Heat Transfer Enhancement of Impinging Jet-Corrugated Solar Air Heaters

For the past few decades, the world has been facing an energy crisis because of an increase in the world population and the depletion of fossil fuels [1]. Fossil fuel is a non-renewable source of energy, and it is responsible for global warming, climatic changes, and environmental pollution due to the greenhouse effect [2]. These issues are triggering the world to look for an environmentally friendly source of energy. Solar has the widest scope of all the renewables because it is a clean, convenient, sustainable, safe, abundant, and cheaper source of energy. Solar air heaters (SAHs) are the widely used application of solar energy. It is used for desalination, space heating, drying crops, laundry, and the process industry.

SAHs have generally low efficiencies due to the low thermal capacity of air, friction losses of the absorber plate, and low heat transfer coefficient between air and the absorbing plate [3]. For this reason, scientists and engineers are nowadays facing the challenges of building highly efficient solar air heaters (SAHs). The passive method of heating and their combinations are mostly preferred, as they do not require any mechanical aids [4–6].

One of the efficient and common methods of increasing turbulence and heat transfer is by means of corrugated passages. Corrugation performs two functions. First, it enhances the turbulence; second, it increases the surface area, which increases the heat transfer directly. Yassen et al. [7] studied the effect of corrugation in integral SAH for household use, and it was reported that the temperature rise is higher in the case of corrugated absorber plates. Tokgoz et al. [8] studied the heat transfer enhancement in corrugated ducts for different aspect ratios of corrugation. An increase of 30% was achieved in the thermal performance factor for an aspect ratio of 0.3 and a Reynolds number value of 3 × 10³. Manjunath et al. [9] performed a numerical study of the sinusoidal corrugated absorber plate. It was concluded that due to higher turbulence, an increase of 12.5% can be achieved in heat transfer as compared to the flat plate collector. Khoshvaght-Aliabadi et al. [10] investigated that sinusoidal corrugation has the highest value of heat transfer to the pumping power (PP) as compared to the triangular and trapezoidal type corrugation, while the highest Nusselt number (Nu) and PP were obtained for trapezoidal type corrugation followed by triangular and sinusoidal corrugations.

Impinging jet is one of the most effective and acquiescent methods of heat transfer due to the very high heat transfer rate between the fluid and the wall. The heat transfer coefficient can be increased thrice of conventional convection cooling methods, which makes it an effective mode of heat transfer in gas turbine blades, electronic components, solar collectors, and critical components of machinery [11–17]. Moreover, it proves itself as a feasible solution in the processes of food drying, material-forming, and annealing. Jet impingement causes Choudhury and Garg [18] computationally report the performance efficiency of jet plate SAHs of 19–26.5% over parallel plate heaters for the air flowrate range of 50–250 kg/hm². Multi-jet impingement cooling systems are favored over single jets because they offer higher and more uniform heat transfer [19]. Strasser et al. studied an isothermal four-jet configuration in a reactor cavity coolant system plenum using a hybrid large eddy simulation (LES)–Reynolds-averaged Navier–Stokes (RANS) approach. It was determined that threshold frequencies lower than 10 Hz are prevalent for thermal stripping. Interferences like asymmetry in the plenum, non-uniformity, and stirring cause premature confluence of jets [20]. Chougule et al. [21] performed the computational fluid dynamics (CFD) study of a 4 × 4 pin fin heat sink with single and 3 × 3 multi-air jet impingement for the Reynolds number range of 7000–11,000. It was concluded that multi-jet impingement shows 3–4 times higher cooling performance as compared to a single jet due to the high convection heat transfer coefficient in the core region of the jet and multiple stagnation points. A uniform temperature distribution and lower temperature were observed in the multi-jet impingent as compared to the single-jet impingement. Chauhan et al. [22] performed the experimental investigation and optimization of jet impingement in SAHs by using the statistical Taguchi method [23]. An optimal design of jet-impinging SAH was obtained with a 37–48.3% increase in thermal performance over the Reynolds number range of 4000–16,000.

