Patent Publication Number: US-2021180523-A1

Title: Systems and methods for operating an engine having variable geometry mechanisms

Description:
TECHNICAL FIELD 
     The application relates generally to engines, and more particularly to engines having variable geometry mechanisms. 
     BACKGROUND OF THE ART 
     During certain aircraft operations, it can be desirable to adjust the engine inlet mass flow, which in turn alters the engine output power. For example, attaining certain levels of aircraft engine performance and operability can be predicated on adjustments to the inlet mass flow. One existing technique for adjusting the engine inlet mass flow involves adjusting the geometry of one or more components of the engine, called variable geometry mechanisms. 
     Existing systems for controlling variable geometry mechanisms may have certain drawbacks. As a result, improvements are needed. 
     SUMMARY 
     In accordance with a broad aspect, there is provided a method for operating an engine having at least first and second variable geometry mechanisms. A spool-specific ratio for at least one spool of the engine is determined, wherein the spool-specific ratio relates to an aerodynamic parameter. The spool-specific ratio is compared to a reference to determine a ratio discrepancy for the at least one spool. An engine-specific ratio relating to the aerodynamic parameter is determined. At least one of a position of the first variable geometry mechanism and a position of the second variable geometry mechanism is adjusted based on the engine-specific ratio and the ratio discrepancy to reduce the ratio discrepancy. 
     In accordance with another broad aspect, there is provided a system for controlling an engine having first and second variable geometry mechanisms. The system comprises a processing unit, and a non-transitory computer-readable medium communicatively coupled to the processing unit. The computer-readable medium comprises computer-readable program instructions executable by the processing unit for: determining a spool-specific ratio for at least one spool of the engine, wherein the spool-specific ratio relates to an aerodynamic parameter; comparing the spool-specific ratio to a reference to determine a ratio discrepancy for the at least one spool; determining an engine-specific ratio relating to the aerodynamic parameter; and adjusting at least one of a position of the first variable geometry mechanism and a position of the second variable geometry mechanism based on the engine-specific ratio and the ratio discrepancy to reduce the ratio discrepancy. 
     In accordance with a further broad aspect, there is provided a method for controlling an engine having first and second variable geometry mechanisms. A first ratio between a first aerodynamic parameter, measured at an inlet of a first spool of the engine, and a second aerodynamic parameter, measured at an intermediate point between the first spool and a second spool of the engine is determined, wherein the first variable geometry mechanism is associated with the first spool, and wherein the second variable geometry mechanism is associated with the second spool. A second ratio between the second aerodynamic parameter and a third aerodynamic parameter, measured at an outlet of the second spool is determined. A third ratio between the first aerodynamic parameter and the third aerodynamic parameter is determined. The first, second, and third ratios are compared to first, second, and third reference ratios, respectively. When the first ratio differs from the first reference ratio beyond a first predetermined range, a first position control signal is generated and output to a controller of the engine to alter a position of the first variable geometry mechanism. When the second ratio differs from the second reference ratio beyond a second predetermined range, a second position control signal is generated and output to the controller of the engine to alter a position of the second variable geometry mechanism. When the third ratio differs from the third reference ratio beyond a third predetermined range, at least one third position control signal is generated and output to the controller of the engine to alter the position of the first variable geometry mechanism and/or the position of the second variable geometry mechanism. 
     Features of the systems, devices, and methods described herein may be used in various combinations, in accordance with the embodiments described herein. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       Reference is now made to the accompanying figures in which: 
         FIG. 1  is a schematic cross-sectional view of an example gas turbine engine; 
         FIG. 2  is a block diagram of an example engine system; 
         FIG. 3  is a flowchart illustrating an example method for operating the engine of  FIG. 1 ; and 
         FIG. 4  is a block diagram of an example computer system for implementing the method of  FIG. 3 . 
     
    
    
     It will be noted that throughout the appended drawings, like features are identified by like reference numerals. 
     DETAILED DESCRIPTION 
       FIG. 1  illustrates an engine  10 , for example of a type provided for use in subsonic flight, generally comprising in serial flow communication an air inlet  11 , a compressor section  12  for pressurizing the air from the air inlet  11 , a combustor  13  in which the compressed air is mixed with fuel and ignited for generating an annular stream of hot combustion gases, a turbine section  14  for extracting energy from the combustion gases; an exhaust outlet  15  through which the combustion gases exit the engine  10 . The engine  10  includes a propeller  16  which provides thrust for flight and taxiing. The engine  10  has a longitudinal center axis  17 . The engine  10  may be a gas turbine engine, as illustrated in  FIG. 1 , or any other suitable type of engine. 
