Patent Publication Number: US-2023143026-A1

Title: Method of controlling the geometrical configuration of a variable geometry element in a gas turbine engine compressor stage

Description:
TECHNICAL FIELD 
     The application relates generally to variable geometry elements in aircraft gas turbine engine compressors and, more particularly, to control methods therefore. 
     BACKGROUND OF THE ART 
     One of the significant areas of focus in compressor design is optimizing compressor performance/efficiency and avoiding undesired aerodynamic behaviors such as surge or stall. In many situations, these areas of focus can come into conflict and some level of performance may need to be sacrificed in order to avoid a risk of undesired aerodynamic behavior. Limiting the amount of performance which is sacrificed in this manner can be a constant concern, and can be a particular challenge in engines having more than one compressor stage and operating across a large operating envelope since choking may occur on different compressor stages at different rotor speeds and, by limiting the mass flow along the main gas path, affect the operating conditions of all other compressor stages. 
     Variable geometry elements have been introduced in a manner to allow changing the geometry of one or more compressor stages as a function of evolving conditions. Even though the control of variable geometry elements in gas turbine engines was satisfactory to a certain degree, there remained room for improvement. Indeed, the process of associating varying values of the variable geometry element to monitored values representing operating conditions could be subject to control inaccuracy which was compensated by safety margins at the cost of a loss in performance in one or more operating condition. There remained room for increasing control accuracy. 
     SUMMARY 
     In one aspect, there is provided a method of controlling the geometrical configuration of a variable geometry element of a compressor stage of a gas turbine engine, the method comprising: determining a mass flow rate W of working fluid circulating through the compressor stage, including determining whether a difference between an expected value of normalized mass flow rate Q HPT  through a high-pressure turbine (HPT) of the gas turbine engine and an actual value of normalized mass flow rate Q curr  through the high-pressure turbine exceeds a threshold value, wherein the actual value of normalized mass flow rate Q curr  is related to a current value of mass flow rate W current , a current value of pressure P current , and a current value of temperature T current  through the high-pressure turbine based on the relationship W curr ·√{square root over (T curr )}/P curr =Q curr , wherein the difference is expected to be below the given threshold when the high-pressure turbine operates in a choked condition; contingent upon the difference exceeding the threshold value, correcting the value of W curr ; and outputting the value of W curr  as a determined value of mass flow rate W; determining a control parameter value associated to the geometrical configuration of the variable geometry element based on the determined value of mass flow rate W; and changing the geometrical configuration of the variable geometry element in accordance with the determined control parameter value. 
     In another aspect, there is provided a computer program product stored in a non-transitory computer readable memory and comprising instructions operative to, when executed by a processor, perform a method of determining a mass flow rate W of working fluid circulating through the compressor stage, including determining whether a difference between an expected value of normalized mass flow rate Q HPT  through a high-pressure turbine of the gas turbine engine and an actual value of normalized mass flow rate Q curr  through the high-pressure turbine exceeds a threshold value, wherein the actual value of normalized mass flow rate Q curr  is related to a current value of mass flow rate W curr , a current value of pressure P curr , and a current value of temperature T curr  through the high-pressure turbine based on the relationship W curr ·√{square root over (T curr )}/P curr =Q curr , where difference is expected to be below the given threshold when the high-pressure turbine operates in a choked condition; if the difference exceeds the threshold value, updating the value of W curr , and returning to the step of determining whether the difference exceeds the threshold value on the basis of the updated value of W curr ; and if the difference does not exceed the threshold value, outputting the value of W curr  as a determined value of mass flow rate W; and determining a control parameter value associated to the geometry of the variable geometry element based on the determined value of mass flow rate W. 
     In a further aspect, there is provided a gas turbine engine comprising a combustor, a high-pressure turbine and a compressor stage having a variable geometry element and an engine controller having a processor and a memory, the memory having stored thereon instructions executable by the processor to determine a mass flow rate W of working fluid circulating through the compressor stage, including determining whether a difference between an expected value of normalized mass flow rate Q HPT  through a high-pressure turbine of the gas turbine engine and an actual value of normalized mass flow rate Q curr  through the high-pressure turbine exceeds a threshold value, wherein the actual value of normalized mass flow rate Q curr  is related to a current value of mass flow rate W curr , a current value of pressure P curr , and a current value of temperature T curr  through the high-pressure turbine based on the relationship W curr ·√{square root over (T curr )}/P curr =Q curr , where the difference is expected to be below the given threshold when the high-pressure turbine operates in a choked condition; if the difference exceeds the threshold value, updating the value of W curr , and returning to the step of determining whether the difference exceeds the threshold value on the basis of the updated value of W curr ; and if the difference does not exceed the threshold value, outputting the value of W curr  as a determined value of mass flow rate W; determine a control parameter value associated to the geometry of the variable geometry element based on the determined value of mass flow rate W; and generate control instructions configured to change the geometry of the variable geometry element in accordance with the determined control parameter value. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       Reference is now made to the accompanying figures in which: 
         FIG.  1    is a schematic cross-sectional view of a gas turbine engine; 
         FIG.  2    is a graphical representation of a compressor operating line defined in terms of relationships between variable parameters and aerodynamic behavior references; 
         FIG.  3    is a block diagram representing functionalities of a variable geometry element controller in accordance with an embodiment; 
         FIG.  4    is a flow chart representing a process of determining a mass flow rate; 
         FIG.  5    is a block diagram representing functionalities of a synthetic value determination module in accordance with an embodiment; 
         FIG.  6 A  is a flow chart representing a control method in accordance with an absolute value control scheme, with  6 B being a graphical representation thereof; 
         FIG.  7 A  is a flow chart representing a control method in accordance with a relative value control scheme, with  FIG.  7 B  being a graphical representation thereof; 
         FIG.  8    is a schematic cross-sectional view of a gas turbine engine showing a plurality of measurement points in accordance with an embodiment; 
         FIG.  9    is a graphical representation of logic to control a low spool compressor variable guide vane geometry on a constant operating line, in accordance with an embodiment; 
         FIG.  10    is a graphical representation of logic to control a high spool compressor variable guide vane geometry on a constant operating line, in accordance with an embodiment; 
         FIG.  11    is an algorithm to compute compressor inlet massflow in accordance with an embodiment; 
         FIG.  12    is an algorithm to compute inter-compressor pressure and temperature, in accordance with an embodiment; 
         FIG.  13    is a block diagram of a computer, in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIG.  1    illustrates an example of a turbine engine. In this example, the turbine engine  10  is a turboprop engine generally comprising in serial flow communication along a main gas path  13 , a compressor section  12  for pressurizing the air, a combustor section  14  in which the compressed air is mixed with fuel and ignited for generating an annular stream of hot combustion gases around the engine axis  11 , and a turbine section  16  for extracting energy from the combustion gases. The turbine engine  10  terminates in an exhaust section. 
