A Parametric Study of Actuator Requirements for Active Turbine Tip Clearance Control of a Modern High Bypass Turbofan Engine

GT2017 - 63472

A PARAMETRIC STUDY O F ACTUATOR REQUIREME NTS FOR ACTIVE TURBI NE TIP CLEARANCE CONTRO L OF A MODERN HIGH B YPASS TURBOFAN ENGINE Jonathan L. Kratz Jeffryes W. Chapman Ten - Huei Guo NASA Glenn Research Center Vantage Partners, LLC NASA Glenn Research Center Cleveland, OH, United States Brook Park, OH, United States Cleveland, OH, United States ABSTRACT variations are the most significant and include the contributions The efficiency of aircraft gas turbine engines is sensitive to of thermal expansion and the elongation of moving components the distance between the tips of its turbine blades and its due to axisymmetric thermal and mechanical loads. Capturing shroud , which serves as its containment structure. Maintaining these components of the tip clearance variation is the focus of tighter clearance between these components has been shown to the tip clearance model used in this study.

increase turbine efficiency , increase fuel efficiency , and reduce A physical explanation of the variation of the tip clearance gap begins with any change in engine operating condition.

the turbine inlet temperature , and this correlates to a longer time - on - wing for the engine. Therefore, there is a desire to Consider an increase in power. As the rotor and blade increase maintain a tight clearance in the turbine , which requires fast in speed, the centrifugal force exerted on these components response active clearance cont rol . Fast response active tip increases causing them to expand. Additionally, as the temperature in the gas path increases the turbine components clearance control will require an actuator to modify the physical or effective tip clearance in the turbine. This paper heat up and expand. Due to differences in size, geometry, evaluates the requirements of a generic active turbine tip materials, and heat transfer rates, the components of the turbine clearance actuator for a modern commercial airc raft engine expand at different rates and reach different steady-state using the Commercial Modular Aero - Propulsion System deformations. Note that throughout this paper deformation will Simulation 40k (C - MAPSS40k) software that has previously be used to characterize an elongation or contraction of a turbine been integrated with a dynamic tip clearance model. A component. This is not to be confused with twisting or bending.

p arametric study was performed in an attempt to evaluate Deformation of the blade and rotor occurs relatively quickly requirements for control actuators in terms of bandwidth, rate due to acceleration of the high pressure spool (HPS). The blade limits, saturation limits, and deadband. Constraints on the deformation is accelerated further by its relatively fast thermal weight of the actuation system and some considerations as to expansion because of its relatively low mass and large surface the force which the actuator must be capable of exerting and area, and its direct exposure to the hot gas path. The rotor and maintaining are also investigated . From the results, the relevant the containment structure around the turbine are larger and range of the evaluated actuator parameters can be extracted. experience weaker heat transfer leading to much slower thermal Some additional discussion is provided on the challenges posed transients and therefore slower expansion. These differences in by the tip clearance control problem and the implications for magnitude and rate of expansion, particularly between the future small core aircraft engines . internal engine components and containment structure, create ‘pinch points’ where the tip clearance is significantly reduced during fast accelerations of the engine that are accompanied by IN TRODUCTION Turbine tip clearance refers to the distance between the rapid changes in the gas path temperature. These pinch points turbine blades and their containment structure. The tip lead to conservative and less efficient design decisions.

Modern commercial gas turbine e ngines employ slow clearance changes over the course of a flight due to thermal expansion, centrifugal forces of the spinning components, and acting thermal management techniques for controlling the tip the mechanical loads applied to the structures by aerodynamic clearance in the high pressure turbine (HPT) a nd low pressure forces and internal stresses. Axisymmetric tip clearance turbine (LPT) [ 1 ] . Due to the lack of tip clearance sensors capab le of withstanding the harsh conditions of the turbine for a turbofan engines [ 5 ] with a small ultra - efficient core that long duration, these control systems rely on a scheduled control demands a higher turbine inlet temperature and h ighly loaded logic [ 2 ] that requires larger than necessary tip clearance gaps turbomachinery [ 6 ]. These changes could exacerbate the tip as a result of t he uncertainty associated with the lack of clearance problem by influencing faster deformation rates for feedback . The control system typically consists of a number of the turbine structure. Furthermore , the smaller annulus height ble eds and secondary flow passages. These passages take air of the small core engines will demand a smaller tip clearance from cooler sections of the engine ’s gas path , such as the be maintained in order to achieve high efficiency due to turbine compressor and fan duct, and ci rculate it through passages efficiency being correlated with the tip clearance as a around the turbine containment structure to induce thermal percentag e of the annulus height . For these reasons , active contraction that shrinks its radius and reduces the tip clearance turbine tip clearance control (ATTCC) is of interest for future gap. The dynamics of these control systems are slow compared commercial aircraft engines. Such systems will need an to the deformation dynamics of the blade a nd rotor. These actuator to maintain the tip clearance such that the engine systems are also limited by the temperatures and mass flow achieves good efficiency w hile maintaining safety mar gins to rates of the bleeds that supply the cooling passages. For these prevent blade rubs that could shorten the life of the engine reasons a conservative tip clearance is built into the turbine to components or lead to an immediate failure in severe cases.

avoid blade rubs during fast transient maneuvers su ch as take - There are various ideas for actuating the turbine tip off and in - flight re - accelerations. This conservative design clearance ranging from well - explored actuation techniques such results in a larger tip clearance during cruise than is necessary. as hydraulic, pneumatic, and piezoelectric actuator systems to Seeing that commercial aircraft spend most of their time flying less mature technologies such as smart materials and plasma at the cruise condition there is ample room for perfo rmance actuation [ 1 , 7 , 8 , 9 , 10 ]. In any case , the actuator will need to improvements over the lifetime of the engine. Also consider be able to maintain a tip clearance that provides enough of a th at as the turbine components degrade over time, t he blade s perf ormance benefit to out - weigh its implementation penalties erode and the tip clearance gap widens leading to a lower while warranting its added complexity to the engine system.

