Robust Tip Gap Measurements: A Universal In-Situ Dynamic Calibration and Demonstration in a Two-Stage High-Speed Turbine

The observation of the rotor gap in turbomachinery is vital to obtain insight into the health of the machine [1], and its understanding is essential since it has a direct effect on the tip aerodynamics [2–4] as well as on the main flow field characteristics [5,6]. More than half of the total heat load in a rotating machine can be associated with the flow-surface friction and mixing of the different fluid structures between the passing blade tips and the stationary shroud, the tip leakage flows [7]. For the same reasons, tip leakage flows are also responsible for a third of the total entropy increase across the stage [6], directly impacting the machine's efficiency. Among various techniques used to live-monitor tip clearance, such as microwave, magnetoresistive, optical, or inductive sensors [1], the more rugged capacitance probes are most frequently used. Capacitance probes mounted along the passage shroud measure the capacitance field generated between their electrode and the rotating blades and return a voltage signal proportional to the magnitude of such field. While capacitive sensors offer comparable accuracies to magnetoresistive, microwave, and optical approaches, they are commonly preferred. Optical measurements, such as Laser Doppler Velocimetry, require continuous equipment alignment and a direct optical access to the blade tip, additional efforts, and design constraints that are not suitable for easy long-term instrumentation. As presented by Geisheimer et al. [8], microwave probes can suffer from repeatability errors caused by drifts in electronic component or temperature sensitivity that affects the sensor's material properties. Both capacitive and magnetoresistive probes feature higher resistance to temperature, simplicity in the design, and small size of the probe itself, suitable attributes for engine monitoring applications. As a drawback, this instrumentation may require complex and detailed calibrations. However, capacitive probe calibrations have achieved accuracies with uncertainties below the twenty microns featured by microresistive probes [9], a crucial parameter when measuring tip clearance variations of less than fifty microns. The most reliable measurements require calibrations in situ, exposing the sensor to the expected range of performance conditions, and fitting the proper curve through the respective measured dataset. The lowest uncertainties are obtained when the calibration is performed within the final operational setup [10], as opposed to using an external calibration benchtop that replicates moving blades [10,11]. Sheards et al. [12] provided a method for this approach and accounted for the errors involved in the process. However, the execution of the suggested procedure requires manually adjusting to set distances the position of the blade tip-sensor clearance during operation. Sheards et al. accomplished this by recessing the probe with linear actuators and displacement encoders, a setup that often is not available. Others use metal shims with different calibrated thicknesses to recess the inserts holding the probes and wear gauges to retrieve the achieved rotor gap [10,13]. This last approach requires numerous independent test sequences during the calibration. After each recess condition, the abraded material in the wear gages needs to be measured, and the next change in clearance must be setup. Consequently, this becomes a time-consuming experimental procedure. The following report proposes a novel in situ dynamic procedure that allows proper capacitance probe calibration with minimum setup, reduced tests, and a single clearance measurement. The suggested approach performs a prediction of the measurements along the operational range of the machine and uses a geometrical feature of the blade tip to optimize the resulting calibration curve.

Moreover, the relevance of the tip leakage flows on the machine's performance losses motivates additional measurements in the gap region. Several studies indicate a significant dependence between the magnitude of peak shroud thermal loads, pressure losses, and unsteadiness [14] with the tip clearance [15] and geometry [16]. Therefore, a correlation between these quantities can return insightful feedback toward turbomachinery's future performance and reliability enhancement. Examples of suggested improvements can be found in tip cooling flows [17] and optimized rim profiles [18] for heat load and pressure loss reductions. Furthermore, an interdependence of such extent becomes a breakthrough for engine testing measurements, as each magnitude can be recovered from acquiring a single signal. The scope of the present work encompasses high-frequency measurements along the shroud to visualize the unsteadiness over the passing blades. Analysis of the time-resolved tip clearance is combined with the high-frequency shroud static pressure and heat flux measurements to demonstrate the relationship between these three measurements.

