Turbomachinery Systems Research Articles

A Low Mach Preconditioned Harmonic Balance Solver for Cavity Flutter Computations

Abstract Labyrinth seal flutter is a critical phenomenon in turbomachinery, as it can lead to severe structural vibrations and potential component damage. Accurate prediction and mitigation of flutter are paramount to ensuring the reliability and performance of modern turbomachinery systems. This paper explores the numerical computation of a labyrinth seal flutter test case using a low Mach preconditioned harmonic balance (HB) solver and investigates how this approach can improve the accuracy and response time of flutter computations. HB solvers have gained prominence in turbomachinery computations for their ability to efficiently capture unsteady flow phenomena and significantly reduce computational time compared to time-domain analyses. In labyrinth seals, however, the flow is often characterized by low Mach numbers, and preconditioning for these conditions has been shown to significantly improve convergence and accuracy. The goal of this paper is to demonstrate how to implement low Mach preconditioning in a HB solver in the frequency domain. We employ iterative preconditioning to alleviate the stiffness associated with density-based solvers under low Mach conditions and analyze the effect of the preconditioning parameters on the convergence rate. Furthermore, we address inaccuracies linked to the classical Roe solver in low Mach scenarios by adapting it to the low Mach preconditioned governing equations. Through the combined utilization of iterative preconditioning and a preconditioned Roe solver, this study aims to improve convergence rates and the overall quality of flutter predictions. We demonstrate the method with an academic labyrinth seal test case originally presented by Corral et al. (“Higher Order Conceptual Model for Labyrinth Seal Flutter,” ASME J. Turbomach., 143(7), p. 071006). While previous investigations have primarily relied on linearized frequency domain solvers and reduce-order models, in this research a preconditioned HB solver is applied to this test case.

Opportunities to Enhance sCO2 Power Cycle Turbomachinery with Bearingless Motor/Generators

Thermal power cycles using sCO2 as a working fluid place extreme demands on their turbomachinery components and their electric motors/generators. In this paper, new system topologies for sCO2 turbomachinery are proposed which take advantage of “bearingless” electric machine technology to improve performance. Bearingless motors/generators are a new type of electric machine which integrate the functionality of active magnetic bearings into the existing hardware of an electric motor/generator. The existing electromagnetic surfaces and materials are reused to enable controllable production of radial forces on the machine shaft. This is envisioned to improve hermetic direct-drive turbomachinery systems by either augmenting existing bearings (i.e., bearing assist) or replacing existing bearings (i.e., bearing removal). The state-of-the-art technologies for several bearing types (gas foil bearings, externally pressurized porous (EPP) gas bearings, and active magnetic bearings) and electric machines are reviewed to motivate the introduction of bearingless technology. Two system designs using bearingless machines are proposed and compared against existing commercial solutions in terms of maximum shaft weight, number of passthroughs into the hermetic environment, cost, and complexity. A case-study bearingless motor/generator is assessed via simulations and a hardware prototype to investigate practical considerations for using bearingless technology in sCO2 turbomachinery. The proposed bearingless solutions have potential to enable a new generation of sCO2 turbomachinery with improved reliability, reduced complexity, and lower cost. This paper shows that by transforming the motor/generator already present in turbomachinery into a bearingless motor/generator, the technical challenges involved with sCO2 can be overcome without adding significant cost.

Aerodynamic optimization design and experimental verification of a high-load axial flow compressor

The performance and stable operating range of compressors are critical to the efficient operation of various turbomachinery systems. This paper proposes a multi-level optimization strategy combining the uni-uniform direct free deformation method, Linux partitioned CPU accelerated parallel computing technology, multi-objective particle swarm optimization algorithm and downhill simplex algorithm, which improves design efficiency. Numerical results show that after optimization design, the average value of peak efficiency and stall margin increases. The flow mechanism of compressor performance improvement after optimization lies in the reduction of a low-velocity separation zone in stator hub region. Moreover, the experiment study confirms the reliability and accuracy of the optimization design method and found that flow instability triggering mode, propagation characteristics of the stall cell, and surge frequency are changed after optimization design. Setting a probability distribution threshold for autocorrelation coefficient and cross-correlation coefficients can be used to predict the arrival of the surge condition.