     The engine  10  has a central core  18  defining a gas path through which gases flow as depicted by flow arrows in  FIG. 1 . The exemplified engine  10  is a “reverse-flow” engine  10  because gases flow through the core  18  from the air inlet  11  at a rear portion thereof, to the exhaust outlet  15  at a front portion thereof. This is in contrast to “through-flow” gas turbine engines in which gases flow through the core of the engine from a front portion to a rear portion. The direction of the flow of gases through the core  18  of the engine  10  disclosed herein can be better appreciated by considering that the gases flow through the core  18  in the same direction D as the one along which the engine  10  travels during flight, Stated differently, gases flow through the engine  10  from a rear end thereof towards the propeller  16 . 
     Although illustrated as a turboprop engine, the engine  10  may alternatively be another type of engine, for example a turbofan engine, also generally comprising in serial flow communication a compressor section, a combustor, and a turbine section, and a fan through which ambient air is propelled. A turboshaft engine may also apply. Similarly, although illustrated as a reverse-flow engine, the techniques described herein can also be applied to through-flow engines. In addition, although the engine  10  is described herein for flight applications, it should be understood that other uses, such as industrial or the like, may apply. 
     Still referring to  FIG. 1 , the engine  10  has multiple spools which perform compression to pressurize the air received through the air inlet  11 , and which extract energy from the combustion gases before they exit the core  18  via the exhaust outlet  15 . According to the illustrated example, the engine  10  is provided in the form of a multi-spool engine having a low pressure (LP) spool  20  and a high pressure (HP) spool  40  independently rotatable about axis  17 . However, it is understood that a multi-spool engine could have more than two spools. It should also be noted that the embodiments described herein also consider the use of single-spool engines. 
     The LP spool  20  includes at least one component to compress the air that is part of the compressor section  12 , and at least one component to extract energy from the combustion gases that is part of the turbine section  14 . More particularly, the LP spool  20  has a low pressure turbine  21  which extracts energy from the combustion gases, and which is drivingly engaged to an LP compressor  22  for pressurizing the air. The LP turbine  21  (also referred to as the power turbine) drives the LP compressor  22 , thereby causing the LP compressor  22  to pressurize the air. Both the LP turbine  21  and the LP compressor  22  are disposed along the axis  17 . In the depicted embodiment, both the LP turbine  21  and the LP compressor  22  are axial rotatable components having an axis of rotation that is coaxial with the center axis  17 . They can include one or more stages, depending upon the desired engine thermodynamic cycle, for example. 
     In the depicted embodiment, the LP spool  20  has a power shaft  23  which mechanically couples the LP turbine  21  and the LP compressor  22 , and extends axially between them. The shaft  23  is coaxial with the central axis  17  of the engine  10 . The shaft  23  allows the LP turbine  21  to drive the LP compressor  22  during operation of the engine  10 . The shaft  23  is not limited to the configuration depicted in  FIG. 1 , and can also mechanically couple the LP turbine  21  and the LP compressor  22  in any other suitable way provided that it transmits a rotational drive from the LP turbine  21  to the LP compressor  22 . For example, the shaft  23  can be combined with a geared LP compressor  22  to allow the LP compressor  22  to run at a different rotational speed from the LP turbine  21 . This can provide more flexibility in the selection of design points for the LP compressor. 
