Comprehensive Experimental Assessment of Unsteady Pressure and Heat Flux in a Small-Core Turbine Over-Tip Shroud

Tip leakage flows in unshrouded turbines lead to high aerothermal penalties in the machine's performance. Pressure gradients across the blade tip drive hot flow from the main passage toward the tip region, increasing the heat loads in the blade tip and the over-tip shroud [1,2]. Within the blade tip region, additional thermal loads arise from air-to-surface friction [3] and pressure losses result from the interaction of the over-tip flows with pre-existing flow structures [4,5]. Eventually, the tip leakage flows exit the tip region, generating and feeding into the tip leakage vortex [6]. This represents another source of entropy due to viscous friction with the main passage flow [3]. Additionally, the development of this tip leakage vortex further influences the exit flow angle and, consequently, impacts the performance of downstream stages [7]. The tip clearance size plays a significant role in the formation and amount of leakage flow [8–11], and therefore influences the magnitude of these phenomena. These penalties become extremely relevant for small-core turbomachinery that feature short flow passage heights and low aspect ratios of blades and vanes. In this novel design configuration, the growth of any vortex toward the main passage generates higher levels of blockage that hinder the turbine efficiency [12]. Small core turbines with very tight clearances below 0.5 mm operate at higher rotational speeds [11,13]. Therefore, the shroud is subject to larger unsteady frequencies and small blade-to-blade tip clearance variations can have substantial effects on the machine [14].

To evaluate a design's performance under various tip clearance conditions, computational tools are often used to carry out unsteady flow simulations. The elevated difficulties and computational costs associated with performing high fidelity direct numerical simulation simulations are often grounds to perform lower fidelity Reynolds-averaged Navier-Stokes (RANS) simulations instead. However, its limitations in resolving unsteady detached and secondary flows in very tight clearance configurations [15,16], and the need for computational tool validation, justify the necessity of complementary experimental studies.

To identify the work processes taking place around the tip clearance region, several studies analyzed the adiabatic wall temperature and heat transfer coefficient. Thorpe et al. [17] related the decrease in temperature with the work extraction processes through the rotor passage. Their results revealed that the blade tip can perform work on the flow, opposing the work extraction of the rotor row, and increase the temperature above the turbine inlet total temperature. While some studies, such as those performed by Wheeler [18,19] and Krishnababu [20,21], demonstrate a significant influence between the clearance size and the aerothermal performance, other research only associated the variations in clearance with the aerodynamic signatures. Lavagnoli et al. [22] studied the Nusselt number and pressure field fluctuations and only the latter showed a direct correlation with tip clearance signatures. A slight match was observed with the adiabatic wall temperature only during spinning-up processes, indicating that blade-to-blade variability was likely generated by transient mechanisms only.

While past results were obtained in large scale, high aspect ratio turbine rigs, this paper presents high frequency measurements of the instantaneous tip clearance, unsteady shroud static pressure and heat flux of a small-core squealer-blade tip turbine configuration. The measurements are taken at engine-representative conditions at various pressure ratios and tip clearance sizes. The understanding of the flow field generated by the passing blades is obtained from the phase-resolved evaluation of the different parameters, and governing relationships are observed from the evaluation of the various blade row signatures.

The tests were performed in the pressure-driven wind tunnels of Purdue Experimental Turbine Aerothermal Lab (PETAL) [23], at Purdue University, schematized in Fig. 1. It features a storage capacity of 56 m³ of compressed dry air at 150 bar (∼2000 psi). Several lines exit from this supply to feed the experimental apparatus. A first supply line provides unheated air directly from the storage tanks. A second line passes through a heat exchanger within a natural gas air heater capable of heating the air to 1500 ′F. The hot and cold supplies are then mixed to obtain the desired air temperature conditions. The mixed flow goes through a calibrated critical venturi that provides an accurate measurement of the air mass flow. Downstream of the venturi, a set of fast actuation butterfly valves direct the flow either through a purge line discharging to the atmosphere, or toward the test section. Immediately upstream of the test section, the flow is conditioned in a settling chamber and equipped with a series of screens and honeycombs to deliver clean, homogeneous, and uniform flow conditions. Downstream of the test section, the air goes through a sonic valve. The flow area of the sonic valve can be adjusted, allowing the operator to set the downstream pressure of the test section, thus ensuring a steady pressure ratio across the test section in subsonic conditions.