Spatiotemporal characteristics of flow in the bend and return channel perturbed by rotor–stator interaction

The flows in turbomachinery systems are strongly perturbed by the rotor–stator interaction (RSI) between the rotating and stationary through-flow components, generating the fluctuating flows. This work presents a numerical investigation of a flow in a test centrifugal pump system consisting of an impeller, diffuser, bend, and return channel at the designed and low flow rates. Both vaneless and vaned diffuser models are considered to determine the perturbation of the diffuser vanes on the flow. The objective is to quantitatively assess the impacts of two influential factors, i.e., the diffuser type and the flow rate, on the spatiotemporal characteristics of the transient flow in the various through-flow components. Particular attention is paid to the generation of the reversed flow, circulating vortices, and temporal fluctuations of the velocity field. It is found from the numerical data that both the flow rate and the diffuser type affect the temporal fluctuations of the flow, primarily via the impact of the RSI-induced large-scale vortices generated in the passages of the impeller and the vaned diffuser. The flow in the bend experiences the streamline curvature on the solid walls; thus, the peak values of the fluctuating amplitude of the streamwise and transverse velocities and the reversed flow may shift between the two halves of the channel close to the inner and outer wall. The boundary layer flow patterns are mainly determined by the flow rate at the low flow rate and by the diffuser vanes at the designed flow rate. This work comprehensively reveals the transient behaviors and unsteadiness of the flow which was not provided in the experimental investigation for the test centrifugal pump system which was widely studied since the essential flow physics are included. The numerical data in the stationary bend and return channel are first provided, which are of engineering significance for this type of centrifugal turbomachinery.

Effect of multi-cavity on the aerothermal performance robustness of the squealer tip under geometric and operational uncertainties

A multitude of uncertainties intertwined within the manufacturing and functioning of gas turbines has often been overlooked in numerous prior investigations regarding the aerothermal performance of blade tips. Consequently, the actual lifespan of the blades falls considerably short of the initially anticipated duration. This study proposes an efficient parallel turbo robustness analysis framework and aims to delve into the uncertain characteristics exhibited by various multi-cavity squealer tips during real-world gas turbine operations. The findings of this research reveal that the inclusion of ribs has an adverse impact on the flow field, leading to heightened chaotic tendencies and a considerable reduction in the expected aerodynamic efficiency of the multi-cavity squealer tip. The leakage flow experiences a notable increase, reaching values of 22.30%, 17.88%, and 24.51% for the three distinct multi-cavity configurations, surpassing the corresponding value of 13.63% observed for the conventional squealer tip. However, integrating the flow field uncertainty into the thermal field uncertainty proves challenging due to the disruption of the cavity vortex system caused by the pressure side ribs. Thus, the heat transfer performance of the multi-cavity squealer tip exhibits superior robustness compared to that of the conventional squealer tip. Furthermore, this paper introduces a novel evaluation index, based on comprehensive uncertainty flow and thermal analyses, to assess the robustness of the aerothermal performance. The present work makes a valuable contribution to the development of digital twins for turbomachinery systems.

Experimental Research on Flow Instability Mechanism of a Highly Loaded Axial Compressor

Abstract The performance and stable operating range of compressors are critical for the efficient operation of various turbomachinery systems. To reveal the flow instability mechanism of a high-speed and high-loaded compressor, a systematic experimental study on a 1.5-stage high-loaded compressor was conducted in this paper. First, the aerodynamic design and aerodynamic performance evaluation of the compressor were carried out. At 100% corrected speed, the measured choked flowrate, peak efficiency, and stall margin were 4.59 kg/s, 87.1% and 17.5%, respectively. Second, the flow instability mechanism of the highly loaded compressor at different corrected speeds was clarified through the experiments. At 50% corrected speed, the compressor rotor developed from a spike-wave stall precursor to a rotating stall; at 70% corrected speed, the compressor developed directly from a spike-wave precursor to surge; at 90% corrected speed, the compressor has undergone the process of modal wave precursor, spike-wave precursor, and surge. Further, at 70% and 90% corrected speed, a classic surge occurred with surge frequencies of 11.91 Hz and 9.59 Hz, respectively. Through the analysis of short-time power spectrum maximum amplitude, the warning time for the surge was 6.7 ms and 15.6 ms, respectively. Finally, as the compressor throttles to stall/surge conditions, the degree of fluctuation of the autocorrelation coefficient and cross-correlation coefficient increases.