     In the embodiment shown in  FIG.  1   , the turboprop engine  10  has multiple compressor and turbine stages, including a high pressure stage associated to a high pressure shaft  20 , and a low pressure stage associated to a low pressure shaft  22 . The low pressure shaft  22  is used as a power source during use. 
     In this specific embodiment, the low pressure stage has a single, axial, compressor stage  24 , whereas the high pressure stage has a sequence of an axial compressor stage  26  followed by a centrifugal compressor stage  28 . Different engines use different numbers and configurations of compressor stages, and the exact configuration can be selected as a function of their intended end use at the design stage. For convenience herein, the expression high pressure turbine stage will be used to refer to the turbine stage which is closest to the combustor along the main gas path, even if an alternate embodiment has a single turbine stage. 
     Each axial compressor stage has a rotor followed by a stator (not shown) as known in the art. Moreover, in this embodiment, each axial compressor stage further has a corresponding set of variable guide vanes  30 ,  32  upstream of the rotor. The variable guide vanes, like stator vanes, includes a set of airfoil shaped vanes which have a length extending across a corresponding portion of the annular gas path. In a compressor stage which is perfectly axially oriented (relative the engine axis  11 ), the length of the variable guide vanes can extend radially, but in practice, the actual orientation can depend on the orientation of the gas path. If the gas path extends or slopes obliquely, the vanes can extend obliquely as well for instance, as in many cases, the optimal orientation of the vanes will be at least roughly transversal to the orientation of the gas path. The vanes of a set of variable guide vanes are circumferentially interspaced from one another around the engine axis  11 . However, unlike the stator vanes, the variable guide vanes  30 ,  32  are configured in a manner to have a variable angle of attack, and to this end are configured to rotate individually and collectively around their individual axes, in a manner to control the swirl angle of the air entering the corresponding rotor. Indeed, compressor functionality can be significantly sensitive to the swirl angle at which the rotor blades receive the incoming air. In alternate embodiments, only one compressor stage may have variable guide vanes, or variable guide vanes may be entirely omitted. 
     In this embodiment, one axial compressor stage  26  has a bleed valve  34 . The bleed valve  34  can be mounted to the outer wall of the gas path, and can be opened at varying degrees of opening between 0% (fully closed) and 100% (fully open), to allow a corresponding flow rate of air to escape the compressor stage in a manner to control pressure therein as a function of varying operating conditions. In alternate embodiments, the bleed valve can be switchable strictly between fully closed and fully open, as opposed to partially openable, though such a scenario may be less common. In alternate embodiments, more than one compressor stage may have a bleed valve, and in still other embodiments, bleed valves may be omitted from the entire engine. 
     Variable guide vanes  32 ,  30  and bleed valves  34  are two examples of variable geometry elements which can be introduced in one or more compressor stages  24 ,  26 ,  28  with an aim of changing the configuration of the compressor stage to adapt to changing operating conditions in a manner to promote greater efficiency while respecting any required safety margin from points of operation representing potentially undesired aerodynamic behaviors. Other embodiments may have other variable geometry elements than variable guide vanes and bleed valves, and in embodiments where more than one variable geometry element is used, different combinations of variable geometry element types can be used depending on the intended use of the engine. 
     Compressor Stage Design 
     In an example process of optimizing compressor stage design, data can be collected by computer assisted simulation, uninstalled engine testing, and/or in-flight aircraft testing to provide a representation of operating conditions which may be expected during operation of the gas turbine engine, and compressor parameters can be determined in a manner to achieve operability and efficiency across the operating envelope. It will be understood that the data used as a basis of compressor stage design only imperfectly matches the actual operating conditions across the operating envelope, and may not account for factors such as variations of engine configuration stemming from variability in production processes or wear which may occur over time for instance, and therefore, a safety margin can be included in the designed parameters to accommodate for any eventual discrepancy between actual operating conditions and expected operating conditions. Such as safety margin typically represents a sacrifice in terms of efficiency and an undesired necessity which should be minimized while respecting other requirements. 
     In modern engines, variable geometry elements can be introduced to reduce the extent of the performance sacrifice made in at least some areas of the operating envelope. Variable geometry elements can include bleed valves, which are used to evacuate compressed air, and thus pressure, from a given compressor stage, and variable guide vanes, which are used to control the swirl angle of the air immediately upstream of the compressor rotor as a function of the operating conditions, in a manner to continuously optimize the compressor stage efficiency, to name two typical examples. 
     In the control of variable geometry elements, the concept of operating line has been introduced and represents a selection of points of operation of a given compressor stage as a function of various parameters representing the varying conditions of operation across the operating envelope. An example operating line  40  represented in terms of a relationship between operating parameters of a gas turbine engine is presented in  FIG.  2   . The points of operation corresponding to the operating line  40  can represent, in each corresponding condition of operation, the highest achievable compressor efficiency while respecting any required safety margin  44  with a point of potential undesired aerodynamic behavior. The limit beyond which potential undesired aerodynamic behavior can include a surge line  42  also defined in terms of a relationship between operating parameters of the gas turbine engine. The safety margin  44  can correspond to the difference between the operating line  40  and the surge line  42 . One or more variable geometry element  46  can be controlled, in real time, such as during flight, in a manner to maintain the operation of the compressor stage as close as possible to the operating line  40 . 
