#
Evaluation of a Combustion-Based Mesoscale Thermal Actuator in Open and Closed Operating Cycles^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Thermal Actuator: Design and Model

#### 2.1. Solving the Open Cycle Model

#### 2.2. Solving the Closed Cycle Model

## 3. Results and Discussion

#### 3.1. Pressure-Volume and Force-Displacement Diagrams

^{3}, while for the open cycle, the density at state 2 is 1.87 kg/m

^{3}. The actuator pressure at the end of heat rejection or blow down process is ambient pressure (${P}_{5}$ = 0 kPa gage) and below the ambient pressure (${P}_{5}$ = −11 kPa gage) for the open and closed cycles, respectively. This is because the open cycle interacts with the surroundings via mass transfer that allows the actuator pressure to quickly equilibrate to the ambient conditions, while in the closed cycle there is no mechanism, i.e., no mass transfer or heat transfer h = 0 W/K to equilibrate the actuator pressure to the ambient conditions.

#### 3.2. Equivalence Ratio and Heat Input Relationship

#### 3.3. Efficiency and Volume Ratios

#### 3.4. Operating Frequency and Power Output

## 4. Conclusions

## Funding

## Conflicts of Interest

## Abbreviations

ER | Expansion Ratio |

CR | Compression Ratio |

CV | Control Volume or Cavity |

TDC | Top Dead Center |

BDC | Bottom Dead Center |

## References

- Bell, D.J.; Lu, T.J.; Fleck, N.A.; Spearing, S.M. MEMS actuators and sensors: Observations on their performance and selection for purpose. J. Micromech. Microeng.
**2005**, 15, S153–S164. [Google Scholar] [CrossRef] - Henriksson, J.; Gullo, M.; Brugger, J. Integrated long-range thermal bimorph actuators for parallelizable Bio-AFM applications. In Proceedings of the 2012 IEEE SENSORS, Taipei, Taiwan, 28–31 October 2012; pp. 1–4. [Google Scholar] [CrossRef]
- Butler, J.T.; Bright, V.M.; Cowan, W.D. Average power control and positioning of polysilicon thermal actuators. Sens. Actuators A Phys.
**1999**, 72, 88–97. [Google Scholar] [CrossRef] - Lu, T.; Hutchinson, J.; Evans, A. Optimal design of a flexural actuator. J. Mech. Phys. Solids
**2001**, 49, 2071–2093. [Google Scholar] [CrossRef] - Bardaweel, H.; Preetham, B.S.; Richards, R.; Richards, C.; Anderson, M. MEMS-based resonant heat engine: Scaling analysis. Microsyst. Technol.
**2011**, 17, 1251–1261. [Google Scholar] [CrossRef] - Nakajima, N.; Ogawa, K.; Fujimasa, I. Study on micro engines-miniaturizing Stirling engines for actuators and heatpumps. In Proceedings of the IEEE Micro Electro Mechanical Systems, ‘An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots’, Salt Lake City, UT, USA, 20–22 February 1989; pp. 145–148. [Google Scholar] [CrossRef]
- Preetham, B.S.; Anderson, M.; Richards, C. Modeling of a resonant heat engine. J. Appl. Phys.
**2012**, 112, 124903. [Google Scholar] [CrossRef] - Formosa, F.; Fréchette, L.G. Scaling laws for free piston Stirling engine design: Benefits and challenges of miniaturization. Energy
**2013**, 57, 796–808. [Google Scholar] [CrossRef] - Preetham, B.S.; Anderson, M.; Richards, C. Estimation of parasitic losses in a proposed mesoscale resonant engine: Experiment and model. J. Appl. Phys.
**2014**, 115, 054904. [Google Scholar] [CrossRef] - Preetham, B.S.; Anderson, M.; Richards, C. Mathematical modeling of a four-stroke resonant engine for micro and mesoscale applications. J. Appl. Phys.
**2014**, 116, 214904. [Google Scholar] [CrossRef] - Burugupally, S.; Weiss, L. Power generation via small length scale thermo-mechanical systems: Current status and challenges, a review. Energies
**2018**, 11, 2253. [Google Scholar] [CrossRef] - Burugupally, S.P. Development of a Small Scale Resonant Engine for Micro and Mesoscale Applications. Ph.D. Thesis, Washington State University, Washington, DC, USA, 2014. [Google Scholar]
- Burugupally, S.P.; Weiss, L. Design and performance of a miniature free piston expander. Energy
**2019**, 170, 611–618. [Google Scholar] [CrossRef] - Burugupally, S.P.; Weiss, L.; Depcik, C. The effect of working fluid properties on the performance of a miniature free piston expander for waste heat harvesting. Appl. Therm. Eng.
**2019**, 151, 431–438. [Google Scholar] [CrossRef] - Preetham, B.; Weiss, L. Investigations of a new free piston expander engine cycle. Energy
**2016**, 106, 535–545. [Google Scholar] [CrossRef] - Ouyang, X.; Ding, S.; Fan, B.; Li, P.Y.; Yang, H. Development of a novel compact hydraulic power unit for the exoskeleton robot. Mechatronics
**2016**, 38, 68–75. [Google Scholar] [CrossRef] - Raibert, M.; Blankespoor, K.; Nelson, G.; Playter, R. Bigdog, the rough-terrain quadruped robot. IFAC Proc. Vol.
**2008**, 41, 10822–10825. [Google Scholar] [CrossRef] - Bradley, D.; Acosta-Marquez, C.; Hawley, M.; Brownsell, S.; Enderby, P.; Mawson, S. NeXOS – The design, development and evaluation of a rehabilitation system for the lower limbs. Mechatronics
**2009**, 19, 247–257. [Google Scholar] [CrossRef] - Pulkrabek, W. Engineering Fundamentals of the Internal Combustion Engine; Prentice Hall: Englewood Cliffs, NJ, USA, 1997. [Google Scholar]
- Heywood, J. Internal Combustion Engine Fundamentals; McGraw-Hill Education: New York, NY, USA, 1988. [Google Scholar]