The test runs described in this paper were performed within the PETAL at Maurice Zucrow Laboratories. The tests were performed on a state-of-the-art, small-core, two-stage high-speed turbine called STARR (Small Turbine Aerothermal Rotating Rig), depicted in Fig. 1. The turbine module shaft extends through the exhaust plenum and connects directly to a high-speed synchronous electric motor of 21,000 rpm range. The motor capability negates the need for a gearbox. The dyno provides a motoring power of up to 1000 HP and has an absorption capability of 1000 kW for loaded tests. An unloaded motoring mode is used to perform the capacitance probe calibration, while the unsteady high-frequency measurements are performed in a fully loaded configuration. Loaded tests with compressed air were performed at engine relevant conditions, reaching rotational speeds over 14,000 rpm at TRL 6. Throughout all the work, squealer-type blades with continuous rims at the tip edge were studied.

The sensors used in the presented procedure were installed in a series of inserts outside the rig and afterward mounted on the test section at different circumferential locations. These inserts were designed accordingly for each sensor. Additionally, they contain a curved surface matching the shroud radius to provide a flush continuous surface transition after installation. A view of these inserts and the instrumentation used is provided in Fig. 2.

The capacitance sensors used throughout this procedure feature a Pseudo-Triaxial configuration, where the probe head is coaxial, and the cable is fully triaxial, shown in Fig. 2(a). The probe tip exposes a central 2.5 mm electrode surrounded by an insulating material and an external stainless-steel housing. The inside of the probe is arranged as a triaxial cable, where the innermost electrode is surrounded by an insulation layer and an external guarding conductive coating, followed by an additional insulation film before the outermost housing. The same voltage is provided to the electrode and guarding lines to keep the charge distribution undisturbed, although only the core electrode is measured. The guarding layer captures the additional capacitance caused by larger charges around the electrode edges, the so-called “side effect.” This arrangement provides a more uniform measurement field from the electrode. Therefore, it resembles an ideal parallel-plates case, where the capacitance is linearly proportional to 1/d, d denoting the distance between the plates. The rig case serves as a ground for the probe housing and the blades. The latter is connected to the case through the bearings and structural housing. This configuration ensures a voltage level difference between the housing and both electrode and guard lines, as well as a potential difference between the blade tips and the sensor electrode. The triaxial cabling arrangement is maintained along the connection to the conditioning and acquisition system. The Fogale Capablade Fusion System [19] is used for the latter, equipped with six MC925 translational modules [20]. The conditioning system applies a 30 V/pF gain to the probes, and the acquisition is continuously performed at a sampling frequency of 2 MHz.

The achieved clearance conditions were measured with wear gauges installed in the same insert adjacent to the capacitance probe, also pictured in Fig. 2(b). These gauges are manufactured in-house from a small brass threaded rod, whose tip is equipped with an abradable material made of an epoxy-filled polyimide. When installed, this abradable material protrudes into the flow passage and is machined by the passing blades, thus providing a direct measurement of the tip gap. The insert is removed from the rig and fixed in a vice to avoid deviations during measurements. A Faro Arm is used to measure the depth left on the wear gauges and the recess present by the capacitance probes, with accuracies better than 40 μm. This setup is shown in Fig. 3. The figure also illustrates that the capacitance probe is recessed within the insert, to prevent potential damage from blade contact.

Unsteady pressure data was measured with Kulite pressure transducers. Sensor models XCE-062-100A and XCE-062-50A were installed in the first and second stages, respectively. Figure 2(c) depicts the Kulite sensor and the corresponding instrumented insert. The pressure transducers were connected to a Precision Filter Kulite Conditioner model 101777 [21]. This system outputs the signal of each sensor into two independent static and dynamic signals. The conditioner applied a Butterworth low-pass filter with a −3 dB cutoff frequency at 322 Hz to the static signal and a −3 dB cutoff frequency at 160 kHz to the dynamic output. A Genesis GEN2tB Transient Recorded and Data Acquisition System then read the output, equipped with two GN8101B cards for independent low and high-frequency acquisitions. The acquisition was performed at a 1 MHz sampling rate. A DC coupling was set for the low-frequency readings, while an AC signal coupling was assigned to the high-frequency ones. An additional low-pass Butterworth filter was applied to both readings with a 250 kHz cutoff frequency.