     Referring now to  FIG.  3   , it will be noted that in practice, the control of variable geometry elements  46  can be performed using relatively complex sets of computer readable instructions including control data  48 , and which can include “schedules”, which can be used as a basis for defining relationships between various values of operating parameters. For instance, the control data can be used to match values of control parameters associated to different possible geometries of the variable geometry element(s) with different sets of monitored parameters, the latter being acquired in real time during operation of the engine using sensors, reference data, instructions, and calculation. Accordingly, a controller  50  of the variable geometry element(s)  46 , which can be integrated as functionalities of the engine controller or embodied separately therefrom, can continuously determine actualized control parameter values  52  corresponding to continuously changing monitored parameter values  54 , and continuously adjust the configuration of the variable geometry elements  46  to match the actualized control parameter values  52 . 
     In practice however, not only may the operating line  40  have been designed based on good, though imperfect data, but the sensors  36  which are integrated to the engine may only provide an imperfect representation of the actual operating conditions which the operating line  40  was designed to fit into, which can impose limitations in terms of which operating parameters can form the basis of the relationship defined by the operating line. Indeed, in many cases, the context of an aircraft engine imposed limits on the possibility of sensing some parameters, either by limiting the degree of accuracy achievable in the measurement of a given monitored parameter or by the measurement of a given monitored parameter simply not being available in a feasible manner. Accordingly, the operating line definition can inherently have inaccuracies stemming from the limitations in the data used to determine it. Moreover, the operating line definition can further have inaccuracies stemming from the constraints associated to the imperfect representation of actual operating conditions due to sensor limitations. This second layer of inaccuracy introduced by the sensor limitations is associated to a second layer of safety margin requirement, which stacks onto to a layer of safety margin requirements associated with limitations in the data available when designing the operating line  40 . 
     Variable Geometry Element Controller 
     The variable geometry elements  46  of the engine  10  can be controlled by a variable geometry element controller  50 , an example of which is presented in  FIG.  3   . In many embodiments, it can be considered practical for the variable geometry element controller  50  to be provided in the form of a corresponding one of several modules/functionalities integrated within a centralized engine controller (a specialized form of computer dedicated to engine control) for instance, whereas in other embodiments, it can be preferred to embody the variable geometry element controller  50  as a standalone computer. 
     In practice, the limited representation of the current operating conditions can be acquired via one or more sensors  36  and made available to the variable geometry element controller  50 . The sensors  36  can produce corresponding signals which can be associated to values of measured parameters, a process which may be based on prior calibration in some or all cases. In some cases the measured parameter values  56  can be used directly as monitored parameter values  54  by a scheduling module  58  of the variable geometry element controller  50 , whereas in other they can be used to produce synthetic parameters which, in turn, can be used as monitored parameter values  54  by the scheduling module  58 . Either one or both measured parameters  56  and synthetic parameters can form a set of monitored parameters  54  which are used by the scheduling module  58  to acquire information about current operating conditions (current values of monitored parameters). Such sensors  36  can include pressure, temperature and torque sensors for instance. 
     Reasons why information about current operating conditions may be limited include that there are some areas in the engine where it may not be considered feasible to integrate a sensor, and that there are some operating condition parameters for which no sensor may be available in actual conditions of intended use of a gas turbine engine  10 . For instance, while such information can be relevant, it may not be feasible to integrate a pressure sensor or a temperature sensor directly within the combustion chamber  14  due to the high temperatures which can be expected there during operation of the engine  10 , and in some cases, it may even not be feasible to integrate a sensor immediately downstream of the combustion chamber  14  or subsequently to the first turbine stage(s) for similar reasons. Moreover, there may be no feasible way of directly measuring mass flow W through the main gas path of an aircraft engine outside of controlled testing conditions, such as during flight. 
     Accordingly, an aim of the variable geometry element controller  50  can be to control the geometrical configuration of the variable geometry element(s)  46  as optimally as possible given i) a discrepancy which can exist between the theoretical optimal operating line  40  which was defined based on the limited data available during engine design and the actual optimal operating line  40  which can be affected by manufacturing tolerances, wear, etc, and ii) the sensor limitations which can exist and which may limit the amount of information about operating conditions made available to the variable geometry element controller  50  during operation of a gas turbine engine  10 , especially during flight. 
     It will be noted that several variations are possible in other embodiments, and that other types of aircraft engines than turboprop engines can have comparable features to those presented above and may thus benefit from the concepts presented below, such as turboshaft engines, turbofan engines, auxiliary power units (APUs), and industrial gas turbine applications. 
     In turbofan engines, for instance, a fan serves to both pre-compress air within a main gaspath and drive propulsion air in a bypass path surrounding the main gaspath, but one or more compressor stages in the main gaspath may have one or more variable geometry element controlled by a variable geometry element controller. 
     Optimization of Variable Geometry Element Control 
       FIG.  3    presents an example variable geometry element controller  50 . During operation, in accordance with computer readable instructions  60 , the variable geometry element controller  50  can obtain values  56  of one or more measured parameters via sensors  36 . As evoked above, such values  56  of measured parameters can be used directly as values of monitored parameters  54 , or indirectly, as an element used in determining a value of a synthetic parameter, the latter of which can then be used as a monitored parameter  54 . The group of functions associated with determining values of synthetic parameters will be referred to herein as a synthetic value determination module  62  for the sake of simplicity and ease of reference, which can form part of the functions constituting the variable geometry element controller  50 . The sensors  36  can include more than one type of sensor (e.g. pressure, temperature, torque), and can be associated to different points along the main gas path and/or to different components of the gas turbine engine (e.g. a torque sensor can be integrated to an engine shaft). 
     The process or processes of associating values of monitored parameters  54 , whether directly measured or synthetic, with values of control parameters  52  of the variable geometry element(s)  46 , whether absolute or relative, can be considered to form part of a scheduling module  58  of the variable geometry element controller  50  for ease of later reference, and to be based on control data  48  and on monitored parameter values  54 , which can be accessible to the scheduling module  58 . The scheduling module  58  can produce control parameter values  52  as an output based on the computer readable instructions  60 . The process or processes of controlling the geometrical configuration of the variable geometry element(s)  46  in accordance with the “scheduled” control parameter values  52  can be considered as forming part of a variable geometry control module  64  of the variable geometry element controller  50  for ease of later reference. The variable geometry control module  64  can include tracking subroutines responsible for monitoring, via sensors integrated to one or more variable geometry element, the current geometrical configuration of the variable geometry element  46  and to confirm whether or not the variable geometry element  46  has indeed responded correctly to the control instructions  66 . 
