Relevant bibliographies by topics / Euler's turbine equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Euler's turbine equation'

Author: Grafiati
Published: 28 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Euler's turbine equation"

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Marwani, Marwani, Muhammad Zahri Kadir, and Ronny Egetha Putra. "INVESTIGATION PERFORMANCE OF PICO HYDRO WATER PIPE TURBINE." Indonesian Journal of Engineering and Science 2, no. 3 (September 8, 2021): 051–58. http://dx.doi.org/10.51630/ijes.v2i3.27.

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The flow of water in the pipeline for household needs is a source of energy that can generate electrical energy through Pico hydro turbines or small-power water turbines. The experiment has been conducted on a 10 Watt Pico hydro turbine mounted on a water pipe against changes in water flow discharge. The turbine performance analysis is conducted experimentally (actual) and theoretically (ideal). The analysis results showed the greater the discharge flow, the greater the power generated by the turbine. In tests with a maximum discharge of 8.9 l/min, the actual power of 1.121 Watts, the torque of 0.005 Nm with a rotation speed of 2146.8 rpm and efficiency of 12.59%; while the ideal power is based on Euler turbine equation of 4.2 Watts and torque of 0.016 Nm. So, the maximum turbine power that can be generated is only 26.67% ideal. Efficiency turbine decreases with increased discharge; in this test, the maximum efficiency was 24.89% at 5.8 L/min flow discharge.
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Draper, S., T. Nishino, T. A. A. Adcock, and P. H. Taylor. "Performance of an ideal turbine in an inviscid shear flow." Journal of Fluid Mechanics 796 (April 28, 2016): 86–112. http://dx.doi.org/10.1017/jfm.2016.247.

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Although wind and tidal turbines operate in turbulent shear flow, most theoretical results concerning turbine performance, such as the well-known Betz limit, assume the upstream velocity profile is uniform. To improve on these existing results we extend the classical actuator disc model in this paper to investigate the performance of an ideal turbine in steady, inviscid shear flow. The model is developed on the assumption that there is negligible lateral interaction in the flow passing through the disc and that the actuator applies a uniform resistance across its area. With these assumptions, solution of the model leads to two key results. First, for laterally unbounded shear flow, it is shown that the normalised power extracted is the same as that for an ideal turbine in uniform flow, if the average of the cube of the upstream velocity of the fluid passing through the turbine is used in the normalisation. Second, for a laterally bounded shear flow, it is shown that the same normalisation can be applied, but allowance must also be made for the fact that non-uniform flow bypassing the turbine alters the background pressure gradient and, in turn, the turbines ‘effective blockage’ (so that it may be greater or less than the geometric blockage, defined as the ratio of turbine disc area to cross-sectional area of the flow). Predictions based on the extended model agree well with numerical simulations approximating the incompressible Euler equations. The model may be used to improve interpretation of model-scale results for wind and tidal turbines in tunnels/flumes, to investigate the variation in force across a turbine and to update existing theoretical models of arrays of tidal turbines.
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Shieh, C. F., and R. A. Delaney. "An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows." Journal of Turbomachinery 109, no. 3 (July 1, 1987): 346–53. http://dx.doi.org/10.1115/1.3262112.

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Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the three-dimensional time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud two-dimensional O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.
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Agbormbai, James, and Weidong Zhu. "Experimental Study of the Performance of a Novel Vertical-Axis Wind Turbine." Applied Sciences 10, no. 8 (April 22, 2020): 2902. http://dx.doi.org/10.3390/app10082902.

