In the present work URANS simulations are presented to describe the unsteady interaction process between the flow ingested/ejected from a cavity system and the main flow evolving into a Low Pressure Turbine stage. Particular care is posed on the analysis of the loss generation mechanisms acting outside the stator row and in the rear part of the axial gap separating the cavity flow ejection section and the leading edge plane of the downstream rotor row. The simulated geometry reproduces a typical engine cavity configuration, with upstream and downstream rotor rows reproduced by means of moving bars. Experimental results have been used to validate the simulations. This experimental data cannot explain and quantify alone the overall interaction process between the cavity flows and the main flow. The results of a simulation made by removing the domain of the cavity have been employed in order to better highlight and quantify the effects due to main flow and cavity flows interaction on total pressure loss. A deep inspection of the loss amount along the axial direction makes evident that losses generated in the vane row are basically increased prior to enter into the downstream rotor bars, due to cavity main flow interaction.

The present paper discusses the results of a large experimental data set describing transitional boundary layers. Time resolved Particle Image Velocimetry (PIV) measurements have been adopted to survey the boundary layer developing over a flat plate under prescribed adverse pressure gradients typical of turbomachinery components. The tests have been performed while varying the pressure gradient, the Reynolds number and the inlet free-stream turbulence intensity (FSTI). Two exemplary cases, referring to bypass and separated flow transition, are discussed by means of principal axis analysis and proper orthogonal decomposition (POD). The POD is used to provide statistical representation of the flow structures and to compute the turbulence production (i.e., the mean flow energy dissipation) due to the dynamical features observed for the different transition types. Reduced order model representations of the flow field are provided and their contribution to the total turbulence kinetic energy production is isolated. This analysis is closed by the inspection of the eigenvectors of the strain rate and Reynolds stress tensors. For the separated flow case, it is shown that the eigenvectors of strain rate and shear tensor are almost perfectly aligned downstream of the maximum displacement of the bubble. The reduced order model reconstruction of the Kelvin-Helmholtz shed vortices provides the largest part of the overall TKE production. For the high FSTI induced transition, the eigenvectors of the shear and stress tensors do not have the same direction. The loss generation is related to the local maximum Reynolds normal stress in the streamwise direction, induced by the boundary layer streaks and their breakdown.

In the present work, Proper Orthogonal Decomposition (POD) has been applied to a large dataset describing the profile losses of Low Pressure Turbine (LPT) cascades, thus allowing: i) the identification of the most influencing parameters that affect the loss generation; ii) the identification of the minimum number of requested conditions useful to educate a model with a reduced number of data. The dataset is constituted by the total pressure loss coefficient distributions in the pitchwise direction. The experiments have been conducted varying the flow Reynolds number, the reduced frequency and the flow coefficient. Two cascades are considered: the first for tuning the procedure and identifying the number of really requested tests, and the second for the verification of the proposed model. They are characterized by the same axial chord but different pitch-to-chord ratio and different flow angles, hence two Zweifel numbers. The POD mode distributions indicate the spatial region where losses occur, the POD eigenvectors provide how such losses vary for the different design conditions and the POD eigenvalues provide the rank of the approximation. Since the POD space shows an optimal basis describing the overall process with a low rank representation (LRR), a smooth kernel is educated by means of Least-Squares method (LSM) on the POD eigenvectors. Particularly, only a subset of data (equal to the rank of the problem) has been used to generate the POD modes and related coefficients. Thanks to the LRR of the problem in the POD space, predictors are low order polynomials of the independent variables (Re, f + and ϕ). It will be shown that the smooth kernel adequately estimates the loss distribution in points that do not participate to the education. Additionally, keeping the same steps for the education of the kernel on another cascade, loss distribution and magnitude are still well captured. Thus, analysis show that the rank of the problem is much lower than the tested conditions, and consequently a reduced number of tests are really necessary. This could be useful to reduce the number of hi-fidelity simulations or detailed experiments in the future, thus further contributing to optimize LPT blades.

A flat plate boundary layer has been surveyed by means of time-resolved particle image velocimetry (PIV) under variable Reynolds number (70000 < Re < 150000) and turbulence intensity level (1.5% < Tu < 2.5%). The PIV visualizations were completed in two measuring planes, that are oriented both normal and parallel to the wall. For the wall-parallel configuration, the measuring plane is located inside the boundary layer. The PIV data were post-processed by applying Dynamic Mode Decomposition (DMD), which provides frequency based modes and their corresponding growth rate. The effects of Re and Tu variation on the amplification of the dominant wavelength within the separated shear layer, which is responsible for transition, is the main subject of the present work. The DMD modes and related eigenvalues were computed with reference to the main streamwise coordinate. This allowed discussing the effects due to the main flow parameters on the amplification of the dominant streamwise wavelengths within the separated shear layer (Kelvin-Helmholtz modes). The growth of such streamwise modes ends with the formation of large scale vortices, whose breakup forces transition. In order to obtain the effective distribution of the maximum growth rate of fluctuations at different locations and times, the DMD domain was continuously extended in the streamwise direction, accounting for a specified number of periods characterizing the large scale K-H vortices. In order to reduce the time-space dependent results obtained by the DMD procedure, a probability density function of the most unstable wavelength and the corresponding growth rate has been computed. For the present data set, the spatial growth rate of fluctuations is found to increase at the higher Reynolds number, while it slightly reduces with increasing the Tu level. The procedure and findings discussed in this work shall be suitable for designing active control systems, such as harmonic blowing for separation control.

