Numerical investigation of heat transfer enhancement of an inclined heated offset jet

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Abstract

Offset jet is a commonly used flow in different industrial applications, such as in cooling electronic devices or heat exchange systems. Determining the exact behaviour of the thermal characteristics of such flow, as a function of several independent parameters, is quite interesting and useful. The aim of the current study of an inclined heated and turbulent offset jet is to investigate numerically the dynamic and thermal characteristics of the flow. To figure out which parameter is the most significant for the heat transfer process, The effects of the Reynolds number (Re), the offset ratio (OR) and the inclination angle(α) were discussed in details. Note that the OR is varied in two domains: from 20,000 to 40,000, from 5 to 15 and the inclination angle is varied from −20° to +20°.

The simulations are carried out using the CFD solver Ansys Fluent. The SST k-ω turbulence model was selected among four different turbulence models and using the velocity-pressure coupling. Velocity and pressure and streamlines, contours are provided to examine the dynamic behaviour of the flow. Furthermore, local Nusselt evolution is presented for different parameter combinations (Re, OR and α) to outline their simultaneous effects on the convective transfer phenomenon. Finally, based on the gathering data, triple-parameter correlations were developed to govern the maximum Nu value and the average Nusselt estimations throughout the different flow's zones. These correlations will broad the current knowledge in different engineering applications to enhance the heat transfer in different heat exchange systems such as electronics cooling systems.

Introduction

Jet flows have been extensively investigated, either through experimental or numerical studies and still, they are the subject of recent and current scientific works. In fact, this particular type of flow is found in a wide range of industrial applications, for example, the mixing process of the boiler in combustion chambers, or during the evaporation, or also in cooling and heating systems…

First, the offset jet is defined when the fluid is discharged from a nozzle, that is located at a certain distance (h) from the horizontal axis. Besides, it is essentially characterized by the “Coanda” effect, which makes the fluid deflect towards the bottom wall due to the creation of a sub-atmospheric pressure zone that promotes the deviation of the fluid. Further, the fluid attaches the bottom wall at one specific point, called “The reattachment point”, which represents the limit point of the recirculation region and the starting point of the impingement one. The Offset jet is still considered as one of the most complicated flows in term of dynamic and turbulent features.