turbine efficiency. The current conventional tip clearance T he actuator should also not be over designed such that the control app roach is not easily adapted to handling component complexity and cost to the engine outweigh the benefit of its degradation by adjusting to the increase d gap. T his not only additional capab ilities. Regardless of the type of actuator, they reduces performance but leads to faster degradation as the all share generic properties that can be evaluated on a general turbine must operate at a higher temperature to achieve the basis such as bandwidth, rate limits, saturation limits, and same thrust . deadband.

It is well es tablished that tip clearance is directly related to This paper documents a parametric study of how the turbine efficiency , which can impact fuel consumption and the variations of gener ic actuator parameters effect tip clearance. In turbine inlet temperature. Re d uction in fuel consumption has particular , the study estimates the minimum maintainable tip obvious benefits in savings on fuel as both a natural resource clearance for a given actuator and evaluates the performance and a monetary exp enditure . It has been shown that t he rate of benefit based on performance metrics such as the TSFC and degradation of turbine blades is at its maximum when turbine inlet gas path temperature a t the cruise condition. Beyond this , temperature is at a maximum [ 3 ] . For large commercial engines weight restrictions and force requirements are discussed. A it is a rule of thumb that a 10mil redu ction in tip clearance simplistic actuator model with a Proportional - Integral (PI) o equates to an increase in turbine efficien cy of ~1% and a ~ 10 C controller utilizing wind - up protection logic was used in this reduction in the turbine inlet temperature , which can mean a study. The actuator model was integr ated with a tip clearance reduced thrust specific fuel consumption ( TSFC ) and a longer model that has been added to the Commercial Modular Aero - time - on - wing for the engine [ 4 ] . Reduction in the turbine inlet Propulsion System Simulation 40k (C - MAPSS40k) engine temperature can not only extend the life of the engine model [ 11 ] . This model is representative of a modern twin compone n ts but also reduce the maintenance costs for the spool high bypass en gine in the 40,000lb thrust class.

f engine over its lifespan. To realize these benefits a fast Therefore , the results of this study are applicable to modern response actuator with a clos ed loop controller is desired [ 2 ] . turbofan engines. This study should provide a basis for T he potential benefits of active clearance control are well investigating actuator requirements for such futuristic engines.

established, the real issue is determining how actuation should This pa per is organized as follows . F irst, the tip clearance be implemented in order to benefit the engi ne ’ s performance at model utilized in this study is overviewed. Then the actuator the system level. modeling and controller design is addressed. This leads into the M odern gas turbine engines do not utilize fast response simulation portion of the paper in which the simulation scenario active tip clearance control . Reasons include the lack of robust is described and results are discussed. Finally, there are some high temperature sensors, actuator weight, sealing issues and concluding remarks .

various other challenges [ 1 ]. However, there is interest for future engine applications. The future of commercial gas turbine engines is moving toward ultra - high bypass ratio σ standard deviation NOMENCLATURE a shape coefficient Subscripts ATTCC Active Turbine Tip Clearance Control A/C aircraft with passengers and luggage BW bandwidth act actual value C - MAPSS40k Commercial Modular Aero - Propulsion System base nominal/baseline value (no active control) Simulation 40k cmd controller command C p heat capacity fb feedback value DB deadband FDM finite differen ce method fuel fuel parameter value h convective heat transfer coefficient inside property of the int erior node neighboring a surface node h coeff coefficient in convective heat transfer coefficient j spatial/node index model HPS high pressure spool reserve fuel reserve sens sensed value HPT high pressure turbine surf property of a surface node IWP integral wind - up protection w/ act property associated with having a tip clearance K p proportional control gain control actuator K Integral control gain i k thermal conductivity L generic length L b length of the blade TIP CLEARANCE MODEL OVERVIEW L 0 known length of a component at temperature T 0 The tip clearanc e model utilized in this study is a modified LPT low pressure turbine version of the model described in Ref. [ 12 ] that itself is based mass flow rate m  on the work documented in Ref. [ 2 ], [ 13 ], and [ 14 ] . For the design mass flow rate for the convective heat  m des sake of completeness , the model will be summarized at a high 0.23 0.8 tr ansfer model, h = h (T/T ) (  / ) , coeff des m m  des level with the modifications described in more detail.

when h = h coeff and T = T des .

The model considers axisymmetric v ariations in the tip number of engines used on a given aircraft n clearance. Specifically , this refers to deformations in the turbine proportional integral PI structure due to centrifugal force, and axis ymmetric proportional integral derivative PID temperature variations . A symmetric deformation s , such as those PLA power lever angle (th rottle command) due to non - uniform heating and non - uniform aerodyna mic R tip clearance reference & flight range loads, are not considered in this model. Since most of the tip r outer radius of the rotor r,out clearance deformation is attributed to axisymmetric r inner radius of the shroud s,in deformations and the important dynamics of the tip clearance RL rate limit transient have been demonstrated, this model is seen to be SL s aturation limit appropriate for t his study.

