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1
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.
2
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.
3
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.
9
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.
10
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.
11
Bonfiglioli, A., P. De Palma, G. Pascazio, and M. Napolitano. "An Implicit Fluctuation Splitting Scheme for Turbomachinery Flows." Journal of Turbomachinery 127, no. 2 (April 1, 2005): 395–401. http://dx.doi.org/10.1115/1.1777576.
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This paper describes an accurate, robust and efficient methodology for solving two-dimensional steady transonic turbomachinery flows. The Euler fluxes are discretized in space using a hybrid multidimensional upwind method, which, according to the local flow conditions, uses the most suitable fluctuation splitting (FS) scheme at each cell of the computational domain. The viscous terms are discretized using a standard Galerkin finite element scheme. The eddy viscosity is evaluated by means of the Spalart-Allmaras turbulence transport equation, which is discretized in space by means of a mixed FS-Galerkin approach. The equations are discretized in time using an implicit Euler scheme, the Jacobian being evaluated by two-point backward differences. The resulting large sparse linear systems are solved sequentially using a preconditioned GMRES strategy. The proposed methodology is employed to compute subsonic and transonic turbulent flows inside a high-turning turbine-rotor cascade.
12
Thakker, A., J. Jarvis, and A. Sahed. "Quasi-Steady Analytical Model Benchmark of an Impulse Turbine for Wave Energy Extraction." International Journal of Rotating Machinery 2008 (2008): 1–12. http://dx.doi.org/10.1155/2008/536079.
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This work presents a mean line analysis for the prediction of the performance and aerodynamic loss of axial flow impulse turbine wave energy extraction, which can be easily incorporated into the turbine design program. The model is based on the momentum principle and the well-known Euler turbine equation. Predictions of torque, pressure drop, and turbine efficiency showed favorable agreement with experimental results. The variation of the flow incidence and exit angles with the flow coefficient has been reported for the first time in the field of wave energy extraction. Furthermore, an optimum range of upstream guide vanes setting up angle was determined, which optimized the impulse turbine performance prediction under movable guide vanes working condition.
13
Pátý, Marek, and Jan Halama. "ON THE USE OF A FLUX-SPLITTING SCHEME IN THE NUMERICAL FLUTTER ANALYSIS OF A LOW-PRESSURE TURBINE STAGE." Acta Polytechnica 61, SI (February 10, 2021): 135–47. http://dx.doi.org/10.14311/ap.2021.61.0135.
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The endeavour to increase the power output of steam turbines results in the design of low-pressure stages with large diameters. Such designs, featuring long and thin blades, are increasingly susceptible to unfavourable aeroelastic effects. The interaction of structure and flow may induce blade vibrations, known as flutter, which act detrimentally on the operational life of the machine. The present work employs a time-marching numerical simulation to investigate the flutter behaviour of a low-pressure transonic turbine cascade. Its blades are subject to a harmonic motion based on the results of a structural analysis and its susceptibility to flutter is evaluated via the energy method. The computations are performed with an in-house Finite Volume Method code. The flow model is based on 2D Euler equations in Arbitrary Lagrangian-Eulerian formulation with the AUSM+-up scheme for inviscid flux discretization. A higher-order spatial accuracy is achieved by using a MUSCL approach, for which both the gradient reconstruction and the slope limiting are given a careful examination-by comparing the convergence and accuracy of multiple methods. The computational model is validated by experimental data on the Fourth Standard Configuration turbine cascade.
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Wei, Su, Wen Wu Song, Fu Jie, and Cao Yong. "A Study of Silt Erosion on Inner Buckets of Pelton Turbines." Applied Mechanics and Materials 716-717 (December 2014): 644–49. http://dx.doi.org/10.4028/www.scientific.net/amm.716-717.644.
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A 3-D model of pelton turbine bucket was built to investigate the motion characteristics of sediment particles in pelton turbines and the erosion caused by the movement. With the assistance of fluid analysis software FLUENT, A continuous phase turbulence model was estimated by the Euler equation which achieved convergence and the selected coupled calculation for solid-liquid two-phase flow with DPM model was built. It can be draw from the numerical analysis that, with the same size and sediment concentration, the inner bucket wall would suffer from the greater erosion by the relatively greater flow velocity; under the same condition of flow velocity and sediment concentration, the more serious erosion was caused by the bigger sized sediments; and the greater sediment concentration led to greater erosion, given the same flow velocity and sediment size. Based on the study, it showed that the erosion of inner wall of buckets was mainly affected by sediment size and concentration, as well as flow velocity.
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Koya, M., and S. Kotake. "Numerical Analysis of Fully Three-Dimensional Periodic Flows Through a Turbine Stage." Journal of Engineering for Gas Turbines and Power 107, no. 4 (October 1, 1985): 945–52. http://dx.doi.org/10.1115/1.3239840.
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Fully three-dimensional periodic flows through a turbine stage of stator and rotor are studied numerically by solving time-dependent three-dimensional Euler equations with the finite-volume method. The phase relation of stator and rotor flows and the related blade-row interaction are accounted for in the time-space domain. The established method of numerical calculation makes a practical contribution to predict actual turbine flows through a turbine stage of stator and rotor which have an arbitrary number of blades.
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Hsu, Ming-Hung. "Dynamic behaviour of wind turbine blades." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 8 (August 1, 2008): 1453–64. http://dx.doi.org/10.1243/09544062jmes759.
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Wind power does not generate pollution and is a clean source. The dynamic problems associated with wind turbine blades are formulated using the differential quadrature method. The Euler—Bernoulli beam paradigm is used to characterize wind turbine blades. The differential quadrature technique is utilized to transform partial differential equations, which presents the dynamic behaviour of wind turbine blades, into a discrete eigenvalue problem. The effects of the number of sample points on the accuracy of the calculated natural frequencies are studied. Numerical results show that the rotational speed impacts significantly the first frequency of the wind turbine blade. The pitch angle could not markedly affect wind turbine blade frequencies.
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Costura, D. M., P. B. Lawless, and S. H. Fankel. "A Computational Model for the Study of Gas Turbine Combustor Dynamics." Journal of Engineering for Gas Turbines and Power 121, no. 2 (April 1, 1999): 243–48. http://dx.doi.org/10.1115/1.2817112.