One of the first scientific works that dealt with Offset jets was the work of Bourque and Newman in 1960 [1], who conducted an experimental investigation to study the mean flow characteristics of an offset jet. The main objective of this work was to determine the reattachment point positions for different offset ratios. Besides, in 1977, Patankar [2] solved numerically a three-dimensional turbulent jet flow field using the Reynolds Average Navier Stocks, RANS, method. Pelfrey and Liburdy [3] conducted an experimental investigation on the dynamic behaviour of a turbulent offset jet having an offset ratio of 7 and a Reynolds number equal to 15,000. A detailed description of the mean flow characteristics, especially in the recirculation and impingement regions, was provided throughout this work. It was proved that the jet curvature and the fluid entrainment depend on the differential pressure across the jet and due to the importance of the curvature strain's magnitude such a flow cannot be modelled as a thin shear layer. Additionally, Pelfrey and Liburdy [4], were investigated the flow turbulence characteristics experimentally. The flow measurements were taken essentially in the recirculation region using a dual shifted Laser Doppler Anemometer (LDA). This experimental setup showed the existence of a stabilizing and destabilizing phenomenon of this flow, on the lower and upper sides respectively. The unstable characteristics in the upper region of the flow intensify the turbulence which influences the root mean square (r.m.s) values along with the position of maximum jet velocity. Nasr and Lai [5] compared experimentally between the dynamic behaviours of a simple offset jet and a two parallel plane jets in the near field. The initial turbulence intensities were fixed for both flows at 0.5% and the Reynolds number was managed to be equal to 11,000. This study revealed the existence of common flow characteristics between these two types of jets, such as the deflection of the fluid towards the bottom wall as a result of the sub-atmospheric and the presence of a recirculation region. However, this comparative study showed that the recirculation region is considerably larger for a single offset jet compared to a two parallel plane jet flows. Besides, it was shown that the offset wall had a retarding effect that gave a stronger reversed flow mainly in the recirculation region of the simple offset jet. Referring to the study of Nasr and al in 1998 [6], the authors confirmed that the use of side plates is mandatory to enhance the two-dimensionality of the flow. They conducted both numerical and experimental investigations on plane turbulent offset jet with small offset ratio of 2.125. Besides, they adopted a two-component Laser Doppler Anemometry (LDA) technique for a detailed examination of the dynamic characteristics of this offset jet flow. The experimental data were used to judge the suitable numerical turbulence model to study this two-dimensional offset jet. As a result, the Standard k-ε proved its efficiency in predicting this flow. Regarding the flow behaviour, turbulence intensities and the Reynolds shear stress contours presented their maximum values mainly in the recirculation region. The groundbreaking result was that the Reynolds number would not have any significant effect on the static pressure distribution when it exceeds 10,000. With regards to the wall inclination effect on the spatial development of an offset jet flow, Nasr et al. investigated experimentally and numerically the inclination effect (β), mainly in the recirculation region [7,8]. Experimentally, a two-component Laser Doppler Velocimeter (LDV) was used to determine the turbulence and mean velocity fields. The inclination value (β) was between 0° and 30°. The valuable results were that the reattachment length rise respectively by 53% and 160% for β equal to 15° and 30° compared to plane jet reattachment length. Besides, it was found that the reattachment point moves downstream with the increase of the inclination angle. Furthermore, the mean velocity and turbulence decays were much significant with the increase of β. As for the numerical turbulence model, it was found that the Reynolds Stress turbulence model is the most adequate in modeling this flow as it proved its agreement with the experimental findings, unlike other models. Similarly, Lai and Lu [9] conducted an experimental work that aimed to investigate the mean flow and turbulence behaviours of a two-dimensional wall jet with an inclined wall. This work concluded that the increase of the wall inclination angle accelerates the centerline velocity decays. Abdel-Salam et al. [10] investigated numerically the effect of the simultaneous variation of the nozzle width and the wall angle inclination. The authors reported that the reattachment point positions varied non-linearly with the inclination angle value. Moreover, a numerical investigation of an oblique offset jet was done by Pramanik and Das [11] in 2013 in which they examined in details the velocity and turbulence characteristics. The offset ratio was equal to 7, the inclination angle was 10° and the flow was at a Reynolds number of 15,000. Among the different turbulence models, the authors chose to use the standard height Reynolds number k-e model. Moreover, they reported a comparative study between the different oblique angles in terms of mean flow and turbulence characteristics. As a result, it was shown that an increase of the inclination angle leads to the extending of the recirculation region, which gave rise of the reattachment length. Besides, the Reynolds stresses values showed that the bottom wall had a retarding and turbulence suppression effects during the development of the offset jet. Another numerical study was performed by Yang and Yeh [12] aiming to investigate the turbulent offset jet with offset ratios of 3.7 and 11 and a Reynolds number of 15,000. The authors investigated the effect of the entrainment boundary condition adopted in this flow. As a result, it was shown that boundary conditions at the entrainment and at the exit of the null normal gradient can be adopted only when the flow is fully developed at the exit and the boundaries are enough far from the region of interest. A dual jet, composed by a plan wall jet and a parallel offset jet, was a research subject for Kumar in 2015 [13]. He conducted a numerical investigation of the flow features of a dual jet adopting the standard k-ε model dedicated to high Reynolds number. In this work, a detailed analysis of an offset jet flow characteristics was presented, having an offset ratio between 3 and 15. Among the interesting findings is the development of mathematical correlations that govern the change of the reattachment point and vortex centre locations. However, these correlations depend only on the offset ratio value and do not consider other parameters. Understanding the dynamic flow field on an