For the last three decades, instead of relying on single cooling techniques, many researchers have incorporated compound cooling techniques by selecting a powerful combination of different cooling techniques to increase heat transfer [24]. One such combination is jet impingement on corrugated plates. Aboghrara et al. [25] performed an experimental investigation of circular jet impingement on a corrugated solar absorber plate. An increase of 14% was observed in thermal efficiency as compared to the smooth channel. Ekiciler et al. [26] performed a numerical study on the effect of jet impingement cooling on sinusoidal, flat, and triangular corrugated surface features for the Reynolds number range of 125–500. An increase of 300% and 50% was observed in the values of average and local Nusselt numbers by using corrugated surfaces as compared to flat plates. It was inferred that the shape of the target plate affects the heat transfer substantially.

From an extensive literature survey, it was perceived that both corrugated absorber plate and jet impingement individually affect the performance of the SAHs significantly. The combination of both cooling techniques is a way that is yet to be explored for a wide range of design and flow conditions by using a multi-objective design methodology. The design of corrugated SAHs with the addition of a jet impingement is proposed in the current study. Therefore, the present work focuses on the investigation of heat transfer as well as friction factor in laminar to turbulent flow regimes, using single and variable multiple jet impingements on smooth, trapezoidal, and wavy corrugated passages over a range of Reynolds numbers and jet-to-target plate spacing by using Taguchi and analysis of variance (ANOVA) method.

The main objectives of this research work include

• numerical assessment of flow and thermal properties of fully developed laminar and turbulent, single and multiple jet impingement on smooth, wavy, and trapezoidal corrugated solar collector plates for SAHs;

• optimization and selection of optimal configuration using Taguchi and ANOVA method;

• development of correlation for Nusselt number and friction factor,; and

• Understanding the physics of heat and fluid flow via CFD.

The method used in the current study is primarily numerical. Modeling and meshing were performed in ansys followed by a mesh independence study. The mathematical model was formulated and validated with the experimental data and literature. After that, design propositions and modifications were performed. The design of experiment (DoE) technique, i.e., the Taguchi method, was applied to reduce the number of cases, and a CFD study of all the cases was performed. In the final stage, the optimal design was selected, and a parametric study was performed to understand the physics of flow and heat transfer, as shown in Fig. 1.

A solar collector generally consists of the main absorber plate, a transparent sheet on the exposed side of the absorber plate, a back plate, and insulation below the back plate. Air flows between the passage of the front and back plate, as shown in Fig. 2(a). In the current novel design, instead of the simple airflow in the passage of SAHs, it is impinged in the form of jets on the corrugated absorber plate to enhance the efficiency of SAH, as shown in Fig. 2(b).

The profile of the collector plate, jet plate, jet-to-target plate distance, and Reynolds number were varied to enhance the efficiency of SAHs.

Three types of target plates, i.e., smooth, trapezoidal, and sinusoidal corrugations, are considered for the current study, having the same blockage ratio (e/D_h) of 0.164 and pitch-to-groove height ratio (p/e) of 4, as shown in Fig. 3 and Table 1.

The jet type was varied to single, 2 × 2 array, and 3 × 3 array for the current study. The jets were designed on the base of the same flow area of 224.96 mm², as shown in Fig. 4.

The main focus of the current work is to study the effect of low Reynolds number. For that purpose, Reynolds number was varied in the laminar to transition flow regimes to three different values of 1740, 2270, and 2700, respectively.

CFD was used for predicting the trends of fluid flow and heat transfer in SAHs. For that purpose, the ansys 14.2 licensed version was used. It is a little bit outdated version, but it was the only licensed version in our lab. It was ensured that the features relevant to us are the same in the available and latest versions.

The schematic from Fig. 2(b) was converted to the physical domain in ansys DesignModeler. The flow enters from the inlet side and gets developed in the straight portion of the channel. Then, it gets converted into fine mini jets in the jet plate section and impinged on the heated corrugated plates, which is representative of the absorber plate of the SAHs. The flow then exited from the outlet section after heat transfer with the absorber plate. The specifications of the geometry for a particular sinusoidal case having a 3 × 3 jets array are shown in Figs. 5(a)–5(d). The flow area of the channel at the inlet and outlet is 463 × 401 mm² with a straight length of 960 mm and 100 mm on the rear side of the target plate. The thickness of the jet plate is 5 mm. The length of the inlet blocks is extended so that flow can be fully developed. At the outlet, an extension in length was also provided to compensate for reverse flows. The dimensions of the target plates and jet plates are provided in Table 1 and Fig. 3.