Design Methodology and Concept Demonstration of Preassembled Additively Manufactured Turbomachinery Systems: Case Study of Turbocharger Based Medical Ventilators

Abstract The present research focuses on analyzing the feasibility of manufacturing complex turbomachinery geometries in a pre-assembled manner through an uninterrupted additive manufacturing process, absent of internal support structures, or postprocessing. In the context of the present COVID-19 pandemic, the concept is illustrated by a three-dimensional (3D)-printable turbine-driven blower-type medical ventilator, which solely relies on availability of high-pressure oxygen supply and a conventional plastic-printer. Forming a fully pre-assembled turbomachine in its final form, the architecture consists of two concentric parts, a static casing with an embedded hydrostatic bearing surrounding a rotating monolithic shell structure that includes a radial turbine mechanically driving a centrifugal blower, which in turn supplies the oxygen enriched air to the lungs of the patient. Although the component level turbomachinery design of the described architecture relies on well-established guidelines and computational fluid dynamics methods, this approach has the capability to shift the focus of additive manufacturing methods to design for pre-assembled turbomachinery systems. Upon finalizing the topology, the geometry is manufactured from polyethylene terephthalate (PETG) plastic using a simple tabletop extrusion-based machine and its performance is evaluated in a test facility. The findings of the experimental campaign are reported in terms of flow and loading coefficients and are compared with simulation results. A good agreement is observed between the two data sets, thereby fully corroborating the applied design approach and the viability of additively manufactured pre-assembled turbomachines. Eliminating long and costly processes due to presence of numerous parts, different manufacturing methods, logistics of various subcontractors, and complex assembly procedures, the proposed concept has the potential to reduce the cost of a turbomachine to capital equipment depreciation and raw material.

Turbulence Structure and Dynamics Investigation of Turbulent Swirl Flow in Pipe Using High-Speed Stereo PIV Data

Turbulent swirl flow, which exists in numerous turbomachinery systems, is the focus of this paper. It consumes a significant amount of energy, so it is a subject of investigation for many researchers. It is even more present in ventilation systems, as numerous axial fans are still installed without guide vanes. The experimental investigation of the turbulent swirl flow behind an axial fan in a pipe, installed in a test rig with a free inlet and ducted outlet, as defined in the international standard ISO 5801, is presented in this paper. Moreover, in this paper, the axially restricted case is studied. A designed axial fan generates a Rankine vortex with a complex structure, and research on the vortex turbulence structure and dynamics is presented. On the basis of the HSS PIV (high-speed stereo particle image velocimetry), measurement results are calculated using invariant maps. All states of turbulence anisotropy are thoroughly analyzed by applying the invariant theory on HSS PIV results. Vortex dynamics is observed on the basis of the total velocity minima positions and their repetitions. Both methods are correlated, and important conclusions regarding vortex behavior are deduced.

Identification of Turbomachinery Noise Sources via Processing Beamforming Data Using Principal Component Analysis

Complex turbomachinery systems produce a wide range of noise components. The goal is to identify noise source categories, determine their characteristic noise patterns and locations. Researchers can then use this information to quantify the impact of these noise sources, based on which new design guidelines can be proposed. Phased array microphone measurements processed with acoustic beamforming technology provide noise source maps for pre-determined frequency bands (i.e., bins) of the investigated spectrum. However, multiple noise generation mechanisms can be active in any given frequency bin. Therefore, the identification of individual noise sources is difficult and time consuming when using conventional methods, such as manual sorting. This study presents a method for combining beamforming with Principal Component Analysis (PCA) methods in order to identify and separate apart turbomachinery noise sources with strong harmonics. The method is presented through the investigation of Counter-Rotating Open Rotor (CROR) noise sources. It has been found that the proposed semi-automatic method was able to extract even weak noise source patterns that repeat throughout the data set of the beamforming maps. The analysis yields results that are easy to comprehend without special prior knowledge and is an effective tool for identifying and localizing noise sources for the acoustic investigation of various turbomachinery applications.

