This paper is devoted to the problem of energy dissipation and it concerns unsteady friction modeling of the liquid flow in hydraulic lines. One dimensional (1D) quasi-steady model of energy dissipation is in common use. It means that the loss of energy is estimated by the Darcy-Weisbach formulae. Such an approximation is close to reality only for slow changes of the velocity field in the pipe cross-section. In case of fast changes, like fast transients, e.g. water hammer, it fails. In this work the wall shear stress τ (defined as an effect of unsteady fluid friction) is presented as a sum of quasi-steady and unsteady components. The unsteady component of the wall shear stress is modeled as an convolution of the local fluid acceleration and a weighting function w(t). The weighting function, in general, makes an allowance for a relation of the historic velocity changes and the unsteady component of the wall shear stress. Primitive weighting functions have usually very complicated structures, and what is more, they make it impossible to perform an efficient simulation of dynamical runs. In this paper, a new weighting function is presented as a sum of exponential components in order to enable efficient calculation of the unsteady component wall shear stress. A few examples of the new effective method of unsteady wall shear stress simulations, in case of the water hammer, are presented. The results of the calculations are compared with experiments known in literature and satisfying results are obtained.
The goal of the presented work is an optimization of the geometrical configuration of the tip seal with a honeycomb land, to reduce the leakage flow in the counter-rotating LP turbine of a contra-rotating open rotor aero-engine. This goal was achieved with the use of the Ansys-CFX commercial code and an in-house optimization procedure. The detailed studies including the mesh influence, the stages of the computational domain simplification, and geometry variants are discussed.
The optimization process is based on a single objective genetic algorithm (SOGA). The automatic grid generation process and the CFD calculations are based on scripts prepared under the Ansys-ICEM and Ansys-CFX software. The whole procedure is written in the Visual Basic for Applications language (VBA), which allows a direct access to the CAD software with the use of macros and allows a proper connection between the CAD environment and the CFD software. The described algorithm allows parallel computing. In addition to the optimization studies, a sensitivity analysis was also performed. For this purpose, the Elementary Effects Method (EEM) was used.
This paper was written within the DREAM European project (Validation of Radical Engine Architecture Systems) of the 7-th Framework Program of the European Union.
This paper presents a description of the method and results of rotor blade shape optimization. The rotor blading constitutes a part of a turbine's flow path.
The optimization consists in selecting a shape that minimizes the polytrophic loss ratio (Puzyrewski R 1992 Fundamentals of Turbomachinery Theory - One Dimensional Approach, Ossolineum, Wroclaw, in Polish). The shape of the blade is defined by the mean camber line and thickness of the airfoil. The thickness is distributed around the camber line based on the ratio of distribution. A global optimization was done by means of Genetic Algorithms (GA) with the help of Artificial Neural Networks (ANN) for approximations. For the numerical simulation of a flow through the model Kaplan turbine, the geometry employed in the model was based on the actual geometry of the existing test stage. The fluid parameters and the boundary conditions for the model were based on experimental measurements which were carried out at the test stand at the Department of Turbomachinery and Fluid Mechanics at the Gdansk University of Technology. The shape of the blading was optimized for the operational point with a maximum efficiency.
This paper cites the original Murray's law about optimal radii. Extensions to some class of non-Newtonian flows that are described by the Ostwald-de Waele model and the Newtonian flows for elliptical cross-sections. A generalisation of Murray's law for multi-objective formulation is also given. It is shown that the original formulation of the optimal condition is a particular case of the multi-objective formulation.
This paper presents a system of equations for an axisymmetric laminar flow, after averaging, through the width of the interdisk slit of a Tesla turbine. Coefficients improving the efficiency of a 1D model were introduced as a result of averaging. The minimal number of such coefficients was determined. The 1D model makes it possible to attain analytical solutions to an accuracy limited by these coefficients. The calibration of a 1D model depends on finding the numerical values of coefficients that yield a sufficient accuracy compared with 3D calculations. A definition of the efficiency coefficient for the Tesla turbine is also given. This definition relies on the 1D model results. Example values of this coefficient are described after the 1D model calibration.