The boundary layer developing over the suction side of a low pressure turbine cascade operating under unsteady inflow conditions has been experimentally investigated. Time-resolved Particle Image Velocimetry (PIV) measurements have been performed in two orthogonal planes, the blade to blade and a wall parallel plane embedded within the boundary layer, for two different wake reduced frequencies. Proper Orthogonal Decomposition (POD) has been used to analyze the data and to provide an interpretation of the most significant flow structures for each phase of the wake passing cycle. To this purpose, a POD based procedure that sorts the data synchronizing the measurements of the two planes has been developed. Phase averaged data are then obtained for both cases. Moreover, once properly sorted, POD has been applied to sub-ensembles of data at the same relative phase within the wake passing cycle. Detailed information on the most energetic turbulent structures at a particular phase are obtained with this procedure (called phased POD), overcoming the limit of classical phase average that just provides a statistical representation of the turbulence field. Furthermore, the synchronization of the measurements in the two planes allows the computation of the characteristic dimension of boundary layer structures that are responsible for transition. These structures are often identified as vortical filaments parallel to the wall, typically referred to as boundary layer streaks. The largest and most energetic structures are observed when the wake centerline passes over the rear part of the suction side, and they appear practically the same for both reduced frequencies. The passing wake forces transition leading to the breakdown of the boundary layer streaks. Otherwise, the largest differences between the low and high reduced frequency are observed in the calmed region. The post-processing of these two planes further allowed us to compute the spacing of the streaks and make it non-dimensional by the boundary layer displacement thickness observed for each phase. The non-dimensional value of the streaks spacing is about constant, irrespective of the reduced frequency.

In the present work the profile losses of a highly loaded low pressure turbine cascade, operating under realistic unsteady conditions, have been measured for different incoming wake parameters. A moving bar system has been used for wake generation, allowing the variation of bar diameter, bar count and axial gap between the bars and the cascade leading edge. The overall test matrix spans three different bar diameters, three different reduced frequencies and two axial gaps, for a total of 18 different conditions tested. For each of them, the time-dependent cascade inflow has been characterized by means of phase-locked hot-wire measurements in order to determine the effects of the wake parameter modification on the turbulence intensity peak and on the incoming wake momentum deficit, that are well known to affect the generation of losses in the downstream cascade. The procedure recently developed by the authors based on the simultaneous acquisition of the signals of two kiel probes, located upstream and downstream of the cascade, has been used to accurately quantify the profile losses for each condition, identifying the contribution due to the wake bowing, tilting and dilation process into the cascade channel and that due to the wake-boundary layer interaction. Additionally, Proper Orthogonal Decomposition (POD) has been applied to the ensemble data matrix constructed from the loss coefficient distributions in the pitchwise direction, measured for the different conditions, with the aim of highlighting the loss trend vs the design space parameter variation. The POD modes obtained from the cross-correlation matrix provide a direct information on the flow region where losses are prevalently produced, while the corresponding POD coefficients give the weight of each parameter in the loss generation. The paper shows the potentiality of this procedure in providing a rapid identification of the main causes of losses, and the dominant parameter affecting the process of loss generation.

The paper presents an experimental data base on transitional boundary layers developing on a flat plate installed within a variable area opening endwall channel. Measurements have been carried out by means of time-resolved PIV. The overall test matrix spans 3 Reynolds numbers, 4 free-stream turbulence intensity levels and 4 different flow adverse pressure gradients. For each condition, 16000 instantaneous flow fields have been acquired in order to obtain high statistical accuracy. The flow parameters have been varied in order to provide a gradual shift of the mode of transition from a bypass process occurring with mild adverse pressure gradients at high free-stream turbulence, to separated flow transition, occurring with low Reynolds number, low free-stream turbulence intensity and elevated adverse pressure gradient. In order to quantify the influence of the flow parameter variation on the boundary layer transition process, the transition onset and end positions, and the turbulent spot production rate have been evaluated with a wavelet based intermittency detection technique. This post-processing technique is in fact able to identify the vortical structures developing within the boundary layer, the intermittency function is then automatically evaluated for each tested condition counting the number of such structures and defining the cumulative probability function. The by-pass transition mode has the longest transition length that decreases with increasing the Reynolds number. The transition length of the separated flow case is smaller than the by-pass one, and the variation of the flow parameters has a similar impact. Similarly, the dimensionless turbulent spot production rate reduces when the Reynolds number is increasing. The variation of the inlet turbulence intensity has a small influence on this parameter except for the condition at the highest turbulence intensity, that always shows the lowest turbulent spot production rate because a by-pass type transition occurs. This large amount of data has been used to develop new correlations used to predict the spot production rate and the transition length in attached and separated flows.

