Numerical analysis of dominant parameters in synthetic impinging jet heat transfer process

Highlights

• The effects of main factors on heat transfer in synthetic jet flow are studied.

• Best heat transfer performance is achieved with St in 0.24–0.48.

• Re or frequency would alter the heat transfer and flow structure separately.

• The variation of Nu and flow field with time show high similarity at same St.

• St and Re govern variation trend and magnitude of heat transfer rate respectively.

Abstract

How forcing frequency of synthetic jet would affect heat transfer attracts wide attention, however, studies conducted by different authors or the same study but with slightly distinct conditions often led to disparate results. In regard to the forcing frequency-induced intricate phenomena in heat transfer process of synthetic jet, a mechanism analysis focusing on the effect of St is proposed in this work. In the present study, the emphases are to explore the effects of frequency (f = 10–75 Hz) and dimensionless parameters, i.e. Reynolds number (Re = 10,000–20,000) as well as Strouhal number (St = 0.1285–0.4498), on these physical processes of synthetic jet. The results demonstrate that there is an interval of St from 0.24 to 0.48 that corresponds to the highest range of time-area averaged Nusselt number under each Re. Moreover, Re or frequency would largely influence amplitude and variation trend of area averaged Nusselt number with normalized time respectively. However, interestingly, the variation trend of area averaged Nusselt number with respect to normalized time exhibits high similarity under the conditions of the same St even with different Re and frequency. Furthermore, the evolutions of flow field with normalized time are also analogous at the same St, which can lead to the similarity in the variation of heat transfer rate.

Introduction

Impinging jet is an approach for enhancing heat and mass transfer between a solid surface (target surface) and an air or liquid jet. It is widely used in engineering applications including cooling microelectronics or gas turbine as well as drying textiles or films for its high localized convective heat transfer coefficient. Apparently, the characteristics of impinging jets, as well as surroundings, determine the overall thermal properties. To improve heat transfer rate, in the aspect of passive methods, many studies have been done experimentally or numerically over the past years. These investigated parameters, mainly focusing on geometric features, cover nozzle shape [1], [2], [3], [4], roughness on target surface [5], [6], [7], target wall curvature [8], as well as nozzle-to-surface distance, etc.

In addition to passive techniques, there is increasing interest about flow characteristics of impinging jet itself. A drawback of traditional steady jet is that hydrodynamic and thermal boundary layers cannot be disrupted once the steady state is reached. To renew the boundary layers thus achieve better heat transfer capacity, one type that gains more attention recently is flow pulsation [9]. Pulsation jet refers to introducing impingement jet of time-dependent (usually periodical) velocity rather than a steady one. In comparison with steady jets, pulsation jets exhibit more complex heat transfer performance. This is because pulsation jet introduces much more influence factors such as waveform [10], [11], [12], duty cycle [13,14], forcing frequency, etc. Nevertheless, the conventional pulsation jet requires an external fluid source for its net mass flow during each period. For the sake of reducing complexity of devices but also taking the advantages of pulsation jet, the synthetic jet arises at the time. The rationale of synthetic jet was clearly reviewed by Glezer and Amitay [15]. Generally, the synthetic jets are generated by advection and interactions of trains of discrete vortices similar to pulsation ones. The actuator oscillates back and forth to induce alternate flow ejection and suction periodically, which introduces zero-net mass flux within each cycle.

How forcing frequency of synthetic jet would affect heat transfer rate attracts great attention, however, more significantly, studies conducted by different authors or the same study but with slightly distinct conditions often led to disparate results. Pavlova and Amitay [16] experimentally investigated the heat transfer performance of synthetic air jet. They explored the effect of jet formation frequency and Re on heat removal at various jet-to-surface distances. Their results indicated that the synthetic jet of higher formation frequency performs better than low frequency jet at small distance while the latter is more effective for larger spacing. Bazdidi-Tehrani et al. [17] numerically analyzed the flow and heat transfer of a synthetic sinusoidal jet impinging on a constant heat flux disk at fixed Re. It was observed that at fixed nozzle-to-surface distance of 4, as the frequency increases in the range of 16–400 Hz, the heat transfer is enhanced. Liu et al. [18] utilized the synthetic air jet for cooling a heated surface at different jet-to-surface distances. In their experiment, the range of Re is from 500 to 1300 and the driven frequency increases from 200 to 800 Hz. Their experiments demonstrated that there is an optimal frequency of 600 Hz that produces the highest Re and Nu. Moreover, they concluded that the higher driven frequency results in better heat removal capacity than lower frequency at the same Re. The previous studies indicated that the effect of forcing frequency on heat transfer might vary a lot with other parameters altering, which implies that evaluating the frequency alone is somehow insufficient.

As a method to assess the influence of frequency on heat transfer and flow field more comprehensively, St or its reciprocal, dimensionless stroke length, is used as an index that considers frequency and jet velocity synthetically. Shuster and Smith [19] how the stroke length and Re impact on the flow field through experiments. They found that the dimensionless stroke controls the near- and far-field regions of synthetic jet flow. In addition, Greco et al. [20] studied the influence of St (0.011, 0.022, 0.044) and jet-to-surface distance (2, 4, 6 nozzle diameter) on the synthetic jet flow by experimental means. Their study indicated that the main force, i.e. the influence of vortex ring and the trailing jet, of the flow field is governed by St. These studies confirm that St is in command of the synthetic jet flow field. Furthermore, the consequent effects on heat transfer are also noteworthy. Valiorgue et al. [21] investigated the heat transfer mechanism of an impinging round synthetic jet flow at an invariable jet-to-surface distance of 2. Their experiment results showed that there exists a critical dimensionless stroke length of 2.5 that marks the divide of two flow regimes, and separates two heat transfer regimes as well. Further, Persoons et al. [22] put forward the correlation for Nu at stagnation point via experimental analysis, involving the effects of Re, jet-to-surface spacing as well as dimensionless stroke length. They identified four heat transfer regimes based on dimensionless stroke length since the flow features of synthetic jets can be characterized by it. McGuinn et al. [23] came to the similar conclusion for free jet flow morphology in their experiments. As summarized in numerical study of Hatami and Bazdidi-Tehrani [24] and experimental investigation of Greco et al. [25], variations in stroke length lead to complex flow field, give rise to distinct heat transfer behaviors thereby. The previous work proved the inseparability between the analysis of the flow field as well as heat transfer behavior in synthetic jet, and more importantly, established St as a protagonist in governing these physical processes. Yet, compared with variations of St, the effects of various conditions at the same St are still unknown to an extent.

The main purpose of this work is to numerically investigate the effects of frequency, Re as well as St on the heat transfer process and flow structure of synthetic water jet based on a two-dimensional model. Firstly, although numerous studies have disscussed the topic, there is less concern on how these parameters affect the physical process evolution over time. The temporal tracks of flow field can facilitate the profound comprehension of heat transfer mechanism. On the other hand, previous studies paid more attention on the local heat transfer rate rather than that of a wider region. As such, two major objectives of present work lie in the points aforementioned. To be specific, the effects of Re and frequency on averaged, i.e. area averaged and time-area averaged Nusselt number, were investigated. Besides, it was studied in detail how the area averaged Nusselt number varing with normalized time under the impact of these factors. More intriguingly, the similarity in temporal evolution of area-averaged Nusselt number as well as flow field at the same St but with different conditions, viz. various Re and frequencies, was also disscussed.