1. Introduction
When discussing heat exchangers (HXs), a primary or direct contact surface is defined as a surface that separates two fluids at different temperatures. As noted by Thulukkanam [
1] and Shah and Sekulic [
2], additional surfaces can be attached to a primary surface to increase the heat transfer area and further improve the heat transfer characteristics of an HX. These secondary appendages are referred to as fins and aid with convective heat transfer.
With recent advancements in brazing and welding technology, most currently manufactured compact heat exchangers (CHX) and plate-fin heat exchangers (PFHX) involve the brazing, semi-welding and all-welding of plates to a core [
3]. Diffusion-bonded HXs have also been applied in high-pressure industrial contexts [
4].
Another important development in HX manufacturing is the introduction of additive manufacturing (AM), which allows for complex geometries and matrices to be fabricated [
5]. As a result, HXs have become more compact and more efficient [
4]. For instance, in a study conducted by Wong et al. [
6], it was concluded that an AM-fabricated lattice-structured HX provided minimal resistance to airflow as compared to traditional plate-fin and pin-fin HXs.
However, the presence of a large number of voids within the lattice structure was shown to not allow the adequate transfer of heat, hindering the heat transfer capabilities of the HX. Another example of AM-fabricated HXs is the topology-optimised pin fin heat exchanger that has been developed by Dede, Joshi and Zhou, as shown in
Figure 1 [
7].
The study conducted by McDonough [
8] presents multiple examples of additively manufactured heat exchangers, highlighting the complexity in design along with the ease of fabrication of such complex shapes. Interested readers are highly encouraged to refer to the above-mentioned study to gain in-depth details of applications of additive manufacturing.
Further details of this are presented in a recently published paper by Vafadar et al. [
9]. This above study discusses the application of metal AM in the development of complex geometries, for different industries, including the civil, electrical, oil and gas sectors. AM is presented in the above paper as a viable alternative to conventional machining (CM) in terms of reducing both costs and energy consumption [
10].
The high thermal performance of CHXs (up to 98%) in combination with an ever-increasing demand for higher rates of heat transfer has prompted the research and development of heat transfer augmentation techniques that have minimal pressure drop penalties via the aid of forced convection. Forced convection, as defined by Sheikholeslami and Ganji [
11], refers to the mechanism of fluid transport where fluid is brought into motion using external sources, such as pumps, fans, blowers, etc. To achieve this, there are two methods of heat transfer augmentation that are widely applied in forced convection: using complex shapes and using surface textures on extended surfaces.
One of the most commonly used types of HXs are PFHXs, which have external fins that increase the overall heat transfer area of an exchanger. These fins can be further modified to introduce turbulence in the flow, which enhances heat transfer [
12]. These modifications may occur in the form of surface textures that are classified as passive methods of heat transfer enhancement, since they do not require any external source of power. Often, this enhancement in heat transfer is accompanied by an increase in pressure drop that requires additional pumping power for fans/blowers [
12]. Hence, investigating surface textures to enhance heat transfer with a reduced pressure drop has become a major area of research for engineers.
Surface textures are an extension of passive methods and include features that are embossed/engraved on the surfaces of HXs to improve thermal and pressure drop performances. One surface texture that has been extensively studied by a range of different researchers is dimples. A number of numerical and experimental studies have been conducted that deal with dimples as a means of improving heat transfer while reducing drag/pressure drop. For instance, Burgess and Ligrani [
13] have investigated the effects of dimple depth on the Nusselt number and friction factor, considering the dimple print diameter to dimple depth ratios (
ε) of 0.1, 0.2 and 0.3 whilst keeping the print diameter constant at 50.8 mm with constant streamwise and spanwise pitches of 82.2 and 41.1 mm, respectively. Streamwise pitch (
s) reflects the spacing between the dimples in the direction of the flow, whereas spanwise pitch (
p) defines the spacing between dimples perpendicular to the flow of the fluid.
