Hysteresis in annular impinging jets

Abstract

Annular impinging air jets were investigated experimentally using the techniques of flow visualization, measurement of the stagnation pressure, and of the mass transfer by the naphthalene sublimation method. The bistability and hysteresis lead to two different alternative flow field patterns (A or B) under identical boundary conditions. The patterns differ in the size of the separated-flow recirculation regions: the pattern A is characterized by recirculation region (bubble) of separated flow quite small and located immediately under the nozzle centerbody. The heat/mass transfer distribution on the impingement wall is bell-shaped, with the maximum in the central stagnation point. On the other hand, the flowfield of the pattern B exhibits a large recirculation region of the separated flow, reaching up to the impingement wall, on which there is a stagnation circle. The entire space between the inner lip of the nozzle exit and the stagnation circle is filled with the recirculating fluid. The heat/mass transfer rate distributions reach the maximum on the stagnation circle. The bistability and hysteresis were found only at small Reynolds numbers, and at small annular nozzle slot widths. An extension of the nozzle centerbody promotes the tendency to the hysteretic behavior. An enhancement effect for the area-average heat/mass transfer coefficients for the pattern B over A has been quantified. The highest achieved increase was quite significant 32%.

Introduction

Impinging Jets (IJs) are flows capable of achieving the highest forced convection heat transfer rate between a single-phase fluid flow and a solid wall. A system of IJs may be well adapted to a particular heated surface shape and allows for achieving also a good localization of the desired heat transfer extremes. Because of these reasons, and because of the relative simplicity and cost effectiveness, IJ became a subject of extensive investigations. The main results have been collected, e.g., in the outstanding monograph by Dyban and Mazur [1], the exceptional study by Martin [2], and in several comprehensive reviews such as Downs and James [3], Jambunathan et al. [4], Viskanta [5], Webb and Ma [6], and Garimella [7].

Bistability and hysteresis are interesting phenomena known in physics in general, and their specific cases occur in various areas of fluid mechanics. The bistability is defined by the existence of two stable steady states for which the boundary conditions alone cannot determine uniquely which of them takes place. The character of the flow depends on previous history of parameter variations. The closely related term hysteresis is used to describe the response to a quasi-steady change in one of the parameters, characterized by a different response of the system when this parameter is increased or decreased. Graphically presented relationship between the parameters exhibits a region called the hysteresis loop. A typical example in fluid mechanics is the behavior of stalled airfoils. The stall hysteresis loop is a function of geometry and history of changes in flow speed or angle of attack – see, e.g., the results of low Reynolds number wind tunnel experiments by Marchman and Abtahi [8] and Marchman et al. [9]. A wind-tunnel study of an airfoil with a single slotted flap revealed the hysteresis to be present even at Reynolds numbers as high as 2.2 × 10⁶ (based on the chord of 0.61 m) – as reported by Biber and Zumwalt [10]. Hysteresis between attached-flow and separated-flow conditions and possibility of control by periodic excitations are discussed in the comprehensive study by Greenblatt and Wygnanski [11].

Examples closer to the present topic of the annular IJ are studies of the hysteretic behavior of swirling jets and tornados – see, e.g., Shtern and Hussain [12], [13], and Vanierschot and Van Den Bulck [14]. The latter authors investigated experimentally (using a two component Laser Doppler Anemometry) four different annular swirling jet regimes, and they observed a hysteretic character of the transition between them. Obviously, the hysteresis is a very complex phenomenon, which is difficult to notice and measure – as is evident from the fact that Chedaille et al. [15] experimentally investigated annular swirling jet under the similar geometry as in [14], without being able to identify any hysteretic effects.

Under some specific conditions, IJs can exhibit the bistable and hysteretic character. A typical bistable behavior of IJs is observed when an obstacle is inserted into the nozzle exit so that the recirculation bubble of separated flow that forms downstream from the obstacle is comparable in size to the nozzle-to-wall spacing. Evidently, the bistability results from influencing the separation bubble by the presence of the impinging wall. Two typical cases are axisymmetric and planar IJs (in other words annular and two-slot IJs, respectively).