     Still referring to  FIG. 1 , the engine  10  includes an output drive shaft  24 . The drive shaft  24  extends forwardly from the LP turbine  21  and is drivingly engaged thereto. In the illustrated example, the drive shaft  24  is distinct from the power shaft  23  and mechanically coupled thereto to be driven by the LP turbine  21 . In the depicted embodiment, the drive shaft  24  and the power shaft  23  are coaxial and interconnected.  FIG. 1  shows that the power and drive shafts  23 ,  24  are interconnected with a spline  25 . The spline  25 , which can include ridges or teeth on the drive shaft  24  that mesh with grooves in the power shaft  23  (or vice versa), allows for the transfer of torque between the drive shaft  24  and the power shaft  23 . In the depicted embodiment, the power shaft  23  lies at least partially within the drive shaft  24 , such that the spline  25  transfers the rotational drive or torque generated by the LP turbine  21  from the drive shaft  24  to the power shaft  23 . The spline  25  can operate so that the power shaft  23  and the drive shaft  24  rotate at the same rotational speed. Other mechanical techniques can also be used to interconnect the power and drive shafts  23 ,  24 . For example, the power and drive shafts  23 ,  24  can be interconnected by curvic coupling, pins, and interference fits. Other configurations of the drive shaft  24  and the power shaft  23  are also possible. For example, the drive shaft  24  and the power shaft  23  can be a single shaft driven by the LP turbine  21 . The drive shaft  24  therefore transfers the rotational output of the LP turbine  21  in a forward direction to drive another component. 
     A rotatable load, which in the embodiment shown includes the propeller  16 , is mountable to the engine  10 , and when mounted, is drivingly engaged to the LP turbine  21 , and is located forward of the LP turbine  21 . In such a configuration, during operation of the engine  10 , the LP turbine  21  drives the rotatable load such that a rotational drive produced by the LP turbine  21  is transferred to the rotatable load. The rotatable load can therefore be any suitable component, or any combination of suitable components, that is capable of receiving the rotational drive from the LP turbine  21 , as now described. 
     In the embodiment shown, a reduction gearbox  31  (sometimes referred to herein simply as “RGB  31 ”) is mechanically coupled to a front end of the drive shaft  24 , which extends between the RGB  31  and the LP turbine  21 . The RGB  31  processes and outputs the rotational drive transferred thereto from the LP turbine  21  via the drive shaft  24  through known gear reduction techniques. The RGB  31  allows for the propeller  16  to be driven at its optimal rotational speed, which is different from the rotational speed of the LP turbine  21 . 
     Still referring to  FIG. 1 , the HP spool  40  is composed of at least one component to compress the air that is part of the compressor section  12 , and at least one component to extract energy from the combustion gases that is part of the turbine section  14 . The HP spool  40  is also disposed along the axis  17  and includes an HP turbine  41  drivingly engaged (e.g. directly connected) to a high pressure compressor  42  by an HP shaft  43  rotating independently of the power shaft  23 . Similarly to the LP turbine  21  and the LP compressor  22 , the HP turbine  41  and the HP compressor  42  can include various stages of axial rotary components. In the depicted embodiment, the HP compressor  42  includes a centrifugal compressor  42 A or impeller and an axial compressor  42 B, both of which are driven by the HP turbine  41 . During operation of the engine  10 , the HP turbine  41  drives the HP compressor  42 . 
     It can thus be appreciated that the presence of the above-described LP and HP spools  20 ,  40  provides the engine  10  with a “split compressor” arrangement. More particularly, some of the work required to compress the incoming air is transferred from the HP compressor  42  to the LP compressor  22 . In other words, some of the compression work is transferred from the HP turbine  41  to the more efficient LP turbine  21 . This transfer of work may contribute to higher pressure ratios while maintaining a relatively small number of rotors. In a particular embodiment, higher pressure ratios allow for higher power density, better engine specific fuel consumption (SFC), and a lower turbine inlet temperature (sometimes referred to as “T4”) for a given power. These factors can contribute to a lower overall weight for the engine  10 . The transfer of compression work from the HP compressor  42  to the LP compressor  22  contrasts with some conventional reverse-flow engines, in which the high pressure compressor (and thus the high pressure turbine) perform all of the compression work. 
     In light of the preceding, it can be appreciated that the LP turbine  21  is the “low-speed” and “low pressure” turbine when compared to the HP turbine  41 . The LP turbine  21  is sometimes referred to as a “power turbine”. The turbine rotors of the HP turbine  41  spin at a higher rotational speed than the turbine rotors of the LP turbine  21  given the closer proximity of the HP turbine  41  to the outlet of the combustor  13 . Consequently, the compressor rotors of the HP compressor  42  may rotate at a higher rotational speed than the compressor rotors of the LP compressor  22 . The engine  10  shown in  FIG. 1  is thus a “two-spool” engine  10 . 
