Improvement of Heat Transfer in a Parabolic Trough Collector Receiver Tube with Hollow Cylindrical Inserts: A CFD Study

Improving the thermal conductivity between a heat transfer fluid (HTF) and a parabolic trough receiver (PTR) is important for many uses, such as making energy [1], desalination [2], cooling [3], and more. Generally, three techniques are used to improve heat transfer between the HTF and the PTR: active, passive, and compound techniques (active and passive). Furthermore, these techniques are designed to minimize the temperature variation inside the PTR to mitigate thermal stresses and, subsequently, decrease the likelihood of failure. An active technique is needed for an external energy source to enhance heat transfer in a PTR. In contrast, a passive technique involves altering the configuration of thermal systems in order to enhance their thermal performance without requiring the use of external energy sources. The compound techniques mix two first techniques: active-active, active-passive, or passive-passive [4].

Broadly, passive techniques are the most commonly used techniques for enhancing the heat transfer rate (Nusselt number) and pressure drop (fraction factor) inside the PTR. Therefore, numerous researchers have extensively studied these techniques to comprehend their mechanisms.

Several experts have conducted numerical studies on the twisted-tape inserts. Ghadirijafarbeigloo et al. [5] investigated the effect of introducing louvered twisted-tape inside a PTR. The results revealed that, in comparison to the plain tube (PT) case, the Nusselt number (Nu) and friction factor (f) factors are 3.5 and 4.1, respectively, while the thermal enhancement factor (TEF) reaches 2.26. Chang et al. [6] analyzed the effect of varying clearness ratios and twisted ratios of twisted-tapes on (Nu) and (f) inside the PTR. The results showed that the maximum factors of the Nu and f can be 2.9 and 2.5 times greater than in the PT. Abbas et al. [7] used twisted-tapes with six different inclination angles inside the PTR. They found the thermal performance increased, especially when the inclination angle was 50°.

Also, a wide group of researchers has also studied the use of the fins inside the PTR to enhance thermal performance. Bellos et al. [8] examined how the length and thickness of longitudinal fins affect the increase of Nu and f within the PTR. In the optimal case, the thermal efficiency reached 68.8%, and the enhancements in Nu and f are 1.652 and 2.00, respectively, compared with the PT case. Laaraba and Mebraki [9] carried out a numerical calculation to ascertain the optimal number, length, and thickness of fins attached to the lower half of the PTR wall. The purpose of this is to enhance the thermal performance of the parabolic trough collector (PTC). They found that at a length of 15 mm and a thickness of 6 mm, the thermal efficiency increased by a maximum of 8.45%. In their paper, Fatouh et al. [10] described in detail a thermal model of adding fins (also known as base rounding) to PTR in order to find the Nu, f, thermal efficiency, and TEF for each model. The thermal model showed an increase in thermal efficiency, reaching 1.363%, and the maximum TEF is 1.644. Al-Aloosi et al. [11] numerically found that the value of Nu in the PTR with inserted fins increased by 51% compared with its value in the PT.

Moreover, various studies have been published to demonstrate the impact of several inserts on the hydraulic-thermal performance within the PTR. Bellos et al. [12] employed several cylindrical longitudinal inserts in the PTR to investigate fifteen scenarios and their impact on the transfer of heat using a CFD tool. The results showed a thermal efficiency improvement when using a higher number of inserts. Chang et al. [13] used a concentric rod and an eccentric rod to study the enhancement in Nu and f compared the PT. In the PTR with a concentric rod, the Nu increased from 1.10 to 7.42, and the value of TEF increased from 1.12 to 3.38 as the dimensionless diameter increased from 0.1 to 0.9. Jafar Kutbudeen et al. [14] experimentally worked to insert the conical strip inside the PTR to study the thermal performance of the PTC. The experimental results indicated that the maximum enhancement values of Nu (2.23%) and f (1.89%) happening in a PTR with a conical strip insert have a twisted ratio of 3. Allam et al. [15] have conducted an experimental investigation on enhancements in Nu and thermal efficiency inside the PTR using rotational helical shift. Their findings revealed that the maximum enhancements in the Nu and thermal efficiency are 2.42 and 46.5%, respectively, and the TEF is 1.24. Said et al. [16] evaluated the thermal performance of an evacuated tube of a PTC with a helical coil and using water as the HTF. They designed a PTC in the Parabolic Calculator 2.0 software and found that the modified tube had the highest value of thermal efficiency (72%).

