Methods and systems for direct fuel quantity measurement

A method for fuel quantity gauging that measures the quantity of liquid fuel in a fuel tank. The method includes the following steps performed while fuel is flowing out of the fuel tank: changing a volume of gas in the fuel tank (e.g., by injecting or venting gas) during a time interval; measuring a rate of change of the volume of gas in the fuel tank during the time interval; measuring a rate of flow of fuel out of the fuel tank during the time interval; measuring a first pressure and a first temperature of the gas in the fuel tank at the start of the time interval; measuring a second pressure and a second temperature of the gas in the fuel tank at the end of the time interval; and calculating a quantity of fuel in the fuel tank based on the acquired measurement data.

BACKGROUND

This disclosure generally relates to methods and systems for measuring a quantity of liquid fuel in a fuel tank, such as a storage tank or other container. More particularly, this disclosure relates to methods and systems for measuring the quantity of liquid fuel in a fuel tank in a manner that does not require the presence of electrical components in the fuel tank.

A need to continuously measure the quantity of liquid fuel in a fuel tank exists in many commercial and military applications. For example, liquid-level sensors are commonly used in the fuel tanks of aircraft, automobiles, and trucks. Liquid-level sensors are also used to monitor liquid levels within storage tanks used for fuel dispensing.

Many transducers for measuring liquid level employ electricity. The electrical output of such transducers changes in response to a change in the liquid level being measured, and is typically in the form of a change in resistance, capacitance, current flow, magnetic field, frequency, and so on. These types of transducers may include variable capacitors or resistors, optical components, Hall Effect sensors, strain gauges, ultrasonic devices, and so on.

Currently most fuel sensors on aircraft use electricity. For example, existing electrical capacitance sensors require electrical wiring inside the tank, which in turn requires complex installations and protection measures to preclude a safety issue under certain electrical fault conditions. This electrical wiring requires careful shielding, bonding, and grounding to minimize stray capacitance and further requires periodic maintenance to ensure electrical contact integrity.

In the cases of commercial and military aviation, it is important for the flight crew to know there is adequate fuel upload for a mission prior to each flight. It is equally important for the crew to know during the flight that there is adequate fuel remaining in the tanks to complete each flight safely. A simple and accurate fuel quantity gauging system is needed. For a typical long-range transport aircraft, it takes a quarter to a half pound of fuel to transport a pound of weight. Extra fuel is dead weight and it takes fuel to transport that extra weight.

It would be advantageous if the amount of liquid fuel in a fuel tank could be measured without introducing electrical current into the fuel tank and without using optical techniques.

SUMMARY

The subject matter disclosed in detail below is directed to methods and systems for fuel quantity gauging that measure the quantity of liquid fuel in a fuel tank directly without the need to accurately locate fuel heights throughout the fuel tank using multiple fuel gauging probes. The method may comprise the following steps performed while fuel is flowing out of the fuel tank: (a) changing a volume of gas in the fuel tank (e.g., by injecting or venting gas) during a time interval; (b) measuring a rate of change of the volume of gas in the fuel tank during the time interval; (c) measuring a rate of flow of fuel out of the fuel tank during the time interval; (d) measuring a first pressure and a first temperature of the gas in the fuel tank at the start of the time interval; (e) measuring a second pressure and a second temperature of the gas in the fuel tank at the end of the time interval; and (f) calculating a quantity of fuel in the fuel tank based on the measurement data acquired in steps (c) through (f). Step (f) is performed by a processing unit. The calculation is simple and does not require the calculation of instantaneous fuel volume topography. The computing power requirement is minimal. Unlike electrical and electronic probes, no electric current in the fuel tank is required.

To meet aviation requirements, two completely independent sets of fuel gauges are required. A typical aircraft may have a multiple-point electronic system for flight and a magnetic or mechanical system available to the ground crew during fuel upload. The system proposed herein could be used as the primary or secondary system. It may also be used in conjunction with the current electronic system, making two independent in-flight capable systems available to the crew. The methodology disclosed herein is not limited to aircraft application but rather may also be used in land and marine vehicles as well as stationary liquid fuel tanks.