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Basic equations for estimating the aerodynamic power captured by the Anderson vertical-axis wind turbine (AVAWT) are derived from a solution of Navier–Stokes (N–S) equations for a baroclinic inviscid flow. In a nutshell, the pressure difference across the AVAWT is derived from the Bernoulli’s equation—an upshot of the integration of the Euler’s momentum equation, which is the N–S momentum equation for a baroclinic inviscid flow. The resulting expression for the pressure difference across the AVAWT rotor is plotted as a function of the free-stream speed. Experimentally determined airstream speeds at the AVAWT inlet and outlet, coupled with corresponding free-stream speeds, are used in estimating the aerodynamic power captured. The aerodynamic power of the AVAWT is subsequently used in calculating its aerodynamic power coefficient. The actual power coefficient is calculated from the power generated by the AVAWT at various free-stream speeds and plotted as a function of the latter. Experimental results show that at all free-stream speeds and tip-speed ratios, the aerodynamic power coefficient of the AVAWT is higher than its actual power coefficient. Consequently, the power generated by the AVAWT prototype is lower than the aerodynamic power captured, given the same inflow wind conditions. Besides the foregoing, the main purpose of this experiment is to investigate the technical feasibility of the AVAWT. This proof of concept enables the inventor to commercialize the AVAWT.
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Mei, Y., and A. Guha. "Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 219, no. 1 (February 1, 2005): 35–47. http://dx.doi.org/10.1243/095765005x6926.

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Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.
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Esmaeelpour, Keyvan, Rouzbeh Shafaghat, Rezvan Alamian, and Rasoul Bayani. "Numerical study of various geometries of breakwaters for the installation of floating wind turbines." Journal of Naval Architecture and Marine Engineering 13, no. 1 (June 15, 2016): 27–37. http://dx.doi.org/10.3329/jname.v13i1.22866.

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The everyday growing populations all over the world and the necessity of increase in consumption of fossil energies have made the human to discover new energy resources, which are clean, cheap and renewable. Wind energy is one of the renewable energy resources. Considerable wind speed has made settling of wind turbines at sea beneficial and appealing. For this purpose, choosing the appropriate plates to set up wind turbines on the surface of sea is necessary. Regarding the installation condition, by choosing suitable geometry for floating breakwaters, offshore wind turbine can be mounted on them. Suitable geometry of breakwater for multifunctional usage could be selected with analyzing and comparing pressure, force and moment produced by incoming waves. In this article, we implement boundary element method to solve governing differential equations by assuming potential flow. On the other hand, for promoting free surface in each time step, we employed Euler-Lagrangian method. Finally, to find the appropriate geometry for installing the wind turbine on the breakwater, moment and wave profile next to the right and left side of breakwater body are calculated. Among simulated geometries, breakwater with trapezoid geometry which its larger base is placed in the water has more sustainability and it is the most suitable geometry for wind turbine installation.
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Song, Kang, Devesh Upadhyay, and Hui Xie. "A physics-based turbocharger model for automotive diesel engine control applications." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 7 (May 19, 2018): 1667–86. http://dx.doi.org/10.1177/0954407018770569.

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Control-oriented models of turbocharger processes such as the compressor mass flow rate, the compressor power, and the variable geometry turbine power are presented. In a departure from approaches that rely on ad hoc empirical relationships and/or supplier provided performance maps, models based on turbomachinery physics and known geometries are attempted. The compressor power model is developed using Euler’s equations of turbomachinery, where the gas velocity exiting the rotor is estimated from an empirically identified correlation for the ratio between the radial and tangential components of the gas velocity. The compressor mass flow rate is modeled based on mass conservation, by approximating the compressor as an adiabatic converging-diverging nozzle with compressible fluid driven by external work input from the compressor wheel. The variable geometry turbine power is developed with Euler’s equations, where the turbine exit swirl and the gas acceleration in the vaneless space are neglected. The gas flow direction into the turbine rotor is assumed to align with the orientation of the variable geometry turbine vane. The gas exit velocity is calculated, similar to the compressor, based on an empirical model for the ratio between the turbine rotor inlet and exit velocities. A power loss model is also proposed that allows proper accounting of power transfer between the turbine and compressor. Model validation against experimental data is presented.
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Alakashi, Abobaker Mohammed, and Bambang Basuno. "Comparison between Cell-Centered Schemes Computer Code and Fluent Software for a Transonic Flow Pass through an Array of Turbine Stator Blades." Applied Mechanics and Materials 437 (October 2013): 271–74. http://dx.doi.org/10.4028/www.scientific.net/amm.437.271.