     As reflected in the example presented in  FIG.  3   , the control of the variable geometry elements  46  can involve the use of control data  48  which may be based on operating lines. The control data  48  can form a basis for matching information acquired about actual operating conditions (values of monitored parameters  54 ) with corresponding values control parameters  52  associated to corresponding geometrical configurations of the variable geometry element(s). This process of matching can be referred to as scheduling. The control data  48  can be designed in a manner to achieve the best compressor stage efficiency possible in a variety of operating conditions, while respecting safety margins with undesired aerodynamic behaviors such as surge or stall. The control data  48  can be provided by a team of compressor stage designers for instance. As expressed above, the accuracy at which the control data  48  can actually reach the aim can be limited both i) based on the completeness of the data made available to the team of designers, and ii) based on the information acquirable about actual operating conditions during operation of the engine. Both these latter sources of inaccuracy are associated to corresponding layers of safety margins which can be sought to be minimized. Accordingly, one may wish to have as much information as possible about the expected behaviour of the compressor stage in different operating conditions and for different control parameter values, which can be achieved to the extent feasible by testing and simulation, and to have as much information as possible about actual operating conditions in flight, which can be achieved to the extent feasible by the use of sensors  36 , in order to allow correlating the sensed operating conditions with the expected behaviour as closely as possible, and thereby minimize safety margins and increase engine performance. 
     The process of producing control data  48  which forms the basis for matching monitored parameter values  54  with control parameter values  52  can involve defining optimal operating points as a function of a number of different parameters, within limits beyond which undesired aerodynamic behavior is considered likely, given layers of safety margin, and can thus be relatively complex. Tools are made available to assist designers in this task. One way to represent the aerodynamic behavior or a compressor stage is to determine a function representing design conditions along which a main parameter should vary relative to a pressure ratio across the compressor. An example of this is represented in  FIG.  2    where the main parameter is corrected mass flow  41 , and the details of the function can further vary based on real time values of one or more secondary parameters  90  (e.g. altitude, ambient temperature, accessory load, current value of control parameter of one or more variable geometry element). The more closely the main parameter correlates to actual engine performance and conditions of operations, the more accuracy may be reached, and the lower the required safety margin. 
     Corrected mass flow can be known to represent a potentially highly accurate source of correlation. By “corrected mass flow” what is implied is that the value of mass flow is corrected to factor in effects of pressure and temperature, e.g W*√{square root over (θin)}/δin. Corrected mass flow will be referred to herein simply as “mass flow” for simplicity and by convention. Representing the aerodynamic behavior in this way can be convenient since a surge line  42 , defined as a value of pressure ratio which varies as a function of mass flow, can be visualized in this manner, and defined within a relatively high degree of accuracy. The surge line  42  can represent a limit operating point beyond which surge can be considered likely to occur. Accordingly, during design, the surge line  42  can be a convenient virtual reference relative to which a operating line  40  (series of operating points varying as a function of one or more monitored parameters) can be defined. The operating line  40  can then be defined in a manner to be spaced apart from the surge line  42  by the safety margin  44 . 
     Given this level of correlation between the monitored parameter of mass flow and such aerodynamic behavior design references, the unavailability of a mass flow measurement during typical operation conditions of an aircraft engine can be inconvenient from the point of view of variable geometry element control. 
     One approach to address this inconvenience is to use an alternative monitored parameter than mass flow rate as a main monitored parameter for the purpose of variable geometry element control. Alternative monitored parameters can include compressor rotor angular speed (e.g. RPM) and compressor stage power, either of which may be conveniently measurable in flight. However, such alternative monitored parameters may correlate less well to the actual aerodynamic behavior references than mass flow rate, leading to an associated layer of potential imprecision, and, in turn, to an additional, undesired, layer of safety margin. 
     Another approach to address this inconvenience is to use a synthetic value of mass flow rate W which can be acquired, even during flight, on the basis of measured values of other monitored parameters. Such another approach may allow achieving better precision than the use of an alternative monitored parameter than mass flow rate and thus allow to reduce safety margins and increase engine efficiency in at least some portions of the operating envelope, in some embodiments. 
     Synthesized Parameter Values 
     Referring back to  FIG.  3   , in some cases, a measured value  56  can be used directly as a monitored value  54 , whereas in other cases, one or more value of a measured parameter  56  can be used as the basis of determining a value of a synthetic parameter which is then used as a monitored value  54 . A given measured value  56  can also be used both directly and as the basis of determining a synthetic value. The process or processes of forming one or more synthetic value based on one or more measured value can be considered to form part of a synthetic value determination module  62  of the variable geometry element controller  50  for ease of reference. 
     In some cases, a monitored parameter value  54  can be synthesized from one or more other measured parameter values  56 , and potentially using one or more other synthesized parameter value, by calculation, i.e. using one or more equation as well as in some cases information about the engine which will collectively be referred to herein as characteristics data  68  for simplicity of reference. Characteristics data  68  can be provided by the designer for instance, and can be based on computer assisted simulation, test results, etc. 
     A somewhat simple example of a synthesized parameter value can be a synthesized pressure measurement value. Indeed, in a gas turbine engine, if pressure is measured at one point, together with other key measurements, relatively simple equations can lead to pressure at another point of the engine. For example, it can be feasible to either directly measure pressure before or after a compressor stage in an aircraft engine, and to determine the pressure of the other, provided other key measurements are also available. Using such principles, it can be relatively straightforward to synthesize pressure inside the combustion chamber using a measurement of pressure acquired immediately upstream of the combustion chamber and factoring in known pressure losses such as those which can be known to occur across the combustion chamber liner, for instance. Acquiring a synthesized value of mass flow rate in an embodiment can represent a significant level of complexity and can require using an algorithm. 