The facility can be operated both in transient and steady modes at pressure ratios across the test section up to 6. The steady operation of the facility for more than 15 min allows studying the thermal equilibrium and the effect of thermal expansion on tip clearance size and, consequently, the effect of varying tip clearance at constant turbine operational conditions.

The empirical measurements were taken in the STARR test section (Small Turbine Aerothermal Rotating Rig), portrayed in Fig. 2. The STARR rig [24] is a small-core, two-stage high-speed turbine rig. The blade rows were equipped with squealer tips featuring a continuous rim all around the blade tip edge, as exemplified in the same figure. The aft end of the turbine shaft extends through the exhaust plenum and sonic valve and connects directly to a high-speed synchronous electric motor. The dyno has a motoring power of up to 100 HP, which is used to spin the turbine up to 3000 rpm to warm the bearings prior to flowing air. Once flow is established through the test section, the dyno has an absorption capability of 1 MW, enabling continuous loaded testing at speeds above 14,000 rpm.

The coupling of the STARR test section with the electric dyno allows setting different rotational speeds, and therefore tip clearance sizes, throughout the entire span of pressure ratios of the facility.

Several high frequency sensors were installed in a series of inserts mounted to the over-tip shroud at different circumferential locations as illustrated in Fig. 2. The inserts follow the shroud curvature and include an O-ring to prevent leakage around the insert. All the over-tip measurements were performed at an axial location equal to $x/c=0.51$⁠, c being the axial blade chord length.

Tip clearance was measured with Pseudo-Triaxial capacitance probes with a 2.5 mm electrode. The Fogale Capablade Fusion System [25] was used as the conditioning and acquisition system. This mainframe was equipped with six MC925 translational modules [26] and applied a 30 V/pF gain to the probes. All the acquisition was continuously performed at a sample frequency of 2 MHz, and the sensor calibrations were performed following the methodologies explained in Refs. [27] and [28].

The unsteady static pressure at the over-tip shroud was acquired with Kulite miniature pressure transducers. Sensor models XCE-062-100A and XCE-062-50A [29] were used on stage 1 and 2, respectively. A Precision Filter Kulite Conditioner model 10,177 [30] output independent static and dynamic signals for each input Kulite sensor. These are obtained by applying a Butterworth low-pass filter with $f−3 dB=322 Hz$ and a high-pass filter of the same type with $f−3 dB=160 Hz$ to each input Kulite signal. The outputs of the conditioning system were recorded by a Genesis GEN2tB Transient Recorded and Data Acquisition System [31]. This was equipped with two GN8101B cards [32] for independent low and high frequency acquisitions. All the measurements were performed at 1 MHz, applying an additional digital low-pass filter with $f−3 dB=250 KHz$ to both readings.

The unsteady heat flux was measured with an Atomic Layer Thermopile (ALTP) [33]. The sensor sensitivity was 31 uV/W/cm², and an amplifier provided a ×200 gain to the sensor output. A Picoscope 5442D MSO [34] recorded the amplified signal at a rate of 2 MHz without any additional filtering.

For blade identification and tracking, all the measurements were triggered by a once-per-revolution signal provided by a Shimpo MCS-655M Retro-reflective Speed sensor [35]. This sensor was installed at top dead center (TDC) (0 deg ALF circumferential location) facing a photoreflective tape in the shaft, providing a square wave between 5 V and 1 V during rotation. The tachometer signal was also recorded by the three mentioned acquisition devices.

