RELATED APPLICATION

[0001]
This application is based on U.S. Provisional Application Ser. No. 60/523,447, filed on Nov. 19, 2003, the contents of which are incorporated herein in their entirety by reference.
BACKGROUND OF THE INVENTION

[0002]
Lubricating oil in the compressor of a heating, ventilation and air conditioning (HVAC) system provides lubrication for moving parts in the compressor. Good lubrication ensures the safe operation of the compressor. For a refrigerant compressor, the oil lubricating capability decreases when the oil is mixed with liquid refrigerant. For example, this may happen when the defrost operation is turned on during the heating season, since under such conditions, the indoor fan is typically shut down, and liquid in the evaporator may not be evaporated. As a result, large amounts of liquid refrigerant may enter the compressor chamber and mix with the lubricating oil.

[0003]
To quantify how much liquid refrigerant is mixed with oil in the compressor, an important index under investigation is oil concentration. For reliable operations, oil concentration needs to be above a certain level such that the viscosity of the oil/refrigerant mixture is large enough to guarantee sufficient lubrication for moving parts in the compressor.

[0004]
All refrigerant compressors circulate some amount of oil through the system. It is essential that oil be returned in the system. However, in an evaporator, when superheat is large and evaporating temperature is low, oil viscosity may become high because liquid refrigerant becomes vapor in the superheat range. If vapor velocity is not sufficient to transport the oil, some oil may remain in the evaporator. Similarly, in suction lines, oil retention may be a problem if refrigerant vapor velocity is not sufficient or the refrigerant temperature is low.

[0005]
For a multievaporator system with a vertical gas line, if the vapor velocity is not high enough, the oil cannot be pushed upward and return to the compressor. When a significant amount of oil remains in the evaporatorcondensergas line circuit or accumulator, the oil in the compressor will be not sufficient to provide reliable lubrication.

[0006]
Conventionally, the amount and concentration of oil in the compressor cannot be directly measured without special sensors. For purposes of research and development on the system, special designs can be used to place costly viscosity sensors at the bottom of the compressor to measure the viscosity of the oil/refrigerant mixture in the compressor, and oil concentration is calculated from the value of viscosity and oil temperature. Through a glass window installed at the side of compressor, the oil/refrigerant mixture liquid level can be measured. Without a viscosity sensor or a special oil concentration meter that is not available in actual application of air conditioning and refrigeration systems, the amount and concentration of oil in the compressor cannot be determined in conventional systems.
SUMMARY OF THE INVENTION

[0007]
This invention provides an innovative method to determine the amount and/or the concentration of lubricant in the compressor of an HVAC system based on HVAC component oil models and heat exchanger observers.

[0008]
In accordance with a first aspect, the invention is directed to an apparatus and method for monitoring a parameter related to lubricant in a first component of a vapor compression cycle system. In accordance with the invention, a parameter related to retained lubricant in a plurality of other components of the vapor compression cycle system is estimated. The estimate of the parameter related to retained lubricant in the plurality of other components is subtracted from a parameter related to a known total lubricant in the vapor compression system.

[0009]
In one embodiment, the first component of the vapor compression cycle system is a compressor. The plurality of other components of the vapor compression cycle system can comprise at least one of an evaporator, an accumulator, a suction gas line, a discharge gas line, a condenser, a liquid line and a receiver. The parameter related to retained lubricant in the plurality of other components of the vapor compression cycle system can be determined using one or more parameters related to the state of each component of the vapor compression system.

[0010]
In accordance with another aspect, the invention is directed to an apparatus and method for monitoring a parameter related to lubricant in a component of a vapor compression cycle system. In accordance with the invention, a parameter related to a state of the component is detected. The parameter related to lubricant in the component is estimated using the parameter related to the state of the component.

[0011]
In one embodiment, the parameter related to lubricant in the component is used to determine an amount of lubricant in the component. In one embodiment, the parameter related to lubricant in the component is used to determine a concentration of lubricant in the component. In one embodiment, the component of the vapor compression cycle system is one of an evaporator, an accumulator, a suction gas line, a discharge gas line, a condenser, a liquid line and a receiver.

[0012]
In accordance with another aspect, the invention is directed to an apparatus and method for monitoring a parameter related to lubricant in a heat exchanger of a vapor compression cycle system. In accordance with the invention, a length of a twophase portion of the heat exchanger is determined. The parameter related to lubricant in the heat exchanger is estimated using the length of the twophase portion of the heat exchanger.

[0013]
In accordance with another aspect, the invention is directed to an apparatus and method for monitoring a parameter related to lubricant in a heat exchanger of a vapor compression cycle system. In accordance with the invention, a length of a singlephase portion of the heat exchanger is determined. The parameter related to lubricant in the heat exchanger is estimated using the length of the singlephase portion of the heat exchanger.
BRIEF DESCRIPTION OF THE DRAWINGS

[0014]
The foregoing and other objects, features and advantages of the invention will be apparent from the more particular description of a preferred embodiment of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

[0015]
FIG. 1A contains a schematic block diagram of a vapor compression refrigeration system in accordance with one embodiment of the present invention.

[0016]
FIG. 1B contains a schematic block diagram of the overall structure of an embodiment of the oil observer in accordance with the invention.

[0017]
FIG. 2 contains a schematic functional block diagram of one embodiment of an evaporator observer in accordance with the invention.

[0018]
FIG. 3 contains a schematic functional block diagram of one embodiment of a condenser observer in accordance with the invention.

[0019]
FIG. 4 contains a schematic diagram of the element model for the condenser twophase flow region in accordance with the invention.

[0020]
FIG. 5 contains a schematic block diagram of the element model for the evaporator twophase flow region in accordance with the invention.

[0021]
FIG. 6 contains a schematic block diagram of a liquid line in accordance with the invention.

[0022]
FIG. 7 contains a schematic diagram of a loworder evaporator model in accordance with the invention.

[0023]
FIG. 8 contains a schematic diagram of a loworder condenser model in accordance with the invention.

[0024]
FIG. 9 contains a graph of the outdoor air temperature profile over time for an experiment performed in accordance with the invention.

[0025]
FIG. 10 contains a graph of the compressor oil viscosity profile over time for the experiment.

[0026]
FIG. 11 contains a graph of the compressor oil temperature profile over time for the experiment.

[0027]
FIG. 12 contains a graph of the discharge pressure profile over time for the experiment.

[0028]
FIG. 13 contains a graph of the suction pressure profile over time for the experiment.

[0029]
FIG. 14 contains a graph of the mass flow rate profile over time for the experiment.

[0030]
FIG. 15 contains a graph of the evaporating temperature profile over time for the experiment.

[0031]
FIG. 16 contains a graph of the condensing temperature profile over time for the experiment.

[0032]
FIG. 17 contains a graph illustrating compressor oil mass estimation error in accordance with the invention.

[0033]
FIG. 18 contains a graph illustrating estimation error of oil concentration in the compressor in accordance with the invention.

[0034]
FIG. 19 contains a graph illustrating a comparison between experimental and estimated oil mass in the compressor in accordance with the invention.

[0035]
FIG. 20, contains a graph of refrigerant mass inventory in the condenser in accordance with the invention.

[0036]
FIG. 21 contains a graph of condenser subcool section length for one pass in accordance with the invention.

