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Abstract
As the digital age engulfs our society, more and more devices surrender to the inevitable fate of digital control.  Routinely, digital electronics replace traditional mechanical systems usually yielding an improvement in cost, size, weight, durability, performance, repeatability, and power consumption. As of the date of this document, no commercially available automobile is equipped with a digitally controlled throttling device for their air conditioning system.  A primary reason for this is economics.  Automotive manufactures cannot justify the additional costs associated with a microcontroller and an electronically controlled throttling device, even if they significantly improve performance and durability.  As electronics become smaller, cheaper, “smarter”, and faster, electronic alternatives to traditional systems become increasingly prevalent.

Most techniques of actively controlling the performance of vapor-compression air conditioning system use evaporator superheat as the feedback parameter. Unfortunately, any amount of superheat causes the evaporator to operate at reduced capacity due to dramatically lower heat transfer coefficients in the superheated region. This document presents and defends a system that allows a vapor-compression air conditioning system to be stably controlled in a regime where liquid and vapor refrigerant are exiting the evaporator.   The uniqueness of this system is attributed to the feedback transducer.  The transducer is able to deliver a signal to the controller that is a function of the amount (by mass) of liquid droplets impinging on the transducer.  By placing the transducer in the stream of refrigerant exiting the evaporator, a refrigerant throttling device can be manipulated to regulate the amount of liquid refrigerant that impinges the feedback transducer. With the signal from this transducer as the feedback in a control scheme, a controller can be constructed that essentially regulates system performance, and is able to control the system in regimes where superheat feedback is unable to operate.

Introduction
A traditional method of controlling evaporator superheat in a vapor compression air conditioning system is the thermostatic expansion valve (TXV).  Such systems are often used in automotive applications.  The TXV depends on superheat to adjust the valve opening.  Unfortunately, any amount of superheat causes the evaporator to operate at reduced capacity due to dramatically lower heat transfer coefficients in the superheated region.  In addition, oil circulation back to the compressor is impeded.  The cold lubricant almost devoid of dissolved refrigerant is quite viscous and clings to the evaporator walls.  A system that could control an air conditioner to operate with no superheat would either decrease the size of its existing evaporator while maintaining the same capacity, or potentially increase its capacity with its original evaporator.  Also, oil circulation back to the compressor would be improved.  To operate at this two-phase evaporator exit condition a feedback sensor would have to quantify the quality or the mass fraction of liquid in a liquid-superheated vapor stream of the refrigerant exiting the evaporator.

Project Goals
The primary objective of the research presented in this document is the development of a system capable of regulating the mass fraction of liquid in the liquid-vapor stream exiting an evaporator. This dimension of controllability will allow exploration of a previously uncontrollable regime resulting in potentially different (and possibly better) COPs, capacities, and other performance quantifiers.  Precursors to the implementation of a control scheme are the development of the feedback transducer and a comprehensive understanding of the behavior of the sensor over a wide range of conditions.
The scope of this research can be concisely summarized in four major goals:

1. design and fabrication of a sensor capable of qualitative assessment of the mass of liquid in a two phase liquid-vapor refrigerant stream exiting an evaporator
2. dynamically characterize and analyze the sensor to obtain insight into its behavior
3. map the systems' operating conditions to the sensor’s response to determine preferred operating regimes
4. develop a controller that utilizes this sensor as feedback

Motivation
One of the most common control schemes for a vapor compression air conditioning system is the use of a thermostatic expansion valve (TXV).  TXV systems use a remote thermal bulb at the exit of the evaporator.  This bulb causes the TXV to open and close in response to changes in superheat of the refrigerant at the evaporator outlet.  If the temperature of the refrigerant increases rapidly, as would be the case when the heat load was suddenly increased, the power element would open the valve and admit more liquid refrigerant to the evaporator.  Once in the evaporator, the liquid refrigerant absorbs heat by changing state from liquid to gas.  By the time it leaves the evaporator, the gaseous refrigerant has been superheated a few degrees.

