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The prediction of aerodynamic damping is a key step towards high fidelity forced response calculations. Without the knowledge of absolute damping values, the resulting stresses from forced response calculations are often afflicted with large uncertainties. In addition, with the knowledge of the aerodynamic damping the aeroelastic contribution to mistuning can be considered. The first section of this paper compares two methods of one-way-coupled aerodynamic damping computations on an axial turbine. Those methods are: the aerodynamic influence coefficient, and the travelling wave mode method. Excellent agreement between the two methods is found with significant differences in required computational time. The average deviation between all methods for the transonic turbine is 4%. Additionally, the use of transient blade row methods with phase lagged periodic boundaries are investigated and the influence of periodic boundaries on the aerodynamic influence coefficients are assessed. A total of 23 out of 33 passages are needed to remove all influence from the periodic boundaries for the present configuration. The second part of the paper presents the aerodynamic damping calculations for a centrifugal compressor. Simulations are predominantly performed using the aerodynamic influence coefficient approach. The influence of the periodic boundaries and the recirculation channel is investigated. All simulations are performed on a modern turbocharger turbine and centrifugal compressor using ANSYS CFX V17.0 with an inhouse pre- and post-processing procedure at ABB Turbocharging. The comparison to experimental results concludes the paper.

Recently bimodal phenomenon in corner separation has been found by Ma et al. (Experiments in Fluids, 2013, doi:10.1007/s00348-013-1546-y). Through detailed and accurate experimental results of the velocity flow field in a linear compressor cascade, they discovered two aperiodic modes exist in the corner separation of the compressor cascade. This phenomenon reflects the flow in corner separation is high intermittent, and large-scale coherent structures corresponding to two modes exist in the flow field of corner separation. However the generation mechanism of the bimodal phenomenon in corner separation is still unclear and thus needs to be studied further. In order to obtain instantaneous flow field with different unsteadiness and thus to analyse the mechanisms of bimodal phenomenon in corner separation, in this paper detached-eddy simulation (DES) is used to simulate the flow field in the linear compressor cascade where bimodal phenomenon has been found in previous experiment. DES in this paper successfully captures the bimodal phenomenon in the linear compressor cascade found in experiment, including the locations of bimodal points and the development of bimodal points along a line that normal to the blade suction side. We infer that the bimodal phenomenon in the corner separation is induced by the strong interaction between the following two facts. The first is the unsteady upstream flow nearby the leading edge whose angle and magnitude fluctuate simultaneously and significantly. The second is the high unsteady separation in the corner region.

The primary focus of this paper is to investigate the loss sources in an advanced GE transonic compressor design with high reaction and high stage loading. This advanced compressor has been investigated both experimentally and analytically in the past. The measured compressor efficiency is significantly lower than the efficiency calculated with various existing tools based on RANS and URANS. The general understanding is that some important flow physics in this modern compressor design are not represented in the current tools. To pinpoint the source of the efficiency miss, an advanced test with detailed flow traverse was performed for the front one and a half stage at the NASA Glenn Research Center. In the present paper, a Large Eddy Simulation (LES) is employed to determine whether a higher-fidelity simulation can pick up any additional flow physics that can explain past efficiency miss with RANS and URANS. The results from the Large Eddy Simulation were compared with the NASA test results and the GE interpretation of the test data. LES calculates lower total pressure and higher total temperature on the pressure side of the stator, resulting in large loss generation on the pressure side of the stator. On the other hand, existing tools based on the RANS and URANS do not calculate this high total temperature and low total pressure on the pressure side of the stator. The calculated loss through the stator from LES seems to match the measured data and the GE data interpretation. Detailed examination of the unsteady flow field from LES indicates that the accumulation of high loss near the pressure side of the stator is due to the interaction of the rotor wake with the stator blade. The strong rotor wake interacts quite differently with the pressure side of the stator than with the suction side of the stator blade. The concave curvature on the pressure side of the stator blade increases the mixing of the rotor wake with the pressure side boundary layer significantly. On the other hand, the convex curvature on the suction side of the stator blade decreases the mixing and the suction side blade boundary layer remains thin. The jet velocity in the rotor wake in the stator frame seems to magnify the curvature effect in addition to inviscid redistribution of wake fluid toward the pressure side of the blade.

In steam turbine plants, the last stages of the low pressure (LP) turbines can deliver up to 20% of the overall power of the plant. It poses lots of challenges to designers especially when the last stages are operated under low volume flow conditions. In the current paper, numerical simulations are conducted to investigate the flow features in a LP steam turbine. In steady calculations, flows under six different mass flow rates are simulated. Performances and flow patterns in last stage rotor (LSR) in low mass flow rates are highlighted. Since the last stage is modeled as a full blade annulus, flow patterns and blade force in circumferential distribution are examined. Results show that under low mass flow rate conditions, vortices occur in the last stage and the diffuser. The LSR acts like a compressor. The periodical distributions of pressure in LSR passages are broken. High amplitude aerodynamic force fluctuations are found on LSR blades in low mass flow cases. By conducting unsteady simulations, the time series of aerodynamic force are demonstrated to have the similar trend and magnitude of that in steady spatial sequence. The mechanism for aerodynamic force excitation is discussed in the current paper. Unsteady pressure fluctuation in tip section of LSR at low mass flow rates seems to have a significant correlation with the aerodynamic force fluctuation level rise.

The unsteady flow field generated by the rotor provides unsteady aerodynamic excitations to the downstream stator, which can result in vibrations such as forced response. In this paper, measurements of the rotor wake and rotor tip leakage flow from an embedded rotor in a multistage axial compressor are presented. A unique feature of this work is the pitchwise traverse of the flow field used to highlight the changes in the rotor exit flow field with respect to the position of the surrounding vane rows. Results acquired at mid-span focus on characterizing an average rotor wake, including the effects on the frequency spectrum, from a forced response perspective. While many analyses use an average rotor wake to characterize the aerodynamic forcing function to the downstream stator, this study explores the factors that influence changes in the rotor wake shape and the resulting impact on the spectrum. Additionally, this paper investigates the flow near the endwall where the tip leakage vortex is an important contributor to the aerodynamic excitations for the downstream vane. For the first time, experimental data are presented at the rotor exit, which show the modulation in size and radial penetration of the tip leakage vortex as the rotor passes through the upstream vane wake. As computational models become more advanced, the ability to incorporate these aerodynamic excitation effects should be considered to provide better predictions for vane vibratory response.Copyright © 2015 by ASME

In this paper unsteady CFD computations are used to study the stability and the rotating stall inception of a transonic radial compressor, considering two different configurations influencing the inlet flow. The prediction of the surge and stall limit for a centrifugal compressor is a key parameter for operating such machines, and hence requires attention already in the early design phase. Moreover, the operating margin can be dramatically influenced by non-uniform inlet conditions due to for example bended pipes mounted close to the inlet, as found more often today due to space limitation and optimization. In this case, it is not trivial to understand how the performance of the machine will be affected. The influence on the stability limit of an elbow installed in front of the compressor inlet is analyzed in this paper by means of unsteady RANS simulations: results for two different configurations, with elbow and with straight inlet placed in front of the compressor, are compared. All simulations are done modeling the whole annulus of the radial machine, using high performance computing, in order to accurately take into account the non-periodic phenomena leading to stall inception. Moreover, mechanisms leading to flow separation for unstable solutions are studied, pointing out how they are influenced by the unsteady interactions of the tip leakage vortices with the main flow and by the distorted flow from the inlet elbow.

