Capillary Tube Flows
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Status: Ongoing

Summary

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.

Objectives

  • To carry out a comprehensive experimental work to understand the phenomena that govern the capillary tubes flows for various running, geometric and faulty conditions
  • To collect data for a model validation exercise and to develop a model for predicting the mass flow rate and heat exchanger effectiveness as functions of geometric and operating conditions

Experimental Facility

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.

Mathematical Modeling

The capillary tube flow models have been developed considering the following key assumptions:

  • The capillary is a straight, horizontal tube with a constant cross-sectional area
  • The viscous compressible flow is one-dimensional in the axial direction
  • The heat diffusion is neglected due to the high (104) Péclèt number
  • The heat conduction through the tube walls is disregarded due to the low (10-3) Biot number
  • The pressure drop along the length of the suction line is neglected
  • The pressure drop at the capillary tube entrance and exit sections is disregarded [12]
  • The suction line is perfectly insulated from the surrounding air
  • The two-phase flow is considered homogeneous [5]
  • The metastable flow is neglected due to its inherent unpredictability [12]

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.

References

Congress Papers

  • Melo C, Ferreira RTS, Pereira RH, Modelling adiabatic capillary tubes: A critical analysis, International Refrigeration Conference: Energy Efficiency and New Refrigerants, West Lafayette, USA, pp.113-122, 1992
  • Seixlack AL, Prata AT, Melo C, Modeling the HFC-134a Flow Through Capillary Tubes Using a Two-Fluid Model, International Refrigeration Conference at Purdue, West Lafayette-USA, July 23-26, 1996, pp.89-94, 1996
  • Mezavila MM, Melo C, CAPHEAT: An homogeneous model to simulate refrigerant flow through  non-adiabatic capillary tubes, International Refrigeration Conference at Purdue, West Lafayette, USA, pp. 95-100, 1996
  • Hermes CJL, Melo C, Negrão COR, Mezavila, M.M., Dynamic simulation of HFC-134a flow through adiabatic and non-adiabatic capillary tubes, International Refrigeration Conference at Purdue, West Lafayette, USA, pp.295-303, 2000
  • Negrão COR, Melo C, Shortcomings of the numerical modeling of capillary tube-suction line heat exchangers, 20th International Congress of Refrigeration, Sydney, Australia, CD-ROM, 1999
  • Melo C, Ferreira RTS, Boabaid Neto C, Gonçalves JM, Pereira RH, Thiessen MR, Evaluation of HC-600a, HFC-134a and CFC-12 mass flow rates through capillary tubes, New Applications to Reduced Global Warming and Energy Consumption Conference, Hannover-Germany, May 10-13, pp. 621-630, 1994
  • Melo C, Ferreira RTS, Boabaid Neto C, Gonçalves JM, Experimentation and analysis of refrigerant flow through adiabatic capillary tubes, AES-Vol.34 Symposium on Heat Pump and Refrigeration Systems Design, Analysis and Applications, ASME International Congress and Exposition, San Francisco-CA, pp.19-29, 1995
  • Melo C, Ferreira RTS, Boabaid Neto C, Gonçalves JM, Analysis of capillary tube performance running with DME (E-170) as working fluid, Internal Report, POLO Laboratories, Federal University of Santa Catarina, Florianópolis, Brazil, 1995 (in Portuguese)
  • Mendonça KC, Melo C, Ferreira RTS, Pereira RH, Experimental study on lateral capillary tube-suction line heat exchangers, International Refrigeration Conference at Purdue, West Lafayette, USA, pp. 437-442, 1998
  • Melo C, Zangari JM, Ferreira RTS, Pereira RH, Experimental studies of non-adiabatic flow of HFC-134a through capillary tubes, International Refrigeration Conference at Purdue, pp. 305-312, West Lafayette, USA, 2000

Journal Papers

  • Melo C, Ferreira RTS, Boabaid Neto C, Empirical correlations for the modelling of HFC-134a flow through adiabatic capillary tubes, ASHRAE Transactions, Vol.105, Part 2, pp.51-59, 1999
  • Melo C, Ferreira RTS, Boabaid Neto C, Gonçalves JM, Mezavila MM, An experimental analysis of adiabatic capillary tubes, Applied Thermal Engineering, Vol.19, No.6, pp. 669-684, 1999
  • Melo C, Vieira LAT, Pereira RH, Non-adiabatic capillary tube flow with Isobutane, Applied Thermal Engineering, Vol. 22, No. 14, pp. 1661-1672, 2002
  • Melo C, Vieira LAT, Pereira RH, Experimental study on adiabatic flow of R-22 alternatives in capillary tubes, International Refrigeration Conference at Purdue, West Lafayette, USA, R-075, 2004
  • Hermes CJL, Melo C, Gonçalves JM, Modeling of non-adiabatic capillary tube flows: A simplified approach and comprehensive experimental validation, International Journal of Refrigeration, Volume 31, Issue 8, December 2008, Pages 1358-1367
  • Hermes CJL, Silva DL, Melo C, Goncalves JM, Weber GC, Algebraic solution of transcritical carbon dioxide flow through adiabatic capillary tubes, International Journal of Refrigeration, 200?
  • Silva DL, Hermes CJL, Melo C, Goncalves JM, Weber GC, A study of carbon dioxide flows through adiabatic capillary tubes, International Journal of Refrigeration, 200?

Figures

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

Principal Investigator

Cláudio Melo, Ph.D.

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