Multi-objective and thermodynamic optimisation of a parabolic trough receiver with perforated plate inserts

doi:10.1016/j.applthermaleng.2014.12.018

Applied Thermal Engineering

Volume 77, 25 February 2015, Pages 42-56

https://doi.org/10.1016/j.applthermaleng.2014.12.018 Get rights and content

Highlights

•
The study focuses on the use of perforated plate inserts in a parabolic trough receiver.
•
Multi-objective and thermodynamic optimisation of the receiver is investigated.
•
Influence of Reynolds numbers, fluid temperature and insert geometry is presented.
•
Pareto optimal solutions and optimal insert configurations are presented.
•
Optimal Reynolds at which entropy generation is a minimum is obtained and presented.

Abstract

In this paper, multi-objective and thermodynamic optimisation procedures are used to investigate the performance of a parabolic trough receiver with perforated plate inserts. Three dimensionless perforated plate geometrical parameters considered in the optimisation include the dimensionless orientation angle, the dimensionless plate diameter and the plate spacing per unit meter. The Reynolds number varies in the range 1.02 × 10⁴ ≤ Re ≤ 1.36 × 10⁶ depending on the fluid temperature. The multi-objective optimisation was realised through the combined use of computational fluid dynamics, design of experiments, response surface methodology and the Non-dominated Sorted Genetic Algorithm-II. For thermodynamic optimisation, the entropy generation minimisation method was used to determine configurations with minimum entropy generation rates.

Introduction

Heat transfer enhancement in heat exchangers and in other thermal applications is of significant importance. Not only does it result in energy savings but has other benefits depending on the application under consideration such as heat exchanger weight and size reduction, reduction in device temperatures and reduction in the temperature difference between process fluids.

In parabolic trough receivers, heat transfer enhancement has potential to reduce absorber tube circumferential temperature gradients [1], [2] and also reduce absorber tube temperatures thus lower receiver thermal loss and improved receiver thermal performance [3], [4], [5]. Moreover, as parabolic trough systems with high optical efficiencies and high concentration ratios become feasible [6], [7], high heat fluxes and high absorber tube temperature gradients will result. As such, improved heat transfer performance will be essential to minimise absorber tube temperature gradients as well as improve the performance and reliability of the receiver at these high concentration ratios. More still, an increase in concentration ratios leads to increased entropy generation rates due to the increased finite temperature differences as concentration ratios increase [8], [9]. As such, heat transfer enhancement can also act to minimise the entropy generation in the receiver. For these reasons, heat transfer enhancement in parabolic trough receivers has received considerable attention in the last few decades.

Passive heat transfer enhancement techniques are widely researched and applied in many industrial applications since they require no direct power input as compared to active techniques. Several researchers have applied some of the passive heat transfer enhancement techniques to improve the performance of parabolic trough receivers. Reddy et al. [10] numerically analysed a receiver with various porous and longitudinal fin geometries. Ravi Kumar and Reddy [11] investigated the performance of the receiver with a porous disc. Different angles of orientation, porous disc heights and distances between the consecutive discs were considered. Muñoz and Abánades [2] analysed an internally helically finned absorber tube to improve the thermal performance of the receiver and minimise the temperature gradients in the receiver's absorber tube. Recently Cheng et al. [12] analysed the heat transfer enhancement of parabolic trough receivers using unilateral longitudinal vortex generators. In these studies, the potential for improved heat transfer performance in receivers with heat transfer enhancement is demonstrated.

Most heat transfer fluids used in parabolic trough receivers decompose rapidly at temperatures above 400 °C [13], [14], leading hydrogen permeation in the receiver's annulus space which exacerbates receiver heat loss. Therefore, heat transfer enhancement mechanism in the receiver's absorber tube should avoid any hot spots and absorber tube surface modification should be done while taking into account likely thermal stresses. Therefore, use of tube inserts appears to be a sure way of avoiding temperature hotspots and thermal stress in the absorber tube. Porous media or perforated inserts present several benefits when compared with solid inserts such as lightweight, low fluid friction and potential for forcing uniform flow distribution [15]. In this study, the use of perforated plate inserts for heat transfer enhancement in a parabolic trough receiver is investigated.

However, besides improving heat transfer performance, heat transfer enhancement techniques also result in an increase in fluid friction. Therefore, to optimise the performance a particular heat transfer enhancement technique, increasing the heat transfer and reducing fluid friction should be considered at the same time. This presents a multi-objective optimisation problem, in which the heat transfer performance is to be maximised and the fluid friction is to be minimised. In this case, the two objectives are conflicting with each other such that as the heat transfer performance increases the fluid friction also increases. There is no single design that is “best” for all the objectives when both objectives are of the same importance.