A non-conformal mesh was generated in the ansys Mechanical module, as shown in Figs. 6(a)–6(f). Multi-zone mesh method was used. On the plate and jet side, 30 layers of inflations, with the first layer, were kept at 0.008 to achieve y plus less than one. While coarse meshing was formed on the flow straightener section. All the mesh parameters were within the range, i.e., minimum orthogonal were above 0.2. The maximum values of aspect ratio and skewness were below 80 and 0.2, respectively. The average value of wall y plus was 0.013, with a maximum value of 0.18 on the corrugated target plate.

The grid independence study was accomplished so that the results can be made irrespective of the mesh size. Three different mesh sizes, 3.4 M, 7.0 M, and 8.6 M, were resolved and compared. The part of the fluid domain, which is near the jet and plate section, was finely meshed. The part other than the jet and target plate section has the coarse mesh.

The whole domain was simulated with all the mesh sizes, and the trend of the Nusselt number was plotted in both x and y directions to get the complete local variation of the Nusselt number in both longitudinal and lateral directions (Fig. 7). The trend of the 7 M mesh size overlapped with 8.6 M meshed domain. So, the mesh of 7 M was selected after mesh independence with a maximum error of 2%, with the next finer meshed geometry at the stagnation point. The corrugated geometries require fine mesh. For that purpose, a mesh size of 0.3 mm, 0.8 mm, 3 mm, and 5 mm was selected on jets, target plate, downstream, and upstream sides, respectively, for all the cases after rigorous study.

The boundary condition is an integral part of the mathematical model, as the whole solution depends upon these conditions. The boundary conditions used for the analysis are listed in Table 3.

The continuity, momentum, energy equations, and turbulence equations were solved for three-dimensional, steady-state, and fully developed laminar to turbulent flow. Besides, turbulence is always a transient phenomenon; we are running a steady-state solver. Due to low turbulence intensity and energetic equilibrium, we can easily resolve turbulence with steady solve, and this is usually associated with RANS formulation. The RANS scheme can fairly predict turbulence up to the extent of primary vortices [21,26,28]. The SIMPLE scheme was used for pressure velocity coupling. The second-order upwind scheme was used for momentum, pressure, turbulent kinetic energy, and turbulent dissipation rate.

The residuals in fluent's cases are problem-specific. Initially, the residuals were set at default. We frequently checked the flux balance and also monitored the change in output parameters. When the change in output parameters is diminished, we assume that the solution has been converged. The residual criteria corresponding to these conditions needed to be the strict one. That is why the residual criteria of 10⁻⁵ were used for continuity, x, y, z velocities, k, and $ε$⁠. While the energy was set at 10⁻⁹ to attain complete convergence and flux balance.

For solving the fluid domain, continuity, momentum, energy, and k-ε model turbulence equations are solved. The mathematical forms of these equations are presented in Eqs. (4)–(10) in Table 4.

An indoor experimental setup was established to study the case of a single jet of air impingement on the smooth plate, as shown in Fig. 8.

The working fluid, ambient air, was supplied via a 550-W centrifugal air blower. A globe valve was installed at the downstream side of a blower to regulate the flowrate of air. A sufficient standard length of 20D has been provided so that flow can get fully developed, followed by a flanged type vortex flowmeter (LUGB DN-100, Tianjin, China), having an operating range of 1.6–16 m³/min for an output range of 4–20 mA with an accuracy of 1.5% full-scale reading, was installed to measure the volumetric flowrate. On the downstream side, a 4″ rubber pipe is attached, followed by a conical diffuser-type duct for the pressure recovery. On the downstream side, a flow straighter section is attached so that flow can be smoothened, followed by a jet plate and test section. The test channel was manufactured using duct GI sheets, having a cross-sectional area of 463 mm × 401 mm, which is equal to almost 4 times scale down model of SAHs, as shown in Fig. 9 [29].

