Performance and design optimization of a low-cost solar organic Rankine cycle for remote power generation

TL;DR: In this article, the authors describe the design of a solar organic Rankine cycle being installed in Lesotho for rural electrification purpose, which consists of parabolic trough solar thermal collectors, a storages tank, and a small-scale ORC engine using scroll expanders.

About: This article is published in Solar Energy.The article was published on 2011-05-01 and is currently open access. It has received 351 citations till now. The article focuses on the topics: Organic Rankine cycle & Rankine cycle.

Summary

1. Introduction

• Concentrating Solar Power (CSP) systems have been implemented with a variety of collector systems such as the parabolic trough, the solar dish, the solar tower or the Fresnel linear collector.
• Recent studies have tended to emphasize optimization of fluid selection for different cycle architectures and collecting temperatures (Wolpert and Riffat, 1996; McMahan, 2006; Delgado-Torres and Garcia-Rodriguez, 2007, 2010; Bruno et al., 0038-092X/$ -see front matter Ó 2011 Elsevier Ltd.
• An overall efficiency of 4.2% was obtained with evacuated tube collectors and 3.2% with flat-plate collectors.
• Most of the above mentioned studies show that the ORC efficiency is significantly improved by inclusion of a han, 2006; Kane et al., 2003; Prabhu, 2006) .

2. System description

• Researchers at MIT and University of Lie `ge have collaborated with the non-governmental organization STG International for the purpose of developing and implementing a small-scale solar thermal technology utilizing medium temperature collectors and an ORC.
• At the core of this technology is a solar thermal power plant consisting of a field of parabolic solar concentrating collectors and a vapor expansion power block for generating electricity.
• Because no thermal power blocks are currently manufactured in the kilowatt range a small-scale ORC has to be designed for this application.
• Scroll machines show the advantage of being widely available, reliable and with a limited number of moving parts (Zanelli and Favrat, 1994) .
• In the proposed system the cycle heat exchangers (evaporator, recuperator and condenser) are sized in order to obtain the required pinch point and pressure drop.

3. Modeling

• A steady-state model of the system presented in Fig. 2 is developed, for the rating and sizing of the different components and to optimize the working conditions on a nominal point.
• In light of this steady state hypothesis, the storage tank is not modeled.
• The water heating heat exchanger is also neglected, since the main goal of the model is to evaluate the electricity generation potential of the system.
• The solar ORC is model within the EES environment (Klein, 2010 ): a model is developed for each subcomponent and included into a module.

3.1. Parabolic trough model

• The trough module, largely adapted from Forristall (2003) , is a one-dimensional energy balance model around a Heat Collection Element (HCE) of user specified dimensions and materials: Radiation impinges on a reflector element with user-input focal length, reflective coefficient, and aperture.
• The remaining absorbed heat is lost at the HCE outer surface, via convection and radiation back through the annulus (process 3-4), conduction through the envelope (process 4-5), radiation between the envelope and the sky (process 5-7) and convection to the ambient air (process 5-6).
• The different heat transfer relations used to compute the heat flows are provided in Table 1 .
• In order to reduce the magnitude of q 34,rad , a selective coating is applied on the collector tube, maximizing the solar absorptivity and minimizing the infra-red emissivity.
• The different parameters used for the modeling of the solar collected are summarized in Table 2 .

5-6 Free convection

• Churchill and Chu correlation for laminar convection from a horizontal cylinder (Incropera and Dewitt, 2002) .
• The heat exchanger is subdivided into three moving-boundaries zones, each of them being characterized by a heat transfer area A and a heat transfer coefficient U (Quoilin et al., 2010) .
• The heat transfer coefficient U is calculated by considering two convective heat transfer resistances in series (secondary fluid and refrigerant sides).
• The total heat transfer area of the heat exchanger is given by: EQUATION N p being the number of plates, L the plate length and W the plate width.