One aspect of the subject matter disclosed in detail below is a system for measuring a quantity of liquid fuel in a fuel tank (e.g., a fuel tank on an aircraft), comprising: a first meter that measures a rate of flow of gas through a gas line that is in fluid communication with the fuel tank; a second meter that measures a rate of flow of fuel out of the fuel tank via the fuel line; a first gauge that measures an ullage temperature in an ullage of the fuel tank; a second gauge that measures an ullage pressure in an ullage of the fuel tank; and a processing unit programmed to calculate a quantity of fuel in the fuel tank based on measurement data from the first and second meters and from the first and second gauges. The system may further comprise a fuel gauge connected to receive and display symbology representing the quantity of fuel.

In accordance with some embodiments, the processing unit is programmed to calculate a quantity of fuel in the fuel tank at a second time subsequent to a first time based in part on respective ullage temperature and pressure measurements taken by the first and second gauges at first and second times.

In accordance with other embodiments, the processing unit is programmed to: calculate a change in mass of gas in the fuel tank by integrating an output of the first meter over a time interval from a first time to a second time; calculate a change in volume of fuel in the fuel tank by integrating an output of the second meter over the time interval; and calculate a quantity of fuel in the fuel tank at the second time based on the calculated changes in mass of gas and fuel in the fuel tank during the time interval and respective ullage temperature and pressure measurements taken by the first and second gauges at the first and second times.

Another aspect of the subject matter disclosed in detail below is a method for measuring a quantity of liquid fuel in a fuel tank while fuel is flowing out of the fuel tank, comprising: (a) changing a volume of gas in the fuel tank during a time interval that starts at a first time and ends at a second time; (b) measuring a rate of change of the volume of gas in the fuel tank during the time interval; (c) measuring a rate of flow of fuel out of the fuel tank during the time interval; (d) measuring a first pressure of gas in the fuel tank at the first time; (e) measuring a first temperature of gas in the fuel tank at the first time; (f) measuring a second pressure of gas in the fuel tank at the second time; (g) measuring a second temperature of gas in the fuel tank at the second time; and (h) calculating a quantity of fuel in the fuel tank based on measurement data acquired in steps (b) through (g), wherein step (h) is performed by a processing unit. The method may further comprise closing a vent in fluid communication with the ullage prior to step (a), wherein step (a) comprises injecting gas into the fuel tank via a gas line during the time interval while the vent is closed, and step (b) comprises measuring a rate of flow of gas into the fuel tank via the gas line. In the alternative, the method may further comprise opening a vent in fluid communication with the ullage prior to step (a), wherein step (a) comprises venting gas out of the fuel tank via the open vent during the time interval, and step (b) comprises measuring a rate of flow of gas out of the fuel tank via the open vent. The method may further comprise displaying symbology representing the quantity of fuel. In one implementation, steps (a) through (h) are performed onboard an aircraft.

A further aspect is a method for measuring a quantity of liquid fuel in a fuel tank onboard an aircraft during flight, comprising: (a) changing a volume of gas in the fuel tank during a time interval that starts at a first time and ends at a second time; (b) measuring a rate of change of the volume of gas in the fuel tank during the time interval; (c) measuring a rate of flow of fuel out of the fuel tank during the time interval; (d) measuring a first pressure and a first temperature of gas in the fuel tank at the first time; (e) measuring a second pressure and second temperature of gas in the fuel tank at the second time; (f) calculating a change in mass of gas in the fuel tank during the time interval; (g) calculating a change in volume of fuel in the fuel tank during the time interval; (h) calculating the quantity of fuel in the fuel tank at the second time based on the calculated changes in mass of gas and volume of fuel in the fuel tank during the time interval, the first and second temperatures, and the first and second pressures; and (i) displaying symbology representing the quantity of fuel, wherein steps (f) through (h) are performed by a processing unit.

Other aspects of methods and systems for measuring the quantity of fuel in a fuel tank are disclosed below.

DETAILED DESCRIPTION

Various embodiments of methods and systems for measurement of the quantity (i.e., volume or mass) of liquid fuel in a fuel tank on an aircraft will now be described in detail for the purpose of illustration. It should be appreciated, however, that the methodology disclosed herein is not limited to aircraft applications but rather may also be used in land and marine vehicles as well as stationary liquid fuel tanks. At least some of the details disclosed below relate to optional features or aspects, which in some applications may be omitted without departing from the scope of the claims appended hereto.

Fuel tanks in vehicles carry fuel that is used to operate the engines of a vehicle. The fuel is flammable in the presence of oxygen or air. When fuel is used, the level of fuel decreases. This decrease in the level of fuel results in a space filled with gas increasing in size above the level of the liquid fuel in the fuel tank. The space above the liquid fuel may contain air and fuel vapors. This space is referred to as an “ullage”.