     The HP turbine  41  and the HP compressor  42  can have any suitable mechanical arrangement to achieve the above-described split compressor functionality. For example, and as shown in  FIG. 1 , the HP spool  40  includes a high pressure shaft  43  extending between the HP compressor  42  and the HP turbine section  41 . The high pressure shaft  43  is coaxial with the power shaft  23  and rotatable relative thereto. The relative rotation between the high pressure shaft  43  and the power shaft  23  allow the shafts  23 ,  43  to rotate at different rotational speeds, thereby allowing the HP compressor  42  and the LP compressor  22  to rotate at different rotational speeds. The HP shaft  43  can be mechanically supported by the power shaft  23  using bearings and/or the like. In the depicted embodiment, the power shaft  23  is at least partially disposed within the HP shaft  43 . 
     The split compressor arrangement also allows bleed air to be drawn from between the HP compressor  42  and the LP compressor  22 . More particularly, in the embodiment of  FIG. 1 , the engine  10  includes an inter-stage bleed  44  port or valve that is aft of the HP compressor  42  and forward of the LP compressor  22 , which may provide for increased flexibility in the available bleed pressures. In a particular embodiment, the bleed pressure design point of the inter-stage bleed  44  is selected based on the pressure ratio of the LP compressor  22 , which runs independently from the HP compressor  42 . For operability, variable inlet guide vanes (VIGV)  51  and variable guide vanes (VGV)  52  can be used on the LP compressor  22  and at the entry of the HP compressor  42 , together with the inter-stage bleed  44 . 
     It should be noted that the engine of  FIG. 1  represents only one example engine, and that the embodiments described herein can be applied to any other suitable manner of engine. 
     In some embodiments, the engine  10  includes one or more variable geometry mechanisms (VGMs) which may assist in achieving optimized engine transient response. In some embodiments, the VGMs consists of one or more VGVs, for instance the VIGV  51  and the VGV  52  (collectively, the “VGMs  51 ,  52 ”), which may be one of inlet compressor guide vanes for directing air into the compressor section  12 , outlet guide vanes for directing air out of the compressor section  12 , variable stator vanes for directing incoming air into rotor blades of the engine  10 , and/or one or more variable nozzles, variable bleed-off valves, for instance the inter-stage bleed  44 , and the like. It should be understood that one or more of the above-mentioned VGMs may be adjusted for the purpose of decreasing the response time of the engine  10  during rapid engine transitions, e.g. from low to high power levels, or vice-versa. Indeed, adjustment of the position (e.g. the angle) of the VGMs can impact the inlet mass flow to the engine  10 , and in turn allow the engine  10  to operate at a required power. 
     In some embodiments, as illustrated in  FIG. 1 , the engine  10  has a dual compression system with a low-spool compression system (LPC), including the LP spool  20 , and a high-spool compression system (HPC), including the HP spool  40 , which are separate from one-another. The VGMs include the VIGV  51  at the air inlet  11  near the LPC and the VGV  52  upstream of the HPC. It should be noted that other VGMs may also be included for both the LPC and the HPC. In other embodiments, the engine  10  includes only one compression system, and includes fewer or more VGMs. 
     With reference to  FIG. 2 , there is illustrated an engine system  200 , which is composed of the engine  10 , a controller  210 , and a plurality of sensors, illustrated here as sensors  232 ,  234 ,  236  (collectively, “sensors  230 ”). It should be understood that certain elements of the engine  10 , as shown in  FIG. 2 , are omitted to facilitate understanding. In addition, arrows  205  are provided to show the direction of airflow, namely from the LP spool  20  to the HP spool  40 . 
     As is described in greater detail hereinbelow, the sensors  230  are configured for measuring an aerodynamic parameter for the engine  10  and/or for one of the spools  20 ,  40 . The sensors  230  are shown as forming part of the engine  10 , but it should be understood that in some embodiments, the sensors  230  can be external to the engine  10 . In addition, in some embodiments, the sensors  230  include more, or fewer, sensors, as appropriate. In the embodiment illustrated in  FIG. 2 , the sensor  232  is located at an inlet to the LP spool  20 , the sensor  234  is located at some intermediate position between an outlet to the LP spool  20  and an inlet to the HP spool  40 , and the sensor  236  is located at an outlet to the HP spool  40 . It should be noted, however, that other embodiments are also considered. In some cases, the sensor  234  is located at the outlet to the LP spool  20 . In some other cases, the sensor  234  is located at the inlet to the HP spool  40 . In some further cases, the sensor  234  is located at or proximate some midpoint between the outlet to the LP spool  20  and the inlet to the HP spool  40 , or is located at any other suitable position. Other embodiments are also considered. Additionally, although illustrated here as physical sensors located at particular locations, it should be understood that in some cases, one or more of the sensors  230  can be virtual sensors, that is to say, instruments which make use of measurements from other sensors (physical or virtual) to derive a desired parameter. 