3.2.1. Single-phase

• Forced convection heat transfer coefficients are evaluated by means of the non-dimensional relationship: EQUATION where the influence of temperature-dependent viscosity is neglected.
• The parameters C, m and n are set according to Thonon's correlation for corrugated plate heat exchangers (Thonon et al., 1995) .
• The pressure drops are computed with the following relation: EQUATION where f is the friction factor, calculated with the Thonon correlation, G is the mass velocity (kg/s m 2 ), q is the mean fluid density, D h is the hydraulic diameter and L is the plate length.

3.2.2. Boiling heat transfer coefficient

• The overall boiling heat transfer coefficient is estimated by the Hsieh correlation, established for the boiling of refrigerant R410a in a vertical plate heat exchanger.
• This heat exchange coefficient is considered as constant during the whole evaporation process and is calculated by (Hsieh and Lin, 2003) : EQUATION where.
• The pressure drops are calculated in the same manner as in Eq. ( 14), using the Hsieh correlation for the calculation of the friction factor.

3.2.3. Heat exchanger sizing

• For a given corrugation pattern (amplitude, chevron angle, and enlargement factor), two degrees of freedom are available when sizing a plate heat exchanger: the length and the total flow width.
• The total flow width is given by the plate width multiplied by the number of channels: EQUATION.
• The two degrees of freedom are fixed by the heat exchange area requirement and the limitation on the pressure drop on the working fluid side: Increasing the total width decreases the Reynolds number.
• This leads to a lower pressure drop and to a higher required heat transfer area, since the heat transfer coefficient is also decreased.
• Therefore, by imposing a pinch point and a pressure drop, it is possible to define the total width and the length of the plate heat exchanger.

3.3. Recuperator model

• The recuperator model is similar to the evaporator model, with one zone (single-phase) instead of three.
• The inputs of the model are the maximum pressure drop and the heat exchanger efficiency, which allows sizing the exchanger in terms of total width and length.

3.4. Expander model

• Volumetric expanders, such as the scroll, screw or reciprocating technologies present an internal built-in volume ratio (r v,in ) corresponding to the ratio between the inlet pocket volume and the outlet pocket volume.
• This can generate two types of losses if the system specific volume ratio is not equal to the expander nominal volume ratio: Under-expansion occurs when the internal volume ratio of the expander is lower than the system specific volume ratio.
• On the other hand, since the device is not optimized for expander applications, experimental results by Lemort et al. showed that the efficiency is reduced by about 10% when working in expander mode (about 60% efficiency) compared to the compressor mode (typically 70%).
• If ambient heat losses are neglected, scroll expanders can be modeled by their isentropic efficiency and by their filling factor, respectively defined by (Lemort et al., 2009b ): EQUATION and EQUATION where V s is the swept volume of the expander and N rot its rotational speed (assumed-to-be-constant at 3000 rpm).
• The polynomial fits are expressed in the following form: EQUATION.

3.4.1. Double-stage expander

• As mentioned above, volumetric expanders are optimized for a given specific volume ratio.
• It appears that the specific volume ratios involved in refrigeration for which the scroll compressors are designed is typically much lower than the specific volume ratios involved in ORC cycles.
• The efficiency also depends on the flow rate going through the expander because a higher flow rate entails a higher output power and makes the constant losses (e.g. friction losses) relatively smaller.
• In the polynomial correlations, the influence of the flow rate is reflected by the dependence in terms of supply vapor density.
• This can be done numerically or analytically.

3.5. Condenser model

• Since air condensers are well-known components in HVAC applications, a simplified model based on manufacturer data (Witt, 2004 ) is used to compute the condenser performance and fan consumption.
• The two inputs are the pinch point, defined as the difference between the condensing temperature and the ambient temperature, and the condensing power.
• Special attention is paid to the fan consumption since it can amount for a non-negligible share of the generated power.
• Two pump consumptions are taken into account: the heat transfer fluid pump and the working fluid pump.
• They are modeled by their isentropic efficiency, defined by (Quoilin et al., 2010) : EQUATION.

