A Virtual EXV Mass Flow Sensor for Applications With Two-Phase Flow Inlet Conditions

In conventional vapor compression systems, electronic expansion valves (EXVs) are used for refrigerant flow control. Subcooled refrigerant enters the expansion device and is expanded to the evaporation pressure while the valve opening is modified to achieve the desired mass flowrate. The relationship between the inlet and outlet conditions, the opening, and the mass flowrate has been extensively studied, e.g. by Park et al. (2007) and appropriate empirical correlations have been developed. However, for certain operating conditions (e.g. low refrigerant charge) or applications that generally have two-phase inlet conditions (e.g. balancing valves used in a hybrid control scheme as proposed by Kim et al. (2008)), these correlations are not applicable, since even low inlet vapor fractions lead to a significant reduction of the valve mass flowrate at a given opening. This paper proposes a continuous correlation that can be used for both two-phase and subcooled valve inlet conditions. The benefit of the continuity is that there is a smooth transition between subcooled and two-phase inlet conditions, which is essential for control and simulation purposes. The new correlation employs the Buckingham-Pi theorem as proposed by Buckingham (1914). The selected dimensionless Pi-groups describe opening of the valve, subcooling, inlet and outlet pressures, driving pressure difference across the valve, inlet density, surface tension, and viscosity. The data that was used to determine the coefficients of the correlation was taken on a dedicated valve test stand, which was sized for the per-circuit capacity of a typical 5-ton R410A heat pump and a 3-ton R404A large room cooling system. The purpose of these tests was mainly to map the valves for the low pressure drops, high inlet qualities and large valve openings that occur when they are used as balancing valves in a hybrid control approach. Two commercially available valves of different rated capacity were tested. Due to the much higher valve capacity for subcooled inlet conditions, valve openings of less than 5% occurred in that case. This led to an accuracy of the correlation for these points that is less than what typically can be found for correlations with subcooled inlet conditions in the open literature. However, for two-phase flow inlet conditions, the resulting RMS of 1.0 g/s for the 8-PI correlation is sufficiently small to use the approach for estimating the refrigerant mass flow and using the EXV as a virtual flow sensor. The limitations of this approach in practical applications, as well as possible applications in fault detection and diagnostics are shown for application as balancing valves within a 5-ton R410A heat pump and a 3-ton R404A large room cooling system.