|Abstract:||In some refrigeration applications, difficulties arise in establishing stable evaporator
operating conditions, especially when using a thermostatic expansion valve. The unstable
superheat signal, sometimes called hunting, of an evaporator was investigated by
developing a mathematical model of a thermostatic expansion valve and a two-passage
concentric-tube evaporator. The model was then used to study the dynamic response of the
evaporator and valve in response to changes in the system operating conditions.
The evaporator model was based on a two-passage concentric-tube heat exchanger
configuration. Equations for the conservation of mass, momentum, and energy were used
to simulate the flow and heat transfer, where differential equations for the length of the
two-phase region and mean void fraction allowed the dynamic behavior of the evaporator to
be investigated. The model also has the capability to examine the effects of refrigerant and
heat flux maldistribution among the passages.
The thermostatic expansion valve model takes into account the pressure forces on
the diaphragm as well as the pressure drop across the orifice when predicting the refrigerant
mass flow rate. The geometrical parameters that were varied in this study included the
orifice size, obstructing pin-tip angle, and diaphragm area. The model also includes the
effects of the spring constant, bulb time constant, and offset temperature-as determined
by the force applied by the obstructing pin when the valve is closed.
Superheat response was investigated by imposing suction line pressure oscillations
that varied over a range of frequencies. Large superheat fluctuations were found to exist in
a given frequency band, where the period was found to be on the order of 50 to 100
seconds, and pressure oscillations in this range should be avoided in operation.
Disturbances outside of this frequency band did not produce significant superheat
responses. Factors influencing the magnitude of the superheat response depend on the
frequency of the perturbations: at high frequencies the valve does not respond to superheatfluctuations (feedback), but is very sensitive to the slope of the flow rate versus superheat
curve as detennined by valve geometry; on the other hand, at low frequencies the valve
behavior is dominated by the superheat feedback, and the flow rate versus superheat curve
The effect of the valve parameters was also investigated by imposing a step increase
of the suction line pressure and simulating the response of· the evaporator superheat over
time. This approach allowed comparison of the steady-state and transient behavior of
superheat with different valve designs.