Their study compared the experimental values obtained for a depth to diameter ratio of 0.1 with other studies possessing depth to diameter ratios of 0.2, 0.3, 0.28 and 0.19 for friction factor values. Their study concluded that the values of friction factors increased with either an increase in depth to diameter ratio or an increase in the number of dimples [
13]. Investigations conducted by Rao, Wan and Xu [
14] on pin-fin dimpled channels with various dimple depths have revealed the dependency of pressure loss behaviour on dimple depth to diameter ratios. Further, their study included dimple depth to diameter ratios of 0.1, 0.2 and 0.3, where the obtained results showed that pin-fin dimple channels with shallower dimples exhibited a reduction of up to 17.6% for the values of friction factors [
14]. Experiments on various density patterns of dimples along with different dimple depths have been conducted by Nesselrooij et al. [
15] to show the sensitivity of drag reduction to the direction of fluid flow and flow conditions such as the bulk velocity. Their study looked at dimple depths of 0.025 and 0.05 with 20 mm and 60 mm dimple print diameters, respectively. Multiple dimple orientations, such as flow aligned and staggered, were also investigated.
Nesselrooij et al. [
15] concluded that for both low-density and high-density patterns, increasing the depth to diameter ratio from 0.025 to 0.05 increased the overall drag at all velocities. The reason for this was attributed to the interactions between the boundary layer and the spanwise velocity component [
15]. In turn, shallow dimples with low-density patterns produced a drag coefficient that was 4% less than the drag coefficient for flat plates [
15]. Although drag reduction for the high-density deeper dimples improved with the Reynolds number, it still produced an 8% increase in drag performance [
15]. Rao and Feng [
16] conducted experimental and numerical studies for spherical and teardrop dimples with a depth to diameter ratio of 0.2. Their study concluded that compared to smooth flat plate, both dimple geometries increased the friction factor with the teardrop dimpled channel having relatively higher friction factor values than those of spherical dimples [
16].
Moon, O’Connell and Glezer [
17] experimentally investigated the effect of the fluid flow channel height on the heat transfer coefficient and friction factor. They tested four different channel heights (6, 13, 19 and 25 mm) while keeping the channel width and length constant. The bottom surface of the test setup was machined to incorporate the dimples.
Their study revealed that heat transfer improved by approximately two-fold, whilst friction factors ranged from 1.6 to 2 times relative to a smooth channel [
17]. Moon, O’Connell and Glezer [
17] also noted that studies conducted by other authors on dimples showed a lower pressure drop in comparison to other turbulators (such as continuous ribs) whilst significantly improving the thermal performance by a margin of 38%. Several other authors, including Abbas et al. [
18], Zhong et al. [
19] and Yan, Yang and Wang [
20], have also conducted studies on the drag reduction properties of dimples on golf balls and cylinders, concluding that the addition of dimples has a significant effect on reducing the overall drag observed.
It is evident from the above review that much research and many experiments have been conducted using dimpled surfaces on a flat plate. Although flat plates provide a good indication of the thermal and pressure drop performances of dimpled HXs, they do not provide information regarding their implementation for plate-fin compact heat exchangers. This is due to the difference in the orientation of PFHXs when compared to flat plates. In practical applications of PFHXs, multiple sides of the fins are exposed to the fluid flow and the fins are indeed perpendicular to the flow. Additionally, there is much disparity within the current literature on dimpled channel heat exchangers in terms of results relating to the thermal and pressure drop performances, a gap which the current study seeks to bridge. The effects of variable dimple diameters and dimple depths on the pressure drop performance of single elliptical plate-fin HXs will be tested. These will be compared to experimental results and conclusions provided by various authors. Based on the results of this current study, future work can be conducted on the thermal performances of various dimple configurations.
It should be noted here that the scope of the current study is limited to the investigation of passive surface textures, as they do not require any additional machines or materials to be formed/created. One of these surface modifications makes use of the dimples as turbulators to improve heat transfer while introducing a minimal pressure drop.