This paper study the non-synchronous vibration (NSV) of a high speed multistage axial compressor using rigid blade and vibrating blade with fluid-structural interaction (FSI). The unsteady Reynolds-averaged Navier-Stokes (URANS) equations and mode based structural dynamic equations are solved. A low diffusion E-CUSP Reimann solver with a 3rd order WENO scheme for the inviscid fluxes and a 2nd order central differencing for the viscous terms are employed. A 1/7th annulus sector of IGV-rotor-stator is used with a time shifted phase lag BC at circumferential boundaries. An interpolation sliding boundary condition is used for the rotor-stator interaction. The URANS simulation for rigid blades shows that the leading edge (LE) tornado vortices, roughly above 80% rotor span, travel backwards relative to the rotor rotation and cause an excitation with the frequency agreeing with the measured NSV frequency. The predicted excitation frequency of the traveling vortices in the rigid blade simulation is a non-engine order frequency of 2603 Hz, which agrees very well with the NSV rig testing. For the FSI simulation, the results show that there exist two dominant frequencies in the spectrum of the blade vibration. The lower dominant frequency is close to the first bending mode. The higher dominant frequency close to the first torsional mode agrees very well with the measured NSV frequency. The simulation conducted in this paper appears to indicate that the NSV is excited by the traveling vortex.

Non-uniform temperature distributions in aircraft turbine and compressor discs result in high thermal stresses, particularly during engine transients. This has an important role in limiting disc life and subsequently engine time on wing between overhauls. Typically, and in the absence of specific engine real-time information, disc life is computed and declared at the design stage, for the whole fleet assuming worst case scenarios and flight profiles. This approach potentially leads to conservativeness in disc life prediction for the majority of the engines in the fleet. The purpose of this paper is to present a novel methodology to estimate the transient temperature distribution of such components in real-time, with the ultimate aim of using such information to improve knowledge about disc life consumed on an engine by engine basis. The paper describes a reduced order dynamic model that estimates the disc temperature distribution in real-time using only measured parameters such as spool speed, atmospheric pressure, and compressor exit temperatures. The model presented is a grey box model consisting of dynamic Linear Parameter Varying transfer functions that relate measured air temperatures to the relevant air temperatures in the disc cavities. Heat transfer from air to disc is modelled using rotor-stator aerothermal theory matched to validated computational fluid dynamic analyses. Lumped capacitance models and simplified explicit conduction models are used to simulate the disc temperature distribution. It is shown that this approach gives a scientifically accurate estimate of the temperature distribution both radially and axially, whilst being computationally efficient enough for real-time Engine Health Management implementation.Copyright © 2014 by Rolls-Royce plc

An important aspect of the aerodynamic flow field in the tip region of axial compressor rotors is the unsteady interaction between the tip clearance vortex and the incoming stator wakes. In order to gain an improved understanding of the mechanics involved, systematic studies need to be performed. As a first step towards the characterisation of the dynamic effects caused by the relative movement of the blade rows, the impact of a stationary wake-induced inlet disturbance on a linear compressor cascade with tip clearance will be analyzed. The wakes were generated by a fixed grid of cylindrical bars with variable pitch being placed at discrete pitchwise positions. Part II of this two-part paper focuses on the numerical studies conducted with the scientific flow solver TRACE. Selected measurements, which are discussed in detail in the first part of this paper, are compared with steady state RANS simulation data to determine the validity of the computational model. For this purpose, the flow field obtained in the passage (PIV), at the cascade exit (five-hole probes) and the endwall pressure distributions were used. The presented numerical results show potentials and limitations of the steady state CFD for the prediction of the investigated flow phenomena. The computations provide the initial conditions for future unsteady calculations, and enable a separate depiction of potential effects of steady and unsteady wake-tip clearance vortex interaction.

This paper describes a methodology and a fully tested and calibrated mathematical model for the treatment of endwall effects in axial compressor aerodynamic calculations. Additional losses and deviations caused by the clearance and secondary flows are analyzed. These effects are coupled with endwall boundary layer losses and blockage development. Stall/surge detection is included and mutual interaction of different loss mechanisms is considered. Individual mathematical correlations for different effects have been created or adopted from earlier papers with the aim of forming one integral model that is completely described in this paper. Separate mathematical correlations and calibration measures are discussed in detail in the first part of the paper. The developed overall model is suitable for application in two-dimensional or mean-line compressor flow calculations. During the development, it was tested, calibrated and validated using throughflow calculations comparing numerical results with experimental data for a large number of test cases. These test cases include compressors with very different configurations and operating ranges. The data on the compressors were taken from the open literature or obtained from industrial partners.

Injecting water in the air upstream of an axial compressor intake is an effective method to increase the efficiency and the power output of a gas turbine application especially at hot days. Reasoned by their complex two phase flow axial compressors which operate in wet compression mode are in the focus of present thermodynamic analysis, numerical investigations and experimental research. Recently the evaporation process of water droplets, especially at high temperature and pressure levels has been investigated with the laser based measurement technique Phase Doppler Particle Analyzer (PDPA) in detail in a stationary test rig at the University of Duisburg-Essen. The focus of these investigations has been laid on the analysis of the evaporation process in a free stream or cross flow behavior without droplet wall interaction. In this paper the first results of the novel four stage axial compressor test rig are published. This test rig is arranged for high amount of water injection with special optical access for laser based measurements. The first part of the paper outlines the general design, geometric facts and aerodynamic reference parameters of the test rig and gives an introduction to the installed conventional measurement technique. Discrete measurement results from dry runs are compared with CFD results to validate the gathered experimental data. In the second part of the paper the previously discussed dry runs are compared with measurement results of runs with water injection. The amount of water to air ratio is varied and the effects on the operating behavior of the four stage axial compressor are pointed out in detail. Furthermore results from the laser based PDPA measurements at the inlet and at the outlet of the compressor outline the impact on the water droplets moving through the compressor in wet compression mode.Copyright © 2014 by ASME