To evaluate the influence of tip clearance, it is necessary to analyze different clearances at the same operating conditions and the same clearance at different operating conditions. This can be achieved due to the versatility of the facility. The turbine can be operated at a single rotational speed with different operating conditions as well as multiple rotational speeds for a given operating setpoint. For any combination of rotational speed and operating conditions, the high frequency instrumentation can be used to identify the impact of the blade-to-blade tip clearance variation on the local flow field. Additionally, tip clearances can be changed without modifying rotational speed or the operating condition through the thermal expansion of the blades and casing. These approaches help to isolate the effects of the thermal and mechanical stresses on the running tip clearance and provide insight into the impacts of the running clearance on the local flow field.

This array of test points allows the study of the same running clearance at different operating conditions, and the impact of the rotational speed on the running clearance at various operating conditions. In addition, run B included 10 min of dwell time at the nominal equivalent speed. This served as a temperature equilibrium test, where any observed change in tip clearance was attributed to thermal expansion of the blades and the shroud. This data addresses the scenario where the running tip clearance is changed while the turbine operating conditions and rotational speed are kept constant. It should be noted that the tip clearances can also be changed by swapping blade tracks, but this requires a new rig build and was outside the scope of the present study.

The high frequency data were phase-locked averaged (PLA) over the revolution period to retrieve the periodic physics. The PLA routine used was based on the instantaneous frequency estimation algorithm presented by Urbanek et al. [37]. This type of time-synchronous averaging was chosen over traditional low pass filtering to avoid the damping effects of small signal features and filtering artifacts as illustrated in Fig. 4. A preliminary recorded signal (top) was low pass filtered with a cutoff frequency ten times the blade passing frequency (BPD) (center). In the bottom figure, the data were phase-lock averaged, including more than 1500 revolution in the averaging. From this comparison, it is evident that the filtered results capture the general trend but fail to maintain the small details that characterize the flow physics.

Recording and including a minimum of 1000 revolution in the PLA reduces the standard error of the mean by two orders of magnitude. Table 1 provides the mean standard deviations and standard error on the means for the three measurements of interest. The largest values are observed in the heat flux signals, although they are still two orders of magnitude lower than the averaged signal. Therefore, the remaining data point plots of this paper do not include visible error bands.

Blade one was defined as the first entire blade at TDC after the tachometer trigger signal. The remaining blades are identified sequentially as they pass through TDC, that is, opposite to the spin direction.

An example of the resulting alignment is displayed Fig. 5(a). From top to bottom, this figure provides the signals of the voltage reading from the tip clearance measurements, the unsteady static pressure and heat flux. The magnitudes have been nondimensionalized as a fraction of the min and max measurements in the data window. The 95% confident interval constructed as two standard deviations is also provided.

Figure 5(b) provides an augmented view of the aligned signals for three blade phases. The location of the suction and pressure side rims are clearly identified from the local maximum featured by the capacitance probe recording. This allows the identification of characteristic values associated with these locations and retrieval of the blade row signature.

As presented in the top plot of Fig. 6, the slight blade-to-blade clearance variations results in a characteristic profile in the clearance for the entire row of blades, identified in this text as row signature. To analyze the clearance influence in the measured aerothermal properties, additional row signatures are constructed with characteristic magnitudes observed from the mutually aligned signals. Identified in Fig. 5(b), these are the magnitudes at the pressure and suction side rims, as well as the relevant feature found in the flow passage: a local maximum in the static pressure and a local minimum in the heat flux. These last ones are used to analyze whether the tip clearance has any influence on the midpassage flow in addition to the over tip flows. Figure 6 also exemplifies the row signatures for the pressure side rim at several equivalent rotational speeds.

The magnitudes in this plot are expressed as a differential value to show the variation with the increasing operational speed. It is observed that the blade rows provide a characteristic signature profile. This signature is generally consistent for every condition, allowing a robust analysis of the features of interest.