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The Finite Volume Method (FVM) is a discretization method which is well suited for the numerical simulation of various types (elliptic, parabolic or hyperbolic, for instance) of conservation laws; it has been extensively used in several engineering fields. The Finite volume method uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations [. the developed computer code based Cell-centered scheme and Fluent software had been used to investigate the inviscid Transonic Flow Pass Through an array of Turbine Stator Blades. The governing equation of fluid motion of the flow problem in hand is assumed governed by the compressible Euler Equation. Basically this equation behave as a mixed type of partial differential equation elliptic and hyperbolic type of partial differential equation. If the local Mach number is less than one, the governing equation will behave as elliptic type of differential equation while if the Mach number is greater than one it will behave as hyperbolic type of differential equation. To eliminate the presence a mixed type behavior, the governing equation of fluid motion are treated as the governing equation of unsteady flow although the problem in hand is steady flow problems. Presenting the Euler equation in their unsteady form makes the equation becomes hyperbolic with respect to time. There are various Finite Volume Methods can used for solving hyperbolic type of equation, such as Cell-centered scheme [, Roe Upwind Scheme [ and TVD Scheme [. The present work use a cell centered scheme applied to the case of flow pass through an array of turbine stator blades. The comparison carried out with the result provided by Fluent Software for three different value of back pressure. The developed computer code shows the result close to the Fluent software although the Fluent software use a Time Averaged Navier stokes equation as its governing equation of fluid motion.
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Swar, Rohan, Awatef Hamed, Dongyun Shin, Nathanial Woggon, and Robert Miller. "Deterioration of Thermal Barrier Coated Turbine Blades by Erosion." International Journal of Rotating Machinery 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/601837.

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A combined experimental and computational study was conducted to investigate the erosion of thermal barrier coated (TBC) blade surfaces by alumina particles ingestion in a single-stage turbine. In the experimental investigation, tests were performed to determine the erosion rates and particle restitution characteristics under different impact conditions. The experimental results show that the erosion rates increase with increased impingement angle, impact velocity, and temperature. In the computational simulations, an Euler-Lagrangian two-stage approach is used in obtaining numerical solutions to the three-dimensional compressible Reynolds-Averaged Navier-Stokes equations and the particles equations of motion in each blade passage reference frame. User defined functions (UDFs) were developed to represent experimentally based correlations for particle surface interaction models and TBC erosion rates models. UDFs were employed in the three-dimensional particle trajectory simulations to determine the particle rebound characteristics and TBC erosion rates on the blade surfaces. Computational results are presented in a commercial turbine and a NASA-designed automotive turbine. The similarities between the erosion patterns in the two turbines are discussed for uniform particle ingestion and for particle ingestion concentrated in the inner and outer 5% of the stator blade span to represent the flow cooling of the combustor liner.
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Huang, Jianyou, Chia-Ou Chang, and Chien-Cheng Chang. "Analysis of Structural Vibrations of Vertical Axis Wind Turbine Blades via Hamilton’s Principle — Part 3: Pitch Angle and Equilibrium State." International Journal of Structural Stability and Dynamics 21, no. 05 (February 20, 2021): 2150070. http://dx.doi.org/10.1142/s021945542150070x.