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A dynamic combustor model is developed for inclusion into a one-dimensional full gas turbine engine simulation code. A flux-difference splitting algorithm is used to numerically integrate the quasi-one-dimensional Euler equations, supplemented with species mass conservation equations. The combustion model involves a single-step, global finite-rate chemistry scheme with a temperature-dependent activation energy. Source terms are used to account for mass bleed and mass injection, with additional capabilities to handle momentum and energy sources and sinks. Numerical results for cold and reacting flow for a can-type gas turbine combustor are presented. Comparisons with experimental data from this combustor are also made.
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Adhikari, S., and S. Bhattacharya. "Dynamic Analysis of Wind Turbine Towers on Flexible Foundations." Shock and Vibration 19, no. 1 (2012): 37–56. http://dx.doi.org/10.1155/2012/408493.
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Offshore wind turbines are considered as an essential part to develop sustainable, alternative energy sources. The structures themselves are both slender and highly flexible, with a subsea foundation typically consisting of a single large diameter monopile. They are subject to intense wind and wave loadings, with the result that significant movement of both the exposed structure and the upper part of the monopile can occur. Although the structures are intended for design life of 25 to 30 years, very little is known about the long term behaviour of these structures. This paper characterizes the dynamic behaviour of these structures. A simplified approach has been proposed for the free vibration analysis of wind turbines taking the effect of foundation into account. The method is based on an Euler-Bernoulli beam-column with elastic end supports. The elastic end-supports are considered to model the flexible nature of the interaction of these systems with the foundation. A closed-form expression of the characteristic equation governing all the natural frequencies of the system has been derived. Theoretical developments are explained by practical numerical examples. Analytical as well as a new experimental approach has been proposed to determine the parameters for the foundation. Some design issues of wind turbine towers are discussed from the point of view of the foundation parameters.
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Polihronov, Jeliazko G., and Anthony G. Straatman. "The vortex tube effect without walls." Canadian Journal of Physics 93, no. 8 (August 2015): 850–54. http://dx.doi.org/10.1139/cjp-2014-0227.
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In a recent publication it was proposed that rotational cooling is due to angular propulsion. While this fact is obscured in a traditional shrouded vortex tube, it is clearly visible when the vortex tube effect is demonstrated without confining walls. It is thus established that the shrouded vortex tube behaves as a rotorless turboexpander, cogenerating both cold and hot gas. The physics of the turboexpander, the shrouded vortex tube, and the vortex without walls is shown to be governed by Eulers turbine equation. It is also concluded that propulsion generating vortices can exist without supporting or confining structures.
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Sazonov, Yuri Appolonievich, Mikhail Albertovich Mokhov, Inna Vladimirovna Gryaznova, Victoria Vasilievna Voronova, Vladimir Valentinovich Mulenko, Khoren Arturovich Tumanyan, Mikhail Alexandrovich Frankov, and Nikolay Nikolaevich Balaka. "Prototyping and Study of Mesh Turbomachinery Based on the Euler Turbine." Energies 14, no. 17 (August 26, 2021): 5292. http://dx.doi.org/10.3390/en14175292.
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This paper presents a scientific development aimed at improving the efficiency of turbomachines through the joint use of rotary-vane and vortex workflows. In the well-known Euler turbine, the rotor flow channels represent a set of curved pipes. The authors propose to consider in more detail the possibilities of using such rotating pipes in the implementation of an ejection (vortex) workflow. A hybrid pump was considered with the conclusion that its workflow can be described using two Euler equations. The results of computer simulation indicate that hybrid turbomachines are promising. The use of additive technology allowed the creation of micromodels of the Euler turbine with various rotor designs. Laboratory hydraulic tests showed that the liquid inlet to the rotor is possible in pulse mode. Laboratory tests of micromodels using compressed air showed that gas (or liquid) motion through curved pipes could be carried out from the rotor periphery to its center and then back, albeit through another curved pipe. The research results demonstrated that the scientific and technical potential of the Euler turbine is not yet fully unlocked, and research in this direction should continue. The study results are applicable in various industries including the energyeconomy, robotics, aviation, and water transport industries.
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Li, Zhi Chuan, Qi Hu Sheng, Liang Zhang, Zhi Ming Cong, and Jin Jiang. "Numerical Simulation of Blade-Wake Interaction of Vertical Axis Tidal Turbine." Advanced Materials Research 346 (September 2011): 318–23. http://dx.doi.org/10.4028/www.scientific.net/amr.346.318.
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To study the blade-wake interaction of vertical axis tidal turbine (VATT)，particles were placed in the flow field to trace blade wake during numerical simulation. Numerical simulations were conducted utilizing Euler-Lagrange model. In the simulations, the continuous phase was solved by Reynolds-averaged Navier-Stocks(RANS) equation combined with SST turbulence model and the particle trajectories of the dispersed phase were determined by momentum equation. Numerical results of predicting instantaneous blade forces and blade wakes showed good agreement with the test data. The model was also compared with previous classic free vortex model (V-DART), vortex method combined with finite element analysis (FEVDTM) and 2-D vortex panel model (VPM2D). It showed that the present model was much better than the former.
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Lewis, J. P., R. A. Delaney, and E. J. Hall. "Numerical Prediction of Turbine Vane-Blade Aerodynamic Interaction." Journal of Turbomachinery 111, no. 4 (October 1, 1989): 387–93. http://dx.doi.org/10.1115/1.3262285.
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A time-accurate analysis for turbine vane-blade interaction is presented. The analysis simultaneously solves the unsteady isentropic Euler equations in the vane and blade rows on a blade-to-blade surface of revolution. The equations are integrated on overlapped O-type grids using a rapid and robust explicit hopscotch algorithm. Vane and blade rows with unequal numbers of airfoils in each row are treated using a single passage model with phase-lagged periodic boundary conditions. Boundary conditions between the rows are set by a combination of bilinear interpolation and a reference plane method of characteristics. Nonreflective inflow and outflow boundary point calculation procedures are incorporated to ensure that outward-radiating planar waves pass out of the solution domain without reflection. Presented results for a turbine stage show significant effects of the interaction on the time-mean airfoil surface pressure distributions.