In such a case, a set of best solutions often called non-dominated solutions or Pareto optimal solutions [16], [17] is sought, such that selecting any one solution in place of another sacrifices quality of one of the objectives while improving the other objective. Genetic algorithms are suited for optimisation of these classes of problems in many applications including fluid flow and heat transfer problems [18]. Detailed description of genetic algorithms and their suitability for use in optimisation of multi-objective problems is provided in Refs. [17], [18]. Researchers who have used genetic algorithms for multi-objective optimisation of heat transfer and fluid flow problems include Kim et al. [19], Ndao et al. [20], Cortes-Quiroz et al. [21], [22] and Karathanassis et al. [23]. Other authors have applied multi-objective optimisation to thermal systems such as refrigeration systems [24] and energy storage systems [25], [26], [27].

Most investigations on heat transfer enhancement use the first law of thermodynamics to characterise the resulting thermo-hydraulic performance. Studies that use the second law of thermodynamics to investigate both the thermo-hydraulic and thermodynamic performance of heat transfer enhancement techniques are not wide spread. The second law of thermodynamics provides a means of specifying the quality of the available energy. In this investigation, we use both multi-objective optimisation and thermodynamic optimisation to optimise the heat transfer, fluid friction and thermodynamic performance of a parabolic trough receiver with perforated plate inserts.

Section snippets

Physical model and computational domain

The physical model of the receiver with perforated plates under consideration in this study is shown in Fig. 1(a) and (b). Similar to the conventional parabolic trough receivers, the space between the absorber tube and the glass cover is considered evacuated. Thus, only the radiation heat loss takes place between the absorber tube and the glass cover.

From Fig. 1(a), three geometrical parameters of the perforated plate are defined: the spacing between the two consecutive perforated plates (p),

Governing equations

Due to the high heat fluxes on the receiver's absorber tube, high flow rates are usually used for better heat transfer performance. Therefore, we considered the flow inside the absorber tube to be steady-state and fully developed turbulent. As such, the governing equations are:

Continuity equation $\frac{\partial (ρ u_{i})}{\partial x_{i}} = 0$

Momentum equation $\frac{\partial}{\partial x_{j}} (ρ u_{i} u_{j}) = - \frac{\partial P}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [μ (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) - \frac{2}{3} μ_{} \frac{\partial u_{i}}{\partial x_{i}} δ_{i j} - ρ \bar{u_{i}^{'} u_{j}^{'}}] + S_{m}$

Energy equation $\frac{\partial}{\partial x_{j}} (ρ u_{j} c_{p} T) = \frac{\partial}{\partial x_{j}} (λ \frac{\partial T}{\partial x_{j}} + \frac{μ_{t}}{σ_{h, t}} \frac{\partial (c_{p} T)}{\partial x_{j}}) + u_{j} \frac{\partial P}{\partial x_{j}} + [μ_{} (\frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) - \frac{2}{3} μ_{} \frac{\partial u_{i}}{\partial x_{i}} δ_{i j} - ρ \bar{u_{i}^{'} u_{j}^{'}}] \frac{\partial u_{i}}{\partial x_{j}}$ where $- ρ u_{i}^{'} u_{j}^{'}$

Multi-objective optimisation

In its general form, a multi-objective optimisation problem can be written as [17]: $\begin{matrix} Minimise / maximise & f_{m} (x), & m = 1,2, \dots \dots \dots, M; \\ Subject to & g_{j} (x) \geq 0 & j = 1,2, \dots \dots \dots, J; \\ h_{k} (x) = 0 & k = 1,2, \dots \dots \dots, K; \\ x_{i}^{(L)} \leq x i \leq x i^{(U)} & i = 1,2, \dots \dots \dots, n . \end{matrix}$ where f_m(x) is the objective function, M is the number of functions to be optimised. A solution x is a vector of n decision variables such that x = (x₁, x₂, … , x_n)^T. g_j(x) and h_k(x) are constraint functions with J representing the inequality constraints and K the equality constraints. The last set

Validation of numerical results

Our numerical model was validated in a number of steps. First, we have compared our results with experimental data from Dudley et al. [28] for temperature gain and collector efficiency to validate that our receiver model is accurate. Good agreement was achieved for both the temperature gain and the collector efficiency with a maximum deviation of less than 8% as shown in Table 3.

