Journal articles on the topic 'Blade cascade theory'

A lifting surface theory is developed to predict the unsteady three-dimensional aerodynamic characteristics for a rotating subsonic annular cascade of swept blades. A discrete element method is used to solve the integral equation for the unsteady blade loading. Numerical examples are presented to demonstrate effects of the sweep on the blade flutter and on the acoustic field generated by interaction of rotating blades with a convected sinusoidal gust. It is found that increasing the sweep results in decrease of the aerodynamic work on vibrating blades and also remarkable reduction of the modal acoustic power of lower radial orders for both forward and backward sweeps.

An experimental and analytical study of flow in the tip clearance gap of a linear turbine rotor blade cascade has been performed. Measurements of wall static pressures and flow velocities are used to verify a flow model involving a vena contracta, near the tip gap entrance, followed by flow mixing to fill the gap. A frequently referenced potential flow theory for flow into a tip gap is found to be in error and the correct theory is shown to model the unloading along the pressure surface of the blade and the endwall static pressure distribution up to the vena contracta accurately. A combined potential flow and mixing model accounts for the pressure rise in the tip gap due to mixing. Turbine tip heat transfer is also discussed and a correlation of local heat transfer rates for essentially incompressible flow over unshrouded turbine rotor blades is presented.

Abstract A method of modelling of nozzle and rotor blade rows of gas turbine dedicated to simulations of gas turbine performance is proposed. The method is applicable especially in early design stage when many of geometric parameters are yet subject to change. The method is based on analytical formulas derived from considerations of flow theory and from cascade experiments. It involves determination of parameters of gas flow on the mean radius of blade rows. The blade row gas exit angle, determined in turbine design point is a basis for determination of details of blade contour behind the throat position. Throat area is then fixed based on required maximum mass flow in critical conditions. Blade leading edge radius is determined based on flow inlet angle to the blade row in the design point. The accuracy of analytical formulas applied for definition of blade contour details for assumed gas exit angle was verified by comparing the results of analytical formulas with CFD simulations for an airfoil cascade. Losses of enthalpy due to non-isentropic gas flow are evaluated using the analytical model of Craig and Cox, based on cascade experiments. Effects of blade cooling flows on losses of total pressure of the gas are determined based on analytical formulas applicable to film cooling with cooling streams blowing from discrete point along blade surface, including leading and trailing edges. The losses of total pressure due to film cooling of blades are incorporated into the Craig and Cox model as additional factor modifying gas flow velocities.

Sweep, when the stacking axis of the blade is not perpendicular to the axisymmetric streamsurface in the meridional view, is often an unavoidable feature of turbine design. Although a high aspect ratio swept blade can be designed to achieve the same pressure distribution as an unswept design, this paper shows that the swept blade will inevitably have a higher profile loss. A modified Zweifel loading parameter, taking sweep into account, is first derived. If this loading coefficient is held constant, it is shown that sweep reduces the required pitch-to-chord ratio and thus increases the wetted area of the blades. Assuming fully turbulent boundary layers and a constant dissipation coefficient, the effect of sweep on profile loss is then estimated. A combination of increased blade area and a raised pressure surface velocity means that the profile loss rises with increasing sweep. The theory is then validated using experimental results from two linear cascade tests of highly loaded blade profiles of the type found in low-pressure aeroengine turbines: one cascade is unswept, the other has 45deg of sweep. The swept cascade is designed to perform the same duty with the same loading coefficient and pressure distribution as the unswept case. The measurements show that the simple method used to estimate the change in profile loss due to sweep is sufficiently accurate to be a useful aid in turbine design.

A time-accurate Navier–Stokes analysis is needed for understanding the relative importance of nonlinear and viscous effects on the unsteady flows associated with turbomachinery blade vibration and blade-row noise generation. For this purpose an existing multi-blade-row Navier–Stokes analysis has been modified and applied to predict unsteady flows excited by entropic, vortical, and acoustic disturbances through isolated, two-dimensional blade rows. In particular, time-accurate, non-reflecting inflow and outflow conditions have been implemented to allow specification of vortical, entropic, and acoustic excitations at the inlet, and acoustic excitations at the exit, of a cascade. To evaluate the nonlinear analysis, inviscid and viscous numerical simulations were performed for benchmark unsteady flows and the predicted results were compared with analytical and numerical results based on linearized inviscid flow theory. For small-amplitude unsteady excitations, the unsteady pressure responses predicted with the nonlinear analysis show very good agreement, both in the field and along the blade surfaces, with linearized inviscid solutions. Based on a limited range of parametric studies, it was also found that the unsteady responses to inlet vortical and acoustic excitations are linear over a surprisingly wide range of excitation amplitudes, but acoustic excitations from downstream produce responses with significant nonlinear content.

This paper extends an existing analytical model of the aeroacoustic response of a rectilinear cascade of flat-plate blades to three-dimensional incident vortical gusts, by providing closed-form expressions for the acoustic field inside the inter-blade channels, as well as for the pressure jump over the blades in subsonic flows. The extended formulation is dedicated to future implementation in a fan-broadband-noise-prediction tool. The intended applications include the modern turbofan engines, for which analytical modelling is believed to be a good alternative to more expensive numerical techniques. The initial model taken as a reference is based on the Wiener–Hopf technique. An analytical solution valid over the whole space is first derived by making an extensive use of the residue theorem. The accuracy of the model is shown by comparing with numerical predictions of benchmark configurations available in the literature. This full exact solution could be used as a reference for future assessment of numerical solvers, of linearized Euler equations for instance, in rectilinear or narrow-annulus configurations. In addition, the pressure jump is a key piece of information because it can be used as a source term in an acoustic analogy when the rectilinear-cascade model is applied to three-dimensional blade rows by resorting to a strip-theory approach. When used as such in a true rectilinear-cascade configuration, it reproduces the exact radiated field that can be derived directly. The solution is also compared to a classical single-airfoil formulation to highlight the cascade effect. This effect is found important when the blades of the cascade overlap significantly, but the cascade solution tends to the single-airfoil one as the overlap goes to zero. This suggests that both models can be used as the continuation of each other if needed.

An inverse design procedure has been developed for the optimum mistuning of a high bypass ratio shroudless fan. The fan is modeled as a cascade of blades, each with a single torsional degree of freedom. Linearized supersonic aerodynamic theory is used to compute the unsteady aerodynamic forces in the influence coefficient form at a typical blade section. The mistuning pattern is then numerically optimized using the method of nonlinear programming via augmented Lagrangians. The objective of the mistuning is to achieve a specified increase in aeroelastic stability margin with a minimum amount of mistuning. It is shown that a necessary but not sufficient condition for aeroelastic stability is that the blades be self-damped. If this condition is met, an optimized mistuning pattern can be found that achieves a given stability margin for a much lower level of mistuning than is required for the alternate mistuning pattern. However, small errors in the implementation of the optimum mistuning pattern severely reduce the anticipated gains in stability margin. These small errors are introduced by the manufacturing process and by the approximation of the optimum mistuning pattern by patterns of a few discrete blade frequencies. Alternate mistuning, which requires only two blade frequencies, is shown to be relatively insensitive to errors in implementation.