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Arts, T. "Calculation of the Three-Dimensional, Steady, Inviscid Flow in a Transonic Axial Turbine Stage." Journal of Engineering for Gas Turbines and Power 107, no. 2 (April 1, 1985): 286–92. http://dx.doi.org/10.1115/1.3239713.
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The aim of this paper is to develop an approach to compute the three-dimensional, rotational, adiabatic, inviscid flow of a perfect gas in a transonic axial turbine stage. The time-dependent Euler equations, expressed in a cylindrical coordinate system, are solved using a time-marching method and a finite volume approach. The absolute flow is calculated in the stator, whereas the relative flow is computed in the rotor. A time-averaged blade row interaction is assumed. The method is applied to a transonic single-stage turbine. The calculated results agree well with the measured performance and three-dimensional aspects of the flow appear clearly.
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Ke, Shitang, Lu Xu, and Tongguang Wang. "Aerodynamic Performance and Wind-Induced Responses of Large Wind Turbine Systems with Meso-Scale Typhoon Effects." Energies 12, no. 19 (September 27, 2019): 3696. http://dx.doi.org/10.3390/en12193696.
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The theoretical system of existing civil engineering typhoon models is too simplified and the simulation accuracy is very low. Therefore, in this work a meso-scale weather forecast model (WRF) based on the non-static Euler equation model was introduced to simulate typhoon “Nuri” with high spatial and temporal resolution, focusing on the comparison of wind direction and wind intensity characteristics before, during and after the landing of the typhoon. Moreover, the effectiveness of the meso-scale typhoon “Nuri” simulation was verified by a comparison between the track of the typhoon center based on minimum sea level pressure and the measured track. In this paper, the aerodynamic performance of large wind turbines under typhoon loads is studied using WRF and CFD nesting technology. A 5 MW wind turbine located in a wind power plant on the southeast coast of China has been chosen as the research object. The average and fluctuating wind pressure distributions as well as airflow around the tower body and eddy distribution on blade and tower surface were compared. A dynamic and time-historical analysis of wind-induced responses under different stop positions was implemented by considering the finite element complete transient method. The influence of the stop position on the wind-induced responses and wind fluttering factor of the system were analyzed. Finally, under a typhoon process, the most unfavorable stop position of the large wind turbine was concluded. The results demonstrated that the internal force and wind fluttering factor of the tower body increased significantly under the typhoon effect. The wind-induced response of the blade closest to the tower body was affected mostly. The wind fluttering factor of this blade was increased by 35%. It was concluded from the analysis that the large wind turbine was stopped during the typhoon. The most unfavorable stop position was at the complete overlapping of the lower blade and the tower body (Condition 1). The safety redundancy reached the maximum when the upper blade overlapped with the tower body completely (Condition 5). Therefore, it is suggested that during typhoons the blade of the wind turbine be rotated to Condition 5.
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Anderson, O. L. "Calculation of Three-Dimensional Boundary Layers on Rotating Turbine Blades." Journal of Fluids Engineering 109, no. 1 (March 1, 1987): 41–49. http://dx.doi.org/10.1115/1.3242613.
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An assessment has been made of the applicability of a three-dimensional boundary-layer analysis to the calculation of heat transfer and streamline flow patterns on the surfaces of both stationary and rotating turbine passages. In support of this effort, an analysis has been developed to calculate a general nonorthogonal surface coordinate system for arbitrary three-dimensional surfaces and also to calculate the boundary-layer edge conditions for compressible flow using the surface Euler equations and experimental pressure distributions. Using available experimental data to calibrate the method, calculations are presented for the endwall, and suction surfaces of a stationary cascade and for the pressure surface of a rotating turbine blade. The results strongly indicate that the three-dimensional boundary-layer analysis can give good predictions of the flow field and heat transfer on the pressure, suction, and endwall surfaces in a gas turbine passage.
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Leclerc, Christophe, and Christian Masson. "Wind Turbine Performance Predictions Using a Differential Actuator-Lifting Disk Model." Journal of Solar Energy Engineering 127, no. 2 (April 25, 2005): 200–208. http://dx.doi.org/10.1115/1.1889466.
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This paper presents a method based on the imposition of velocity discontinuities to model flow perturbation due to the existence of vortical structures. The proposed method uses actuator-disk and lifting line concepts in order to provide a framework of analysis that respects conservation laws for momentum, energy, and vorticity, which is not always the case for engineering methods used in the wind industry. The flow field is described by the Euler equations. In the proposed mathematical model, the attitude toward flow determination is entirely linked to the vorticity structure of the flow, which is modeled by velocity discontinuities. The numerical method has been applied to four wind turbines: NREL phases II, IV, and VI rotors, as well as to the Tjaereborg rotor, and has shown satisfactory predictions compared to measurements up to peak power. Comparisons have also been undertaken with the results of a previous method, developed by the same authors, where the velocity field is not allowed to be discontinuous and the actuator disk is analyzed as a source of external forces only. In the stall regime of the turbine, the relative differences in power output between the two methods have been evaluated at 5% on the average.
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Hao, Junbo, Zedong Wang, Wenwu Yi, Yan Chen, and Jiyao Chen. "Influence of the Flexible Tower on Aeroelastic Loads of the Wind Turbine." Applied Sciences 11, no. 19 (September 24, 2021): 8876. http://dx.doi.org/10.3390/app11198876.
Full textAbstract:
The finite element discretization of a tower system based on the two-node Euler-Bernoulli beam is carried out by taking the cubic Hermite polynomial as the form function of the beam unit, calculating the structural characteristic matrix of the tower system, and establishing the wind turbine-nacelle-tower multi-degree-of-freedom finite element numerical model. The equation for calculating the aerodynamic load for any nacelle attitude angle is derived. The effect of the flexible tower vibration feedback on the aerodynamic load of the wind turbine is studied. The results show that, when the stiffness of the tower is large, the effect of having tower vibration feedback or not on the aeroelastic load of the wind turbine is small. For the more flexible tower system, wind-induced vibration time-varying feedback will cause larger aeroelastic load variations, especially the top of the tower overturning moment, thus causing a larger impact on the dynamic behavior of the tower downwind and crosswind. As the flexibility of the tower system increases, the interaction between tower vibration and pneumatic load is also gradually increasing. Taking into account the influence of flexible towers on the aeroelastic load of a wind turbine can help predict the pneumatic load of a wind turbine more accurately and improve the efficiency of wind energy utilization on the one hand and analyze the dynamic behavior of the flexible structure of a wind turbine more accurately on the other hand, which is extremely beneficial to the structural optimization of wind turbine.