4. System performance and fluid comparison

• This section aims at understanding the influence of different cycle parameters on the system and to compare several working fluids and cycle architectures.
• These conditions are typical of the mid-season or winter time conditions in the highlands of Lesotho.
• Three main degrees of freedom are available to control the working conditions of the cycle: the heat transfer fluid flow rate, the working fluid flow rate and the expander swept volume or rotational speed.
• Setting the heat transfer fluid flow rate allows defining the temperature glide in the collector.
• According to Yamamoto et al. (2001) , the superheating should be maintained as low as possible when using high molecular weight working fluids.

4.1. Influence of the temperature glide in the collector

• Modifying the heat transfer fluid flow rate entails two main antagonist effects: on the one hand, the overall temperature level in the collector is modified (Fig. 7 ), which will impact its thermal efficiency via the various heat loss mechanisms.
• On the other hand, changing the fluid flow rate affects the heat transfer coefficient between the heat transfer fluid and the absorber, which also impacts the collector efficiency.
• Fig. 8 shows that the second effect is predominant:.
• For high temperature glides, the overall efficiency is lowered by the low heat transfer coefficient in the collector.
• This value is obtained with the "Golden Section Search" algorithm.

4.2. Influence of the evaporating pressure

• The selection of the optimal evaporating temperature results in a tradeoff between collector efficiency and cycle efficiency.
• An optimal overall efficiency is stated around 150 °C, which is just below the critical point (154 °C for R245fa).
• Fig. 10 shows that with high evaporating temperature levels, smaller swept volumes are needed for both expanders since the inlet densities are higher.
• Fig. 11 also shows that a modification of the evaporating temperature has a very limited effect on the required recuperator area.
• A similar behavior is stated for alternative working fluids.

4.3. Working fluid and architecture comparison

• The critical point of the working fluid should be similar to the target temperature range (100-200 °C).
• In the simulations, R134a is therefore used with single-stage expansion architecture.
• On the contrary, when using a two-stage expansion, the efficiency is limited by the critical temperature or by unrealistic working conditions such as very high specific volume ratios.
• Solkatherm is the fluid showing the highest efficiency, with a maximum close to 8%.
• The bold characters indicate the most advantageous value for each column.

4.4. Influence of the working conditions

• The developments proposed above were conducted for nominal conditions, defined in Section 4.
• The selection of these working conditions can have a non-negligible influence on the simulation results.
• A parametric study is therefore performed to evaluate the influence of the nominal working conditions on the overall efficiency: this study is performed for the SES36 working fluid and an evaporating temperature imposed at 150 °C (third line in Table 4 ).
• Fig. 14 shows the influence of the wind speed, of the ambient temperature and of the solar beam insolation on the system performance.
• Fig. 14 shows that this second influence is predominant: for a 3-30 °C evolution of the ambient temperature, the collector efficiency is increased by 2%, while the ORC cycle efficiency is decreased by 15%, resulting in a 13% decrease of the overall efficiency.

5. Conclusions

• Small-scale solar Organic Cycles are well adapted for remote off-grid areas of developing countries.
• This work focused on the evaluation of the thermodynamic performance of the system.
• Components specifically developed for the target applications (e.g. a high volume ratio expander, optimized for the ORC working fluid) could significantly increase the system performance.
• The comparison between working fluids showed that the most efficient fluid is Solkatherm.
• R245fa also shows a good efficiency and has the advantage of requiring much smaller equipment.

Figures

Fig. 5. Two-stage expander.

Fig. 1. Solar ORC prototype installed by STG in Lesotho.

Fig. 4. Plate heat exchangers sizing process.

Table 3 Evaporator model parameters.

Fig. 11. Required heat transfer area vs. evaporation temperature.

Fig. 12. Specific volume ratio vs. evaporation temperature.

Fig. 3. Heat transfer in the absorber.

Fig. 10. Required swepts volumes vs. evaporating temperature.

Fig. 13. Overall efficiency for different working fluids.

Fig. 6. Global model parameters, inputs and outputs.

Fig. 8. Influence of the HTF temperature glide.

Fig. 7. T–s diagram of the ORC process.

Fig. 9. Influence the evaporation temperature on the performance.