[0037]
FIG. 22 contains a graph of the oil mass in the condenser in accordance with the invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

[0038]
FIG. 1A contains a schematic block diagram of a vapor compression refrigeration system in accordance with one embodiment of the present invention. Referring to FIG. 1A, the vapor compression system includes a condenser 1 connected to a compressor 3 via a gas discharge line 2. An accumulator 4 collects refrigerant flowing through the system and is connected to the compressor 3. An evaporator 6 is connected to the accumulator 4 via a gas suction line 5. An expansion valve 8 is connected to the evaporator 6 via a liquid line 7. A receiver 9, which receives and stores liquid refrigerant flowing through the system is connected between the condenser 1 and the expansion valve 8. It should be noted that although not shown in the drawing of FIG. 1A, the vapor compression system of the invention can also include additional components such as an oil separator, a gas cooler, an internal heat exchanger or other components. The invention is applicable to systems that include these and other components of vapor compression refrigeration systems.

[0039]
In this invention, a dynamic nonlinear observer to estimate the oil concentration and the amount of oil in a refrigerant compressor is described. This oil observer is based on 1) integrated oil/refrigerant distribution and circulation model to estimate oil mass and refrigerant mass in each HVAC component, 2) heat exchanger observers to estimate the twophase section lengths of the evaporator and condenser, and the subcool section length of the condenser, 3) mass conservation for oil and refrigerant in the whole machine. Dynamic simulation based on the oil/refrigerant model requires the initial conditions for all state variables. However, most of the initial conditions for the state variables cannot be measured by sensors. The dynamic nonlinear observer of the invention described herein can estimate unmeasured variables such as oil concentration and oil amount in the compressor using available sensor information such as evaporating temperature, condensing temperature, etc.

[0040]
To synthesize an oil observer, integrated models for oil/refrigerant circulation and distribution have been developed for each main component of an air conditioning and refrigeration system. Components include evaporator, condenser, gas line, liquid line, accumulator and compressor. Oil retention and refrigerant mass in each component are estimated based on void fraction model and estimated geometry of heat exchangers such as length of twophase section in evaporator and lengths of twophase section and sub cooled onephase liquid section in condenser.

[0041]
There are no sensors to measure length of the twophase section in the evaporator and the lengths of the twophase section and sub cooled onephase liquid section in the condenser. In accordance with the invention, a dynamic evaporator observer is used to estimate length of the twophase section in the evaporator based on available sensor information of evaporating temperature. A dynamic condenser observer is used to estimate lengths of the twophase section and sub cooled onephase liquid section in the condenser based on available sensor information of condensing temperature.

[0042]
This invention is applicable to reciprocating compressors, scroll compressors, rotary and swing compressors, centrifugal compressors, and screw compressors. This invention is applicable to residential air conditioners and heat pumps, commercial air conditioners and heat pumps, chillers, multievaporator systems, refrigerators, refrigeration systems and other types of machines working on the vapor compressor cycle principle. This invention is applicable to all combinations of micible oil and refrigerant.

[0000]
1. Oil Observer Structure.

[0043]
An oil observer described herein in accordance with the invention is based on oil models that will be described below in Section 2 and uses a sensor measurement such as evaporating temperature, condensing temperature, superheat, subcool, etc., to estimate the oil concentration and oil amount in the compressor, without an expensive viscosity sensor.

[0044]
FIG. 1B is a schematic block diagram of the overall structure of an embodiment of the oil observer 10 in accordance with the invention. In FIG. 1B, the evaporator oil model 12 is used to estimate oil mass and refrigerant mass in the evaporator. The twophase length of the evaporator Lei is obtained from the evaporator observer 14, which is described in Section 4 below. The structure of the evaporator observer 14 is shown in FIG. 2, which is a schematic functional block diagram of the evaporator observer 14. The evaporator observer is a dynamic observer taking evaporating temperature Te as an input, and whose output is the twophase length Lei (that is I in the model equation).

[0045]
The condenser oil model 16 is used to estimate oil mass and refrigerant mass in the condenser. The twophase length of the condenser L_{c2 }and the subcool section length L_{c3 }are obtained from the condenser observer 18, which is described in Section 4 below. FIG. 3 is a schematic functional block diagram of the condenser observer 18. The condenser observer 18 is a dynamic observer that is similar to the evaporator observer 14, taking condensing temperature Tc, subcool SC, etc., as input, and having twophase length L_{c2 }and subcool section length L_{c3 }as outputs. The gas line oil model 20 is used to estimate oil mass and refrigerant mass in the gas line using parameters provided by the gas line observer 60. The liquid line oil model 22 is used to estimate oil mass and refrigerant mass in the liquid line using parameters provided by the liquid line observer 62. The accumulator oil model 24 is used to estimate oil mass and refrigerant mass in the accumulator. The accumulator oil model 24 receives input information including liquid volume in the accumulator, which is measured from the accumulator glass window or other measurement/estimation methods 26. For an air conditioning or refrigeration system without an accumulator, the accumulator oil model 24 in FIG. 1B is not used. The receiver oil model 64 is used to estimate oil mass and refrigerant mass in the receiver.

[0046]
With the estimation of oil mass in the evaporator, condenser, gas line, liquid line and accumulator, the oil mass in the compressor is obtained since total oil mass in the machine is constant. With the estimation of refrigerant mass in the evaporator, condenser, gas line, liquid line and accumulator, refrigerant mass in the compressor is obtained since total refrigerant mass in the machine is constant. Furthermore, the liquid refrigerant in compressor can be estimated and then the oil concentration can be calculated based on estimated oil mass and liquid refrigerant mass in the compressor.

[0000]
2. Component Oil/Refrigerant Models

[0047]
In this section, models for estimating oil mass and refrigerant mass in the evaporator, the condenser, the gas line, the liquid line and the accumulator are described. To estimate the oil mass and refrigerant mass the in evaporator and condenser accurately, important factors are 1) proper void fraction model, 2) accurate volumes for onephase subcool liquid section length in the condenser and twophase section lengths, 3) and oil circulation rate.

[0000]
2.1 Condenser Oil Model: Refrigerant and Oil Mass in Condenser

[0048]
FIG. 4 is a schematic diagram of the element model for the condenser twophase flow region. The condenser can be divided into three sections as shown in FIG. 4: the superheated section 28 having length L_{c1}, the twophase section 30 having length L_{c2 }and the sub cooled section 32 having length L_{c3}. Lengths L_{c2 }and L_{c3 }are obtained from the condenser observer 18.

[0049]
The twophase section 30 of the condenser can be divided into N elements i. At i=1, the vapor quality x=0; at i=N, x=1. For a condenser, it is assumed that the heat flux from the heat exchange is constant. Then the vapor quality decreases linearly. The twophase region is divided into N elements as shown in FIG. 4,0so that within each element the thermodynamic property differences in each phase are negligible.