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Roduner, C., P. Ko¨ppel, P. Kupferschmied, and G. Gyarmathy. "Comparison of Measurement Data at the Impeller Exit of a Centrifugal Compressor Measured With Both Pneumatic and Fast-Response Probes." Journal of Turbomachinery 121, no. 3 (July 1, 1999): 609–18. http://dx.doi.org/10.1115/1.2841359.
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The main goal of these investigations was the refined measurement of unsteady high-speed flow in a centrifugal compressor using the advanced FRAP® fast-response aerodynamic probe system. The present contribution focuses on the impeller exit region and shows critical comparisons between fast-response (time-resolving) and conventional pneumatic probe measurement results. Three probes of identical external geometry (one fast and two pneumatic) were used to perform wall-to-wall traverses close to the impeller exit. The data shown refer to a single running condition near the best point of the stage. The mass flow obtained from different probe measurements and from the standard orifice measurement were compared. Stage work obtained from temperature rise measured with a FRAP® probe and from impeller outlet velocity vectors fields by using Euler’s turbine equation are presented. The comparison in terms of velocity magnitude and angle distribution is quite satisfactory, indicating the superior DC measurement capabilities of the fast-response probe system.
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Cizmas, Paul G. A., Corbett R. Hoenninger, Shun Chen, and Harry F. Martin. "Influence of Inter-row Gap Value on Turbine Losses." International Journal of Rotating Machinery 7, no. 5 (2001): 335–49. http://dx.doi.org/10.1155/s1023621x01000288.
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This paper presents the results of a numerical investigation of the gap influence on the turbine efficiency. The rotor-stator interaction in a (1/2)-stage turbine is simulated by solving the quasi-three-dimensional unsteady Euler/Navier-Stokes equations using a parallelized numerical algorithm. The reduced turnaround time and cost/MFLOP of the parallel code was crucial to complete the numerous run cases presented in this paper. The inter-row gap effect is evaluated for 4 gaps, 3 radial positions and 3 angular velocities. As expected, the results presented in this paper show that the efficiency increases and losses decrease while the gap size increases. The maximum efficiency location, however, corresponds to values of the gap size which may be too large for practical use (approximately inch). Fortunately, a local maximum efficiency and minimum losses location has been found at approximately 0.5 inches gap size. The efficiency variation near the local optimum is large, in some configurations being as high as 1.4 points for a gap size variation of only 0.076 inches. Data produced by the numerical simulations can be used to develop a design rule based on the inter-row gap size.
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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 1: General Formulation." International Journal of Structural Stability and Dynamics 20, no. 09 (August 2020): 2050098. http://dx.doi.org/10.1142/s0219455420500984.
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Energy harvesting by wind turbines is of great concern in many countries/areas, yet its safety is inevitably related to the structural vibration of the turbine system. In this study, we present a complete linear analysis of structural vibrations for vertical axis wind turbines (VAWTs) based on Euler’s beam theory by Lagrangian mechanics. The un-deformed blade is assumed to be vertically straight. There are several findings from solving the resultant equations which represent four dimensions of deformation, involving motion: lateral bending-chordwise bending-axial torsion-axial extension (BBTE) (1) There is no deformation coupling between axial tension and axial torsion. (2) The natural frequencies of the blade are mainly determined by lateral bending, and [Formula: see text] ([Formula: see text]) denote the natural frequencies determined solely by lateral bending. (3) The centrifugal force credited to blade deformation is the primary factor that modifies the natural frequencies. (4) The Coriolis force can exist only in the coupled system, but in any case, the Coriolis force will not be generated by coupling lateral bending and axial tension. (5) The Coriolis force, when lateral bending is coupled with chord bending or axial torsion, can only slightly modify the natural frequencies. (6) In the case of fixed speed of rotation, [Formula: see text], where [Formula: see text] is angular speed and [Formula: see text] is the distance from the rotation axis to the elastic center of the blade: given [Formula: see text]-the blade length to chord ratio, it is found that the natural frequencies [Formula: see text] of the blade are, in close approximations, inversely proportional to [Formula: see text], i.e. [Formula: see text], where [Formula: see text] is the base chord length and [Formula: see text] is the base blade length. (7) In the general case of rotating blade ([Formula: see text], we let [Formula: see text] denote the [Formula: see text]th natural frequency when [Formula: see text]. It is found that the natural frequencies [Formula: see text] are closely approximated by [Formula: see text] (8) The material damping yields the imaginary part of the modified system frequency [Formula: see text], which deteriorates the energy absorption rate of the blade. Perturbation analysis with a solvability condition is performed to determine the imaginary part of [Formula: see text]. Given the same material, [Formula: see text] is inversely proportional to [Formula: see text], i.e. [Formula: see text].
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Soemarwoto, Bambang I., Okko J. Boelens, and Toni Kanakis. "Aerodynamic design of gas turbine engine intake duct." Aircraft Engineering and Aerospace Technology 88, no. 5 (September 5, 2016): 605–12. http://dx.doi.org/10.1108/aeat-02-2015-0063.
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Purpose The purpose of this paper is to provide a design solution of an engine intake duct suitable for delivering air to the compressor of a gas turbine engine of a general aviation turboprop aircraft, where the initial duct shape suffers a problem of flow distortion due to flow separation at the compressor inlet. Design/methodology/approach Aerodynamic design uses a three-dimensional inverse-by-optimization approach where the deviation from a desirable target pressure distribution is minimized by means of the adjoint method. Findings By virtue of a minimization algorithm, the specified target pressure distribution does not necessarily have to be fully realizable to drive the initial pressure distribution towards one with a favourable pressure gradient. The resulting optimized engine intake duct features a deceleration region, in a diverging channel, followed by an acceleration region, in a contracting channel, inhibiting flow separation on the compressor inlet plane. Practical implications The flow separation at the compressor inlet has been eliminated allowing proper installation of the engine and flight testing of the aircraft. Originality/value Placement and shaping of the intake duct of a turboshaft and turboprop gas turbine engine is a common industrial problem which can be challenging when the available space is limited. The inverse-by-optimization approach based on a reduced flow model, i.e. inviscid flow based on the Euler equations, and a specification of a simple target pressure distribution constitutes an efficient method to overcome the challenge.