Table 1 Absorber heat transfer models.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Performance and design optimization of a low-cost solar organic rankine cycle for remote power generation" ?

The paper describes the design of a solar organic Rankine cycle being installed in Lesotho for rural electrification purpose. 

Q2. What is the sizing of a solar organic Rankine cycle?

Theptimization of a low-cost solar organic Rankine cycle for remote powerinputs of the model are the maximum pressure drop and the heat exchanger efficiency, which allows sizing the exchanger in terms of total width and length. 

Q3. What are the two main representative variables of the working conditions?

The two selected working conditions are the fluid inlet density qsu and pressure ratio over the expander rp since they turned out to be the two main representative variables of the working conditions. 

Q4. What is the effect of increasing the evaporating temperature on the cycle efficiency?

In the particular case of an ORC using volumetric expanders, increasing the evaporation temperature also increases the under-expansion losses and reduces the cycle efficiency, which constitutes an additional influence. 

Q5. How many degrees of freedom are available when sizing a plate heat exchanger?

For a given corrugation pattern (amplitude, chevron angle, and enlargement factor), two degrees of freedom are available when sizing a plate heat exchanger: the length and the total flow width. 

Q6. What are the advantages of an organic Rankine cycle?

Particularly in the case of small-scale systems, an organic Rankine cycle (i.e. a Rankine cycle using an organic fluid instead of water) may show a number of advantages over the steam cycle. 

Q7. Why is the water heating heat exchanger neglected?

The water heating heat exchanger is also neglected, since the main goal of the model is to evaluate the electricity generation potential of the system. 

Q8. How is the isentropic efficiency of the air condenser calculated?

In order to determine the optimal first-stage pressure ratio, the overall isentropic efficiency is maximized using the following equation:de drp;1 ¼ d drp;1 h1 h3 h1 h3s ¼ 0 ð20Þ 

Q9. What is the effect of ambient temperature on the cycle performance?

The ambient temperature influences the cycle performance in two different ways: the ambient heat losses of the collector are increased with a lower ambient temperature, and the cycle efficiency is increased because of a lower condensing temperature. 

Q10. What is the effect of the wind speed on the efficiency of the system?

The influence of the wind speed is straightforward: the higher the speed, the lower the overall efficiency since the heat transfer coefficient from the collector to the ambient is increased. 

Q11. What is the way to maintain the superheating?

According to Yamamoto et al. (2001), the superheating should be maintained as low as possible when using high molecular weight working fluids. 

Q12. What is the optimal singlestage pressure ratio?

If the expander efficiency was only dependent on the pressure ratio, the optimal singlestage pressure ratio would be defined as the square root of the overall pressure ratio ðrp;1 ¼ rp;2 ¼ ffiffiffiffi rp p Þ 

Q13. What is the effect of the heat transfer fluid flow rate on the collector?

Modifying the heat transfer fluid flow rate entails two main antagonist effects: on the one hand, the overall temperature level in the collector is modified (Fig. 7), which will impact its thermal efficiency via the various heat loss mechanisms. 

Q14. How much can be achieved with a real expander?

With conservative hypotheses, and real expander efficiency curves, it was shown that an overall electrical efficiency between 7% and 8% can be reached. 

Q15. What is the effect of the low heat transfer coefficient in the collector?

Sol. Energy (2011), doi:10.1016/j.solener.2011.02.010efficiency is lowered by the low heat transfer coefficient in the collector. 

Q16. What is the effect of the evaporator on the flow area?

A similar effect is stated for the heat transfer area of the evaporator (Fig. 11): for a given pressure drop, a higher vapor density allows reducing the passage area, which in turn reduces the required area. 

Q17. What is the efficiency of the n-pentane working fluid?

This plant uses n-pentane as working fluid and shows an overall efficiency of 12.1%, for a collector efficiency of 59% (Canada et al., 2004). 

Q18. What is the effect of changing the flow rate on the collector efficiency?

On the other hand, changing the fluid flow rate affects the heat transfer coefficient between the heat transfer fluid and the absorber, which also impacts the collector efficiency.