In modern high pressure turbine, a certain amount of cooling air is bled off from compressor and then directly injected into the inter-stage gap between the stationary and rotating components. This paper presents a computational study of the interaction between mainstream flow and purge flow, with the objectives of evaluating the impacts of purge flow on turbine aerodynamic design parameters, tracing the loss sources involved with the injection of purge flow and describing the secondary flows near the hub region. The purge flow through the rim seal has been varied between 0–2% of the main flow and the axial position of rim seal has been also changed. Steady-state simulation using a 3D RANS solver is presented with particular emphasis on the mechanisms of loss production. It is found that purge flow has a primary effect on the spanwise distribution of turbine aerodynamic design parameters, especially near the hub region. The losses brought about by the injection of purge flow can be divided into four parts: reaction redistribution between vane and blade in one stage, a shear layer between purge flow and mainstream flow due to different circumferential momentum, hub passage vortex interaction and decrease of output work near the end wall. However these four loss sources are not independent of each other. Shear induced vortex (SIV) and slot leakage vortex (SLV) appear near the hub region after purge flow is introduced. The shear induced vortex is formed due to the shear interaction between mainstream flow and purge flow which develop into hub passage vortex. The slot leakage vortex is formed due to the relative motion of the cavity disks and its strength is relatively weak compared with the shear induce vortex. The results gained from this paper may give some useful guidelines for turbine aerodynamic design and end wall profile optimization.

The experimental investigation of the unsteady flow field in a highly loaded single stage low pressure axial compressor, also called a booster, is presented in this paper. The compressor design is representative of an advanced direct drive turbofan booster. Tests were performed on different speed lines at choke, design, and near stall, in the VKI-R4 closed loop compressor test rig. The rotor casing was instrumented with fast response pressure transducers to perform a detailed survey of the tip flow features. Simultaneous time-resolved measurements with fast response aerodynamic pressure probes were performed by radial and circumferential traverses to map the unsteady flow field at rotor and stator exit. The originality of this paper also resides in the fact that unsteady flow angle data are presented as the probe was used in a virtual 3-hole mode. The casing measurements allow to map the direction and extension of the tip leakage vortex. The flow path measurements show its extension at the exit of the rotor blade passage and its evolution as throttling is increased towards the compressor stability limit. The results are presented in terms of periodic and random fluctuations. These experimental results are combined to provide a three-dimensional view of the experimental flow field. They are discussed and compared to CFD simulations, showing that, in some regions, important features are not captured by the numerical model. In particular, the presence of a second wake has been observed in the unsteady yaw angle map at rotor exit. This uncommon feature is currently under further investigation.Copyright © 2013 by ASME

The effect of blade row interaction and hub leakage flow on the performance of moderately loaded NASA transonic hybrid compressor stage (Rotor 35 / Stator 37) is investigated through three-dimensional steady state and time-accurate, Navier Stokes calculations of the stage using the ANSYS CFX code at peak efficiency and near stall operating conditions. Understanding unsteady flow phenomena in compressor stages requires the use of time-accurate CFD simulations. Due to the inherent differences in blade counts between adjacent blade rows, the flow conditions at any given instant in adjacent blade rows differ. Depending on the blade counts, it may be necessary to model the entire annulus of the stage; however, this requires considerable computational time and memory resources. Several methods for modeling the transient flow in turbo machinery stages which require a minimal number of blade passages per row, and therefore reduced computational demands, have been presented in the literature. Recently, some of these methods have become available in commercial CFD solvers. The paper describes the steady and the unsteady CFD approaches used for investigating the ability to predict the measured performance of the NASA transonic axial stage design known as the hybrid stage, which consists of the axial Rotor35 and the axial stator 37. The steady approach employs the mixing-plane while the unsteady approaches are URANS with one based on full annulus simulation for the stage and the second enables simulations for the stage using reduced computational model, with a single passage from each blade row based on the time-tilting or the time-transformation technique. The above methods are evaluated and compared in terms of computational efficiency and comparison is made to steady stage simulations. Comparisons to overall performance data and two-dimensional Laser Doppler Velocimeter measurements of the velocity field are used to assess the predictive capabilities of the methods. Computed flow features are examined, and compared with reported measurements. This paper presents validation and calibration of methods used for determining blade row interactions and the respective predictive capabilities against the full annulus and the experimental test data.

An efficient numerical method is applied to investigate the influence of different tip gap shapes on the performance of an axial-flow compressor stator under the condition of rotating hub or stationary hub. Tip gap shapes considered in this paper include zero gap, uniform gap, and linearly varying gap. The analysis of the results shows, at least for these test cases, tip leakage vortex can be found to generate earlier for stationary hub cases than for rotating hub cases. On the same working conditions, the blade row with zero gap has not the highest efficiency, while the blade row with smaller tip gap can attain higher efficiency due to the role of tip leakage flow the direction of which is opposite to the secondary flow in the passage near the hub. For the same circumferential leakage area in the tip region, the blade row with linearly expanding gap can obtain higher efficiency. The work of this paper can provide a useful reference for optimum design of compressor stator.Copyright © 2001 by ASME

This paper is Part I of a comprehensive study on the blade leading edge sweep/bend of supersonic and transonic axial compressors. The objective of the paper is to develop an analytical shock surface model which links a blade leading edge with the 3-D shock structure, and can be eventually explored as a means to estimate the direct and indirect shock losses. The model surface is composed of helixes on a set of cylinders with aerodynamically determined ascendent for each helix. One kind of the relation between the ascendent and 2-D aerodynamics on S1 stream surface has been established for a leading edge attached shock surface. The succeeding research has revealed that the concepts of a forward/backward swept shock surface, and their qualitative and quantitative natures, can be analysed by the model in uniformity. The model is constructed as such that it can also be used in the inverse method of design process. Two leading edge shock surfaces from two high loading transonic fans are simulated by the model.Copyright © 1999 by ASME

Throughflow theory, as a design problem, is extensively used in the design of transonic axial flow compressors and fans. The losses caused by a simplified passage shock named shock loss model were taken into account in the design of transonic stages. However, the influences of shock waves on flow fields are still under development for transonic design. This problem is studied in the present paper. The basic equations of the throughflow method are re-derived under the concept of discontinuous passage averaging, and then, the distribution shock forces acied on the averaged throughflow fields are obtained. To evaluate these effects on averaged throughflow fields, a passage shock structure model is developed based on the previous models. Finally, the shock influences are assessed and compared in the present paper. It is demonstrated that the distribution shock forces have dramatically effects on the results of design.

This paper describes the synchronous vibration instability problem that occurred on a series of large overhung centrifugal compressors. The first part of this paper deals with the identification and display of the instability phenomenon: cyclic vibration amplitude variations and phase angle rotation occuring during testing of overhung centrifugal compressors. After numerical simulations and analysis of the test results, the bearing design has been identified as the cause of the problem. The second part describes the numerical study of the instability of the compressor. This problem is related to the eccentricity of the shaft in the bearing and to the shape of its orbit. We have investigated and propose different solutions to avoid this unstable dynamic behavior. These solutions have been tested on different compressors and have confirmed the results of the numerical analysis. The third part reminds a link between the thermal effect occurring in the bearings, the numerical results and the tested dynamic behavior of the compressor. Recently, some authors such as Keogh et al. (1994) and Liebich et al. (1994) have noticed and studied this unstable behavior. Althougth the nature of the phenomenon seems to be known (de Jongh et al., 1984) (Faulkner et al., 1997a, 1997b), no universal technical solution to this important problem has been found. The contribution of this work is to present another case of the influence of the thermal effect on the dynamic behavior of an overhung compressor. We present the typical symptoms of the phenomenon, explain it, and propose the solutions we have used to avoid the problem.