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ElAlaoui, Rabie, Hamid Mounirv, Boudi El Mostapha, and Abdellatif El Marjani. "Theoretical study to calculate the vibration modes of a wind turbine blade with a new composite material." World Journal of Environmental Research 8, no. 1 (May 25, 2018): 17–25. http://dx.doi.org/10.18844/wjer.v8i1.3946.
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A precise understanding of the dynamics of a blade is essential for its design, especially in the development of new structures and the resolution of noise and vibration problems. This understanding involves the study of experimental and/or theoretical modal analysis. These latter present effective tools for describing, understanding and modelling the dynamic aspect of each structure, in the present work, we are going to establish the Eigen-mode of a wind turbine blade made by a new composite material ‘hemp fibre’ using theoretical calculation for flap-wise, edge-wise and torsional mode using the finite element method applied to a structure consisting of a beam embedded at one end, based on the Euler-Bernoulli hypothesis and the equation of beam’s motion. Furthermore; we compare the obtained results with those of composite material made by fibreglass.
Keywords: Blade, Eigen-mode, hemp fibre, flap-wise, edge-wise, torsional, fibreglass.
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Tran, L. T., and D. B. Taulbee. "Prediction of Unsteady Rotor-Surface Pressure and Heat Transfer From Wake Passings." Journal of Turbomachinery 114, no. 4 (October 1, 1992): 807–17. http://dx.doi.org/10.1115/1.2928034.
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The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations that govern the inviscid flow are solved using a time-accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations that govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values that can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.
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Furukawa, M., T. Nakano, and M. Inoue. "Unsteady Navier–Stokes Simulation of Transonic Cascade Flow Using an Unfactored Implicit Upwind Relaxation Scheme With Inner Iterations." Journal of Turbomachinery 114, no. 3 (July 1, 1992): 599–606. http://dx.doi.org/10.1115/1.2929184.
Full textAbstract:
An implicit upwind scheme has been developed for Navier–Stokes simulations of unsteady flows in transonic cascades. The two-dimensional, Reynolds-averaged Navier–Stokes equations are discretized in space using a cell-centered finite volume formulation and in time using the Euler implicit method. The inviscid fluxes are evaluated using a highly accurate upwind scheme based on a TVD formulation with the Roe’s approximate Riemann solver, and the viscous fluxes are determined in a central differencing manner. The algebraic turbulence model of Baldwin and Lomax is employed. To simplify grid generations, a zonal approach with a composite zonal grid system is implemented, in which periodic boundaries are treated as zonal boundaries. A new time linearization of the inviscid fluxes evaluated by Roe’s approximate Riemann solver is presented in detail. No approximate factorization is introduced, and unfactored equations are solved by a pointwise relaxation method. To obtain time-accurate solutions, 30 linear iterations are performed at each time step. Numerical examples are presented for unsteady flows in a transonic turbine cascade where periodic unsteadiness is caused by the trailing edge vortex shedding.
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He, L. "An Euler Solution for Unsteady Flows Around Oscillating Blades." Journal of Turbomachinery 112, no. 4 (October 1, 1990): 714–22. http://dx.doi.org/10.1115/1.2927714.
Full textAbstract:
A time-marching Euler calculation for 2-D and quasi-3-D unsteady flows in oscillating blade rows is presented, based on a finite volume scheme with cell-vertex discretization in space and 2-step Runge-Kutta integration in time. Extra fluxes due to the deformation of the moving finite volumes are directly included in the conservation equations in the physical coordinate system. A zonal moving grid technique is used, in which only subregions near oscillating blades are moved to fit both the moving (blade) boundaries and fixed regions. For phase-shifted periodic conditions, the conventional “Direct Store” method is used as a basis for comparison. Two alternative methods to save computer storage are proposed and preliminary demonstrations of their usefulness are given in the present calculations. Calculated results for unsteady flows in an oscillating flat plate cascade are in good agreement with those from two well-established linear methods, LINSUB and FINEL. The unsteady pressure distribution and aerodynamic damping calculated by the present method for a turbine blade test case (Aeroelasticity Workshop Standard Configuration No. 4 cascade) agree well with the corresponding experimental data. Computations for an oscillating biconvex cascade in transonic flow conditions are performed, which show some strong nonlinear behavior of shock wave movement.
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Ricci, Martina, Roberto Pacciani, and Michele Marconcini. "The exploitation of CFD legacy for the meridional analysis and design of modern gas and steam turbines." E3S Web of Conferences 197 (2020): 11013. http://dx.doi.org/10.1051/e3sconf/202019711013.
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In the last decades, the consolidation of 3D CFD approaches in the industrial design practices has progressively moved throughflow codes from the top of design systems to somewhere in between first development stages and the final aerodynamic optimizations. Despite this trend and the typical limitations of traditional throughflow methods, designers tend to still consider such methods as fundamental tools for drafting a credible aero-design in a short turnaround time. Recently a considerable attention has been devoted to CFDbased throughflow codes as suitable means to widen the range of applicability of these tools while smoothing the predictive gap with successive threedimensional flow analyses. The present paper retraces the development and some applications of a modern and complete CFD-based throughflow solver specifically tuned for multistage axial turbine design. The code solves the axisymmetric Euler equations with an original treatment of tangential blockage and body force. It inherits its numerical scheme from a state-of-the-art CFD solver (TRAF code) and incorporates real gas capabilities, three-dimensional flow features (e.g. secondary flows, tip leakage effects), coolant flow injections, and radial mixing models. Also geometric features of actual blades, like fillets, part-span shrouds, and snubbers, are accounted for by suitable models. The capabilities of the code are demonstrated by discussing a significant range of test cases and industrial applications. They include single stage configurations and entire multistage modules of steam turbines, with flow conditions ranging from subsonic to supersonic. Computational strategies for design and off-design analyses will be presented and discussed. The reliability and accuracy of the method is assessed by comparing throughflow results with 3D CFD calculations and experimental data. A good agreement in terms of overall performance and spanwise distributions is achieved in both design and off-design operating conditions.