In the field of axial flow turbomachines, the two-dimensional cascade model is often used experimentally or numerically to investigate fundamental flow characteristics and overall performance of the impeller. The core of the present work is a design method for axial fan cascades aiming to derive inversely the optimum blade shape based on the requirements of the impeller and not using any predefined aerofoil profiles. While most design strategies based on the aerofoil theory assume constant total pressure at all streamlines, i.e. free-vortex flow, this paper investigates the possibility of varying the total pressure along the blade and based on that, an analytical expression of the outlet blade angle is determined. When computing the blade profile at a specified radius, critical parameters reflecting on the flow characteristics are observed and adjusted (i.e. sufficient lift and controlled deceleration of the flow on the contour) so that the resulting profile is derived for minimum losses. The validation of this design strategy is given by the numerical results obtained when employed as an optimization tool for an industrial fan: 10–20 per cent absolute increase in the static efficiency of the optimized impeller.

An application of a simple aeroelastic model to an advanced supersonic axial flow fan is presented. Lane’s cascade theory is used to determine the unsteady aerodynamic loads. Parametric studies are performed to determine the effects of mode coupling, Mach number, damping, pitching axis location, solidity, stagger angle, and mistuning. The results show that supersonic axial flow fan and compressor blades are susceptible to a strong torsional mode flutter having critical reduced velocities that can be less than one.

The development of hub and casing boundary layers through a turbomachine is difficult to predict, giving rise to uncertainty in the boundary conditions experienced by each blade row. Previous studies in turbine cascades disagree on the sensitivity of endwall loss to such inlet conditions. This paper explores the problem computationally, by examining a large number of turbine cascades and varying the inlet boundary layer thickness. It is demonstrated that the sensitivity of endwall loss to inlet conditions is design dependent, and determined by the component of endwall loss associated with the secondary flow. This Secondary-Flow-Induced loss is characterised by a vorticity factor based on classical secondary flow theory. Designs that produce high levels of secondary vorticity tend to generate more loss and are more sensitive to inlet conditions. This sensitivity is largely driven by the dissipation of Secondary Kinetic Energy (SKE): thickening the inlet boundary layer causes the secondary vorticity at the cascade exit to be more dispersed within the passage, resulting in larger secondary flow structures with higher SKE. The effects are captured using a simple streamfunction model based on classical secondary flow theory, which has potential for preliminary design and sensitivity assessment.

A computational method is presented for predicting the unsteady aerodynamic response of a vibrating blade row that is part of a multistage turbomachine. Most current unsteady aerodynamic theories model a single blade row isolated in an infinitely long duct. This assumption neglects the potentially important influence of neighboring blade rows. The present “coupled mode” analysis is an elegant and computationally efficient method for modeling neighboring blade row effects. Using this approach, the coupling between blade rows is modeled using a subset of the so-called spinning modes, i.e., pressure, vorticity, and entropy waves, which propagate between the blade rows. The blade rows themselves are represented by reflection and transmission coefficients. These coefficients describe how spinning modes interact with, and are scattered by, a given blade row. The coefficients can be calculated using any standard isolated blade row model; here we use a linearized full potential flow model together with rapid distortion theory to account for incident vortical gusts. The isolated blade row reflection and transmission coefficients, interrow coupling relationships, and appropriate boundary conditions are all assembled into a small sparse linear system of equations that describes the unsteady multistage flow. A number of numerical examples are presented to validate the method and to demonstrate the profound influence of neighboring blade rows on the aerodynamic damping of a cascade of vibrating airfoils.

The growth of losses, secondary kinetic energy, and streamwise vorticity have been studied in a high turning rotor cascade. Negative vorticity associated with the passage vortex agreed well with predictions of classical secondary flow theory in the early part of the blade passage. However, toward the exit, the distortion of the flow by the secondary velocities rendered the predictions inaccurate. Areas of positive vorticity were associated with the feeding of loss into the bulk flow and have been related to separation lines observed by surface flow visualization.

The sound generated by the interaction between convected vortical and entropic disturbances and a blade row is a significant component of the total noise emitted by a modern aeroengine, and the blade geometry has an important effect on this process. As a first step in the development of a general prediction scheme, we model in this paper just the action of the blade mean loading by treating the blades as flat plates aligned at a non-zero incidence angle, δ, to the oncoming stream, and consider harmonic components of the incident field with reduced frequency k. We then use asymptotic analysis in the realistic limit k[Gt ]1, δ[Lt ]1 with kδ=O(1) to make a consistent asymptotic expansion of the compressible Euler equations. The flow is seen to consist of inner regions around each leading edge, in which sound is generated by the local gust–airfoil and gust–flow interactions, and an outer region in which both the incident gust is distorted according to rapid distortion theory and the out-going sound is refracted by the non-uniform mean flow. The complicated multiple interactions between the sound and the cascade are included to the appropriate asymptotic order, and analytical expressions for the forward radiation are derived. It is seen that even a relatively small value of δ can have a significant effect, thanks to both the O(δk1/2) change in the amplitudes and the O(kδ) change in the phases of the various radiation components, corresponding to the additional source mechanisms associated with the flow distortion around each leading edge and the effects of propagation through the non-uniform flow, respectively. Further work will extend this analysis to include the effects of camber and thickness.

Abstract The article discusses the phenomenon of stator Wake/Rotor cascade (W/R) interaction in a steam turbine stage, and the ability to capture it in turbine stage design calculations making use of standard numerical codes. Firstly, the W/R interaction is analysed by comparing its real, experimentally recorded course with the numerical results obtained using vortex theory models and methods. This part of the analysis ends with formulating a conclusion about stochastic nature of the W/R interaction and indicating its reason, which is the vortex structure of the stator wake. Next, a question is discussed whether and how this stochastic nature of the examined phenomenon can be taken into account in calculations of Reynolds Averaged Navier-Stokes (RANS) equations. Differences are indicated between the uniform pattern of the stator wake obtained using a RANS code and the vortex structure of the real wake. It is concluded, however, that despite these differences the RANS results correctly reflect the time-averaged course of the real W/R interaction, and the process of averaging the flow parameters on the sliding plane between stator and rotor calculation areas can be treated as sort of “numerical averaging” of different realisations of the W/R interaction.

This paper describes an Eulerian/Lagrangian two-phase model for nucleating steam based on classical nucleation theory. The model provides an approach for including spontaneous homogeneous nucleation within a full Navier-Stokes solution scheme where the interaction between the liquid and gas phases for a pure fluid is through appropriately modeled source terms. The method allows for the straightforward inclusion of droplet heat, mass, and momentum transfer models along with nucleation within complex flow systems as found, for example, in low pressure steam turbines. The present paper describes the solution method, emphasizing that the important features of nucleating steam flow are retained through comparison with well-established 1-D solutions for Laval nozzle flows. Results for a two-dimensional cascade blade and three-dimensional low pressure turbine stage are also described.

With the development of the city sewage treatment, the request of the specific speed of axial flow pump has been higher and higher. At present China is lack of the system theory and method to design axial flow pump above 1400 specific speed. Selection methods of design parameters depend on experience. This paper used the improved lifting method to design axial flow pump. Optimize design of axial flow pump from cascade solidity, blade number, ratio hub and the airfoil of impeller. The feasibility of such optimize methods had been validated from theoretical analysis. Put forward new selection methods of design parameters. Design an impeller model. The rated condition of flow rate is 3000 m3/h and the rated condition of lift is 1 m. A useful reference of axial flow pump design, improvement and optimization was obtained.