T temperature The tip clearance model requires an es timation of the T turbine inlet temperature deformation in three basic components of the engine; the T design fluid temperature for the convective heat des 0.23 0.8 shroud, rotor, and blade. The shroud is the containment transfer model, h = h coeff (T/T des ) ( m  /  ) , m des structure on the outside of the HPT flow path. It is assumed to when h = h coeff and m  =  .

m des consist of a n outer structural layer an d an inner abradable layer T temperature of the fluid in contact with the surface ∞ that acts as a thermal barrier. The r otor is the structural member node that connect s the blade to the shaft . The blade is the structural t time member that extends from the rotor into the HPT gas path that TC tip clearance extr act s work fro m the flow. The tip clearance is simply derived TSFC thrust specific fuel consumption from geometry as can be seen in Fig. 1 and is given by Eq. ( 1 ) .

V air speed W weight w f fuel flow rate

  L r r TC   

(1) b out r in s , , X actuator position x spatial variable In Eq. ( 1 ) TC is the tip clearance, r is the radius of the inner s ,in ZOH zero - order hold surface of the shroud, r r,out is the outer radius of the rotor, and L is the length of the blade. Each of these terms is a function Greek b α thermal expansion coefficient of temperature a nd where appropriate shaft speed. For the δ distance between nodes purposes of the model , the shank depicted in Fig. 1 that Δ difference/change connects the blade to the rotor is treated as an extension of the η turbine efficiency rotor.

ρ density variations within the same material are handled using the discretized equations from Ref. [ 15 ] .

The boundary conditions were enforced through the boundary node equat ions , which address convection and neglect radiation . The boundary nodes were assumed to be half the thickness of their neighboring interior node . Eq. ( 3 ) and ( 4 ) below provide the boundary node equations for planar and cylindrical geometries respe ctively.

T  k x  surf

    T T h T T C      (3)

surf surf inside p  x t   2 T  k 2 surf 2 2

    T T x x C    ... 

surf inside in out p 2 2

  x x t  / ln

(4) in out 1 1

  T T hx   2

surf surf  In Eq. ( 3 ), Δ x is the node thickness of the neighboring interior Figure 1 . Schematic of the HPT and surrounding node. In both equat ions, T is the temperature of the surface surf structure [ 2 ] node, T is the temperature of the neighboring interior node, inside T is the temperature of the fluid in contact with the surface ∞ The methods for determining the therma l expansion of node, and h is the convectiv e heat transfer coefficient. T he each of the modeled components has been updated to account values of x , x , x , and x in Eq. ( 4 ) are dependent on in1 ou t1 in2 out2 for temperature dependent properties based on work presented whether the give n surface node is the inner or outer surface in Ref. [ 15 ] . The more general form of the 1 - D heat equation node.

shown i n Eq. ( 2 ) was solved for both the rotor and the shroud.

Inner surface node:       1 T T ak k T   x x  x x  surf in 1 2 surf in    k (2)         x x x x C t      p x x  2 / x x x    inside out 1 2 inside out Here T is the temperature solution, t is the time, x is the spatial Outer surface node: variable, k is the thermal conducti vity, C is the heat capacity, p x x  x x x    2 / inside in 1 inside in 2 and ρ is the density. Eq. ( 2 ) is applicable to planar geometries when a = 0 and applicable to cylindrical geometries when a = x x  x x  surf out 1 surf out 2 1. Recall from Ref. [ 12 ] that the rotor is modeled with a 1 - D approach across the rotor disc’s width due to the dominance of As discussed in Ref. [ 15 ], Eq. ( 3 ) and ( 4 ) can be discretized in convective heat transfer from cooling flows on its front and a similar manner as Eq. ( 2 ) and included in the system of back surfaces. Therefore , a planar geometry assumption is most equations with the interior nodes , which is solved appropriate. The shroud resembles a hollow cylindrical shell simultaneously to obtain the temperature solution.

and so a cylindrical geometry is mos t appropriate in this Ref. [ 12 ] assumes the convective heat transfer coefficient instance.

is constant. In reality , the convective heat transfer coefficients From Ref. [ 15 ], Eq. ( 2 ) was solved using a fin ite difference in the gas path and cooling flow paths will vary though the method (FDM) approach via the Crank - Nicolson method course of a flight. It is expected to be a strong function of mass described in Ref. [ 16 ]. A general non - uniform spatial flow r ate and could be significantly impacted by the gas discretization was considered [ 15 ]. Eq. ( 2 ) was discretized temperature. In particular, one would expect the convective according to Ref. [ 15 ] and solved using Thomas’ s Algorithm heat transfer to be strengthened at low altitude and high power [ 16 ] . Although t he discretization contains t erms that are capable settings while it will be weaker at high altitude and low power of considering changes in material properties, a large abrupt setting condition s. The tip clearance mod el has been updated to change in thermal properties due to a transition in materials can allow the convective heat transfer coefficient to be interpolated lead to inaccuracy in results , particularly in the estimation of based on data or computed using the following expression the derivative of thermal conductivity wi th respect to the spatial leveraged from Ref. [ 17 ] .

variable. Therefore , the method from Ref. [ 12 ] was applied for handling material transitions in the shroud but thermal property 8 . 0 23 . 0 ACTUATOR AND CONTROL LER MODELING     m T  I n this study , the tip clearance i s assumed to be sensed and      h h (5) coeff     m T  the actuator movement is described in terms of displacement     des des from the nominal containment structure position (without active control). I n reality , the actuator may exist in a different form  This general empirical model was used where T and m are the and have a different range of movement. However, in the end current temperature and mass flow rate of the fluid, and T des the effect is essentially the same. The actuator was modeled and m  are the temperature and mass flow ra te at some known des using a generic first order transfer function with a specified data point where h = h . bandwidth ( BW ). No n - linear dynamics were added through coeff The updated approach for determining the thermal enforcement of saturation limits ( SL ), rate limits ( RL ), and deformation of each component uses the average temperature deadband ( DB ). The saturation limit and rate limit were applied of each respective component as was done in Ref. [ 12 ] but it to the actual actuator position response X while the deadband act differ s by accounting for temperature - dependent thermal was applied to the feedback p osition X .

