Thermodynamic analysis of a gamma-type stirling engine driven by Scotch Yoke mechanism

ABSTRACT

In this study, thermodynamic analysis of a gamma-type Stirling engine driven by Scotch Yoke mechanism was conducted. The advantages of Scotch Yoke mechanism over classical crank mechanism were discussed in detail. In the analysis hydrogen was used as working gas. Working space was divided into 16 nodal volumes. Solution of conservation of mass and energy equation were obtained for each nodal volume. Wall temperatures of nodal volumes were assumed to be constant and temperature variations in nodal volumes were calculated by means of the first law of the thermodynamics. Maximum engine power was obtained as 1105 W at 800 rpm engine speed and gas mass of 0.3 g for 1200 W/m²K heat transfer coefficient. The optimum phase angle, which was not affected significantly by hot end temperature, gas mass, and heat transfer coefficient variations, was determined as 90° degrees at engine speed of 600 rpm. However, it was determined that engine speed has a great impact on optimum phase angle and a variable phase angle mechanism may be useful to obtain maximum specific power from the engine at different engine speeds. At engine speed of 600 rpm, the maximum specific power of the engine was 695 W/l for 1.65 compression ratio and 90° degrees phase angle.

KEYWORDS:

• Gamma-type Stirling Engine
• Scotch Yoke mechanism
• thermodynamic analysis
• nodal analysis
• engine optimization

Nomenclature

$A_p$	=	area of piston top and displacer top (m2)
$A_{dr}$	=	area of displacer rod top (m2)
$A_{hd}$	=	heat transfer area of hot side of displacer cylinder (m2)
$A_{cd}$	=	heat transfer area of cold side of displacer cylinder (m2)
$A_{ws}$	=	heat transfer area of expansion cylinder (m2)
$A_n$	=	heat transfer area of the nodal volume k (m2)
$C_p$	=	specific heat at constant pressure (J/kg K)
$C_v$	=	specific heat at constant volume (J/kg K)
$D_p$	=	piston and displacer top radius (m)
$h_n$	=	heat transfer coefficient in nodal volume n (W/m2 K)
$h_d$	=	lengths of the power piston and displacer (m)
$H_n^i$	=	specific enthalpy of entering fluid from a nodal volume n (J/kg)
$H_n^i$	=	specific enthalpy of outgoing fluid from a nodal volume n (J/kg)
$m_n$	=	instantaneous gas mass in nodal volume n (kg)
$\mathrm{\Delta }{m}_n$	=	mass variation in the nodal volume n within time step $\mathrm{\Delta }t$ (kg/s)
$m_n^f$	=	mass of working fluid in nodal volume n at pervious time step (kg)
$m_t$	=	total gas mass (kg)
$p$	=	pressure (Pa)
$p_n$	=	gas pressure in the nodal volume indicated by n (Pa)
$R$	=	crank radius (m)
$\mathrm{\Delta }t$	=	time step (s)
$T_c$	=	cold end temperature (K)
$T_h$	=	hot end temperature (K)
$T$	=	temperature (K)
$T_n$	=	gas temperature in nodal volume n within the current time step (K)
$T_n^w$	=	wall temperature of a nodal volume n within the time step $\mathrm{\Delta }t$ (K)
$T_n^f$	=	gas temperature in nodal volume n within the previous time step (K)
$\mathrm{\Delta }{T}_n$	=	temperature variation in nodal volumes within time step $\mathrm{\Delta }t$ (K)
$U$	=	length of displacer and piston cylinders (m)
$U_d$	=	length between the crank center to the top of the displacer cylinder (m)
$V_c$	=	volume of cold side of displacer cylinder (m3)
$V_h$	=	volume of hot side of displacer cylinder (m3)
$V_w$	=	volume of expansion cylinder (m3)
$\mathrm{\Delta }{V}_n$	=	variation of the volume in the cell k during a time step (m3)
$x_w$	=	location of power piston top (m)
$y_c$	=	location of displacer bottom (m)
$y_h$	=	location of displacer top (m)
$z_d$	=	length of the displacer rod (m)
Greek symbols	=
$\epsilon$	=	the length of between piston top and cylinder top (m)
$\mathrm{\Re }$	=	specific gas constant (J/kg K)
$\mathrm{\Theta }$	=	a dummy variable to avoid dividing zero
$\theta$	=	phase angle (rad)
$\omega$	=	engine speed (rpm)
Superscripts and subscripts	=
$f$	=	former time
$i$	=	inlet
$o$	=	outlet
$n$	=	number of nodal volumes
$w$	=	wall
$r$	=	regenerator nod counter