offset jet in terms of velocity field and turbulence characteristics was the main purpose of the previously mentioned scientific works. However, as the offset jets exist in several thermal systems, it seemed mandatory to examine the thermal characteristics of different application of offset jet flows. That is why several other studies were performed aiming to understand its thermal behaviour under certain conditions. In this regard, Holland and Liburdy studied experimentally a heated and turbulent offset jet attaching an adiabatic wall [14]. For this study, different nozzle exits temperatures, various offset ratio and a Reynolds number of 15,000 were taken as boundary conditions. During this work, the buoyancy effect was neglected. Meanwhile, the temperature field measurements gave evidence on the dependence of the thermal behaviour on the offset ratio value, essentially near the wall region. In 1996, Kim and Yoon conducted an experimental study on a two-dimensional offset jet [15]. The fluid was issued from a 20 mm width nozzle. The investigated Reynolds numbers were between 6500 and 39,000 and the bottom flat plat is uniformly heated. Furthermore, the thermal and dynamic characteristics of the flow were examined for different offset ratios from 0 to 20 to investigate its effect. The reattachment point position moves streamwise with the increase of the offset ratio, similarly to what explained previously. The authors reported the presence of a secondary vortex, located just at the bottom left corner. In this region, the local Nusselt number presented an upward trend. Besides, it was found that the maximum Nusselt number coincide nearly with time-averaged reattachment point positions. Moreover, Kim and Yoon correlated the local Nusselt number distribution to geometrical parameters through empirical expressions. Furthermore, Song [16] examined simultaneously the effects of the wall inclination and the offset ratio variation on the flow dynamic behaviour and the flow thermal characteristics. An experimental setup was modelled in order to investigate a two-dimensional offset jet oblique wall attaching, in terms of studying its turbulent and heat transfer characteristics. The liquid crystal technique was used in conduction measurements of the thermal field characteristics. The jet characteristics, such as the mean flow velocity, the wall static pressure coefficient and the turbulence intensities, were calculated for a Reynolds number of 53,200, an offset ratio between 2.5 and 10 and an inclination angle in the range from 0° to 40°. It was reported that the length of the recirculation region increases with the oblique angle and the offset ratio values. Besides, fixing the oblique angle to 40° makes the flow similar to a free jet flow but without a strong reversal flow near the wall. In this study the maximum Nusselt number position turned out to coincide with the reattachment point for all the oblique angles. Recently, in 2015, Gao [17] examined the Reynolds number and the offset ratio effects on the measurements of the convective heat transfer coefficient for a planar offset attaching jet. They studied an offset jet with small offset ratio between 0.2 and 1 while the Reynolds number was varied from 21,800 to 54,000. The results showed that the local heat transfer coefficient from the wall to the jet presented a peak where the fluid attaches to the wall and then it returns to decrease with the downstream direction. Which means that the maximum heat transfer coefficient coincides with the reattachment point. Besides it was reported that it decreases with the offset distance, for a given Reynolds number, while its location from the jet wall gets farther with Re for the smallest offset ratios. In 2017, Hnaein et al. [18], investigated numerically the heat transfer characteristics of turbulent offset jet combined to a wall jet. The authors tested two different thermal boundary conditions, which were the constant wall heat flux and the constant wall temperature. This study revealed the sufficient credibility of the standard k-ω turbulence model in the resolution of this particular flow. Besides, two parameters: Re and the bottom wall inclination, were examined in order to figure out their effects on the heat transfer process and to correlate them with several convection characteristics such as the average and local Nusselt number and heat flux. As findings, this study showed that the heat transfer was more intense for low inclination angles. Besides, the convective heat transfer was enhanced with the increase of the Reynolds number. Moreover, for a Re = 15,000 and an inclination angle varying from 0° to 25° counter-clockwise direction, the local and average Nusselt values were predicted to be higher for a constant heat flux boundary condition compared to a constant temperature boundary condition. Kanna and Das [19] studied a conjugate heat transfer of a two-dimensional laminar incompressible offset jet. The governing equation system was solved using the unsteady stream function and vorticity formulation. The effects of the Re, Pr, solid slab thickness-to-jet slot ratio (S/h) and conductivity ratio (k) were investigated in detail. Among the reported findings of this work is the fact that the increase of Re reduces the thermal layer thickness. Besides, for low Pr value, the heat transfer process is mainly dominated by the conduction mode. In addition, the thicker the slab is, the less is the heat transfer magnitude, which increase with the incrementation of k. In fact, the effect of these four parameters appear significant especially in the recirculation region, where the maximum local Nusselt number is located. Hence, the evolution of the local Nu is quite sensitive in the nozzle wall and recirculation regions. Moreover, noting also that its average value is reduced when the slob is thicker, while it increases with the incrementation of Re, Pr and k. More recently, in 2017, Monda et al. [20] studied a conjugated heat transfer, taking into consideration turbulent convection in fluid and the conduction through an S thickness solid slab, for a combined turbulent offset jet and wall jet. The numerical resolution was conducted with the use of the unsteady Reynolds averaged Navier-Stokes equations. Besides a quadratic non-uniform grid distribution was adopted during computations. The authors investigated the effect of Re in the range from 10,000 to 20,000, Pr between 1 and 4, the solid slab thickness-to-jet slot ratio (S/w) lying in the range of 1–10, and finally the conductivity ratio (k) varying from 1000 to 4000. The fluid field revealed the presence of an unsteady flow phenomenon in the near nozzle-wall region. Further, this work showed that the mean local Nusselt number, throughout the interface depends only on the fluid proprieties Re and Pr. Meanwhile, the mean interface temperature and the mean local heat transfer depend on all the investigated parameters.