[0050]
The length of each element is dl_{2}=Lc_{2}/N and vapor quality x(i) in section i can be evaluated:
$\begin{array}{cc}x\left(i\right)=\frac{i1}{N1}& \left(1\right)\end{array}$
It is assumed that Lc_{2 }is the length of twophase section, x is the vapor quality of the oil/refrigerant mixture at a location of condenser, C_{oil }is the oil circulation rate (wt %) defined as the ratio of oil mass flow rate and total oil/refrigerant mixture mass flow rate, and a is void fraction which can be estimated by different void fraction models. The following equations (2) through (4) are used in accordance with one embodiment of the invention to estimate mean void fraction a based on Hughmark's void fraction model that is dependent on mass flow rate.
$\begin{array}{cc}\alpha ={K}_{H}\beta & \left(2\right)\\ \beta =\frac{x/{\rho}_{g}}{\left(x/{\rho}_{g}\right)+\left(1x\right)/{\rho}_{l}}& \left(3\right)\end{array}$
where the parameter K_{H }has been fitted to a polynomial:
$\begin{array}{cc}\begin{array}{c}{K}_{H}=0.72664773.481988\times {10}^{4}{Z}_{k}\\ \frac{0.845427}{{Z}_{k}}+0.0601106{Z}_{k}^{1/3}\end{array}& \left(4\right)\end{array}$
while Z_{k }depends on viscosity, averaged Reynold number Re (depending on mass flux etc.), the Froude number Fr, and the liquid volume fraction Y_{L}.
$\begin{array}{c}{Z}_{k}=\frac{{\mathrm{Re}}^{1/6}{\mathrm{Fr}}^{1/8}}{{y}_{L}^{1/4}}\\ \mathrm{Re}=\frac{\mathrm{DG}}{{\mu}_{l}+\alpha \left({\mu}_{v}{\mu}_{l}\right)}\\ \mathrm{Fr}=\frac{1}{\mathrm{gD}}{\left(\frac{\mathrm{Gx}}{\beta \text{\hspace{1em}}{\rho}_{v}}\right)}^{2}\\ {y}_{L}=1\beta \end{array}$
where D is tube hydraulic diameter, G is refrigerant mass velocity, g is acceleration due to gravity, and μ_{v }is dynamic viscosity of refrigerant vapor, and μ_{l }is viscosity of liquid mixture.

[0051]
For each element in the twophase section 30, the void fraction is calculated based on the Hughmark's void fraction mode using the parameters in that element. For a certain element with vapor quality x and calculated void fraction value α, the total liquid volume (liquid refrigerant+oil) in that element is dQ_{liquid}=dV(1−α)=A_{c}dz(1−α). Assuming that the oil is well mixed with the liquid refrigerant, the following equation (5) is used to estimate the oil mass retention in that element.
$\begin{array}{cc}{\mathrm{dM}}_{\mathrm{oil}}=\mathrm{dV}\left(1\alpha \right)\frac{{C}_{\mathrm{oil}}}{\left(1x\right)}{\rho}_{\mathrm{liquid}}& \left(5\right)\end{array}$
where ρ_{liquid }is the density of oil/refrigerant mixture and is calculated as follows:
$\begin{array}{cc}{\rho}_{\mathrm{liquid}}=\frac{{\rho}_{\mathrm{oil}}}{1+\frac{1x{C}_{\mathrm{oil}}}{1x}\left({\rho}_{\mathrm{oil}}/{\rho}_{R}1\right)}& \left(6\right)\end{array}$
where ρ_{oil }is pure oil density and ρ_{R }is density of refrigerant liquid and
$\frac{1x{C}_{\mathrm{oil}}}{1x}$
is mass fraction of refrigerant in the oil/refrigerant mixture.

[0052]
The vapor refrigerant mass in that element can be obtained by:
dM_{ref,vapor}=dVαρ_{g } (7)

[0053]
The liquid refrigerant mass in that element can be obtained by:
$\begin{array}{cc}{\mathrm{dM}}_{\mathrm{ref},\mathrm{liquid}}=\mathrm{dV}\left(1\alpha \right)\frac{1x{C}_{\mathrm{oil}}}{1x}{\rho}_{\mathrm{liquid}}& \left(8\right)\end{array}$

[0054]
Then, the liquid refrigerant mass in the entire condenser can be obtained by:
$\begin{array}{cc}\begin{array}{c}{M}_{\mathrm{ref},\mathrm{liquid}}=\left(1{C}_{\mathrm{oil}}\right){A}_{c}{L}_{\mathrm{c3}}{\rho}_{\mathrm{liquid}}+\\ {\int}_{z=0}^{z={L}_{\mathrm{c2}}}\left(1\alpha \left(x\left(z\right)\right)\right){\rho}_{\mathrm{liquid}}\text{\hspace{1em}}\frac{1x\left(z\right){C}_{\mathrm{oil}}}{1x\left(z\right)}{A}_{c}dz\\ =\left(1{C}_{\mathrm{oil}}\right){A}_{c}{L}_{\mathrm{c3}}{\rho}_{\mathrm{liquid}}+\\ \sum _{i=1}^{N}\text{\hspace{1em}}\left(1{\alpha}_{i}\right){\rho}_{\mathrm{liquid}}\frac{1{x}_{i}{C}_{\mathrm{oil}}}{1{x}_{i}}{A}_{c}d{l}_{2}\end{array}& \left(9\right)\end{array}$

[0055]
The vapor refrigerant mass in the condenser can be obtained by:
$\begin{array}{cc}{M}_{\mathrm{ref},\mathrm{vapor}}={\int}_{z=0}^{z={L}_{\mathrm{c2}}}\alpha \left(x\left(z\right)\right){\rho}_{g}{A}_{c}\text{\hspace{1em}}dz+{\alpha}_{N}{A}_{c}{L}_{\mathrm{c1}}{\rho}_{g}& \left(10\right)\\ \text{\hspace{1em}}=\sum _{i=1}^{N}\text{\hspace{1em}}{\alpha}_{i}{\rho}_{g}{A}_{c}d{l}_{2}+{\alpha}_{N}{A}_{c}{L}_{\mathrm{c1}}{\rho}_{g}& \text{\hspace{1em}}\end{array}$

[0056]
The oil mass in the condenser can be obtained by
$\begin{array}{cc}{M}_{\mathrm{oil}}={A}_{c}{L}_{\mathrm{c3}}{\rho}_{\mathrm{liquid}}{C}_{\mathrm{oil}}+{\int}_{z=0}^{z={L}_{\mathrm{c2}}}\left(1\alpha \left(x\left(z\right)\right)\right){\rho}_{\mathrm{liquid}}\frac{1{C}_{\mathrm{oil}}}{1x\left(z\right)}{A}_{c}\text{\hspace{1em}}dz+\text{\hspace{1em}}\left(1{\alpha}_{N}\right){A}_{c}{L}_{\mathrm{c1}}{\rho}_{\mathrm{oil}}\text{}\text{\hspace{1em}}={A}_{c}{L}_{\mathrm{c3}}{\rho}_{\mathrm{liquid}}{C}_{\mathrm{oil}}+\sum _{i=1}^{N}\text{\hspace{1em}}\left(1{\alpha}_{i}\right){\rho}_{\mathrm{liquid}}\frac{1{x}_{o}{C}_{\mathrm{oil}}}{1{x}_{i}}{A}_{c}d{l}_{2}+\text{\hspace{1em}}\left(1{\alpha}_{N}\right){A}_{c}{L}_{\mathrm{c1}}{\rho}_{\mathrm{oil}}& \left(11\right)\end{array}$

[0057]
The total refrigerant mass in condenser is
M _{ref} =M _{ref,vapor} +M _{ref,liquid } (12)

[0058]
The above condenser oil model obtains information including Lc2, Lc3 from the condenser observer 18, condensing temperature T_{c}, oil circulation rate C_{oil}, and mass flow rate for calculating void fraction. Mass flow rate can be estimated based on the compressor mass flow model. It should be noted that the length of the subcool section Lc3 is the key value for accurate estimation of refrigerant mass inventory in the condenser, since in the subcool section, all refrigerant is high quality liquid that has much higher density than vapor refrigerant density. Another important factor is the selection of void fraction model. The Hughmark model is selected in embodiment of the invention because some other models tend to underestimate the liquid mass. Generally, the condenser can hold about 40% to 48% of total refrigerant charge.