The method of characteristics leads to the blade geometry of a centrifugal pump. The method is built taking the advantage of the governing equations of fluid mechanics written in a non-orthogonal coordinates system. The coordinate system is based on an analytically described boundary of a centrifugal pump. Some of the information concerning the designed geometry should be introduced in advance. The mass conservation equation needs the information of the blockage factor resulting from the blading thickness. In the momentum conservation equation the body force replaces the blading force together with the friction force. In the energy conservation equation the dissipation effects are represented by a loss coefficient. It is shown that while simplifying the body force vector, the set of equations reduces to a hyperbolic system which allows applying the method of characteristics. The shapes of surfaces representing the designed blading can be built from the trajectories of fluid particles.
The presented paper shows our first step into the numerical modelling of the thermoacoustic phenomenon. The thermoacoustic effect has a great application potential, for instance, in thermoacoustic engines or thermoacoustic mixture separation. These two applications are in the centre of our interest. The modelling of thermoacoustic effects consists in a solution of transport equations, mass, momentum and energy, to identify the influence of heat transfer on the sonic oscillation and vice versa. The numerical modelling of such sensitive and sophisticated phenomena requires a high quality numerical tool. The commercial CFD code ANSYS CFX 12 was chosen as the numerical tool. This investigation will be supported by using the finite time thermodynamic theory. At the beginning preliminary numerical tests were performed in order to validate the numerical methods and the boundary conditions implemented in CFX. The numerical calculations of the Rijke tube were carried out and the results were validated against analytical relations.
The paper presents a new extension of the γ-Re_{θ t} model to account for both the laminar-turbulent transition and the surface roughness. The new modeling approach takes into account the pressure gradient, turbulence intensity and roughness height and density. In the transition region both the intermittency transport equation and the momentum thickness Reynolds number Re_{θ t} transport equation, supplemented by the correlation of Stripf et al. (2009) suitable for rough wall boundary layers are used. An additional modification of the SST turbulence model allows for modeling a full turbulent boundary layer over surfaces with sand roughness. A comprehensive validation of the new method using transitional and fully turbulent test cases was performed. Flat plate data with a zero and non-zero pressure gradient test case as well as a high pressure turbine blade case were used for this purpose The studies proved that the new modeling approach appeared to be sufficiently precise and enabled a qualitative prediction of the boundary layer development for the tested flow configurations.
The paper presents the results of LES simulation of two different turbulent channels with inlet conditions corresponding to the Reynolds number Re_{τ}=395. In both cases a varying pressure gradient was obtained by an adequate curvature of one of the walls. The first case is treated as a benchmark and is used to validate the numerical procedure. This case is characterized by the same cross-section area at the inlet and outlet and a bump of a smooth profile located on one of the walls designed to be identical to the one used in the experiment conducted at Laboratorie de Mecanique de Lille (LML) (Marquillie et al., 2008). The second case corresponds to the geometry which reproduces the real geometry of the turbomachinery test section of the Czestochowa University of Technology. The test section was created in such a way as to produce the pressure gradient which would correspond to the conditions present in the axial compressor blade channel. The shape of both channels produced initially favorable (FPG) and then adverse pressure gradients (APG), and in this way created conditions for boundary layer separation. Due to a reverse flow where the turbulence transport is dictated by the dynamics of the large-scale eddies such a case is well suited to demonstrate predictive features of the LES technique.
A strong, normal shock wave, terminating a local supersonic area on an airfoil (or a helicopter blade), not only limits the aerodynamic performance, but also becomes a source of High-Speed Impulsive (HSI) noise. The application of a passive control system (a cavity covered by a perforated plate) on a rotor blade should reduce the noise created by the moving shock. This article describes numerical investigations focused on the application of a passive control device on a helicopter blade in high-speed transonic hover conditions to weaken the shock wave - the main source of HSI noise.
The authors conducted a series of experimental studies using a flow tunnel to determine the hydrodynamic characteristics of small axial turbines. The results obtained were confronted with the results obtained from the authors' own numerical codes based on vortex methods. This article describes the experiment and the numerical method and also discusses the results obtained.
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