A theoretical model to explain observed rapid large-scale surface heat transfer rate fluctuations associated with the impingement of nozzle guide vane trailing edge shock waves on a transonic turbine rotor blade is described. Experiments were carried out in the Oxford Isentropic Light Piston Cascade Tunnel using an upstream rotating bar system to simulate the shock wave passing. High-frequency surface heat transfer and pressure measurements gave rapidly varying, large, transient signals, which schlieren photography showed to be associated with the impingement of passing shock waves on the surface. Heat transfer rates varying from three times the mean value to negative quantities were measured. A simple first-order perturbation analysis of the boundary layer equations shows that the transient adiabatic heating and cooling of the boundary layer by passing shock waves and rarefactions can give rise to high-temperature gradients near the surface. This in turn leads to large conductive heat transfer rate fluctuations. The application of this theory to measured fluctuating pressure signals gave predictions of fluctuating heat transfer rates that are in good agreement with those measured. It is felt that the underlying physical mechanisms for shock-induced heat transfer fluctuations have been identified. Further work will be necessary to confirm them in rotating experiments.

Using the facility described in Part 1 [23], 11 detailed velocity and turbulence intensity profiles are obtained on the pressure surface of a double circular arc compressor blade in cascade. Two profiles are obtained in the near wake. Laminar boundary layer profiles, which agree well with profiles calculated from Falkner–Skan theory at the local pressure gradient, persist through 57.2 percent chord. The measurements indicate that the onset of transition occurs near 60 percent chord—a value in good agreement with the sublimation flow visualization studies (see Part 1). The lack of a logarithmic region in the data measured at the last chord position (97.9 percent chord) indicates that transition is not complete. The thin laminar boundary layers near the leading edge lead to some measurement problems, which are characterized by large turbulence intensities, in using the laser-Doppler velocimeter (LDV). Close examination of this problem shows that a combination of velocity-gradient broadening and a vibration of the LDV measurement volume causes an elevation of the measured turbulence levels. Fortunately only small errors in mean velocity are introduced. Because of the detached boundary layer on the suction surface, both of the near-wake velocity profiles exhibit regions of backflow. As expected, these near-wake velocity profiles do not exhibit similarity when tested against criteria derived for the far wake.

The available literature on aerodynamic and acoustic properties of axial fans with swept blades is presented and discussed with particular emphasis on noise mechanisms and the influence of high-intensity inlet turbulence on “excess” noise. The acoustic theory of Kerschen and Envia for swept cascades is applied to the problem of axial fan design. These results are compared to available data and a provisional model for specifying sweep angles is presented. The aerodynamic performance theory for swept-bladed rotors of Smith and Yeh is adapted for use in designing low-speed axial fans. Three prototype fans were designed using the resultant computer codes. One is a baseline fan with blade stocking lines radially oriented, and two are fans having swept blades of increasingly greater forward sweep. Aerodynamic testing shows that performance of the fans lies within a band width of about ± 2 percent of volume flow rate and pressure rise predictions in the region of design performance, effectively validating the design procedure for selection of the blading parameters. Noise testing of the fans was carried out and the results show an average noise reduction for the swept-bladed fans of about 7 dBA overall, and a reduction of pure tone noise at blade-pass frequency of about 10 dB compared to the zero-sweep baseline model, in close agreement with the theory of Kerschen and Envia.

This paper aims at evaluating the characteristics of the wakes periodically shed by the rotating bars of a spoked-wheel type wake generator installed upstream of a high-speed low Reynolds linear low-pressure turbine blade cascade. Due to the very high bar passing frequency obtained with the rotating wake generator (fbar = 2.4−5.6 kHz), a fast-response pressure probe equipped with a single 350 mbar absolute Kulite sensor has been used. In order to measure the inlet flow angle fluctuations, an angular aerodynamic calibration of the probe allowed the use of the virtual three-hole mode; additionally, yielding yaw corrected periodic total pressure, static pressure and Mach number fluctuations. The results are presented for four bar passing frequencies (fbar = 2.4/3.2/4.6/5.6 kHz), each tested at three isentropic inlet Mach numbers M1,is = 0.26/0.34/0.41 and for Reynolds numbers varying between Re1,is = 40,000 and 58,000, thus covering a wide range of engine representative flow coefficients (ϕ = 0.44−1.60). The measured wake characteristics show fairly good agreement with the theory of fixed cylinders in a cross-flow and the evaluated total pressure losses and flow angle variations generated by the rotating bars show fairly good agreement with theoretical results obtained from a control volume analysis.

The paper describes the theory and the numerical implementation of a three-dimensional finite volume scheme for the solution of the linearized, unsteady Favre-averaged Navier–Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangles and quadrilaterals in two dimensions, and of tetrahedra, triangular prisms, and hexahedra in three dimensions. The linearized unsteady viscous flow equations are derived by assuming small harmonic perturbations from a steady-state flow and the resulting equations are solved using a pseudo-time marching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow computations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element meshes, the use of a Laplacian operator, which results in a nearest neighbor stencil, and the full linearization of the Spalart–Allmaras turbulence model. Four different test cases are presented for the validation of the proposed method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the second test case is to check the computational results against the asymptotic analytical solution derived by Lighthill for an unsteady laminar flow. The third test case examines the implications of using inviscid, frozen-turbulence, and fully turbulent models when linearizing the unsteady flow over a transonic turbine blade, the so-called 11th International Standard Configuration. The final test case is a rotor/stator interaction, which not only checks the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady flow data for the last two cases and good overall agreement was obtained.

A linear design system, already in use for the forward and inverse design of three-dimensional turbine aerofoils, has been extended for the design of their end walls. This paper shows how this method has been applied to the design of a nonaxisymmetric end wall for a turbine rotor blade in linear cascade. The calculations show that nonaxisymmetric end wall profiling is a powerful tool for reducing secondary flows, in particular the secondary kinetic energy and exit angle deviations. Simple end wall profiling is shown to be at least as beneficial aerodynamically as the now standard techniques of differentially skewing aerofoil sections up the span, and (compound) leaning of the aerofoil. A design is presented that combines a number of end wall features aimed at reducing secondary loss and flow deviation. The experimental study of this geometry, aimed at validating the design method, is the subject of the second part of this paper. The effects of end wall perturbations on the flow field are calculated using a three-dimensional pressure correction based Reynolds-averaged Navier–Stokes CFD code. These calculations are normally performed overnight on a cluster of work stations. The design system then calculates the relationships between perturbations in the end wall and resulting changes in the flow field. With these available, linear superposition theory is used to enable the designer to investigate quickly the effect on the flow field of many combinations of end wall shapes (a matter of minutes for each shape). [S0889-504X(00)00902-8]

The goal of the paper is to describe wake parameters of wakes from turbine cascades in compressible flows especially in planes where the leading edge of the following blade row would be located. Data from experiments with turbine cascades in compressible flow will be used to derive a theoretical approach which describes the wake growth and the recovery of the velocity deficit. The theory is based on similarity assumptions. The derived equations depend on simple and readily available parameters such as overall losses, exit angle, and Mach or Laval number. In compressible turbine flows, the influence of the inviscid flow field is of great importance. In this paper, an approach to take this influence into account when determining the behavior of the wake is presented. Correlations for basic characteristics of wakes in compressible flows are not readily available. Such correlations are necessary as input to unsteady flow and heat transfer calculation procedures for turbomachine blades. Based on available data on wake behavior in the compressible flow behind turbine blades, the correlations presented describe the wake behavior from the trailing edge to the confluence of the wakes of adjacent blades.