Increased safety for fuel tanks may be provided through the use of an inert gas system. The inert gas system may generate and distribute an inert gas to reduce the oxygen content that may be present in the fuel tanks. In particular, the space (i.e., ullage) above the surface of the fuel in the fuel tank is filled with an inert gas. The inert gas displaces air that contains oxygen in the fuel tank. The inert gas may also displace fuel vapors and other elements. This process is called “inerting”. The inert gas reduces the oxygen content in this space in a manner that reduces a possibility of a combustion event, including ignition, detonation, or deflagration. The combustion event may be the combustion of the fuel, fuel vapor, or both.

An on-board inert gas generation system (OBIGGS) may be used to generate oxygen-depleted (i.e., inert) gas to inert the ullage in fuel tanks. Inerting the ullage portion of the fuel tank reduces the oxidizing agents in the fuel tank and therefore reduces the flammability of the vapor therein. This inert gas may be, for example, nitrogen, nitrogen-enriched air, carbon dioxide, and other types of inert gases.

FIG. 1is a block diagram showing major components of a system onboard an aircraft for converting liquid fuel into power and inerting the fuel tank. The system comprises an on-board inert gas generation system (OBIGGS)2. Air is delivered to the OBIGGS2. The OBIGGS2is in fluid communication with a fuel tank4. Oxygen is separated from air in the OBIGGS2and the remaining oxygen-depleted air is sent to the fuel tank4. The interior volume of the fuel tank4contains ullage gas8overlying liquid fuel10. The typical OBIGGS2separates oxygen and nitrogen, the two main components of air. The oxygen is not used and nitrogen-enriched air is pumped into the fuel tank4to reduce the oxygen concentration of the ullage gas8. In some embodiments, the OBIGGS2produces nitrogen-enriched air from engine bleed air (i.e., pressurized air that is bled from different engine compressor stages for pneumatic system consumers on the aircraft). The ullage gas8can be vented overboard from the fuel tank4. Fuel from the fuel tank4is delivered to the engines or to an auxiliary power unit (APU)6, thereby enabling the generation of power as the fuel is combusted. The OBIGGS2is normally turned on after fuel upload prior to each flight. For military aircraft, the system is typically on. On commercial flights, the system may be turned off in flight.

Gas (including ullage gas in a fuel tank) is compressible, which means that when a given mass of gas is pressurized, its volume decreases, i.e., more mass can be compressed into the same volume under increasing pressure. Both air and nitrogen-enriched air are compressible and are ideal gases. Ideal gas behaviors are governed by the ideal gas law:
PV=MRT
where P is pressure, V is volume, M is amount (e.g., mass), R is the ideal gas constant, and T is temperature. In SI units, P is measured in pascals, V is measured in cubic meters, M is measured in moles, and T is measured in degrees Kelvin. R has the value 8.314 J·K−1·mol−1or 0.08206 L·atm·mol−1·K−1if using pressure in standard atmospheres (atm) instead of pascals, and volume in liters instead of cubic meters.

In contrast to the compressibility of gas, liquid is incompressible, which means that when a liquid is pressurized, its volume does not change. Liquid fuel is incompressible.

In various embodiments, the aircraft includes two major types of fuel metering systems: an engine fuel flow meter and a fuel tank fuel quantity gauge. The engine fuel flow meter is on the fuel line in the engine. It gives a very accurate instantaneous fuel flow reading of fuel supplied to each engine. Summing the readings from all the fuel flow meters and integrating over flight time gives the crew total fuel consumed in flight. The problem with this system alone is that only the quantity of fuel going into the engine is known. The fuel flow meters do not provide how much fuel is in each fuel tank.

There are at least five types of fuel tank fuel quantity gauges used in aviation: (1) sight glass, (2) mechanical, (3) electrical; (4) electronic, and (5) optical. Because of fuel tank complexity, flight condition variation, and the attitude of the aircraft is not constant, multiple location readings in the tank are needed for accuracy. A typical small commercial aircraft may require a minimum of twenty fuel gauging probes and a large aircraft may have over sixty. Total system weight is high and failure of any one probe compromises accuracy. To convert the instantaneous probe data and flight data to fuel quantity, a sophisticated algorithm is required. The algorithm requires much computing power. When there is a design change such as plumbing re-routing in the fuel tank, fuel quantity software update is required. In addition to fuel gauging probes, the aircraft may require a probe compensator to compensate for variation in fuel permittivity, a densitometer to measure fuel density, and a temperature sensor to measure fuel temperature. In flights where most time is spent in level cruise, the fuel and ullage interface line is relatively calm and level. Under these conditions, level sensing gauges provide accurate data. In flights where an aircraft is maneuvered constantly, these gauges may not provide desirable results.