Figures 5 and 6 provide a preliminary understanding of the overtip flows. The former provides time-resolved results. Starting from the main passage toward the pressure side of the blade, the shroud’s static pressure gradually decreases, identifying a flow acceleration toward the blade tip. The progressively increasing flow speed also results in an enhancement in convective heat flux with the shroud, with a peak value localized at the bladés pressure side rim, where the static pressure is minimum. This agrees with the simulations and observations performed by Ameri et al. [38], Lee et al. [39] and Bunker et al. [40] The flow then undergoes an expansion and deceleration after the first rim, reflected in a decrease in convective heat transfer. Within the tip cavity, several interactions of the leakage flow and pre-existing flow structures lead to some oscillations in both studied magnitudes as reported by Zou et al. [41], Maesschalk et al. [42], and Mischo et al. [4]. The flow eventually exits the tip region feeding into the tip leakage vortex. At this location, the static pressure gradually increases toward the main passage. Oppositely, the heat flux experiences a sudden reduction prior to the gradual increase toward the following blade tip. This sudden local drop in heat flux hints at an abrupt change of adiabatic wall temperature as previously observed by Lavagnoli et al. [22].

Figure 6 reveals that the increasing rotational speeds results in tighter tip clearances due to the larger mechanical loads on the blades. In this transition, the static pressure at the pressure side rim doesn’t show the same trend, as it increases when speeding up to 90% equivalent speed and decreases afterwards. The heat flux also features a different pattern than the tip clearance, but it opposes the behavior of the heat flux: it shows a decrease for the first speed transition and then it increases for the remaining two conditions.

A deeper analysis of all the magnitudes is performed in Secs. 4.1–4.5, identifying the potential governing relationships.

To evaluate a potential dependance with tip clearance, it is necessary to analyze first the variation of this parameter at the various performance points. This is provided in Fig. 7. The left plot shows the variation in tip clearance referenced to the minimum value measured. Each dataset contains all the blades clearances at a 130 deg ALF circumferential location measured at the respective operating equivalent speed ratio.

The increasing mechanical loads result in a difference close to 100 microns between the slowest and the overspeed conditions. The difference in clearance between runs results from the operating history. Runs A and B were performed consecutively in the same test; therefore, the undergoing thermal expansion of blades during the first run is noticeable in the slightly lower clearances featured in run B. The right plot provides the evolution of the clearance during the temperature equilibrium test after run B. It is apparent that the thermal expansion of the casing widens the clearance size over time, reaching a total increase of 10 microns. Run C and D were also performed within the same tests. In this case, the larger pressure ratios require higher operating temperatures to match the equivalent speed. The earlier thermal strains are observed from the tighter clearances than run A and B. Additionally, the shroud thermal expansion is also noticeable in run D.

The time-resolved shroud's unsteady pressure at the different operating conditions is provided in Fig. 8. Each plot corresponds to the different operating pressure ratios, and the magnitudes are normalized with the shroud's static pressure at the entrance of the rotor row (between stator and rotor) Two blade phases are illustrated, with the various equivalent speeds in different colors.

For all the conditions, increasing rotational speeds results in larger flow speeds and consequently a decrease in static pressure. Oppositely, the increase of pressure ratio within the tip region for increasing rotational speed indicates a potential dependance with tip clearance that needs to be further investigated.

The bottom plot corresponds to the temperature equilibrium dwell time. A slight decrease in magnitude is observed from the local maximum in the main passage to the suction side tip rim of the previous blade. This also suggests a dependance with the variation in clearance.

An additional unsteadiness is revealed as a series of small oscillations throughout the entire signal for all conditions tested. These are more evident within the tip region and the pressure side region of the main passage. No reference to these trends was found in the previous studies, and without explicit reaction to the different operating conditions, no influence of tip clearance is inferred in this behavior. However, being that these profiles are a result from the phase-lock averaging over more than 1000 revolutions, it is suspected that these oscillations represent a real physical phenomenon related to the tight running clearances and high rotational speeds of the small-core turbine.

The homologous analysis performed for the convective surface heat flux measurements is provided in Fig. 9. At the pressure side rim, increasing the equivalent speed results in local heat flux enhancement. This is common for all the runs except for run A, where the trend is the opposite. Considering the lower operating pressure ratio of this condition, the resulting decrease of heat flux is explained by a reduction of leakage mass flow as the clearance tightens. The same enhancement behavior is noticed in the suction side rim. However, it is observed that the values at 110% equivalent speed are lower than at nominal speed, which can also be explained by a reduction of over-tip mass flow at the overspeed condition.