Inverse design of cascades for low Reynolds number can be applied for the aerodynamic development of fans and compressors. The present contribution describes a complete design procedure by taking into account the transition from laminar to turbulent boundary layer flow. A shape factor distribution is prescribed along the suction surface of the blades. The inverse boundary layer calculation is performed by the application of a finite difference method. On the pressure side the velocity distribution is prescribed in such a way that the given flow angles in front of and behind the cascade are realized. An inverse calculation based on potential theory is applied in order to determine the geometry of the cascade. At the end of the present contribution a cascade is designed by the described inverse design procedure and the flow is simulated by the application of CFD.

Boundary layers on turbomachinery blades develop in a flow that is periodically disturbed by the wakes of upstream blade cascades. These wakes have a significant effect upon laminar-turbulent boundary-layer transition. In order to study these effects, detailed velocity measurements using hot-wire probes were performed within the boundary-layer of a plate in flow periodically disturbed by wakes produced by bars moving transversely to the flow. The measurements were evaluated using the ensemble-averaging technique. The results show how the wake disturbance enters the boundary-layer and leads to a turbulent patch, which grows and is carried downstream. In favorable pressure gradients, transition due to wake turbulence occurred much earlier than predicted by linear stability theory. Between two wakes, laminar becalmed regions were observed far beyond the point at which the undisturbed boundary-layer was already turbulent.

The modified total-variation-diminishing scheme and an improved dynamic triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unsteady Euler equations are solved. To validate the accuracy of the present approach, transonic flow around a single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculated instantaneous pressure coefficient distribution during a cycle of motion compare well with the related numerical and experimental data. To evaluate further the present approach involving nonzero interblade phase angle, the calculations of transonic flow around an oscillating cascade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coefficient distributions and time history of lift coefficient, the present approach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using this solution procedure, transonic flows around an oscillating cascade of four biconvex blades with different oscillation amplitudes, reduced frequencies, and interblade phase angles are investigated. From the distributions of magnitude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimental data than those from the linearized theory in most of the cases. For every quarter of one cycle, the pressure contours repeat and proceed one pitch distance in the upward or downward direction for interblade phase angle equal to −90 deg or 90 deg, respectively. The unsteady pressure wave and shock behaviors are observed. From the lift coefficient distributions, it is further confirmed that the oscillation amplitude, interblade phase angle, and reduced frequency all have significant effects on the transonic oscillating cascade flows.

This two-part article presents recent advances in boundary layer research that deal with the unsteady boundary layer transition modeling and its validation. A new unsteady boundary layer transition model was developed based on a universal unsteady intermittency function. It accounts for the effects of periodic unsteady wake flow on the boundary layer transition. To establish the transition model, an inductive approach was implemented; the approach was based on the results of comprehensive experimental and theoretical studies of unsteady wake flow and unsteady boundary layer flow. The experiments were performed on a curved plate at a zero streamwise pressure gradient under a periodic unsteady wake flow, where the frequency of the periodic unsteady flow was varied. To validate the model, systematic experimental investigations were performed on the suction and pressure surfaces of turbine blades integrated into a high-subsonic cascade test facility, which was designed for unsteady boundary layer investigations. The analysis of the experiment's results and comparison with the model's prediction confirm the validity of the model and its ability to predict accurately the unsteady boundary layer transition.

An aeroelastic analysis is presented that accounts for the effect of steady aerodynamic loading on the aeroelastic stability of a cascade of compressor blades. The aeroelastic model is a two-degree-of-freedom model having bending and torsional displacements. A linearized unsteady potential flow theory is used to determine the unsteady aerodynamic response coefficients for the aeroelastic analysis. The steady aerodynamic loading was caused by the addition of (1) airfoil thickness and camber and (2) steady flow incidence. The importance of steady loading on the airfoil unsteady pressure distribution is demonstrated. Additionally, the effect of the steady loading on the tuned flutter behavior and flutter boundaries indicates that neglecting either airfoil thickness, camber, or incidence could result in nonconservative estimates of flutter behavior.

This paper describes a new time marching calculation of blade surface cavitation based on a linearized free streamline theory using a singularity method. In this calculation, closed cavity models for partial and super cavities are combined to simulate the transitional cavity oscillation between partial and super cavities. The results for an isolated hydrofoil located in a 2-D channel are presented. Although the re-entrant jet is not taken into account, the transitional cavity oscillation with large amplitude, which is known to occur when the cavity length exceeds 75 percent of the chord length, was simulated fairly well. The partial cavity oscillation with relatively high frequency was simulated as damping oscillations. The frequency of the damping oscillation agrees with that of a stability analysis and of experiments. The present calculation can be easily extended to simulate other cavity instabilities in pumps or cascades.

In order to meet noise specifications for future foreseen aircraft propulsion systems, such as for ultrahigh bypass ratio turbofans and contra-rotating open rotors, the dominant turbomachinery noise mechanisms need to be modeled accurately at an early design stage. Two novel methods are presented here, which could significantly improve the existing analytical noise models. For the high-solidity ultrahigh bypass ratio, a mode-matching technique based on a modal expansion of acoustic and vortical variables in each subdomain of a blade row is shown to accurately reproduce sound generation and propagation in two-dimensional bifurcated channels and in three-dimensional annular unstaggered flat-plate cascades. For the low solidity contra-rotating open rotors, several extensions to Amiet’s compressible isolated airfoil theory are coupled with Curle’s and Ffowcs Williams and Hawkings’ acoustic analogy in the frequency domain within a strip theory framework, to yield both far-field tonal and broadband noise. Including sweep in both tonal and broadband noise models is shown to significantly improve the comparison with experiments on a stationary swept airfoil in a uniform turbulent stream and on a realistic contra-rotating open rotor geometry at approach conditions.

Introduction. It is possible to give rise to synergy as a result of science-intensive industries combination with innovative eco-technologies for subsoil use only by developing a brand new approach to nature-like auxiliary technologies. Insufficient adaptability of turbomachines that ensure industrial safety increases the production cost of the mining and oil and gas complexes of the Russian Federation by more than 15%, reducing its competitiveness. Research methodology. Based on the hypothesis of the hydrodynamic analogy of the mechanisms of deceleration of the flow around the airfoil and the formation of its profile resistance, Karman's theory of attached and free vortices, the Zhukovsky-Chaplygin-Kutta hypothesis, the method of conformal transformations, the theory of similarity, the method of singular points by Chaplygin S. A., the criteria for the similarity of natural proportionality are obtained, that is, for the hydrodynamic similarity of the mechanism of energy interaction between the blades of the turbomachine impeller and the wing of a bird. Results. It has been proved that the dominant control over the nature-like proportionality of the aerodynamics of turbomachines is the ratio between the speed and flow acceleration circulation around the airfoil. It has been established that the coefficients of the airfoil resistance, lift and aerodynamic quality of the airfoil cascade are hydrodynamic analogs of the coefficients of the circulation of the velocity and acceleration of the flow and their ratio. Conclusions. It has been experimentally confirmed that the use of the proposed criterion of natural proportionality in the design of turbomachines increases their coefficient of aerodynamic adaptability by more than 2 times, increasing the area of economical operation by 83%.