Supplementary heat transfer measurements were performed using Atomic Layer Thermopile (ALTP) sensors. Two probes were installed simultaneously in the first and second stages of the rig, as shown in Fig. 2(d). The sensors' sensitivities were 31 muV/W/cm² and 34 muV/W/cm², respectively. The signals from both sensors were scaled by a factor of 200 with independent amplifiers before the acquisition system. A Picoscope 5442D MSO was used for this purpose. The raw signals were recorded at 2 MHz without additional filtering.

All the measurements were triggered and synchronized with the blades by a once-per-revolution signal provided by a photodiode sensor. This sensor was installed facing a photoreflective tape in the shaft, thus providing a square wave from 1 V to 5 V as the shaft rotates. Each acquisition system additionally recorded the signal of the photodiode. This wave was later used to align all the data, accounting for any variations in the rotational speed of the machine.

The acquired raw voltage signal from the capacitance probes is first filtered to extract valuable information from the tip clearance data. A fifth-order low-pass Butterworth filter is applied, with a cutoff frequency equal to ten times the blade passing frequency of the corresponding stage. The different features of the signal are then associated with the dimensional traits of the squealer blades. The squealer tip geometry generates a distinctive signal profile with two local maximums corresponding to the suction and pressure side rims. A local minimum between these extremes is associated with the in-between-rims region, referred to in this text as the “valley” or “cavity.” The region between consecutive blade profiles provides the lowest voltage reading. Taking this minimum as a reference, the entire signal is expressed as a voltage difference reading, as plotted in Fig. 4(a).

During operation, higher speeds and heat loads cause the blades to strain, closing the tip gap and leading to higher voltage readings. The tightest clearance of a blade is provided by the largest voltage peak, corresponding in this case to one of the rims. A signature of the row of blades is then obtained from these points. The signature profile of the blades remains consistent for any RPM condition. This characteristic is portrayed in Fig. 4(b), where each voltage point was computed as an average per blade over 1000 revolutions. The standard deviation of all the voltage measurements throughout the present work are of the order of 10⁻³ Volts. Therefore, voltage data are displayed without error bars to provide a clearer representation. Moreover, the order of magnitude of the standard deviation demonstrates a reliable repeatability of voltage data to further compute the gap clearance.

where the degree of the polynomial is a chosen parameter and the coefficients a_i result from the curve regression through the empirical data.

where a₂ defines the vertical asymptote of the curve and must follow a₂ > 0 from the previous explanation.

Therefore, the final calibration curve is only a function of the vertical asymptote coordinate, a₂.

While the purpose of this paper is to use the dimensional features of the squealer blade, a simple plot of the measured rim and valley voltages at the respective clearances demonstrates that a unique calibration curve cannot define both data sets. Figure 5(a) provides this proof. It depicts the tightest clearance data for different speed conditions against the matching voltage reading. The rim clearances displayed correspond to past tests following a calibration method defined by Sheards et al. [12] and validated by the Fogale system calculations [22]. The valley clearances were obtained by adding the rim height to the rim clearance and associating them with the respective valley voltages. This representation features an explicit offset in depth and an overlapping of voltages between rim and valley regions. Consequently, each dataset must be described by independent curves due to the change in the capacitance field as the blade passes. The blade itself acts as the opposing electrode to the probe, hence, when the valley region directly faces the probe, the size of the simulated electrode increases, and so does the capacitance field. Therefore, the signal values read during the valley region are larger than that of an equivalent clearance with a smaller electrode surface area (like the tip rim region). Consequently, the rim voltages dataset will be most interesting as it corresponds to the closest clearance to the shroud.

The proposed fit line was validated using the rim dataset as represented in Fig. 5(b). In this plot, the modified ideal Eq. (4) and suggested formulation (5) were fit through the dataset using a least squares approach. The implementation of the constraint stated in Eq. (6) was also studied for both expressions, and the R2 value was analyzed for all four cases. The ideal relationship shows the worse fit regardless of the constraint condition. The suggested real form features a perfect fit when the empirical point constraint is not included. However, at least one point must be recorded for a calibration. The almost perfect fit of the suggested formula (5) applying constraint (6) validates the proposal to use such a relation.