The tip cavity profile shows an evolution with the turbine pressure ratio operating condition. Run A presents one local maximum in this region regardless of the equivalent speed. This extremum shifts toward the suction side rim in run B, and is no longer present in run C. The mismatch between these profiles and the previous surface pressure signals indicates that the mechanisms that govern the heat transfer are dependent on the operating pressure ratio, whereas the heat flux magnitude itself is influenced by clearance size.

The local minimum in the suction side is observed to differ between runs. For all tests, the location shifts toward the suction side with increasing speed. However, run A shows a larger magnitude with increasing speed, run B is steady, and runs C and D decrease. These trends suggest the existence of some compressibility effect being performed by the moving blade on the forward flow, as extensively discussed by Thorp et al. [43].

The temperature equilibrium case displays a general positive shift of the heat flux. Two effects contribute to this phenomenon. First, upstream temperature equilibrium reduces the upstream heat losses, therefore the flow has more energy at the measuring location and the heat flux therefore increases. Second, tip clearance widens, allowing more leakage flow and an enhancement in heat flux.

Therefore, the adiabatic convective heat transfer coefficient is found as the slope of the linear fit, and the adiabatic wall temperature is retrieved at null heat flux.

The temperature equilibrium study at the end of run B was used to determine the adiabatic wall properties as constant operating conditions were maintained and the clearance increase is minimum as presented earlier in Fig. 7. Therefore, the flow properties can be assumed constant in this period and the only variable is the shroud temperature.

In this formulation, $kair$ is the thermal conductivity of air, and the local characteristic length was chosen to be the local hydraulic diameter $Dh(φ)$⁠, whose values are in very close proximity to the local clearance. With this selection, the characteristic length drastically changes between the flow passage, the blade tip rims and blade tip cavity. The large changes in this magnitude result in local Nusselt values of different orders of magnitude, as shown by the logarithmic scale on the y-axis of the corresponding plot in Fig. 10(c).

The adiabatic wall temperature (the driving temperature) features a sudden drop right before the suction side of the incoming blade, matching the expansion and recirculation of the tip leakage vortex. The amount of expansion in this location results in driving temperature values below the shroud wall temperature, reversing the heat flux direction and producing a cooling work from the airflow to the shroud. Toward midpassage the driving temperature rises gradually above the wall temperature and heat is transferred back toward the shroud. The enhancement in heat transfer in the tip region follows the increase of the driving temperature in this area. The adiabatic wall temperature doesn't display values above the turbine inlet total temperature, opposing elevated compressive work levels reported in Refs. [22,43]. This disagreement suggests that the passage of small-core small aspect ratio turbines is highly influenced by the developed detached secondary flows.

The adiabatic heat transfer coefficient also features localized larger values within the tip region, indicating a different flow field than the main flow passage. Local maximums are observed matching the tip rims, the locations of tightest clearance and peak flow speed. The oscillations of this coefficient within the cavity correspond to the different flow expansions and recirculation regions.

Excellent match was found by assuming a fully developed flow around 90% of the blade chord, agreeing with the results provided by Solano et al. [48]. Within the tip region, no correlation in the open literature was found to provide a good match with the obtained results, although the values agree with the tip measurements of some previous studies [49]. This indicates the presence of highly complex flow structures within squealer tips.

The profiles of the different contributions are displayed in Fig. 11 and their influence into the overall heat flux and overall unsteady heat flux is indicated in Table 2. The magnitude of the unsteady components contributes to almost half of the overall heat flux. This is seen in the normalized profile shown in Fig. 11, depicting the unsteady component to periodically oscillate between −150% and 150% of the steady value. Within the unsteady heat flux, the changes in the adiabatic wall temperature display the largest influence, accounting for one-third of the overall heat flux processes. Variations in the boundary layer represent almost 20% of the overall unsteady heat flux. The lowest contribution is displayed by the $qh&T′$ term, also included in the lowest plot of Fig. 11, with an influence of only 3.5% of the total heat transfer processes.