     Synthesized Mass Flow Rate 
     It can be somewhat more elaborated to synthesize mass flow rate within a satisfactory degree of precision. However, due to the principle of mass conservation, if mass flow rate is precisely known at one point along the main gas path, it can be determined precisely at any other point along the main gas path. Accordingly, if mass flow rate can be determined anywhere along the main gas path, it can be determined for the compressor stage in question. Moreover, a normalized flow rate Q HPT  in the high-pressure turbine (HPT), of which Q HPT =W HPT ·√{square root over (T HPT )}/P HPT =Q curr , where W HPT , T HPT  and P HPT  are mass flow rate across the high-pressure turbine, temperature and pressure upstream of the high-pressure turbine, respectively, can be a suitably good working approximation in some embodiments. Q HPT  can be known to be constant, or can otherwise be determinable within a relatively high degree of accuracy, across a wide range of operating conditions. For instance, in many alternate gas turbine engine embodiments, the inlet side of the high-pressure turbine receives the largest mass flow rate (air+fuel) for its surface area, and when it is choked, which can be true in many portions of the operating envelope it can be responsible for setting the mass flow rate through the main gas path. The value of Q HPT , as long as the main gas path is choked, can thus be known from computer assisted simulation and/or engine testing, and can be provided by the design team. With this in mind, a synthesized value of mass flow rate W across a given compressor stage can be acquired and used as a monitored parameter for controlling one or more variable geometry element associated to one or more compressor stage. 
     To acquire such a synthesized value of mass flow rate W, other synthesized values may need to be acquired. In particular, T HPT  may not be measurable. However, temperature at one or more points upstream or downstream of the high-pressure turbine may be measurable, and the amount of power extracted from any intervening turbine stage, or otherwise said the rate of energy extracted from the fluid in between may also be known. For instance, a torque sensor and an angular rotation speed sensor may be used on a spool and power can be determined from the values of torque and angular rotation speed acquired from these sensors. On such basis, for instance, the only missing value to allow synthesizing an estimated value of T HPT  may be mass flow rate. P HPT , however, may be calculated from pressure measured immediately upstream of the combustor and known pressure drop between the point of pressure measurement and the combustor. The only remaining variable being mass flow rate, W. 
     While W HPT  cannot be practically measured directly on gas turbine engine installed on an aircraft in service during typical conditions of operation, a process can be used to acquire a synthesized value for it. In one embodiment, this process can simultaneously lead to a synthesized value of T HPT . 
     An example embodiment of this latter process is represented in the flow chart presented in  FIG.  4   . The process can change a value of W, referred to instantaneously in the context of the process as W curr . For simplicity and clarity, the variable representing W and on which the process operates will be referred to as W curr , and will be understood to change over time through an iterative process. The process begins  400  with an initial value of W curr  and T curr , which can be referred to as guess values. In the embodiment illustrated, the initial values of T curr  and W curr  are rough estimates based on current conditions as sensed by the available sensors and on the known geometry of the engine/engine behavior, but other embodiments can use alternate ways of generating the initial value of T curr  and W curr , such as a value known to have previously been determined in similar conditions on the same engine and stored in a computer readable memory for later reference to name one example. 
     As presented above, the value of T HPT  is typically not measurable directly and thus needs to be synthesized as well. One way of synthesizing  402  it is based on the temperature sensed downstream and measured power generated by engine components, amongst various parameters. However, the variable of mass flow rate W, which is a priori unknown, also comes into play in this latter determination. The latter deadlock can be broken by using the current value of mass flow rate, W curr , in the synthesis  102  of T, and as the value of T will vary with the value of W curr , it can be referred to as T curr , until the process has converged. The value of P HPT  can be synthesized on the basis of the pressure measured immediately upstream of the combustor, and from known pressure losses which can be determined based on simulation or testing for instance. Since the value of P HPT  is likely to change over time, it can also be referred to as P curr  in the context of the algorithm, whether it is actualized over subsequent algorithm steps or not. At that point, a current value of normalized mass flow rate Q curr  can be synthesized  404  using W curr , T curr , and P curr , ng the relationship W curr ·√{square root over (T curr )}/P curr =Q curr , for instance. 
     Before going further, it will be noted that the specific relationship Q HPT =W HPT ·√{square root over (T HPT )}/P HPT , is but one example of how Q can be defined, and can represent the relationship with the most significant variables. In other embodiments, it may be preferred to use more elaborated relationships, which can cater for other effects at play such as variations of gas properties with temperature and tip clearance effects. In one example, the relationship 
     
       
         
           
             
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                     ) 
                   
                 
               
             
           
         
       
     
     can be used, for instance, where y can be a function of temperature. Such relationships, even if implementing additional corrections, will be considered as being based on the relationship Q HPT =W HPT ·√{square root over (T HPT )}/P HPT  in the context of this specification. 
     As evoked above, in conditions where the high-pressure turbine is choked, Q HPT  can be accurately predicted independently of variations W HPT , T HPT , and P HPT , and acquirable for a given engine within a relatively high degree of precision based on simulation or testing, and storable within computer readable memory. Given potential expectable inaccuracy in determining the initial value of W curr , after the first sequence, the determined value of Q curr  can be expected to be different from Q HPT . This difference provides an indication that W curr  is not a correct value of W. The difference between Q curr  and Q HPT  can be established  408  directly by comparing Q curr  and Q HPT , or indirectly, such by calculating a value of W HPT  based on the relationship W HPT ·√{square root over (T curr )}/P curr =Q HPT , and comparing the value of W HPT  with the value of W curr . The latter method can lead to determining  406  that the difference between Q curr  and Q HPT  is below a threshold value as well. However, the first method may be preferred for simplicity. If the determined difference between Q HPT  and Q curr  is low, such as if it is below the expected accuracy in the determination of Q HPT  or any other threshold value considered suitable for the intended purpose, W curr  can be considered to correspond to W HPT , and W curr  can be outputted  412  as such, however, this is likely to not be the case after the first sequence. 
     In one embodiment, the difference between Q curr  and Q HPT  is determined  408  and characterized in terms of amplitude and sign (positive or negative). Interestingly, not only does the fact that the difference between Q HPT  and Q curr  exceed the threshold value represent an indication that W curr  does not correspond to the actual value of W HPT  (and simultaneously that T curr  does not correspond to the actual value of T HPT ), but the ratio between Q HPT  and Q curr  can be an indication of the ratio between W curr  and W HPT  Accordingly, the ratio between Q HPT  and Q curr  can be used in imparting a correction  410  to the value of W curr  to produce a new value of W curr  likely to be closer to the actual value of W HPT . In one embodiment, correcting  410  W curr  can be based directly on the ratio between Q HPT  and Q curr , such as by changing W curr  directly and proportionally to the ratio between Q HPT  and Q curr , whereas in another embodiment, correcting  410  W curr  can be based indirectly on the ratio between Q HPT  and Q curr , such as by factoring in a proportionality value and/or one or more additional variables in accordance with one or more equations as per calibration, simulation or testing for instance. The way in which W curr  is modified based on the ratio between Q HPT  and Q curr  can be based on simulation or testing, for instance. Depending on how W curr  is corrected, in some embodiments, the corrected value of W curr  may be useable as is, and considered a satisfactory approximation of W HPT , and may thus be outputted  412  as such. In other embodiments, the corrected value of W curr  may not be considered to be a satisfactory approximation of W HPT  at this time, or may not be considered to be a satisfactory approximation with a sufficiently high degree of certitude, and greater precision may be sought. 
