Review of Low-Temperature Vapour Power Cycle Engines with Quasi- 5 Isothermal Expansion 6 7 8 Opubo N

*Manuscript Click here to download Manuscript: Vapour power cycles with isothermal expansion RevisedClick 10 hereno figs.docx to view linked References 1 2 3 4 Review of low-temperature vapour power cycle engines with quasi- 5 isothermal expansion 6 7 8 Opubo N. Igobo, Philip A. Davies 9 10 Sustainable Environment Research Group, School of Engineering and Applied Science, Aston University, 11 Birmingham, B4 7ET, UK email: [email protected] 12 13 14 15 Abstract 16 17 External combustion heat cycle engines convert thermal energy into useful work. Thermal energy 18 resources include solar, geothermal, bioenergy, and waste heat. To harness these and maximize work 19 output, there has been a renaissance of interest in the investigation of vapour power cycles for quasi- 20 isothermal (near constant temperature) instead of adiabatic expansion. Quasi-isothermal expansion 21 has the advantage of bringing the cycle efficiency closer to the ideal Carnot efficiency, but it requires 22 heat to be transferred to the working fluid as it expands. This paper reviews various low-temperature 23 vapour power cycle heat engines with quasi-isothermal expansion, including the methods employed to 24 realize the heat transfer. The heat engines take the form of the Rankine cycle with continuous heat 25 addition during the expansion process, or the Stirling cycle with a condensable vapour as working 26 fluid. Compared to more standard Stirling engines using gas, the specific work output is higher. 27 28 Cryogenic heat engines based on the Rankine cycle have also been enhanced with quasi-isothermal 29 expansion. Liquid flooded expansion and expander surface heating are the two main heat transfer 30 methods employed. Liquid flooded expansion has been applied mainly in rotary expanders, including 31 scroll turbines; whereas surface heating has been applied mainly in reciprocating expanders. 32 33 34 35 Keywords : 36 Vapour power cycle 37 Quasi-isothermal expansion 38 Renewable energy 39 40 Waste heat utilisation 41 42 Contents 43 44 1. Introduction…………………………………………………………………….……………2 45 2. Quasi-isothermal expansion………………………………………………………………....3 46 2.1. Methods of effecting quasi-isothermal expansion…………….…………………....3 47 48 2.1.1. Expander surface heating…………………………………………….……....4 49 2.1.2. Secondary fluid heating………………………………………………..….....5 50 3. Quasi-isothermal Rankine cycle engine…………………………………………..…………...7 51 3.1. Liquid flooded Rankine cycle engine…………………………………………..…..7 52 53 3.2. Surface heated Rankine cycle engine………………………………………….…...8 54 4. Cryogenic heat engine……………………………………………………………………..…10 55 5. Vapour Stirling cycle engine………………………………………………………….……..13 56 57 6. Conclusion…………………………………………………………………………………...15 58 References…………………………………………………………………………….……...16 59 60 61 62 63 1 64 65 1 2 3 4 1. Introduction 5 6 7 Owing to the global energy challenges associated with fossil fuel – rising cost, energy security and 8 climate change – there has been growing interest into sustainable alternatives or renewable energy 9 sources such as: wind, solar, geothermal, biomass and waste heat. Presently, renewable energy 10 sources account for less than 15% of the global energy supply [1], of which biomass is a major 11 contributor. However, solar has recorded the fastest growth, and renewables have been projected to 12 become the world’s second largest source of power generation by 2015 [2]. Studies have already 13 shown that the renewable heat sources have the potential of meeting the global energy demand several 14 times over [3]. As a means of encouraging the exploitation of the renewable heat sources, ‘heat 15 policies’ (including incentives) have been introduced in some countries [4]. Globally, solar, biomass 16 o 17 and waste heat are readily available in distributed form as low-grade (<250 C) heat, and are well 18 suited for decentralized small-scale (<100 kW) applications . Thus there has been a renaissance of 19 interest in small-scale external combustion heat engines (gas and vapour power cycles) to convert the 20 thermal energy into useful work, with particular emphasis on improving performance. Isothermal 21 expansion is one technique for achieving such improvement . 