Two- and three-dimensional modal and non-modal instability mechanisms of steady spanwise-homogeneous laminar separated flow over airfoil profiles, placed at large angles of attack against the oncoming flow, have been investigated using global linear stability theory. Three NACA profiles of distinct thickness and camber were considered in order to assess geometry effects on the laminar–turbulent transition paths discussed. At the conditions investigated, large-scale steady separation occurs, such that Tollmien–Schlichting and cross-flow mechanisms have not been considered. It has been found that the leading modal instability on all three airfoils is that associated with the Kelvin–Helmholtz mechanism, taking the form of the eigenmodes known from analysis of generic bluff bodies. The three-dimensional stationary eigenmode of the two-dimensional laminar separation bubble, associated in earlier analyses with the formation on the airfoil surface of large-scale separation patterns akin to stall cells, is shown to be more strongly damped than the Kelvin–Helmholtz mode at all conditions examined. Non-modal instability analysis reveals the potential of the flows considered to sustain transient growth which becomes stronger with increasing angle of attack and Reynolds number. Optimal initial conditions have been computed and found to be analogous to those on a cascade of low pressure turbine blades. By changing the time horizon of the analysis, these linear optimal initial conditions have been found to evolve into the Kelvin–Helmholtz mode. The time-periodic base flows ensuing linear amplification of the Kelvin–Helmholtz mode have been analysed via temporal Floquet theory. Two amplified modes have been discovered, having characteristic spanwise wavelengths of approximately 0.6 and 2 chord lengths, respectively. Unlike secondary instabilities on the circular cylinder, three-dimensional short-wavelength perturbations are the first to become linearly unstable on all airfoils. Long-wavelength perturbations are quasi-periodic, standing or travelling-wave perturbations that also become unstable as the Reynolds number is further increased. The dominant short-wavelength instability gives rise to spanwise periodic wall-shear patterns, akin to the separation cells encountered on airfoils at low angles of attack and the stall cells found in flight at conditions close to stall. Thickness and camber have quantitative but not qualitative effect on the secondary instability analysis results obtained.

In the roadrunner cartoons, the unlucky coyote, in hot pursuit of the roadrunner, frequently finds himself running off the edge of a precipice. In sympathy with the coyote's plight, the laws of physics suspend their action. Gravity waits to exert its force until the coyote realizes his situation and resigns himself to the inevitable. Only then does the coyote fall, miraculously surviving the near-disaster without serious damage. What does this have to do with cell biology at the turn of the millennium? Blame it on JCS's Caveman or at least the infectiousness of the troglodyte's point of view. But it strikes this Editor that for much of cell biology, no less than for the roadrunner, the laws of physics are seemingly suspended. Pick up any contemporary text book or review article and look at the cartoons (diagrams) that grace the pages. You will find diagrams replete with circles, squares, ellipsoids and iconic representations of molecular components, supramolecular assemblies or membrane compartments. Arrows define signal cascades, pathways of transport and patterns of interaction. Even better, check out any of the supplementary instructional CDs that accompany text books and view the animations. You will see cell toons - molecules moving on smooth trajectories to interact with their partners, assembling into cellular machinery or arriving at cellular destinations. They all seem to know where to go and what to do in their cell toon life. It doesn't matter whether we are talking about DNA replication, protein synthesis, mitochondrial respiration, membrane trafficking, nuclear import, chromatin condensation or assembly of the mitotic spindle to mention just a few examples. In each case, the process unfolds before us as a molecular ballet choreographed by a hidden director. Or should I say anonymous animator. Please don't get me wrong. Cartoon diagrams are a necessary part of science. They help us to form and communicate concepts. Adages such as ‘a picture is worth a thousand words’ do not come into existence for nothing. Further, simplification is necessary to sharpen Occam's razor. Science progresses faster if a hypothesis is honed to the point where it can be readily refuted. Of course, it is best to be right. Next best is to be wrong. But the worst thing that can be said about a concept is that it is so hedged or ambiguous that it cannot even be wrong. Cartoons are invaluable in presenting clear alternatives. And cartoons, by definition, do not attempt to portray reality. We understand and accept that they deliberately omit details which may be important in some other context but which are extraneous to the story line. We do not have to know how the coyote recovers from his disastrous fall. It is sufficient that he resumes the chase. Likewise, much of Cell Biology can satisfactorily be ‘explained’ in terms of the behavior of toons. My thesis for this essay is that cell biology at the turn of the millennium has, for the first time, the real opportunity to burst the frames of the cartoons. The field has progressed to the point where the maxim that cells obey the laws of physics and chemistry can be made more than a creed. The time is approaching for the mystery of the hidden directornymous animator to be dispelled. What is driving this new orientation and what is required to bring it to fruition? Advances in structural biology provide part of the explanation. Atomic structures have been determined for a large variety of proteins, with the number increasing on a daily basis. Structural genomics will succeed genomics. It is possible to foresee that in the not too distant future atomic structures will be known for most if not all the major proteins in a cell. Not only individual proteins but supramolecular assemblies as complex as the ribosome have yielded to structural analysis. Of course, structures per se are static entities, but biology has taught that function is inherent in structure. Knowledge of molecular structures has provided atomic explanations for ligand binding, allosteric interaction, enzymatic catalysis, ion pumps, immune recognition, sensory detection and mechano-chemical transduction. When combined with kinetics, structural biology provides the chemical bedrock of cell biology. But the bedrock of structural biology, while necessary for the new cell biology, is almost certainly not sufficient. A major gap is in understanding the complex properties of self-organizing systems. Cells are ensembles of molecules interacting within boundaries. Some of the molecules are organized into supramolecular assemblies that have been likened to molecular machines. Examples include multi-enzyme complexes, DNA replication complexes, the ribosome and the proteasome. Understanding the operation of these molecular machines in chemical and physical terms is a major challenge in that they display exotic behavior such as solid-state channeling of substrates, error-checking, proof-reading, regulation and adaptiveness. Nevertheless, the conceptual basis for their formation is thought to rest on well-established principles: namely, the equilibrium self-assembly of molecular components whose specific affinities are inherent in their 3-D structure. However, other aspects of cellular organization manifest properties beyond self-assembly. The cytoskeleton, for example, is a steady-state system which requires the continuous input of energy to maintain its organization. It displays emergent properties of self-organization, self-centering, self-polarization and self-propagating motility. Membrane compartments such as the endoplasmic reticulum, the Golgi apparatus and transport vesicles provide additional examples of cellular organization dependent upon dynamic processes far from equilibrium. A further level of complexity is introduced by the fact that the self-organization of one system, such as membrane compartments, may be dependent upon another, such as the cytoskeleton. A challenge for the new cell biology is to go beyond ‘toon’ explanations, to understand the emergent, self-organizing properties of interdependent systems. It is likely that an adequate response to this challenge will be multidisciplinary, involving approaches not normally associated with mainstream cell biology. We are likely to be in for a heavy dose of biophysics, computer modeling and systems analysis. A serious problem will be to identify functional levels of decomposition and reconstitution. Because of the microscopic scale, thermal energy, randomness and stochastic processes will be an intrinsic part of the landscape. Brownian motions may present a Damoclean double edge. They are commonly thought to be responsible for the degradation of order into disorder. But, counterintuitively, random thermal processes may also provide the raw energy which, if biased by energy-dependent molecular switches and motors, generates order from disorder. Non-deterministic processes and selection from among alternative pathways may be a common strategy. Fluctuation theory, probabilistic formulations and rare events may underpin the capacity of molecular ensembles to ‘evolve’ into ordered configurations. Further, biological properties such as error-checking and adaptiveness imply an ‘intelligence’, which suggests that the systems analysis may have ‘software’ as well as ‘hardware’ dimensions. Molecular logic may be non-deterministic, ‘fuzzy’ and able to ‘learn’. The evolvability of the system may itself be an important consideration in understanding the design principles. The belief that cells obey the laws of physics and chemistry means that, in terms of the molecular ballet, the director is not only hidden - he doesn't exist. One is tempted to say that the challenge is to understand how the ballet came to be self- choreographed. But even this formulation misses the point that the individual dancers have no definite positions on the stage. Organization in the cell is a continuity of form, not individual molecules. The challenge is to understand how the ensemble is able to perform the dance with chaotic free substitution.