     In the latter case, the corrected value of W curr  can be used to synthesize  402  a corrected value of T curr , and both these values can then be used to synthesize  404  a new value of Q curr  In other words, another iteration of the first sequence of steps can be performed, and the algorithm can be said to “return” to the step of determining  406  whether a difference between Q curr  and Q HPT  exists/exceeds the threshold value. At this point, determining that the difference is below the threshold value may lead to outputting  412  W curr  as a monitored parameter value of W directly. Alternately, such as if the difference is determined to be greater than the threshold value, a further correction can be made  410  to W curr , which can be based on the amplitude and sign of the difference, after which W curr  can be outputted  412  as a value of W, or the algorithm can return to the step of synthesizing  402 ,  404  a new Q curr  and thereby perform another iteration. In some embodiments, many iterations will be necessary for the difference between Q curr  and Q HPT  to be below the threshold value, and these iterations can be performed quickly enough for the resulting value of W curr  to be satisfactorily useable  414  as a monitored parameter value by the scheduling module to determine control parameter values used in the control of the geometrical configuration of one or more variable geometry element(s). In practice, the mass flow rate along gas path remains constant based on conservation of mass, and the acquired value of W HPT  can be used to determine the mass flow rate through a compressor stage, and thereby be used as a monitored parameter to control a variable geometry element of that compressor stage. 
     At least in some embodiments, using control data  48  in which one or more values of mass flow rate W synthesized as presented above are used to establish a correlation with desired control parameter values  52  of geometrical configurations of the variable geometry elements can allow a higher degree of correlation, and thus of precision, than using instead a value of a directly measurable parameter such as compressor rotation speed, or even another synthesizable value such as compressor power, to establish the basis of the correlation, thereby allowing a gain in terms of reducing safety margin. 
     In some embodiments, the synthesized value of W HPT  will be used 414 as a monitored parameter value to control the geometrical configuration of the variable geometry elements only when the high-pressure turbine has first been determined  416  to be in a choked condition, and alternately, if the high-pressure turbine is not in a choked condition, the value of a monitored parameter other than W HPT  will be used 418 instead, such as rotor angular speed for instance. 
       FIG.  5    presents an example synthetic value determination module  62  which can include functions associated with determining a synthetic value of W HPT  in accordance with an embodiment. The synthetic value determination module  62  can include a high-pressure turbine temperature estimator  70  used to acquire a synthetic value of high-pressure turbine temperature T curr , a high-pressure turbine mass flow rate estimator  72  used to determine a synthetic value W curr , a high-pressure turbine pressure determiner  74  used to determine a synthetic value of high-pressure turbine pressure P curr , a normalized mass flow rate calculator  76  used to determine a result value of normalized mass flow rate mass flow rate Q result , and a normalized mass flow rate comparator  78  which can be used to determine a ratio between the result value Q curr  and the design value Q HPT  of normalized mass flow rate. The synthetic value determination module  62  can further include a function to perform an iterative process based on varying potential values of W curr  until a match is found between the resulting normalized value Q curr , and the corresponding design value Q HPT , at which point the latest value of mass flow rate W curr  can be considered to be correct and outputted in the form of a synthetic mass flow rate value for use as an input in the scheduling module  58 . 
     The high pressure turbine is the turbine closest to the combustor, in the main gaspath. In an engine having a single turbine stage, the single turbine stage is considered the high pressure turbine from the point of view of this specification. 
     Control Methods 
     It will be noted that different processes can be performed by a variable geometry element controller  50  to control the control parameters of the variable geometry element(s)  46  based on the monitored parameter values  54 . Generally, some of such processes can be classified into two different approach types: absolute value control and relative value control.  FIG.  6    presents an example of an absolute value control scheme whereas  FIG.  7    presents an example of a relative value control scheme. These examples will now be detailed for the purpose of exploring different avenues. 
     Referring to  FIGS.  6 A and  6 B , the absolute value control scheme can be based on establishing  420  a match between a specific value of one or more monitored parameter  54 ,  90  and a specific value of one or more control parameter  52  on the basis of relationships  80  such as functions or tables (an example of which is graphically represented in  FIG.  6 B ). The relationships  80 , which are stored in computer readable memory in the form of control data  48 , can be defined by the design team, based on simulation and/or testing. For instance, based on simulation and/or testing, the design team may determine which value of one or more control parameter  52 , such as variable guide vane angle or bleed valve opening % for instance, are expected to produce an operating point corresponding to a given operating line  84  (an example of which is graphically represented in  FIG.  7 B ), for a given combination of values of monitored parameters  54 , including a main parameter (here W) and potentially several other parameters. In the absolute value control scheme, it is this value or values of the one or more control parameters  52  which are associated directly to values of other monitored parameters  54  by the control data  48 , and the variable geometry control module  64  ( FIG.  2   ) can then simply control  414  the variable geometry element(s)  56  to achieve the determined value(s) of the control parameters. 
     The absolute value control scheme is not based on the use feedback as to whether or not, in the actual engine in its current state of operation, setting the control parameters to the determined values did indeed produce the intended operating point or not. Accordingly, and with reference back to  FIG.  2   , any discrepancy between the expected (e.g. design) relationship  80  and the actual relationship will produce a difference  86  between the actual operating point  82  and the intended operating point  84 . This is not ideal, but the resulting degree of inaccuracy can satisfactorily be compensated by setting associated safety margins  44  in some embodiments. 