[0000]
2.2 Evaporator Oil Model: Refrigerant and Oil Mass in Evaporator

[0059]
FIG. 5 is a schematic block diagram of the element model for the evaporator twophase flow region. The evaporator can be divided to two sections as shown in FIG. 5: a superheated section 34 having length Le2, and a twophase section 36 having length Le1. Twophase section length Lei is obtained from evaporator observer 14. The twophase region is divided into N elements i. At i=1, the vapor quality x=x_{0 }at i=N, x=1C_{oil}. The calculation for the evaporator is similar to that of the condenser. It is assumed that the vapor quality decreases linearly. The twophase region is divided into N elements as shown in FIG. 5, so that within each element the thermodynamic property differences in each phase are negligible.

[0060]
The length of each element is dl_{l}=L_{el}/N, and vapor quality in section i can be evaluated:
$\begin{array}{cc}x\left(i\right)={x}_{0}+\frac{i1}{N1}\left(1{x}_{0}\right)& \left(13\right)\end{array}$

[0061]
For each element in the twophase section, the void fraction is calculated based on the Hughmark's void fraction mode using the parameters in that element. Then, the liquid refrigerant mass in the evaporator can be obtained by:
$\begin{array}{cc}{M}_{\mathrm{ref},\mathrm{liquid}}={\int}_{z=0}^{z={L}_{\mathrm{e1}}}\left(1\alpha \left(x\left(z\right)\right)\right){\rho}_{\mathrm{liquid}}\frac{1x\left(z\right){C}_{\mathrm{oil}}}{1x\left(z\right)}{A}_{c}\text{\hspace{1em}}dz\text{}\text{\hspace{1em}}=\sum _{i=1}^{N}\text{\hspace{1em}}\left(1{\alpha}_{i}\right){\rho}_{\mathrm{liquid}}\frac{1{x}_{i}{C}_{\mathrm{oil}}}{1{x}_{i}}{A}_{c}d{l}_{1}& \left(14\right)\end{array}$

[0062]
The oil mass in the evaporator can be obtained by:
$\begin{array}{cc}{M}_{\mathrm{oil}}={\int}_{z=0}^{z={L}_{\mathrm{e1}}}\left(1\alpha \left(x\left(z\right)\right)\right){\rho}_{\mathrm{liquid}}\frac{1{C}_{\mathrm{oil}}}{1x\left(z\right)}{A}_{c}\text{\hspace{1em}}dz+\left(1{\alpha}_{N}\right){A}_{c}{L}_{\mathrm{e2}}{\rho}_{\mathrm{oil}}\text{}\text{\hspace{1em}}=\sum _{i=1}^{N}\text{\hspace{1em}}\left(1{\alpha}_{i}\right){\rho}_{\mathrm{liquid}}\frac{1{x}_{o}{C}_{\mathrm{oil}}}{1{x}_{i}}{A}_{c}d{l}_{1}+\text{\hspace{1em}}\left(1{\alpha}_{N}\right){A}_{c}{L}_{\mathrm{e2}}{\rho}_{\mathrm{oil}}& \left(15\right)\end{array}$

[0063]
The vapor refrigerant mass in the evaporator can be obtained by
$\begin{array}{cc}{M}_{\mathrm{ref},\mathrm{vapor}}={\int}_{z=0}^{z={L}_{\mathrm{e1}}}\alpha \left(x\left(z\right)\right){\rho}_{g}{A}_{c}\text{\hspace{1em}}dz+{\alpha}_{N}{A}_{c}{L}_{\mathrm{e2}}{\rho}_{g}\text{}\text{\hspace{1em}}=\sum _{i=1}^{N}\text{\hspace{1em}}{\alpha}_{i}{\rho}_{g}{A}_{c}d{l}_{1}+{\alpha}_{N}{A}_{c}{L}_{\mathrm{e2}}{\rho}_{g}& \left(16\right)\end{array}$

[0064]
The total refrigerant mass in evaporator is
M _{ref} =M _{ref,vapor} +M _{ref,liquid } (17)

[0065]
The above evaporator oil model obtains information of twophase section length L_{el }from the evaporator observer 14, evaporating temperature T_{c}, inlet vapor quality x_{0}, oil circulation rate C_{oil}, and mass flow rate for calculating void fraction. Generally, the evaporator can hold about 10% to 16% of total refrigerant charge.

[0000]
2.3 Liquid Line Oil Model: Refrigerant and Oil Mass in Liquid Line

[0066]
FIG. 6 is a schematic block diagram of a liquid line. It is assumed that V is the total volume of the liquid line, x is the average vapor quality of oil/refrigerant mixture of the liquid line, and α is mean void fraction of the liquid line and can be estimated by different void fraction models. In accordance with the invention, the Hughmark model or the following equation is used to estimate mean void fraction α
$\alpha =\frac{1}{1+\frac{1x}{x}{\left(\frac{{\rho}_{g}}{{\rho}_{l}}\right)}^{\frac{2}{3}}}$
where ρ_{g }is the saturated vapor density and ρ_{l }is the saturated liquid density

[0067]
When the void fraction value α is obtained, the total liquid volume (liquid refrigerant+oil) in the liquid line is Q_{liquid}=V(1−α). Assuming that the oil is well mixed with the liquid refrigerant; the following equation is used to estimate the oil mass retention in the liquid line.
$\begin{array}{cc}{M}_{\mathrm{oil}}=V\left(1\alpha \right)\frac{{C}_{\mathrm{oil}}}{\left(1x\right)}{\rho}_{\mathrm{liquid}}& \left(18\right)\end{array}$

[0068]
The vapor refrigerant mass in the liquid line can be obtained by:
M_{ref,vapor} =αVρ _{g } (19)

[0069]
The liquid refrigerant mass in the liquid line can be obtained by:
$\begin{array}{cc}{M}_{\mathrm{re},\mathrm{liquid}}=V\left(1\alpha \right)\frac{1x{C}_{\mathrm{oil}}}{1x}{\rho}_{\mathrm{liquid}}& \left(20\right)\end{array}$
2.2 Gas Line Oil Model: Refrigerant and Oil Mass in Gas Line

[0070]
In the gas line, it is assumed that the void fraction is the same as the superheated section and there is no liquid refrigerant. Assuming that V is the total volume of the gas line, α is mean void fraction of gas line. The vapor refrigerant mass in the gas line can be obtained by:
M_{ref,vapor}=αVρ_{g } (21)
the oil mass retention in the gas line is
M _{oil} =V(1−α)ρ_{oil } (22)

[0071]
Gas line and liquid line oil models use information of averaging vapor quality, averaging refrigerant temperature, oil circulation rate C_{oil}, and total mass flow rate.

