## 1. Introduction

The compound parabolic concentrator (CPC) is a non-imaging concentrator that utilizes the principle of edge optics. Its history goes back to the late 1950s, when Tabor proposed the concept of the free-tracking concentrating static concentrator [

1]. Winston et al. [

2] initiated research on non-imaging concentrators in the late 1960s. In 1974, the U.S. Argonne National Laboratory established research on non-imaging concentrators, naming these concentrators as compound parabolic concentrators (CPCs), also establishing the utilization principles of CPCs [

3,

4]. The basic design of the CPC employed a flat absorber, but a circular tube groove was later proposed [

3]. Different additions to the original CPC design have been proposed such as a secondary compound parabolic reflection [

5], an optimal gap between the concentrator and receiver [

6], non-imaging condensers [

7], internal cusp reflectors with a heat pipe [

8], truncated CPCs [

9], and W-shaped and multi V-shaped surfaces [

10,

11].

Practical design issues such as the use of vacuum technology with the CPC have been analyzed to raise the working temperature [

12,

13]. With fluid temperatures up to 100 °C, no vacuum would be necessary [

12,

13], but if using a glass cover, a high thermal efficiency could be reached [

14]. At low concentration ratios, the effects of the incidence angle on the thermal efficiency could be less than 10% [

15], which would be beneficial for stationary applications. Studies to optimize CPCs through different thermal-optical analyses are ample, e.g., a CPC with a tubular receiver [

16,

17] and the reduction of slit optical losses of CPCs [

18,

19], efficiency enhancement with a vacuum tube receiver [

20], and multiple-row low-concentration CPCs, which could reach a thermal efficiency of 50% at 150 °C [

21].

Though CPC research and development has been extensive, in the 1980s in particular, the literature on CPCs with tubular receivers is more limited. Similarly, CPC technology has so far made only a modest market impact, though the potential for low-temperature industrial and residential applications is considerable [

22,

23,

24]. However, the interest in industrial solar low- and intermediate-temperature heat utilization has recently increased [

25] for which reason the CPC technology would again be highly relevant. The CPC shows a quite broad application range for solar thermal utilization: Stationary CPCs are applicable for the medium-temperature range (60 °C–150 °C), and tracking CPCs for the medium- and high-temperature range (100 °C–250 °C) [

26].

Table 1 shows the positioning of the CPC among the different collector types.

CPC technology is typically offered with a tubular absorber or flat absorber. The tubular absorber CPC is more suitable for fluid media and for heating a fluid, also yielding a higher heat collection efficiency. Therefore, the focus of this review is on the tubular absorber CPC.

A comprehensive review of the tubular absorber CPC is carried out in this paper. The structure of the paper is as follows: In

Section 2, design considerations of the tubular absorber CPC are presented such as the formula curve, gap design, truncation, and deformation of the CPC. In

Section 3, the external/internal concentrating tubular absorber CPC is presented. The structure of the tubular absorber CPC is discussed in

Section 4. Applications including high-temperature solar thermal utilization, building-integrated solar systems (BISS), photovoltaics (PV)/T systems, refrigeration, hydrogen production, distillation/desalination, and photo-degradation of wastewater are reviewed in

Section 5. Conclusions are presented in

Section 6.

## 2. Design Considerations of Tubular Absorber CPC

This section focuses on the issues that need to be considered in the design of the tubular absorber CPC. First, the design curve formula of the CPC is determined. Based on this, the design of gaps and truncation of the CPC will be discussed, reflecting the application for which the CPC is used. It is also necessary to check that the production process is able to match with the allowable optical error of the CPC.

#### 2.1. Formula Curve of Tubular Absorber CPC

The two-dimensional curve of the tubular absorber CPC includes an involute segment and curved segment. There are mainly two types of curves for the tubular absorber CPC (

Figure 1), in which the involute segment is similar and the curved segment is different. Winston [

4] and Ortabasi et al. [

8] proposed the first type of curve and derived its curve formula (

Figure 1a). Another type uses a flat CPC curve by replacing the flat receiver with a tubular absorber and an involute segment. The other side of the curve is a part of the parabola (

Figure 1b). This paper analyzes the CPC based on the first type of curve, which is called the “ideal concentrator.” It is superior to the second type of curve in terms of height, concentration ratio, and average number of reflections.

A CPC reflects all light within the maximum half acceptance angle

θ_{max} to the receiver, where

θ_{max} is defined as the maximum angle between the incident light, which can reach the receiver, and the axis of symmetry of the CPC. Each CPC has a theoretical maximum concentration ratio, which can be calculated from

θ_{max} (here, 2-D geometry) [

4]:

The profile curve of a tubular absorber CPC contains an involute segment and a curve segment. The coordinates of the CPC curve are given by Equations (2) and (3) [

8].

For involute segments,

I(

t) is given by Equation (4):

For curve segments,

I(

t) is given by Equation (5):

where

r is the radius of the tubular absorber,

t is angle variable parameter, and

θ_{a} is acceptance half angle.

#### 2.2. Gap Design of Tubular Absorber CPC

In practical applications, the CPC absorber and the reflector cannot be in contact as physical contact could cause heat losses through heat conduction and the thermal stress could deform the reflector. In addition, for an external concentrating tubular absorber CPC, contact is not possible, due to the vacuum collector tube used [

18]. Therefore, a gap between the bottom of the absorber and the reflector for the tubular absorber CPC is required, which will, however, reduce the concentration ratio and cause some loss of solar radiation. Previous studies have shown that the gap loss of solar energy varies from 5% to 20% [

10,

11,

12,

14]. Rabl [

12] proposed three ways to create gaps: (a) Reducing the radius of the tubular absorber; (b) cutting the sharp corner of the reflector; (c) changing the shape of the absorber (

Figure 2). In practice, the method of moving the absorber up is mostly employed (

Figure 2d). Mcintire proposed a W-shaped curve instead of the sharp corner of the reflector to avoid gap loss, but this reduced the concentration ratio by 15% [

10,

11]. Ortabasi [

8] proposed another method to form a gap in the CPC by changing the starting point of the involute.

