Elsevier

Energy

Volume 144, 1 February 2018, Pages 679-693
Energy

A numerical study on applying slot-grooved displacer cylinder to a γ-type medium-temperature-differential stirling engine

https://doi.org/10.1016/j.energy.2017.12.010Get rights and content

Highlights

  • Study on Stirling engine heat transfer enhancement with 3 types of grooves.

  • Type 1 grooves performance is mixed because of inadequate heat transfer.

  • Contrary, type 3 grooves can largely reduce inadequate heat transfer.

  • Type 2 grooves are in the regenerative channel and yield the best performance.

  • Type 2 grooves produce about 50% increase in indicated power.

Abstract

In this study, the effects of heat transfer enhancement on engine performance by introducing slot grooves on walls of the displacer cylinder of a γ-type medium-temperature-differential Stirling engine have been investigated using computational fluid dynamics. Cases include smooth displacer-cylinder wall with heat source and heat sink extension on displacer cylinder circumferential wall and slot-grooved displacer-cylinder walls with grooves at different locations and numbers. The grooves are at displacer cylinder circumferential wall or at top and bottom walls. The slot grooves are classified into three types according to their locations. It is found that the circumferential wall is very important on engine's heat transfer behavior. Extending heat source and heat sink on this wall can improve indicated power but losing efficiency. Type-1 grooves enhance both positive and inadequate heat transfer, hence its effects on enhancing engine performance is mixed. In contrast, Type-3 grooves mainly enhance positive heat transfer thus yield improvement on indicated power and efficiency as the number of grooves increases. However, Type-2 grooves, which enhance heat transfer on regenerative wall, have been shown to yield the best performance. Compared with the engine without any heat-transfer-enhancement measure, a case with 96 Type-2 grooves improves indicated power up to 49%.

Introduction

The Stirling engine was invented and patented by Robert Stirling in 1816 to replace steam engines which were notorious for frequently exploding and claiming innocent lives at that time. To achieve higher power and efficiency, Stirling engines need to be operating at higher temperatures. Nevertheless, in 19th Century there were no such materials that could properly cope with the increasing temperature demands for higher power output, resulting in frequent operation failures. In late 19th Century, internal combustion engines experienced a rapid development and could operate at lower temperature difference given the same power output as Stirling engines. Eventually, Stirling engines were only confined to be used as a safe and reliable source for low-power domestic applications (mostly for pumping water), failing to fulfill its initially intended purpose. In early 20th Century, the role of the Stirling engines gradually gave way to electric motors and small internal combustion engines as they could produce larger output power than Stirling engines with the same volume. However, in recent decades, with the increasing focus on environmental issues and the quest for cleaner, more efficient power generation, the Stirling engine technology has been back in the spotlight as a highly potential “green” solution. Because Stirling engines are “external combustion” machines, they can tap into a large variety of heat sources, inclusive of solar, nuclear, biomass fuel, geothermal energy, waste heat, etc. Essentially, anything that generates heat can serve as the heat source of Stirling engines. Stirling engine technology is therefore now considered to be one of the most feasible approaches to tackle the problems of global warming and the depletion of natural resources from our mother nature. Although Stirling engine industry is experiencing a glorious revival because of its unique advantages, for this technology to become more and more prevalent and be adopted in even wider applications, it is crucial that the performance of the engine, namely power output, efficiency, power-to-weight ratio, be continuously ameliorated so that it can rival other already mature and popular engine technologies.

Stirling engines can be generally classified into α-, β-, and γ-types according to their mechanical configurations. Among these configurations, α- and β-type configurations are normally associated with high-temperature differential (HTD) variants. The γ-type, on the other hand, provides a lower compression ratio and is structurally simpler, making it particularly suitable for MTD or LTD operation conditions as well as multi-cylinder applications. These engines usually feature a relatively large volume of working gas and displacer to compensate for the small amount of energy available when running under relatively small temperature difference. Although having a relatively low efficiency compared with the other two types, MTD or LTD γ-type Stirling engines can be manufactured using low-cost materials and in relatively simple structure. Furthermore, lower temperature difference happens to be one of these Stirling engines' greatest advantages as they can be easily powered by low-energy-intensity external heat sources such as biomass, solar energy, geothermal energy, or even industrial waste heat. These advantages make them attractive to various potential applications, which could be a huge market. For instance, they can serve as the prime movers in small- and micro-scale combined heat and power (CHP) systems, waste heat recovery systems for small businesses, or generators in agricultural areas where biomass waste is abundant. Potentially having the above-mentioned advantages, it is imperative that thorough research on improving the overall performance of MTD and LTD Stirling engines will be continuously conducted and the obtained knowledge being put into practice.