The perforated plate model was validated using data from Gan and Riffat [43]. The variation of the pressure

Conclusion

In the present study, the use of multi-objective optimisation and thermodynamic optimisation in arriving at optimal solutions for a receiver with perforated plate inserts was presented. In the multi-objective optimisation part, the NSGA-II algorithm was used to obtain Pareto optimal solutions for the Nusselt number and pressure drop. Using a goal-based, weighted, aggregation-based decision ranking method, representative design candidates were obtained and presented.

In the thermodynamic

Acknowledgements

The funding received from NRF, TESP, and Stellenbosch University/University of Pretoria, SANERI/SANEDI, CSIR, EEDSM Hub and NAC is duly acknowledged and appreciated.

References (47)

J. Muñoz et al.
Analysis of internal helically finned tubes for parabolic trough design by CFD tools
Appl. Energy
(2011)
Y. He et al.
A MCRT and FVM coupled simulation method for energy conversion process in parabolic trough solar collector
Renew. Energy
(2011)
A. Schweitzer et al.
ULTIMATE TROUGH^® – Fabrication, erection and commissioning of the world's largest parabolic trough collector
Energy Procedia
(2014)
A. Mwesigye et al.
Numerical investigation of entropy generation in a parabolic trough receiver at different concentration ratios
Energy
(2013)
A. Mwesigye et al.
Minimum entropy generation due to heat transfer and fluid friction in a parabolic trough receiver with non-uniform heat flux at different rim angles and concentration ratios
Energy
(2014)
K. Ravi Kumar et al.
Thermal analysis of solar parabolic trough with porous disc receiver
Appl. Energy
(2009)
Z.D. Cheng et al.
Numerical study of heat transfer enhancement by unilateral longitudinal vortex generators inside parabolic trough solar receivers
Int. J. Heat Mass Transf.
(2012)
J. Li et al.
Hydrogen permeation model of parabolic trough receiver tube
Sol. Energy
(2012)
Z.F. Huang et al.
Enhancing heat transfer in the core flow by using porous medium insert in a tube
Int. J. Heat Mass Transf.
(2010)
A. Konak et al.
Multi-objective optimization using genetic algorithms: a tutorial
Reliab. Eng. Syst. Saf.
(2006)

H. Kim et al.

Multi-objective optimization of a cooling channel with staggered elliptic dimples

Energy

(2011)

S. Ndao et al.

Multi-objective thermal design optimization and comparative analysis of electronics cooling technologies

Int. J. Heat Mass Transf.

(2009)

C.A. Cortes-Quiroz et al.

Analysis and multi-criteria design optimization of geometric characteristics of grooved micromixer

Chem. Eng. J.

(2010)

I.K. Karathanassis et al.

Multi-objective design optimization of a micro heat sink for Concentrating Photovoltaic/Thermal (CPVT) systems using a genetic algorithm

Appl. Therm. Eng.

(2013)

M. Aminyavari et al.

Exergetic, economic and environmental (3E) analyses, and multi-objective optimization of a CO2/NH3 cascade refrigeration system

Appl. Therm. Eng.

(2014)

A. Shirazi et al.

Thermal–economic–environmental analysis and multi-objective optimization of an ice thermal energy storage system for gas turbine cycle inlet air cooling

Energy

(2014)

M. Navidbakhsh et al.

Four E analysis and multi-objective optimization of an ice storage system incorporating PCM as the partial cold storage for air-conditioning applications

Appl. Therm. Eng.

(2013)

S. Sanaye et al.

Four E analysis and multi-objective optimization of an ice thermal energy storage for air-conditioning applications

Int. J. Refrig.

(2013)

T. Shih et al.

A new k–ε eddy viscosity model for high Reynolds number turbulent flows

Comput. Fluids

(1995)

O. García-Valladares et al.

Numerical simulation of parabolic trough solar collector: improvement using counter flow concentric circular heat exchangers

Int. J. Heat Mass Transf.

(2009)

S.C. Mullick et al.

An improved technique for computing the heat loss factor of a tubular absorber

Sol. Energy

(1989)

S.V. Patankar et al.

A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows

Int. J. Heat Mass Transf.

(1972)

G. Gan et al.

Pressure loss characteristics of orifice and perforated plates

Exp. Therm. Fluid Sci.

