Scholarly article on topic 'Parametric Study of Supercritical Rankine Cycle and Earth-air-heat-exchanger for Low Temperature Power Generation'

Parametric Study of Supercritical Rankine Cycle and Earth-air-heat-exchanger for Low Temperature Power Generation Academic research paper on "Earth and related environmental sciences"

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Abstract of research paper on Earth and related environmental sciences, author of scientific article — R. Vidhi, D.Y. Goswami, E.K. Stefanakos

Abstract In this paper, a supercritical cycle coupled with an earth-air heat-exchanger (EAHE) has been studied for power generation from low to medium temperature heat sources. A number of organic refrigerants (R32, R125, R134a, R143a, R170 and R218) were studied as working fluids. The temperature range of 125-200°C was considered for the heat source while ambient air, cooled using EAHE, was used as the sink. The effect of various parameters (operating pressure, outlet temperature of the heat source and geometry of the EAHE) on the efficiency of the thermodynamic cycle was studied. An optimum operating pressure was obtained for all the fluids studied, except R32. Practical limitations, such as vapor quality in the turbine and pinch point in the heat exchangers, were considered in the analysis. Sinusoidal yearly variation in daily average air temperature was also taken into account in modelling the system. The soil temperature increased only for a short distance around the pipe while the bulk temperature remained unaffected.

Academic research paper on topic "Parametric Study of Supercritical Rankine Cycle and Earth-air-heat-exchanger for Low Temperature Power Generation"

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Energy Procedía 49 (2014) 1228 - 1237

SolarPACES 2013

Parametric study of supercritical Rankine cycle and earth-air-heat-exchanger for low temperature power generation

R. Vidhia*, D. Y. Goswamia, E. K. Stefanakosa

aClean Energy Research Center, University of South Florida, 4202 E Fowler Avenue, Tampa, 33620 USA

Abstract

In this paper, a supercritical cycle coupled with an earth-air heat-exchanger (EAHE) has been studied for power generation from low to medium temperature heat sources. A number of organic refrigerants (R32, R125, R134a, R143a, R170 and R218) were studied as working fluids. The temperature range of 125-2000C was considered for the heat source while ambient air, cooled using EAHE, was used as the sink. The effect of various parameters (operating pressure, outlet temperature of the heat source and geometry of the EAHE) on the efficiency of the thermodynamic cycle was studied. An optimum operating pressure was obtained for all the fluids studied, except R32. Practical limitations, such as vapor quality in the turbine and pinch point in the heat exchangers, were considered in the analysis. Sinusoidal yearly variation in daily average air temperature was also taken into account in modelling the system. The soil temperature increased only for a short distance around the pipe while the bulk temperature remained unaffected.

© 2013 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selection andpeer reviewbythescientific conference committee ofSolarPACES2013underresponsibilityofPSEAG. Final manuscript published as received without editorial corrections.

Keywords: Supercritical Rankine cycle, Low temperature power generation, Earth-air-heat-exchanger, Parametric analysis

1. Introduction

The environmental problems related to fossil fuels have made it necessary to explore alternate sources of energy. There are several low to medium temperature heat sources, such as solar thermal, geothermal and waste heat, that are abundantly available and the amount of energy contained in those sources is high enough to fulfil all the energy requirements of the world [1]. However, the conventional power generation methods, such as the steam Rankine

* Corresponding author. Tel.: +1-813-974-6604; fax: +1-813-974-6438 E-mail address: rachana@mail.usf.edu

1876-6102 © 2013 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons. org/licenses/by-nc-nd/ 3.0/).

Selection and peer review by the scientific conference committee of SolarPACES 2013 under responsibility of PSE AG.

Final manuscript published as received without editorial corrections.

doi:10.1016/j.egypro.2014.03.132

Cycle, result in very low efficiencies for these sources. As the efficiency of power conversion depends largely on source and sink temperatures; and the source temperature is low, other factors such as alternative configuration for the power cycle, appropriate working fluid, optimum operating pressure and lower sink temperature, need to be considered to obtain a viable method of power generation. Organic Rankine cycles have been preferred over other configurations because of their simple design and cost effectiveness [2].

A supercritical organic Rankine cycle has the same working principle but the fluid is pressurized beyond its critical point. Figure 1 shows the difference between subcritical and supercritical organic Rankine cycles. The heating profile of the working fluid in a supercritical Rankine cycle (SRC) is much straighter and so provides better thermal match with the heat source [3]. Organic working fluids have been observed to provide better efficiency in a supercritical cycle than the conventional ORC [3-10].

D -♦—'

E 0 I-

Entropy

Figure 1. T-S diagram of the Supercritical Rankine cycle.