As it is mentioned, the offset jets are still an interesting research subject owing to their complex flow field characteristics, their sensitivity, towards several parameters, and most important their wide range of applications, especially for electronic equipments cooling. Despite that, the previously mentioned scientific works studied offset jet flows with only one to two varying geometrical parameters. Further, even the provided correlations didn't show a large flexibility in terms of the number of variables, that was limited to one or two as well. This paper aims mainly to study the simultaneous effects of three different and independent parameters (Re, OR and α) and to determine the most significant parameters that affect the heat transfer phenomenon and enhance it. Thereby, a two-dimensional and turbulent offset jet, having a Re in the range from 20,000 to 40,000, an OR between 5 and 15 and an inclination angle from −20° to +20°, will be investigated.

In fact, we inspired the present investigated configuration from the detailed “experimental study on the fluid flow and heat transfer characteristics … for a two-dimensional jet issuing parallel to a flat plate” of Kim and Yoon [15].

Thereupon, the present investigated flow is as well an offset jet attaching a heated wall. Furthermore, it has a variable inclination angle, from −20° to +20°, as defined in Fig. 1, when α equal to 0° we return to Kim and Yoon's original configuration. The fluid is ejected from different offset distances, giving a range of offset ration (OR = h/d) from 5 to 15, and with various inlet velocities (U0) that correspond to Re numbers ranging from 20,000 to 40,000. The Re was calculated based on the nozzle width using this expression: Re = (U0 x d)/ υ. Moreover, the nozzle, from which the fluid is ejected, has dimensions of 800 mm × 20 mm (l x d), which gives an aspect ratio (AR = l/d) of 40. This fact proves the two-dimensionality of the flow, since it is reported in [21] that “a region of statistically two-dimensional (2-D) mean velocity field is achieved only for AR>20”.

Throughout the rest of the introduction, several numerical and experimental studies are depicted. However, as far as the authors know, none of these works studied the simultaneous effects of OR, Re and α on the flow development and on the heat transfer characteristics. Actually, these varying geometrical parameters may occur in several industrial applications, for instance in the combustion chambers. Having Re in the range [20,000; 40,000], gives us the opportunity to investigate relatively high air velocities ranging from 14.6 m/s to 29.2 m/s, which is needed for the fuel-air mixing and entrainment process. Moreover, even the variation of α compromises the presence of fins, in the combustion chamber, which are preventing the heat exchange surfaces from having one single level.”.

Thereupon, the effects of these changing parameters will be discussed and presented in this present work.

Section snippets

Geometric configuration

In this current work, the same geometric configuration as Kim and Yoon [15] of a no inclined offset jet is considered. As it is represented in (Fig. 1), the air is issuing from a two-dimensional nozzle. Besides, the lower wall is subjected to a constant heat flux. The working domain dimensions were 100xd and 50xd in the (OX) and (OY) directions, respectively. They guaranteed no effect on the flow propagation and behaviour.

Assumptions and simplifications

As the geometry is not complicated, the governing equations can be

Grid independence and model validation

As mentioned previously, the correct choice of grid density and turbulence model is mandatory to prove the efficiency of our numerical code. Therefore, we compared our code's numerical results of the local Nusselt number on the heated wall with the experimental one extracted from Kim and Yoon's work. For a fixed OR at 7.5, a Reynolds number of 39,000 and a constant heat flux of 1951 W/m2, we tested three different mesh sizes to examine the grid dependency effect and four distinct turbulence

Conclusion

A numerical investigation was conducted to study a heated inclined offset jet using Ansys Fluent as a CFD solver. The fluid was issued from a two-dimensional nozzle with different velocity values that correspond to Reynolds numbers between 20,000 and 40,000. Besides, the OR varied from 5 to 15, while the bottom wall, which was uniformly heated with constant heat flux, had an inclination angle in the range from −20° to +20°. The purpose of this present study is to examine in details the flow

Author statement

In this paper, Ajmi, Hnaien and Marzouk conceived and designed the numerical experiments. Ajmi and Hnaien performed the Numerical executions. Ghachem, Kolsi, Ben Aissia and Almeshaal analyzed the data. Ghachem and Kolsi checked the paper against misprints and grammatical errors. Ajmi, Kolsi and Marzouk wrote the paper.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in the following paper:

Acknowledgment

This research was funded by the Deanship of Scientific Research at Princess Nourah bint Abdulrahman University through the Fast-track Research Funding Program.

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