To evaluate the limitations of commonly used computational tools, RANS simulations were performed for the turbine geometry and compared against the empirical measurements. Computational fluid dynamics (CFD) simulations of the entire 2 stage turbine were performed using ANSYS Fluent 2023R2. The experimentally obtained tip gap height was used in the CFD model. The mesh, represented in Fig. 12(a), was generated using the embedded meshing tool in Fluent. An unstructured polyhedral mesh in the core and prism layers at the wall was generated securing a y+ value strictly below 1. A mesh convergence study was executed to identify a sufficient resolution of the core mesh. The tip mesh has at least 44 cells in radial direction at any location of the tip. The k − ω shear stress transport turbulence model was applied. The boundary conditions for inlet turbulence intensity, total inlet temperature, and total inlet pressure, as well as the static outlet pressure were set in accordance with the experimental values for the run B dwell time.

Figure 12(b) displays the computational and experimental results for the shroud surface convective heat flux normalized by the respective means. The location of the blade tip in the predictions was returned by the computational tool and aligned with the experimental measurements. Two sets of computational results are provided: one at the axial chord location matching the experimental measurements and a second set resulting from its averaging over the ALTP sensor measuring area. There is good agreement between the results in the main passage region. A heat flux reduction is experienced near the suction side and progressively increases toward the pressure side. The predicted peak heat flux is located at the entrance of the pressure side rim, coinciding with the maximum pressure drop rate. Although the measured peak heat flux is lower than the computational punctual result, very good agreement is observed when compared against the area averaged prediction. However, the experimental maximum is found further into the blade rim, suggesting the existence of a vena contracta as reported by Moore et al. [8], Lee et al. [39], and Ameri et al. [2]. Within the blade cavity, the simulations infer a larger flow deceleration and heat flux reduction prior to the suction side rim, where a local maximum is again predicted. This trend is observed also in the area-averaged results at a lower rate. The experimental results indicate a lower flow deceleration and a more progressive reduction toward the suction side rim. This mismatch suggests a limitation of the computational tool to precisely resolve the complex detached flows within the cavity region and evidences the necessity for the complimentary experimental data.

The blade row signatures provide a first analysis on a potential tip clearance influence. This is illustrated in the top three plots of Fig. 13, providing the normalized pressure values at the main passage, suction, and pressure side rim. As aforementioned, the pressure in the main passage decreases with increasing rotational speed, whereas the values at the blade tip rims increase. The conservation of the signature profile at every location and condition indicates that the tip clearance influences the pressure field both within the blade tip and the main passage regions.

Negative values indicate lower pressure at the pressure side rim than the suction side rim, indicating flow acceleration from the main passage toward the pressure side rim and over-tip flows from the pressure side toward the suction side. Oppositely, positive values result from pressures in the pressure side rim above the magnitude on the suction side rim, and therefore higher flow speeds in the latter location. This scenario indicates the existence of reverse over-tip flows from the suction side toward the pressure side. The bottom plots of Fig. 13, exemplify these row signatures for the runs of lowest and highest operating turbine pressure ratio (runs A and D). In run A, only the slowest equivalent speed features negative pressure ratios. As the equivalent speed increases and the clearance decreases, the pressure ratios become positive and barely change with increasing speed. In the case of run D, lower values are experienced at the slowest speed, increasing with higher spin, and positive pressure ratios are only displayed at the largest equivalent speed and at some blades at nominal speed. Therefore, it is inferred that for a given operating turbine pressure ratio, there exists a clearance threshold below which the over-tip flow structures change, and reverse over-tip flows are experienced as predicted by the simulations of Andreoli [51] and de-Maesschalck [11].