Due to their complex shape and complicated flow configuration, the volutes of turbocharger compressors and turbines appear to be a difficult component for both numerical modelling and experimental measurements. This paper presents some 3-D Reynolds Averaged Navier-Stokes (RANS) calculations for a volute with a trapezoidal cross-sectional shape. Flow recirculation under the ‘tongue’ and treatment of radial outflow boundary condition are two important aspects of the current calculations. The results are compared with available experimental data and the reasons for the discrepancies are discussed. The flow features highlight the fact that very strong secondary velocities are present and hence the conventional one-dimensional analyses are not adequate for design purposes. The paper also highlights the typical problems faced by a numerical analyst from grid generation point of view and briefly describes a procedure for handling the problems. Generated grids for two different volutes are presented here in order to show the capability of the grid generation method.Copyright © 1998 by ASME

This paper presents an attempt of a quantitative evaluation of deterioration, due to fouling, in the performance of gas turbine units of different schemes (one-shaft, two-shaft and three-shaft) but with axial compressors of the same type and dimensions. This paper also examines the influence of the gas turbine unit initial parameters (inlet turbine temperature and pressure ratio) on the gas turbine unit sensitivity to axial compressor fouling. The evaluation of the gas turbine unit sensitivity to fouling is performed based on the small deviations method. The index of sensitivity to fouling (ISF) proposed in (Tarabrin et al, 1996) is used. It is proposed that not only the ISF characterizing the axial compressor sensitivity to fouling but also the scheme and the initial gas turbine unit parameters influencing the gas turbine unit sensitivity to axial compressor fouling, should be taken into consideration.

A throughflow method for designing and analysing compressors has to be supplied with loss, deviation, and blockage estimates for every blade row. The earliest methods used empirical correlations for profile loss and deviation, together with an empirical blockage or “work done” factor, and empirical estimates of additional losses near the endwalls. Previous papers by the author have described how to replace the empirical blockage factor and endwall corrections by explicit calculations using a new mathematical model of the endwall phenomena. Those papers illustrated the application of the method near design conditions, using either design profile loss and deviation figures or computations by a viscous-inviscid interaction blade-to-blade method. In order to estimate off-design performance rapidly over the whole operating range, some way of estimating off-design profile loss and deviation must be chosen. In this paper, the previously-derived design point loss and deviation figures are retained, and an empirical correlation due to Miller, Wasdell, and Wright is used to predict the changes in loss and deviation off-design. It is shown by means of sample three-dimensional Navier-Stokes computations that the endwall model remains applicable off-design. The method has been tested against two low speed and two high speed compressors, one of each example having controlled-diffusion blading. The low speed compressor characteristic maps are predicted only approximately, but the predicted high speed compressor maps are good. It is widely believed that endwall flow separation can initiate stall or surge. As stall or surge was approached the shape factor of the annulus wall boundary layer at one location rose sharply, but no single stall-predicting value could be found.

Previous RAE papers have described the application of an S1-S2 flow calculation system, which does not model spanwise mixing, to the RAE C147 high speed research core compressor. Although this has proved a valuable design and analysis tool, it is shown by comparison with detailed interstage traverse measurements that it does not model accurately the radial profiles of stagnation temperature, pressure and flow angle as they develop through the C147. Published work utilising low speed compressor measurements has shown that the inclusion of spanwise mixing terms in throughflow analysis can improve the modelling of radial profiles while allowing more realistic loss models to be used. This paper describes the application of the Gallimore/Cumpsty spanwise mixing model to the C147 compressor. A brief description of the modelling is given, especially the simple annulus wall model not covered by the Gallimore/Cumpsty papers. Then a model of the C147 flow is constructed using simple endwall loss and deviation assumptions, together with other changes needed to represent what seems to be a hub stall. It is concluded that the mixing terms enable realistic radial distributions of loss and deviation to reproduce the observed flow. The temperature mixing terms are particularly important in a high speed unit because they prevent the erroneous accumulation of high temperatures near the walls.Copyright © 1992 by ASME

This paper describes the design of realistic blade shapes using an inverse method. Special attention is given to the geometrical and mechanical constraints imposed upon the blade. Examples presented in this paper illustrate how a better understanding of the theoretical relations between imposed velocity and resulting geometry can help satisfy the geometrical restrictions. Another method using a numerical procedure for finding a compromise between the target velocity distribution and geometrical restrictions is also proposed and illustrated by an example. A blade design procedure using an inviscid inverse method and a boundary layer calculation method is described and applied to the design of a shock free transonic compressor cascade. The iterative character of the procedure provides a blade shape control good enough to design sufficiently thick blades resulting in realistic geometries. The blade shape coordinates are given as a possible bench mark for inviscid or viscous two-dimensional methods.

A measuring technique based on multi-sensor hot-wire anemometry has been developed to determine the unsteady three-dimensional velocity vector and the structure of turbulent flows. It then has been applied to the passage and the exit flow of an annular compressor cascade, which is periodically disturbed by the wakes of a cylinder rotor, located about 50 percent of blade chord upstream. In Part I of this paper the decay of the rotor wakes will be described first without stator and secondly through a stator passage. The time-dependent turbulent flow field downstream of this stator is discussed in Part II of this paper. The rotor wakes have a major influence on the development of three-dimensional separated regions inside the compressor cascade, and this interaction will be addressed in both parts of this paper.

For the next generation of aero-engines, manufacturers are planning to increase the overall compressor pressure ratio from existing values around 50:1 to values of 70:1. The requirement to control the tight clearances between the blade tips and the casing over all engine-operating conditions is a challenge for the engine designer attempting to minimise tip-clearances losses. Accurate prediction of the tip clearance requires an accurate prediction of the radial growth of the compressor rotor, which depends on the temperature distribution of the disc. The flow in the rotating cavities between adjacent discs is buoyancy-driven, which creates a conjugate heat transfer problem: the disc temperature depends on the radial distribution of Nusselt number, which in turn depends on the radial distribution of disc temperature. This paper focuses on calculating the radial growth of a simplified compressor disc in isolation from the other components. Calculations were performed using one-dimensional (1D) theoretical and two-dimensional finite-element computations (2D FEA) for overall pressure ratios (OPR) of 50:1, 60:1 and 70:1. At each pressure ratio, calculations were conducted for five different temperature distributions; the distribution based on an experimentally-validated buoyancy model was used as the datum case, and results from this were compared with those from linear, quadratic, cubic and quartic power laws. The results show that the assumed distribution of disc temperature has a significant effect on the calculated disc growth, whereas the pressure ratio has only a relatively small effect. The good agreement between the growth calculated by the 1D theoretical model and the FEA suggests that the 1D model should be useful for design purposes.