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Cinnella, P., P. De Palma, G. Pascazio, and M. Napolitano. "A Numerical Method for Turbomachinery Aeroelasticity." Journal of Turbomachinery 126, no. 2 (April 1, 2004): 310–16. http://dx.doi.org/10.1115/1.1738122.
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This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier-Stokes equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roe’s second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The dual-time-stepping technique is used to evaluate the nonlinear residual at each time step. The state-of-the-art second-order accuracy of unsteady transonic flow solvers is thus carried over to flutter computations. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, for the very severe 11th Aeroelastic Standard Configuration, namely, transonic flow through a turbine cascade at off-design conditions, benchmark solutions are provided for various values of the inter-blade phase angle.
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Bra¨unling, W., and F. Lehthaus. "Investigations of the Effect of Annulus Taper on Transonic Turbine Cascade Flow." Journal of Engineering for Gas Turbines and Power 108, no. 2 (April 1, 1986): 285–92. http://dx.doi.org/10.1115/1.3239901.
Full textAbstract:
In a test facility for rotating annular cascades with three conical test sections of different taper angles (0, 30, 45 deg), experiments are conducted for two geometrically different turbine cascade configurations, a hub section cascade with high deflection and a tip section cascade with low deflection. The evaluation of time-averaged data derived from conventional probe measurements upstream and downstream of the test wheel in the machine-fixed absolute system is based on the assumption of axisymmetric stream surfaces. The cascade characteristics, i.e., mass flow, deflection, and losses, for a wide range of inlet flow angles and outlet Mach numbers are provided in the blade-fixed relative system with respect to the influence of annulus taper. Some of the results are compared with simple theoretical calculations. To obtain some information about the spatial structure of the flow within the cascade passages, surface pressure distributions on the profiles of the rotating test wheels are measured at three different radial blade sections. For some examples those distributions are compared with numerical results on plane cascades of the same sweep and dihedral angles and the same aspect ratios. The computer code used is based on a three-dimensional time-marching finite-volume method solving the Euler equations. Both experimental and numerical results show a fairly good qualitative agreement in the three-dimensional blade surface pressure distributions. This work will be continued with detailed investigations on the spatial flow structure.
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Hale, A., and W. O’Brien. "1997 Best Paper Award—Education Committee: A Three-Dimensional Turbine Engine Analysis Compressor Code (TEACC) for Steady-State Inlet Distortion." Journal of Turbomachinery 120, no. 3 (July 1, 1998): 422–30. http://dx.doi.org/10.1115/1.2841733.
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The direct approach of modeling the flow between all blade passages for each blade row in the compressor is too computationally intensive for practical design and analysis investigations with inlet distortion. Therefore a new simulation tool called the Turbine Engine Analysis Compressor Code (TEACC) has been developed. TEACC solves the compressible, time-dependent, three-dimensional Euler equations modified to include turbomachinery source terms, which represent the effect of the blades. The source terms are calculated for each blade row by the application of a streamline curvature code. TEACC was validated against experimental data from the transonic NASA rotor, Rotor 1B, for a clean inlet and for an inlet distortion produced by a 90-deg, one-per-revolution distortion screen. TEACC revealed that strong swirl produced by the rotor caused the compressor to increase in loading in the direction of rotor rotation through the distorted region and decrease in loading circumferentially away from the distorted region.
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Hwang, C. J., and J. L. Liu. "Analysis of Steady and Unsteady Turbine Cascade Flows by a Locally Implicit Hybrid Algorithm." Journal of Turbomachinery 115, no. 4 (October 1, 1993): 699–706. http://dx.doi.org/10.1115/1.2929305.
Full textAbstract:
For the two-dimensional steady and unsteady turbine cascade flows, the Euler/Navier–Stokes equations with Baldwin-Lomax turbulence model are solved in the Cartesian coordinate system. A locally implicit hybrid algorithm on mixed meshes is employed, where the convection-dominated part in the flow field is studied by a TVD scheme to obtain high-resolution results on the triangular elements, and the second- and fourth-order dissipative model is introduced on the O-type quadrilateral grid in the viscous-dominated region to minimize the numerical dissipation. When the steady subsonic and transonic turbulent flows are investigated, the distributions of isentropic Mach number on the blade surface, exit flow angle, and loss coefficient are obtained. Comparing the present results with the experimental data, the accuracy and reliability of the current approach are confirmed. By giving a moving wake-type total pressure profile at the inlet plane in the rotor-relative frame of reference, the unsteady transonic inviscid and turbulent flows calculations are performed to study the interaction of the upstream wake with a moving blade row. The Mach number contours, perturbation component of the unsteady velocity vectors, shear stress, and pressure distributions on the blade surface are presented. The physical phenomena, which include periodic flow separation on the suction side, bowing, chopping and distortion of incoming wake, negative jet, convection of the vortices and wake segments, and vortex shedding at the trailing edge, are observed. It is concluded that the unsteady aerodynamic behavior is strongly dependent on the wake/shock/boundary layer interactions.
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Hwang, C. J., and J. L. Liu. "Inviscid and Viscous Solutions for Airfoil/Cascade Flows Using a Locally Implicit Algorithm on Adaptive Meshes." Journal of Turbomachinery 113, no. 4 (October 1, 1991): 553–60. http://dx.doi.org/10.1115/1.2929114.
Full textAbstract:
A numerical solution procedure, which includes a locally implicit finite volume scheme and an adaptive mesh generation technique, has been developed to study airfoil and cascade flows. The Euler/Navier–Stokes, continuity, and energy equations, in conjunction with Baldwin-Lomax model for turbulent flow, are solved in the Cartesian coordinate system. To simulate physical phenomena efficiently and correctly, a mixed type of mesh, with unstructured triangular cells for the inviscid region and structured quadrilateral cells for the viscous, boundary layer, and wake regions, is introduced in this work. The inviscid flow passing through a channel with circular arc bump and the laminar flows over a flat plate with/without shock interaction are investigated to confirm the accuracy, convergence, and solution-adaptibility of the numerical approach. To prove the reliability and capability of the present solution procedure further, the inviscid/viscous results for flows over the NACA 0012 airfoil, NACA 65-(12)10 compressor, and one advanced transonic turbine cascade are compared to the numerical and experimental data given in related papers and reports.