Recently, the newspapers and journals were bubbling with articles and editions devoted to various kinds of millennium and Y2K perspective. Some were retrospective and others prospective; some simply comprised lists of ‘greatests’. Interpreting the past with accuracy and insight is challenging, as is predicting the future. Fortunately, many others have already done that. So, instead, I will look at our discipline, cell biology, defined very broadly and to include molecular biology, both prospectively and retrospectively in the context of some perhaps prosaic but pertinent questions about the discipline that are surfacing as the centuries change. Many greats: One approach to summarizing the past is through lists of the greatest participants or classic papers in a given area. These lists appear frequently in areas like physics and mathematics, where progress is, or at least was, heavily influenced by heroic individuals who opened or sustained a field. In these areas, most participants and observers would develop a very similar list of the ‘greatests’, and nearly everyone working in the discipline would know what their contribution was. Is this true in cell biology? Are there names that everyone would know, or a canon of papers that everyone has read? Did the cell biology of the last 50–100 years evolve because of heroic individuals? Or were there only some insightful pioneers, followed by a large number of important accomplishments that occurred in many different laboratories? Interestingly, none of the major journals has compiled a ‘greatest’ list or even a “classic papers” list in cell biology. This is revealing. Perhaps it tells us that there were no great cell biologists - i.e. that the recent, great progress that we have witnessed didn't require great individuals. More likely, however, there are too many - that is, the advances in cell biology tend to be incremental, with many more bright sparks and contained blazes than forest fires. Seminal observations are frequent and arise in unexpected places. Progress may be better measured as the integral of many important contributions and contributors. Thus, cell biology is the product of many many great scientists, who interact, synergize and stand on each other's shoulders. The attractiveness of cell biology lies in this open, frontier culture. And the result is that the pie of success is large and that many have been rewarded. An interesting consequence of our frontier culture is that it is too exciting and fast paced for anyone to take the time to develop a sense of history and accomplishment. Sidney Brenner makes this point in his review of a book entitled ‘The lac Operon: A short history of a genetic paradigm’, by Benno Muller-Hill (Nature 386, 235). Brenner writes: “This book opens with the lament that for young molecular biologists history does not exist, and that they have no interest in the long struggle that has made the subject what it is today. I hold the weaker view that history does exist for the young, but it is divided into two epochs: the past two years, and everything that went before. That these have equal weight is a reflection of the exponential growth of the subject, and the urgent need to possess the future and acquire it more rapidly than anybody else does not make for empathy with the past.” A few years ago I read a list of the names of biomedical Nobel Laureates to some colleagues. They knew only a handful of the names and what their contributions were. It seems that so much is being accomplished so quickly it is hard for individuals to stand out. And the consequent focus on the collective achievement is what makes our discipline so rewarding for so many. But how long will this frontier culture last? The emergence of big biology, through government and private-foundation initiative, is changing the landscape. The rate of progress continues to accelerate. Will one soon require a very big lab to survive? Will creative minds find cell biology fertile territory? There are answers to big science. Most important is to embrace what it produces and look ahead. Another is to develop multi-institutional collaborative networks in which the product can far exceed the contributions of single individuals. And, finally, there are always trails to blaze and syntheses to make. They require little more than hard work, organization, good sense, perseverance, and some luck. Is it almost over? Extrapolating the rapid progress that we are witnessing, can one realistically predict what our discipline will be like over the next few decades? Will the questions that we are investigating now be answered or passe, and, if so, how soon? How long will cell biology continue to be on the center stage? Will there be new, fundamental, concepts or a paradigm shift? What ‘unexpecteds’ might we expect? At meetings over beer and at dinner tables with seminar speakers, the question “Is it almost over?” creeps in with increasing frequency. The concern is that the big picture will be in place soon - that is, the outlines of the fundamental cellular processes will be largely understood at a molecular level. This concern, of course, reflects the depth with which one wants to understand the cell. Clearly, we now know vastly more than we did even a decade ago. There is an emerging sense that a rudimentary understanding of the most basic cellular processes is in sight; one sees this even in the undergraduate cell biology textbooks. Of course, progress will continue. However, the questions about fundamental processes will become increasingly refined, and the answers more detailed - more likely to occupy space in specialty treatises than in undergraduate cell biology texts. The approaches and concepts will become more deeply linked to chemistry and physics, eventually focusing on subtleties of mechanism and structure. Some of these details will change our basic concepts dramatically; but the frequency of such occurrences will dwindle. These details are also necessary for the applications of cell biology that are beginning to emerge and for a true marriage of cell biology with the molecular world. This level of inquiry and detail, or increasing reductionism, may not sustain the interest of or resonate well with many of our colleagues. However, for others, it's just the beginning and is opening doors for a cadre of new colleagues trained in physics and chemistry to enter with fresh ideas, insights and technologies. Will it ever end? But is it almost over? Do we really know how cells do what they do? How is the thicket of seemingly redundant pathways and networks, molecules, and supramolecular assemblies coordinated spatially and temporally? Which of the many pathways and redundant mechanisms revealed in culture are utilized in vivo. How are cellular phenomena, as revealed in the spatial and temporal coordination required for cell division or migration, for example, integrated? How do groups of cells integrate and coordinate to effect tissue function, embryonic development, and pathology, for example? As we begin to observe cellular phenomena in situ, they can appear very different from those observed in culture. The compensation and redundancy seen in knockout, transgenic or mutated organisms also reveals a diversity of possible mechanisms. It seems that the cell has different ways of doing the same thing. How does the cell do it normally, and when, if ever, are the other mechanisms used? We have tended to focus the majority of our efforts on a few cell types. What about the other cells? How do they do it? These questions are especially pertinent in developmental biology and pathobiology, where the cellular environments are changing; they also point to a class of challenging, important new avenue of investigation. As the canon of cellular phenomena becomes understood at an increasingly refined level, it provides the basis for explaining integrative phenomena. It also becomes the source of interesting and important practical applications. In this way, cell biology can become the language for understanding complex integrative phenomena like learning and memory, behavior and personality - areas in which the genome project and genetics might merge to provide unique insights. In addition, cell biology is the source of endless practical applications and, in some sense, sits in the center of a booming biotechnology industry that includes novel therapeutic strategies, designer animals and plants, tissue replacements, biomaterials and biosensors. The possibilities here seem endless. What does genomics bode for cell biology? A great deal of opportunity. Do sequences, homologies, binding interactions, changes in expression, and even knockouts provide a satisfactory understanding of function? Isn't the genomic bottleneck the assignment of cellular functions to different genes? In its essence, gene function can be viewed as a cell biological issue and perhaps not fully amenable to high-throughput analysis. Thus, the genome project promises to keep cell biology on the center stage. And maybe, therefore, we will have too much to do. The devil is in the detail: A major product of the successes in cell biology is a mind-numbing number of facts, particulars, data and details. The volume of information and detail that we are generating in genome studies and cell signaling, for example, unsettles some. Will the molecular paradigm, which has been so successful and brought us here, lead us to the next level? In the reductionist paradigm, the cell can be viewed as a complex chemical system that obeys the laws of physics and the principles of chemistry. In this view, one needs to know the relevant chemical properties for all of the cellular components. Once this is known, the cellular dynamics and equilibria can be computed, and ultimately cell behavior modeled. For small systems and isolated processes, this has had an important predictive value and has been insightful and revealing. Most importantly, it uses the principles of chemistry, which is a common language that is known and understood by nearly all participants. Can this approach be usefully extrapolated to a highly complex system like an entire cell? It may take a while, as it poses some interesting challenges. How many complex differential equations, which must cover both temporal and spatial distributions, would be involved? How accurately will the concentrations and rate constants need to be measured? How does one deal with the non-ideal nature of the cell interior and exterior? The differential equations required to describe the systems of interacting pathways or networks found in a cell will necessarily be very complex and contain many terms. How does the error in measurements of the rate constants and concentrations, for example, propagate - that is, given any reasonable measurement error, can one derive anything that is meaningful and useful? The situation is complicated further by the nature of the cell. What are the effective concentrations (the activities) of the components? How does one address reactions that are occurring on surfaces or macromolecular assemblies that can be dynamic? These are formidable challenges. Chemistry faces them continually, as do other sciences that deal with complex phenomena. Natural phenomena have strong roots in the principles of physics and the concepts of chemistry. Yet the mathematics that backs them up does not readily yield to highly complex phenomena. Maybe different approaches - perhaps one based in the complex-systems theory that is so familiar to engineers - will provide an alternative. Where's the big picture? Are there other ways of dealing with our flood of details and particulars? There is a call for mathematicians, computer scientists, engineers and/or theorists to help bring order to this information flood. Can they make sense of this complexity? Are there overarching and unifying concepts that will allow us to think in generalities, rather than in particulars? There may already be some unifying concepts. One is the genetic paradigm, which views a cell's behavior as a consequence of its expressed genes. The geneticist's point of view has already provided an important, empirical and quantitative way of looking at cellular and organismal phenomena. This view of a cell or organism, or even a disease like cancer, differs greatly from that of a biochemist, which focuses on mechanisms and specifics. In some respects, it shifts attention away from the particulars and sticky mechanistic issues, and thus can be simplifying. Genetics has been a very powerful driver in many areas, not only as a tool to determine function but also as a way of looking at a process. The marriage of genetics with developmental biology is only one of many examples. A number of other examples derive from modeling. The Hodgkin-Huxley equation is one prominent and useful example. It models the axon as an electrical entity. For other purposes, the cell has been likewise treated as a mechanical entity and modeled in the jargon of mechanics. There are other ways of modeling the cell and its component processes - for example, through signal and systems theory, network and graph theory, Boolean algebra, and statistics. Each of these treatments can be meaningful and useful to those well versed in that particular discipline. But are these useful to those not versed in them? Is there a unifying theory or model that avoids a proliferation of models. How does one connect them to our chemical roots? In physics, the simplest is accepted as correct. Cell biology has a different reality. It is derived evolutionarily, and therefore, the simplest model may not be correct or even useful. Perhaps, in the future, there will even be a synthesis - like the periodic table or quantum mechanics for physics and chemistry - that allows us to deal with the mega-detail that we are generating. Big surprises in small packages: To date, cell biology has progressed rapidly because of its qualitative nature. Differences in localization are often characterized by fluorescence intensities that are described qualitatively as brighter or dimmer or as more or less localized. Similarly, differences in expression are often characterized by the intensity of bands on western blots or SDS gels; these are often described as bigger or smaller. Many changes are, in fact, very large, and this level of characterization is likely to be adequate. But have we missed anything? Is there a need for more quantitative measurements? When differences in expression are analyzed by gene array, where does one draw the line? Is a tenfold change more significant than a 2–3-fold change? Many measurements would not detect changes that are only 2–3-fold, and in others we have tended to ignore them. We wouldn't see such a small change in fluorescence intensity by eye, for example, nor would we readily identify changes in concentration that arise from differences in localization rather than expression. Ignoring small changes assumes that biological readouts are not highly poised. But is this true? Systems that have interacting components, undergo conformational changes or enzymatic modifications, or are part of amplifying cascades, for example, can be highly poised. Thus 2–3-fold changes in expression or in substrate/ligand concentration can have effects that are very large. Of course, the converse follows as well. Large changes might have only modest consequences - for example, if one is well removed from the Kd. Examples of small changes having large effects and vice versa are common features of complex systems and are now beginning to appear in the cell biology literature. It seems likely there will be many more as our measurements become increasingly quantitative. Downstream signals: What can one make of all of this? (1) This is a very, very good time for cell biology. Questions that have loomed for decades and centuries are becoming understood in a meaningful way. The progress is breathtaking; it wasn't this easy only a couple of decades ago. (2) Many are participating in the success; they are all contributing to something useful and important. (3) The devil is in the detail but so are the opportunities. (4) Big science is here to stay - perhaps a consequence of our success. As investigators, we need to embrace it and look ahead. (5) The only constant in our research will be change. We will need to be flexible in our approaches and questions. (6) We must translate our progress to the public through education and the popular press in ways that sustain their interest and support and attract new minds to our discipline. (7) The surge in new technology will continue to drive our progress, which will come to nearly anyone who works hard, chooses a good problem, and takes a reasonable approach. (8) We need to develop strategies to deal with the information flood; it won't ebb soon. And the anticipated simplifications from the mathematicians, computer scientists and modelers may take quite a while. (9) Enjoy your successes. This might be about as good as it gets.