[0000]
2.5 Accumulator Oil Model: Refrigerant and Oil Mass in Accumulator

[0072]
Assuming that T_{r }is refrigerant temperature in accumulator, the saturated liquid density ρ_{l }and saturated vapor density ρ_{g }can be determined from T_{r }based on thermodynamics properties. Oil density ρ_{oil }is a function of T_{r}. It is assumed that the total volume of accumulator is V, and the liquid volume V_{L }can be calculated based on liquid level measurement through the glass window at the side of accumulator.

[0073]
The vapor refrigerant mass in the accumulator can be obtained by:
M _{ref,vapor}=(V−V _{L})ρ_{g } (23)

[0074]
The oil mass in the accumulator is
M_{oil}=V_{L}ρω_{oil } (24)
where ρ is the density of oil/liquid refrigerant mixture and is expressed by
$\begin{array}{cc}\rho =\frac{{\rho}_{\mathrm{oil}}}{1+\left(1{\omega}_{\mathrm{oil}}\right)\left({\rho}_{\mathrm{oil}}/{\rho}_{R}1\right)}& \left(25\right)\end{array}$
and ω_{oil }is the oil concentration of oil/liquid refrigerant mixture in accumulator. The liquid refrigerant mass in the accumulator can be obtained by:
M _{ref,liquid} =V _{L}ρ(1−ω_{oil}) (26)
3. Oil Observer for Estimation of Oil Concentration and Oil Mass in Compressor

[0075]
In Section 2 above, models to estimate oil mass and refrigerant mass in condenser, evaporator, gas line, liquid line and accumulator were described. In this section, estimation of the oil mass and refrigerant mass in the compressor based on the conservation of oil and refrigerant mass inside the machine is described. Oil concentration in the compressor can be derived in accordance with the following.

[0076]
Oil mass conservation for the entire machine is
M ^{cir} _{oil} +M ^{accu} _{oil} +M ^{comp} _{oil} =M ^{total} _{oil }
where M^{total} _{oil }is the total oil mass charged into the machine and has a known value, M^{cir} _{oil}=M^{evap} _{oil}+M^{cond} _{oil}+M^{gas} ^{ — } ^{line} _{oil} +M ^{liquid} ^{ — } ^{line} _{oil }is the total oil retention in the refrigerant circuit including the condenser, evaporator, gas line and liquid line. M^{accu} _{oil }is the oil retention in the accumulator. If there is no accumulator in a machine, this value is zero. M^{cir} _{oil }and M^{accu} _{oil }are estimated based on oil models described in Section 2 above.

[0077]
Based on oil mass conservation, the estimated oil mass in the compressor {circumflex over (M)}^{comp} _{oil }from the oil observer shown in FIG. 1B can be expressed by
{circumflex over (M)} ^{comp} _{oil} =M ^{total} _{oil} −M ^{cir} _{oil} −M ^{accu} _{oil } (27)

[0078]
Refrigerant mass conservation for the entire machine is
M ^{cir} _{ref} +M ^{accu} _{ref} +M ^{comp} _{ref} =M ^{total} _{ref }
where M^{total} _{ref }is the total refrigerant mass charged into the machine and has a known value, M^{cir} _{ref }is the total refrigerant mass inventory in the refrigerant circuit including the condenser, evaporator, gas line and liquid line. M^{accu} _{ref }is the refrigerant mass in the accumulator. If there is no accumulator in a machine, this value is zero. M^{cir} _{ref }and M^{accu} _{ref }are estimated based on models described in Section 2 above.

[0079]
Based on refrigerant mass conservation, the estimated refrigerant mass in the compressor {circumflex over (M)}^{comp} _{ref }from the oil observer shown in FIG. 1B can be expressed by
{circumflex over (M)} ^{comp} _{ref} =M ^{total} _{ref} −M ^{cir} _{ref} −M ^{accu} _{ref } (28)

[0080]
In order to estimate the oil concentration in the compressor, the liquid refrigerant mass in compressor is estimated. With the estimation of {circumflex over (M)}^{comp} _{ref }from Equation (28), the liquid refrigerant mass {circumflex over (M)}^{comp} _{ref,Liquid }is equal to
{circumflex over (M+EE ^{ comp } _{ ref,Liquid } ={circumflex over (M)})} ^{comp} _{ref}−ρ_{g}(V ^{comp} −V ^{comp} _{Liquid}) (29)
where the second term of Equation (29) is vapor refrigerant mass in the compressor, ρ_{g }is the density of vapor refrigerant in the compressor, V^{comp }is the total compressor volume where refrigerant presents, V^{comp} _{Liquid }is the liquid volume of oil/liquid refrigerant mixture and can be determined by the measurement of liquid level at the glass window of the compressor.

[0081]
Based on the estimated oil mass from Equation (27) and the estimated liquid refrigerant mass from Equation (29), the estimated oil concentration in the compressor can be expressed by
$\begin{array}{cc}{w}_{\mathrm{oil}}^{\mathrm{comp}}=\frac{{\hat{M}}_{\mathrm{oil}}^{\mathrm{comp}}}{{\hat{M}}_{\mathrm{oil}}^{\mathrm{comp}}+{\hat{M}}_{\mathrm{ref},\mathrm{Liquid}}^{\mathrm{comp}}}& \left(30\right)\end{array}$

[0082]
In one embodiment, the invention is achieve 20% estimation error for oil concentration, that is
$\begin{array}{cc}\uf603\frac{{w}_{\mathrm{oil}}^{\mathrm{comp}}{w}_{\mathrm{oil}}^{\mathrm{sensor}}}{{w}_{\mathrm{oil}}^{\mathrm{sensor}}}\uf604*100\%<20\%& \left(31\right)\end{array}$
where W^{sensor} _{oil }is experimental oil concentration that is correlated from measurement of viscosity by a viscosity sensor installed at the bottom of the compressor.
4. Heat Exchanger Observers
4.1 Modelbased Nonlinear Observers for Evaporator

[0083]
FIG. 7 contains a schematic diagram of the loworder evaporator model in accordance with the invention. T_{e }is the evaporating temperature. l is the length of the twophase section. T_{w }is the wall temperature of the tube. T_{α} is the room air temperature. {dot over (m)}_{in }and {dot over (m)}_{out }are the inlet and outlet refrigerant mass flow rates, respectively. q is the heat transfer rate from the tube wall to the twophase refrigerant. q_{α} is the heat transfer rate from the room to the tube wall.

[0084]
Assuming a uniform temperature throughout the evaporator tube wall, the heat transfer equation of the tube wall is as follows:
$\begin{array}{cc}{\left({c}_{p}\rho \text{\hspace{1em}}A\right)}_{e}\frac{d{T}_{w}}{dt}=\pi \text{\hspace{1em}}{D}_{o}{\alpha}_{o}\left({T}_{a}{T}_{w}\right)\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}\left({T}_{w}{T}_{e}\right)& \left(32\right)\end{array}$

[0085]
The first term on the right hand side represents the heat transfer rate per unit length from the room to the tube wall. The second term represents the heat transfer rate per unit length from the tube wall to the twophase refrigerant.

[0086]
Assuming the mean void fraction {overscore (γ)} is invariant, the liquid mass balance equation in the twophase section of the evaporator is
$\begin{array}{cc}{\rho}_{l}\left(1\stackrel{\_}{\gamma}\right)A\frac{dl\left(t\right)}{dt}=\frac{q}{{h}_{1g}}+{\stackrel{.}{m}}_{i\text{\hspace{1em}}n}\left(1{x}_{0}\right)& \left(33\right)\end{array}$

[0087]
In equation (33), the left hand side is the liquid mass change rate in the evaporator. On the right hand side, q/h_{lg }represents the rate of liquid evaporating into vapor, and {dot over (m)}_{in}(1−x_{0}) is the inlet liquid mass flow rate.