Air at high velocity, based upon the value of Reynolds number, ejects from the jet plate, after which it is impinged on the heated plates attached on the front side of the heater. This assembly of the heater and plate can slide in the test section so that the jet-to-target plate distance can be varied. Instead of simulating actual solar radiations, an electric loop heater, made up of Nichrome wire, having a resistance of 58 Ω, was directly attached to the plates to supply a uniform heat flux in the range of 100–1450 W/m² to the absorber plate, which is considered to be reasonably good value of heat energy input for testing SAHs [30,31]. A variable transformer is attached to the heaters to adjust the voltage range according to the requirements. The heating power of the heater is measured by a digital multimeter with 1% accuracy.

The temperature of the heated test section plate is measured by using nine wide-range K-type riveted thermocouples, having an accuracy of 0.75%, arranged in a 3 × 3 array, and the average value was calculated. This is necessary to achieve isothermal conditions. A set of two absolute pressure transducers having a range of 0–0.1 bar with an accuracy of 0.2% were installed, one on the upstream and the other on the downstream side of the jet plate to get pressure difference according to the ISO D-D/2 standard. The air velocity was measured by using a pitot tube attached to the Dwyer (Magnehelic Series-2000, Michigan, USA) differential pressure gauge, with an uncertainty of 1 Pa. Table 5 shows the list of instrumentations installed in the test rig. The experiment was repeated three times, and the mean value was computed.

For the purpose of validation, a case of smooth plate corresponding to the 1 × 1 jet array was tested corresponding to the Reynolds number and L/D_h value of 2700 and 14.6, respectively. Various models like k-ω and k-ɛ were used and compared with the experimental data, as shown in Fig. 10. The values of stagnation values of Nusselt numbers at the absorber plate are plotted. It was decided that the low Re k-ɛ model is in good agreement with experimental data, with a percentage error of 12%, hence selected for further study. The uncertainty analysis of experimental data is presented in the  Appendix.

In this section, the results of thorough CFD results will be presented to depict the effect of different parameters on flow and heat transfer characteristics.

A total number of nine cases were studied to compute the values of Nu, ΔP, PP, and f. The mean and SNR values were computed corresponding to each run, as shown in Table 6. The SNR values are plotted for each parameter, as shown in Fig. 10.

From Figs. 11(a)–11(d), it can be observed that multiple jet impingement has far better heat transfer properties as compared to the single jet. The reason that can be attributed to such a trend is that multi-jet impingement produces small jets of high velocity for the same value of Re, which removes the heat more significantly, and more area is cooled.

Trapezoidal corrugation has far better properties as compared to sinusoidal and smooth plates. This is because the smooth channel has a thick thermal boundary layer, while corrugation produces vortices, due to which efficient mixing of core fluid and hot wall fluid takes place. Hence, more heat transfer occurs. The trapezoidal corrugation has a sharp throat crest region, due to which more flow recirculations occur, and as a result, heat transfer increases, as opposed to the sinusoidal corrugation, which has the sinusoidal profile throughout, resulting in smooth removal of fluid.

It can be seen that as L/D_h increases, the jet expands and loses its ability to cool the plate. If it is decreased below a certain point, then cooling can be reduced as the fluid is in the developing flow regime.

Re has an increasing trend with the heat transfer as it directly increases the turbulence of the fluid, which results in more heat transfer.

The optimum value of the output parameters was decided based on SNR. The maximum values show the optimized ones in Fig. 10. In the case of Nu, the larger-the-better approach was used. So, from Fig. 11(a), it is observed that the jet plate of 3 × 3 holes, with jets of fluid exited at the Re value of 2700, impinged on the trapezoidal corrugated plate, placed at L/D_h of 5.08, is the optimum condition to maximize the Nu.

From Figs. 11(b) and 11(c), the optimum condition for the ΔP and PP is achieved for the single jet plate, with a jet of fluid issued at the Re value of 1740, while the target plate and L/D_h seem to be insignificant.

From Fig. 11(d), the optimum value of f was achieved for the 3 × 3 multiple jet plate, having a D/D_hs value of 0.33, while all other factors seem to be insignificant. This is due to the fact that jets of smaller size result in less flow recirculation and separation zones. As a result, less friction losses showed up in the system. The smaller-the-better approach was used for the last three parameters. To consider the optimized configuration, the thermal performance factor was calculated from Eq. (20) to incorporate the effect of both heat transfer and friction factor enhancement.