Finite element based stress and vibration analysis of axially functionally graded rotating beams

This study presents a comprehensive numerical dynamic finite element analysis to investigate the dynamic behavior and induced stresses of axially functionally graded rotating beam, for the first time. The material properties of the rotating beam are assumed to continuously vary nonlinearly along the longitudinal direction according to the power law. Based on Timoshenko beam theory (TBT), the Hamiltonian principle is applied to derive governing equations of motion. The dynamic finite element equation of motion for axially functionally straight rotating cantilever beam is derived. Both stress and vibration responses are detected and analyzed. The proposed computational procedure is verified by comparing the obtained results with the corresponding results in the literature and good agreement is observed. Effects of the material gradation index and the rotating speed on the dynamic behavior of functionally graded rotating cantilever are investigated and analyzed. The obtained results show the significant effect of the material gradation index and the rotating speed on the dynamic behavior of axially functionally graded beams. The proposed model can be used effectively in design of wind turbine, rotation shafts and turbomachinery systems.

The Hydrodynamic Cavitation Manifestation in Small Chips

Cavitation is a phase change phenomenon generated by the static pressure reduction of a liquid medium at a constant temperature. This process has been considered as a disadvantageous mechanism in most turbomachinery systems, however, its potential in releasing energy at the bubble collapse stage has received lots of attention in recent decades. Particularly, the applicability of this phenomenon in micro scale gives rise to the research studies in different fields, i.e., wastewater treatment and medical imaging. In this study, microfluidic devices housing small microchannels have been fabricated to study the generation of the cavitating flow patterns bubbles. The main focuses in this work are on the surface and side wall roughness together with the size reduction effects on cavitation bubble generation. Accordingly, the microfluidic devices were fabricated using the techniques adopted from semiconductor based micro- fabrication. The experiments were performed at relatively higher upstream pressure, 4 to 7 MPa, to investigate the durability of the devices and flow patterns features. The results show that the side wall roughness elements are very effective in the small microchannels in terms of facile cavitating flow generation, while the size reduction in the diameter of the channel does not lead to intensified cavitating flow necessarily. The results show that the cavitation bubbles extended to the outlet of the side wall roughened microchannel even at the upstream pressure of 5.5 MPa, while the supercavitation flow regime was observed at high upstream pressure of 7 MPa.

An experimental investigation of a square supersonic jet and impinging jet on an inclined plate

Supersonic free jets and impinging jets are found in many engineering applications, such as short and vertical take-off and landing vehicles, cold gas dynamic spray processes, hot surface cooling mechanisms, and turbomachinery systems. The flow characteristics of a supersonic square jet discharging into the ambient and a supersonic jet impinging on a 45° inclined surface were experimentally investigated for nozzle-pressure-ratios (NPRs) of 4.8 and 5.9. Experimental measurements of impinging jets were acquired for nozzle-to-plate distances of 0.82Dj and 1.8Dj, where Dj is the jet hydraulic diameter. The velocity fields in the central plane of the jet were obtained using planar particle image velocimetry. The flow characteristics of the supersonic jets, including mean velocity and turbulent kinetic energy, were computed from the acquired two-dimensional two-component velocity vector fields, and statistical profiles were compared for different NPRs and nozzle-to-plate distances. For supersonic free jets, the acquired statistical results revealed the presence of multiple shock cells along the streamwise direction. Impinging jet measurements revealed the presence of shock cells in the vicinity of the nozzle outlet, oblique plate shocks near the impingement location, and several tail shocks along the streamwise direction. Spatial turbulent velocity cross correlations were calculated for various points located along the shear layers to investigate the characteristics of turbulent features, such as the shape, orientation, and integral length scales of the studied configurations. In addition, a proper orthogonal decomposition analysis was applied to the instantaneous velocity fields to identify the statistically dominant flow structures that play an important role in the flow field characteristics of supersonic free jets and supersonic impinging jets.

