Influence of Geometric Parameters of Alternate Axis Twisted Baffles on the Local Heat Transfer Distribution and Pressure Drop in a Rectangular Channel Using a Transient Liquid Crystal Technique

Abstract

This paper reports the effects of alternate axis twisted baffle geometric parameters on the heat transfer and flow characteristics within rectangular channels. In our experiments we used modified shapes of alternate axis twisted baffles according to relative pitch ratios (s/w) equal to 2–12 and twist ratios (y/w) equal to 1–5, under conditions where the angle of attack (α) was 90° and the relative blockage height (e/D_h) was at a constant value of 0.095. The results for the Reynolds numbers based on the duct hydraulic diameter ranged from 9000 to 24,000 at a constant Prandtl number, Pr = 0.707, using air as a working fluid. A 0.05 mm thick stainless-steel foil was used as a heater, and a thermochromic liquid crystal technique was used to obtain the local temperature distribution on the heated surfaces. Images were captured in areas with periodic, fully developed regions in the channel. The results show that rectangular channels equipped with alternate axis twisted baffles demonstrated 80%–185% greater heat transfer than rectangular channels with no baffles. Channels with alternate axis twisted baffles at higher twist ratios (y/w) and smaller relative pitch ratios (s/w) showed increased heat transfer, as well as pressure loss within the system, compared with other types of twisted baffles. The thermal enhancement factor of the rectangular channels equipped with alternate axis twisted baffles was higher than that for transverse baffles and smooth channels under similar operating conditions.

1. Introduction

As the world’s population and energy use continue to grow, the demand for energy continues to increase significantly. New innovations and technology require energy to support the manufacturing of tools and equipment needed for society’s technological growth. Heat transfer systems are commonly used in energy transfer. A variety of heat exchangers are used in numerous applications, such as car radiators, boilers, solar air preheaters, and air conditioners. Heat transfer equipment efficiently use energy. Therefore, it is necessary to develop advanced heat transfer equipment that is needed in various industries for efficiency and cost-effective energy use [1,2]. Liu and Sakr [3] classified convection heat transfer modes into three categories: passive techniques, active techniques, and a combination of the two. Passive heat transfer does not require external energy, while active heat transfer techniques require energy to increase the heat transfer rate. The third technique combines both methods (passive and active techniques). Passive heat transfer techniques increase heat transfer through the installation of baffles [4,5], ribs [6], and twisted tapes [7]. Revamping channel surfaces is another method of increasing heat transfer [8]. This technique increases the surface area required for heat transfer and enhances heat flow by generating turbulence across the flow surface.

An impressive example of revamping surfaces for convection heat transfer is the plate heat exchanger (PHE). It is a device widely used in numerous industries to increase or decrease the temperature of a system. Such devices are used in thermal processing, in-line pasteurization, and evaporative concentration [9]. Plate heat exchangers use thin plates with wavy and curved surfaces that are stacked on top of one another. These heat transfer surfaces are arranged so that each plate has a cooling fluid on one side and a heating fluid on the other. Flow channels direct the two flows so that there is no mixing of the fluids. Plates are assembled on a frame that is tightened with bolts. The area for heat transfer can be increased by adding more plates to the frame. This type of heat exchange is depicted in Figure 1.

The size and number of plates in a particular heat exchanger are designed to provide adequate heat transfer for the application at hand. Turbulent flow is achieved, and this aids in increasing heat transfer and reducing the fouling of heat exchange surfaces [10]. One of the challenges in controlling convective heat transfer is the use of a fluid as a coolant for gas turbine blades. In the modern design of aircraft engines, one essential condition is to achieve a high driving force-to-weight ratio while using as little fuel as possible. One way to increase this ratio is to enhance the thermal performance of the gas turbine blades. This can be done by increasing the inlet temperature of the gas turbine. To avoid melting the turbine blades, the working fluid is used as a coolant [11].

Figure 2 shows an example of cooling (fluid as a coolant) gas turbine blades with a cooler air stream that flows from the base into an internal space and out to the openings at various positions. In general, the cross section of a cooling channel changes at various positions along the turbine blades. The cross sections may be wedged, square, rectangular, or trapezoidal in relation to the shape of the turbine blades. However, gas turbine blades are complex in structure, which affects the efficiency of cooling at various positions. Therefore, numerous methods have been introduced to increase the rate of convective heat transfer within the cooling channels of turbine blades. Generally, cooling at the end of the air pans will require a method referred to as “impingement cooling” along with “film-cooling,” while “pin fin cooling” is essential at the back. The portion at the center, which takes up the most volume of the turbine blades, has various flow channels and requires enhanced surface cooling through the use of ribs, dimpled surfaces, and surfaces with arrays of protrusions and rough surfaces. It can be seen that the cross-sectional flow at the surfaces of the flow channels has a rectangular shape that makes it difficult to enable heat transfer out of the flow channel corners. This is among the most interesting challenges in cooling turbine blades. Previous research introduced solutions to the problem, mainly methods enhancing rotating flows. In such methods, surface protrusions or turbulators are installed to enhance convective heat transfer. These approaches increase heat transfer, as well as the pressure drop across the system, which is directly related to the loss of energy. Therefore, it is essential to consider these economics in the manufacturing of heat transfer equipment. In general, selecting a method to enhance heat transfer considers increased convective heat transfer while controlling the pressure losses within a system. Consequently, an optimal design strategy would achieve the highest heat transfer possible with the lowest pressure drop within the system (i.e., the best thermal enhancement factor (TEF)). TEF refers to the ratio of convective heat transfer within the flow channels with enhanced heat transfer surfaces and the convective heat transfer of smooth surface channels under a condition of similar pump power [12].