Maki and Yabe [16] experimentally investigated the annular impinging jet case and identified four flow regimes of the flow field; three of these regimes were characterized as a recirculating unsteady flow. The other experimental study by the same authors Maki and Yabe [17] was performed with the annular nozzle of relatively large inner diameter D_i/D_o = 0.80–0.98 (where D_i and D_o are the inner and outer exit diameters, respectively). They clarified three flowfield patterns by measurements with a hot-wire anemometer and measurements of the pressure distribution and the mass transfer on the wall by the naphthalene sublimation technique. An existence of these flowfield patterns was unambiguously determined by the magnitude of the nozzle-to-wall distances – i.e., Maki and Yabe [16], [17] did not encounter any hysteresis.

Recent study by Tesař and Trávníček [18] discussed annular impinging jets, in which five different flow regimes were identified by numerical computations. On the demarcation boundary between two of these regimes they found bistability. However, no hysteresis was reported by Tesař and Trávníček in this study [18]. A subsequent investigation by Tesař and Trávníček [19] was focused on the two main flow regimes of annular impinging jet. Again, no hysteresis was found. Apparently, the hysteresis phenomenon is very complex and depends on the particular flowfield geometry.

Another variant of the bistable annular impinging jet was studied by Trávníček et al. [20]. The nozzle was designed to allow switching the jet by an on/off fluidic control, and the hysteresis effects were identified. Because the hysteresis was highly undesirable for the jet controllability, it was suppressed by means of a passive flow control (and was not studied any more at that time).

The paper by Trávníček and Tesař [21] dealt with an annular impinging synthetic jet (zero-net-mass-flux jet). Two flowfield regimes were revealed: one of them was characterized by a relatively small recirculation bubble located just at the nozzle centerbody. It occurred at a higher driving frequency, namely 693 Hz. The second flow state, with the bubble expanded vertically into a large separated flow area reaching up to the impingement wall, was found at lower frequencies, 106–263 Hz. In other words, the two alternative states were uniquely determined by the excitation frequency and no hysteresis was identified.

Acoustically excited annular impinging jets were investigated by Trávníček and Tesař [22]. Two different regimes of the time-mean flow were adjusted, differing in the size of the recirculation region – either a small recirculation bubble with the central stagnation point or a large recirculation bubble with the stagnation circle on the wall. The acoustic excitation switched the small recirculation bubble into the large one in the whole investigated range of frequencies, corresponding to the Strouhal numbers from 0.38 to 2.47. An effective stabilization of the large recirculation bubble and a remarkable augmentation of average heat/mass transfer (23%) were achieved at the Strouhal number value 0.94. No hysteresis was identified by Trávníček and Tesař [22].

For the planar geometry, the phenomenon of bistability and hysteresis of impinging jets was investigated experimentally by Trávníček and Křížek [23]. They measured a two-dimensional impinging jet from a two-slot nozzle, i.e. from a slot nozzle divided into two halves by an inserted fixed partition bar. An advanced variant of this nozzle geometry was studied by Trávníček and Maršík [24], where the hysteretic behavior was identified in a relatively large range of the nozzle-to wall-distances 6.5 b to 10.0 b (where b is the sum of two widths of both nozzle exit halves).

For the axisymmetric geometry, bistability and associated hysteretic character of IJ has been so far predicted only by means of numerical simulations – see Kokoshima et al. [25]; they called the two corresponding bistable flowfield regimes of the annular IJ a “closed” and “open” flow patterns. The annular IJs are quite promising for various heat and mass transfer applications, so that it is a practically important fact that the bistability and hysteretic behavior can significantly influence their performance and controllability (cf. Trávníček et al. [20]).

Despite these facts, to the best of the authors’ knowledge, there is no systematic experimental study of the hysteretic phenomenon in annular IJs in available literature (except that some preliminary results were presented by the present authors – Trávníček and Tesař [26]). As a continuation of these earlier investigations, the main motivation of the present study is to provide an explanation of the governing role which the flowfield geometry as well as flow parameters exert over the hysteretic phenomenon in annular IJs.