Additional studies about using rings were presented by Chasemi and Ranjbar [17] and Ahmed and Natarajan [18]. The first group numerically tested the behavior of convective heat transfer in PTR by inserting porous rings at different distances and sizes. The results indicated that the Nu and f increase as the distance between the porous rings decreases and the size of the porous rings increases. The author group presented an investigation into the use of toroidal rings inside the PTR. They found the increase in thermal efficiency to be 3.74%, and the factors of the Nu and f are found to be 2.33 and 1.49, respectively.

The current state of the literature reveals that several studies have been published to evaluate improved heat transfer between PTR walls and HTF using multiple types of inserts. It was noted that there is an improvement in heat transfer by increasing the size or number of these inserts, but at the expense of pressure. Therefore, the primary objective of this work is to develop novel model inserts that can improve the transfer of heat while still ensuring optimal pressure within the PTR. These inserts are hollow cylindrical inserts (HCI) that contain a cross-shaped intersection to allow the HTF to pass through them. Thus, the HTF molecules collide with the inner walls of those inserts, and the cross-shaped shape increases the swirling movement, which also enhances the heat transfer process. To better understand heat transfer techniques, this study provides a numerical simulation of the fluid structure and thermal processes in PTC tubes fitted with inset turbulators using ANSYS Fluent 2020 R2.

The Navier-Stockes equations regulate the phenomena under investigation, and the model of k-ε realizable is the suitable turbulence model since it has been selected in several analogous investigations and was created by Patankar and Spalding [20]:

The continuity:

$\frac{\partial\left(\rho \bar{u}_i\right)}{\partial x_i}=0$    (2)

The momentum:

$\begin{gathered}\frac{\partial\left(\rho \bar{u}_i \bar{u}_j\right)}{\partial x_i} =\frac{\partial}{\partial x_j}\left[\mu\left(\frac{\partial \bar{u}_i}{\partial x_j}+\frac{\partial \bar{u}_j}{\partial x_i}\right)-\frac{2}{3} \mu \frac{\partial \bar{u}_i}{\partial x_i} \delta_{i j}-\rho \bar{u}_i \bar{u}_j\right]-\frac{\partial \bar{P}}{\partial x_i}\end{gathered}$     (3)

The energy:

$\begin{gathered}\frac{\partial\left(\rho \bar{u}_j c_p \bar{T}\right)}{\partial x_j}=\frac{\partial}{\partial x_j}\left(\lambda \frac{\partial \bar{T}}{\partial x_j}+\frac{\mu_T}{\delta_{h, T}} \frac{\partial\left(c_p \bar{T}\right)}{\partial x_j}\right)+ {\left[\bar{\mu}_j \frac{\partial P}{\partial x_j}+\mu\left(\frac{\partial \bar{u}_i}{\partial x_j}+\frac{\partial \bar{u}_j}{\partial x_i}\right)-\frac{2}{3} \mu \frac{\partial \bar{u}_i}{\partial x_i} \delta_{i, j}-\rho \bar{u}_i \bar{u}_j\right] \frac{\partial \bar{u}_i}{\partial x_j}}\end{gathered}$      (4)

The incident solar radiation on the reflector of a PTC is determined by multiplying the aperture area of the collector by the beam solar radiation [8, 10, 16]:

$Q_{ {inc }}=A_a I_b$        (5)

The area of the aperture ($A_a$) is calculated from [21]:

$A_a=\left(W_a-d_o\right) L$      (6)

The useful energy for heating the HTF will be calculated from the average outlet temperature of the HTF that is obtained from the CFD tool; hence, the useful energy is [12, 22]:

$Q_{u s e}=\dot{m} c_p\left(T_{f 0}-T_{f i}\right)$        (7)

The heat transfer coefficient between the PTR and the HTF can be estimated from [10]:

$h=\frac{Q_{ {use }}}{A_a\left(\bar{T}_w-T_b\right)}$       (8)