This paper focuses on the buoyancy-induced unsteady flow phenomenon inside high-pressure compressor disk cavities. In order to understand the flow structure in a realistic configuration, a 10-stage core compressor of the NASA/GE Energy Efficient Engine is adopted as a computational target. The numerical flow simulation is conducted on a full annulus model, where the temperature distribution on the wall is modeled based on the core test results. The time-averaged flow fields are obtained by detached eddy simulation (DES) and two-dimensional axisymmetric Reynolds-averaged Navier-Stokes (RANS) simulation, and the difference is discussed in detail. The DES result showed large-scale, vortical structures with significant radial velocity fluctuations especially in the rear part of the compressor. These fluctuations create radial arm-like structure in the temperature distribution in the cavity, and greatly enhance the mixing between the bore coolant and hot air near the cavity wall. In addition, it is observed that the hot air discharged from the cavities creates a large cell at bore region, which extends across several rear stages. Although the present study successfully illustrates the entire structure of unsteady flow in heated compressor disk cavities including full stages, a more detailed validation will be needed to further confirm the applicability of DES for the targeted flow.

Gas turbine blades feature serpentine internal cooling passages connected by 180-degree bends, through which coolant bled off from the compressor is routed to cool the internal walls. Under the influence of Coriolis force and centrifugal buoyancy force induced by rotation, the heat transfer for radially outward flow enhances on the trailing side (pressure side) and reduces on the leading side (suction side). A reverse trend in heat transfer is observed for radially inward flow. Rotation induced forces result in non-uniform heat transfer coefficient distribution which results in non-uniform metal temperatures under steady state condition. Present study addresses the problem of non-uniform heat transfer distribution due to rotation effect, by experimental investigation of two configurations where Coriolis effect was negated by aligning the coolant flow vector and rotation vector such that their cross product was effectively a null vector. This paper presents a novel design for serpentine cooling passages which are arranged along the chord of the blade which has similar heat transfer coefficient distribution on both leading and trailing walls. The two configurations were four-passage and six-passage serpentine smooth channels. Detailed heat transfer coefficients were measured using transient liquid crystal thermography under stationary and rotating conditions. Heat transfer experiments were carried out for Reynolds numbers ranging from 12294 to 85000 under stationary conditions. Rotation experiments were carried out at Rotation numbers of 0.05 and 0.11. Heat transfer enhancement levels of approximately two times the Dittus-Boelter correlation (for developed flow in smooth tubes) were obtained under stationary conditions. Under rotating conditions, we found that the four-passage configuration had slightly lower heat transfer compared to stationary case, and the six-passage configuration had higher heat transfer on both leading and trailing sides compared to stationary case. The leading and trailing side heat transfer characteristics were near-similar to each other, for both the configurations and the rotating heat transfer was near-similar to the stationary condition heat transfer.

The cavities between the rotating compressor discs in aeroengines are open, and there is an axial throughflow of cooling air in the annular space between the centre of the discs and the central rotating compressor shaft. Buoyancy-induced flow occurs inside these open rotating cavities, with an exchange of heat and momentum between the axial throughflow and the air inside the cavity. However, even where there is no opening at the centre of the compressor discs — as is the case in some industrial gas turbines — buoyancy-induced flow can still occur inside the closed rotating cavities. The closed cavity also provides a limiting case for an open cavity when the axial clearance between the cobs — the bulbous hubs at the centre of compressor discs — is reduced to zero. Bohn and his co-workers at the University of Aachen have studied three different closed-cavity geometries, and they have published experimental data for the case where the outer cylindrical surface is heated and the inner surface is cooled. In this paper, a buoyancy model is developed in which it is assumed that the heat transfer from the cylindrical surfaces is analogous to laminar free convection from horizontal plates, with the gravitational acceleration replaced by the centripetal acceleration. The resulting equations, which have been solved analytically, show how the Nusselt numbers depend on both the geometry of the cavity and its rotational speed. The theoretical solutions show that compressibility effects in the core attenuate the Nusselt numbers, and there is a critical Reynolds number at which the Nusselt number will be a maximum. For the three cavities tested, the predicted Nusselt numbers are in generally good agreement with the measured values of Bohn et al. over a large range of Raleigh numbers up to values approaching 1012. The fact that the flow remains laminar even at these high Rayleigh numbers is attributed to the Coriolis accelerations suppressing turbulence in the cavity, which is consistent with recently-published results for open rotating cavities.

Vibrational resonances of centrifugal compressor and radial inflow turbine impellers are usually identified using either Kushner’s or Singh’s parametric equations in product design and failure analysis. These equations were developed based on positive work accumulated within a certain time period. However, some resonances observed in simulation and testing cannot be understood with those resonance equations. This paper presents an alternative method to derive vibrational resonance conditions. A new model of general pressure pulsations is developed by taking into account the disturbances resulting from stationary obstacles and rotating blades. Analytical solutions of the forced vibration responses of a rotating disk subjected to different pressure pulsations are then formulated. From the forced responses, both Kushner’s and Singh’s equations can be derived. They can further prove to be equivalent though they focus on different physics. A general resonance condition is derived from the analytical solutions. This condition is a necessary condition, i.e. all resonances must meet this condition while a system following the condition may or may not be in resonance, depending upon excitation sources. It is noticed that the excitation sources could be related to harmonics due to stationary obstacles, harmonics with combined harmonic orders, or even harmonics to be understood. This general resonance condition can hence provide more “possible resonance points” and assist identifying resonances from more representative modes and more excitation sources. It has been validated by predicting vibrational resonances observed in three centrifugal compressors. This condition has also been successfully employed in the failure analysis and design modification of a radial inflow turbine impeller.

A promising flow analytical way to offset the respective shortcomings for the experimental measure and numerical simulation methods is presented. First, general topological rules which are applicable to the skin-friction vector lines on the passage surface, to the flow patterns in the cross-section of the cascade as well as on the blade-to-blade surface were deduced for the turbomachinery cascades with/without suction/blowing slots in this paper. Second, the qualitative analysis theory of the differential equation was used to investigate the distribution feature of the flow singular points for the limiting streamlines equation. The topological structure of the flow pattern on the cascade passage surfaces was discussed in detail. Third, the experiment and numerical simulations results for a linear compressor cascade passage with highly-loaded compound-lean slotted blade, which were combined to topologically examine the flow structure with penetrating slot injections through the blade pressure side and suction side. The results showed that the general topological rules are applicable and effective for flow diagnosis in highly-loaded compressor blade passage with slots. Finally, an integrated vortex control model, in which the blade compound-lean effect and the injection flow through the slots were coupled, was presented. The model shows that reasonable slot injection configurations can effectively control the concentrated shedding vortices from the suction surface of a highly-loaded compressor cascades passage, thereby the aerodynamic performance for the blade passage is remarkably improved. The present work provides a novel theoretical analysis method and insights of the flow for the turbine blade passage with cooling structures, aspirated compressor blade passage and other applications with new flow control configurations in turbomachinery field.

