In refrigeration systems, a capillary tube is simply a small bore tube connecting the condenser to the evaporator. Liquid refrigerant flows into one end and expands until reaching the evaporating pressure. In doing so it maintains the refrigerant at the desired mass flow rate. A capillary tube appears to be quite simple, but the refrigerant flow inside this component is rather complex. The flow offers several challenges for a phenomenological description: turbulence, heat transfer, phase-change, compressibility and non-equilibrium effects all occur in the flow through capillary tubes. The expansion process is driven by two major effects: shear stress between the fluid flow and the tube walls, and flow acceleration when the liquid turns into vapor. The refrigerant pressure drop, as it passes through the capillary tube, is accompanied by a reduction in temperature brought about by the transfer of enthalpy from the remaining liquid to provide the enthalpy of evaporation of the flash vapor. At any stage during the expansion process the vapor formed at that point has performed its function and has no other function until it is recompressed by the compressor. In many applications the capillary tube forms a counter-flow heat exchanger with the suction line, in order to increase evaporator capacity and to prevent slugging of the compressor and sweating of the suction line. Two types of the so-called capillary tube-suction line heat exchanger are usually found: lateral and concentric. In the lateral configuration the capillary tube is brazed to the suction line, whereas it passes inside the suction line in the concentric arrangement.
Due to the importance of capillary tubes to the refrigeration industry, their thermo-hydrodynamic behavior has been extensively investigated at our laboratories for almost two decades. Here, studies have been carried out both theoretically and experimentally. Experimental investigation has generated a dataset of 1346 data points for adiabatic and 353 data points for non-adiabatic flows of various working fluids (CFC-12, HFC-134a, HC-600a, DME, HCFC-22, R-404A, R-407C, R-507A and, more recently, R-744). Theoretical investigation, on the other hand, has produced simulation algebraic and computational models for adiabatic and non-adiabatic capillary tube flows. Moreover, the behavior of the partially-clogged capillary tubes due to the deposition of POE oils have also been studied. These results have been extensively published in the open literature.
Three generations of test rigs have been built along the years to study adiabatic and non-adiabatic capillary tube flows of different various refrigerants. The state-of-the-art rig, illustrated below, is able to reproduce either a transcritical or a subcritical refrigeration cycles while controlling and recording all the relevant parameters (pressures, temperatures and mass flow rate). The test section, originally designed only for adiabatic capillary tubes, was modified in order to make also possible testing capillary tube suction line heat exchangers. The test rig was constructed with stainless steal pipes and fittings due to the high pressures involved (~13 MPa). The refrigerant is firstly pumped by two 1.75 cm3 reciprocating compressors working in parallel (C1, C2). The discharged refrigerant then passes through three oil separators (OS1, OS2, OS3) where it is diverted in two different streams (St1, St2). One stream returns the oil and part of the refrigerant to the suction line while the other carries the refrigerant to a row of filters (FC1, FC2, FP1), to guarantee a oil-free circulation of CO2 in the high-side pressure part of the rig. The high-side pressure is controlled by a PID-driven valve (V15), which allows the returning flow of refrigerant to the compressors. After the filters, the refrigerant passes through a water cooled gas-cooler, whose capacity is controlled by a valve (V20) that regulates the water flow rate. A PID-controlled electrical heater is used to fine tune the refrigerant temperature at the inlet of the capillary tube. A liquid accumulator was placed at the evaporator exit to avoid liquid carryover to the compressor. The capillary tube suction line heat exchanger was placed inside a partially dismountable wooden box, filled with polystyrene blocks that guaranteed the necessary thermal insulation, as illustrated in Fig. 3. The capillary tube was kept straightened and horizontal by two couplers (CP1, CP2). The refrigerant temperatures at the capillary tube inlet and suction line inlet and exit section were measured by immersion T-type thermocouples (IT), while the temperatures along the capillary tube wall were measured by standard 0.13 mm in diameter T-type thermocouples (T) with a maximum uncertainty of 0.2° C. The refrigerant inlet and exit absolute pressures were measured by strain gage transducers (P) with maximum uncertainties of ±10 and ±5 kPa, respectively. Finally, the mass flow rate was measured by a Coriolis-type flow meter with maximum uncertainties of ±0.04 kg/h. The experiments are usually planned following a factorial experimental technique, and the experimental data are usually reduced using dimensionless groups.
The capillary tube flow models have been developed considering the following key assumptions:
The governing equations, derived from the mass, momentum and energy conservation laws, are expressed by the following set of ordinary differential equations:
where v, p, h, and z are the specific volume [m3 kg-1], pressure [Pa], specific enthalpy [J kg-1], and axial coordinate [m], respectively, d is the capillary inner diameter [m], G the mass flux [kg s-1•m-2], τ=fG2v/8 the shear stress on the tube walls [Pa], f the Darcy friction factor, q=U(ts–tc) the heat flux [W m-2], U the overall heat transfer coefficient [W m-2 K-1], and tc and ts are the capillary tube and the suction line flow temperatures [K], respectively. In addition, considering that only superheated vapor flows through the suction line, the refrigerant flow through this part can be described by the following energy balance:
The boundary conditions are the thermodynamic states at the entrance of the capillary tube (condensing pressure and enthalpy) and at the entrance of the suction line (evaporating pressure and temperature). It should be noted that there are 4 boundary conditions and only 3 equations, but one boundary condition (evaporating or sonic pressure) has to be used for the mass flux iterative calculation. For simultaneously solving equations (1) to (3), the suction line exit temperature must be initially guessed and successively corrected according to the difference between the actual and calculated temperature at the entrance of the suction line.
Schematic of a capillary tube suction line heat exchanger
Summary of capillary tube research at POLO
Schematic representation of the test rig
Schematic diagram of the test section
Screenshot of the opening window of the CAPTUBE software
Model validation – adiabatic and subcritical flows
Model validation – non-adiabatic and subcritical flows
Study of transcritical flows of R-744 through adiabatic capillary tubes
Cláudio Melo, Ph.D.