Energy Analysis of Scroll Compressor Conversion into Expander for Rankine Cycles with Various Working Fluids

Abstract

In this study, a refrigeration scroll compressor as expander for power generation applications with Rankine cycle is analyzed through a mathematical model. The methodology adopted has three phases. In the first phase, a scroll compressor is selected from a refrigeration manufacturer catalog namely Copeland ZF06K4E. Based on the catalog data and thermodynamic model the specific parameters of the compressor such as built-in volume ratio and leakage coefficient are determined through mathematical regression as 7.3 and 1.36 × 10⁻⁶, respectively. In the second phase, the scroll parameters and the efficiency of the Rankine cycle are determined, which use the selected scroll machine in reverse, namely as expander, without any geometrical modifications and keeping the range of temperatures and pressures constant as the same as that characterizing the compressor operation. An expander model is developed to predict the efficiency of the prime mover and of the Rankine cycle for the working fluids such as R404a, Toulene, R123, R141b, R134a, and NH₃. The highest energy efficiency is obtained with R404a as 18 % by applying supercritical conditions for the working fluid, and it is observed that the expander does not operate optimally when converted from a compressor without any modifications. In the third phase, the geometry of the expander is modified with respect to rolling angle in order to obtain the appropriate built-in volume ratio which assures better efficiency of the Rankine heat engine. R404a clearly gave the best results for the modified geometry and the energy efficiency is increased to 25 % from 19 %. The results show that it is possible to improve the efficiency of the cycle by adjusting the scroll geometry for the fluids used.

Nomenclature

A:

Area (m²)

c_p :

Specific heat at constant pressure (J/kg K)

c_v :

Specific heat at constant volume (J/kg K)

C_d :

Discharge coefficient

C_f :

Specific flow coefficient

D:

Diameter (m)

E:

Total internal energy (J)

g:

Gravity of earth (m/s²)

h:

Specific enthalpy (J/kg)

h_c :

Convective heat transfer coefficient (W/m²−K)

h_s :

Scroll height (m)

k:

Specific heat ratio

L:

Length (m)

m:

Mass (kg)

$\dot{m}$ :

Mass flow rate (kg/s)

N:

Rotational speed (Hz)

P:

Pressure (Pa)

Q:

Heat (J)

$\dot{Q}$ :

Heat rate (J/s)

r:

Radius (m)

r_b :

Radius of the basic circle of the scroll (m)

r_o :

Orbiting radius of the rotating scroll (m)

r_v :

Built-in volume ratio

s:

Specific entropy (J/kg−K)

t:

Scroll thickness (m)

T:

Temperature (°C)

u:

Specific internal energy (J/kg)

U:

Internal energy (J)

v:

Velocity (m/s)

v :

Specific volume (m³/kg)

V:

Volume (m³)

V_ed :

Expander discharge chamber volume (m³)

V_ee :

Expander expansion chamber volume (m³)

V_ei :

Expander intake chamber volume (m³)

W:

Work (J)

$\dot{W}$ :

Work rate (J/s)

W_in :

Total work input to the compressor (J)

W_out :

Net work output from the expander (J)

W_s :

Total work output for the expander (J)

z:

Height (m)

v :

Specific volume (m³/kg)

w:

Rotational speed (rad/s)

ƺ:

Leakage flow coefficient

δ:

Gap (m)

Δ:

Difference

ε:

Effectiveness

η:

Efficiency

θ:

Orbiting angle (rad)

ρ:

Density (kg/m³)

φ:

Involute angle (rad)

φ_e :

Rolling angle (involute ending angle) (rad)

φ_i,s :

Starting angle of the inner involute (rad)

φ_i0 :

Initial angle of the inner involute (rad)

φ_o,s :

Starting angle of the outer involute (rad)

φ_o0 :

Initial angle of the outer involute (rad)

a:

Actual

amb:

Ambient

b:

Base circle

c:

Curvature

conj:

Conjugate

cp:

Compressor

CV:

Control volume

d:

Discharge

diss:

Dissipated

e:

Expansion

en:

Ending

exh:

Exhaust

exp:

Expander

fix:

Fixed

i:

Initial

l:

Low

leak:

Leakage

loss:

Mechanical loss

mot:

Motor

o:

Outer orbiting radius

orb:

Orbiting

plen:

Plenum

rad:

Radial

s:

Isentropic

su:

Supply

suc:

Suction