Research regarding enhanced heat transfer by rib turbulators and their associated pressure drop in single channels or multi-pass channels has examined experimental parameters, such as the relative roughness pitch (P/e), relative roughness height (e/H or e/D_h), angle of attack (α), and modified shapes. Prasad and Saini [13] studied the effects of relative roughness pitch and relative roughness height on heat transfer coefficients and friction factors during turbulent flow within a solar air heater with enhanced surface roughness. The results showed a characteristic flow pattern downstream of the ribs as a function of the relative roughness pitch. They observed that the maximum heat transfer coefficient occurred in the vicinity of the reattachment point due to the phenomenon of separation and reattachment of flow. It could be seen that the average value of the Nusselt number and friction factor along the rough surface channels was improved by factors of 2.10, 2.24, and 2.38 and 3.08, 3.67, and 4.25 compared with those of the smooth surface channels with relative roughness heights (e/D_h) equal to 0.020, 0.027, and 0.033, respectively. The Nusselt number and friction factor for the roughened surface channels was 2.38, 2.14, and 2.01 and 4.25, 3.39, and 2.93 times greater than those of the smooth surfaced channels when the relative roughness pitch (P/e) was 10, 15, and 20, respectively. The highest heat transfer and friction factor values were 2.38 and 4.25 times greater, respectively, compared with those of the smooth surface channels. Aharwal et al. [14] studied the effects of inclined rib positioning within rectangular channels inside a solar air heater considering the gap width ratio (g/e) and gap position ratio (d/w) parameters. Thus, the increases in the Nusselt number and friction factor were within the range of 1.48–2.59 and 2.26–2.9 times greater than those of the smooth surface channels. Momin et al. [15] analytically investigated the impacts of relative roughness height and attack angle at a fixed relative roughness pitch of 10 with Reynolds numbers ranging from 2500 to 18,000 for V-shaped ribs. It was observed that there was an increase in the Nusselt number with the increase of the Reynolds number. Consequently, as the Reynolds number decreased, the friction factor increased. With relative a roughness height of 0.034, the V-shaped ribs produced an increase in the Nusselt number that was 1.14 and 2.30 times greater, respectively, than that of the transverse ribs and smooth surface channels.

Several studies have examined the installation of twisted tapes in parallel channels. Eiamsa-ard [16] reported on thermal and fluid flow characteristics in turbulent channel flows with multiple twisted tape vortex generators (MT-VG). This study demonstrated that channels with installed MT-VG aided heat transfer to a 10.3%–169.5% greater degree than smooth surface channels. A channel with low twist ratio twisted tapes and a low free-space ratio resulted in higher heat transfer and friction factor values. The thermal enhancement factor was reported to range from 0.94 to 1.4. Kumar et al. [17] studied the thermo-hydraulic performance of a solar air heater with twisted ribs over its absorber plate. The experimental parameters included relative roughness pitch (P/e), rib inclination angle (α), and twist ratio (y/e). The experiment was done under turbulent flow conditions at Reynolds numbers of 3500–21,000, with the highest rate of heat transfer and the friction factor being 2.58 and 1.78 times higher, respectively, than those of the smooth surfaced channels in the case where P/e = 8, y/e = 3, and α = 60°.

Measuring temperature is very important in the study of heat transfer, especially for the measurement of surface heat transfer coefficients. The primary method of temperature measurement is the use of thermocouple devices installed directly on the surface of the equipment [18]. However, in the case where a detailed temperature distribution is required, a large number of these devices will be needed. In constrained spaces, such as an experimental setup, it may be difficult, and errors in temperature measurement may result. This leads to errors in estimation of convective heat transfer coefficients. Infrared thermometry is another convenient and simple method to measure temperature that requires no direct contact. It measures temperature from thermal radiation from various surfaces. Therefore, it is essential to know the radiation coefficient of the surface being measured to obtain accurate temperature values. However, there are some cases in which this technique cannot be used. These include temperature measurements of surfaces immersed in a fluid. In such cases, radiation cannot pass through the liquid molecules. The application of this technique tends to be quite expensive [19]. The purpose of this research is to study the effects of the relative pitch ratio and twist ratio of “alternate axis twisted baffles,” focusing on the impacts of twisted baffles on the distribution of the Nusselt numbers. We solve the heat transfer distribution using a transient liquid crystal technique installed on heated surfaces. This technique takes advantage of the color changes of thermochromic liquid crystal sheets on heat transfer surfaces. Imagery is recorded using a high-resolution digital camera and analyzed using a computer program to aid in the determination of the temperature distribution on the heated surfaces.