     The controller  210  is provided to control various aspects of the operation of the engine  10 . To this end, the controller  210  is communicatively coupled to a variety of instruments associated with the engine  100 , including the sensors  230 , to acquire information therefrom. The controller  210  can be implemented as part of a full-authority digital engine control (FADEC) or other similar device, including electronic engine control (EEC), engine control unit (EUC), engine electronic control system (EECS), and the like. For example, the controller  210  is configured controlling operation of the VGMs  51 ,  52  based on, inter aria, information acquired from the sensors  230 , which can include altering a position and/or an orientation of the VGMs  51 ,  52 . 
     In some embodiments, the sensors  230  provide the controller  210  with an aerodynamic parameter. Aerodynamic parameters are measures of the aerodynamic work performed by the engine  10 . In some instances, the sensors  230  are pressure sensors, and provide the controller  210  with pressure measurements. In some other instances, the sensors  230  are temperature sensors, and provide the controller  210  with temperature measurements. In some still further embodiments, the sensors  230  include combinations of one or more of the above, or use other sensors which provide a reading of an aerodynamic parameter of the engine. The controller  210  can be provided with values for the aerodynamic parameters substantially in real-time, on a punctual basis, in response to requests issued by the sensors, and the like. 
     In some embodiments, the controller  210  is configured for calculating one or more ratios of the aerodynamic parameters for parts of the engine  10 . For example, the controller  210  can calculate one or more spool-specific ratios of the aerodynamic parameters. The spool-specific ratios can include a ratio for the LP spool  20 , the HP spool  40 , and/or a ratio for any other spool which may form part of the engine  10 . For instance, if the sensors  232 ,  234  provide pressure measurements, the controller  210  can determine a spool-specific pressure ratio for the LP spool  20  by dividing the pressure measurement from sensor  234  by the pressure measurement from sensor  232  (this ratio is sometimes referred to as a “compressor pressure ratio”). Similarly, if the sensors  234 ,  236  provide pressure measurements, the controller  210  can determine a spool-specific pressure ratio for the HP spool  40 . Other ratios can be determined for other measurements, depending on the nature of the sensors  230 . The controller  210  can determine any suitable number of spool-specific ratios, as appropriate. The controller  210  can also be configured for calculating one or more ratios of the aerodynamic parameters for the engine  10  as a whole. For example, the controller  210  can calculate a pressure ratio for the engine  10 , based on pressure measurements provided by the sensors  232 ,  236 . 
     In some embodiments, the controller  210  can be configured for controlling the VGMs  51 ,  52  to achieve or maintain predetermined values for the aerodynamic ratios. The aerodynamic ratios can be associated with particular operating mode or conditions for the engine  10 . For instance, operation of the engine  10  can be optimized for certain pressure ratios for the spools  20 ,  40 , and/or for the engine  10  as a whole. In another instance, certain outcomes can be achieved based on maintaining certain aerodynamic ratios, such as better fuel efficiency, lower engine wear, and the like. Other outcomes can also be achieved by maintaining certain aerodynamic ratios. As a result, the controller  210  is configured for adjusting the position and/or orientation of the VGMs  51 ,  52  to achieve certain aerodynamic ratios. 
     For example, the controller  210  is configured for determine one or more ratios of aerodynamic parameters, for instance for the spools  20 ,  40 , and for the engine  10 . The controller  210  compares the spool-specific ratios to predetermined references for the spool-specific ratios to determine ratio discrepancies for each of the spools  20 ,  40 . The ratio discrepancies are a measure of the difference between the measured spool-specific ratio and the reference, and can be expressed as an absolute number, as a percent variation, or the like. The controller  210  can also compare the engine ratio to a predetermined reference to determine a ratio discrepancy for the engine  10 . Similarly to the spool-specific ratio discrepancies, the ratio discrepancy for the engine  10  is also a measure of the difference between the measured engine-specific ratio and the reference for the engine  10 . 
