Blade Loss Research Articles

A Time-Marching Method for the Calculation of Nonsimilar 3D Boundary Layers on Turbomachinery Blades

A method is presented for the computation of three-dimensional boundary layers on turbomachinery blades. The method is based on a finite difference approach on a body-fitted curvilinear coordinate system, in which the time-dependent 3D boundary layer equations are marched in time until the steady-state solution is found. The method does not employ a similarity law and can therefore be applied to nonsimilar boundary layers. The method not only enables one to compute the skin friction and displacement of the boundary, but also provides information on the sources of entropy generation on the blades. The entropy generation is in fact split into three main components, which correspond to heat conduction, streamwise shear stress, and cross-flow shear stress. By considering each of the components of shear stress, at the design stage considerable insight can be found on the best way of modifying the blade geometry in order to reduce blade losses. The method is validated by comparison with analytical data for a laminar flat plate, experimental results for a helical blade in turbulent flow, and an axial compressor blade. Finally, the method is applied to the prediction of boundary layers on a subsonic centrifugal compressor impeller blade.

Shock-Loss Model for Transonic and Supersonic Axial Compressors with Curved Blades

Reliable efŽ ciency calculation of high-subsonic and transonic compressor stages requires a detailed and accurate prediction of the  owŽ eld within these stages. Despite the tremendous progress in turbomachinery computational  uid mechanics, the compressor designer still uses different loss correlations to estimate the total pressure losses and thus the efŽ ciency of the compressor stage. A new shock-loss model is presented for transonic and supersonic axial compressors with circular arc blade proŽ les. The model calculates the shock position, Mach number, expansion angle, and the shock total pressure losses. The model is integrated into a loss calculation procedure, where the shock, proŽ le, secondary, and total losses are calculated. To validate the model and to establish new loss correlations, available experimental data for several transonic compressor rotors were used. Detailed loss calculation results show that the blade tip region with high Mach numbers cause shock losses that are approximately one-third of the total pressure losses. In addition, correlations are presented for total pressure-loss coefŽ cient, proŽ le-loss coefŽ cient, and secondary  ow-loss coefŽ cients. These correlations allow the compressor designer to accurately estimate the blade losses and, therefore, the stage efŽ ciency.

Transient Thermoelastohydrodynamic Study of Tilting-Pad Journal Bearings Under Dynamic Loading

Nowadays, tilting-pad journal bearings are submitted to more and more severe operating conditions. The aim of this work is to study the thermal and mechanical behavior of the bearing during the transient period from an initial steady state to a final steady state (periodic). In order to study the behavior of this kind of bearing under dynamic loading (Fdyn) due to a blade loss, a nonlinear analysis, including local thermal effects, realistic boundary conditions, and bearing solid deformations (TEHD analysis) is realized. After a comparison between theoretical results obtained with four models (ISO, ADI, THD, and TEHD) and experimental data under steady-state operating conditions (static load Ws), the evolution of the main characteristics for three different cases of the dynamic load (Fdyn/Ws < 1, Fdyn/Ws = 1 and Fdyn//Ws > 1) is discussed. The influence of the transient period on the minimum film thickness, the maximum pressure, the maximum temperature, and the shaft orbit is presented. The final steady state is obtained a long time after the appearance of a dynamic load.

PI Control of HSFDs for Active Control of Rotor-Bearing Systems

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

Advanced Compressor Loss Correlations, Part II:Experimental Verifications

Reliable efficiency calculation of high‐subsonic and transonic compressor stages requires a detailed and accurate prediction of the flow field within these stages. Despite the tremendous progress in turbomachinery computational fluid mechanics, the compressor designer still uses different loss correlations to estimate the total pressure losses and thus the efficiency of the compressor stage. The new shock loss model and the modified diffusion factor, developed in Part I, were implemented into a loss calculation procedure. In this part, correlations for total pressure loss, profile loss, and secondary loss coefficients are presented, using the available experimental data. Based on the profile loss coefficients, correlations were also established for boundary layer momentum thickness. These correlations allow the compressor designer to accurately estimate the blade losses and therefore the stage efficiency.