The paper reports on numerical investigations into the effects of inlet boundary layer skew on the aerodynamic performance of a low aspect ratio, high turning compressor cascade. The cascade geometry corresponds to the hub section geometry of a low aspect ratio stator of a highly loaded single-stage axial-flow low-speed compressor (fan). The skewed cascade flow simulates the reenergized stator hub flow and brings about a much better performance with inlet skew than without. However, the performance improvements caused by a skewed inlet boundary layer decrease with increasing inlet angle.Copyright © 2016 by ASME

This paper describes the method to improve the stall margin of transonic axial flow compressor by controlling the boundary layer on the suction surface of the rotor blade tip through natural aspiration. Aspiration slots in the compressor blade are intended to energize the flow by increasing its momentum on the suction surface. This phenomenon of boundary layer control can delay the flow separation and hence results in enhancement of the stall margin of the compressor stage. Flow behavior with aspiration slots and its performance are evaluated using commercially available numerical software. Steady state RANS simulations with three dimensional implicit pressure-based coupled solver and turbulence model SST k-ω are used. The effect of natural aspiration slot on the rotor blade performance is computed numerically. The main objective of the study was to identify the optimum location of the aspiration slot along the chord of the compressor on the rotor blade. The axial location chosen for the performance evaluations were 20%,40%,50%,60% and 70% of the rotor blade axial tip chord. By comparing the numerical simulation results with the steady state behavior in the absence of the aspirated slots, the optimized location of the aspiration slot that results in maximum stall improvement is identified. At the optimized location, natural aspiration slots on the rotor blade tip improved the stall margin with the minimum reduction in efficiency and stage pressure ratio when compared to base model. After critically understanding the performance with straight aspiration slots the compressor stage performance has enhanced further by orienting the aspiration slots. The numerical three dimensional results conclude an optimal improvement in the stall margin for the slots near the trailing edge of the rotor. The prediction shows that with the inclined aspiration slots at proper location it is possible to improve the stall margin of the compressor stage and also to restore the stage efficiency.

The air required for the combustion process in automobiles is provided by an air induction system. The air induction system induces air naturally through air ramming the automobile or artificially using a compressor while the automobile is in operation. During the induction process it is important to measure the air flow rate supplied for the combustion process as the amount of fuel supplied for combustion is dependent on the air intake. In air induction systems with high turbulence intensity the measurement of air flow rate has high noise. The high noise value affects the rate of fuel supplied for combustion. The current study focuses on using grid mesh structures to reduce the turbulence intensity in the induced air flow and improve the air flow metering. An experimental and numerical simulation study have been performed to correlate the effect of grid mesh size, distance of the grid from the measurement device (Hotwire) and flow Reynolds number. The paper provides details of experimental and numerical study which indicate that adopting mesh grid structures will reduce the turbulence intensity (noise) and also provide the ideal location for the flow measurement device such that it outputs less noise.Copyright © 2015 by ASME

The boundary layers on compressor blades are sensitive to the conditions at which transition occurs and transition can be affected by the convection of wakes from upstream blade rows. This paper and its companion, Part 2 by the same authors, describes an experiment to study the effect of the moving wakes on the boundary layer of a compressor blade. This paper describes the background and facility devised to introduce wakes together with results obtained on the blades in tests without the wakes present. Part II describes the measurements made with the wakes present and presents conclusions for the whole project. Further details of all aspects of the work can be found in Dong (1988).Copyright © 1989 by ASME

For many years, there has been a significant effort, both experimental and theoretical, to better understand the rotating stall phenomenon. For very practical reasons, most of the experimental investigations have focussed on laboratory compressors with very low stage pressure ratios. The aim of the present study was to extend the range of available data to industrial-size compressors operating in a typical real life environment. This paper reports results of detailed flow measurements made on the first four stages of a 10 stage compressor operating as part of a turbojet engine mounted on a test stand. Hot sensor anemometer measurements made at a number of axial and tangential locations showed clear evidence of rotating stall in the front stages during part-speed operation of the engine. Stall cell configuration and rotative speed, and details of flow speed and angle at hub, mid and tip radii are presented in the paper. On the basis of the measurements it is concluded that (1) although rotating stall has its origins in a flow instability, it is a highly reproducible phenomenon, (2) reverse flow can occur within the cells, as has been reported by several other observers and (3) the cells retain an axial (as opposed to helical) configuration on passing from stage to stage through the compressor.Copyright © 1988 by ASME

In this paper the transonic flow field in a vaned diffuser of a contrifugal compressor has been studied. Different geometries of the diffuser blades have been considered. Particularly with respect to the pressure field it is important to understand their influence on the development of the shock waves. For this problem a centrifugal compressor with high pressure ratio per stage has been examined. It is assumed that the impeller speed is so large that the flow may become transonic at the impeller exit. To calculate flows with shocks a time-marching method is used for solving the two-dimensional Euler equations in a conservative form. A MacCormack’s second order difference scheme is applied. There are two important points which have been studied in this paper. Firstly the geometry of the blades as far as the thickness distribution is concerned is kept unchanged and only the stagger angle has been altered. The performance maps of these diffusers and their effect on the whole machine will be discussed. Secondly the results which have been obtained by using vanes with different thickness distributions will be presented. Mean values of the quantities used for the performance map will be shown. Wall pressure distributions as well as fields of isobars and of constant Mach numbers will be demonstrated to provide a better understanding of the pressure recovery in centrifugal compressor diffusers.Copyright © 1984 by ASME

The performance of a compressor is known to be affected by the ingestion of liquid droplets. Heat, mass and momentum transfer as well as the droplet dynamics are some of the important mechanisms that govern the two-phase flow. This paper presents numerical investigations of three-dimensional two-phase flow in a two-stage centrifugal compressor, incorporating the effects of the above mentioned mechanisms. The results of the two-phase flow simulations are compared with the simulation involving only the gaseous phase. The implications for the compressor performance, viz. the pressure ratio, the power input and the efficiency are discussed. The role played by the droplet-wall interactions on the rate of vaporization, and on the compressor performance is also highlighted.Copyright © 2015 by ASME and United Technologies Corporation

Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.