**Figure 1.**Proposed thermal actuator (

**a**) schematic sketch and (

**b**) lumped model. CV denotes the cavity or control volume with state parameters: pressure P, volume V, and temperature T at time t. The valve on the left is used for the intake or exhaust of the working fluid (air). The valve is connected to the ambient atmosphere (${P}_{o},{T}_{o}$) during the intake and exhaust processes. For the closed cycle, the valve remains closed over the entire operating cycle.

**Figure 2.**Ideal pressure-volume diagram of the actuator in open and closed cycle operations. Processes 1→2: Compression; 2→3: Heat addition for duration ${t}_{q}$; and 3→4: Expansion. For closed cycle, process 4→1 is heat rejection for duration ${t}_{q}$. For open cycle, processes 4→5: Blowdown phase of exhaust; 5→6: Displacement phase of exhaust; 6→7→1: Intake. Note the piston positions at states 6 and 7 are ‘Top Dead Center’ (TDC) and states 4 and 5 are ‘Bottom Dead Center’ (BDC), respectively.

**Figure 4.**Open and closed cycle pressure-volume and force-displacement diagrams for (

**a**) the reference actuator (

**b**) an actuator with b = 27.5 N-s/m, ${b}_{p}$ = −40 N-s/m and $\varphi $ = 0.51.

**Figure 5.**Relationship between the heat input and equivalence ratio for the reference actuator for open and closed cycle operations.

**Figure 7.**Comparison of the indicated thermal efficiencies of the reference actuator in open, closed, and Otto cycles.

**Figure 8.**Performance metrics of the reference actuator in open and closed operating cycles: (

**a**) Operating frequency and (

**b**) Power output.

**Table 1.**Comparison of the performance metrics for the reference actuator in closed and open cycles with equivalence ratio $\varphi $ = 0.51.

Performance Parameter | Closed Cycle | Open Cycle |
---|---|---|

Indicated thermal efficiency (%) | 47.66 | 38.41 |

Brake thermal efficiency (%) | 44.33 | 34.64 |

Heat added per cycle (J/cycle) | 35.6 | 138.5 |

Cycle frequency (Hz) | 37.03 | 13.37 |

Compression ratio, CR | 5.05 | 1.76 |

Expansion ratio, ER | 5.05 | 4.13 |

Average piston speed (m/s) | 4.75 | 4.77 |

Power output (W) | 584.7 | 641.6 |

Mass of air in cylinder (kg/cycle) | 2.41 × 10${}^{-5}$ | 9.28 × 10${}^{-5}$ |

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**MDPI and ACS Style**

Burugupally, S.P.
Evaluation of a Combustion-Based Mesoscale Thermal Actuator in Open and Closed Operating Cycles. *Actuators* **2019**, *8*, 73.
https://doi.org/10.3390/act8040073

**AMA Style**

Burugupally SP.
Evaluation of a Combustion-Based Mesoscale Thermal Actuator in Open and Closed Operating Cycles. *Actuators*. 2019; 8(4):73.
https://doi.org/10.3390/act8040073

**Chicago/Turabian Style**

Burugupally, Sindhu Preetham.
2019. "Evaluation of a Combustion-Based Mesoscale Thermal Actuator in Open and Closed Operating Cycles" *Actuators* 8, no. 4: 73.
https://doi.org/10.3390/act8040073