It was estimated in 2010 that the industrial sector consumed about one-half of the world's total delivered energy and the amount is projected to keep increasing linearly in the future [1]. 20–50% of that energy is finally discharged into the environment as waste heat. Therefore, harvesting energy from industrial waste heat is of great potential and worth investigating. This can not only reduce the overall energy consumption but also reduce thermal pollution from industries. Some studies, for example Hsu et al. [2] and Chang and Ko [3] were conducted to support the possibility of generating power using Stirling Engines with the hot end heated by the combustion chamber of an incinerator. By using a cycle-averaged heat transfer model, Hsu et al. [2] concluded that a realistic thermal efficiency of the system will be about 20–35%. The review study by Kongtragool and Wongwises [4] indicated that the LTD Stirling engines have drawn great interest as they have the capability of generating power from various low temperature waste heat sources in which the temperature is often less than 100 °C. Despite that the calculated thermal efficiency appears to be rather low, LTD Stirling engines can be powered by cheap or even free low temperature sources and can be constructed using lightweight and cheap materials such as plastic which really makes it stand out among other engines. Kongtragool and Wongwises [4] also performed an experimental study on a four-power-piston solar γ-type LTD Stirling engine using non-pressurized air as the working fluid and it can generate a maximum shaft power output at 6.1 W under a heat input of 1378 W. Although the efficiency of the engine is only 0.44%, the fact that the Stirling engine can be powered by an emission-free heat source such as solar power makes it attract attention and further development for this highly potential clean energy.

Although γ-type Stirling engines possess a great advantage of being able to utilize low-energy-intensity heat sources, tapping into such heat sources, at the same time, happens to be its Achilles' heel because the low exergy this kind of heat sources can offer. It results in the engine's overall performance inferior compared with other already mature and widely used engine technologies. Therefore, to successfully promote the prevalence of γ-type Stirling engines, it is crucial that improvements on engine performance such as thermal efficiency and power output be made. Improvement on the performance of Stirling Engines depends heavily on theoretical or numerical analyses, hence parameters of Stirling Engines should be studied thoroughly to narrow down to more specific directions that future improvement researches can follow. There have been many experimental studies on Stirling engines. Kongtragool and Wongwises [4] studied the performance of a solar LTD Stirling engines, Karabulut et al. [5] reported a helium charged Stirling engine. In the meantime, many numerical methods have also been developed to analyze Stirling engine cycles. For example, Parlak et al. [6] developed a thermal dynamic model to study a γ-type Stirling engine, Timoumi et al. [7] formulated a second-order model to optimize GPU-3 Stirling engines. Mahkamov [8] gave a detailed review on numerical methods for Stirling engine analyses, including first-, second-, and third-order methods. Mahkamov [8] and Mahkamov [9] also conducted CFD studies on different Stirling engines and concluded that CFD can return more accurate predictions than other conventional numerical methods such as first- and second-order methods. Chen et al. [10] and Chen [11] used CFD to study the effects of 7 different geometrical parameters on the performance of a γ-type LTD Stirling engine. It was found that CFD can analyze the effects caused by some geometrical parameters which are not associated with engine's compression ratio. This demonstrated the capability of CFD to study and optimize some fine geometrical details of a Stirling engine. Such a capability is very crucial for designing a real Stirling engine.