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Giles, M., and R. Haimes. "Validation of a Numerical Method for Unsteady Flow Calculations." Journal of Turbomachinery 115, no. 1 (January 1, 1993): 110–17. http://dx.doi.org/10.1115/1.2929195.
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This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier–Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier–Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space–time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.
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Robinson, Mouafo Teifouet Armand, and Zhenyu Wang. "The effect of the TMD on the vibration of an offshore wind turbine considering three soil-pile-interaction models." Advances in Structural Engineering 24, no. 12 (April 16, 2021): 2652–68. http://dx.doi.org/10.1177/13694332211008316.
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In this paper we propose the use of the power series method and the Newmark-Beta algorithm to study the mitigation by the tuned mass damper (TMD) of an offshore wind turbine(OWT). The monopile of the OWT is taken as slender beam buried in a homogeneous soil while the tower is considered as tapered slender beam. Mathematically, both monopile and tower are modeled as elastic Euler-Bernoulli beams, with a point mass at the tower top representing the rotor nacelle assembly (RNA). First of all, the power series method is utilized to calculate the first natural frequencies of AF and CS models. The obtained results are compared with the first natural frequency of DS model obtained from FEM-Abaqus with good satisfaction. Next, the obtained mode shapes are used to establish the system of ordinary differential equations (ODE) governing the dynamic of OWT subjected to a TMD. Afterwards, the Newmark-Beta algorithm is employed to solve the ODE. Accuracy of the introduced approach is verified by setting a comparison between our results with those obtained using FEM-Abaqus. Finally, the influence of several parameters on the performance of TMD is shown in some plots.
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RICHTER, CHRISTOPH, HANNES LÜCK, ŁUKASZ PANEK, and FRANK THIELE. "METHODS FOR SUPPRESSING SHEAR LAYER INSTABILITIES FOR CAA." Journal of Computational Acoustics 19, no. 02 (June 2011): 181–203. http://dx.doi.org/10.1142/s0218396x11004420.
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The rearward propagation of tonal noise from the main fan and the engine core of modern high bypass aeroengines is one of the current demanding applications of CAA methods. One of the main features of this problem is the radiation of tones from main fan and turbine through the shear layers of core and bypass jets. This can approximately be described by a solution of the linearized perturbed Euler equations over a sheared turbulent averaged base flow field. However, these equations not only describe sound propagation, but also provide a stability analysis for the sheared base flow. Three techniques with the potential to calculate an acoustic solution and at the same time to suppress the instability are compared in this paper. The radiation of a source from a two-dimensional hot jet, chosen from a CAA workshop on benchmark problems, is considered first. Then, the techniques are adopted for the simulation of a single azimuthal mode radiating from the bypass duct of a turbofan engine, as an example for the realistic application. The first technique is based on filtering the mean flow field, over which the perturbation equations are solved. A low-order filter is applied. Subsequently, an adaption of this method, which considers a filtering of the mean flow derivatives in addition, is proved to be very beneficial. The result then reflects the analytical solution of the benchmark problem very well. The second technique filters the source terms in the governing equations. In a first attempt, all mean flow derivatives are neglected to suppress the instability. A more physical motivated variant of the approach neglects only source terms in the momentum equations. However, both provide unsatisfactory predictions of the acoustic field for the benchmark. Finally, a third technique is implemented, which considers the modification of the velocity derivatives in the momentum equations, as this method has demonstrated one of the best predictions for the benchmark problem. Nevertheless, the latter technique has no 3D extension and thus fails in suppressing the instability waves in the turbofan application.
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Grimm, Felix, Jürgen Dierke, Roland Ewert, Berthold Noll, and Manfred Aigner. "Modelling of combustion acoustics sources and their dynamics in the PRECCINSTA burner test case." International Journal of Spray and Combustion Dynamics 9, no. 4 (July 7, 2017): 330–48. http://dx.doi.org/10.1177/1756827717717390.
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A stochastic, hybrid computational fluid dynamics/computational combustion acoustics approach for combustion noise prediction is applied to the PRECCINSTA laboratory scale combustor (prediction and control of combustion instabilities in industrial gas turbines). The numerical method is validated for its ability to accurately reproduce broadband combustion noise levels from measurements. The approach is based on averaged flow field and turbulence statistics from computational fluid dynamics simulations. The three-dimensional fast random particle method for combustion noise prediction is employed for the modelling of time-resolved dynamics of sound sources and sound propagation via linearised Euler equations. A comprehensive analysis of simulated sound source dynamics is carried out in order to contribute to the understanding of combustion noise formation mechanisms. Therefrom gained knowledge can further on be incorporated for the investigation of onset of thermoacoustic phenomena. The method-inherent stochastic Langevin ansatz for the realisation of turbulence related source decay is analysed in terms of reproduction ability of local one- and two-point statistical input and therefore its applicability to complex test cases. Furthermore, input turbulence statistics are varied, in order to investigate the impact of turbulence on the resulting sound pressure spectra for a swirl stabilised, technically premixed combustor.
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Jivkov, Venelin S., and Evtim V. Zahariev. "High-Speed Rotor Analytical Dynamics on Flexible Foundation Subjected to Internal and External Excitation." Journal of Theoretical and Applied Mechanics 46, no. 4 (December 1, 2016): 3–18. http://dx.doi.org/10.1515/jtam-2016-0018.