2. Thermochromic Liquid Crystals

Measuring temperature with thermochromic liquid crystals (TLCs) is a technique that determines temperature without direct contact. TLCs change color with temperature. This method is inexpensive and convenient. It requires no equipment or complicated measurements. Temperature change is determined from the color of thermochromic surfaces. Digital cameras enable high-resolution capture of thermochromic data. Software is used for facile image processing and analysis. Thus, accurate temperature distributions can easily be determined [20]. Nevertheless, thermochromic liquid crystal temperature measurements require knowledge for the selection of liquid crystal types that most closely suit the temperatures to be measured. Calibration of colors as a function of temperature is required as well. In general, there are two types of commercial TLCs available based on their bandwidths, namely narrowband and wideband. Wideband TLCs are widely applied in many engineering fields, because they can measure temperature distribution in the range of 5–20 °C, whereas narrowband TLCs can measure temperature distribution in the range of 0.5–2 °C. Most heat transfer investigations are concerned with temperature differences over 5 °C. Wideband TLCs have; therefore, been employed in several studies [18,19]. In this study, we selected wideband thermochromic liquid crystal sheets and calibrated them to measure temperature distributions within various rectangular channels to determine convective heat transfer coefficients on heated surfaces.

2.1. Molecular Structure of TLCs

Thermochromic liquid crystal materials are organic substances that alter their form (solid or liquid) with temperature changes. They take the form of a transparent solid when exposed to white light. When the temperature increases to a certain point, their molecular structure changes. Then, they reflect light at wavelengths that continuously change with temperature. When the temperature of such a substance reaches its red start point (T_rs), its color changes from transparent to gray and then to red, orange, yellow, and green as the temperature increases. At higher temperatures, the material reaches its blue start point (T_bs). Then, as the temperature increases, its color changes to purple and then to dark purple before returning to its initial state of transparency. Thermochromic liquid crystals come in various types. Such materials may take the form of oil, powder, small capsules, liquid applied to surfaces, or polymer sheets that can be applied to measure temperature on complex surfaces, such as those examined in the current study [21].

2.2. TLC Calibration

Grassi et al. [22] introduced a technique for thermochromic liquid crystal calibration that is important for accurately measuring temperature. The process can be done in two ways—isothermal calibration and temperature gradient calibration. Calibration in this study was done on an isothermal surface. This method keeps the temperature of a thermochromic liquid crystal surface stable. A Nikon D5100 digital camera captured the resulting colors to achieve data calibration between color and temperature. Although the equipment and calibration process is not complicated, calibration required considerable time, because measurements at various temperatures were needed to obtain enough data for adequate temperature measurement. Additionally, the image settings, such as exposure, camera settings, lighting angles, and image angles, had to be similar to those used in the experiments.

Figure 3a shows the equipment used in the calibration process. The inner dimensions of the 304-stainless steel bucket were 400 (height) × 400 (length) × 400 (width) mm³, with a 0.8 mm thickness. A 2-kW heater, controlled by an adjustable AC power source, was used to raise the water temperature. To reduce the temperature gradient inside the water, a stirrer was installed in the bucket. In the areas surrounding the test sample, insulation was installed to reduce heat losses to the environment. At the bottom of the test stand, a rectangular 200 mm wide and 200 mm long section was opened for installation of a 0.05 mm thick stainless-steel sheet. This was used to receive heat from the water at a constant flux. A thermochromic liquid crystal sheet was attached to the stainless-steel sheet. A high-resolution digital camera was installed in front of the TLCs to capture color images. An RTD Pt100 was used to monitor the temperature, while three RTD Pt100s measured the surface temperatures of the stainless-steel sheet. In each color calibration, the temperature ranged from 25 to 40 °C, which is the point at which the thermochromic liquid crystals are no longer black, to the point where the TLCs turn dark blue or dark purple. The temperature calibration of the TLCs was done by comparing the measured temperatures and images captured once the temperatures of the stainless-steel sheet were unchanged for 10 s. Color calibration was done during both heating (25–40 °C) and cooling (40–25 °C) to check for possible hysteresis. The temperature during calibration was increased in 0.1 °C steps. Calibration measurements were done in triplicate. The specifications of the instruments used to perform the calibration and experiments are listed in

Table 1. Specifications of the instruments used to perform the calibration and experiment.

No.	Instruments	Description	Specification
1	Nikon DSLR D5100	take TLC surface pictures	effective pixels: 16.2 million
	camera		(4928 × 3264 pixels for large size)
2	TLC sheet	temperature indicating sheet	accuracy: ±0.1 °C,
		(heating surface)	30–35 °C (86–95 °F)
3	RTD Pt100	temperature sensor	accuracy: ±0.001 Ώ at 0 °C
		(inlet and outlet temperature)	(−130 to +95 °C ±0.05 °C)
4	TSI/Alnor 9565-A	air velocity measurement	accuracy: ±3% for reading
	thermo-anemometer		(±0.015 m/s), range: 0–50 m/s
			resolution: 0.01 m/s
5	Dwyer MS-111	differential pressure sensor	accuracy: ±2% for 250 Pa,
		(orifice meter)	±1% for 250–1250 Pa
6	Dwyer DM-2004	differential pressure sensor	accuracy: ±1% full scale at 70 °C
		(test section)
7	HIOKI LR8401	temperature recorder	10 ms high-speed sampling
	data logger		(with 30-channel as standard)

.

