Question

A throttling calorimeter shown below is used to determine the quality of a two-phase mixture of R-134a refrigerant that is flowing in a tube. The calorimeter operates by bleeding offa small fraction of the flow stream and throttling it to a lower pressure. The device is based upon the fact that over a wide range of temperatures and qualities, the two-phase refrigerant can be throttled to a superheated vapor state. In this case, it is possible to estimate the stream quality through the use of an energy balance and measurements of the temperature inside the tube and pressure exiting the throttling valve. Assuming that the two-phase refrigerant is atia temperature of 50 F and the stream is throttled to 4 psia, then do the following: Determine the minimum and maximum possible exit temperatures from the throttle that will allow determination of quality. a. b. What is the minimum quality that this device would be capable of measuring?

Answer 1

Given data Superheated refrigerant pressure, Pup-45 psia Temperature of wet refrigerant, T 50 F Consider the figure of the given throttled calorimeter shown below. state 1 two-phase R-134a superheated R-134a P 4 psia Figure I From the table for superheated refigerant 134-a at 4 psia or 0.02756 MPa Tat49.66 C -57.388 F And hat 368.2 kJ/kg Here, Tt is the temperature of the saturated vapor refrigerant 134-a, ts the enthalpy of saturated vapor refrigerant 1 34-a Hence, the minimum possible exit temperature from the throttle is 57.388 F

From the table for superheated refrigerant 134-a at 4 psia or 0.02756 MPa p 371.5J/kg c 0.7224 kJ/kg °C gp 45 °c And And =-49 F Here, hup is the enthalpy of superheated refigerant 134-a and cp is the specific heat at constant pressure of superheated refrigerant 134-a Hence, the maximum possible exit temperature from the throttle is -49 F From the table for saturated refrigerant 134-a at 50 K And 404.5 kJ/kg Here, h is the enthalpy of the saturated liquid refrigerant 134-a and h is the enthalpy of the saturated vapor refrigerant 134-a at 50K Write the expression for minimum quality 4+x(4-4)-(A)50K + x(4-4)-(hsat),psia Here, h throttling, which is a constant enthalpy process, it becomes equal to the enthalpy of the saturated vapor at 4 psia is the enthalpy of the initial state, when the refrigerant was two -phase, and after 50K

Substitute the values 213.6kJ/kg xx(404.5 kJ/kg 213.6kJ/kg) 368.2 kJ/kg x0.81 Hence, the minimum quality the throttling device would be capable of measuring is 0.81