Academic literature on the topic 'Blade cascade theory'

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Journal articles on the topic "Blade cascade theory"

1

Kodama, H., and M. Namba. "Unsteady Lifting Surface Theory for a Rotating Cascade of Swept Blades." Journal of Turbomachinery 112, no. 3 (July 1, 1990): 411–17. http://dx.doi.org/10.1115/1.2927675.

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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.
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Moore, J., and J. S. Tilton. "Tip Leakage Flow in a Linear Turbine Cascade." Journal of Turbomachinery 110, no. 1 (January 1, 1988): 18–26. http://dx.doi.org/10.1115/1.3262162.

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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.
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Sznajder, Janusz. "Modelling of Vane and Rotor Blade Rows in Simulations of Gas Turbine Performance." Journal of KONES 26, no. 1 (March 1, 2019): 183–90. http://dx.doi.org/10.2478/kones-2019-0022.

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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.
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Pullan, Graham, and Neil W. Harvey. "Influence of Sweep on Axial Flow Turbine Aerodynamics at Midspan." Journal of Turbomachinery 129, no. 3 (July 14, 2006): 591–98. http://dx.doi.org/10.1115/1.2472397.

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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.
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Dorney, D. J., and J. M. Verdon. "Numerical Simulations of Unsteady Cascade Flows." Journal of Turbomachinery 116, no. 4 (October 1, 1994): 665–75. http://dx.doi.org/10.1115/1.2929459.

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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.
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POSSON, HELENE, M. ROGER, and S. MOREAU. "On a uniformly valid analytical rectilinear cascade response function." Journal of Fluid Mechanics 663 (September 27, 2010): 22–52. http://dx.doi.org/10.1017/s0022112010003368.

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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.
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Crawley, E. F., and K. C. Hall. "Optimization and Mechanisms of Mistuning in Cascades." Journal of Engineering for Gas Turbines and Power 107, no. 2 (April 1, 1985): 418–26. http://dx.doi.org/10.1115/1.3239742.

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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.
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Pascu, M., M. Miclea, P. Epple, A. Delgado, and F. Durst. "Analytical and numerical investigation of the optimum pressure distribution along a low-pressure axial fan blade." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 3 (December 1, 2008): 643–57. http://dx.doi.org/10.1243/09544062jmes1023.

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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.
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Kielb, R. E., and J. K. Ramsey. "Flutter of a Fan Blade in Supersonic Axial Flow." Journal of Turbomachinery 111, no. 4 (October 1, 1989): 462–67. http://dx.doi.org/10.1115/1.3262294.

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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.
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Coull, John, Christopher Clark, and Raul Vazquez. "The sensitivity of turbine cascade endwall loss to inlet boundary layer thickness." Journal of the Global Power and Propulsion Society 3 (March 26, 2019): OEYMDE. http://dx.doi.org/10.22261/jgpps.oeymde.

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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.
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Dissertations / Theses on the topic "Blade cascade theory"

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Chromec, Tomáš. "Aerodynamický návrh větrné turbíny pro zvolenou lokalitu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231651.

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This master‘s thesis focuses on wind turbines. The first part describes the basic attributes of wind energy and wind turbines and is accompanied by a many images. The next section is a statistical processing of measured meteorological data from measuring stations of the Czech Hydrometeorological Institute. These data are then used for calculations of the blades of wind turbines. The calculations are carried by two different methods. The first method is called the blade element momentum theory, the second method is the theory of blade cascade. Using these methods are obtained by two different blades. The last section compares the two blades in terms of geometric and performance.
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Žabka, Marek. "Aerodynamický návrh větrné turbíny pro zvolenou lokalitu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-378728.

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This Master’s thesis focuses on the wind turbines. It describes the basic attributes of the wind energy and the wind potential of Slovak Republic, as well as the environmental impact of this sector. Meteorological data for the selected location are processed according to the Weibull distribution and they are used for the aerodynamic design of the wind turbine blades. Aerodynamic design is processed by using two methods. The first is the blade cascade theory, which is used to design prismatic and twist blades. The second method is called the blade element momentum, which is used to design wind turbine but only twist blades are designed by using this theory. Calculated aerodynamic shapes are compared and the best economic solution for the selected location is chosen.
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Mahdal, Ondřej. "Návrh turbíny přílivové elektrárny." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-400487.