2.3. Imaging System

Figure 3b shows a calibration using a thermochromic liquid crystal sheet at various temperatures. The images obtained from the color calibration were analyzed in an RGB (Red, Green, Blue) color system and later changed to the HSI color system. Image processing software used the following equations:

$$H=\left\{\begin{array}{l}\theta \\ 360-\theta \end{array}\right\}\left\{\begin{array}{l}ifB\le G\\ ifB>G\end{array}\right\}$$

(1)

where

$$\theta ={\cos }^{-1}\left\{\frac{\frac{1}{2}\left[\left(R-G\right)+\left(R-B\right)\right]}{{\left[{\left(R-G\right)}^2+\left(R-B\right)+\left(G-B\right)\right]}^{\frac{1}{2}}}\right\}$$

(2)

$$S=1-\frac{3}{\left(R+G+B\right)}\left[\min \left(R,G,B\right)\right]$$

(3)

$$I=\frac{1}{3}\left(R+G+B\right).$$

(4)

H (hue) is a value that indicates a true, initial color from the acquisition of primary colors (red, green, and dark blue). In such cases, an angle is formed around the vertical axis in the range of 0–360°. Each angle has a color value of 60°, rotated to form a hexagon. S (saturation) is a property used to measure the rate at which pure color is diluted with white, where the value ranges from 0 to 1. Lastly, I (intensity) is a property that indicates the depth (crispness) or the brightness of colors.

Equations (1)–(4) were used to calculate the average hue value at various temperatures using the MATLAB program. Thus, a graphical relationship between the temperature and the hue was developed, as shown in Figure 4. Hysteresis in TLCs is a phenomenon where TLCs exhibit different colors depending on whether they are being cooled or heated. Hysteresis was observed by a number of researchers [18,21,22,23,24], as it occurs when TLCs are heated to or cooled from temperatures above their clearing point. Calibrations of TLCs are typically considered to be repeatable, duplicable, and reversible, and they are assumed to not exhibit hysteresis.

Figure 4 shows that no hysteresis errors or output signal differences were observed during calibration. The correlation of the averaged hue and temperature values were fitted to a third-order polynomial form with an R-square value of 0.9884 and was shown as follows:

$$T_w=0.000262H^3-0.112715H^2+16.167973H-744.041481.$$

(5)

Equation (5) can only be used to find the wall temperature (T_w) of each image pixel over the temperature range of 29–38 °C.

3. Experimental Apparatus and Its Operation

The equipment used in the experiment consisted of an entrance section, an electric ring blower, and a heating device. A schematic diagram of the equipment used in the experiment is shown in Figure 5. The rectangular entrance length was 1800 mm, and it was constructed to avoid the disturbance of air flow and enable flow control before entering the test section. The design and construction of the channel entrance used in the experiment followed the recommendations of Ower and Pankhurst [25].

The geometry of the test section with alternate axis twisted baffles and its structure are shown in Figure 6a,b. The test section was made out of a 10 mm thick acrylic material, with a cross-sectional area of 150 mm (W) and 40 mm (H). The twisted baffles used in the experiment were made of polylactic acid (PLA). Each tape had a similar length (l), height (w), and thickness (t) of 150, 6, and 1 mm, respectively. In the experiment, various pitch values (y) were used, 6, 12, 18, 24, and 30 mm, so that they corresponded to twist ratios (y/w) of 1, 2, 3, 4, and 5, respectively. The distance between the twisted baffles (s) was then equal to 12, 24, 36, 48, 72, and 84 mm, respectively. The relative pitch ratios (s/w) were 2, 4, 6, 8, 10, 12, and 14, respectively, as shown in

Table 2. Dimensionless quantities and other parameters used in test channel experiments.

No.	Parameter	Range
1	Reynolds number (Re)	9000–24,000 (six values)
2	Relative blockage height (e/Dh)	0.095 (one value)
3	Relative pitch ratio (s/w)	2–12 (six values)
4	Twist ratio (y/w)	1–5 (five values)
5	Angle of attack (α)	90° (one value)