4. Discussion of Results
The results from the wind tunnel testing of smooth NACA/elliptical fin, and fins with 2 mm, 4 mm and 6 mm dimples, are presented in
Figure 7,
Figure 8,
Figure 9,
Figure 10, respectively. These include the five individual runs to determine the accuracy of the measurement as well as the average of these five runs. These average runs were then compared to each other, as seen in in
Figure 11, for their relative pressure drop performances. It can be observed in
Figure 11 that with an increase in diameter as well as depth of the dimples, there was a noticeable increase in the pressure drop of the fins. A similar trend has been observed by Ting [
27] in relation to golf balls, where initially increasing the surface roughness of golf balls via dimples reduced the coefficient of drag. The above study also observed that after a certain limit is reached for dimple depth, a further increase in the depth of dimples had the opposite effect, where the coefficient of drag increased significantly. In the current study, fins with dimples outperformed the smooth fin in terms of pressure drop performance up to velocities of 20 m/s, after which the pressure drop for the dimpled fins increased significantly. These observations can be attributed to the fact that the addition of dimples delays the boundary layer separation, which subsequently induces a narrower wake behind the fin leading to reduced form drag. These dimples introduce localised turbulence within and around the dimple cavity, which re-energizes the boundary layer and delays boundary layer separation. As a result of this localised turbulence, the boundary layer sticks to the surface for a longer duration and reduces the overall wake behind the fin. This contributes to a reduction in form drag, which is seen as the initial decline in the friction factor or the lower pressure drop observed with a low Reynolds number. Form drag is highly dependent on flow separation, whereas friction drag is a function of shear stresses observed on the surface of a geometry [
28]. With an increase in the Reynolds number, there is an increase in shear stresses, which in turn increases the overall friction drag. For the case of dimpled fins, shear stresses are further magnified due to the introduction of localised turbulence by dimples, where as a result there is a significant increase in the pressure drop for dimpled fins starting at a velocity of 20–22 m/s, which is equivalent to a Reynolds number of approximately 7 × 10
4–7.5 × 10
4. Experiments conducted by Chowdhury et al. [
29] have shown that increasing the depth of dimples lowers the critical Reynolds number, where the transition to turbulent flow happens earlier within the flow in comparison to smooth fins. Even though this shift in transition has the possibility of increasing the coefficient of drag in the transcritical regime, as observed by Chowdhury et al. [
29], it also creates local turbulence within dimples. This local turbulence can be controlled via the depth of the dimples and used to energise the boundary layer, which delays the aforementioned separation. Accordingly, as can be observed in
Figure 11, the fin with 2 mm dimples showed a higher pressure drop at 12 m/s relative to 4 mm and 6 mm dimples, both of which experienced negligible differences in the pressure drop performance at 12 m/s. Starting at 14 m/s, the fin with 2 mm dimples showed a consistently lower pressure drop, followed by fins with 4 mm and 6 mm dimples, respectively. This trend could be observed up until 26 m/s, after which the fin with 2 mm dimples surpassed the 4 mm-dimpled fin and showed an increase in pressure drop. It is worth noting here that the difference in pressure drop between 2 mm- and 4 mm-dimpled fins was quite insignificant when compared with 6 mm dimples. As suggested by various authors, including Ge, Fang and Liu [
30], this could be attributed to the threshold of dimple depth and diameter, whereby if the depth and diameter of dimples is increased beyond a limit, the favourable effect of pressure reduction is negated and an increase in pressure drop can consequently be observed.
Figure 12 shows the friction factor calculated using Equation (1) provided in the theory section. The friction factor allows for the comparison of head loss within an open-channel flow, where flow can be observed in a pipe measured over a specific distance [
31]. In this study, friction factor values were plotted against the Reynolds number for a smooth fin and dimpled fins (2 mm, 4 mm and 6 mm). This allowed the authors to determine the relationship between the head loss observed within the wind tunnel for various dimpled and non-dimpled fins relative to the Reynolds number. It is evident from the trends observed in
Figure 12 that the friction factor for the smooth NACA fin was the highest up to a Reynolds number of 6.5 × 10
4, whereas the 2 mm dimples provided the lowest friction factor for Reynolds numbers ranging from 4.6 × 10
4 to 7.2 × 10
4. Experiments conducted by Choi, Jeon and Choi [
32] found that with an increase in the Reynolds number, a sharp decrease in the coefficient of drag can be observed for dimpled spheres as compared to smooth spheres. A similar trend is also visible in
Figure 12 for the 2 mm-dimpled fin and the smooth fin, where a sharp decrease in the friction factor can be observed for the 2 mm-dimpled fin between Reynolds numbers of 4 × 10
4 and 5 × 10
4, and for the smooth fin between the range of 4 × 10
4 and 6 × 10
4. The same study by Choi, Jeon and Choi [
32] further concluded that the coefficient of drag hit a constant value after the sharp decline region. Their study examined dimpled spheres with varied surface roughness values (
ε), with a higher surface roughness indicating deeper dimples. The results published in the above study further summarised that the coefficient of drag for higher surface roughness (
ε) spheres showed a sharp decline at a lower Reynolds number while maintaining a higher constant value than spheres with lower surface roughness values (
ε). Similar observations are evident in
Figure 12 where, on the one hand, the equipment could not capture the sharp decline of the friction factor for deeper dimples (4 mm and 6 mm), as was observed for the 2 mm-dimpled fin and the smooth fin. On the other hand, it can be clearly observed that the friction factor starts to plateau at a Reynolds number of approximately 6.8 × 10
4, with 6 mm dimples showing the largest head loss, and 2 mm dimples exhibiting the lowest head loss. The overall trend for the coefficient of drag as observed by Choi, Jeon and Choi [
32] in their experimental studies can also be observed in
Figure 12 for the plot of the friction factor. This similarity in the overall trend can be explained by the formation of a separation bubble within the dimples resulting in delayed boundary layer separation, as mentioned earlier, leading to a reduction in the overall drag and consequently reducing the overall pressure drop.