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Abstract The paper presents a geometrical approach to dynamics simulation of a rigid and flexible system, compiled of high speed rotating machine with eccentricity and considerable inertia and mass. The machine is mounted on a vertical flexible pillar with considerable height. The stiffness and damping of the column, as well as, of the rotor bearings and the shaft are taken into account. Non-stationary vibrations and transitional processes are analyzed. The major frequency and modal mode of the flexible column are used for analytical reduction of its mass, stiffness and damping properties. The rotor and the foundation are modelled as rigid bodies, while the flexibility of the bearings is estimated by experiments and the requirements of the manufacturer. The transition effects as a result of limited power are analyzed by asymptotic methods of averaging. Analytical expressions for the amplitudes and unstable vibrations throughout resonance are derived by quasi-static approach increasing and decreasing of the exciting frequency. Analytical functions give the possibility to analyze the influence of the design parameter of many structure applications as wind power generators, gas turbines, turbo-generators, and etc. A numerical procedure is applied to verify the effectiveness and precision of the simulation process. Nonlinear and transitional effects are analyzed and compared to the analytical results. External excitations, as wave propagation and earthquakes, are discussed. Finite elements in relative and absolute coordinates are applied to model the flexible column and the high speed rotating machine. Generalized Newton - Euler dynamics equations are used to derive the precise dynamics equations. Examples of simulation of the system vibrations and nonstationary behaviour are presented.
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Ott, P., A. Bo¨lcs, and T. H. Fransson. "Experimental and Numerical Study of the Time-Dependent Pressure Response of a Shock Wave Oscillating in a Nozzle." Journal of Turbomachinery 117, no. 1 (January 1, 1995): 106–14. http://dx.doi.org/10.1115/1.2835625.
Full textAbstract:
Investigations of flutter in transonic turbine cascades have shown that the movement of unsteady normal shocks has an important effect on the excitation of blades. In order to predict this phenomenon correctly, detailed studies concerning the response of unsteady blade pressures versus different parameters of an oscillating shock wave should be performed, if possible isolated from other flow effects in cascades. In the present investigation the correlation between an oscillating normal shock wave and the response of wall-mounted time-dependent pressure transducers was studied experimentally in a nozzle with fluctuating back pressure. Excitation frequencies between 0 Hz and 180 Hz were investigated. For the measurements, various measuring techniques were employed. The determination of the unsteady shock position was made by a line scan camera using the Schlieren flow visualization technique. This allowed the simultaneous use of unsteady pressure transducers to evaluate the behavior of the pressure under the moving shock. A numerical code, based on the fully unsteady Euler equations in conservative form, was developed to simulate the behavior of the shock and the pressures. The main results of this work were: (1) The boundary layer over an unsteady pressure transducer has a quasi-steady behavior with respect to the phase lag. The pressure amplitude depends on the frequency of the back pressure. (2) For the geometry investigated the shock amplitude decreased with increasing excitation frequency. (3) The pressure transducer sensed the arriving shock before the shock had reached the position of the pressure transducer. (4) The computed unsteady phenomena agree well with the results of the measurements.
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LEUNG, A. Y. T. "DYNAMICS AND BUCKLING OF THIN PRE-TWISTED BEAMS UNDER AXIAL LOAD AND TORQUE." International Journal of Structural Stability and Dynamics 10, no. 05 (December 2010): 957–81. http://dx.doi.org/10.1142/s0219455410003956.
Full textAbstract:
Free vibration and buckling of pre-twisted beams exhibit interesting coupling phenomena between compression, shears, moments and torque and have been the subject of extensive research due to their importance as models of wind turbines and helicopter rotor blades. The paper investigates the influence of axial compression and torque on the natural vibration of pre-twisted straight beam based on the Euler-Bernoulli theory. The derivation begins with the three-dimensional Green strain tensor. The nonlinear part of the strain tensor is expressed as a product of displacement gradient to derive the strain energy due to initial stresses. The Frenet formulae in differential geometry are employed to treat the pre-twist. The strain energy due to elasticity and the linear kinetic energy are obtained in classical sense. From the variational principle, the governing equations and the associated natural boundary conditions are derived. To the best knowledge of the author, the buckling of pre-twisted beam due to initial torque has not been studied in details. The major contribution of the paper is in the consideration of the influence of initial stresses caused by initial shears, moments and torques for pre-twisted beam-columns by means of the Frenet formulae and second order strains. A number of numerical examples are given. Some particular cases are compared with existing results. It is noted that the first mode increases together with the rate of twist but the second decreases seeming to close the first two modes together. The gaps close monotonically as the rate of twist increases for natural frequencies and buckling compressions.
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Luo, Jiaqi, Juntao Xiong, Feng Liu, and Ivan McBean. "Three-Dimensional Aerodynamic Design Optimization of a Turbine Blade by Using an Adjoint Method." Journal of Turbomachinery 133, no. 1 (September 27, 2010). http://dx.doi.org/10.1115/1.4001166.
Full textAbstract:
This paper presents the application of an adjoint method to the aerodynamic design optimization of a turbine blade. With the adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. The formulations including imposition of appropriate boundary conditions for the adjoint equations of the Euler equations for turbomachinery problems are presented. Two design cases are demonstrated for a turbine cascade that involves a high tip flare, characteristic of steam turbine blading in low-pressure turbines. The results demonstrate that the design optimization method is effective and the redesigned blade yields weaker shock and compression waves in the supersonic region of the flow while satisfying the specified constraint. The relative effects of changing blade profile stagger, modifying the blade profile shape, and changing both stagger and profile shape at the same time are examined and compared. Navier–Stokes calculations are performed to confirm the performance at both the design and off-design conditions of the blade designed by the Euler method.
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Senn, Stephan M., Martin Seiler, and Ottmar Schaefer. "Blade Excitation in Pulse-Charged Mixed-Flow Turbocharger Turbines." Journal of Turbomachinery 133, no. 2 (October 21, 2010). http://dx.doi.org/10.1115/1.4001186.
Full textAbstract:
In this article, a fully three-dimensional computational modeling approach in the time and frequency domain is presented, which allows to accurately predicting fluid-structure interactions in pulse-charged mixed-flow turbocharger turbines. As part of the approach, a transient computational fluid mechanics analysis is performed based on the compressible inviscid Euler equations covering an entire engine cycle. The resulting harmonic orders of aerodynamic excitation are imposed in a forced response analysis of the respective eigenvector to determine effective stress amplitudes. The modeling approach is validated with experimental results based on various mixed-flow turbine designs. It is shown that the numerical results accurately predict the measured stress levels. The numerical approach can be used in the turbine design and optimization process. Aerodynamic excitation forces are the main reason for high cycle fatigue in turbocharger turbines and therefore a fundamental understanding is of key importance.