Investigations Of Heat And Momentum Transfer in Vapor- Liquid Isobutane Injector

Kamil ŚMIERCIEW1, Dariusz BUTRYMOWICZ 1* , Tomasz PRZYBYLINSKI 2

(1) Bialystok University of Technology, Bialystok, Poland (2) Institiute of Fluid-Flow Machinery, PAS, Gdansk, Poland ó Introduction

ó Mathematical model of two-phase injector

ó Analysis of isobutane two-phase injector

ó Conclusions Introduction

Mechanical liquid liquid is the only element of the ejector refrigeration system that consume electric power. Without consumption of electric power to drive the system would be fully thermal driven.

The general motivations of application of the two-phase injector pump are:

• two-phase injector operates also as pre-heater of liquid phase supplied to the vapour generator that additionally improve the system efficiency;

• this type of injector is more simple and reliable than mechanical liquid pump since it has no moving parts as well as is not influenced to possible that may occur in mechanical .

• this type of injector is more simple and reliable than mechanical liquid pump since it has no moving parts as well as is not influenced to possible cavitation that may occur in mechanical pumps. Schematic of vapour-liquid injectors: a) subsonic; b) supersonic: SN – vapour motive nozzle; WN – liquid nozzle; MC – mixing chamber; DF – diffuser, t – throat

Classic ejection refrigeration system Modified ejection refrigeration system with two-phase injector as a liquid pump Mathematical model of two-phase injector

Motive vapour nozzle Liquid nozzle nozzle is adiabatic with irreversible losses p = p = p ρ = ρ(p ,T ) continuity balance equation V1 L1 1 L1 V1 L0 = ρ ρ = ρ mL0 AL1 L1wL1 w AV 0 V 0wV 0 AV1 V1wV1 & L1 energy balance equation w2 w2 w2 h + V 0 = h + 1sV = h + V1 V 0 2 1sV 2 V1 2

2 2 w  w  wV1 = + ()− 2 1sV = 2 + ()− 2  + V 0  c = hV1 h 1sV 1 cv cv h 1sV 1 cv hV 0  v 2  2  w 1sV Mathematical model of two-phase injector

Assumptions : vapour phase is saturated in the mixing chamber both phases at the throat constitute homogeneous mixture

common velocity w2, i.e. there is no slip between the phases ρ = ρ + ρ A2 2w2 AV 1 V 1wV 1 AL1 L1wL1 Mixing chamber m w + A p + (A − A ) p = m w + m w + A p & 2 2 2 2 1 2 MC &V 1 V1 & L1 L1 1 1 balance equations  w2   w2   w2   + 2  =  + V 1  +  + L1  m& 2 h2  m& V 1hV 1  m& L1hL1   2   2   2 

The mixture enthalpy h2 may be evaluated from the relations describing of the thermodynamic properties of temperature TL2 of liquid phase is homogenous two-phase flow below the saturation temperature since subcooled liquid enters the = ( ρ )= + − ρ h2 h p2 , 2 ,TL2 x2hV ,sat ( p2 ) 1( x2 )hL2 ( L2 ,TL2 ) injector ρ ρ − ρ ( p ,T ) ∆ = − V ,sat ( p2 ) ϕ = 2 L2 2 L2 TL2 TV ,sat ( p2 ) TL2 x = ϕ 2 2 2 ρ ρ − ρ ( p ,T ) 2 V 2 L2 2 L2 Testing stand

1 – tested injector; 2,3 – control ; 4 – condenser; 5,8 – circulating pump of ; 6,9 – mass flow meter; 7 – vapour generator; 10 – liquid subcooler; 11 – circulating pump of glycol; 12 – mass flow meter; 13 – electric heater; 14 – circulating pump of glycol, 15 – fan cooler; 16 – control valve; 17 – mass flow meter Testing stand – tested injector

throat diameter of the motive nozzle: 1.5 mm; diameter of the mixing chamber: 2.2 mm

Definitions compression efficiency – power of isochoric compression of liquid in reference to motive power p− p η = U d sL c ρ ()− dLh V h dL injector efficiency – power of liquid compression + powier of liquid heating in reference to motive power U p− p  η =d sL +h − h e − ρ dL sL  hV h dL dL  p compression ratio π = d e psL ∆ = − superheating of liquid TL T dL T sL c∆ T Jakob number Ja = pL L hfg Results

η Relationship between total injector efficiency e versus Jakob number Ja Results

liquid throat 0.13 mm liquid throat 0.21 mm liquid throat 0.30 mm 1.4

1.2 compression

1 10 15 20 25 30 35 liquid temperature increase [K]

Performance characteristics of the injector operations for various liquid nozzle gaps thickness Results

1

0.5 heat transfer coefficient heat transfer [MW/m2K] 0 0 5 10 liquid temperature increase in mixing chamber [K]

Condensation film heat transfer coefficient versus temperature increase of liquid phase. Results

p0 = 8 bar Compression ratio versus 1.4 p0 = 10 bar liquid phase temperature 1.3 increase for various motive pressures 1.2 compression

1.1

1 18 20 22 24 26 liquid temperature increase [K]

liquid throat 0.21 mm Compression ratio liquid throat 0.30 mm versus liquid phase 1.4 temperature increase 1.2 for: U = 3.5, compression pV = 10 bar 1 15 20 25 30 liquid temperature increase [K] Results

Vapour superheating = 7 K Variable vapour superheating Compression ratio versus 1.3 liquid phase temperature increase for various ompression 1.2 c vapour superheating: 1.1 U = 4.5, pV = 8 bar, δ = 0.21 mm 1 1 19 20 21 22 23 24 25 Liquid temperature increase [K]

Compression ratio Vapour superheating = 7 K Variable vapour superheating versus vapour 1.3 superheating: ompression

c 1.2 U = 4.5, pV = 8 bar, δ 1 = 0.21 mm 1.1

1 −2 0 2 4 6 8 Vapour superh ea ting [K] Conclusions

• The experimental investigations covered the measurement of the performance of the two-phase injector for isobutane as working fluid in terms of the compression ratio, heat transfer, and mass entrainment ratio. It was shown that intensive condensation heat transfer occurs inside the mixing chamber of the injector in spite of the unfavourable thermokinetic properties of isobutene as working fluid. • The effect of the liquid gap thickness lays crucial role on momentum and heat transfer in the mixing chamber of the injector. • The effect of incomplete condensation process strongly affects heat and momentum transfer inside the injector. • Exceptionally high level of heat transfer coefficient was achieved in the injector so that the tested device may be thought not only as an alternative thermally driven liquid pump but also an effective direct contact condenser