow alone was investigated, the plate illustrated at the downstream end of the solution domain of Fig. 3 was absent.

Boundary conditions

To complete the problem definition, it is necessary to specify the boundary conditions. For the velocity problem, all components are zero on all solid surfaces. At the duct inlet, a uniform velocity of magnitude U is prescribed. The velocity magnitude may be quantified in terms of the Reynolds number Re defined asRe=Ubνwhere b is the narrow dimension of the jet-producing slot as illustrated in Fig. 2, and ν is the kinematic viscosity.

The other boundaries of the solution domain are treated

Velocity results

The critical dependence of the heat transfer results on the velocity field and the novel nature of the latter motivate a brief presentation of certain relevant features of the velocity solutions. The most significant among these is a demonstration of the meaning of axis switching. This information is conveyed in Fig. 5 which consists of a succession of contour diagrams in planes identified by their dimensionless distance x/b downstream of the duct exit. The contours correspond to values of the

Average heat transfer coefficients

The average heat transfer coefficients were evaluated from the definitionh¯=QΔT(ab)where Q is the rate of heat transfer on the impingement surface, ΔT is the temperature difference between the impinging fluid and the plate surface, and the quantity (ab) is the cross-sectional area of the aperture in the orifice plate. In other situations, the area used in the definition of the average heat transfer coefficient is that of the surface through which heat is flowing. In the case of the impinging

Concluding remarks

This investigation deals with a new mode of convective heat transfer that relates to jet impingement. The work builds on an already documented fluid-flow phenomenon, termed jet-axis switching, wherein a non-circular free jet experiences a major change of shape with increasing downstream distance from the plane of jet origination. For example, a rectangular jet which originates from a horizontal slot stretches vertically, passing successively through circular and vertical-weighted

Conflict of interest

There is no conflict of interest.

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