(1997)

Cited by (77)

Performance evaluation of a parabolic trough collector with a uniform helical wire coil flow insert
2024, Results in Engineering
Solar energy is an extremely useful and dependable renewable energy source for meeting our society's diverse energy demands. Solar concentrator-based energy systems are currently the most efficient methods of using solar energy. Among these technologies, the parabolic trough collector is a mature and effective concentrating solar power technology with a wide range of real-world applications using solar alone or in combination with other energy sources. Flow insert is a potential approach for improving parabolic trough solar collector performance through enhanced heat transfer and heat absorption. The purpose of this study is to determine the feasibility of using a uniform helical wire coil flow insert in the LS-2 parabolic trough solar collector module. A computational fluid dynamic model developed in Ansys 18.1 is used in the current investigation. A uniform helical wire coil flow insert is modeled and compared with the plain tube without any insert inside it. Flow analysis, overall efficiency, exergy efficiency, and thermal efficiency are compared in the evaluation process. The overall efficiency and exergy efficiency of the parabolic trough collector are the most critical criteria in determining its performance. The parabolic trough collector is examined using a range of inlet fluid temperatures ranging from 303 K to 603 K and a volumetric flow rate of 50 L per minute to 250 L per minute. The pumping work is found to be the lowest, indicating that the increase in pressure drop has a negligible effect on the overall system performance. For the flow rate of 50 L per minute and inlet heat transfer fluid temperature of 303 K, the overall, exergy and thermal efficiency using a uniform helical wire coil flow insert are found to be 2.07 %, 2.1 %, and 2.2 %, respectively.
Thermal performance analysis of eccentric double-selective-coated parabolic trough receivers with flat upper surface
2024, Renewable Energy
The Parabolic trough collector (PTC) system combined with molten salt energy storage system has gathered increasing attention owing to its advantages of high operating temperature and stable power output. However, the substantial heat loss experienced by parabolic through receivers (PTR) under high temperatures imposes limitations on the thermal efficiency and power generation potential of the PTC system. In this study, a novel eccentric double-selective-coated parabolic trough receiver is proposed. The upper surface of the receiver is flattened to further reduce radiation heat loss. Various distances from collector focus are explored to determine the most suitable opening angle of secondary selective coating, ensuring the highest thermal efficiency. The results show that, although the eccentricity causes partial optical loss, the reduced upper surface area and the resultant larger secondary coating opening angle contribute to a significant reduction in heat loss and an improved thermal efficiency of the novel receiver. The thermal efficiency of the new absorber can be improved by up to 20.59 % (under direct normal irradiance of 600W/m² and a receiver surface temperature of 600 °C). Furthermore, the higher the emissivity and the lower the absorptivity of the solar selective coating, the better the performance of the novel absorber tube.
Impact of vortex generator, magnetic field, and magnetic two-phase hybrid nanofluid on the performance of a dual-tube heat exchanger: Hydrodynamic and exergy analyses
2023, Engineering Analysis with Boundary Elements
In this study, a three-dimensional model of a counter-flow dual-tube heat exchanger is developed. The heat exchanger is equipped with a vortex generator, and the working fluid used is a hybrid nanofluid consisting of water and iron-copper oxide. The effects of using the hybrid nanofluid and pure water are investigated. Turbulent flow conditions are assumed within a Reynolds number (Re) range of 30,000 to 48,000, employing the realizable k-ε turbulence model. The coupled algorithm is employed to solve the velocity and pressure equations, and the equations are discretized using the least square method. The vortex generator is utilized with various pitch ratios (Ω). Furthermore, the magnetic field affects the middle section of the inner tube, with Hartmann numbers (Ha) of 35, 65, 95, and 125. The study reveals that an increase in the volume fraction (φ) positively impacts the exergy of the heat exchanger, while an enhancement in Ω negatively influences it. Furthermore, the energy efficiency improves with increasing Re. By applying the magnetic field, the maximum power of the system in producing work corresponds to Re = 36,000 because η_ex is reduced when Re > 36,000. At all values of Re, the increase in Ha improves η_ex.
An innovative small-sized double cavity PTC under investigation and comparison with a conventional PTC
2022, Sustainable Energy Technologies and Assessments
Citation Excerpt :