fb expansion coefficients using the following fundamental The actuator was assumed to be connected or otherwise equation. incorporated wi th the containment structure; therefore , the actuator position is defined relative to the inner circumference T of the containment structure with the positive direction pointi ng     dT T L L ) ( 1  (6) 0 inward toward the turbine blade. The tip clearance and actuator



  T   0 position feedback sensors were assumed to be perfect in the sense that they react instantaneously upon being sampled and In Eq. ( 6 ) L is a generic length for the component of interest, L provide the exact value of the sensed variable. The sensor s is the length of the component at temperature T T is the 0 , signal s were constructed using a zero - order hold (ZOH) model.

current temperature, and α is the thermal expansion coefficient.

The reference signal R to the controller was the difference Unlike the previous approach , this model accounts for between the sensed tip clearance TC and the command sens expansion of the abradable layer of the shroud , which is TC . The change in actuator position ΔX was computed using cmd subtracted from the inner structural layer radius to obtain r s,in .

a Proportional Integral (PI) controller. The commanded In a similar manner, temperature depen dence of actuator local loop closure position X was the sum of the cmd mechanical properties such as Young’s Modulus and Poisson’s sensed feedback position of the actuator X and ΔX . Figure fb,sens Ratio were considered. The expressions for centrifugal 2 provides a schematic of the described model.

deformation provided in Ref. [ 12 ] are general enough to be The controllers used in this stu dy were designed using the applicable to tempe rature dependent m echanical properties and ® MATLA B Control Systems Toolbox’s (version 9.9) pidtune therefore no changes were required other than interpolating the function. To promote a level playing field for all of the mechanical properties each time - step of the simulation based actuators in the study, each actuator implemented a PI control on the current average temperature of the given component.

logic with a proportional control gain K and integral control p The components were assumed to be made of the same gain K determined using the same tuning algorithm. For each i materials as they were in Ref. [ 12 ]. The rotor, blade, and o actuator the phase margin was set to 90 to encourage a robust structural layer of the shroud were all assumed to be made of a design with a conservative response time. The step response of material similar to Inconel 718 while the abradable mate rial of the closed loop system was designed to be critically damped.

the shroud was assumed to be Zirconium Oxide. The size of the The control design was evaluated for a spectrum of cross - over components were inferred based on best engineering guesses frequencies and the controller design that produced the fastest and measurements for engines in the same thrust - class as settling time with no overshoot was sele cted for use in the C - MAPSS40k which is a 40,000lb thrust engine [ 18 ].

f simulation. Limiting overshoot was seen as advantageous to this application where excessive overshoot could result in a blade rub event. Minimizing the settling time was seen as a way to put all of the actuators on the same playing fiel d while also Figure 2 . Schematic of the actuator and tip clearance control model Figure 3 . Tip clearance control logic promoting the performance of the system , which could be to open up the tip cleara nce gap as mu ch as possible and valuable in assessing the potential benefits of active tip resume active control shortly after the engine restarts. With this clearance control. A schematic of the control logic is provided assumption, the worst - case condition seems to be the take - in Fig. 3 . off/climb scenario or an in - flight deceleration and re - A clamp ing circuit was integrated with the controller for acceleration as suggested by Ref. [ 1 ] and [ 19 ].

integral windup protection , mainly a gainst actuator saturation. Given that the model only accounts for axisymmetric tip The clamping circuit works by stop ping integration when the clearance variations , it was assumed that the actuator would actuator is saturated. Specific ally the input to the discrete - time seek to address axisymmetric tip clearance variation s as much integrator is set to zero when the pre - saturated position as possible while maintaining a clearance margin to address command is outside of the saturation limits and the pre - asymmetric tip clearance variations. From Ref. [ 19 ] , the integrator term and pre - saturation command have the same sign asymmetric tip clearance variation was recorded to be as much (i.e. when the actuator is saturated and the controller is going to as 15mils . An additio nal 5mils was added to a ddress command the actuator furth er into saturation). unaccounted for factors such as sensor bias, control system delays, an d additional uncertainties . The goal then was to find the minimum maintainable tip clearance for each actuator SIMULATION considered in the study and its associated p erformance such that 20mils of tip clearance was maintained during all This section describ es the simulation scenario that was transients. This was done iteratively by adjusting the regulated applied to access the actuator requirement and it also presents and discusses the results. tip clearance.

Seeing as the maximum anticipated axisymmetric change Minimum Clearance Margin & Baseline Clearance in tip clear ance is expected to be ~30mils and a 20 mil clearance should be carried at minimum due to asymmetric Ref. [ 19 ] evaluated the HPT tip clearance for the JT9D changes in tip clearance , the tip clearance at ground idle was engine for various scenarios including takeoff/climb, in - flight restart, thrust reversal, a hard turn, and aircraft stall. set to be 55mils. The additional 5mils in this case is attributed Axisymmetric and asymmetric deformations were considered. to conservativeness in the current design based on the inability t o actively measure and control the tip clearance. Note that the The JT9D engine is similar in size and thrust to the class of assumption is that the baseline tip clearance is directly related engine that is represented by C - MAPSS40k and therefore the information in the study was used to verify realistic behavior of to the potential benefits that could be extracted with active the tip clearance model . The largest axisymmetric closure turbine tip clearance control. If the baseline tip clearance we re to be larger , then the po tential performance benefits could be change was obs erved for an in - flight restart and was ~39mils even higher then what is presented in this paper.