Since the efficiency of a thermodynamic cycle also depends significantly on the sink temperature, a significant part of this research is devoted to heat sinks for thermal power. At sites where water is not available for cooling and the ambient air temperature is high, efficient power generation from low grade heat sources is a challenge. Use of earth as a heat sink can improve the performance by increasing the efficiency and lowering the fluctuations caused by the variation in the ambient air temperature. Although the ambient temperatures vary over the year by a large amount, the underground temperatures vary within a narrow range throughout the year. It has been observed that the temperature at a depth of a few meters remains nearly constant at the average annual ambient temperature [11, 12]. Earth-to-air heat exchangers operate on the ability of the underground temperatures to heat or cool the ambient air. Buried pipes are used through which air is circulated and the difference in temperatures is utilized for heating or cooling the air. This method has been used extensively for air-conditioning of buildings and greenhouses [12-24]. This method can also be used with the condenser of a power cycle by using the air or water cooled by an EAHE to cool the working fluid in the power block.

In the current study, the use of organic fluids in a SRC and passive cooling in the condenser has been investigated for low temperature power generation. Several organic fluids have been studied as the working fluid in the SRC. The fluid giving the highest efficiency is considered for further analysis with an Earth-air-heat-exchanger.

Nomenclature

T Temperature

U Overall heat transfer coefficient h Convective heat transfer coefficient Cp Specific heat

Subscript

n Element from the inlet

s Surface of the tube

e Earth

m Mass flow rate

A Differential area

8 Penetration depth

r Radial distance

q' Heat transfer per unit area

2. Supercritical Rankine cycle (SRC)

Organic fluids with low critical temperatures were used as working fluids in the SRC. The critical temperatures and pressures of the selected fluids are given in Table 1. All the selected fluids have zero ozone depletion potential. A MATLAB model was used for analysing the cycle and the thermo-physical properties of the fluids were obtained using the NIST REFPROP program.

Table 1. Critical properties of the selected fluids

Fluids Critical temperature (0C) Critical pressure (Bars)

R32 78.11 57.8

R143a 72.71 37.6

R134a 101.05 40.6

R170 32.18 48.7

R125 66.02 36.2

R218 71.87 26.4

2.1 Effect of pressure

The efficiency of the supercritical Rankine cycle was optimized for each working fluid by varying the operating pressure. The low pressure was fixed to obtain complete condensation at the condenser outlet. Table 2 shows the condensation pressures when the sink temperature was 200C. The working fluid was cooled to 300C in the condenser and the table shows the minimum pressure needed for complete condensation at this temperature. Figure 2 shows the effect of source temperature on the optimum operating pressure for each fluid. It can be observed that the fluid with the lowest critical temperature (R170) has the highest condensation pressure. This is because condensing a fluid with low critical temperature becomes more difficult under typical ambient cooling conditions. Hence the operating pressure needed becomes much higher in order to obtain a high pressure ratio. The fluid with the highest critical temperature, R134a, had the lowest condensation and operating pressures. R32 was removed from this figure because the pressure needed for maximum efficiency resulted in a poor vapor quality inside the turbine. For R32, the maximum pressure at which a vapor quality of more than 95% could be obtained will be considered for further study.

Table 2. Condensation pressures of the working fluids

Fluid Condensation pressure (Bar) at 300C

R32 19.3

R143a 14.3

R134a 7.7

R170 46.5

R125 15.7

R218 9.9

Heat source temperature (C)

Figure 2. Optimum pressure as a function of heat source temperature for 200C sink temperature.

Figure 3 shows the variation in efficiency as a function of the heat source temperature when the sink temperature is 200C. It can be observed that the R134a based cycle had the highest efficiency under the given conditions, while R143a, R125 and R218 based cycles had approximately the same efficiencies. The R32 based cycle has a lower efficiency at higher temperatures but becomes very close to that of R125 at lower temperatures. Since REFPROP database didn't provide accurate properties for R32 beyond 1650C and for R218 beyond 1700C, the plots for these fluids were limited to those temperatures.

Figure 3. Efficiency as a function of heat source temperature for each organic fluid.

3. Earth-air-heat-exchanger (EAHE)

The condenser of the SRC was coupled with an earth-air-heat-exchanger, using the earth as the heat sink. Figure 4 shows a schematic diagram of an EAHE system. Ambient air is blown through the tunnel buried underground using a blower. As it flows through the tunnel, the air exchanges heat with the soil. In the summer, when the ground temperature is lower than the ambient, heat is rejected into the ground. However, in the winter season, the ambient air temperature may be lower than the soil temperature. In this case, the ambient air is directly used in the condenser for cooling the working fluids.

Figure 4. Schematic of an EAHE.

The effect of various system parameters on the performance of the SRC was investigated. Since R134a was found to have the maximum efficiency for the temperature range considered above, it was chosen for further analysis with the EAHE.

3.1 Methodology

A two dimensional model was used to analyze the cooling of the air in the underground tunnel. The expressions developed by Dhaliwal and Goswami [25-27] were used in MATLAB for this study. The entire length of the tunnel was divided into several differential elements and an energy balance was applied to each segment.

• Heat transfer in air

Assuming that air remains unsaturated, equation 1 shows the temperature of the air leaving the nth element.