Transient Analysis of Plain and Tilt Pad Journal Bearings Including Fluid Film Temperature Effects

The paper considers vibration response of spinning shafts supported by flexible fluid film bearings to sudden mass imbalance (blade loss). A time transient study of the plain journal bearing with thermal effects is performed. A comparison between three transient analyses is performed. The three transient analyses studied are, the full nonlinear analysis, linear analysis using dynamic coefficients, and pseudo transient analysis using static application of dynamic loads. The validity of the nonlinear transient analysis is checked by matching the lower unbalance results with the linear analysis and the static equilibrium position results with Newton-Raphson iterative scheme. A nonlinear transient analysis of the tilt pad journal bearing is also performed, and a comparison is drawn between the three approaches.

Transient Analysis of Tilt Pad Journal Bearings Including Effects of Pad Flexibility and Fluid Film Temperature

The paper considers vibration response of spinning shafts supported by flexible tilt pad journal bearings, to large mass imbalance (blade loss). A time transient study of the tilt pad journal bearing with thermal effects and without pad deformations, and with pad deformations and without thermal effects, is performed. Influence of the inclusion of thermal effects on the journal center’s orbit, the minimum film thickness, and the maximum film temperature is evaluated, and also the influence of pad deformations due to the fluid film forces on the journal center’s orbit and the minimum film thickness is studied. Inclusion of thermal effects had little effect on the orbit, while the inclusion of pad deformations had considerable effect on the journal orbit and the minimum film thickness. Three cases are studied in this paper; static load without imbalance, static load with low imbalance, and static load with high imbalance.

Control of Unbalance Vibration on the Magnetic Bearings.

In a rotating machine, imbalance of the rotor is formidable since it causes resonance synchronized with the rotation of the rotor. In order to suppress this unfavorable vibration, an active vibration control system, which accommodates changes of rotor dynamics, is desired. In this paper we propose a vibration control system on the active magnetic bearings to cope with a sudden sinusoidal disturbance, which simulates a turbine blade loss. Experimental results reveal that our vibration control system is effective enough to suppress the whirling motion of the rotor caused by a sudden disturbance.

Nonlinear Transient Response Analysis of a Rotor System due to Blade Loss.

In the present paper, an analytical method is presented for predicting the nonlinear transient response of an aircraft engine due to the loss of a fan blade. The casing of an aircraft engine and rotors are modeled as Timoshenko beams and analyzed using the incremental transfer matrix method with the Newmark-β or Wilson-θ method. The local deflection effect of a casing cross section and the support stiffnesses are examined by FEM and are taken into account in the model. Nonliner elements are considered for contact and rubbing of the fan with casing and squeeze film dampers. Although some numerical problems still remain when very short time steps are chosen for the time integration, the present calculation method is fairly efficient and useful.

Development of Porous Squeeze Film Damper Bearings for Improving the Blade Loss Dynamics of Rotor-Support Systems

An efficient oil film damper known as porous squeeze film damper (PSFD) is developed based on conventional squeeze film damper (SFD) for more effective and reliable rotor vibration control and especially for improving the blade loss dynamics for rotor support system. The permeability of the outer race of PSFD could remarkably improve the squeeze film damping properties. The transient response of a simple rigid rotor and flexible Jeffcott’s rotor supported on PSFD and SFD subjected to sudden unbalance of blade loss are investigated. Time transient simulation show that PSFD could operate effectively under much greater unbalance as compared with SFD, especially under relative large impact loading of blade loss. Furthermore, the effective eccentricities of PSFD with small transmissibilities (T<1.0) extend to a range of ε<0.9, and optimum film stiffness and damping distribution within the whole film clearance could be achieved.

Wake Measurements and Loss Evaluation in a Controlled Diffusion Compressor Cascade

The results of two component laser-Doppler velocimeter (LDV) surveys made in the near wake (to one fifth chord) of a controlled diffusion (CD) compressor blade in a large-scale cascade wind tunnel are reported. The measurements were made at three positive incidence angles from near design to angles thought to approach stall. Comparisons were made with calibrated pressure probe and hot-wire wake measurements and good agreement was found. The flow was found to be fully attached at the trailing edge at all incidence angles and the wake profiles were found to be highly skewed. Despite the precision obtained in the wake velocity profiles, the blade loss could not be evaluated accurately without measurements of the pressure field. The blade trailing edge surface pressures and velocity profiles were found to be consistent with downstream pressure probe measurements of loss, allowing conclusions to be drawn concerning the design of the trailing edge.