During testing, limited equipment often hinders direct tip clearance measurements while the machine is spinning during a capacitance probe calibration, as is the case of the setup used throughout this case study. Therefore, the test runs must be interrupted after each clearance condition to measure the achieved gap, as provided by the wear gauges in this instance. To minimize the number of direct measurements during the procedure, the previously introduced reference point [V₀, d₀] is the only empirical clearance point to be acquired during this calibration. Consequently, the total run time of the calibration is considerably reduced. Represented in Fig. 6(a), this measurement provides the rim clearance corresponding to the rim voltage reading. The knowledge of the rim height further yields the valley clearance associated with its measured voltage. For the present procedure, this point was acquired after spinning at 1000 rpm.

Additional experimental datasets are needed to fit any calibration curve. Ideally, any supplementary datasets are obtained while keeping the test runs uninterrupted. In this case, the easiest way to achieve them is to change the rotational speed of the motoring test and measure the voltage reading provided by the capacitance sensor. Using this approach, a map like the one depicted in Fig. 6(b) can be generated. Each blade provides a maximum peak voltage for each rotational speed tested. While the number of blades is fixed, the map can be further populated with as many speed setpoints as desired. As speed increases, the blades adjust and expand, reducing their clearance with the shroud and leading to larger voltage measurements. As the speed, voltage, and clearance are all directly related, it is argued that it is possible to substitute the desired clearance-voltage relation with a voltage-speed relation, and then later transform between them. This is an optimum approach for relating the voltage to clearance, as it only takes a few seconds to spin the turbine at a certain velocity and record the voltage.

Applying this approach, only two rig tests are required to obtain the necessary data for the calibration. An initial short run at low speed to measure the reference distance-voltage point, and a second longer rig test to populate the voltage-speed map for several speed conditions.

With the analysis just provided, it is then possible to predict the evolution of the largest blade's voltage provided its value at the reference speed.

Combining all the information from previous sections, a final calibration curve can be created, which passes through the reference measured point [V₀, d₀] and returns rim and valley clearances with a difference equal to the rim height.

The steps involved in each iteration of the optimization are depicted in Fig. 8 and described below. And additional flowchart for the entire calibration procedure is also provided in Fig. 9.

1. A preliminary guess for Eq. (5) is generated by passing through the reference measured point [V₀, d₀], thus fulfilling constraint (6). From this curve and applying the rim height, the ideal voltage that would be read at the valley is computed. Figure 8(a) shows this initial step.

2. The computed valley voltage is introduced into the speed relation to obtain a prediction of its evolution throughout the range of operational speeds. An example of this prediction is provided in Fig. 8(b).

3. The obtained distribution of valley voltages is located within the guessed curve, returning a clearance. These data are represented with black dot markers in Fig. 8(c). The maximum rim voltages are also introduced in the fitted curve to compute the tip gap in such regions, denoted with blue markers in the same figure. The red markers in this plot represent the corresponding valley clearance after adding the rim height to the rim values.

4. The difference between rim and valley clearances is computed and compared against the rim height. Figure 8(d) depicts this error for all the rotational speeds studied.

5. Update the guess for the coefficient a₂ to generate the next guessed curve.

While the user can select the method to refine the guessed curve, the present case was resolved using an SQP algorithm implemented in the built-in fmincon Matlab function,

After a few iterations, the optimization algorithm converged to a solution, and the results are provided below. Figure 10(a) represents the final calibration curve, indicating in blue and red markers the rim and valley clearances throughout the calibration test. In this same picture, the validating curve is also represented. This one is constructed by regressing the curve form (5) and constraint (6) to the entire dataset of previously resolved data. The difference in clearance provided by both curves reduces with increasing voltage. This difference is computed and illustrated in Fig. 10(b). Among the measured voltages, the largest calibration error is located at the valley voltage of the widest clearance, with a value near 12 μm. The calibration error is reduced as voltage increases until there is no error at the point of empirical measurement. This point corresponds to the minimum rim voltage and largest tip clearance. Recall that this point was selected at 1000 rpm and is the unique empirical clearance measured during this procedure, thus constraining both curves to pass through it. Larger voltages correspond to higher speeds and are more representative of the performance range of the machine. The error in this region increases again, reaching maximum absolute values close to 1.5 μm at the largest range speed.