From Taguchi’s design, the optimized configuration was observed to be one with a 3 × 3 jet impinged on trapezoidal corrugation for the Reynolds number value of 2740 and jet-to-target plate distance of 5.1. Table 7 shows the thermal performance factor of all the cases. Confirmation experimentation was performed at the optimized configuration, and a thermal performance factor value of 11.4% was achieved as compared to the base case (case 3), which is the highest among all the cases. Although this configuration is hard to implement due to an increase in design complexity, pressure losses, and manufacturing cost as compared to the conventional design of SAHs, it is believed that this configuration can increase the efficiency of the SAH sufficiently.

The mean values of all the performance parameters are shown in Table 8. The contribution ratio of each control factor on the SNR values of the output parameters is presented in Table 9. In this table, the level is the experimental data point, rank is the grading of the parameter based on significance toward output, and delta is the change in the value of the output parameter from the highest to the lowest value when the input parameters are varied. The optimum conditions are shown in bold letters. From Table 8, it is clear that the dependence of the control factors is different on different output parameters.

The velocity streamlines, contours of Nu, and plots of stream-wise and span-wise Nu on the target plate are presented to understand the effect of Re, target plate, jet plate configuration, and L/D_h on flow and thermal properties, as shown in Figs. 11–18.

From the flow and thermal fields of Fig. 12, it can be seen that a jet of 3 × 3 creates mini jets of large velocities as compared to a single jet of the same Reynolds number. As a result, an increase in the flow profiles is manifested, which, in turn, is responsible for an increase in turbulence. Due to this phenomenon, more vortices are formed, and rigorous mixing of the vortices takes place. The boundary layer will get thinner. The efficient mixing of cold core fluid and hot wall fluid took place. As a result, more area is cooled, and also more cooling took place. Instead of single peaks, multiple peaks of Nu are observed in 3 × 3 and 2 × 2 jet configurations as compared to the single-jet impingement. So 3 × 3 is the optimized jet configuration.

From Fig. 13, it can be seen that an inverse relation of Nu with L/D_h is manifested. It can be seen that when L/D_h is 5.1, the flow jet has more momentum, as shown in the streamlines, and, hence, higher is the ability to cool the plates. When the distance rises to 14.6, the jet expands with high magnitude, and it no longer has the ability to cool the plate, and less value of Nu is manifested. So the L/D_h value of 5.1 is the optimized one.

From Fig. 14, it can be seen that the trapezoidal plate has the highest value of Nu, followed by the sinusoidal corrugated and smooth plate. This phenomenon can be understood in this way that corrugation causes turbulence in the form of vortices dominant flow. Hence, more heat transfer occurs due to the rigorous mixing of core and wall fluid. It can be seen that in the case of a smooth channel, a single peak is observed at the stagnation point, while in the case of corrugation, multiple peaks are formed due to the effect of increased turbulence with maximum value at the stagnation point and continuously decreasing in the radial direction. At the crest of the corrugation, minima is formed, and maxima is formed on the trough side. As a result, more area is cooled in the case of corrugation and effective heat transfer. If the trapezoidal and sinusoidal corrugation is observed, the trapezoidal profile has a sharp throat area in the crest region. As a result, the local fluid velocity is increased, and a higher temperature gradient exists between the wall and core region. As a result, more mixing occurs between the wall and core fluid due to intense flow recirculations. Hence, the thermal boundary gets thinner, and efficient heat transfer occurs. In the case of a wavy profile, the flow profile is smooth; hence, the boundary layer remains thick. In the case of smooth channels, low heat transfer occurs due to a very thick thermal boundary layer.

It can simply be seen from Fig. 15 that Re increases the flow velocity, which, in turn, increases the turbulence in the form of vortices, as can be seen in the streamlines. The boundary layer will be disturbed. As a result of this, more heat transfer occurs; hence, Nu is increased significantly. So the Reynolds number value of 2700 is the optimized configuration. Hence, an increasing trend was observed.

From the above discussion, it can be inferred that 3 × 3 jets when impinged on the trapezoidal corrugated plate, placed at the jet-to-target plate distance of 5.1 for the Reynolds number value of 2700 is the optimized configuration.