. One portion of the twisted baffle had a different (counterclockwise) direction of rotation, where its length (l) ranged from 0 to 75 mm. In the installation of typical transverse baffles, heat transfer was low in the areas behind the baffles. However, the installation of the twisted baffles aided in the separation of flow and the segregation of flow layers within the channels [17]. The installation of these baffles was similar to that of discrete baffles [26,27]. A 150 mm wide and 900 mm long electric polyimide film heater (8000 W/m²) was used. The test section was heated at a constant flux, with a heater installed at the bottom wall (interior) of the test section. The heating coils were connected to a variac transformer to control heat flux. The exterior of the test section was insulated to prevent heat loss from the system. The test section was constructed of clear and transparent acrylic to enable image capture. TLCs were installed on the interior bottom wall to measure temperature changes of the channel wall surfaces, as shown in Figure 5. The color changes of the TLCs were then captured using a high-resolution camera, and an image processing program was used to analyze the temperature of the channel wall surfaces. TLCs were calibrated using a digital image processing program under the same experimental conditions, including the illuminating light used and the camera-viewing angle [18,21,22,24]. A total of 11 RTDs were installed at both the entrance and the exit to measure air temperatures. A data logger was used to record this information and display real-time temperature changes at the entrance and the exit. The calibrated RTDs were used to measure inlet and outlet air temperatures of the test section, which could be further calculated to obtain the characteristics fluid temperature (T_b = (T_i + T_o)/2). The inlet and outlet temperatures of fluid were measured by four RTDs. At the exit of the test section, three RTDs were mounted to measure the outlet fluid temperatures (T_o). In the turbulent channel flow, the fluid/air temperature inside a channel increased linearly with axial distances (x/D_h) due to the high mixing of the testing fluid caused by turbulence, and vortex flows induced baffle turbulators. Therefore, three measured outlet fluid/air temperatures at three various positions in a mixer chamber were sufficient to represent the mean outlet temperature (T_o). The pressure drop across the test section was measured using a differential pressure transmitter. Heat transfer and pressure drop experiments were carried out separately. The heat transfer experiment was done under a constant heat flux. The pressure drop across the test section was measured isothermally with no energy supplied through the heating coils [28].

The air flow rate was read from an orifice meter, which was designed according to ASME Standard recommendations [29]. The experiment involved a comparison between a hot-wire anemometer that measured the air flow rate across the tube. This experiment was carried out at Reynolds numbers ranging from 9000 to 24,000 (turbulent flow). Reduced data obtained from the experiment were identified to quantify the uncertainties of measurements. Indefinite average velocity (U), static pressure (P), and temperature (T) were all estimated based on ANSI/ASME methods [30] and were found to be within ±5.2%, ±4.2%, and ±0.5% of the measured values, respectively. The maximum indefinite value of non-dimensional parameters was found to be ±4.6% for the Reynolds number, ±3.2% for the Nusselt number, and ±2.3% for the friction factor.

4. Data Reduction

The aim of this experiment was to increase heat transfer within rectangular channels by installing alternate axis twisted baffles. The experimental data for both the channel wall and air temperature at various points were recorded under a constant heat flux with the above air mass flow rates. Experimental data were used to find the Nusselt numbers and friction factors within the rectangular duct. The following expression was used to calculate the mass flow rate using the pressure differential (ΔP_o) across an orifice plate. The mass flow rate was then calculated according to [31]:

$$\dot{m}=C_d{A}_o{\left[\frac{2\rho \Delta P_o}{1-{\left(d_2/d_1\right)}^4}\right]}^{1/2}.$$

(6)

The coefficient of discharge (C_d) of the orifice meter was 0.624, which was determined from the calibration of the orifice meter with a hot-wire anemometer.

Velocity (V) of air was calculated from the expression of mass flow rate, which can be obtained from the following:

$$V=\frac{\dot{m}}{\rho WH}.$$

(7)

The Reynolds number (Re) of air flowing in the test section was as follows:

$$\mathrm{Re}=\frac{V{D}_h}{\nu }$$

(8)

where the hydraulic diameter was the following:

$$D_h=\frac{4A_c}{P}=\frac{4\left(WH\right)}{2\left(W+H\right)}.$$

(9)

The thermo-physical properties of gas at atmospheric pressure were estimated using the Duffie and Beckman relationship [32]:

$$\rho =1.204\left(\frac{293}{T}\right)$$

(10)

$$\mu =181\times {10}^{-5}{\left(\frac{T}{293}\right)}^{0.735}$$

(11)

$$c_p=1006{\left(\frac{T}{293}\right)}^{0.0155}$$

(12)

$$k=0.0275{\left(\frac{T}{293}\right)}^{0.86}.$$

(13)

The heat transfer rate (Q_abs) obtained from the heated surface to the air stream was determined using the mass flow rate, where there was a temperature increase across the test section given as:

$$Q_{abs}=\dot{m}{c}_p\left(T_o-T_i\right)$$

(14)

where T_i and T_o can be obtained from the following:

$$T_i=\frac{T_{i,1}+T_{i,2}+T_{i,3}}{3}$$

(15)

$$T_o=\frac{T_{o,1}+T_{o,2}+T_{o,3}+T_{o,4}+\dots +T_{o,8}}{8}.$$

(16)

The local heat transfer coefficient (h_x) can be calculated by using the heat flux (q), average wall temperature along the y-axis at any x-position (T_wx), and the local characteristics fluid temperature (T_bx), which was implemented by a linear interpolation approach between inlet and outlet air temperatures of the test section as follows:

$$h_x=\frac{q}{\left(T_{wx}-T_{bx}\right)}.$$

(17)

The average heat transfer coefficient (h) throughout the test section was calculated by using the heat transfer rate (Q_abs), average inside wall temperature of the plate (T_w,avg) converted from the surface image of TLCs and calculated by Equation (5), and the characteristics fluid temperature (T_b), which was assumed to be as follows:

$$h=\frac{Q_{abs}}{A_{hs}\left(T_{w,avg}-T_b\right)}.$$

(18)