Experimental data describing laminar separation bubbles developing under strong adverse pressure gradients, typical of Ultra-High-Lift turbine blades, have been analyzed to define empirical correlations able to predict the main features of the separated flow transition. Tests have been performed for three different Reynolds numbers and three different free-stream turbulence intensity levels. For each condition, around 4000 Particle Image Velocimetry (PIV) snapshots have been acquired. A wavelet based intermittency detection technique, able to identify the large scale vortices shed as a consequence of the separation, has been applied to the large amount of data to efficiently compute the intermittency function for the different conditions. The transition onset and end positions, as well as the turbulent spot production rate are evaluated. Thanks to the recent advancements in the understanding on the role played by Reynolds number and free-stream turbulence intensity on the dynamics leading to transition in separated flows, guest functions are proposed in the paper to fit the data. The proposed functions are able to mimic the effects of Reynolds number and free-stream turbulence intensity level on the receptivity process of the boundary layer in the attached part, on the disturbance exponential growth rate observed in the linear stability region of the separated shear layer, as well as on the nonlinear later stage of completing transition. Once identified the structure of the correlation functions, a fitting process with own and literature data allowed us to calibrate the unknown constants. Results reported in the paper show the ability of the proposed correlations to adequately predict the transition process in the case of separated flows. The correlation for the spot production rate here proposed extends the correlations proposed in liter-ature for attached (by-pass like) transition process, and could be used in γ–Re ϑ codes, where the spot production rate appears as a source term in the intermittency function transport equation.

A new rig has been designed and commissioned at the University of Genova to study the flow field within a turbine interstage cavity and its interaction with the main flow path. The rig is a large scale one-and-half stages, rotating test facility, opportunely designed to reproduce the main features characterizing the cavity flows developing in real low pressure modules of turbogas engines. The effects due to swirl factor and the coolant injected into the cavity to prevent the thermomechanical failure of the disks have been investigated. The rig allows the evaluation of the leakage mass flow rate and the measurement of the seal discharge coefficient in the different operating conditions, as well as the characterization of viscous, rotational and coolant related effects on the main flow path, especially in terms of secondary flow structures and vane row efficiency. Pressure signals acquired into the cavity provide a direct measure of the pressurization level of the fore and rear cavities, as well as the analysis of the effects induced by rotation and coolant flow on the pressure drop provoked by the teeth. Results clearly show that once the cooling flow rate reaches a datum threshold level an iso-pressure condition (with respect to the main flow at the vane leading edge) is established into the fore part of the cavity, and the gas ingestion from the main annulus is avoided. This “purged” condition significantly modifies the near wall flow developing across the vane. The boundary layer entering the vane row is not sucked into the cavity, and simultaneously at the vane exit plane there is poor interaction between the cavity flow and the near wall flow leaving the vane. Total pressure measurements upstream and downstream of the vane clearly highlight the modification of the secondary flow structures for the different conditions tested. Overall, results reported into the paper demonstrate the capability of the new rig to provide a direct estimation of the discharge coefficient of a realistic turbine cavity system for different coolant flow rates and swirl factors, as well as to understand the effects on the flow path near wall behavior due to cavity-main flows interaction, that should be properly accounted for during the design phases, and should be properly reproduced during cascade testing.

The present paper describes the application of Proper Orthogonal Decomposition (POD) to Large Eddy Simulation (LES) of the T106A low-pressure-turbine profile with unsteady incoming wakes at two different flow conditions. Conventional data analysis applied to time averaged or phase-locked averaged flow fields is not always able to identify and quantify the different sources of losses in the unsteady flow field as they are able to isolate only the deterministic contribution. A newly developed procedure allows such identification of the unsteady loss contribution due to the migration of the incoming wakes, as well as to construct reduced order models able to highlight unsteady losses due to larger and/or smaller flow structures carried by the wakes in the different parts of the blade boundary layers. This enables a designer to identify the dominant modes (i.e. phenomena) responsible for loss, the associated generation mechanism, their dynamics and spatial location. The procedure applied to the two cases shows that losses in the fore part of the blade suction side are basically unaffected by the flow unsteadiness, irrespective of the reduced frequency and the flow coefficient. On the other hand, in the rear part of the suction side the unsteadiness contributes to losses prevalently due to the finer scale (higher order POD modes) embedded into the bulk of the incoming wake. The main difference between the two cases has been identified by the losses produced in the core flow region, where both the largest scale structures and the finer ones produces turbulence during migration. The decomposition into POD modes allows the quantification of this latter extra losses generated in the core flow region, providing further inputs to the designers for future optimization strategies.