     Referring to  FIGS.  7 A and  7 B , the relative value control scheme can include a step of determining  422  a difference  86  between an actual operating point  82  and a desired operating point  84  on a operating line  88 . The scheme can be based on establishing  424  a match between i) a relative difference  86  between an actual operating point and a operating line and ii) a corresponding value of a difference between a current value of one or more control parameter  52  and a new value of one or more control parameter  52  expected to bring the operating point  82  closer to a operating line point (desired operating point)  84  in accordance with control data  48 . These matches can be performed on the basis of relationships  88  such as functions or tables, and the relationships  88  can further factor in additional monitored parameters  90 . The relationships  88 , which can be stored in computer readable memory in the form of control data  48  accessible to the scheduling module  58 , can be defined by the design team, based on simulation and/or testing. For instance, based on simulation and/or testing, the design team may determine which difference  92  ( FIG.  6 B ) in values of one or more control parameter  52 , such as variable blade angle α or bleed valve opening % for instance, are expected to produce which changes  86  to the operating point, in a given combination of values of monitored parameters  54 ,  90 . In the relative value control scheme, it is these differences  92  in values of the one or more control parameters  52 , by contradistinction with the absolute, target values used in the absolute value control scheme, which are associated the differences in other monitored parameters  54  associated to the operating point  82  and operating line  88  by the control data  48 , as opposed to absolute values, and the variable geometry control module  64  ( FIG.  2   ) can then simply perform  414  the determined changes in the variable geometry element(s) to bridge the gap  86  between sensed and desired monitored parameters. 
     The relative value control scheme uses feedback based on resulting operating points  82  as acquired  426  on the monitored parameters, and because of this, it has the potential to iterate and converge onto the intended operating line  88  independently of any inaccuracy which may exist between the expected relationship  80  between control parameters and monitored parameters, and the actual relationship  88  between monitored parameters  54 ,  90  and operating points  82 ,  84 . This may allow to reduce the safety margin requirements to maintain an equivalent level of safety in some embodiments. 
     On the other hand, however, the relative value control scheme provides a significant degree of authority to the variable geometry controller  50 , which may lead to behaviors other than the intended design behaviours. To this end, in some embodiments, it can be desired to limit the level of authority of the variable geometry controller  50  by imposing  428  a limit, or threshold, to the allowable extent of change in the values of the control parameters  52 . This limit can be on a per iteration basis, for example. Accordingly, if the change in the values of the control parameters  52  determined by the relative value control scheme is determined  428  to exceed a given change threshold, the control parameter values can be set (limited) to the change threshold, and the control of the variable geometry element  46  can be performed in accordance with the limited control parameter value, instead of being based on the greater change value initially determined. 
     In an embodiment, the processes of  FIG.  6    and of  FIG.  7    can be combined, with the process of  FIG.  6    being used to set initial values of the control parameters in a manner to generate an actual operating point  82  which is close to the design operating point  84 , and the process of  FIG.  7    can be used subsequently, and potentially iteratively, to determine a gap  86  between the actual operating point  82  resulting from the process of  FIG.  6    and the designed operating line  88 , and change  414  the value(s) of the control parameter(s) in a manner to close the gap  86 . 
     Detailed Example Embodiment 
     A detailed example embodiment will now be described using a context where gas turbine engine  100  has a set of sensors as indicated on  FIG.  8   . More specifically, A VIGV/VGV control scheme can be provided that targets a compressor operating line (pressure ratio vs flow) using a way of calculating the compressor flow and inter-stage pressure and temperature in service. Proposed logic to control low spool variable geometry (VIGV) on a constant operating line is presented in  FIG.  9   , whereas proposed logic to control high spool variable geometry VGV on a constant operating line is presented in  FIG.  10   . 
     1. With reference to  FIGS.  9  and  10   : 
     a) Initial VIGV/VGV values are computed at steps  101  &amp;  201 . Typical Initial Guess VIGV/VGV schedules are shown in  FIG.  6 B  in which the various schedules can be function of Parm  1 , Parm  2 , Parm  3 , etc. . . . where Parm  1  . . . N can be Altitude, Ambient Temperature, Accessory Load, Bleed, etc. . . . ; 
     b) The compressor massflow is computed at steps  102  &amp;  202  from the algorithm depicted in  FIG.  11    (described below); 
     c) At step  103 , measurements of low-spool compressor inlet pressure and temperature are obtained; 
     d) At step  203 , the Inter-Compressor Temperature (T 25 ) and Pressure (T 25 ) are calculated from the algorithm depicted in  FIG.  12   . Note: T 25  and P 25  could also come from engine sensors if available but here they are synthesized from other engine sensors; 
     e) At steps  104  &amp;  204 , a compressor inlet corrected flow is calculated as W*√(T/Tref)/(P/Pref) from the massflow, pressures and temperatures obtained from 1b to 1d above; 
     f) At steps  105  &amp;  205 , the target Pressure Ratio at the massflow calculated in  1   e  above is obtained. Typical Pressure Ratio vs Massflow schedules are shown in  FIG.  7 B  in which the various schedules can be function of Parm  1 , Parm  2 , Parm  3 , etc. . . . where Parm  1  . . . N can be Altitude, Ambient Temperature, Accessory Load, Bleed, etc. . . . ; 
     g) At step  106 , the low spool compressor pressure ratio is calculated using values from 1c and 1d above; 
     h) At step  206 , the compressor discharge pressure (P 3 ) measurement is obtained and the high spool compressor pressure ratio is calculated based on P 3  and 1d above; 
     i) At steps  107  &amp;  207 , the actual pressure ratio is compared to the target pressure ratio from 1f above; 
     j) At steps  108  &amp;  208 , a bias is applied to the Initial Guess VIGV/VGV schedules in order to achieve the target pressure ratio. Note that the bias can be directed to stay within the allowed range/authority given to the software; and 
     k) Steps  101 / 201  to  108 / 208  are repeated until convergence (i.e. PR error becomes suitably close to 0, or considered negligible, which can be achieved by comparing to a given threshold or by the sensitivity of the measurement instruments, in one example, the PR error can be considered to be zero when it is below 0.1% for instance) 
     2. With reference to  FIG.  11   , an example algorithm to compute W 1  can be as follows: 
     a) Initial Guess T 4  and W 1  from current flight condition and engine power level; 
     b) At step  301 , compute P 4  from P 3  measurement; 
     c) At step  302 , compute Q 4 _Target from High-Pressure (HP) Turbine vane characteristic. If vane is choked, Q 4  is almost constant; 
     d) From Q 4 _Target, P 4  and T 4 , compute W 4  (flow at HT vane); 
     e) At step  303 , compute W 1  (compressor inlet flow) based on W 4 ; 
     f) At step  304 , compute the low-pressure compressor load (LPC_SHP) from W 1  and engine measurements and/or synthesized parameters; 
     g) At step  305 , compute engine output shaft power (SHP) from output shaft speed (NP) and torque (TQ); 
     h) At step  306 , compute the low-pressure turbine load (LPT_Load) from engine power (SHP), low-pressure compressor load (LPC_SHP) and engine parasitic assumptions; and from EGT (T 6 ) temperature measurement and LPT_load, compute T 45 ; 
     i) At step  307 , compute the compressor exit flow (W 3 ) from compressor inlet flow (W 1 ); 
     j) At step  308 , compute the High Pressure Spool load (HPC_SHP) from W 3  and engine measurements and/or synthesized parameters; 
     k) At step  309 , Compute W 4  (flow at HT vane) from W 1 ; 
     I) At step  310 , compute the HP load from compressor load and from HPC_Load, W 4  and T 45 , compute T 4 ; 
     m) At step  311 , compute Q 4  from W 4 , T 4  and P 4 ; 
     n) At step  312 , quantify Q 4  error (Q 4  vs Q 4 _target); 
     o) At step  313 , apply correction to W 1  based on Q 4  error; and 
     p) Loop until convergence and output final W 1 . 