[0088]
The inlet refrigerant mass flow rate {dot over (m)}_{in }is dependent on the expansion valve opening A_{v}, the low pressure P_{e }and high pressure P_{c}, and can be expressed by
{dot over (m)} _{in} =A _{v} ^{α} g _{v}(P _{e} ,P _{c}) (34)
where α and g_{v }(P_{e}, P_{c}) can be identified for a given expansion valve. P_{e }and P_{c }can be measured by two pressure sensors. For the twophase section, the pressure is an invariant function of the temperature. Therefore, the inlet refrigerant mass flow rate {dot over (m)}_{in }can be expressed as
{dot over (m)} _{in} =A _{v} ^{α} g _{v}(T _{e} ,T _{c}) (35)

[0089]
Assuming that the vapor volume is much larger than the liquid volume in the lowpressure side, the vapor mass balance equation in an evaporator is:
$\begin{array}{cc}\frac{d{M}_{v}}{dt}=v\frac{d{\rho}_{g}\left({T}_{e}\right)}{d{T}_{e}}\frac{d{T}_{e}}{dt}={\stackrel{.}{m}}_{i\text{\hspace{1em}}n}{x}_{o}+\frac{q}{{h}_{1g}}{\stackrel{.}{m}}_{\mathrm{out}}& \left(36\right)\end{array}$
where M_{v }is the total vapor mass and V is the total volume of the lowpressure side. h_{g}−h_{l}=h_{lg}, where h_{l }and h_{g }are refrigerant saturated liquid and vapor specific enthalpies. The outlet refrigerant mass flow rate is the same with the compressor mass flow rate which is dependent on the compressor speed, the low pressure P_{e }and high pressure P_{c}, and can be expressed by
{dot over (m)} _{out } =ωg(P _{e} ,P _{c}) (37)
where g(P_{e},P_{c}) can be identified for a given compressor. As described above, the pressure is an invariant function of the temperature for the twophase section. Therefore, the outlet refrigerant mass flow rate can be expressed as
{dot over (m)} _{out } =ωg(T _{e} ,T _{c}) (38)

[0090]
Equation (36) can be written as
$\begin{array}{cc}\frac{d{T}_{e}}{dt}=\frac{\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}}{{\mathrm{kh}}_{1g}}l\left({T}_{w}{T}_{e}\right)+\frac{{x}_{o}}{k}{\stackrel{.}{m}}_{i\text{\hspace{1em}}n}\frac{1}{k}{\stackrel{.}{m}}_{\mathrm{out}}\text{}\mathrm{where}\text{\hspace{1em}}k=V\frac{d{\rho}_{g}\left({T}_{e}\right)}{d{T}_{e}}.& \left(39\right)\end{array}$

[0091]
Based on equations (32), (33) and (39), the state space representation for the low order evaporator model is as follows, where T_{e}, l and T_{w }are the three states of the model.
$\begin{array}{cc}\left(\begin{array}{c}{\stackrel{.}{T}}_{e}\\ {\stackrel{.}{T}}_{w}\\ \stackrel{.}{l}\end{array}\right)=\left(\begin{array}{c}\frac{\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}}{{\mathrm{kh}}_{1g}}l\left({T}_{w}{T}_{e}\right)+\frac{{x}_{o}}{k}{\stackrel{.}{m}}_{i\text{\hspace{1em}}n}\frac{1}{k}{\stackrel{.}{m}}_{\mathrm{out}}\\ \frac{1}{{\left({C}_{p}\rho \text{\hspace{1em}}A\right)}_{e}}\left(\pi \text{\hspace{1em}}{D}_{o}{\alpha}_{o}\left({T}_{a}{T}_{w}\right)\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}\left({T}_{w}{T}_{e}\right)\right)\\ \frac{1}{{\rho}_{l}\left(1\stackrel{\_}{\gamma}\right)A}\left(\frac{\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}l\left({T}_{w}{T}_{e}\right)}{{h}_{1g}}+{\stackrel{.}{m}}_{i\text{\hspace{1em}}n}\left(1{x}_{o}\right)\right)\end{array}\right)& \left(40\right)\end{array}$

[0092]
Where T_{α}, {dot over (m)}_{in}, and {dot over (m)}_{out }are the inputs to the system.

[0093]
Since only T_{e }can be easily measured using a thermocouple, an observer in accordance with the invention is used in estimating the value of l, the length of twophase section of the evaporator.

[0094]
The following are the dynamics of the nonlinear observer described herein.
$\begin{array}{cc}\left(\begin{array}{c}{\stackrel{.}{\hat{T}}}_{e}\\ {\stackrel{.}{\hat{T}}}_{w}\\ \stackrel{.}{\hat{l}}\end{array}\right)=\left(\begin{array}{c}\frac{\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}}{{\mathrm{kh}}_{1g}}\hat{l}\left({\hat{T}}_{w}{\hat{T}}_{e}\right)+\frac{{x}_{o}}{k}{\stackrel{.}{m}}_{i\text{\hspace{1em}}n}\frac{1}{k}{\stackrel{.}{m}}_{\mathrm{out}}\\ \frac{1}{{\left({C}_{p}\rho \text{\hspace{1em}}A\right)}_{e}}\left(\pi \text{\hspace{1em}}{D}_{o}{\alpha}_{o}\left({T}_{a}{\hat{T}}_{w}\right)\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}\left({\hat{T}}_{w}{\hat{T}}_{e}\right)\right)\\ \frac{1}{{\rho}_{l}\left(1\stackrel{\_}{\gamma}\right)A}\left(\frac{\pi \text{\hspace{1em}}{D}_{i}{\alpha}_{i}\hat{l}\left({\hat{T}}_{w}{\hat{T}}_{e}\right)}{{h}_{1g}}+{\stackrel{.}{m}}_{i\text{\hspace{1em}}n}\left(1{x}_{o}\right)\right)\end{array}\right)\text{}\text{\hspace{1em}}\left(\begin{array}{c}{L}_{1}\\ {L}_{2}\\ {L}_{3}\end{array}\right)\left({\hat{T}}_{e}{T}_{e}\right)& \left(41\right)\end{array}$
where L_{1}, L_{2}, and L_{3 }are observer gains. For the observer, the contraction theory is used in accordance with the invention to ensure that the estimated state variables will converge to the actual states in the plant The contraction theory states that the system {dot over (x)}=f(x, t) is said to be contracting if
$\frac{\partial f}{\partial x}$
is uniformly negative definite. All system trajectories then converge exponentially to a single trajectory, with convergence rate λ_{max}, where λ_{max }is the largest eigenvalue of the symmetric part of
$\frac{\partial f}{\partial x}.$
Therefore, if we can make sure the ax actual states are particular solutions of the observer and the observer is contracting, then we can conclude that all the trajectories of the observer will converge to the particular solutions that are the actual states.

[0095]
From the observer dynamics, if {circumflex over (T)}_{e }is equal to T_{e}, the observer dynamics are the same with the system dynamics. So the actual states that are the solutions of this set of equations are particular solutions of the observer. If the symmetric part of the Jacobian matrix of the observer dynamics is uniformly negative definite, then the trajectory of the observer dynamics will converge to the particular solution which means the observed states are the same as the actual states.