In study [9] a PTC with an integrated wavy-shaped metal tape was examined and it was found that the use of the tape reduces the thermal losses by approximately 18%, leading to an enhanced thermal efficiency. A novel insert geometry was introduced in study [10]. In particular, several perforated plates parallel among them were used as flow inserts inside the absorber tube of a PTC for enhancing the thermal performance.
In this study, a novel evacuated double cavity receiver parabolic trough collector is being examined in detail and compared with a conventional geometry. The collectors were investigated optically and thermally. Firstly, the optical efficiency of the cavity configuration was optimized and a tracking error analysis was conducted. Next, the collectors were optimized regarding the mass flow rate and the thermal analysis followed. Syltherm-800 was used as the working medium of this analysis. Several different inlet temperatures were examined (20°C–300°C) considering the optimum volumetric flow rate in each case. The comparison showed a clear prevalence of the suggested collector in the whole operating range with the mean enhancement reaching approximately 16%. These geometries were, also, compared with the same to the double cavity geometry, where the inner cavity surfaces are non-selective. The results indicated that the non-selective configuration exceeds the conventional one in thermal performance by 10.73% on average. The simulation results were, also, validated with several theoretical models and a sufficient agreement was achieved. In particular, the deviations were found to be less than 5% in both models for the Nusselt number and the Darcy friction factor. SolidWorks was used as the design and the simulation tool of this study.
Improving the efficiency of parabolic solar collector (PSC) containing magnetic nanofluid with absorber pipe equipped with square twisted turbulator
2022, Sustainable Energy Technologies and Assessments
The effects of a twisted tape (TWT) with a square cut within the collector absorber pipe on heat transfer between the fluid and the absorber pipe, as well as energy and exergy efficiency, are quantitatively studied. Nanofluids (NFs) 66 -Therminol ${Fe}_{3} O_{4}$ with nanoparticles volume fraction (NPVF) of 1%, 2%, and 4% is used as the working fluid. For numerical simulation SIMPLEC algorithm, FVM have been used. Turbulent flow simulations are performed using the RNG k-ε model at three Re of 15000, 25000, and 35000. When compared to a pipe without a tape, the findings showed that using a square TWT improves the rate of heat transfer. The maximum thermal performance coefficient occurs at Re of 15,000 and a NPVF of 4%. The findings show that employing NPs suspended in the base fluid improves the solar collector's energy and exergy efficiency, with a volume fraction of 4% providing the greatest performance. The maximum PEC occurs at Re of 15,000 and a NPVF of 4%, which is equal to 1.59, indicating an increase of 67% compared to the performance of the absorber pipe with the same working fluid and without a TWT.
Enhancing the thermal efficiency of parabolic trough collector using rotary receiver tube
2022, Sustainable Energy Technologies and Assessments
The performance of the parabolic trough collector is studied experimentally using a rotary receiver tube. The parameters such as temperature increase, friction factor and thermal efficiency at receiver tube speed of 0, 2 and 4 rpm are investigated. Tests were performed for varied inlet temperatures and flow rates. From the achieved results, it is found that the friction factor increases dramatically due to the usage of rotary receiver tube. Furthermore, for receiver tube speeds of 4, 2 and 0 rpm the maximum values of temperature differences are found to be 18.5 °C, 12.5 °C and 4.0 °C respectively. It is found that the enhancement of the thermal efficiency is due to decreasing the inlet temperature and by increasing the flow rate. Moreover, the highest thermal efficiency improvement of the collector is due to the usage of rotary receiver tube. Maximum efficiency improvement for a tube speed of 4 and 2 rpm is found to be 190.3% and 158.6% respectively in comparison with the stationary receive tube.

View all citing articles on Scopus

View full text

Research paperMulti-objective and thermodynamic optimisation of a parabolic trough receiver with perforated plate inserts

Highlights

Abstract

Introduction

Section snippets

Physical model and computational domain

Governing equations

Multi-objective optimisation

Validation of numerical results

Conclusion

Acknowledgements

Appl. Energy

Renew. Energy

Energy Procedia

Energy

Energy

Appl. Energy

Int. J. Heat Mass Transf.

Sol. Energy

Int. J. Heat Mass Transf.

Reliab. Eng. Syst. Saf.

Energy

Int. J. Heat Mass Transf.

Chem. Eng. J.

Appl. Therm. Eng.

Appl. Therm. Eng.

Energy

Appl. Therm. Eng.

Int. J. Refrig.

Comput. Fluids

Int. J. Heat Mass Transf.

Sol. Energy

Int. J. Heat Mass Transf.

Exp. Therm. Fluid Sci.

Research paper
Multi-objective and thermodynamic optimisation of a parabolic trough receiver with perforated plate inserts