The fuel gauging system proposed herein overcomes many of the shortcomings described in the preceding paragraphs. For each fuel tank, the fuel gauging system comprises an incoming gas line, a vent line with a valve, an ullage gas pressure gauge, and an ullage gas temperature gauge. A pressure measurement and a temperature measurement are taken during each fuel quantity reading.

FIG. 2is a block diagram showing a fuel tank4containing liquid fuel10and ullage gas8, a pressure gauge12for measuring the pressure of the ullage gas inside the fuel tank4, and a temperature gauge14for measuring the temperature of the ullage gas inside the fuel tank4. The system shown inFIG. 2also comprises one or more injection nozzles (not shown) for injecting nitrogen-enriched air (indicated by the dashed arrow labeled “Gas ΔM”) into the fuel tank4via an incoming gas line (not shown), a vent line16for fuel tank venting (pressure equalization) and discharging ullage gas, and a climb/dive valve18on the vent line16to control venting. With the valve18on the vent line16closed, a small amount (i.e., mass) of gas, indicated by ΔM inFIG. 2, is injected into the fuel tank4. The amount ΔM is limited by the fuel tank overpressure design limit. The readings on the pressure and temperature gauges12,14seen inFIG. 2are intended to indicate the ullage pressure and temperature at the start (also referred to below as “Time 1”) of a time interval (which time interval ends at Time 2, where Time 2−Time 1=ΔT). The dashed arrow labeled “Gas ΔM” inFIG. 2indicates gas injection occurring at Time 1. The gas injection continues until at least Time 2.

FIG. 3is a block diagram showing the same components as depicted inFIG. 2after the injection of an amount of gas equal to ΔM (indicated by the solid arrow labeled “Gas ΔM”) during the time interval from Time 1 to Time 2. In other words, ΔM represents the change in mass of the ullage gas during ΔT. As will be described in more detail later, ΔM can be computed by integrating the rate at which gas is flowing into the fuel tank4over the time interval from Time 1 to Time 2.

Although not indicated inFIGS. 2 and 3, liquid fuel10is also flowing out of the fuel tank4as gas is being injected into the fuel tank4. As will be described in more detail later, a decrease in fuel volume ΔV can be computed by integrating the rate at which fuel is flowing out of the fuel tank4over the time interval from Time 1 to Time 2.

As gas is injected into and fuel10flows out of the fuel tank4, the pressure and temperature of the ullage gas8changes, as indicated by the readings on pressure and temperatures gauges12,14seen inFIG. 3as compared to the respective readings on the same gauges seen inFIG. 2.

In accordance with one methodology, a first pressure measurement and a first temperature measurement are taken at Time 1, as indicated by the readings of pressure gauge12and temperature gauge14shown inFIG. 2. A second pressure measurement and a second temperature measurement are taken at Time 2, as indicated by the readings of pressure gauge12and temperature gauge14shown inFIG. 3. As gas is added to the ullage8during the time interval from Time 1 to Time 2 (while the valve18of the vent line16is closed), since gas is compressible and the ullage is constrained, the measured ullage pressure and ullage temperature should both increase. Conversely, the fuel is incompressible. Therefore, although the ullage pressure increases as gas is injected, the fuel volume does not change due to this increase in ullage pressure (although it does change due to the flow of fuel to the engine).

In cases where OBIGGS is not available or for aircraft without an OBIGGS, engine bleed air can be used as the injected gas. Engine bleed air can be hot, so pre-cooling may be required. In the case of gas injection, the gas flow rate can be measured by a gas flow meter located along the incoming gas line. By integrating gas flow rate between Time 1 and Time 2, the gas mass change ΔM is obtained. The fuel flow rate (gpm or lb/hr) to the engine is measured at the engine and is a known quantity during flight. By integrating fuel flow rate between Time 1 and Time 2, the fuel volume change ΔV is obtained. This change in fuel volume will be equal and opposite to the change in ullage volume during the time interval since the volume of the fuel tank is constant.