To improve the thermal efficiency of SAHs, the novel corrugated jet-impinging channel is used for the absorbing plate. A study has been performed for three different arrangements of jets, i.e., 1 × 1, 2 × 2, and 3 × 3 jet array with three channels, i.e., smooth, trapezoidal, and wavy, corrugated over the Re range of 1740–2700 and L/D_h value of 5.1–14.6. An optimization study was performed using the Taguchi method. The accomplished work is summarized below:

• The optimum value of Nu was found for the trapezoidal corrugated target plate, with 3 × 3 multiple jet-impinging type, L/D_h, and Re values of 5.1 and 2700, respectively.

• An increase of 11.4 times was observed in the thermal performance factor as compared to the base case.

• D_h/D_hs was found to be the most significant factor for Nu, followed by L/D_h, corrugation profile, and Re, while for the pumping power and pressure loss, D/D_hs followed by Re are the two significant parameters.

• The optimum value of f was found for 3 × 3 jet impinging, while all other factors were found to be insignificant.

• CFD results lie within an error band of ±12% of the experimental data.

The authors acknowledge the computational support of Mechanical and Nuclear Department of Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore, Islamabad.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

e =

depth of grooves, m

f =

coefficient of friction (friction factor)

h =

coefficient of convective heat transfer, W/(m²K)

k =

turbulence kinetic energy, J/kg

l =

length of plate, m

n =

number of jets

p =

pitch, m

q =

net heating power, W

v =

velocity, m/s

w =

width of plate, m

A =

area, m²

N =

number of grooves

P =

pressure, Pa

Q =

volumetric flowrate, m³/s

R =

resistance, Ω

T =

temperature, °C

V =

voltage applied across heater, V

$m˙$ =

mass flowrate, kg/s

q″ =

heat flux, Wm⁻²

k_c =

thermal conductivity, W/(mK)

D_h =

hydraulic diameter, m

D_h/D_hs =

jet diameter ratio

L/D_h =

jet-to-target plate distance ratio

Nu =

Nusselt number

p/e =

pitch-to-groove height ratio

Re =

Reynolds number

e/D_h =

blockage ratio

PP =

pumping power, W

ɛ =

turbulence dissipation rate, m²s⁻³

η =

thermal performance factor

μ =

dynamic viscosity, kgm⁻¹s⁻¹

ρ =

density, kg/m³

  ∈ =

emissivity

c =

channel

d =

downstream side

h =

hydraulic

HT =

heat transfer

j =

jet plate

 loss =

losses

ss =

steady-state

tot =

total

u =

upstream side

f =

flat plate

t =

trapezoidal plate

w =

wavy plate

ANOVA =

analysis of variance

CFD =

computational fluid dynamics

SAH =

solar air heater

SNR =

signal-to-noise ratio

Due to uncertainty in the measurement of different measuring devices, the error propagates further in the calculations. For that purpose, uncertainty analysis was performed to estimate the reliability of our results and correlations [37]. This propagation of errors in heat transfer coefficient, Nusselt number, friction factor, and thermal performance factor was calculated based on the basic rules of propagation [38].

The dimensions were measured using a Vernier caliper, with the least count of 0.05 mm. Since uncertainty is half of the least count. it will be ±0.025 mm.

To calculate the relative error in the heat transfer coefficient, the relative error in heat transfer rate $δqq$⁠, heat transfer area $δAHTAHT$⁠, and temperature difference $δΔTΔT$ are needed to calculate.

A total number of nine thermocouples were used on the test section plate, and the arithmetic mean value was computed. So, uncertainty in temperature values of thermocouples can be calculated from Eq. (A9).

An uncertainty analysis is performed to assess the accuracy of the measurements using the basic error propagation rules. Uncertainties for Nusselt number and friction coefficient are evaluated.

An uncertainty analysis is performed to assess the accuracy of the measurements using the basic error propagation rules. Uncertainties for Nusselt number, friction coefficient, and thermal performance factor are evaluated. An uncertainty of 2.4% and 3.3% was found in the Nusselt number and friction factor, respectively, which shows the error band of our experimental data.