while for the more common scenario of a takeoff/climb the axisymmetric deformation was ~31mils. Asymmetric and flight load closures during these scenarios increased the total closure Simulation Scenario change to ~42mils and ~46m ils respectively. Though the in - The flight scenario consists of several segments and includes take - off, climb, cruise, an acceleration to full - power flight restart scenario could produce more severe axisymmetric deformations , it was not considered as the worst case for this fr om cruise, a deceleration to idle at altitude followed by an study. The reason for this is that if the engine has to be restarted acceleration back to full power, descent, and a go - around upon during fl ight then efficiency is not the biggest concern , a landing attempt. The flig ht profile is plotted in Fig. 4 . PLA refers to the power lever angle , which is the pilot ’ s throttle especially seeing that the engine is not using fuel or producing o thrust to begin with. Therefore , in this scenario it seems command to the engine controller. On the plotted scale , 40 o reasonable to build control logic in to the actuator control loop corresponds to idle and 80 corresponds to full - power. Note Figure 4 . Simulation flight profile that the portion of flight between 30 and 47.5min is not typical of a commercial flight profile. This portion of flight was added for the purpose of evaluating the potential worst case scenario of a deceleration to idle followed by an abrupt acceleration to full - power after the engine has been provided time to cool down. The maneuver does not consider changes in Mach number or altitude that may result from the decrease in engine thrust but instead assumes other engines and or flight controls are used to maintain altitude and speed.

To provide a means of compariso n, a baseline simulation Figure 5 . Baseline response was conducted to determine the tip clearance response and engine performance when no fast response actuation is implemented. The results of this si mulation are provided in Fig.

5 and 6 . The performance during steady - state cruise is of the most interest . The cruise segment of the flight profile in Fig. 4 spans from ~21 - 29min but a slow transient persists through most of this time as a r esult of thermal expansion that shifts the operating point of the engine until all components have reached their steady - state temperature. Steady - state cruise is considered to be reached when all transients, including the thermal transients have ceased. This st ate was reached by the end of the cruise segment ( ~29min ). S ince the engine wil l spend most of its time at this operating point , the tip clearance and performance parameters were extracted from this data point and used in evaluating the benefit of each act uator. Each actuator was compared against the baseline quantities provided in Table 1 . Note that T is the turbine inlet temperature, η is the turbine efficiency, w is the fuel flow rate, and TSFC is the f thrust specific fuel consumption.

Table 1 . Baseline performance metrics at cruise Variable Value Tip Clearance , TC 50.31mils Turbine Efficiency , η 0.8922 Fu el Flow Rate , w f 1.401lb m /sec T hrust Specific Fuel Consumption , TSFC 0.2428 o Turbine Inlet Temperature , T 4 2840 R Figure 6 . Baseline p erformance metrics flight such that acceptable margins are maintained . Specifically Evaluation of Basic Actuator Parameters Various actuator parameters were evaluated through the the minimum tip clearance th roughout the flight should be close course of this study. First, bandwidth was considered alone to to but no less than 20mils. Observation of these results led to an establish the appr opriate range of actuator speed . Once this was appropriate bandwidth range being identified as 0.1 – 1rad/sec.

This is inferred based on the observation that there is a ste ep established, several bandwidth and rate limit combinations were considered. Based on results from these studies, actuator fall - off in performance b enefits for a bandwidth below posit ion responses were used to infer appropriat e actuator 0.1rad/sec and little reward for increasing the bandwidth range requirements. The next several paragraphs discuss the beyond 1rad/sec.

Next a set of simulations were performed to evaluate the results of these studies.

The range of appropriate bandwidths was determined by impact of rate limit contraints. Each simulation enforced rate varying the bandwidth of the actuator through several limits that were a percentage of the maximum actuation rate.

simulations of the previously defined flight profi le while For actuator bandwidths of 0.1, 0.2, and 0.5rad/sec these rate limits were 100%, 90%, 75%, 62.5%, and 50 % of the enforcing no saturation limits or rate limits and assuming the deadband to be zero. The results of these sim ulation s are maximum actuation rate . In the case where the actuator summarized in Fig. 7 , which plots the tip clearance and bandwidth was 1rad/sec , the rate limit range was restrict ed to performance parameters at t he cruise point for various amounts 100%, 90%, 75%, and 68%. The reason for this was controller of actuator bandwidth. Recall that the tip clearance at cruise is induced performance degradation at lower rate limits , which constrained by transients experienced during the rest of the was attributed to wind - up in the integ ral term of the control logic. Recall that t he control law was developed based on the linear system that considers the bandwidth but not the rate limit. Due to the actuator not responding as fast as the controller expects, error accumulates in the integral term during the transients , which can lead to dela ys in the actuator response, un anticipate d o vershoot, and oscillations that could produce results that do not follow the expected trends.

Results for the tested combinations of bandwidth and rat e limit are summarized in Fig. 8 . The relevant range of bandwi dth and rate limits for fast response turbine tip clearance control could be d etermined by considering Fig. 9 , which relates each combination to its reduction in TSFC . Note that it is possible that actuators in the unconsidered region , characterized by high bandwidth and relatively low rate limit , could be applicable if the co ntroller was redesigned. Due to the nature of this problem, it may require alterations to be made to Figure 7 . Tip clearance and performa nce metrics at the control algorithm . This is not ide al for evaluating the cruise for actuators with various bandwidths Figure 8 . Tip clearance and performance metrics at cruise for actuators with various combination of bandwidth and rate limit the decel eration, as indicated in Fig. 11 , were to be ignored then theoretically the actuator range could be r educed to ~35mils with the current containment structure or even to ~30mils if the radius of the containment structure were to be decreased. Based on these observations the actuator ranges seem to be very reasonable. Given that there is a steep fall - off in the benefit to engine performance for tip clearances larger than what is maintained here, limiting the movement range any further may not be worth the investment in implementing active clearance control. This also leads into the concern of integral wind - u p for saturated tip c learance control actuators that would be exacerbated by the smaller saturation limits.