An inviscid model for the base pressure of transonic turbine cascade

An inviscid base pressure model for transonic turbine blade has been presented. It has been shown that for a given back pressure the base pressure at the trailing edge, and the profile loss of a turbine blade are fixed according to the model and the base pressure can be calculated with the help of an inviscid numerical scheme. A parameteric study on the model shows that a blade profile with positive curvature downstream of the throat is advantageous for generating less loss, whilst the worst situation is when the exit flow reaches the sonic condition.

The Trailing Edge Loss of Transonic Turbine Blades

Trailing edge loss is one of the main sources of loss for transonic turbine blades, contributing typically 1/3 of their total loss. Transonic trailing edge flow is extremely complex, the basic flow pattern is understood but methods of predicting the loss are currently based on empirical correlations for the base pressure. These correlations are of limited accuracy. Recent findings that the base pressure and loss can be reasonably well predicted by inviscid Euler calculations are justified and explained in this paper. For unstaggered choked blading, it is shown that there is a unique relationship between the back pressure and the base pressure and any calculation that conserves mass, energy and momentum should predict this relationship and the associated loss exactly. For realistic staggered blading, which operates choked but with subsonic axial velocity, there is also a unique relationship between the back pressure and the base pressure (and hence loss) but the relationship cannot be quantified without knowing a further relationship between the base pressure and the average suction surface pressure downstream of the throat. Any calculation that conserves mass, energy and momentum and also predicts this average suction surface pressure correctly will again predict the base pressure and loss. Two-dimensional Euler solutions do not predict the suction surface pressure exactly because of shock smearing but nevertheless seem to give reasonably accurate results. The effects of boundary layer thickness and trailing edge coolant ejection are considered briefly. Coolant ejection acts to reduce the mainstream loss. It is shown that suction surface curvature downstream of the throat may be highly beneficial in reducing the loss of blades with thick trailing edges operating at high subsonic or low supersonic outlet Mach numbers.

Transient vibration of lightweight rotor due to sudden imbalance.

The transient vibration due to imbalance of a lightweight rotor that comprises flexible blades, disk, shaft, and rigid bearings is analyzed by a finite element method. The dimensions of matrices used in the computation are reduced by representing the shaft and blades by beam elements, and the disk by annular elements. The computed results are compared with the experimental data obtained by a test conducted on a small model rotor with a blade loss simulator. A fairly good agreement was obtained between the computed and experimental results.

Active Control of Transient Rotordynamic Vibration by Optimal Control Methods

Although considerable effort has been put into the study of steady-state vibration control, there are few methods applicable to transient vibration control of rotor-bearing systems. In this paper optimal control theory has been adopted to minimize rotor vibration due to sudden imbalance, e.g., blade loss. The system gain matrix is obtained by choosing the weighting matrices and solving the Riccati equation. Control forces are applied to the system via a feedback loop. A seven mass rotor system is simulated for illustration. A relationshp between the number of sensors and the number of modes used in the optimal control model is investigated. Comparisons of responses are made for various configurations of modes, sensors, and actuators. Furthermore, spillover effect is examined by comparing results from collocated and noncollocated sensor configurations. Results show that shaft vibration is significantly attenuated in the closed-loop system.

Mixed fungal populations and lignocellulosic tissue degradation in the bovine rumen.