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The present time demands emission-free and carbon-free sources of energy. This fact is not only subject of international agreements and European Union regulations, but also the state of environment points out to an essential change in energy generation of mankind. Tidal stream provides very stable and predictable source of “green” energy. Compared to other renewable energy sources tidal stream turbines in exceptional localities are able to supply energy continuously, making them base load source. The aim of the thesis was to create an extensive document with recent tidal stream power information, which has not been available in Czech language yet. Last part of the research is focused on co-locating tidal stream and off-shore wind turbines. Second part of the thesis is dedicated to aerodynamic design of single-stage horizontal axis tidal stream turbine with rated electric power of 1 MW. Calculation according to the blade cascade theory was used to design blade geometry and to find rotor diameter of 14 meters for rated stream velocity of 3.05 m/s.
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Books on the topic "Blade cascade theory"

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Hanson, Donald B. Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. Contents: Vol. 1- Theory development and parametric studies -v.2- Documentation for computer code CUP2D. Cleveland, Ohio: Lewis Research Center, 1994.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Program, 1994.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Program, 1994.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Program, 1994.

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Coupled 2-dimensional cascade theory for noise and unsteady aerodynamics of blade row interaction in turbofans. [Washington, DC]: National Aeronautics and Space Administration, Scientific and Technical Information Program Division, 1994.

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United States. National Aeronautics and Space Administration., ed. Small-amplitude disturbances in turbomachine flows with swirl. [Washington, DC: National Aeronautics and Space Administration, 1994.

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United States. National Aeronautics and Space Administration., ed. Small-amplitude disturbances in turbomachine flows with swirl. [Washington, DC: National Aeronautics and Space Administration, 1994.

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Small-amplitude disturbances in turbomachine flows with swirl. [Washington, DC: National Aeronautics and Space Administration, 1994.

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Conference papers on the topic "Blade cascade theory"

1

Kodama, Hidekazu, and Masanobu Namba. "Unsteady Lifting Surface Theory for a Rotating Transonic Cascade of Swept Blades." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-178.

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A lifting surface theory is developed to predict the unsteady three-dimensional aerodynamic characteristics for a rotating transonic annular cascade of swept blades. An improved 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, in the case of transonic rotors, the magnitude of total aerodynamic work due to the blade vibration is reduced at large sweep angles, however blade sweep is not beneficial for noise reduction.
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Kodama, Hidekazu, and Masanobu Namba. "Unsteady Lifting Surface Theory for a Rotating Cascade of Swept Blades." In ASME 1989 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/89-gt-306.

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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.
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3

Namba, Masanobu, and Ayumi Kubo. "Aerodynamically Coupled Flutter of Multiple Blade Rows." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-50315.

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This paper deals with the aeroelastic instability of vibrating multiple blade rows under aerodynamic coupling with each other. A model composed of three blade rows, e.g., rotor-stator-rotor, in which blades of the two rotor cascades are simultaneously vibrating, is considered. The generalized aerodynamic force on a vibrating blade consists of the component induced by the vibrating motion of the blade itself and those induced by vibrations not only of other blades in the same cascade but also of blades in another cascade. To evaluate the aerodynamic forces, the unsteady lifting surface theory for the model of three blade rows is applied. The equations describing motions of blades are coupled via the aerodynamic forces. The so-called k method is applied to determine the critical flutter conditions. A numerical study has been conducted. The flutter boundaries are compared with those for a single blade row. It is shown that the effect of the aerodynamic coupling significantly modifies the critical flutter conditions.
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aus der Wiesche, Stefan, Steffen Wulff, Felix Reinker, and Karsten Hasselmann. "Development of a Cost-Efficient Test Rig for Turbine Loss Education." In ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/fedsm2014-21027.

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A large number of approaches have been made to predict the total pressure loss coefficients and flow deviation angles to the geometry of turbine cascades and the incoming flow. Students feel typically uncomfortable when faced with turbine loss coefficients during their education, and it is challenging to fully understand turbine losses only by means of theory. The integration of a turbine cascade facility into academic courses might be useful but such test facilities are expensive or not available for a large number of engineering schools. To overcome this issue, a cost-efficient test rig for measurements of the flow through a two-dimensional cascade of turbine blades was designed. This test rig enabled the measurement of the flow through a blade cascade and the formation of wakes. The effect of the inlet flow angle on the cascade performance was investigated easily by students. Based on own measurements, the students were able to apply the most prominent approaches for determining loss coefficients. Furthermore, they compared their results with literature data and predictions of available correlations. By doing that, the importance of blade spacing and Reynolds number level on profile loss coefficients became more transparent and invited to further studies.
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Liu, Gao-Lian, and Shan Yan. "A Unified Variable-Domain Variational Approach to Hybrid Problems of Compressible Blade-to-Blade Flow." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-169.