     3. Now with reference to  FIG.  12    an algorithm to compute the inter-compressor pressure and temperature (P 25  and T 25 ) can work as follows: 
     a) Initial Guess Qexit from current flight condition and engine power level; 
     b) At step  301 , compute low-spool inlet temperature (T 21 ) from engine inlet temperature measurement (T 1 ) and compressor charge heating/air system assumptions; 
     c) At step  302 , compute low spool normalized speed (NLM_LC) from speed sensor (NL) and T 2 ; 
     d) At step  303 , obtain normalized low-spool compressor flow (WCM), delta enthalpy (DHM) and pressure ratio (PRM) from compressor characteristics using Qexit, low-spool normalized speed (NLM_LC) and VIGV position; 
     e) At step  304 , compute low-spool inlet pressure (P 21 ) from engine inlet pressure measurement (P 1 ) and compressor inlet loss assumptions; 
     f) From low-spool compressor normalized flow (WCM), inlet temperature (T 21 ) and pressure (P 21 ), obtain low-spool compressor mechanical flow (WG_LC1M); 
     g) At step  305 , obtain low-spool compressor exit pressure (P 25 ) from inlet pressure (P 21 ), pressure ratio (PR), low-spool mechanical flow (WG_LC1M) and high-spool mechanical speed (NH); 
     h) At step  306 , obtain low-spool compressor exit temperature (T 25 ) from inlet temperature (T 21 ), delta enthalpy (DH), low-spool mechanical flow (WG_LC1M) and high-spool mechanical speed (NH); 
     i) At step  307 , obtain low-spool compressor inlet corrected flow from T 21 , P 21  (see step  301  &amp;  304 ) and W 1  (see W 1  algo in 2) above); 
     j) At step  309 , obtain guess low-spool compressor inlet corrected flow (WC_GUES) from WCM, T 21  &amp; P 21 ; 
     k) At step  309 , quantify WC error (WC vs WC_GUES) and obtain Qexit; 
     I) At step  310 , apply correction to Qexit based on WC error; 
     m) Loop until convergence and output final P 25  &amp; T 25 . 
     Using the example embodiment presented above, the compressors (low spool and high spool) can always operate on the same operating line which can make the engine less sensitive to deterioration effects. Surge margin benefits can also occur since items related to deterioration can be removed or significantly reduced in surge margin audit (SMA) requirements. It will be noted that in the embodiment presented, engine measurements in service are limited, hence why the proposed inventions includes algorithms to synthesized various parameters generally unavailable in service. However, it should be understood that if those corresponding parameters are measured, measurements could be used (and may be more accurate than using synthesized parameters, depending on sensors accuracies). 
     Referring to  FIG.  13   , it will be understood that the expression “computer”  400  as used herein is not to be interpreted in a limiting manner. It is rather used in a broad sense to generally refer to the combination of some form of one or more processing units  412  and some form of memory system  414  accessible by the processing unit(s). The memory system can be of the non-transitory type. The use of the expression “computer” in its singular form as used herein includes within its scope the combination of a two or more computers working collaboratively to perform a given function. Moreover, the expression “computer” as used herein includes within its scope the use of partial capabilities of a given processing unit. 
     A processing unit can be embodied in the form of a general-purpose micro-processor or microcontroller, a digital signal processing (DSP) processor, an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, a programmable read-only memory (PROM), an electronic engine controller EEC, a full authority digital engine controller (FADEC), to name a few examples. 
     The memory system can include a suitable combination of any suitable type of computer-readable memory located either internally, externally, and accessible by the processor in a wired or wireless manner, either directly or over a network such as the Internet. A computer-readable memory can be embodied in the form of 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) to name a few examples. 
     A computer can have one or more input/output (I/O) interface to allow communication with a human user and/or with another computer via an associated input, output, or input/output device such as a keyboard, a mouse, a touchscreen, an antenna, a port, etc. Each I/O interface can enable the computer to communicate and/or exchange data with other components, to access and connect to network resources, to serve applications, and/or perform other computing applications by connecting to a network (or multiple networks) capable of carrying data including the Internet, Ethernet, plain old telephone service (POTS) line, public switch telephone network (PSTN), integrated services digital network (ISDN), digital subscriber line (DSL), coaxial cable, fiber optics, satellite, mobile, wireless (e.g. Wi-Fi, Bluetooth, WiMAX), SS7 signaling network, fixed line, local area network, wide area network, to name a few examples. 
     It will be understood that a computer can perform functions or processes via hardware or a combination of both hardware and software. For example, hardware can include logic gates included as part of a silicon chip of a processor. Software (e.g. application, process) can be in the form of data such as computer-readable instructions stored in a non-transitory computer-readable memory accessible by one or more processing units. With respect to a computer or a processing unit, the expression “configured to” relates to the presence of hardware or a combination of hardware and software which is operable to perform the associated functions. 
     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.