Anaerobic fungi in ruminal fluid from cows eating Bermuda grass hay plus a grain and minerals supplement were evaluated for diversity in sporangial morphotypes and colony growth patterns and for the degradation of various lignocelluloses. In selective cultures containing streptomycin and penicillin, an active population of ruminal fungi colonized leaf blades and degraded fiber at rates and extents almost equal to that of the total ruminal population. Three major sporangial morphotypes were consistently observed on leaf blades: oval, globose, and fusiform. Fungal colonies representing three distinct growth types consistently developed in anaerobic roll tubes inoculated with strained ruminal fluid. Sporangial morphotypes could not be matched to colony types due to multiple sporangial forms within a colony. Under identical growth conditions, one type exhibited a monocentric growth pattern, while two types exhibited polycentric growth patterns previously unreported in ruminal fungi. Mixed ruminal fungi in selective cultures or in digesta taken directly from the rumen produced a massive clearing of the sclerenchyma. Quantitation of tissue areas in cross sections by light microscopic techniques showed that fungal incubations resulted in significant (P = 0.05) increases in sclerenchyma degradation compared to whole ruminal fluid incubations. The mestome cell wall was at times penetrated and partially degraded by fungi; the colonization was less frequent and to a lesser degree than with the sclerenchyma. Conversely, ruminal bacteria were not observed to degrade the mestome sheath. Phenolic monomers at 1 mM concentrations did not stimulate to a significant (P = 0.05) extent the dry weight loss or fungal colonization of leaf blades; at 10 mM concentrations cinnamic and benzoic acids were toxic to ruminal fungi.

An Experimental Investigation Into Unsteady Blade Forces and Blade Losses in Axial Compressor Blade Cascade

The unsteady flow problem in the axial compressor has been simulated in wind-tunnels by means of high-speed rotating cylinders upstream of the blade row. To obtain the dynamic changes in the flow properties 20 high-response pressure transducers and 20 high-response hot-film, which are embedded at the surface of the selected blade, have been used in connection with a periodic sampling and averaging technique in digital data acquisition and reduction. The fluctuating forces and the fluctuating drags acting on the blade due to passing wakes shedding through the blade row are carried out.

Dual Clearance Squeeze Film Damper for High Load Conditions

Squeeze film dampers are widely used to control vibrations in aircraft turbine engines and other rotating machinery. However, if shaft unbalance rises appreciably above the design value (e.g., due to a turbine blade loss), a conventional squeeze film will be overloaded, and will no longer be effective in controlling vibration amplitudes and bearing forces. This paper describes a new damper concept characterized by two oil films. Under normal conditions, only one low-clearance film is active, allowing precise location of the shaft centerline. Under high unbalance conditions, both films are active, controlling shaft vibration in a near-optimum manner, and allowing continued operation until a safe shutdown can be made.

A Blade Loss Response Spectrum for Flexible Rotor Systems

A shock spectrum procedure is developed to estimate the peak displacement response of linear flexible rotor-bearing systems subjected to a step change in unbalance (i.e., a blade loss). A progressive and a retrograde response spectrum are established. These blade loss response spectra are expressed in a unique non-dimensional form and are functions of the modal damping ratio and the ratio of rotor spin speed to modal damped whirl speed. Modal decomposition using complex modes is utilized to make use of the unique feature of the spectra for the calculation of the peak blade loss displacement response of the rotor system. The procedure is applied to three example systems using several modal superposition strategies. The results of each are compared to true peak displacements obtained by a separate transient response program.

Seasonal growth of two subtidal species of rhodophyta off the isle of man

Whole plants of Delesseria sanguinea (Huds.) Lamour. and Odonthalia dentata (L.) Lyngb. were collected from 2 m below lowest astronomical tide on Port Erin breakwater and 1 to 17 m off Spanish Head, Isle of Man, Irish Sea. In shallow water there was a four- and three-fold seasonal variation respectively in mean plant weight in the two species. Individual blades were measurable by mid-February and doubled in weight about every 2 wk between then and late March. Growth was slow by June but continued until August. In Odonthalia there was a loss of whole blades in late summer but little reduction in blade size while in Delesseria both losses occurred in autumn. In deeper water blades of each species grew more slowly, particularly early in the year. A minimum age could be ascertained for each part of Odonthalia plants and from this it was apparent that few blades survived the first year but those that did lost little weight. This species was shown to accumulate tissue over the years, older plants being capable of bearing more tissue of each year's growth. In shallow water Odonthalia plants probably often lived > 5 yr and Delesseria plants probably longer. In deeper water plants were shorter lived and smaller. There was slender evidence for some dependence on stored material for early spring growth.