Figure 9 . Cr uise TSFC as a function of actuator bandwidth and rate limit actuators on a consistent basis and therefore actuators in this region are not considered in this study.

Based on the observed range of actuator movement during the simulation, some saturation limit requirements are suggested. Two scenarios are considered. In the first , it is desired to regulate the tip clearance during all maneuvers including those that open the clearance such as decelerations , whereas the second only considers regulating tip clearance during steady state operatio n and transients that reduce the tip clearance. In the latter case, the control logic or physical Figure 11 . Actuator position ( BW = 1rad/sec) with the actuator limits could prevent the actuator fr om moving beyond circled regions identifying tran sients that could be a given position . Based on the results of the bandwidth study, as summarized in Fig. 10 , it appears that the actuator position ignored ranges from ~ - 8mils to ~48mils. For any given actuator bandwidth the overall range of movement was ~36mils to Weight and Force Considerations ~42mils. For the bandwidth range of interest, it seems Weight restrictions for the tip clearance actuation system reasonable to suggest that an actuator range of ~40mils is could be evaluated in several ways . A starting point wa s to look appropriate for this application. If the actuator transient during at the weight of the fuel saved through use of an actuator to cont rol the tip clearance. Figure 12 uses fuel flow rate data from the simulations to provide an idea of the fuel savings as a function of c ruise ti me. The top plot in Fig. 12 indicates the fuel saving for a single engine. The C - MAPSS40k engine may be applicable to a 2 - engine narrow - body jet or a 4 - engine wide - body jet. Note that modern wide body aircraft are conver ging toward a 2 - engine configuration. However, given the thrust clas s of the C - MAPSS40k engine, a 2 - engine configuration would not be appropriate, hence the 4 - engine configuration.

The estimated t otal fuel saving s for both of these types of aircraft are sh own in Fig. 12 . The bottom plots in Fig. 12 indicate the total fuel saved for the 2 - engine narrow body and 4 - engine wide body configuration s . The average and one standard deviation ( 1 σ ) lines were derived from data extracted for numerous f lights occurring on September 19, 2016 and September 20 , 2016 , available from Ref. [ 20 ] for Boeing 737 - Figure 10 . Actuator range from the bandwidth study 800 flights and Boeing 777 - 300ER flights respectively .

Figure 12 . Potential weight saving as a result of carrying less fuel The information in Fig. 12 could be used to evaluate trades W is the weight of the aircraft with passengers and luggage, A/C when considering the financial saving of using less fuel. and W is the weight of the fuel that is carried in reserve in rese rve However, the constraint on the weight o f the actuation system is the case of an emergency. Ref. [ 2 2 ] indicates that the FAA not as simple as consideri ng it to be the weight of the fuel requires domestic airlines carry enough fuel to continue to an saved. A more appropriate assessment of the actuator weight alternate airport, plus an additional 45min after. Furthermore, restriction is to determine the weight that can be added to an the alternate airport must have a good weather forecast. Ref.

aircraft while still achieving the same range and carrying the [ 2 2 ] continues to suggest that on average an extra 70mi n of same payload. This is because range and payload are constant additional fuel is carried in reserve. The parameter t refers reserve parameters for commercial flights and the real goal is to get the to this flight time in which the reserve fuel is capable of payload to the destination using less fuel. Using the Breguet extending the flight. W is the weight of the fuel used during fuel range equation [ 2 1 ], the maximum weight of the ti p clearance the flight, n is the number of engines used by the aircr aft, R is actuation system, W , can be evaluated by solving the equation the range or distance between airports, and V is the average air act below: speed , which is taken to be the cruise speed since that is where the aircraf t will likely spend the majority of its time. Most commercial aircraft cruise around the same Mach number and   /    n W W W W / , / , / act act w fuel act w reserve C A   ln altitude , which are ~0.8 and 35,000ft , respectively. Using   /   n W W W TSFC / , / / act act w reserve C A act w   standard atmosphere tables , the ambient temperature and (7) subsequently the speed of sound at this altitude was     W W W , , / base fuel base reserve C A   determined , thus allowing for dete rmination of the cruise speed .

0 ln      W W TSFC The subscript “ bas e ” refers to the baseline value that , / base reserve C A base   corresponds to the use of no fast response actuator. The subscript “ w/ act ” refers to the value corresponding to use of a where fast response actuator.