A Statistical Characterization of the Effects and Interactions of Small and Large Mistuning on Multistage Bladed Disks

Abstract As turbomachinery systems continue to push the limits of modern technology, the modeling techniques being developed also continue to push modern computational limits. While modeling the pristine system during the design process is important, it is equally important to model behavior of mistuned systems, due to wear or manufacturing processes. This work carries out a statistical analysis on a two-stage system consisting of integrally bladed rotors. Various forms of large geometric mistuning, such as missing mass, bends, and dents, are considered. These forms of large mistuning are based on previously reported damage seen in actual engines that have ingested volcanic ash. This work also aims to investigate the interaction of these large mistuned systems with various levels of small mistuning to further understand this complex interaction. For every case studied, a reduced-order model (ROM) will be constructed that includes the effects of small and large mistuning. Large mistuning will only be applied to a single sector of a single stage. Random patterns of small mistuning will be applied to each case of large mistuning after which a modal analysis and a forced response analysis are run. By observing the energy distribution of each mode for the mistuned system, a qualitative trend can be created between various types and levels of large mistuning and the impact they have on changing the dynamics of the multistage system. The amplification factors from the forced response analyses help in understanding the impact small mistuning has when coupled with large mistuning and when the effects of small mistuning dominate over the large mistuning effects.

Flowfield Characteristics of a Supersonic Jet Impinging on an Inclined Surface

The study of the flowfield and noise characteristics of supersonic impinging jets is important as these configurations can be found in many engineering applications, such as short takeoff and landing vehicles, hot surface cooling mechanisms, cold gas dynamic spray processes, and turbomachinery systems. This study experimentally investigates the flowfield characteristics of supersonic jets impinging on an inclined surface with nozzle-to-plate distances of and ( is the jet hydraulic diameter) and nozzle pressure ratios () of 3.7 and 5.9. The two-dimensional two-component velocity fields were acquired in the central plane of the test nozzle and along the 45° inclined impingement surface by using a planar particle image velocimetry (PIV) technique. The flow characteristics of supersonic impinging jets, such as mean velocity and turbulent kinetic energy, were computed from the acquired PIV velocity vector fields, and the statistical profiles were compared to study the effects of the impingement surface and on the flow characteristics. The obtained statistical results have shown the presence of shock cells near the nozzle outlet, oblique plate shocks near the impingement, and tail shocks along the inclined surface. In addition, spatial two-point cross-correlations of turbulent velocity were computed using the PIV velocity vectors to study the sizes, shapes, and orientation of turbulent flow structures in the impinging jets. Finally, a proper orthogonal decomposition analysis was performed on the collections of velocity snapshots extracting the coherent flow structures of a supersonic jet impinging on an inclined surface.

A stabilized ALE method for computational fluid–structure interaction analysis of passive morphing in turbomachinery

Computational fluid–structure interaction (FSI) and flow analysis now have a significant role in design and performance evaluation of turbomachinery systems, such as wind turbines, fans, and turbochargers. With increasing scope and fidelity, computational analysis can help improve the design and performance. For example, it can help add a passive morphing attachment (MA) to the blades of an axial fan for the purpose of controlling the blade load and section stall. We present a stabilized Arbitrary Lagrangian–Eulerian (ALE) method for computational FSI analysis of passive morphing in turbomachinery. The main components of the method are the Streamline-Upwind/Petrov–Galerkin (SUPG) and Pressure-Stabilizing/Petrov–Galerkin (PSPG) stabilizations in the ALE framework, mesh moving with Jacobian-based stiffening, and block-iterative FSI coupling. The turbulent-flow nature of the analysis is handled with a Reynolds-Averaged Navier–Stokes (RANS) model and SUPG/PSPG stabilization, supplemented with the “DRDJ” stabilization. As the structure moves, the fluid mechanics mesh moves with the Jacobian-based stiffening method, which reduces the deformation of the smaller elements placed near the solid surfaces. The FSI coupling between the blocks of the fully-discretized equation system representing the fluid mechanics, structural mechanics, and mesh moving equations is handled with the block-iterative coupling method. We present two-dimensional (2D) and three-dimensional (3D) computational FSI studies for an MA added to an axial-fan blade. The results from the 2D study are used in determining the spanwise length of the MA in the 3D study.