These results also coincide with the trends observed by Rao, Wan and Xu [
14], Nesselrooij et al. [
15] and Patel and Borse [
33] where the introduction of dimples was shown to reduce pressure drop relative to a flat plate. Further, a study conducted by Rao, Wan and Xu [
14] also concluded that shallower dimples perform better at reducing the pressure drop as compared to deeper dimples, since shallower dimples reduce the velocity near the upstream half of the dimples which consequently reduces turbulent mixing in the main flow. With deeper dimples, even though turbulent mixing is reduced in the upstream half of the dimples, there is a strong flow impingement near the downstream rim of the dimples [
14]. Interested readers may refer to the above-mentioned study by Rao, Wan and Xu [
14] for additional insight regarding the pressure loss due to flow impingement.
This flow impingement introduces additional pressure loss within the flow. This is visible in
Figure 11, where the fin with 2 mm dimples provided the lowest pressure drop, followed by fins with 4 mm and 6 mm dimples, respectively. At low velocities of up to 22 m/s, a maximum pressure drop reduction of 58% was observed using 4 mm dimples relative to the smooth NACA fin, whereas at high velocities above 22 m/s, a 34% increase in pressure drop was observed with 6 mm dimples relative to the smooth NACA fin.
Figure 13 presents the percentage difference in pressure for all three configurations of dimples tested against the smooth fin.
It should be observed here that the results obtained by several authors including Choi, Jeon and Choi [
32] as well as Abbas et al. [
18] for drag coefficients coincide with the trends observed in
Figure 12 for friction factor values. As a result, it can be summarised from
Figure 12 that deeper dimples induce drag reduction at a lower Reynolds number, which can be seen in the sharp decline in the friction factor value for 2 mm dimples. This sudden decrease in friction factor could not be captured in the 4 mm and 6 mm dimples due to the limit of the measuring equipment and the reasons outlined in
Section 2.4 of the current study. However, from the similarity of the trends observed in the literature and
Figure 12, the critical regime of the sudden decrease in drag for 4 mm and 6 mm dimples should lie beyond a Reynolds number <4 × 10
4. This is evident from the values for a friction factor of 4 mm- and 6 mm-dimpled fins, as they are observed to increase when going from a Reynolds number of 5 × 10
4 to 4 × 10
4, suggesting a linear increase in overall drag at velocities lower than 12 m/s. Consequently, it can also be concluded from
Figure 12 that deeper dimples induce a higher pressure drop at a higher Reynolds number of >7 × 10
4 when compared to shallower dimples. This is evident from the trend where friction factor values start to plateau within the transcritical regime (
Re, 6.5 × 10
4—9 × 10
4), whereby at that stage the 6 mm dimpled fins have the highest friction factor values, followed by the 4 mm- and 2 mm-dimpled fins. The smooth NACA fin provided the lowest frictional resistance. In summary, it is apparent that deeper dimples are preferred for reducing drag at lower velocities with a larger pressure drop an in the transcritical regime. Shallower dimples are preferred for medium to high velocities with a smaller pressure drop in the transcritical regime.