     The references can be stored in a memory or other storage system available to the controller  210 . In some embodiments, the controller  210  is provided with multiple sets of references, and selects one or more of the sets of references when performing the comparison. For example, different sets of references are associated with a particular phase or more of operation of the engine  10 , or with a particular phase or mode of operation of a larger system of which the engine  10  is a component. For instance, the engine  10  can be operated in the context of an aircraft, and the references can be associated with different phases of a flight mission. Different references can be provided for a ground idle phase, for a takeoff phase, for a cruise phase, for a descent phase, and the like. In another example, different sets of references are associated with an external condition within which the engine  10  is operating, or within which a larger system, of which the engine  10  is a component, is operating. For instance, the references can be associated with an altitude of operation of the engine  10 , an ambient temperature of the environment in which the engine  10  is operated, or the like. 
     Based on the ratio discrepancies and/or the spool-specific and engine ratios, the controller  210  can adjust the position and/or orientation of the VGMs  51 ,  52  to achieve or maintain certain aerodynamic ratios for the spools  20 ,  40 , and/or for the engine  10 . Put differently, the controller  210  adjusts the position and/or orientation of the VGMs  51 ,  52  to reduce the ratio discrepancies for the spool-specific ratios and/or for the engine-specific ratio. For example, the controller  210  issues commands to actuators associated with the VGMs  51 ,  52  which effect changes in the position and/or orientation of the VGMs  51 ,  52 . In another example, the controller  210  issues commands to a VGM controller which interfaces with the VGMs  51 ,  52 , or with actuators thereof. 
     In some embodiments, the controller  210  adjusts the position and/or orientation of the VGMs  51 ,  52  so that the actual aerodynamic ratios for the spools  20 ,  40 , and/or for the engine  10  are substantially equal to the references, or so that the ratio discrepancies are substantially null. In other embodiments, the controller  210  adjusts the position and/or orientation of the VGMs  51 ,  52  so that the actual aerodynamic ratios for the spools  20 ,  40 , and/or for the engine  10  are sufficiently similar to the references. For example, a predetermined tolerance around the reference can be considered acceptable (e.g., within 5%, within a predetermined value of kPa or atm, or the like). In some cases, the tolerance can vary with different sets of references. In some other embodiments, the references specify ranges for the aerodynamic ratios, and the controller  210  adjusts the position and/or orientation of the VGMs  51 ,  52  so that the actual aerodynamic ratios for the spools  20 ,  40 , and/or for the engine  10  are within the specified ranges. Other approaches are also considered. 
     In this fashion, the VGMs  51 ,  52  are not scheduled to particular positions based on an internal reading of the output of the engine  10  or of the compressors  22 ,  42 , for example internal temperature, output power, shaft speed, or the like. Instead, the VGMs  51 ,  52  are scheduled to produce a predetermined aerodynamic result irrespective of the output of the engine  10 . The predetermined aerodynamic result can vary based on the phase of operation of the engine  10 , in order to ensure flexibility in operation of the VGMs  51 ,  52 . It should be noted that this approach for adjusting the position and/or orientation of the VGMs  51 ,  52  can be used in cases where the LP spool  20  and the HP spool  40  are decoupled, such that measures of the output of the LP spool  20  do not necessarily correspond to measures of the output of the HP spool  40 . 
     In certain situations, the position of only one of the VGMs  51 ,  52  is adjusted, based on the ratio discrepancies and/or the spool-specific and engine ratios. For instance, if the engine-specific ratio is sufficiently different from the associated reference value, the spool-specific ratios can then be assessed. If only one of the spool-specific ratios is sufficiently different from its associated reference, then the position of only one of the VGMs  51 ,  52  is adjusted. In some other situations, the particular coupling between the LP and HP spools  20 ,  40  may cause a change for one of the spools  20 ,  40  to affect the other one of the spools  20 ,  40 . For example, if the LP spool  20  feeds substantially directly into the HP spool  40 , an adjustment to the VGM  51  associated with the LP spool  20  can change the spool-specific ratio for the HP spool  40 , and require a change in the position and/or orientation of the VGM  52 . Thus, a ratio discrepancy for one of the spools may require adjustments to the position and/or orientation of both VGMs  51 ,  52 . 