For this Reynolds definition, the tip clearance (C) was considered a better choice for the characteristic length than the blade tip radius as it is more realistic representation of the flow within the tip clearance. As portrayed in Fig. 14 (left), well-defined clusters for each equivalent speed linearly increase with tighter tip clearance. A linear fit through each group allows computing the transitional Reynolds. This threshold is represented against the equivalent speed in Fig. 14 (right). The revealed linear dependance between these two parameters provides a solid reference for turbine design, providing knowledge on the leakage flow structure from the rotational tip Reynolds.

The same analysis approach was used to investigate heat flux dependances on tip clearances. The top three plots of Fig. 15 illustrate the heat flux signatures referenced to the absolute minimum measured for the key local features. While these plots seem to maintain comparable signatures at different speeds, it isn't as remarkable as the previous pressure signatures, indicating only a partial influence of tip clearance on the different magnitudes. An additional relevant outcome from these plots is the position of the outlaying feature. This one corresponds to blade 4 on the pressure side and suction side and blade 3 in the passage signature (recall that the passage feature was grouped with the forward blade). This shift indicates that the magnitude of the sudden decrease in heat flux at the suction side tip is dependent on the clearance of such blade tip and not on the forward blade clearance like the pressure profile.

The peak heat flux in the blade tip is then evaluated against the rotational tip Reynolds. Figure 15 illustrates again the lowest and highest-pressure ratio runs (A and D). Like the pressure analysis, each equivalent speed displays a defined bundle. However, increasing speed doesn't result in a common shift for both sets of data. Within each speed ensemble, a positive linear relationship is discerned with the tip rotational Reynolds. The low slopes of these trends indicate an existing, but low contribution of tip clearance in the determination of the heat flux magnitude.

A deeper knowledge of tip clearance influence is obtained by analyzing its relationship with the different unsteady heat flux components as portrayed in Fig. 16. Figure (a) identifies the characteristic features being studied for each contribution (pressure and suction side rims, and the location of local minimum of heat flux prior to the suction side). Figure (b) provides the evaluation against the tip clearance. This figure only contains data for the dwell time postrun B as only this one allowed retrieving the unsteady heat flux components. The results reveal linear trends between the overall unsteady heat flux and the tip clearance value for the tip region (pressure and suction side rims). It is observed that the heat flux due to boundary layer variations and the unsteady term $haw′TAw′$ show constant values regardless of the clearance size. The tip clearance shows the largest influence on the adiabatic wall temperature unsteady heat flux. These results show a reduction of unsteady heat flux in the pressure side rim with decreasing clearance, and an opposing trend in the suction side rim. The values of heat flux upstream to the suction side show no correlation with the tip clearance, resulting in a homogeneous range for the entire span of clearances. These behaviors again agree with the transition to reverse over-tip flows and reductions in leakage flow with smaller clearances predicted in Refs. [11] and [51].

A final study is performed to investigate potential relationships between the measured static pressure fields and convective heat flux. To that end, a first analysis was performed between the unsteady heat flux components and the blade tip pressure ratio as computed per Eq. (14). The results are displayed below in Fig. 17, indicating again in the left the signal features being evaluated. The linear trends observed in the overall unsteady heat flux indicate an increase in heat load in the suction side rim and opposing decay in the pressure side rim for increasing pressure ratio. Again, this trend supports the existence of reverse flow structures as more positive pressure ratios result in larger overtip flow speeds in the suction side compared to the pressure side. No additional dependance is noticeable between the local minimum prior the suction side with tip pressure ratio.