While the calibration error is computed against a predefined curve built from past data, a new calibration oftentimes does not have this knowledge for comparison. Figure 8(d) represents the prediction error in one of the first iterations of the routine, and Fig. 10(c) provides the resolved prediction error for the optimized solution. It is evident from this graphical representation that the prediction errors are larger than the curve errors, thus providing a conservative knowledge of the uncertainty level for the latter. Additionally, the profile described by these values shows no clear dependence on the conditions tested. This indicates that the prediction error results exclusively from the accuracy of the fits performed to evaluate the voltage evolution and the uncertainty in the voltage and speed measurements involved in such a process.

Compared against previously used techniques, the presented calibration routine offers several advantages. The most noticeable benefit for the experimentalist is the duration of the procedure. The requirement of a single tip clearance value, retrieved from the wear gauge, allows to complete the entire test in less than 20 minutes. Previous followed procedures [10] required multiple interruptions to read the achieved clearance, lasting over 1 hour to cover a wide range of clearances. Second, the speed measurement errors of the proposed method can be easily mitigated through a frequency analysis of the acquired signal, obtaining reliable readings of the passing blade frequency and the rotational speed. The dynamic and in situ nature of this calibration further contribute to reduce the final uncertainty. Dynamic calibrations have proven to provide lower uncertainties than static ones [10], in addition to avoid complex calibration benches [22]. Considering the in situ characteristic, while other procedures provide different clearances by recessing the probe at constant rotational speed [10,12], the proposed technique fixes the probe in place and modifies the tip clearance through different rotational speeds. This approach resembles the real operation of the machine and, therefore, the same capacitive field is measured by the sensor during the calibration. The combination of all the previous points results in an improved accuracy of the final curve. The residuals and errors commonly found in the range of five to of twenty microns [12,23] are reduced to a maximum of 1.5 microns within the operational range of the machine.

With a reliable capacitance probe calibration, a series of performance tests were carried out. During these runs, unsteady pressure and heat flux measurements were taken on the shroud. A qualitative analysis was performed on these quantities against the tip clearance. Results are provided below in Fig. 11, complemented by Fig. 12 presenting computational work found in the open literature, and Fig. 13.

The first illustration depicts a direct comparison of the three measurements. The signals pictured are filtered at a cutoff frequency eight times the blade passing frequency. An additional Hampel filter was applied to the ALTP data to eliminate electrical noise from the dyno controller. The once-per-revolution signal provided by the photodiode allowed the alignment between the signals with time. In this figure, the waveforms are represented against the blade pitch phase to provide a better understating of the passing blades' effect. The quantities have been nondimensionalized as a percentage of their range. Figure 11(b) provides an augmented view across four blade pitch phases. This figure also represents the points corresponding to the suction and pressure side rims of each blade.