     It should be noted that the approach outlined herein can also be applied to engines having more than two spools. For example, an engine could have three spools, each with at least one associated VGM. Spool-specific ratios can be determined for each of the spools using relevant aerodynamic parameters, and adjustments to the some or all of the VGMs can be performed to reduce spool-specific discrepancies for all three spools. Adjustments to some of the three spools may affect the spool-specific ratios for the others, which can in turn require additional adjustments. In some embodiments, the controller  210  is configured for concurrently adjusting all VGMs to account for these related effects. 
     With reference to  FIG. 3 , there is illustrated a method  300  for operating an engine having at least first and second variable geometry mechanisms, for example the engine  10  with VGMs  51 ,  52 . In some embodiments, the method  300  can be implemented, in whole or in part, by the controller  210 . It should be noted other embodiments are also considered, for instance in which the engine  10  has more than two VGMs, more than two spools which can each have one or more associated VGMs, and the like. In some embodiments, the engine  10  is operated as part of an aircraft or other vehicle. 
     At step  302 , a spool-specific ratio, for one or more spools of the engine  10 , is determined, for instance for the spools  20 ,  40 . The spool-specific ratio relates to an aerodynamic parameter. The aerodynamic parameter can be pressure, temperature, or the like. For example, a spool-specific pressure ratio is determined for LP spool  20 . In another example, spool-specific temperature ratios are determined for spools  20 ,  40 . In some embodiments, the spool-specific ratios can be determined based on measurements of aerodynamic parameters at one or more locations within the engine  10 . For example, pressure measurements for the inlet to the LP spool  20  and for an intermediate point between the LP spool  20  and the HP spool  40  can be acquired, and used to determine the spool-specific pressure ratio for the LP spool  20 . An additional pressure measurement at the outlet to the HP spool  40  can be acquired and then used, along with the pressure measurement at the intermediate point, to determine the spool-specific pressure ratio for the HP spool  40 . For completeness, it is noted that in certain cases, spool-specific ratios are determined for all spools of the engine  10 , which can include the spools  20 ,  40 , as well as any other spool of the engine  10 . 
     Optionally, at step  304 , a reference is selected, based on the operating conditions of the engine  10 . For example, one or more references are selected for each of the spool-specific ratios determined at step  302 . Also optionally, a reference can be selected for an engine-specific ratio. The references can be selected based on a phase or mode of operation of the engine  10 , based on an external condition within which the engine  10  is operating, or the like. 
     At step  306 , the spool-specific ratio is compared to the reference, in order to determine a ratio discrepancy for the spool(s)  20 ,  40 . In some embodiments, each of the spool-specific ratios is compared to a respective reference. For example, the spool-specific ratio for the LP spool  20  is compared to a first reference, and the spool-specific ratio for the HP spool  40  is compared to a second, different reference. The ratio discrepancies can be expressed as an absolute value, as a relative value, or in any other suitable fashion. 
     At step  308 , an engine-specific ratio, relating to the aerodynamic parameter, is determined. In some embodiments, the engine-specific ratio can relate to the same aerodynamic parameter as did the spool-specific ratios. For instance, the aerodynamic parameter for both the spool-specific ratios and the engine-specific ratio are pressure. In some such cases, the engine-specific ratio can be determined using measurements previously obtained during step  302 . In other cases, separate measurements can be performed to determine the engine-specific ratio, for instance from the sensors  230 , or using different sensors. 
     It should be noted that in some cases, steps  302 ,  304 , and  306  can be performed substantially concurrently with step  308 . For example, once measurements for determining the spool- and engine-specific ratios are acquired, whether at step  302  or at some other time prior thereto, the spool-specific ratio(s) can be determined substantially at the same time as the engine-specific ratio. Alternatively, in some embodiments, step  308  is performed prior to performing steps  302 ,  304 , and/or  306 . For example, the engine-specific ratio is determined at step  308 , and if the engine-specific ratio sufficiently corresponds to an associated reference value, then steps  302 ,  304 , and  306  are omitted. In this fashion, the engine-specific ratio determined at step  308  serves as a primary check on the operation of the engine, and subsequent checks are only performed in the event that the engine-specific ratio sufficiently differs from a predetermined reference value. 