Another source of pressurized air comes from cabin air. For commercial aircraft, the air in the cabin is changed constantly. The air is dumped overboard. For long-range aircraft, this air may be used to pressurize the ullage. The pressure in an aircraft cabin is typically set at 8,000 ft pressure altitude or eleven pounds per square inch. The ambient air pressure at a cruise altitude of 35,000 ft is 3.5 pounds per square inch. There is ample air pressure in the cabin air to run the fuel gauging system. In addition, the cabin air is a wasted air; therefore it does not cost fuel for pressurization.

The ideal gas law is then used to calculate the ullage volume (V+ΔV) at Time 2. The two gas laws at Times 1 and 2 are as follows:
P1V=MRT1
P2(V+ΔV)=(M+ΔM)RT2

The pressure P1and temperature T1are measured at Time 1 (at or after the start of gas injection); the pressure P2and temperature T2are measured at Time 2 (while gas injection continues); and ΔM is measured over the time interval (from Time 1 to Time 2) during which gas is being injected. R is the ideal gas constant. The initial ullage volume V and initial gas mass M in the fuel tank4at Time 1 are the only two unknowns. The respective equations for thermodynamic states at Times 1 and 2 are solved simultaneously for ullage volume V at Time 1 and ullage gas mass M at Time 1. The ullage volume calculated in each instance is the true ullage volume regardless of the shape of the ullage or how many gas bubbles make up the ullage volume.

The difference between the interior volume of the fuel tank and the ullage volume (V+ΔV) at Time 2 is the fuel volume at Time 2. Similarly, the fuel volume at a Time 3 (subsequent to Time 2) can be computed by using either the ideal gas laws for Times 2 and 3 or for Times 1 and 3. In each instance, the product of the fuel volume and the fuel density is the fuel weight.

The measurement and calculation processes continue until the ullage gas pressure reaches a pre-specified limit. The limiting ullage pressure is always below the fuel tank overpressure design limit. When the limiting ullage pressure is reached, the valve18is opened to allow the ullage to depressurize. During depressurization, the ullage gas pressure and temperature measurements continue. The only difference is that the change in the mass of ullage gas ΔM is now negative.

FIG. 4is a flowchart showing steps of a method for direct measurement of the quantity of liquid fuel in a fuel tank while gas is being injected into and fuel is flowing out of the fuel tank in accordance with one embodiment. First, the vent valve is closed (step20). Then gas is injected into the fuel tank via a gas line during a time interval that starts at time T and ends at Time (T+ΔT) while the vent valve is closed (step22). The rates at which gas is flowing into and fuel is flowing out of the fuel tank are measured throughout the time interval (step24). In addition, the pressure and temperature of the gas in the fuel tank are measured at time T (step26) and at time Time (T+ΔT) (step28). A change in volume of fuel in the fuel tank during the time interval ΔT is then calculated (step30). Likewise a change in mass of gas injected into the fuel tank during the time interval ΔT is calculated (step32). The ullage gas mass M and ullage gas volume V at Time T are then calculated using the respective gas law equations for Times T and (T+ΔT) as previously described (step34). The fuel volume at Time (T+ΔT) can then be calculated (step36). At the same time, a determination is made whether the ullage gas pressure has reached the preset maximum pressure or not (step38). If the preset maximum pressure has been reached, then gas injection is stopped (step40). If the preset maximum pressure has not been reached, then gas injection continues and the process returns to step28, i.e., the pressure and temperature of the gas in the fuel tank are measured again after the passage of a second time interval that starts at Time (T+ΔT) and ends at (T+2ΔT). Successive datapoints can be acquired at regular time increments ΔT, i.e., at successive times (T+nΔT), where n=1, 2, 3, etc.