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Pitch angle is one of the most important parameters of wind turbine blade. This study is aimed to investigate the effect of the pitch angle on the deformation of a VAWT. Lagrangian mechanics and Euler’s beam theory are used to derive the motion equations of linear structural vibration for straight blade vertical axis wind turbine blade with the pitch angle [Formula: see text]. The complete equations of motion take account of the 4-DOF deformation of flexural–flexural–torsion–extension as well as the material damping. Vibration analysis of generalized displacement about the equilibrium state (GDAES) is carried out with respect to the displacement of the equilibrium state (DOES), which is separated from the motion of vibration. After simplifying the equilibrium equation of 4-DOF into 1-DOF system, the exact solution of displacement [Formula: see text] of the equilibrium state is derived. The correction [Formula: see text] of [Formula: see text] due to the pitch angle and the characteristics of [Formula: see text] with constant linear speed are analyzed. Furthermore, we investigate the coupling effect of lateral bending and axial extension of the blade on [Formula: see text] is analyzed. Finally, the exact solution of [Formula: see text] is verified by the central difference method.
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Dissertations / Theses on the topic "Euler's turbine equation"

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Podešva, Adam. "Použití běžného odstředivého čerpadla jako turbíny." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444636.

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This work deals with the use of a centrifugal pump in turbine mode and control of the system where this machine is operated. The introduction describes and divides the various types of pumps and discusses the issue of Euler's pump and turbine equations. The flow control options are also described here. Part of the work is a research that examines the advantages and disadvantages of using a centrifugal pump in turbine mode, the possibilities of using this system and real applications in the Czech Republic and in the world. The main part is the design of a mathematical model in Microsoft Excel, which solves the regulation of the piping system with a pump operating in turbine mode, especially out of the optimal operating parameters.
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Rydin, Ylva. "Modeling Sound Propagation from Wind Turbines using Linearized 3D Euler Equations." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-301607.

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In this report sound propagation from wind turbines is modeled using the 3D linearized Euler equations which allows varying atmospheric fields containing wind. The Euler Equations are linearized and a stable high order finite difference approximation of the equations in 1D and 3D is obtained. Stability and convergence of the problem are proven and numerically verified.
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McCallum, Marcus Anthony. "The simulation of wet steam flow in a turbine." Thesis, University of Strathclyde, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366697.

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Pavlík, Jan. "Širokopásmová Francisova turbina." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2011. http://www.nusl.cz/ntk/nusl-229667.

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his diploma thesis deals with hydraulic design of vane wheel impeller of wide range Francis turbine; in addition to hydraulic calculation it consists overview of used theory, modelling in SolidWorks and computing in Fluent.
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Books on the topic "Euler's turbine equation"

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Escudier, Marcel. Flow through axial-flow-turbomachinery blading. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0014.

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This chapter is concerned primarily with the flow of a compressible fluid through stationary and moving blading, for the most part using the analysis introduced in Chapter 11. The principles of dimensional analysis are applied to determine the appropriate non-dimensional parameters to characterise the performance of a turbomachine. The analysis of incompressible flow through a linear cascade of aerofoil-like blades is followed by the analysis of compressible flow. Velocity triangles for flow relative to blades, and Euler’s turbomachinery equation, are introduced to analyse flow through a rotor. The concepts introduced are applied to the analysis of an axial-turbomachine stage comprising a stator and a rotor, which applies to either a compressor or a turbine.
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F, Crawley Edward, and United States. National Aeronautics and Space Administration., eds. A final report on NASA grant NSG 3079 entitled A linearized Euler analysis of unsteady flows in turbomachinery. Cambridge, MA: Gas Turbine Laboratory, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 1987.

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J, Yu N., and United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch., eds. Flow prediction for propfan engine installation effects on transport aircraft at transonic speeds. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986.

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A, Delaney Robert, and United States. National Aeronautics and Space Administration., eds. Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. [Washington, DC: National Aeronautics and Space Administration, 1993.

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A, Delaney Robert, Bettner James L, and Lewis Research Center, eds. Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems.: Final report. [Washington, D.C.]: National Aeronautics and Space Administration, 1990.

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A, Delaney Robert, and United States. National Aeronautics and Space Administration., eds. Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems.: Final report. [Washington, DC: National Aeronautics and Space Administration, 1993.

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A, Delaney Robert, Bettner James L, and United States. National Aeronautics and Space Administration., eds. Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems: Task II, unsteady ducted propfan analysis. [Washington, D.C.]: National Aeronautics and Space Administration, 1991.