The balk temperature ($T_b$) of the HTF in Eq. (8) can be calculated from [10]:

$T_b=\frac{T_{f o}-T_{f i}}{2}$     (9)

Then, we can calculate the Nusselt number by [1, 10, 23]:

$N u=\frac{h}{k} d_i$         (10)

For circular tubes, the Reynolds number is given as [24]:

$\mathrm{Re}=\frac{4 \dot{m}}{\pi \mu d_i}$       (11)

The friction factor can be obtained from [23, 25]:

$f=\left(\frac{2 d_i}{L \rho u^2}\right) \Delta p$        (12)

The efficiency of PTC is defined as the amount of useful energy divided by the incident solar energy; it can be calculated from [9, 10, 21]:

$\eta=\frac{Q_{ {use }}}{Q_{ {inc }}}$            (13)

Hence,

$\eta=\frac{\dot{m} c_p\left(T_{f o}-T_{f i}\right)}{A_a I_b}$         (14)

The theoretical Nusselt number ($N u_{t h}$) and the theoretical friction factor ($f_{t h}$) to valid the PT can be estimated using the empirically measured correlation of Dittus-Boelter for a smooth-surfaced tube with turbulent flow [26]:

$N u_{\text {th }}=0.023 \mathrm{Re}^{0.8} \mathrm{Pr}^{0.4}$           (15)

$f_{\text {th }}=\frac{0.184}{\operatorname{Re}^{0.2}}$    (16)

Finally, a common method for determining the thermal enhancement factor (TEF), which is also a performance evaluation criteria (PEC), is by comparing the heat transfer coefficient between each tube and the PT. However, this method fails to account for the critical pressure drops that are essential to the system's sustainability when calculating this parameter directly. So, this factor is modified in order to compare the newly designed tubes with the PT under the identical operating conditions. The TEF is given as [22, 24]:

$T E F=\frac{\left[N u / N u_0\right]}{\left[f / f_0\right]^{1/ 3}}$         (17)

This section showcases the accuracy of the model, which underwent a validation test. More precisely, this work compares the model findings to the experimental correlations established by Dittus and Boelter in 1985. The model results are analysed for different Reynolds numbers by evaluating various mass flow rates ranging from 0.6 kg/s to 1.0 kg/s, while maintaining an input temperature of 300 K.

The results of the Nu of the PT case showed a mean deviation of -2.2% from the results of Eq. (15), as shown in Figure 5, whereas the results of the fraction factor of the PT case showed a mean deviation of 1.3% from the results of Eq. (16), as shown in Figure 6.

The observed variances were found to be negligible, suggesting that the data obtained from the PT exhibits a high level of dependability. Hence, the collected data may be used as a point of reference for assessing the performance of the tube when including the HCI.

5.png

Figure 5. Validation of Nusselt number for various Reynolds numbers

6.png

Figure 6. Validation of the fraction factor for various Reynolds numbers

This work investigates the use of hollow cylindrical inserts inside the PTR. In addition to the PT, a total of eleven modified PTRs have been constructed and subjected to simulation. The study is conducted utilizing the Nusselt number (heat transfer rate), the fraction factor (pressure drop), and the thermal efficiency. The key findings of this study are outlined below:

The hollow cylindrical inserts inside the PTR can dramatically improve the hydraulic-thermal system and increase the temperature field's uniformity.

Based on the simulated results, the studied parameters have an effect on the heat transfer rate, pressure drop, and thermal efficiency, especially the length and number of hollow cylindrical inserts.

The optimal tube has 15 hollow cylindrical inserts with a 40 mm length and a 2 mm thickness. In this tube, the maximum enhancement in the Nusselt number and fraction factor are 1.63 and 1.33 times compared with the PT. Also, the thermal enhancement factor is calculated to be 1.73, and the increase in thermal efficiency is 54%.

As a result, inserts have comparable results in improving the collector's thermal efficiency. This method offers benefits in comparison to the utilization of interior fins since it can be implemented on the current PTC without any alterations to the PTR, which are linked to several operational difficulties. In future investigations, it would be beneficial to compare this study with experimental research to validate and explore additional factors that improve heat transport within the PTR.