     At step  310 , the position and/or orientation of one or more of the VGMs  51 ,  52  of the engine  10  is adjusted, based on the ratio discrepancy determined at step  306 , and based on the engine-specific ratio determined at step  308 . In some embodiments, adjusting the position and/or orientation of the VGMs  51 ,  52  involves outputting a control signal to a VGM controller or to actuators associated with the VGMs  51 ,  52 . For instance, the VGMs  51 ,  52  can be controlled by a servo-valve or similar actuator, which can be configured for adjusting the position of the VGMs  51 ,  52  via an analog input from, for example, the controller  210 . In other instances, the controller  210  can output a digital signal to the aforementioned VGM controller. The control signal may be transmitted using any suitable communication medium. 
     In some embodiments, the adjustments to the position and/or orientation of one or more of the VGMs  51 ,  52  can be performed to minimize or eliminate the ratio discrepancies. In some other embodiments, the adjustments to the position and/or orientation of one or more of the VGMs  51 ,  52  can be performed to ensure that the spool- and engine-specific ratios are within a range specified by the references. Other embodiments are also considered. It should be noted that in some cases, the method  300  is performed substantially continuously and in real-time to ensure minimization of the ratio discrepancies, or to ensure that the spool- and engine-specific ratios are substantially constantly within the range specified by the references. Other approaches are also considered. 
     In some embodiments, the engine-specific ratio is compared to an associated reference to determine a ratio discrepancy for the engine  10 . The adjustments to the position and/or orientation of one or more of the VGMs  51 ,  52  can be performed to ensure that one or more, or each, of the spools  20 ,  40 , and that the engine  10 , substantially correspond to their associated references. For example, the references can specify a pressure ratio of “2” for the LP spool  20 , a pressure ratio of “3” for the HP spool, and a pressure ratio of “6” for the engine  10 . The controller  210  can substantially continually adjust the position and/or orientation of the VGMs  51 ,  52  to ensure that the pressure ratios specified by the references are produced within the spools  20 ,  40  and the engine  10 . It should be noted that the values provided in the above example are provided only for the purpose of illustration. 
     With reference to  FIG. 4 , the method  300  may be implemented by a computing device  410 , which can embody part or all of the controller  210 . The computing device  410  comprises a processing unit  412  and a memory  414  which has stored therein computer-executable instructions  416 . The processing unit  412  may comprise any suitable devices configured to implement the method  300  such that instructions  416 , when executed by the computing device  410  or other programmable apparatus, may cause the functions/acts/steps performed as part of the method  300  as described herein to be executed. The processing unit  412  may comprise, for example, any type of general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, a central processing unit (CPU), an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, other suitably programmed or programmable logic circuits, or any combination thereof. 
     The memory  414  may comprise any suitable known or other machine-readable storage medium. The memory  414  may comprise non-transitory computer readable storage medium, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. The memory  414  may include a suitable combination of any type of computer memory that is located either internally or externally to device, for example random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM) or the like. Memory  414  may comprise any storage means (e.g., devices) suitable for retrievably storing machine-readable instructions  416  executable by processing unit  412 . 
     It should be noted that the computing device  410  may be implemented as part of a FADEC or other similar device, including electronic engine control (EEC), engine control unit (EUC), engine electronic control system (SECS), and the like. In addition, it should be noted that the techniques described herein can be performed by a controller of the engine  10  substantially in real-time. 
     The methods and systems described herein may be implemented in a high level procedural or object oriented programming or scripting language, or a combination thereof, to communicate with or assist in the operation of a computer system, for example the computing device  410 . Alternatively, the methods and systems described herein may be implemented in assembly or machine language. The language may be a compiled or interpreted language. Program code for implementing the methods and systems described herein may be stored on a storage media or a device, for example a ROM, a magnetic disk, an optical disc, a flash drive, or any other suitable storage media or device. The program code may be readable by a general or special-purpose programmable computer for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. Embodiments of the methods and systems described herein may also be considered to be implemented by way of a non-transitory computer-readable storage medium having a computer program stored thereon. The computer program may comprise computer-readable instructions which cause a computer, or more specifically the processing unit  412  of the computing device  410 , to operate in a specific and predefined manner to perform the functions described herein, for example those described in the method  300 . 
     Computer-executable instructions may be in many forms, including program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments. 
     The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure. 
     The embodiments described in this document provide non-limiting examples of possible implementations of the present technology. Upon review of the present disclosure, a person of ordinary skill in the art will recognize that changes may be made to the embodiments described herein without departing from the scope of the present technology. Yet further modifications could be implemented by a person of ordinary skill in the art in view of the present disclosure, which modifications would be within the scope of the present technology.