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Book chapters on the topic "Euler's turbine equation"

1

Eliasson, Peter. "Numerical Solution of the Incompressible Euler Equations in a Water Turbine Using a Multi-Block Approach." In 3D-Computation of Incompressible Internal Flows, 85–92. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-89452-6_7.

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Conference papers on the topic "Euler's turbine equation"

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Shieh, C. F., and R. A. Delaney. "An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-200.

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Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the 3-D time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud 2-D O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.
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Liu, Gao-Lian. "Generalized Euler’s Turbomachine Equation and Free Vortex Sheet Conditions in Separated/Cavitated Turbo-Flows." In ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/95-gt-171.

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In the present paper four fundamental problems in turbomachinery aerodynamic theory are studied in depth: (1) It is shown that the well–known Euler’s equation for turbomachine power is valid only for shrouded impellers. Then, a generalization of it to unshrouded impellers is carried out. (2) An equation relating the free trailing vortex distribution along the blade span to that of the swirl moment rVθ is derived, yielding a condition for the vanishing of free trailing vortex sheets. (3) The free surface conditions in separated flow are shown to be entirely different from those in cavitated flow. (4) Generlized Kutta conditions for 3–D rotor bladings in separated and caviated flows are also derived. All these results are of fundamental value in both analytical and numerical handlings of fully 3–D rotor–flows.
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Cha, Chong M. "The Dissipation Function-Based Efficiency for Turbomachinery: Part 2 — The Power of a Cooled Turbine." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42660.

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Euler’s turbine equation is generalized to include cooling flow addition. Euler’s turbine equation for the uncooled case is still used for the design and analysis of today’s cooled turbines. A simple, one-dimensional control volume model is developed to illustrate the impact of cooling flow addition on the turbine power and efficiency. The efficiency measures include the familiar isentropic turbine efficiencies and the dissipation function-based measure, introduced in Part 1 [1] of this work.
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Abdallah, S., and C. F. Smith. "Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines." 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-140.

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A primitive variable formulation is used for the solution of the incompressible Euler’s equation. In particular, the pressure Poisson equation approach using a non-staggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a non-staggered grid. Numerical solutions of the momentum equations are obtained using the second order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive over-relaxation method. Three turbomachinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.
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Denton, J. D., and L. Xu. "A New Approach to the Calculation of Transonic Flow Through Two Dimensional Turbomachine Blade Rows." In ASME 1985 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1985. http://dx.doi.org/10.1115/85-gt-5.

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All methods of solving the Euler equations face the problem of errors in entropy. These errors are especially important at the leading edge of blade rows where any numerical errors will cause entropy to be produced and to convect downstream to influence the downstream flow, especially that on the blade surfaces. A new numerical method is described which overcomes this problem by solving a conservation equation for entropy. This equation effectively replaces the usual momentum equation along streamlines. Sources of entropy are introduced to allow for shock loss with the magnitude of the source being determined from the Rankine-Hugoniot relations. A semi-implicit scheme is used to solve the continuity equation whilst the entropy and flow direction are updated by conventional explicit methods. The flow through a selection of test cascades has been calculated with this new method and its predictions compared with exact solutions as well as with experimental data and with a conventional Euler solver. The results show that the new method is more accurate than the conventional one, it converges in fewer iterations but requires slightly longer computer times.
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Nakhjiri, Mehdi, and Peter F. Pelz. "Turbomachines Under Periodic Admission: Axiomatic Performance Prediction." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-68398.

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In calibration tasks under engine conditions, steady-state manufacturer performance maps are applied to periodic turbocharger operation. This procedure is exposed to considerable uncertainties. In this work the axiomatic form of the energy equation as well as Euler turbomachinery equation are used to generate a general form of the respective equations which allow for periodicity. Thus, the concept of apparent speed and apparent efficiency is introduced. The latter can attain values greater than unity.
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Afzali, Fatemeh, Onur Kapucu, and Brian F. Feeny. "Vibration Analysis of Vertical-Axis Wind-Turbine Blades." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60374.