Wang et al. [

27] proposed a tubular absorber CPC with a V-shaped profile at the bottom of the reflector based on the edge-ray principle (

Figure 3 and

Figure 4). They also studied its key parameters such as geometrical optical efficiency, reflectance, and transmittance and absorption ratio, based on geometrical optics and ray tracing. They showed how to create a gap in the CPC based on the size of the designed CPC gap, and proved that a CPC with a V-shaped profile has a high optical efficiency and good application prospects. The overall efficiency is defined as the product of the relative concentration ratio and the gap efficiency. As the overall efficiency is a relative value, some methods may have an efficiency greater than unity under the condition of reducing the acceptance range.

#### 2.3. Truncation of Tubular Absorber CPC

The complete CPC, especially with a small acceptance angle, has a larger height-to-width ratio and needs more material for the reflector than the general collectors. The reflectors at both ends of the CPC have little effect on the concentration of solar radiation. Therefore, the height of the CPC and the material of the reflector can be reduced by truncating the CPC.

Some researchers have studied the truncation of CPCs [

4,

5,

8], and presented a relationship between the truncation ratio and length to aperture ratios with different acceptance angles. Winston [

4] studied the truncation of CPCs based on the average number of reflections. The recommended truncation ratio can be selected based on the

N_{min} curve in

Figure 5, where

C is the geometric concentration ratio and

N_{min} is the reference average number of reflections.

The truncation ratio is defined as the ratio of

h_{c}_{’} to

h_{c}, as shown in

Figure 6 [

29].

Yu et al. presented the relationship between the concentrating ratio, the acceptance angle, and the truncation ratio [

27,

30] (

Figure 7). It can be seen from the figure that the larger the truncation ratio, the greater influence of the truncation on the concentration ratio. When the CPC truncation ratio is 0.4, the loss of concentration ratio is less than 5% [

30].

#### 2.4. Deformation of Tubular Absorber CPC

Errors may occur when the CPC is manufactured and installed, which can affect the concentrating effect of the CPC. Rabl [

12] showed that for a tubular absorber CPC with radius

r, when the displacement deviation of the receiver or reflector is

g, the optical loss is as follows.

Xu et al. [

31] studied the deformation of a tubular absorber CPC by the Monte Carlo ray-tracing method, and analyzed the effects of the deformation factor such as the rotation of the reflector, translation of the reflector, and position offset of the absorber. Their research showed that when the rotation and translation deviation of the reflector reached a critical value, the optical loss significantly increased, and the effect of downward, rightward, and leftward offsets of the absorber was greater than that of the upward offsets (

Figure 8,

Figure 9 and

Figure 10,

C is the concentration ratio,

Ct is the CPC truncation ratio,

ω is the rotation angle of the reflector,

κ is a dimensionless parameter of reflector translation,

λu is a dimensionless number of absorber position offset, and

θ is the angle of incident light).

#### 2.5. Summary

Based on the above analysis, the following conclusions can be made:

- (1)
For the formula curve of the tubular absorber CPC, it is recommended to choose the curve formula in

Figure 1a, and Equations (2)–(5).

- (2)
The CPC gap should be designed according to the size of the gap given in

Table 2.

- (3)
For the truncation of a tubular absorber CPC, ratios in

Table 3 are recommended.

- (4)
The design, processing, and installation errors of the CPC should be limited to a range defined by Monte Carlo ray-tracing calculations, which can significantly reduce the impact of these errors on the CPC performance.

## 6. Conclusions

A comprehensive review on recent research progress and developments of the tubular absorber CPC has been presented. The concept and design principles have been presented, including recent modifications and analyses on two-dimensional profile types, as well as recent new design concepts and improvements on the CPC structure.

Based on the state-of-the-art on solar thermal applications of the tubular absorber CPC in both domestic and industrial aspects, the main progress on tubular absorber CPC applications was presented.

The main observations from the review are the following:

- (1)
The tubular absorber CPC is diverse, efficient, systematic, and especially suitable for industrial and other medium-temperature heat applications;

- (2)
There is no “perfect CPC”, as the acceptance angle and the concentration ratio cannot be improved at the same time. Therefore, the most suitable CPC curve and structure form need to be chosen according to the purpose and requirements of the application;

- (3)
Regarding the efficiency of tubular CPCs, due to differences in the calculation methods and basis of efficiency in the literature, no comparative analysis was made in this article, but improving the efficiency of the CPC will still be an important research direction;

- (4)
Better integration of the tubular CPC with the heat utilization system, while reducing the manufacturing cost and system integration cost, will be important in order to further commercialize the CPC technology;

- (5)
For low- and medium-temperature collectors, reducing the investment costs and maintenance and improving operational stability will be important. Through the scaling-up and standardization of CPC products, these challenges will also be gradually mitigated;

- (6)
The research interest on tube CPC collectors, heat pipe CPCs, internal and external concentrating combined CPC, and TCPC modules is increasing;

- (7)
Main applications will include building-integrated solar systems, industrial thermal energy-saving transformation, and refrigeration applications.