A second analysis was performed to investigate a potential governance between the static pressure and the adiabatic heat transfer coefficient contribution, as small oscillations where observed in both (visible in Fig. 8 for the static pressure and the bottom plot of Fig. 11 for the heat flux component). To the best of the author's knowledge, this phenomenon has not been reported in the open literature. A frequency analysis was performed to assess the potential correlation between both effects. As the PLA only returns features that are periodic to the averaging period, the presence of these oscillations indicates a phenomenon that is a harmonic of the blade passing frequency. Figure 18(a) provides superimposition of the pressure signal and the unsteady component $qh′$⁠. Figure 18(b) presents the frequency components for both signals, where the x-axis has been normalized by the blade passing frequency to return the harmonic numbers, and the y-axis is expressed in decibels. Aside from the BPD, the frequency content of the heat flux contribution is always larger than the harmonic contributions of the pressure signal. It is noticed that the harmonics 9 and 10 display very similar contribution for both signals, and these numbers match the number of oscillations counted within the blade periods displayed in Fig. 18(a). However, this match does not display any predominant weight with respect to the remaining harmonics. Consequently, it is not possible to assure a robust correlation between the high-frequency low-magnitude components observed in the static pressure and the studied heat flux component.

This paper has presented a comprehensive experimental assessment of the shroud's unsteady static pressure and heat flux for a small core squealer-tip-blades turbine. A suitable facility and test section allowed performing the empirical measurements at engine representative conditions of pressure ratio, equivalent speeds, and tip clearance values. The proper phase-lock averaging of all the measurements allowed retrieving the true periodic physics behind each magnitude with standard errors of the mean below 0.35% of the measured value.

The evaluation against the computational simulations has evidenced the necessity of complimentary experimental data to validate the performance of unsteady simulations in resolving highly detached flows in low aspect ratio turbomachinery.

The obtained results have revealed a large influence of the tip clearance size in the over-tip flow characteristics. A direct relationship has been observed between the rotational tip Reynolds and the pressure ratio through the tip clearance region. It has been evidenced that for a given equivalent rotational speed, there is a critical tip Reynolds, and therefore clearance, below which reverse over-tip flows are experienced.

The analysis of the shroud's unsteady heat flux revealed an outstanding contribution of the unsteady terms into the overall over-tip shroud heat flux, amounting to almost 45% of contribution. Within the unsteady heat flux components, a large dominance was noticed from the variations in the adiabatic wall temperature, resulting in 1/3 of the total influence on the overall heat flux. Posterior analysis revealed that tip clearance size has a direct influence on the enhancement of this specific unsteady heat flux component within the tip region.

Final inspections between the shroud's static pressure and heat flux supported the existence of reversed over-tip flows resulting in heat load enhancement in the suction side rim and reduction in the pressure side rim.

All the empirical work presented in this text was assisted by the members of the STARR team within the PETAL research group as well as the project sponsor Rolls Royce members, Matthew Bloxham and Eugene Clemens, who provided guidance and insightful discussion on the several findings.

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

C =

tip clearance

$Dh$ =

hydraulic diameter

$haw$ =

adiabatic convective heat transfer coefficient

N =

rotational speed

$Nrevs$ =

number of revolutions

$Nsamples$ =

number of samples

$Nu$ =

Nusselt number

$Nuz$ =

circumferential local Nusselt number

$Nu∞$ =

fully developed flow Nusselt number

$N¯$ =

equivalent rotational speed

P =

static pressure measured signal

$PPASS$ =

maximum static pressure in the flow passage

$PPS$ =

static pressure at the pressure side rim

$PSS$ =

static pressure at the suction side rim

$P2,Stg1$ =

static pressure between vane and blade in Stg1

$PRT−S$ =

total-to-static turbine pressure ratio

$Q˙$ =

heat flux

R =

ideal gas constant

$Rshroud$ =

shroud radius

$Rtip$ =

tip radius

$ReTIP$ =

rotational Reynolds number at the blade tip

$Taw$ =

adiabatic wall temperature

$Twall$ =

wall temperature

$T0$ =

total temperature

$VC$ =

tip clearance voltage signal

x =

axial location

$γ$ =

specific heat ratio

$ΠTIP$ =

static pressure ratio across the blade tip

$σ$ =

standard deviation

$φ$ =

phase

$Ω¯$ =

equivalent rotational speed ratio

Acronyms

ALF =

aft looking front

CFD =

computational fluid dynamics

PLA =

phase-locked average

RANS =

Reynolds averaged Navier–Stokes

SEM =

standard error on the mean

TDC =

top dead center