[{l--)Tn_i + UTs\

where,

Heat transfer in soil

Tn = --u-1 (1)

U =■

The temperature in the soil in cylindrical coordinates is given by equation 2.

d2T(r,t) ldT(r,t) _ ldT(r,t)

dr2 + r dr a dt ' ^

The solution to equation 2, using an integral method [25-27], was obtained for this analysis and is given by equation 3, as

q'R/k( S r\2 ( 1 \ ( r/R \

where, Te is the bulk earth temperature and 8 is the penetration depth beyond which the temperature of the soil remains unchanged.

• Ambient air temperature

The average ambient air temperature varies sinusoidally over a day and also over a year. A sinusoidal profile for a yearly variation, which is close to practical conditions, was selected; while Erbs Model (equation 4) was used for the diurnal variation.

T(t) = Tavq + AT[0.4632 cos(a - 3.805) + 0.0984 cos(2a - 0.360) + 0.0168 cos(3a - 0.822) +

0.0138 cos(4a - 3.513)]

2n(t - 1)

where a =-—-,and t is the hour

3.2 Improvement with EAHE

Figure 5 shows the inlet and outlet temperatures for the 10 days of operation. It can be observed that the change in outlet temperature is much smaller than the inlet temperature, which suggests that we not only obtain a lower sink temperature for the power cycle, but also a more stable temperature profile with lower fluctuations.

Figure 5. Inlet and outlet temperature for 10 days for a 25 m long pipe buried at 2 m.

The outlet air was used for cooling the working fluid in the power cycle. As the temperature of the air inlet to the EAHE increased, the outlet temperature also increased. Since higher sink temperatures resulted in lower efficiency of the power cycle, the trend of variation of efficiency was opposite to the trend of the temperature. Figure 6 shows the variation in efficiency of the power cycle with and without the EAHE for 10 days. We observe that an efficiency increase of about 1 % was obtained when EAHE was used for the condenser.

Figure 6. Efficiency of SRC with and without EAHE for 10 days.

3.3 Effect oof depth

The depth of EAHE was varied from 1m to 4m. Since the variation in the underground temperature is reduced with depth, the operating time of the EAHE system is different for each depth. At the depth of 1 m, the lag between ambient temperature and soil temperature is much smaller than at larger depths (Figure 7). When the ambient air temperature decreases, the soil temperature at a smaller depth also decreases. However, the soil temperature at larger depths varies in a small range and also the time lag with the ambient temperature is larger. So, the ambient air temperature is lower than the soil temperature at 1 m for a shorter time compared to the soil temperature at 4 m. With increasing depth, the soil temperature in the winter season is higher than the ambient air temperature for a longer duration. So, although a larger depth provides a greater advantage in the summer season, the system is useful

Figure 7. Ambient air temperature and underground temperature at different depths.

The effect of depth on the efficiency of the SRC can be observed in figure 8. The efficiency is better for larger depths in the summer season. During colder weather, the ambient air can be used directly for cooling the working fluid.

Figure 8. Efficiency of SRC for different depths of EAHE.

3.4 Effect of length

Three different lengths of the underground tunnel, 25, 50 and 75 m, were analysed for a pipe radius of 25 cm and a depth of 2 m. With increasing length, the outlet temperature of the air was lower. Figure 9 shows the variation of the air temperature for different tunnel lengths. As the length of the pipe increases, the variation in the temperature of the air at the EAHE outlet decreases. The outlet air temperature approaches the undisturbed soil temperature and so, it can be observed that, the annual profile of the outlet air follows that of the soil. As seen in Figure 9, the time lag between the inlet air temperature and the outlet air temperature profiles increases with the pipe length as the outlet air starts to follow the soil temperature profile more closely.

CD k—

25 m 50 m -75 m — 100 m Ambient temperature

220 30 60 90 120 150 180 210 240 270 300 330 365

Figure 9. Annual variation of the outlet air temperature at different pipe lengths.

Figure 10 shows the effect on the cycle efficiency for different lengths of the EAHE. It can be observed that the cycle efficiency increases by 0.5% when the length is increased from 25m to 50m , and by 0.7% when it is increased to 100m, however, further increases in length resulted in negligible efficiency improvements.

Figure 10. Annual variation of SRC efficiency for different lengths of EAHE.

4. Summary and conclusions

The supercritical Rankine cycle coupled with an earth-air-heat-exchanger was studied for power generation from low temperature heat sources. The optimum pressures for each working fluid were obtained at different heat source temperatures and the energy efficiencies as a function of heat source temperature are reported. The effects of the EAHE geometry on the efficiency of the SRC were analysed. From this analysis it was found that:

• Among the working fluids studied, the R134a based cycle had the highest efficiency.

• The optimum pressure increases with the heat source temperature.

• Use of an EAHE improves the efficiency of the SRC and reduces daily fluctuations.

• Larger depths of the EAHE improve the efficiency of the SRC, however, the useful time of the year is smaller.

• Increasing the length of the EAHE improves the SRC performance but the increase is very small as the pipe exceeds a certain length.

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