Loss models for on and off-design performance of radial inflow turbomachinery

It is critical to accurately predict the performance of radial inflow turbomachinery in the preliminary design stages. Preliminary design of radial inflow turbomachinery uses basic geometry information and does not have access to detailed blade design. Experimentally derived models using an optimised geometry are widely used to develop a correlation between real world performance and basic design parameters of the turbine. Yet, these correlation models are primarily based on ideal working fluids. Modern turbomachinery systems operate with new complex fluids such as CO2 and R143a which have non-linear compressibility and non-ideal viscosity. Additionally, modern turbomachinery systems are expected to run with reliable performance at off-design conditions.This paper develops a new loss model configuration suitable for the analysis of turbomachinery operating with CO2 and R143a working fluids where off-design performance estimation is critical and temperature fluctuation may be expected. The paper systematically analyses over 1.5 million loss model configurations developed through the enumeration of analytical models for each loss mechanism from within literature. Each loss model configuration is compared against computational simulations of a turbine running at a wide range of off-design conditions. Primary findings of the paper are that loss model configurations must capture the appropriate physics. A loss model configuration must account for slip, as well as interaction between the turbine and immediate downstream components. Furthermore, models that were directly derived from experimental data showed better predictive performance. Specifically, due to the inclusion of appropriate physics and models directly derived from experiments, the proposed loss model within this work showed high accuracy, with a maximum error between the model and CFD of less than 2%. Many performance analysis methods focussed on the on-design performance of turbomachinery alone; the present work extends the application to incorporate more in-depth analysis of the off-design performance of turbomachinery. The paper provides a loss model configuration that is immediately useful for the development of radial inflow turbomachinery operating with CO2 and R143a and can be easily adopted to the early cycle design phase to ensure that performance is consistently high.

Multistage Blisk and Large Mistuning Modeling Using Fourier Constraint Modes and PRIME

Current efforts to model multistage turbomachinery systems rely on calculating independent constraint modes for each degree-of-freedom (DOF) on the boundary between stages. While this approach works, it is computationally expensive to calculate all the required constraint modes. This paper presents a new way to calculate a reduced set of constraint modes referred to as Fourier constraint modes (FCMs). These FCMs greatly reduce the number of computations required to construct a multistage reduced order model (ROM). The FCM method can also be integrated readily with the component mode mistuning (CMM) method to handle small mistuning and the pristine rogue interface modal expansion (PRIME) method to handle large and/or geometric mistuning. These methods all use sector-level models and calculations, which make them very efficient. This paper demonstrates the efficiency of the FCM method on a multistage system that is tuned and, for the first time, creates a multistage ROM with large mistuning using only sector-level quantities and calculations. The results of the multistage ROM for the tuned and large mistuning cases are compared with full finite element results and are found in good agreement.

Reprint of ‘‘Computational study of the particle size effect on a jet erosion wear device’’

Computational fluid dynamics (CFD) is a useful tool to predict the erosion behaviour over geometries exposed to conditions of severe erosion wear. This work shows how CFD can be used to virtually characterize the wear behaviour of materials used in several hydraulic components, including turbomachinery systems, in which it is important to consider the effect of particle size. In addition, this work develops a methodology for determination and validation of the constants involved in the well-known Tabakoff-Grant model for erosion prediction using the erosion wear obtained via erosion testing in a jet tribometer reported in the literature as a reference. From the experimental data, an optimization algorithm was performed to determine the optimal values of Tabakoff-Grant model constants for ASTM A743 grade CA6NM martensitic stainless steel. The simulated erosion rate agrees with the experimental data for the material analysed in jet erosion simulations with impact angles ranging from 15° to 90°. The change of the angle of maximum erosion rate for small particles, which has been reported in the literature via experimentation, was explained satisfactorily. The results showed that the erosion rate with smaller particles is affected by fluid flow, since small particles tend to follow the flow streamlines, while larger particles move according to the conditions imposed by the jet at its outlet. The effective impingement angle against the surface for small particles is lower than the impingement angle for large particles; therefore, the angle of maximum erosion rate, measured between the jet and the sample's surface, for small particles increases.