Fluid properties were obtained at the characteristic fluid temperature (T_b = (T_i + T_o)/2), while the area weighted wall temperature (T_w,avg) can be found by Equation (5). The Nusselt number (Nu) was then calculated from the heat transfer coefficient (h), hydraulic diameter (D_h), and thermal conductivity (k) as follows:

$$Nu=\frac{h{D}_h}{k}.$$

(19)

The friction factor (f) was obtained from the pressure drop within the test section and the velocity (V) of air flowing through the test section using the basic equation introduced by Darcy–Wiesbash [31]:

$$f=\frac{\Delta P_t}{\left(\frac{L}{D_h}\right)\left(\rho \frac{V^2}{2}\right)}.$$

(20)

5. Validity Test of the Experiment Setup

Before the extensive data collection for rectangular ducts with alternate axis twisted baffles was conducted, a validity test was performed. The Nusselt number (Nu) and friction factor (f) of a smooth surfaced channel were acquired from the experiments. The experimental Nusselt number was compared with values obtained from the Dittus–Boelter general equation [31] and the Gnielinski equation [17]. The results from the general modified Blasius equation [14,31] and Pethkhov equation [33] were compared with the experimentally-derived friction factor values. These equations take the form of the following:

(a)

Dittus–Boelter equation (for 6000 ≤ Re ≤ 5 × 10⁷ and 0.5 ≤ Pr ≤ 120)

$$N{u}_s=0.023{\mathrm{Re}}^{0.8}{\mathrm{Pr}}^{0.4};$$

(21)

(b)

Gnielinski equation (for 3000 ≤ Re ≤ 5 × 10⁶)

$$N{u}_s=\frac{\left(f/8\right)\left(\mathrm{Re}-1000\right)\mathrm{Pr}}{1+12.7{\left(f/8\right)}^{0.5}\left({\mathrm{Pr}}^{0.66}-1\right)};$$

(22)

(c)

Modified Blasius equation

$$f_s=0.085{\mathrm{Re}}^{-0.25};$$

(23)

(d)

Pethkhov equation

$$f_s=0.431{\mathrm{Re}}^{-0.292}.$$

(24)

A comparison of the experimental results with the Nusselt numbers and friction factors obtained from the basic equations is shown in Figure 7a,b, respectively.

The average absolute deviations between the experimental values and those from Equations (21)–(24) were 3.2% and 2.3% for the Nusselt number and friction factor, respectively. The results show sufficient experimental and measurement accuracy.

6. Results and Discussion

Heat transfer and pressure loss values for the rectangular duct equipped with alternate axis twisted baffles were calculated using the experimental data compiled for various sets of geometric values of alternate axis twisted baffles and analyzed as follows.

6.1. The Effect of Reynolds Number (Re)

Figure 8a,b shows the effects of the Reynolds number (Re) on both the Nusselt number and the friction factor for rectangular channels equipped with alternate axis twisted baffles (AATBs) under the conditions of e/D_h = 0.095, s/w = 10, y/w = 5, and α = 90°; transverse baffles (TBs) under the conditions of e/D_h = 0.095, P/e = 10, and α = 90°; and a smooth surface channel. When the Reynolds number increased, the friction factor decreased due to the suppression of the viscous sub-layer. On the contrary, the Nusselt number increased with the Reynolds number due to the ratio of conduction resistance and convective resistance of heat flow, which was also caused by a decrease in the boundary layer thickness. Therefore, when the convective resistance decreased, the Nusselt number increased. This was attributed to the increase of turbulence as the Reynolds number increases, leading to an amplification of convective heat transfer (see Figure 9a,b). The data obtained in this research is consistent with those of Eiamsa-ard et al. [34] and Lee et al. [35]. The results of the experiments show that the rectangular duct with alternate axis twisted baffles demonstrated the highest values of heat transfer compared with those with transverse baffles and smooth channels. Rectangular channels in which alternate axis twisted baffles and transverse baffles were installed had average Nusselt numbers that were 1.97 and 1.83 times higher than that with smooth channels, respectively.

Figure 10a–c shows the local span-wise Nusselt number distribution and Nusselt number contour for a rectangular channel with alternate axis twisted baffles, transverse baffles, and a smooth channel at a Reynolds number of 9000. The effect of the transverse baffles was significant in the production of flow patterns, as it generated two separate regions of flow—one on each side of the transverse baffles. Turbulence occurred through the generation of vortices. Hence, enhancement of both heat transfer, as well as friction loss, took place. Figure 10b and Figure 11a show the importance of the flow pattern downstream of transverse baffles. It can be observed that the point of the highest heat transfer occurred in areas near the reattachment point due to the separation and reattachment of the flow.

The results obtained from this research on rectangular channels with alternate axis twisted baffles are shown in Figure 10c and Figure 11b. The flow pattern can be explained by the separation of a free shear layer from the twisted baffle tip and its reattachment on the downstream side of the twisted baffles. The intensity of reattachment with the alternate axis twisted baffles was lower than those of the transverse baffles due to disturbances from the air flow, which passed through the gap distance of the twisted baffles.