The bowed-twisted-swept modeling technology of three-dimensional blade has been widely used in the gas impeller machinery and achieved good results. This paper introduces the two-dimensional flow theory and the bowed-twisted-swept modeling ideology into hydraulic turbine design. Simultaneously combined with the popular NSGA-II multi-objective optimization algorithm, a complete set of hydraulic turbine cascade design method was proposed. Taking the last-stage low aspect ratio hydraulic cascade of Ф175 type turbine as an example, the parametric model of this cascade was reconstructed by a high-precision automatic bridge coordinate measuring machine. The multi-objective optimization design of three-dimensional modeling of cascade was completed with the single-stage turbine output torque, efficiency and pressure drop as the objective targets. Finally the influence of the bowed-twisted-swept modeling technology on the hydraulic turbine performance was explored in detail by a professional rotating machinery CFD software. Numerical analysis shows that the twisted blade design achieves a 1.5 times increase in torque and 2 to 4 times increase in pressure diff at same working condition. Moreover, when bowing optimization design and sweeping optimization design are applied on the twisted blade individually, the output torque and the stage efficiency of the hydraulic turbine are respectively improved, and when both two methods are simultaneously applied on the twisted blade, it is beneficial to reduce the pressure drop loss. However, it is noticeable that when the bowed-swept modeling technology used in a straight blade using almost have no effect on the turbine performance.