[0000]
4.2 Modelbased Nonlinear Observers for Condenser

[0096]
In the oil observer described in Section 1 above, the length of twophase and length of subcooled liquid section of a condenser are used to estimate the oil in the condenser, since the oil calculation models are different for different phase sections.

[0097]
In this section, the model of the condenser is described. The condenser model is similar to the evaporator model. FIG. 8 contains a schematic diagram of a loworder condenser model in accordance with the invention.

[0098]
The vapor balance equation is as follows
$\begin{array}{cc}\frac{d{M}_{v,c}}{dt}={V}_{c}\frac{d{\rho}_{g}\left({T}_{c}\right)}{d{T}_{c}}\frac{d{T}_{c}}{dt}={\stackrel{.}{m}}_{i\text{\hspace{1em}}n,c}\frac{\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}{L}_{\mathrm{c2}}\left({T}_{c}{T}_{w,c}\right)}{{h}_{1g}}& \left(42\right)\end{array}$
where T_{c }is the condensing temperature, L_{c2 }is the two phase length and T_{w,c }is the wall temperature of the condenser.

[0099]
The heat transfer equation is as follows:
$\begin{array}{cc}{\left({c}_{p}\rho \text{\hspace{1em}}A\right)}_{c}\frac{d{T}_{w,c}}{dt}=\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}\left({T}_{c}{T}_{w,c}\right)\pi \text{\hspace{1em}}{D}_{o,c}{\alpha}_{o,c}\left({T}_{w,c}{T}_{o,c}\right)& \left(43\right)\end{array}$
where T_{a,c }is the outdoor air temperature.

[0100]
The liquid mass balance equation in the condenser model is expressed in equation (44). It is a little bit different from the evaporator model. Two sections have liquid refrigerant. One is the liquid phase section, the other is the twophase section.
$\begin{array}{cc}{A}_{c}\left(1\stackrel{\_}{\gamma}\right){\rho}_{l}\frac{d{L}_{\mathrm{c2}}}{dt}+{A}_{c}{\rho}_{l}\frac{d{L}_{\mathrm{c3}}}{dt}=\frac{\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}{L}_{\mathrm{c2}}\left({T}_{c}{T}_{w,c}\right)}{{h}_{1g}}{\stackrel{.}{m}}_{\mathrm{out},c}& \left(44\right)\end{array}$
where L_{c3 }is the subcool liquid phase length.

[0101]
It can be seen that there are four unknowns but three equations. One of the unknowns is eliminated for the observer design. One assumption made is that the length change of the superheated phase is very slow
$\frac{d{L}_{\mathrm{c1}}}{dt}\approx 0.$
We have
$\begin{array}{cc}\begin{array}{c}{A}_{c}\left(1\stackrel{\_}{\gamma}\right){\rho}_{l}\frac{d{L}_{\mathrm{c2}}}{dt}+{A}_{c}{\rho}_{l}\frac{d\left(L{L}_{\mathrm{c1}}{L}_{\mathrm{c2}}\right)}{dt}={A}_{c}\left(1\stackrel{\_}{\gamma}\right){\rho}_{l}\frac{d{L}_{\mathrm{c2}}}{dt}{A}_{c}{\rho}_{l}\frac{d{L}_{\mathrm{c2}}}{dt}\\ ={A}_{c}\stackrel{\_}{\gamma}{\rho}_{l}\frac{d{L}_{\mathrm{c2}}}{dt}\\ =\frac{\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}{L}_{\mathrm{c2}}\left({T}_{c}{T}_{w,c}\right)}{{h}_{1g}}{\stackrel{.}{m}}_{\mathrm{out},c}\\ {L}_{\mathrm{c3}}=L{L}_{\mathrm{c1}}{L}_{\mathrm{c2}}\end{array}& \left(45\right)\end{array}$

[0102]
Therefore the liquid mass balance equation can be written as
$\begin{array}{cc}\frac{d{L}_{\mathrm{c2}}}{dt}=\frac{\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}{L}_{\mathrm{c2}}\left({T}_{c}{T}_{w,c}\right)}{{A}_{c}\stackrel{\_}{\gamma}{\rho}_{l}{h}_{1g}}& \left(46\right)\end{array}$

[0103]
Equations (42), (43) and (44) are the condenser model. The modelbased observer for the condenser is described as follows
$\begin{array}{cc}\left(\begin{array}{c}{\stackrel{\stackrel{\xb7}{^}}{T}}_{c}\\ {\stackrel{\stackrel{\xb7}{^}}{T}}_{w,c}\\ {\stackrel{\stackrel{\xb7}{^}}{L}}_{\mathrm{c2}}\end{array}\right)=\left(\begin{array}{c}{\stackrel{.}{m}}_{\mathrm{in},c}/k\frac{\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}{\hat{L}}_{\mathrm{c2}}\text{(}{\hat{T}}_{c}{\hat{T}}_{w,c}\text{)}}{k\text{\hspace{1em}}{h}_{1g}}\\ \frac{1}{{\left({C}_{p}\rho \text{\hspace{1em}}A\right)}_{c}}\text{(}\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}\text{(}{\hat{T}}_{c}{\hat{T}}_{w,c}\text{)}\pi \text{\hspace{1em}}{D}_{o,c}{\alpha}_{o,c}\text{(}{\hat{T}}_{w,c}{T}_{a,c}\text{)}\text{)}\\ \frac{1}{{A}_{c}\stackrel{\_}{\gamma}{\rho}_{l}}\left(\frac{\pi \text{\hspace{1em}}{D}_{i,c}{\alpha}_{i,c}{\hat{L}}_{\mathrm{c2}}\text{(}{\hat{T}}_{c}{\hat{T}}_{w,c}\text{)}}{{h}_{1g}}{\stackrel{.}{m}}_{\mathrm{out},c}\right)\end{array}\right)\left(\begin{array}{c}{L}_{1}\\ {L}_{2}\\ {L}_{3}\end{array}\right)\text{(}{\hat{T}}_{c}{T}_{c}\text{)}& \left(47\right)\end{array}$
where L_{1}, L_{2}, and L_{3 }are observer gains.

[0104]
The length of the superheated portion of the evaporator can be calculated by subtracting the length of the twophase portion of the evaporator from its total length. With regard to the condenser, the length of the superheated portion of the condenser can be calculated by subtracting the length of its twophase and subcool portions from its total length.

[0000]
4.3 Gas Line Observer and Liquid Line Observer

[0105]
During system startup, steady state and other transient operations, if the refrigerant at the exit of the evaporator is at the twophase state, the gas line is filled with twophase flow. When the refrigerant at the exit of the evaporator is superheated vapor, the gas line is filled with superheated vapor flow. The gas line observer is used to detect whether the refrigerant in the gas line is at twophase state or superheated state based on the length of the twophase section of the evaporator. If the length of the twophase section of the evaporator is smaller than the total length of the evaporator, then the gas line observer will indicate that the gas line is filled with superheated vapor, and the oil mass and refrigeration mass in the gas line will be estimated accordingly. If the length of the twophase section of the evaporator is equal to the total length of the evaporator, the gas line observer will indicate that the refrigerant in the gas line is at the twophase refrigerant state, and the oil mass and refrigeration mass in the gas line will be estimated accordingly.