Nonlinear unsteady streaks engendered by the interaction of free-stream vorticity with a compressible boundary layer

The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated theoretically and numerically. The free-stream Mach number is assumed to be of $O(1)$ and the effects of compressibility, including aerodynamic heating and heat transfer at the wall, are taken into account. Attention is focused on low-frequency perturbations, which induce strong streamwise-elongated components of the boundary-layer disturbances, known as streaks or Klebanoff modes. The amplitude of the disturbances is intense enough for nonlinear interactions to occur within the boundary layer. The generation and nonlinear evolution of the streaks, which acquire an $O(1)$ magnitude, are described on a self-consistent and first-principle basis using the mathematical framework of the nonlinear unsteady compressible boundary-region equations, which are derived herein for the first time. The free-stream flow is studied by including the boundary-layer displacement effect and the solution is matched asymptotically with the boundary-layer flow. The nonlinear interactions inside the boundary layer drive an unsteady two-dimensional flow of acoustic nature in the outer inviscid region through the displacement effect. A close analogy with the flow over a thin oscillating airfoil is exploited to find analytical solutions. This analogy has been widely employed to investigate steady flows over boundary layers, but is considered herein for the first time for unsteady boundary layers. In the subsonic regime the perturbation is felt from the plate in all directions, while at supersonic speeds the disturbance only propagates within the dihedron defined by the Mach line. Numerical computations are performed for carefully chosen parameters that characterize three practical applications: turbomachinery systems, supersonic flight conditions and wind tunnel experiments. The results show that nonlinearity plays a marked stabilizing role on the velocity and temperature streaks, and this is found to be the case for low-disturbance environments such as flight conditions. Increasing the free-stream Mach number inhibits the kinematic fluctuations but enhances the thermal streaks, relative to the free-stream velocity and temperature respectively, and the overall effect of nonlinearity becomes weaker. An abrupt deviation of the nonlinear solution from the linear one is observed in the case pertaining to a supersonic wind tunnel. Large-amplitude thermal streaks and the strong abrupt stabilizing effect of nonlinearity are two new features of supersonic flows. The present study provides an accurate signature of nonlinear streaks in compressible boundary layers, which is indispensable for the secondary instability analysis of unsteady streaky boundary-layer flows.

Computational study of the particle size effect on a jet erosion wear device

Computational fluid dynamics (CFD) is a useful tool to predict the erosion behaviour over geometries exposed to conditions of severe erosion wear. This work shows how CFD can be used to virtually characterize the wear behaviour of materials used in several hydraulic components, including turbomachinery systems, in which it is important to consider the effect of particle size. In addition, this work develops a methodology for determination and validation of the constants involved in the well-known Tabakoff-Grant model for erosion prediction using the erosion wear obtained via erosion testing in a jet tribometer reported in the literature as a reference. From the experimental data, an optimization algorithm was performed to determine the optimal values of Tabakoff-Grant model constants for ASTM A743 grade CA6NM martensitic stainless steel. The simulated erosion rate agrees with the experimental data for the material analysed in jet erosion simulations with impact angles ranging from 15° to 90°. The change of the angle of maximum erosion rate for small particles, which has been reported in the literature via experimentation, was explained satisfactorily. The results showed that the erosion rate with smaller particles is affected by fluid flow, since small particles tend to follow the flow streamlines, while larger particles move according to the conditions imposed by the jet at its outlet. The effective impingement angle against the surface for small particles is lower than the impingement angle for large particles; therefore, the angle of maximum erosion rate, measured between the jet and the sample's surface, for small particles increases.