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In this work the derivation of a vibration model for an H-rotor/Giromill blade is investigated. The blade is treated as a uniform straight elastic Euler-Bernoulli beam under transverse bending and twisting deformation. The derivation of the energy equations for the bending and twisting blade and a simplified aerodynamic model is issued. Lagrange’s equations are applied to assumed modal coordinates to obtain nonlinear equations of motion for bend and twist. A single quasi-steady airfoil theory is applied to obtain the aeroelastic loads. The behavior of the linearized equation for bend only is examined.
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Hoskoti, Lokanna, Ajay Misra, and Mahesh Manchakattil Sucheendran. "Vortex Induced Vibration of a Rotating Blade." In ASME 2017 Gas Turbine India Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gtindia2017-4709.

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The vortex-induced vibration (VIV) of a rotating blade is studied in this paper. Euler-Bernoulli beam equation and the nonlinear oscillator satisfying Van der Pol equation are used to model the rotating blade and vortex shedding, respectively. While the fluctuating lift due to vortex shedding acts on the blade and the blade is coupled with fluid through a linear inertial coupling, resulting in a fluid-structure interaction problem. The coupled equations are discretized by using modes which satisfy the Eigenvalue problem. The work attempts to understand the instabilities associated with the frequency lock-in phenomenon. The method of multiscale is used to obtain the frequency response equation and frequency bifurcation diagrams of the coupled system. They are obtained for the primary (1:1) resonance for different values of the coupling parameter. The stability of the solution is presented by examining the nature of the Eigenvalues of the Jacobian matrix.
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Li, Deying, Huanlong Chen, Yanping Song, Ke Cui, and Hiroharu Ooyama. "Numerical Investigation of Two-Phase Wet Steam Flow With Spontaneous Condensation Based on Euler S2 Calculation Method." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42254.

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The Euler equation suitable for the S2 stream surface calculation is derived in the arbitrary orthogonal coordinate system firstly. The numerical method for the two-phase wet steam flow with the spontaneous condensation is then developed on basis of the Euler S2 calculation code, the Eulerian/Eulerian multiphase model and the classic nucleation theory. To adapt the complex geometry of the turbine blades, the Euler equations for the S2 stream surface calculation method are derived in the body-fitted coordinate system. The mathematical model for the third order TVD scheme with the non-conservative variables is also developed for the gas phase governing equation. The 2nd order NND and the VanLeer scheme are applied to the variable reconstruction and the numerical flux calculation respectively in the liquid equations solving process. The pressure and the droplet radii distribution fit well with the experimental data for both the high pressure nozzle and the low pressure nozzle. The S2 calculation method is also employed to predict the performance of a 3-stage low pressure steam turbine with spontaneous steam condensation, and the reasonable results are obtained. The numerical method developed in the present work is able to predict the real wet steam flow with the spontaneous condensation and its impact on the flow field and the aerodynamic parameters distribution reasonably, supplying a fast and accurate technic and method to the steam turbine design.
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Lyman, F. A. "On the Conservation of Rothalpy in Turbomachines." In ASME 1992 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/92-gt-217.

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Abstract:
The conditions under which rothalpy is conserved are investigated by means of the energy and moment-of-momentum equations for unsteady flow of a viscous, compressible fluid. Differential and integral equations are given for the total enthalpy and rothalpy in both stationary and rotating coordinates. From the equations in rotating coordinates it is shown that rothalpy may change due to: (1) pressure fluctuations caused by flow unsteadiness in the rotating frame; (2) angular acceleration of the rotor; (3) work done by viscous stresses on the relative flow in the rotating frame; (4) work done by body forces on the relative flow; (5) changes in entropy due to viscous dissipation and heat transfer. Conclusions of this investigation are compared with those of previous authors, some of whom have stated that rothalpy is conserved even in viscous flows. A modified Euler’s turbomachine equation which includes viscous effects is derived and errors in previous derivations noted.
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