[0106]
During the start up, steady state and other transient operations, if the refrigerant at the exit of the condenser is at the twophase state or the subcooled liquid state, the liquid line is filled with twophase flow. When the refrigerant at the exit of the condenser is superheated vapor, the liquid line is filled with superheated vapor flow. The liquid line observer is used to detect whether the refrigerant in the liquid line is at the twophase state or the superheated state based on the length of the superheated vapor section of the condenser. If the length of the superheated vapor section of the condenser equals the total length of the condenser, then liquid line observer will indicate that the liquid line is filled with superheated vapor, and the oil mass and refrigeration mass in the liquid line will be estimated accordingly. Otherwise, the length of superheated vapor section of the condenser is smaller than the total length of the condenser, and the liquid line observer will indicate that the refrigerant in the liquid line is at the twophase refrigerant state, and the oil mass and refrigeration mass in the liquid line will be estimated accordingly.

[0000]
5. Experimental Comparison

[0107]
In order to verify the oil observer and oil models described herein, experimental testing has been conducted. The comparison results show the error for estimation of oil concentration in accordance with the invention is less than 20%.

[0000]
5.1 Experimental SetUp

[0108]
The machine under testing was a split type residential air conditioner. The refrigerant used in this machine is R410A. The total refrigerant charge is 900 g. The lubricating oil is FVC50K, and 400 ml of oil was charged into the machine (about 370 g). The cooling capacity of the machine is 2.8 kW. All sensors (temperature, pressure, and two mass flow meters, viscosity sensor) are all connected to National Instrument data acquisition board and then connected to a PC.

[0000]
5.2 Experimental Testing

[0109]
Experimental testing was done for several dynamic processes such as change of outdoor temperature by removing several insulation boards of the container, change of compressor speed, and change of expansion valve opening, etc. Experimental data for dynamic process with the outdoor temperature change from 35 C to 27 C is described in details in this subsection, and the comparison for oil concentration in the compressor described in the following subsection is based on this testing.

[0110]
After the startup and running of the testing machine for more than 30 minutes, the operation is almost steady state. The operation condition is as follows:

 1) Outdoor temperature: 35 C
 2) Indoor temperature: 20 C
 3) Compressor Speed: 70 Hz
 4) Expansion Valve: 15 Steps
 5) Indoor fan speed: 1250 rpm
 6) Outdoor fan speed: 630 rpm

[0117]
The outdoor temperature is changed from 35 C to 27 C and then the system is allowed to reach another steady state as shown in FIG. 9, which is a graph of the outdoor air temperature profile over time for the experiment.

[0118]
FIG. 10 is a graph of the compressor oil viscosity profile over time for the experiment. FIG. 10 illustrates that the oil viscosity is changed from about 0.0035 Pa.s to 0.0039 Pa.s. FIG. 11 is a graph of the compressor oil temperature profile over time for the experiment. As shown in FIG. 11, oil temperature is changed from about 57 C to 52 C. FIG. 12 is a graph of the discharge pressure profile over time for the experiment. As shown in FIG. 12, discharge pressure is changed from 2.8 MPa to 2.4 MPa. FIG. 13 is a graph of the suction pressure profile over time for the experiment. FIG. 14 is a graph of the mass flow rate profile over time for the experiment. FIG. 15 is a graph of the evaporating temperature profile over time for the experiment. FIG. 16 is a graph of the condensing temperature profile over time for the experiment.

[0000]
5.3 Comparison results

[0119]
The comparison between oil concentration estimated by the oil observer of the invention and experimental measurement of oil concentration by a viscosity sensor are set forth in this subsection. The first comparison is made under the initial condition.

[0000]
Measurement at the Initial Condition:

[0120]
1) Evaporating temperature: 7.8 C

[0121]
2) Evaporating pressure: 0.8 MPa

[0122]
3) Condensing temperature: 48.2C

[0123]
4) Condensing pressure: 2.77 MPa

[0124]
5) Subcool: 6 C

[0125]
6) Mass Flow Rate: 0.0185 kg/s

[0126]
7) Oil Temperature: 57 C

[0127]
8) Oil Viscosity: 0.0035 N/m{circumflex over ( )}2*s (Pa*s)

[0128]
9) Liquid Volume in Accumulator: 130 cc

[0129]
10) Liquid Volume in Compressor: 330 cc

[0000]
Comparison

[0130]
1) Estimation Error of Oil Concentration in Compressor=13%

[0131]
2) Estimation Error of Oil Mass in Compressor: 10%

[0132]
It is assumed that

[0133]
1) Oil Circulation Rate in the Circuit is 0.5% (no sensor to measure)

[0134]
2) Refrigerant Concentration in accumulator is 65% (no sensor to measure)

[0135]
For the dynamic conditions in which the outdoor temperature is changed from 35 C to 27 C described in subsection 5.2, the comparison results are shown in FIGS. 1719. That is, FIG. 17 is a graph illustrating compressor oil mass estimation error. FIG. 18 is a graph illustrating estimation error of oil concentration in the compressor. FIG. 19 is a graph illustrating a comparison between experimental and estimated oil mass in the compressor in accordance with the invention. The estimation error is smaller than 10% in most cases.

[0136]
During this dynamic process, the refrigerant mass in the condenser is changed from 380 g (42.2% of total refrigerant mass) to 420 g (46.7% of total refrigerant mass), as shown in FIG. 20, which is a graph of refrigerant mass inventory in the condenser for the experiment. FIG. 21 is a graph of condenser subcool section length for one pass in the experiment. The length of the subcool section L_{c3 }estimated from the condenser observer is shown in FIG. 21.

[0137]
FIG. 22 is a graph of the oil mass in the condenser for the experiment. With the subcool section length being changed from 1.9 m to 2.62 m, the refrigerant mass inventory is increased from 42.2% of total refrigerant mass to 46.7% of total refrigerant mass.

[0138]
Table 1 shows the estimated oil distribution in the air conditioning machine at time t=10 minutes in accordance with the invention.
TABLE 1 


Estimated Oil Mass in Each Component 
 Component  % of Total Oil Mass 
 
 Compressor  68.2% 
 Condenser  5.6% 
 Evaporator  2.8% 
 Gas Line (Suction)  8.1% 
 Gas Line (Discharge)  2.9% 
 Accumulator  12.3% 
 Liquid Line  0.1% 
 Total  100% 
 
 Table 2 shows the estimated refrigerant mass distribution in the air conditioning machine at time t = 10 minutes. 

[0139]
TABLE 2 


Estimated Refrigerant Mass in Each Component 


% of Total Refrigerant 

Component 
Mass 



Compressor 
19.2% 

Condenser 
46.8% 

Evaporator 
14.7% 

Gas Line (Suction) 
1.5% 

Gas Line (Discharge) 
2% 

Accumulator 
11.7% 

Liquid Line 
4.1% 

Total 
100% 



[0140]
Hence, the present invention includes a systemlevel oil observer to estimate oil concentration and oil mass in the compressor of a vapor compression system. The invention includes oil distribution and refrigerant distribution models for the condenser, evaporator, gas line, and liquid line to estimate oil mass and refrigerant mass in each component. Heat exchanger observers (for evaporator and condenser) and oil models are integrated into the compressor dynamic oil observer. Experimental testing was performed to validate the oil observer and develop comparison results that illustrate less than 10% error.

[0141]
While this invention has been particularly shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.