Eq. ( 7 ) was solved for var ious ranges using results from t nw W  reserve base f base reserve , , various actuators in the study that have displayed different R levels of TSFC and fuel flow rate at cruise. This analysis was nw W  base f base fuel , , done for a narrow - body jet application and a wide - body jet V application. Similar to the fuel savings s tudy, the narrow - body t nw W  reserve act w f act w reserve / , / , jet configuration was assumed to use 2 engines while the wide - body jet was assumed to use 4 engines based on the thrust R nw W  needs of aircraft in these classes. The aircraft weights were act w f act w fuel / , / , V based off the empty weight and passenger occupancy l imits for Figure 13 . Maximum actuator weight estimations based on the need to fly the same range and carry the same payload the Boeing 737 - 800 aircraft and the Boeing 777 - 300ER terms of the relevant pressures inside the en gine that will likely aircraft. This information was taken from Ref. [ 23 ] and [ 24 ] drive the force requirements for many actuator desig ns.

and assumes that each passenger on average weigh s 15 0lb and The pressure differential that generates the pressure force m has 70lb of luggage. Figure 13 plots the solutions to Eq. ( 7 ) on the actuation system was investigated on a worst case basis m that quantifies the maximum weight that the tip clearance under s implified geometric assumption s . Two scenarios were actuation system can add to the engine while still achieving the considered, the first when t he actuator surface is to be same ra nge as the baseline engine and carrying the same modulated bet ween the hot gas path and the cooling plenum payload. Figure 13 provides an estimate of the ranges in which around the shroud , which is filled with compressor discharge narrow - body and wide - body jets typically fly based on dat a air as depicted in Fig. 14 . The second scenario considers the from Ref. [ 20 ] that was extracted for flights tak ing place on the actuato r surface moving against a pres sure differential created selected dates. This was done to allow one to infer what the between the hot gas path and the cowl cavity that defines the expected actuator weight constraint might be for these two region of air between the engine cas ing and the bypass duct.

classes of aircraft. No te that the presented weight analysis is The pressure differentials were calculated based on rules of rough and simplified. Additionally, there may be more factors thumb provided in Ref. [ 25 ] and [ 1 ]. Fig. 15 plots these to consider, some of which are application specific. pressure differentials for each of the two described scenario s, Another concern for a tip clearance ac tuator is the force for the flight profile in F ig. 4 . G iven the area of the actuation requirement . Some actuator concepts such as those employing surface the pressure differential could be translated to a force.

fluidic control and plasma actuation may avoid this Therefore , Fig. 15 should give an idea of the range of force that consideration but those considering mechanical actuation of an actuator may have to apply. Furthermore, t he bottom plot in any sort , such as hydraulic or pneumatic actuation , will likely have the need to exert some amount of force in - order to maint ain the tip clearance position and to change position when needed. Many actuation concepts consider modulation of the shroud , which itself is a pressure vessel. Pressure forces would surely be the dominant force to consider but additional capability may be needed to overcome friction, the weight of the actuator, and inertia forces due to aircraft and engine accelerations and aerodynamic forces applied to them .

Furthe rmore , the actuator would have to exceed the static force requirements in - order to assure th e ability to generate enough excess force to accelerate the actuator to an appropriate speed .

Obviously , there are many things to consider when evaluating the force requirements for tip clearance actuation systems and the requirement will be dependent on t he actuator design.

Therefore, the extraction of a general assessment was not Figure 14 . Axial pressure distribution across HPT blade tip seal cross section [ 25 ] sought after. However, some information can be provided in Fig. 15 is a blow n up view of the first transient in the top plot. 20mil safety m argin was maintained. However , when a This plot is meant to provide an idea for the required rate of saturation limit of +/ - 20mils was enforced with no IWP logic , change in applied force for the actua tor to maintain its position. the tip clearance reaches a minimum of ~10mils. Even with IWP logic the tip clearance reaches a minimum of ~13mils. In either case this could have r esulted in a blade rub event.

Two factors could play a role in this: (1) the anti - windup technique may not be able to discharge all of the error in time to respond fast enough to the transients , and (2) since the actuator is saturated when the tip clearan ce transient begin s , the tip clearance gap begins to close before th e actuator starts to react to the transient ( i.e. when the measured tip clearance dips below the regulated tip clearance value) . This provides the tip clearance transient with a “ running s tart ” before the actuator has an opportunity to react . Because of this, extra safety margins will be needed to address potential saturation scenarios regardless of the integral windup problem.

Figure 15 . Approximated pressure differential that th e tip clearance control actuator will have to work against Additional Considerations There are several additional factors to consider in actuator design and selection as well as the development of control laws. Two such factors that will be discussed here are integral windup for pro portional integral derivative ( PID ) controller s and deadband. Finally, a comprehensive example o f a reasonable actuator application is illustrated.

Integral windup refers to the situation where a large change in set - point occurs and the integral term of the c ontrol law accumulates significant error during the rise that causes the Figure 16 . Tip clearance and actuator position response control input to increase or decrease as the accumulated error is ( BW = 0.2rad/sec, RL = 4.12mils/sec, SL = 20mils, no unwound. This can cause excessive overshoot in the system IWP) response , which for active tip clearance control could resu lt in a blade rub event. The issue of integral windup is worsened when the control logic is executed but the system does not respon d to it. This may occ ur when an actuator is saturated.

While the control logic commands the actuator to move to a position th at is outside of its physical capability, error accumulates. When a change in the system occurs , such as a sudden acceleration of the high speed shaft, the integral term must discharge or “un - wind” its excess error before the actuator will become unsaturat ed and begin to move . This may cause a significant delay in the actuator response. There are integral - windup protection (IWP) techniques that can be used to alleviate this issue but none are perfect. Figure 16 and Fig. 17 shows the impact of integral windup on the actuator position and tip clearance response when the upper saturation l imit is set to 20mils. Figure 16 shows the response wh en IWP logic is not used and Fig. 17 are the results when the clamping technique Figure 17 . Tip clearance and actuator position response described earlier is impleme nted. It was observed in previous ( BW = 0.2rad/sec, RL = 4.12mils/sec, SL = 20mils, simulation s that when no saturation limits were enforced , the clamping technique) To help with these issues , rigorous effort should be put These figures show the tip clearance response before and after towa rd designing a robust IWP logic. Alternatively , or in the take - off transient of the previously de fined flight scenario addition, it ma y be possible to add logic that dictates when the begins . Imagine integrating the error between the actual tip controller itself is active. This may prevent the controller from clearance and the command clearance ( at ~26.64mils ) in Fig.