It can be observed from Figure 8a,b that the Nusselt numbers of rectangular channels with alternate axis twisted baffles and transverse baffles were close in magnitude. However, the friction factor for the alternate axis twisted baffles was 3.37 times that those of the smooth channel and the transverse baffles. This was due to the perforation (a gap distance resulting from the twisting of the baffles) offering lower resistance to the flowing fluids. Hence, alternate axis twisted baffles can be considered ideal candidates for further development to aid in the enhancement of heat transfer, as well as for pressure reduction within the system.

6.2. Effects of Twisted Ratio (y/w)

Figure 12a displays the Nusselt number (Nu) variation for various twist ratios (y/w), with fixed values of e/D_h = 0.095, s/w = 10, and α = 90°. It can be observed that when y/w = 5, the Nusselt number (Nu) was at its highest value under all ranges of the flow parameters. The decreased twist ratio resulted in an increase in the relative gap distance in the twisted baffles. In general, air that flows through the gap will result in jet mixing and will increase the jet flow. This results in an increased area for heat transfer at the gap between the twisted baffles, as shown in Figure 13 and Figure 14. However, the decreased range of the twist ratio leads to decreased levels of impingement and refraction of flow to the channel wall from the decreased angle impingement that occurs due to the twisted baffles. The latter directly impacts heat transfer at the channel wall, where the twisted baffles decrease in number, as shown in Figure 14.

Figure 13a–e shows the local span-wise Nusselt number and Nusselt number contour for the installation of twisted baffles with a modified twist ratio (y/w) that ranges from 1 to 5, with fixed values of s/w = 10 and α = 90° and a Reynolds number equal to 9000. In the case where the twist ratio was increased, resulting in the impingement and refraction of the flow that impacted the channel wall, the levels of intensity significantly increased. This led to increased flow turbulence, as well as higher heat transfer. The impacts of the twist ratio on the friction factor were studied, where e/D_h = 0.095, s/w = 10, and α = 90°, for each phase of the experiment. The Reynolds number used is shown in Figure 12b. It can be observed that the friction factor increased over the range of the twist ratio. The increased twist ratio decreased the gap distances, as well as the amount of jet flow, which increased areas of flow blockage, resulting in an increased friction factor. Alternatively, decreasing the range of the twist ratio resulted in a decreased angle impingement from the twisting baffles or a decrease in the area of flow blockage. This led to a decreased pressure drop within the system.

6.3. Effects of Free-Spacing Ratios (s/w)

Figure 15a shows the effects of the relative pitch ratio (s/w), which has an impact on the Nusselt number (Nu) for fixed values of specific geometric parameters (e/D_h = 0.095, y/w = 5, and α = 90°). It can be observed that the highest Nusselt number occurred at a phase in which the relative roughness pitch (s/w) equaled 2. It appears that the free shear layer separated from the twisted baffle tip, which resulted in a reattachment between the twisted baffles downstream. However, reattachment resulted in less impact than for the flow separation that may occur downstream of the twisted baffle. This was caused by the intensity of the reattachment, with a disturbance of the air that flowed through the gap between the twisted baffles, as shown in Figure 16a–f. Thus, the primary factor that aided in the enhancement of the heat transfer was the separation that occurred at the gap, where impingement flow was refracted so that it contacted the heated surface near locations where the twisted baffles were installed, as shown in Figure 17.

Figure 16a–f shows the local span-wise Nusselt number and Nusselt number contour for the twisted baffles with relative pitch ratios (s/w) in the range of 2–12, with fixed values of y/w = 5 and α = 90° and a Reynolds number of 9000. The decreased relative pitch ratio resulted in continuous heat transfer, specifically in the area with twisted baffles. This was due to continuous disturbance and prevention of a free shear layer. Alternatively, if s/w increased, the distance between rib elements increased. This led to a decrease in the area for heat transfer (with twisted baffles) per length in the flow direction and a subsequent decrease in heat transfer.

Figure 15b shows the effects of the relative pitch ratio on the friction factor for a fixed value of relative blockage height (e/D_h) of 0.095 and a twist ratio (y/w) of 5. It can be observed that the friction factor decreased as the Reynolds number (Re) increased for the entire set of roughness parameters. At the phase where the relative roughness pitch equaled 2, the friction factor was at its highest value and the Reynolds number equaled 9000, and the friction factor decreased when the relative pitch ratio increased. This was due to the increased inter-baffle distance, which further led to decreased pumping power that lowered the characteristic flow friction.

6.4. Thermal Enhancement Factor (TEF)

It is essential to geometrically design a turbulator within a rectangular channel with the most suitable parameters. This is not only to enhance heat transfer, but also to keep the pressure levels within the system as low as possible.