Since the heat input and output of a Stirling engine can only rely on its walls, the characteristics of wall heat transfer, especially those associated with displacer-cylinder wall are of great importance to engine performance. Hence, heat transfer enhancement is required to maintain the output of high-power HTD Stirling engines. In these engines, heat transfer enhancement is normally implemented through dozens of heat transfer pipes welded circumferentially on the hot end of displacer cylinder. However, these pipes increase engine's dead volume, and welding so many leak-proof pipes within a confined space is a difficult and expensive engineering undertaking. These are probably the main reasons that such a practice has not commonly been implemented on other inexpensive variants of Stirling engines. Some other types of heat transfer enhancement methods such as slot grooves may be more suitable for MTD or LTD Stirling engines. Grooves of different shapes have been used in circular tubes to enhance heat transfer. Cheng et al. [12] have reported an experimental study on the heat transfer enhancement using Ω-shaped grooved tube and R134a as the working fluid. They found increase in heat transfer coefficients between 1.5 and 3.3 times compared with smooth tube in various test conditions. Zheng et al. [13] conducted a numerical study on the heat transfer enhancement of a heat exchanger tube by applying discrete inclined grooves. Within the range of groove parameters that they have investigated, the heat transfer is found to be enhanced by a factor between 1.23 and 2.17 with the penalty of an increase in friction coefficient between 1.02 and 3.75 folds. These studies do show the effectiveness of applying grooves in tube flows to enhance heat transfer. In terms of Stirling engines, Karabulut et al. [14] performed an experimental study on the performance of a MTD β-type Stirling engine with the inner surface of its displacer cylinder wall augmented by slots. Data for smooth displacer cylinder wall engine have also been measured. The slotted displacer cylinder has 214% larger inner surface than the smooth displacer cylinder, and the former has been found to produce about 50% more power than the latter under a variety of operational conditions. The authors argued that the increase in power was lower than expectations; nevertheless, the results prove the positive effect of slot-grooved-wall heat transfer enhancement on improving engine performance. Aksoy and Çinar [15] presented a thermodynamic analysis of a β-type Stirling engine with smooth or slot-grooved displacer cylinders. The inner heat-transfer area of the slot-grooved displacer cylinder is assumed to be enlarged by 90 axial slots with 1.5 mm width and 3 mm depth, resulting in regenerator volume increase of 60 cm3 and heat-transfer area increase of 720 cm2. By assuming a convective heat transfer coefficient of 300 Wm−2K−1 and operation conditions of 500 rpm, TH = 773 K, TL = 300 K, and 2 bar charged pressure, engine with grooved and smooth displacers produce 21.37 J and 18.4 J cycle work, respectively. The engine with grooved displacer cylinder is also found to perform much better at different operation conditions. The authors concluded that slot grooves increase both heat transfer area and regenerative volume and hence the performance of the engine is improved. Such results are promising, however, by adopting a constant convective heat transfer coefficient suggests that the amount of heat input is proportional to heat transfer area. Given the flow in a Stirling engine is much more complicated than the flow in a tube, this simple relationship may not be always true.

Since slot grooves are effective, simple, and inexpensive to machine, fitting slot grooves directly on displacer cylinder walls can be a good solution for enhancing heat transfer in MTD Stirling engines. It could offer great benefit of significantly improving MTD Stirling engines' performance by a small cost of doing some simple machining work. This study employs CFD, which is more accurate than conventional thermodynamic analysis, to investigate the impact of slot-grooved displacer cylinder heat transfer enhancement on the performance of a MTD γ-type Stirling engine. Just like heat transfer enhancement using pipes, slot grooves also increase engine's dead volume and introduce some negative effects on engine performance. Therefore, the positive effects of heat transfer enhancement must outweigh the negative effects for such a measure to be worthwhile. The purpose of this study is not to propose a high-performance MTD Stirling engine fitted with slot-grooved displacer cylinder. Instead, a generic Stirling engine is adopted here, and it merely serves as a platform to study and understand the general effects on heat transfer caused by different slot-groove arrangements; hence the results will be relevant to other Stirling engines with similar configurations. Effects of different groove parameters, namely locations and numbers, on engine performance will be systematically investigated, and recommendations useful for designing slot grooves to enhance heat transfer in MTD Stirling engines will be given.

Section snippets

Mathematical model

The model in this study is based on the twin-power-piston γ-type Stirling engine reported in Chen et al. [16]. The configuration and geometrical parameters of the engine are illustrated in Fig. 1, and the dimensions of parameters are given in Table 1. Fig. 1(a) and (b) show the original engine reported in Ref. [16]. The engine has two power pistons and only one displacer. The advantages of using twin power pistons are first to avoid using a single big and heavy piston and second to let gas flow

Numerical procedure

Commercial CFD software STARCCM has been used here to perform the numerical simulation. This is an unstructured-mesh, collocated, finite-volume code, employing SIMPLE for pressure correction. To simulate a Stirling engine cycle, some sorts of moving mesh strategies are needed to deal with the motions of displacer and power piston. In a γ-type Stirling engine, the power piston is in contact with power-cylinder wall, forming an airtight seal at all time; whereas, the displacer is not in contact

Code validation

The first step to validate the code is to find a mesh and a time-step interval to achieve mesh- and time-step-independent solutions. To perform this task, a baseline case, Case 4, is selected. The details, in terms of dimensions, boundary conditions, and operation conditions, of Case 4 will be given in Section 4.2. Here, three meshes with 563,810, 1049163, and 1963826 cells have been constructed; and three numbers of time steps per cycle are tested, namely 200, 400, and 800 time steps per

Conclusions

In this study, effects of heat transfer enhancement on engine performance by introducing slot grooves on DCCW have been examined using CFD. The CFD approach has been validated against theoretical adiabatic p-V relation and an experimental p-V diagram of a LTD Stirling engine. Parameters investigated here include the length of heat-source and heat-sink extensions on DCCW, location of grooves, and number of grooves. The grooves are classified into three different types based on their locations on

Acknowledgement

This work was supported by the Ministry of Science and Technology, Taiwan, Republic of China, under the grant number MOST 105-2221-E-006-257. The authors are very grateful for the financial support.

References (21)

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