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A unified theory of various hybrid problems for blade-to-blade compressible flow is developed herein via the functional variation with variable domain. Two variational principle (VP) families for three typical hybrid problems are derived, following a systematic approach (Liu, 1990a). Full advantage is taken of the natural boundary condition and suction/blowing along the blade surface are accommodated. This theory is aimed at offering a new theoretical basis for the finite element method (FEM) and various ways for blade design and/or modification, and it also constitutes an important part of optimal cascade theory (Liu,1987b). Based on these VPs, a new FEM with self-adjusting nodes is also suggested, and the numerical tests yield good results.
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Fransson, T. H., and M. Pandolfi. "Numerical Investigation of Unsteady Subsonic Compressible Flows Through an Oscillating Cascade." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-304.

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A method for solving numerically the fully time-dependent two-dimensional Euler equations, applied to unsteady subsonic flow through vibrating turbomachine cascades with thin blades, is developed. The blades are assumed to vibrate at a constant interblade phase angle and the computed region is reduced to one blade passage, with the implementation of the interblade phase angle as a periodicity condition. The reliability of the method is validated by comparing it with an analytical flat plate theory, and the importance of radiative inlet and outlet boundary conditions for unsteady flow calculations is shown in an example. The method can be used to compute the aerodynamic force and damping coefficients acting on the blades and to investigate the propagation of unsteady disturbances through a cascade in flutter conditions.
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Dorney, Daniel J., and Joseph M. Verdon. "Numerical Simulations of Unsteady Cascade Flows." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-087.

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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, nonreflecting 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.
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Phillipsen, Bent. "A Simple Inverse Cascade Design Method." In ASME Turbo Expo 2005: Power for Land, Sea, and Air. ASMEDC, 2005. http://dx.doi.org/10.1115/gt2005-68575.

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The design of profile sections is a key task in the axial turbomachinery design process. Both direct and inverse methods are in use for this purpose. Though it is relatively easy to fulfill mechanical and geometrical constraints with a direct method, where the complete geometry is specified, it can be difficult to obtain the desired distribution of velocity along the profile with this method. On the other hand, it can be difficult to get an acceptable geometry with an inverse method, where the velocity is prescribed and the geometry calculated. A simple inverse cascade design method, which combines the advantages of both the direct and the traditional inverse design method, is described. The theory behind this method directly shows how the prescribed loading distribution and the cascade design data, such as flow angles and blade thickness, influence the cascade geometry. Various practical aspects of the turbomachinery cascade design task and their relation to the described method are shown. The usefulness of the method is demonstrated through the recovery of the geometry of various cascades published in the literature. The method is valid for subsonic and shock free transonic turbine and compressor cascade design, but good results can also be obtained for turbine cascades with weak shocks, i.e. when shocks are not the dominating feature of the design.
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Ji, L. C., and J. Chen. "Edge Matching: Part I — Theory and Implementation." In ASME Turbo Expo 2005: Power for Land, Sea, and Air. ASMEDC, 2005. http://dx.doi.org/10.1115/gt2005-68474.

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Theory and implementation of Edge Matching (EM) are presented in this paper. The EM concerns the spatial relation between a blade trailing edge and the leading edge of the sequent blade row. It reflects spanwise distribution of phase angles of certain performance parameter variation versus unsteady inflow. While EM theory is described first. Two methods of implementing EM, namely spanwise integration (SI) and full optimization (FO), are described. After theoretical analysis, the interaction between linear turbine cascade and upstream wake is used to illustrate EM numerically. More specific and detailed numerical investigations are presented in accompanying paper ([1]). All these suggest that EM provides a new degree of freedom (DOF) for turbomachinery design with potentials of improving aerodynamic, aeroelastic, aeroacoustic and other performances by matching phase angles of unsteady flow along the whole span.
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Chen, Huanlong, Huaping Liu, Dongfei Zhang, and Linxi Li. "Vortex Structures for Highly-Loaded Subsonic Compressor Cascades With Slot Injection." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-63781.

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