FIG. 5is a flowchart showing steps of a method for direct measurement of the quantity of liquid fuel in a fuel tank while gas is being vented and fuel is flowing out of the fuel tank in accordance with another embodiment. First, the vent valve is opened (step60). Then ullage gas is vented out of the fuel tank via a vent line (e.g., using a gas pump) during a time interval that starts at time T and ends at Time (T+ΔT) while the vent valve is open (step62). The rates at which gas and fuel are flowing out of the fuel tank are measured throughout the time interval (step24). In addition, the pressure and temperature of the gas in the fuel tank are measured at time T (step26) and at time Time (T+ΔT) (step28). A change in volume of fuel in the fuel tank during the time interval is then calculated (step30). Likewise a change in mass of gas being vented out of the fuel tank during the time interval is calculated (step64). The ullage gas mass M and ullage gas volume V at Time T are then calculated using the respective gas law equations for Times T and (T+ΔT) as previously described (step34). The fuel volume at Time (T+ΔT) can then be calculated (step36). At the same time, a determination is made whether the ullage gas pressure has reached zero (relative to ambient pressure) or not (step66). If the ullage gas pressure has reached zero, the vent valve is closed (step20). If the ullage gas pressure has not reached zero, then the venting of gas continues and the process returns to step28, i.e., the pressure and temperature of the gas in the fuel tank are measured again after the passage of a second time interval as previously described.

FIG. 6is a block diagram identifying components of a system for measuring a level of liquid fuel in a fuel tank in accordance with the embodiments described above. All calculations are performed by a processing unit44which receives measurement data from the pressure gauge12, the temperature gauge14, a fuel flow meter48and a gas flow meter50. The processing unit44is programmed to execute algorithms for quantifying the amount of fuel in a fuel tank. The processing unit44outputs the fuel quantity data to a fuel gauge46, which displays symbology representing the quantity of fuel. The fuel gauge46may take the form of a display device having a display processor programmed to display the measurement results (e.g., the fuel level) graphically and/or alphanumerically on a display screen. The readings provided by the processing unit44to the fuel gauge46may be integrated or averaged before presentation and may be provided in real time substantially continuously or at different time intervals.

The processing unit44may be a dedicated microprocessor or a general-purpose computer. In accordance with one embodiment, the algorithms executed by the processing unit44include: (1) an algorithm for computing a change in volume ΔV of fuel in the fuel tank during a time interval by integrating a rate of flow of fuel out of the fuel tank (provided by a fuel flow meter48) during the time interval; (2) an algorithm for computing a change in mass ΔM of gas in the fuel tank during the time interval by integrating a rate of flow of gas into or out of the fuel tank (provided by a gas flow meter50) during the time interval; (3) an algorithm for computing the ullage gas mass M and ullage gas volume V at the start of the time interval based on ΔV, ΔM, pressure measurements taken at the start and end of the time interval by the pressure gauge12, and temperature measurements taken at the start and end of the time interval by the temperature gauge14; and (4) an algorithm for calculating the fuel volume at the end of the time interval based on (V+ΔV) and the fixed volume of the fuel tank. The fuel weight can be computed as the product of the fuel volume and the fuel density.

One advantage of the system described above is that it measures the ullage, not the fuel level (i.e., fuel surface location). Neither the attitude of the aircraft nor the flight condition affect the reading or accuracy of the measurement.

Most aircraft have multiple fuel tanks. Similar to the current fuel system practice, each fuel tank can be provided with its own individual fuel quantity gauging system. For fuel tanks with multiple partitions, more than one temperature probe may be required.

Ullage gases are not limited to OBIGGS nitrogen-enriched air or engine bleed air. Other gases or inert gas such as carbon dioxide can be used. For non-aircraft and stationary tank applications, pressurized air or bottled gas can be used.

Furthermore, ullage gas is not limited to ideal gas. Any gas can be used. For example, when a Van Der Waals gas is used, the Van Der Waals equation and the corresponding Van Der Waals constants for the gas can be used.

Mixing two different gases, i.e., the gas added is different from what is in the fuel tank, works but it may make the final calculation more tedious.

All aircraft systems are required to have backup system for redundancy. This fuel gauging system is lightweight and inexpensive. Redundancy can be achieved by duplicating the entire system in the fuel tanks as long as they are independent of each other.

While methods for measuring the quantity of liquid fuel in a fuel tank have been described with reference to various embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the teachings herein. In addition, many modifications may be made to adapt the concepts and reductions to practice disclosed herein to a particular situation. Accordingly, it is intended that the subject matter covered by the claims not be limited to the disclosed embodiments.

In addition, the method claims set forth hereinafter should not be construed to require that the steps recited therein be performed in alphabetical order (any alphabetical ordering in the claims is used solely for the purpose of referencing previously recited steps) or in the order in which they are recited. Nor should they be construed to exclude any portions of two or more steps being performed concurrently or alternatingly.