Abstract
This paper describes the development of a mathematical model for a beta-type Stirling engine with rhombic drive mechanism. This model is based on thermodynamics, heat transfer, mass transfer, and machine dynamics considerations, and it estimates the power output and efficiency of a beta-type Stirling engine depending on different geometric and operational variables. The model is used to conduct a parametric investigation on the effect of various geometric and operational parameters on the overall performance of the engine and to shed light on the underlying mechanisms responsible for the observed trends. The results show that the geometric parameters such as the height of the displacer and crank length affect the engine performance by altering the compression ratio of the engine, whereas the impact of width of the regenerative channel is through pumping losses for fluid flow between the hot and cold chambers of the engine. The operational variable, engine speed, is shown to influence the amount of heat transfer to and from the working fluid since it directly affects the residence time of fluid in the hot and cold chambers and accordingly it has a bearing on the engine performance.
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Abbreviations
- \(d_{1}\) :
-
Displacer diameter (mm)
- \(d_{2}\) :
-
Inside diameter of cylinder (mm)
- \(G\) :
-
Width of regenerative channel (mm)
- \(h\) :
-
Enthalpy (kJ/kg)
- \(l_{1} ,l_{2} ,l_{3} ,l_{4}\) :
-
Link lengths (mm)
- \(l_{\text{d}}\) :
-
Displacer cylinder length (mm)
- \(l_{t}\) :
-
Engine length (mm)
- \(L\) :
-
Distance between the gears (mm)
- \(L_{\text{dt}}\) :
-
Total length of displacer and its rod (mm)
- \(L_{\text{Pt}}\) :
-
Total length of power piston and its rod (mm)
- \(m\) :
-
Mass of the working fluid (kg)
- \(\dot{m}\) :
-
Mass flow rate (kg/s)
- \(P\) :
-
Pressure (kPa)
- \(Q\) :
-
Volumetric flow rate (m3/s)
- \(Q_{\text{in}}\) :
-
Input heat transfer per cycle (kJ/cycle)
- \(\dot{Q}\) in :
-
Input heat transfer rate (kJ/cycle)
- \(r_{1}\) :
-
Displacer radius (mm)
- \(r_{2}\) :
-
Inside radius of cylinder (mm)
- \(r\) :
-
Radial coordinates
- \(R\) :
-
Characteristic gas constant of working fluid (J/kg k)
- \(R_{\text{d}}\) :
-
Crank length (mm)
- \(R_{t1}\) :
-
Overall resistance to heat transfer between hot source and working fluid in the expansion chamber (°C/kw)
- \(R_{t2}\) :
-
Overall resistance to heat transfer between cold source and working fluid in the compression chamber (°C/kw)
- \(t_{{\mathrm{max}}}\) :
-
Computation maximum time (s)
- \(t\) :
-
Time (s)
- \(t_{\text{P}}\) :
-
Time period (s)
- \(t_{\text{o}}\) :
-
Reference time (s)
- \(T\) :
-
Temperature (k)
- \(T_{\text{H}}\) :
-
Heat source temperature (k)
- \(T_{\text{L}}\) :
-
Heat sink temperature (k)
- \(U\) :
-
Internal energy (kJ/s)
- \(V\) :
-
Volume (m3)
- \(v\) :
-
Velocity (m/s)
- \(\dot{W}\) out :
-
Power output (kJ/s)
- \(W_{\text{out}}\) :
-
Net work output per cycle (kJ/cycle)
- \(Y\) :
-
Displacement
- \(z\) :
-
Axial coordinate
- \({\text{c}}\) :
-
Compression chamber
- d:
-
Displacer
- e:
-
Expansion chamber
- P:
-
Piston
- r:
-
Regenerative channel gap
- \(\theta\) :
-
Crank angle (rad)
- \(\varepsilon\) :
-
Regeneration effectiveness
- \(\int\) :
-
Fluid density (kg/m3)
- \(\eta\) :
-
Efficiency
- \(\varpi\) :
-
Engine speed (rpm)
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Raghavendra, H., Suryanarayana Raju, P. & Hemachandra Reddy, K. Effect of Geometric and Operational Parameters on the Performance of a Beta-Type Stirling Engine: A Numerical Study. Iran J Sci Technol Trans Mech Eng 46, 1–13 (2022). https://doi.org/10.1007/s40997-020-00406-0
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DOI: https://doi.org/10.1007/s40997-020-00406-0