integrating error during portions of the flight where tip 19 during the time just before the transient begins at ~100sec .

clearance is not of concern , such as ground idle and The largest error is accumulated by the actuator with the 2mil decelerations. In addition, when such events are detected the deadband and in Fig. 20 and it can be observed that this integrator could be reset. Another idea is to detect the actuator has the worst performance. Note that anti - windup saturation and temporarily change the commanded tip clearance control logic was used during these simulations. It seems that to the current measured value (assu ming it is larger than the the small amount of error build up in the integrator is desired regulation value) such that no error is accumulated. significant enough to make a noticeable impact. Refe rring to When the actuator becomes unsaturated the commanded value Fig. 18 , it can be seen that the period of the oscil lations for can be reduced. Another approach would be avoiding the each actuator is the same but the amplitude increase s with integral windup problem by designing the controller wit h deadband. Based on thi s information and the observation about different techniques , although this may not help in addressing error accumulation, it can be said that the larger the deadband, issues with factor (2) listed above. Some control techniques the larger the potential for degradation in the actuator r esponse.

such as model - predictive control could have the potential to alleviate this issue by using knowledge of how the tip clearance is g oing to react and thus can stay ahead of the system response. In general, predictive control techniques have been shown to be advantageous to tip clearance control in Ref. [ 26 ] .

The issue of actuat or dea dband refers to a zone of actuator movement in which no action occurs. It is often the result of slop in gears, linkages, and other mechanical parts in the actuation system. The direct effect of deadband is a delay in the response of the system being actua ted when the actuator changes directions. When the actuator is attempting to regulate the output of the system , the deadband can result in oscillations about the set - point as shown in Fig. 18 that can ef fect steady - state accuracy and transient behavior by changing the initial Figure 19 . Error accumu lation due to deadband condition of the actuator system at the start of the transient.

Figure 18 capture s oscillation during the cruise segment of the f light scenario that was described previously. Deadband can also degrade the performance of the controller. For instance, the oscillations about the commanded tip clearance can result in error accumulation in the PI integrator that can resu lt in an integral - windup issue as i s demonst rated in Fig. 19 and 20 .

Figure 20 . Impact of actuator deadband on the tip clearance response during the take - off transient Given the inconsistency in the results it makes it hard to predi ct the impact that a given dead band would have. It is even hard to say what the worst case scenario would be. A few scenarios to consider would be if a tip clearance closing Figure 18 . Tip clearance oscillations about the set - point transie nt begins: due to deadband (1) when the actuator is on the verge of changing CONCLUSION direction, moving toward the blade , and it s Improvements to a tip clearance model have been accumulated error is at a maximum presented and that model has been used to study the needs for (2) when the actuator is sitting at a position that puts the turbine tip clearance actuation system s for a modern gas turbine tip clearan ce below the commanded value engine. The actuator has been modeled without any (3) sometime d uring the tra nsition from a large tip assumptio ns of the type of actuator allowing for general clearance to a smaller tip clearance when the actuator recommendations to be made for actuators in terms of is moving toward the blade properties such as bandwidth, rate limit, saturation limits, and Investigating this problem further was not within the scope of weight trade . Additionally, investigation s were conducted for this research. Therefore, no g eneral recommendations are given deadband, integral wind - up, and force requirements. The here other than to say that less deadband is advantageous. results of the study suggest that an appropriate active turbine Given that the 2mil d eadband case observed in Fig. 19 and 20 tip clearance control actuator sho uld sustain a bandwidth of 0.1 was close to worst case scenario ( 1 ) given above and only to 1rad/sec, rate limits greate r than ~4mils/sec, a range of res ulted in ~1mil clearance change, 2mils seems like it could be 40 mils or more, and a relatively small amount of deadband , a reasonable value for the deadband but a more exhaustive which is suspected of being on the order of 1mil. The study would be needed to say that definitively. Such a study evaluation of actuator requirements was based on the minimum should also address the impact of deadband in combination tip clearance achievable with a given actuator while respecting with other actuat or parameters such as bandwidth and rate defined safety margins. The study was done using a simul ation limit , and consider the impact of the control logic . of an engine that is representative of those currently in use by Based on the comprehensive findings of this study, an commercial aircraft. Future commercial engine designs may actuator with reasonable characteristics has been chosen and present a new set of requirements for tip clearance actuation simulated for illustration of its impac t on the engine system. sy stems and so similar studies need to be pursue d to The chosen actuator has a bandwidth of 0.5rad/sec, a rate limit characterize these needs. There is also room to investigate the of 5 mils/sec, a range of 4 0mils , and a deadband of 1mil. Figure development of control logic to optimize engine performance 21 compares the closed loop and open loop tip clearance through tip clearance modulation. I f the tip clearance set - point response s . Add itionally, Table 2 compares the steady - state were to be scheduled based on flight regimes then the clearance cruise performance of the closed loop system to the baseline and in - turn per formance of the e ngine could be improved results in Table 1 . further . The issue of integral wind - up and its mitigation, and issues related to saturation are also potentially rich areas of research th at were revealed by the analyses conducted here.

ACKNOWLEDGEMENTS The author s would like to acknowledge the creators of C - MAPSS40k. This work supports the objectives and goals of NASA’s Advanced Air Transportation Technology (AATT) Project funded by the Aeronautics Research Mission Directorate (ARMD).

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