To understand the physical effects taking place in this region, an analysis of the evolution of the local tip leakage flow is followed. The tip leakage flow is originated from the main passage flow, which accelerates toward the pressure side of the tip blade as this one approaches. A small separation bubble at the pressure side rim generates a further flow contraction described as vena contracta [24]. This acceleration process is evident in Fig. 11, portraying the end wall static pressure decrease until it reaches a local minimum at the pressure side rim. This progressive increase in flow velocity results in the continuous enhancement of heat transfer. It is observed that the rate of heat flux growth spikes abruptly at the pressure side rim, corresponding to the final flow acceleration produced by the area contraction of the rim and the separation bubble effect. This also results in its maximum peak at the rim. These observations lay in agreement with the tip clearance heat transfer studies performed by Ameri et al. [25], Krishnababu et al. [26,27], Cis De-Maesschalck et al. [28,29] and A.P.S Wheeler et al. [30]. Passed the pressure side rim, Mischo et al. [31], and Wei Li et al. [32] performed a detailed description of tip leakage structures appearing within the cavity region. To complement the understanding of the recorded signals, a graphical representation of the squealer tip region flows is provided in Figs. 12(a) and 12(b). The images in this figure have been retrieved from the numerical simulations of the mentioned researchers [28,31], published in the ASME Journal of Turbomachinery in 2021 and ASME Turbo-Expo proceedings in 2006, respectively. The resulting flow effects are also recognized in Fig. 11. A rim boundary layer roll-up vortex appears as the rim ends, inducing a separation bubble and flow expansion into the cavity region. The flow velocity is locally reduced, resulting in a slight increase on the shroud's static pressure and the corresponding reduction in heat flux. Across the tip cavity, the expanded flow encounters the casing vortex. This vortex was generated at the leading edge and travels along the tip cavity, defining a region of low entropy. This region is inferred in the acquired data as the constant or slight variation of heat transfer and static pressure in between the tip rims. The interaction with this casing vortex redirects the leaked flow toward the suction side rim. An additional recirculation bubble appears at the suction side rim edge with the cavity wall. This one contracts the flow again, which accelerates toward the rim, featuring a second peak of minimum static pressure and associated spike in heat flux. From the suction side rim, the leakage flow feeds into the tip leakage vortex, whose development has been investigated by Kegalj and Schiffer [33]. The tip leakage vortex redirects the exiting tip flow toward lower blade radii. This effect results in a sudden decrease of flow speed and mass flow at the shroud, which is recognizable from the abrupt decrease on measured heat flux and the progressive increase of static pressure. The latter keeps increasing gradually toward the center of the main passage. In this same direction, the shroud's heat flux also presents an increase in magnitude as the additional scraping and main passage vortices deliver more mass flow and momentum to the main passage flow. The presented sequence is then repeated as the approach of the following blade adds momentum of the main passage flow.

A second analysis was performed to clarify the relation between these three magnitudes. For this one, the three signals were phase-locked averaged over a complete revolution phase. The resulting profiles maintain the same shape as observed in the filtered signals depicted in Fig. 11(a), indicating good repeatability throughout the test. The magnitude of the identifying features of a passing blade was represented against the number of blades to generate the blade row signatures of each quantity. Figure 13 portrays these profiles and the signal feature used to create them. Again, the magnitudes have been nondimensionalized as a percentage within their range. The relationship between the measured quantities is consistent and clear. The rotor gap and shroud pressure show a similar pattern. With increasing tip clearance, the shroud's minimum static pressure is higher. The heat flux exhibits an opposing trend to the other two. Lower tip rim pressures and tighter clearances pair with larger values on heat flux.

After adjusting the ideal capacitance-distance equation, a suitable formulation to describe tip clearance in turbomachinery has been presented. An optimization routine has been developed to generate a capacitance probe calibration curve with as few empirical clearance data as possible. The error on the resulting curve from the proposed algorithm validates the method's performance by featuring uncertainties of a few microns. This novel procedure imposes an experimental advantage over other calibration approaches. It reduces the number of clearance measurements required to only one, thus considerably shortening the test duration for this goal. Unsteady pressure and heat flux measurements along the shroud have shown a direct relationship with tip clearance. A time-resolved comparison of the three measurements reveals local extrema matching the squealer tip rims. A final phase-locked average analysis demonstrates the direct relationship between tip clearance and shroud static pressure, as well as the inverse relationship between the unsteady heat flux and the previous two quantities. This outcome is the foundation for solid correlations between tip clearance and the aerothermal magnitudes in the tip region. Prospective work entails defining such relationships and the uncertainty involved in the process. This future step would imply a milestone for engine testing, as various valuable data could be retrieved from a single simple measuring approach, such as pressure sensors.

The experimental procedures performed for this work included assistance on the experimental runs from the members of the STARR teams within the PETAL research group. (Lakshya Bhatnagar, Connor McQueen, and Diego Sanchez) as well as the project sponsor Rolls Royce members (Matthew Bloxham and Eugene Clemens). Additional recognition is given to Konstantin Huber from Hochschule Landshut for bringing ALTP sensors to the team and demonstrating their implementation.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

C =

capacitance

d =

tip clearance (distance)

d₀ =

reference measured clearance

E =

error function

$hrim$ =

rim height

R =

recess distance from probe to shroud surface

rpm =

rotational speed

S =

surface area

V =

voltage

V₀ =

reference measured voltage

$ϵ0$ =

vacuum dielectric constant

$ϵr$ =

medium relative dielectric constant