In this paper, a quasi-steady method is developed for predicting the coupled bending-torsion flutter in a compressor cascade during classic surge. The classic surge is one of the major compressor flow field instabilities involving pulsation of the main flow through the compressor. The primary reason for the occurrence of the classic surge is the stalling of the blade rows and if the conditions are favorable this can trigger flutter, which is a self-excited aero elastic instability. The classic surge flow is modeled by using the well-established model of Moore and Greitzer and the obtained flow condition is used to determine the aerodynamic loads of the cascade using the linearized Whitehead's theory. The cascade stability is then examined by solving the two dimensional structural model by treating it as a complex eigenvalue problem. The structural stability is analyzed for a range of values of the frequency ratio and primary emphasis is given for the frequency ratio value of 0.9 as many interesting features could be revealed. The cascade shows a bifurcation from bending flutter to the torsional one signifying that only one of the flutter modes are favored at any instant in time. The torsional flutter is found to be the dominant flutter mode for a range of frequency ratios during classic surge whereas the bending flutter is found to occur only for some values of frequency ratio very close to unity as the torsional loads acting on the blades are found to be orders of magnitude higher than the bending loads. A rapid initiation of torsional flutter is seen to occur during classic surge for frequency ratio values very close to unity and it is perceived that during blade design, frequency ratios should be kept below 0.9 to prevent the flutter possibilities. An estimate of structural energy variation with time indicates that even if the total structural energy is negative one of the modes can go unstable during classic surge.

The present study focuses on the study of topological properties of flow in a turbine cascade. Critical-point theory is used to explain the flow phenomenon. Examination and analysis of skin-friction line patterns on three-dimensional bodies such as turbine cascade, compressor cascade, cylinder, etc. enables enhanced understanding of the three-dimensional flow. Topology of flow means types of critical points formed, their interconnection, and relation between numbers of different types of critical points. Present work focuses on rules with regard to the topological consistency of a flow field. It consists of two parts, one is the connectivity of different critical points, and another is deriving the relation between the number of nodal and saddle points of a tangent vector field. Relation between the number of nodal and saddle points is derived for flows such as a turbine cascade with and without tip clearance, turbine cascade with the end wall fence, flow over a three-dimensional obstacle, etc. Relevant mathematical background necessary for derivation is discussed. The results derived for the turbine cascade is independent of the end wall contouring, leading edge modification, trailing edge modification, and blade shape. The derived relations also hold for a compressor cascade. Flow visualization based on CFD calculations is presented for the turbine cascade with and without an end wall fence.

In a companion paper (2008, “Vorticity Dynamics in Axial Compressor Flow Diagnosis and Design,” ASME J. Fluids Eng., 130, p. 041102), a study has been made on the critical role of circumferential vorticity (CV) in the performance of axial compressor in through-flow design (TFD). It has been shown there that to enhance the pressure ratio, the positive and negative CV peaks should be pushed to the casing and hub, respectively. This criterion has led to an optimal TFD that indeed improves the pressure ratio and efficiency. The CV also has great impact on the stall margin as it reflects the end wall blockage, especially at the tip region of the compressor. While that work was based on inviscid and axisymmetric theory, in this paper, we move on to the diagnosis and optimal design of fully three-dimensional (3D) viscous flow in axial compressors, focusing on the boundary vorticity flux (BVF), which captures the highly localized peaks of pressure gradient on the surface of the compressor blade, and thereby signifies the boundary layer separation and dominates the work rate done to the fluid by the compressor. For the 2D cascade flow we show that the BVF is directly related to the blade geometry. BVF-based 2D and 3D optimal blade design methodologies are developed to control the velocity diffusion, of which the results are confirmed by Reynolds-averaged Navier–Stokes simulations to more significantly improve the compressor performance than that of CV-based TFD. The methodology enriches the current aerodynamic design system of compressors.

This paper describes an innovative, three-day, turbomachinery research project for Japanese and British high-school students. The project is structured using modern teaching theories that encourage student curiosity and creativity. The experience develops teamwork and communication and helps to break down the cultural and linguistic barriers between students from different countries and backgrounds. The approach provides a framework for other hands-on research projects that aim to inspire young students to undertake a career in engineering. The project is part of the Clifton Scientific Trust's annual UK–Japan Young Scientist Workshop Programme. This work focuses on compressor design for jet engines and gas turbines. It includes lectures introducing students to turbomachinery concepts, a computational design study of a compressor blade section, experimental tests with a low-speed cascade, and tutorials in data analysis and aerodynamic theory. The project also makes use of 3D printing technology, so that students go through the full engineering design process, from theory, through design, to practical experimental testing. Alongside the academic aims, students learn what it is like to study engineering at university, discover how to work effectively in a multinational team, and experience a real engineering problem. Despite a lack of background in fluid dynamics and the limited time available, the lab work and end-of-project presentation show how far young students can be stretched when they are motivated by an interesting problem.

Prior to the detailed design of components, turbomachinery engineers must guide a mean-line or throughflow design toward an optimum configuration. This process requires a combination of informed judgement and low-order correlations for the principle sources of loss. With these requirements in mind, this paper examines the impact of key design parameters on endwall loss in turbines, a problem which remains poorly understood. This paper presents a parametric study of linear cascades, which represent a simplified model of real-engine flow. The designs are nominally representative of the low-pressure turbine blades of an aero-engine, with varying flow angles, blade thickness, and suction surface lift styles. Reynolds-averaged Navier–Stokes (RANS) calculations are performed for a single aspect ratio (AR) and constant inlet boundary layer thickness. To characterize the cascades studied, the two-dimensional design space is examined before studying endwall losses in detail. It is demonstrated that endwall loss can be decomposed into two components: one due to the dissipation associated with the endwall boundary layer and another induced by the secondary flows. This secondary-flow-induced loss is found to scale with a measure of streamwise vorticity predicted by classical secondary flow theory.

The two-step method for optimizing net positive suction head required (NPSHr) of axial-flow pumps is proposed in this paper. First, the NPSHr at the impeller tip is optimized with impeller diameter based on experimental data of 2D cascades in available wind tunnels. Then, it is optimized again with the velocity moment at the impeller outlet, which is expressed in terms of two parameters. The blade geometry is generated and flow details are clarified by using the radial equilibrium equation, actuator disk theory, and 2D vortex element method in the optimizing process. The NPSHr response surface has been established in terms of these two parameters. The results illustrate that the second optimization allows NPSHr to be reduced by 37.5% compared to the first optimization. Therefore, this two-step method is effective and expects to be applied in the axial-flow pump impeller blade design. The simulations of 3D turbulent flow with various cavitation models and related confirming experiments are going to be done in the axial-flow impellers designed with this method.

There are two strands to the history of the aircraft gas turbine engine and jet propulsion in Britain. One strand has been told by Sir Frank Whittle (figure 1), the inventor of the turbojet engine, in Jet - the story of a pioneer (1953). 1 The other, less well known, was started by Dr Alan Arnold Griffith 2 (figure 2) of the Royal Aircraft Establishment (RAE). In 1926, in a report entitled ‘An aerodynamic theory of turbine design’ 3 , he proposed the use of a gas turbine as an aircraft power plant. In October of that year he put his proposals to a small committee from the Air Ministry and the Aeronautical Research Committee, which expressed itself unanimously in favour of prelim inary experiments. Accordingly, two sets of experiments were started. The first was on a stationary cascade of aerofoils and was reported by R.G. Harris and R.A. Fairthorne in September 1928 (figure 3).4 The other was on a model comprising a row of turbine and compressor blades of 4 inches outside diameter, mounted on one shaft and tested by sucking air through the blading (figure 4). From measurements of the losses, the efficiencies of stages could be deduced. The results, reported by W.C. Clothier in December 19295, showed that a maximum efficiency of 90% was obtained and an efficiency of 88.3% at a pressure ratio of 1.16.