This paper presents a numerical investigation to explore the effects of vortex generators on a high speed compressor cascade. Secondary flow effects like the corner separation vortex have an influence on the performance of a compressor cascade such as leading to increased losses. In order to control the corner separation vortex and reduce losses, an extensive study of vortex generators applied to a compressor cascade is conducted. A preliminary study by steady 3D RANS simulations is performed using the Spalart-Allmaras turbulence model. The aerodynamic performance as well as the behavior of the corner separation vortex is investigated in the compressor cascade without vortex generators. Then, a vortex generator is added to the cascade, which is numerically simulated. Various configurations are considered, which are decided by the height and installation angle of the vortex generator. Comparison of the performance attained by these configurations results in an optimum scheme that has minimum losses. Furthermore, unsteady 3D DES simulations are performed with the optimum configuration. This method that predicts the flow field more precisely could help verify the accuracy of the RANS results. Finally, by analyzing all the resulting aerodynamic performance and numerical flow phenomena, the mechanism of vortex-vortex interaction is presented and discussed, which could be a criterion to reduce the corner separation flow and enhance the performance of axial compressors.Copyright © 2015 by ASME

The paper investigates the effect of trailing edge filing in the impeller on the performances of impeller and compressor stage. The 3D viscous numerical simulations are carried out under different positions, thicknesses and lengths of filing. The results show that, the filing on the trailing edge has an obvious effect on the pressure ratios of impeller and compressor stage. The trailing edge filing has little effect on the impeller efficiency while the filing on the pressure side is favorable to improving the stage efficiency. Then, through correcting the blade angles at the suction and pressure sides, considering the viscosity and 3D characteristics of the flow, a modified slip factor formula is proposed for the centrifugal impeller with a trailing edge filing. The validation to the proposed formula shows that the proposed formula can be used to predict the slip factors of different filing cases with a good accuracy. It can provide a theoretical guidance for the quantitative calculation when using the filing technology to improve the performance of centrifugal impeller as well as the stage.Copyright © 2015 by ASME

The majority of natural gas compressors operate on gas mixtures with molecular weights (MW) less than air. For these machines, performance acceptance tests are run on air at reduced speed. For multistage compressors, each stage is tested individually. The test speeds and inlet temperatures are selected to closely match the inlet to exit density ratios and the machine Mach numbers per the ASME PTC10 test code. The specified test inlet pressure (limited by the test variable speed motor power capacity) is always high enough to assure that the test Reynolds number is above the required PTC10 minimum; the density ratio and machine Mach number do not depend on inlet pressure. The air test data is converted to the specified natural gas conditions using similarity laws, and an in-house stage matching program is used to determine the overall machine performance. For compressors used in liquefied natural gas (LNG) transport, the MW of the natural gas mixture is lower than air. However, the inlet temperatures are so low that an air test at typical ambient temperatures needs to be run at a speed higher than design to closely match density and machine Mach number ratios. It is impractical to run air tests at higher than design speeds (especially for 60 Hz machines), thus these machines are tested on air at design speed. As before, the air test data is reduced to the specified natural gas conditions using the similarity laws. An additional “compressibility” correction is made to account for the mismatch of density ratio between test and design conditions. Running a test at lower than the required PTC10 speed means that the test density ratio will be lower than the corrected density ratio and the stage would pass more flow than the test data conversion indicates. The method used to account for the density ratio mismatch, i.e. a “compressibility” correction is discussed in detail in this paper.

Installing the variable-camber inlet guide vanes (VIGV) on aero-engine can both adjust inlet flow of next bladerow and change the pre-spin. In this paper, flow field is numerically predicted at different curvatures of the VIGV. The rotational speed set at 63% of design rotational speed, turbulence model is Spalart - Allmaras, and central difference scheme is chosen as the discrete scheme. Nonlinear harmonic method is adopted to analyzing how the unsteady flow and wake affect next blade row at different time step when curvatures of VIGV set to be 0° and −5°. The effect of wake on relative velocity and outlet flow angle at 0.25T, 0.5T, 0.75T and 1T from 10% to 90% height were analyzed. The results show that wake of rotor affects flow above 50% height, but it has less effect on flow near the hub. The wakes of VIGV have less effect on rotor, but the wake of rotors has more effect on next bladerow. Wake affects less flow of next bladerow when VIGV is adjusted to 0°. Overall, the velocity of −5° VIGV is higher than that of 0° VIGV in rotor passage, and total pressure ratio of −5° VIGV is higher than that of 0° VIGV. The scale of 0° VIGV vortex is bigger than that of −5° VIGV in first stators when the compressor operates near the surge line. Stability range of −5° VIGV is wider than that of 0° VIGV. The performance of the −5° VIGV is better than that of 0° VIGV when operating condition is close to surge line. On the whole, by installing VIGV the performance of aero-engine can be improved, which provides guidance for compressor designers.Copyright © 2015 by ASME

This paper gives an overview of numerical and experimental investigations on super-critical CO2 flow through carbon floating ring seals (CRS). The established simulation model considers the real gas effect, temperature deformation and the shaft rotation. For validation extensive measurements of the leakage rates, pressures and temperatures at various positions within the seal were conducted on a compressor prototype. Details of the measurement setup and the test procedure are given. The experimental results are discussed. A comparison of the measured data to the model prediction shows an overall good agreement.Copyright © 2015 by ASME

An advanced GE compressor design with high reaction and stage loading, demonstrated front stage efficiencies significantly lower than predicted by CFD calculations. The source of the efficiency miss has proven difficult to pinpoint with conventional inter-stage instrumentation. A test was performed in the NASA Glenn W7 facility with the compressor operating as both a single stage and a two stage machine allowing for the acquisition of detailed traverses at each station throughout the compressor. This paper presents the data from this test and the GE interpretation of what the data implies, concentrating particularly on one operating point, the stage one peak efficiency point. Tracking of the calculated fluid entropy between the exit of the rotor and the exit of the stator leads to the conclusion that there is significant entropy increase in the freestream fluid outside the stator wakes and this loss is believed to be attributable to mixing loss in the rotor wakes. The loss due to wake mixing is largest, and may indeed be amplified, where the rotor wakes pile up on the pressure surface of the stator.

The difference of a stationary forced response situation of a turbine or compressor blade relative to a transient resonance sweep is well known and documented in the literature. Different approaches have been used to understand the effect on transient amplitude in comparison with forced response. The dependencies on damping levels and resonance passage speed have been noted. Estimates for a critical or/and maximum sweep velocity have been given. The understanding of transient response during resonance sweep is of practical importance for instance when running a certification stress test for an aircraft engine, where it needs to be decided upfront which acceleration rate (increase in rpm per second) to use to ensure that the maximum airfoil response that could be attained under stationary condition is being measured with sufficient precision. A second reason for understanding of transient response is the verification of correct, if relevant lower, component life usage during transient regimes in operation. This paper gives a proposal for a simple 1D method based on one degree of freedom (1-dof) system considerations for estimating the transient response dependency on the sweep velocity, damping levels and resonance frequency. The method is verified with 3D analyses of more complex blade-disc structures, which have been validated with air jet excitation rig and aero engine tests. Using the results of the 1-dof analysis, an estimate of the expected stationary resonance response increase can be formulated even in cases where the measured data are based on a significant deviation from the desired sweep velocity, where transient effects would be significant.