The paper analyzes losses and the loss generation mechanisms in a low-pressure turbine cascade by Proper-Orthogonal-Decomposition (POD) applied to measurements. Total pressure probes and time resolved particle image velocimetry (TR-PIV) are used to determine the flow field and performance of the blade with steady and unsteady inflow conditions varying the flow incidence. The total pressure loss co-efficient is computed by traversing two Kiel probes upstream and downstream of the cascade simultaneously. This procedure allows a very accurate estimation of the total pressure loss coefficient also in the potential flow region affected by incoming wake migration. The TR-PIV investigation concentrates on the aft portion of the suction side boundary layer downstream of peak suction. In this adverse pressure gradient region the interaction between the wake and the boundary layer is the strongest, and it leads to the largest deviation from a steady loss mechanism. POD applied to this portion of the domain provides a statistical representation of the flow oscillations by splitting the effects induced by the different dynamics. The paper also describes how POD can dissect the loss generation mechanisms by separating the contributions to the Reynolds stress tensor from the different modes. The steady condition loss generation, driven by boundary layer streaks and separation is augmented in presence of incoming wakes by the wake-boundary layer interaction and by the wake dilation mechanism. Wake migration losses have been found to be almost insensitive to incidence variation between nominal and negative (up to −9deg), while at positive incidence the losses have a steep increase due to the alteration of the wake path induced by the different loading distribution.

A time resolved Particle Image Velocimetry (TR-PIV) system has been employed to investigate a laminar separation bubble which is induced by a strong adverse pressure gradient typical of Ultra-High-Lift lo pressure turbine blades. Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are described and applied within the paper. These techniques allow reducing the degrees of freedom of complex systems producing a low order model ranked by the energy content (POD) or by the modal contribution to the dynamics of the system itself (DMD), useful to highlight the dominant dynamics. The time-space evolution of the laminar separation bubble is characterized by rollup vortices shed in the surround of the bubble maximum displacement as a consequence of the Kelvin-Helmholtz instability process as well as by a low frequency motion of the separated shear layer. The decomposition techniques proposed allow the identification of these coherent structures and the characterization of their modal properties (e.g. temporal frequency, spatial wavelength and growth rate). The POD separates the different dynamics that induce velocity fluctuations at different frequencies and wavelength looking at their contribution to the overall kinetic energy. The DMD provides complementary information: the unstable spatial frequencies are identified with their growth (or decay) rates. DMD modes associated with the Kelvin-Helmholtz instability and the corresponding vortex shedding phenomenon clearly dominate the unsteady behavior of the laminar separation bubble, being characterized by the highest growth rate. Modes with longer wavelength describe the low frequency motion of the laminar separation bubble and are neutrally stable. Results reported in the paper prove the ability of the present methods in extracting the dominant dynamics from a large dataset, providing robust and rapid tools for the in dept analysis of transition and separation processes.

The paper analyzes the unsteady interaction between an impinging wake and the suction side boundary layer of a low pressure turbine cascade operating under unsteady inflow conditions. The instantaneous flow fields are obtained with Particle Image Velocimetry (PIV) for two different free-stream turbulence intensities (FSTI) and two orthogonal measurement planes (a blade-to-blade and a wall-parallel plane, respectively). The large data set has been post-processed by means of Proper Orthogonal Decomposition (POD) to provide a solid statistical interpretation of the physics of this complex unsteady interaction. For the analysis of the blade-to-blade plane measurements, the paper takes advantage of the POD properties, which consist in splitting spatial (POD modes) and temporal (POD eigenvector) information. The phase identification of each PIV image within the wake passing period is then extracted from the eigenvectors of properly selected POD modes in order to reconstruct a phase-averaged velocity field. This post-processing allow us to separately account for the contribution to deterministic and stochastic unsteadiness as well as to have a look at the most significative scales of turbulence generating during the different phase of the wake-boundary layer interaction process. The detailed analysis is completed by the measurements in a wall-parallel plane (aligned with the blade span). Instantaneous images and POD modes in this plane allow recognizing the presence of three-dimensional disturbances, induced by low and high speed travelling streaks (Klebanoff mode). These coherent structures have been shown to play a significant role in the unsteady transition process of the boundary layer at both low and elevated FSTI, and results reported in the paper further characterize their role in the transition process.