By allowing the evaporator to operate with some non-zero superheat at its exit, some portion of the evaporator will have only vapor flowing through it (no liquid).  This situation decreases the refrigerant-side heat transfer.  This portion of the evaporator is not able to vaporize refrigerant, and is only able to transfer heat via the sensible heating of the refrigerant.  This process can reduce the capacity of the evaporator.

Any control scheme that uses superheat as its control signal (e.g. TXV systems) must have some non-zero superheat.  Such a system is unable to control the plant to operate in a regime of saturated liquid/vapor at the exit of the evaporator.  The minimum amount of superheat that such a system can use and maintain stability is dependent on the method of measuring the superheat.
The difficulty of a temperature measurement is in part due to the non-equilibrium flow of refrigerant as it exits the evaporator only slightly superheated.  The flow is said to be non-equilibrium because saturated liquid droplets are entrained in superheated vapor. There is just not enough time for the liquid to vaporize and reach equilibrium.  This phenomenon can be attributed to mal distribution of liquid/vapor refrigerant throughout the evaporator and to the nature of two-phase flow.  The saturated liquid droplets in superheated vapor flow regime cause temperature transducers to exhibit large variances.
In evaporators with imperfectly distributed exit streams, a mixture of superheated vapor and droplets often exits the evaporator.  Some channels or circuits that are thermally overloaded have superheated vapor at the exit, while others where thermal loads are not sufficient to evaporate all liquid that enters will have some droplets at the exit.  The mixture of these streams is in thermal non-equilibrium.  After sufficient time (or length of pipe) the droplets would completely evaporate, reducing superheat.  But if the sensible heat available in the superheated vapor is not enough energy to vaporize all droplets, then the exit stream is in the true two-phase quality region.  Liquid-mass-fraction (LMF), which is the mass of liquid in vapor of any state, is a measure to describe the state at the evaporator exit, as described in Shannon, Hrnjak, and Leicht.  A temperature transducer measuring the temperature of refrigerant in this non-equilibrium flow regime can read the saturation temperature (if a liquid droplet is on the transducer), or can read the temperature of the superheated vapor (which may not be constant), or can read any value in between.  A large variance in a control signal (e.g. superheat) can cause a controller to hunt.  Since the non-equilibrium flow has superheated vapor along with liquid droplets, quality cannot be used to correctly describe the state of the refrigerant.

Please see A Sensor for Estimating the Liquid Mass Fraction of the Refrigerant Exiting an Evaporator for details on the development of the sensor.

Conclusions
This project presented the complete history of the development of a controller that is capable of regulating the liquid-mass-fraction (LMF) of refrigerant exiting an evaporator of a vapor-compression air conditioning system.  The feedback sensor of the controller is a constant temperature RTD.  This sensor is responsible for estimating relative amounts of liquid refrigerant in a stream of refrigerant. The voltage across the RTD and the temperature of the free-stream refrigerant was estimated and used to used to compute the surface-to-free-stream thermal conductance, or hA.  hA is a parameter that was defined in this document and that parameter was used as an estimate of the LMF. The sensor’s output (hA) was correlated with LMF data to prove that the sensor could predict LMF.

Once it was determined that the sensor’s output was some function of LMF, data was taken to correlate the hA parameter to various system performance characteristics.  Numerical values of hA were mapped to the performance of the system (using parameters such as COP and evaporator capacity to define the performance of the system).  This was done so that hA could be used as a measure of the system’s performance.

A controller was designed and built to regulate the hA of the system.  First, a fifth-order linear approximation of the plant was developed.  Then a lag compensator and a PI controller were designed to give the controller the desired dynamics.  The control algorithm was implemented on a DSP-based controller.  The controller was tested and determined to be able to regulate hA with a constant hA setpoint, with a step change in the hA setpoint, and with a ramp change in the thermal load of the evaporator.

By using the data collected in chapter 4 (appendix B) regulating hA can be interpreted as regulating various system performance characteristics.  For example, the hA that corresponds to the maximum capacity can be regulated.

last modified 1 august 2000