22 23 Ideally, certain gas power cycles (such as Stirling and Ericsson cycles) perform work by the 24 isothermal (constant temperature) expansion of a compressed and heated gas working fluid (which 25 remains gaseous throughout the entire cycle). They are noted for having the high theoretical 26 efficiencies of the Carnot cycle – which is the maximum obtainable efficiency for given temperature 27 limits [5]. On the other hand, for vapour power cycles (typically the Rankine cycle), the working fluid 28 is a condensable vapour, and is intermittently vaporised and condensed; the expansion process is 29 adiabatic (i.e. the fluid expands without experiencing heat transfer during the process) and produces 30 less work than its isothermal counterpart [6]. Nevertheless, in comparison to the gas compression 31 work of the gas power cycles, less input work is required to pressurize the condensed liquid of the 32 vapour power cycles, and the total cycle pressure-volume characteristics exhibit greater work output 33 34 than the gas cycles. Thus the vapour cycle engines have higher specific work output [7]. The vapour 35 power cycles can also have advantages over gas cycle equivalents because the phase change allows 36 smaller surface areas and temperature differences to drive the boiling/condensation required by the 37 cycle. This inference arises from the higher heat transfer coefﬁcients associated with phase change (by 38 orders of magnitude) relative to that of forced convection for gas [8]. The smaller surface areas lead to 39 compact heat exchangers and engine size [9]; this together with the higher work output gives the 40 vapour cycle engines higher power density; and the low temperature differences aid better 41 performance (relative to the gas cycles) in low-grade heat applications. This has been demonstrated in 42 a study that showed the Rankine cycle to be more efficient than Stirling cycle for temperature range of 43 150 – 300 oC [10]. 44 45 In power plants operating on the Rankine cycle, reheating is a practical approach to improve the cycle 46 efficiency and specific work output. As the number of stages of reheating increases, the expansion and 47 reheat processes approximate an average isothermal process and the cycle efficiency increases [11]. 48 49 But in the reheating process, the steam must be returned back to the boiler for each reheat, which, 50 besides requiring many additional components, inevitably adds complexity to the plant layout and 51 geometry, and results to heat and pressure losses [12]. Alternatively, the vapour cycle engine could be 52 designed in such a way that (like the Stirling or Ericsson engines) heat is continuously transferred to 53 the working fluid during the expansion process thus resulting in isothermal expansion, or more 54 realistically, quasi-isothermal expansion – which may be somewhere between the adiabatic and ideal 55 isothermal processes. 56 57 In this paper, relevant research works with emphasis on low temperature vapour power cycles with 58 quasi-isothermal expansion will be presented. Various methods employed to effect quasi-isothermal 59 operation, including concepts, studies and results, will be reviewed to provide an insight into their 60 practicality, system performance and energy efficiency. The first part (section 2) of the paper presents 61 62 63 2 64 65 1 2 3 4 the general theoretical advantage of quasi-isothermal expansion, including the various heat transfer 5 methods used to achieve it. The second part (section 3-5) of the work covers the power cycles to 6 which the methods are applied. For each power cycle, the theory and principle of operation is 7 explained, and then specific studies are reviewed in which these cycles have been implemented. Fig. 1 8 classifies the methods and vapour power cycles for quasi-isothermal operation according to the 9 approach used in this review. 10 11 12 2. Quasi-Isothermal expansion 13 14 15 The paths of both the isothermal and adiabatic expansion processes can be illustrated graphically on a 16 pressure-volume (P-v) plane as shown in Fig. 2, using the gas equation . The expansion index n is equal to 1 and k for isothermal and adiabatic processes respectively) [13],) where k is the 17 ͊ͥͪͥ Ɣ ͊ͦͪͦ 18 ratio of the specific heats (C p/C v) of the gas, and is always >1[14]. For example, under a substantial 19 range of operating conditions, k is about 1.4 for nitrogen gas and steam [15]. 20 21 22 The work output is simply the integral ( ) between the two end states (1 and 2), as is 23 represented by the area under the path curves. Hence, from the figure it can be seen that the area under Ȅ ͊͐͘ 24 the curve (i.e. the expansion work output) for the adiabatic expansion is less than that of an isothermal 25 expansion having the same initial operating conditions. This can also be seen numerically from the 26 integration of both curves from state 1 (start of expansion) to state 2 (end of expansion). 27 28 29 The work done by isothermal expansion can be given as [16]: 30 31 32 33 ͊ͥ ͑$.* Ɣ ǹ ͊͐͘ Ɣ ͊ͥͪͥ ln ƴ Ƹ ʚ1ʛ 34 ͊ͦ 35 Similarly, the work done by adiabatic expansion can be expressed as: 36 37 uġ 38 ġ ͥ 39 ͊ 1 Ǝ ʠ͊ͦʡ 40 ͑ Ɣ ǹ ͊͐͘ Ɣ ͊ͥͪͥ ʚ2ʛ ͢ Ǝ 1 41 Hence, from the above equations, the relative improvement of the isothermal expansion work over the 42 adiabatic work can be expressed in terms of the expansion index and pressure ratio as: 43 44 ͦ+ Ɣ ͊ͥ⁄͊ͦ 45 46 47 ͑$.* ʚ͢ Ǝ 1ʛ ln Ƴͦ+Ʒ ͙͕͙͌ͨͪ͠͝ ͙͙ͤͦͣͪͨ͢͝͡͡ Ɣ Ǝ 1 Ɣ Ʈ ͥͯ) Ʋ Ǝ 1 ʚ3ʛ 48 ͑ ) 49 Ƴ1 Ǝ ͦ+Ʒ 50 51 For example, with and n = 1.4, eq.

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