Thus, in determining the optimal value, it is best to simultaneously consider heat transfer and pressure losses within the system. Promvonge and Thianpong [36] introduced a variable referred to as the thermal enhancement factor (TEF). It can be calculated from the heat transfer coefficient. In the case where the channel has an installed turbulator, and compared with those of smooth channels under a similar pumping power, the TEF can be calculated as follows:

$$\mathrm{TEF}=\frac{\left(Nu/N{u}_0\right)}{{\left(f/f\right)}^{1/3}}.$$

(25)

The thermal enhancement factor with twisted baffle roughness for the Reynolds numbers in the current study had modified relative roughness pitch and twist ratios, as shown in Figure 18.

It can be seen that the highest thermal enhancement factor occurred in rectangular channels equipped with alternate axis twisted baffles under the conditions where the relative pitch ratio (s/w) equaled 2 and the twist ratio (y/w) equaled 5, yielding values that ranged from 1.06 to 1.71, compared with those of the smooth surface channels under a constant blower power. Figure 18a shows the highest thermal enhancement factor values, where the relative pitch ratio equaled 2. It can be further explained that the range where s/w < 2, an area with continuous heat transfer, was due to a disturbance and a reduced viscous sub-layer caused by the twisted baffles. Therefore, convective resistance was decreased, which then led to higher Nusselt numbers. Alternatively, when s/w > 2, the distance between the twisted baffles increased, which resulted in a fully-developed flow of fluids though the twisted baffles and the creation of a viscous sub-layer, further decreasing heat transfer. Figure 18b shows that an increased twist ratio range leads to an increased thermal enhancement factor. However, the thermal enhancement factor decreases with an increase in the Reynolds number. It is true that at high twist ratios the number of twisted baffles will decrease. Therefore, the amount of jet flow decreases as well. However, as the angle impingement increases and triggers higher impingement intensity, the thermal enhancement factor is increased.

6.5. Comparison with Previous Work

Rectangular channels equipped with alternate axis twisted baffles and those with turbulators in earlier studies were compared under various geometric configurations and flow parameters, as shown in

Table 3. Comparison of various geometric parameters.

Researcher	Roughness	Operating Condition	TEF
Momin et al. [15]	V-shaped ribs	Re = 2500–18,000, P/e = 10, α = 30–90°, W/H = 10.15, e/Dh = 0.02–0.034	1.76
Eiamsa-ard [16]	Multiple twisted tapes	Re = 2700–9000, AR = 10, y/w = 2.5–3.5, s/w = 1.0–1.66	1.41
Promvonge [28]	Multiple 60° V-baffles	Re = 5000–25,000, AR = 10, e/H = 0.1–0.3, PR = 1–3	1.87
Albaldawi et al. [37]	Angle-ribbed tape	Re = 3400–20,800, α = 10–90°, BR = 0.2, PR = 1	1.30
Singh et al. [38]	Discrete V-down ribs	Re = 3000–15,000, AR = 12, d/w = 0.2–0.8, P/e = 10, e/Dh = 0.043, α = 60°	2.03
Karwa et al. [39]	Chamfered ribs	Re = 3750–16,350, φ = 15°, P/e = 4.58–7.09, AR = 6.88–9.38, e/Dh = 0.0197–0.0441	1.39
Promvonge et al. [40]	Combined rib and delta-winglet	Re = 5000–22,000, α = 30–60°, e/H = 0.2, b/H = 0.4, Pt/H = 1, Pl/H = 1.33	1.38
Sriromreun et al. [41]	Multiple V-ribs with combined staggered ribs	Re = 12,681–35,000, α = 30°, e/H = 0.1–0.3	2.05
The present study	Alternate axis twisted baffles	Re = 9000–24,000, AR = 3.75, s/w = 2–12, e/Dh = 0.095, y/w = 1–5, α = 90°	1.71

. The results of this study show that the thermal enhancement factor (TEF) was higher in the current study than in other cases, comparing the use of multiple twisted tapes [16], angle-ribbed tapes [37], chamfered ribs [38], and combined rib and delta-winglets [39]. However, thermal enhancement factor values are lower only when the channel V-shaped ribs [15], multiple 60° V-baffles [28], discrete V-down ribs [40], or multiple V-ribs with combined staggered ribs are installed [41].

7. Conclusions

The experimental results of the current study were thoroughly analyzed to find the rate of heat transfer, as well as air flow characteristics using alternate axis twisted baffles at an area with heated surfaces under a condition of uniform heat flux. The impacts of relative pitch ratio, twist ratio, and the Reynolds number on the Nusselt number and friction factor can be summarized as follows:

• The Nusselt number increased, while the friction factor decreased. The Reynolds number (Re) increased with the Nusselt number when the relative pitch ratio (s/w) decreased and when the twist ratio (y/w) increased. However, with the friction factor, there is a possibility that it decreased in value when the relative pitch ratio (s/w) increased and when the twist ratio (y/w) decreased.
• The highest values of the Nusselt number and friction factor were 2.99–3.16 times and 6.01–6.29 times higher than those of the smooth channels with alternate axis twisted baffles when s/w = 2 and y/w = 5, respectively.
• The optimal value of the thermal enhancement factor was 1.71 with a Reynolds number of 9000. The optimum roughness parameter (based on the TEF parameter criterion) was with a lower relative pitch ratio and higher twist ratio.