This paper aimed to improve the volute’s efficiency at both design point and off-design conditions by a robust shape optimization of the volute cross section. The objective function was to maximize the minimal value among volute static pressure coefficient at 90 percent, 100 percent and 110 percent of design flow rate respectively. The design parameters included the cross-section shape of volute and the radial position of volute cross-section. The optimization problem was solved by constrained optimization using response surfaces (CORS) method. During the process of optimization, three dimensional flow fields were analyzed using Navier-Stokes equations with SST model. The comparative results showed that the optimal volute had higher efficiency, higher static pressure recovery coefficient and lower total pressure loss coefficient and achieved an increase of 7 percent of efficiency at both design point and off-design conditions. The characteristic curves of the optimal volute changed more smoothly than those of the original one. The compressor’s overall efficiency also had an increase of 0.4 percent for the optimal volute.Copyright © 2015 by ASME

This paper presents a novel method for identifying the dynamic parameters of a gas bearing, whose force coefficients are strong functions of frequency. The method is based on the analysis of the phase diagram with the model assuming a mass-damper-spring system with time-dependent force coefficients. Usually, it is necessary a controlled mechanism to find the transfer function, this condition limits the application of the method. On the other hand, estimation of the damping and stiffness parameters under real loading is very cumbersome and requires a special care on identifying the excitation forces. One of the main difficulties is the isolation of noise and those vibration signals with an unidentified source. In this work, the excitation force was taken from the unbalance loading of a rotor test. Therefore, there is no need for a special test rig. The dynamic parameters can be estimated analyzing data from the actual rotor mounted on the gas bearings. Identifying the parameters that cause gas bearing instabilities is a big challenge. The gas properties are very sensitive to temperature and pressure changes, and, as a consequence the bearing rotor-dynamic coefficients change drastically and the rotor behaves chaotically, which means that the dynamic parameters are nonlinear. In this research a methodology based on the phase diagram construction to identify nonlinear instabilities of gas bearings is presented. The results show the method capability to estimate the dynamic coefficients by the analysis of the energy variation. Among nonparametric methods, the phase diagram or phase space is in use to identify nonlinearities in dynamic systems. The identification is conducted through the analysis of the energy variations. The energy variations can be represented as a three dimensional function E(x,v,t). In this way the phase diagram can be related to the frequency and the dynamic parameters of the system. According to Taken’s theorem, a dynamic system can be obtained by reconstructing the phase diagram. Then, using this method, the damping and stiffness coefficients are estimated.

One of the design criteria for centrifugal compressor piping systems is the prevention of piping and valve failures from high pulsation amplitudes and vibration caused by vortex-shedding induced (VSI) pulsations of gas flow past closed piping branches (stubs). Most vortex-shedding analyses are performed on the basis of frequency avoidance. If a coincidence is predicted between the acoustic natural frequency of a piping segment and the flow induced vortex shedding frequency, piping changes must be made to avoid the coincidence, since there is currently no known method for accurately predicting the severity of the resulting pulsation amplitudes and, therefore, the possibility of piping failures. Often, these piping changes are expensive and time consuming and likely unnecessary for smaller bore piping (10-inch or less), assuming the flow-acoustic coincidence does not coincide with a mechanical resonance. The majority of research performed to date on vortex-shedding excitation of piping stubs focuses on predicting the frequencies of excitation using an experimentally determined Strouhal number or range of numbers for a given geometry or piping feature. However, to properly design a piping system using a combination of support structures and piping changes, reliable prediction of the pulsation amplitude is essential for determining the shaking forces acting on the piping system and the resulting vibration and stress amplitudes. Due to the expense of experimental testing and availability of equipment, it is difficult to obtain accurate amplitude measurements of VSI pulsations of fluids at Reynolds numbers typically associated with natural gas transmission. This paper describes a series of experimental tests performed to record vortex-shedding induced pulsation amplitudes in three test facilities. Three different process fluids were utilized varying the operating conditions to obtain gas flows with Reynold’s numbers between 1e5 and 2e7. Steady state flow, temperature and pressure data was recorded with ASME PTC-10 compliant instrumentation. Transient pressure data was taken with dynamic pressure transducers installed at each stub end as well as in the main piping near the tee. The geometry configurations, pulsation amplitudes, and calculated Strouhal numbers associated with each test configuration are presented. Comparison was made between the test results and several previously published formulas. From the test results, a predictive method was developed to best represent the limit of the pulsation amplitudes.

Roughness below a certain, admissible level will not increase an aerofoil’s skin friction and thus will not impact on engine performance. In this paper a simple model is developed that demonstrates how this admissible roughness height changes through the engine. The model is determined by combining existing analytical models and is backed up by computational validation where necessary. It is shown that, given a fixed inlet/exit stagnation temperature and pressure to a blade row, the admissible roughness height is only a weak function of chord Reynolds number and Mach number for typical gas turbine blades. The aerofoil geometry/duty is also shown to have little impact. This allows the model to give a general picture of where roughness matters, irrespective of the exact details of the flow conditions/blade geometries. The model shows that the admissible roughness height decreases as the stagnation pressure increases. The lowest admissible roughness level occurs at the high pressure end of the compressor at sea-level; the admissible roughness increases as the stagnation pressure drops towards the front of the compressor. Turbines are also most sensitive to roughness close to the combustor, but even there the admissible roughness will be around three times greater than at the rear of the compressor.

Casing treatments are widely used in compressors for increasing range, stability and aerodynamic performance. However, applications in centrifugal compressors, as commonly used in turbochargers, are rare and mostly applied at the inlet region in terms of bleed slots. This paper presents the application of circumferential grooves, which are known to increase stability and performance in axial compressors, to the rear part of the impeller shroud casing in a centrifugal compressor. Experimental and numerical investigations of three different configurations have been performed and compared with the initial geometry. Experiments were conducted on a hot gas test facility where static pressure and temperature measurements up- and downstream of the compressor were acquired. The results indicate only small changes in operating range except for one speedline, where a considerable improvement is observed. Efficiency remains nearly unaffected for all configurations whereas the pressure ratio is increased at some operating points. For detailed examination of the compressor flow field, CFD analyses were conducted using steady-state RANS calculations. Structured meshes with node to node connections were used to suspend any possible influences stemming from interfaces in regions of interest. Validation with test data yields good agreement concerning choke margin and gradient trends. CFD results confirm that the investigated configurations of circumferential grooves have only small impact on efficiency and pressure ratio. Investigations on the mechanism which balances the additional losses due to increased groove surface friction and increases pressure rise are presented.Copyright © 2015 by ASME