Pavel Rudolf

Proper Orthogonal Decomposition of Pressure Fields in a Draft Tube Cone of the Francis (Tokke) Turbine Model

The simulations of high head Francis turbine model (Tokke) are performed for three operating conditions - Part Load, Best Efficiency Point (BEP) and Full Load using software Ansys Fluent R15 and alternatively OpenFOAM 2.2.2. For both solvers the simulations employ Realizable k-e turbulence model. The unsteady pressure pulsations of pressure signal from two monitoring points situated in the draft tube cone and one behind the guide vanes are evaluated for all three operating conditions in order to compare frequencies and amplitudes with the experimental results. The computed velocity fields are compared with the experimental ones using LDA measurements in two locations situated in the draft tube cone. The proper orthogonal decomposition (POD) is applied on a longitudinal slice through the draft tube cone. The unsteady static pressure fields are decomposed and a spatio-temporal behavior of modes is correlated with amplitude-frequency results obtained from the pressure signal in monitoring points. The main application of POD is to describe which modes are related to an interaction between rotor (turbine runner) and stator (spiral casing and guide vanes) and cause dynamic flow behavior in the draft tube. The numerically computed efficiency is correlated with the experimental one in order to verify the simulation accuracy.

Decomposition of the swirling flow field downstream of Francis turbine runner

Practical application of proper orthogonal decomposition (POD) is presented. Spatio-temporal behaviour of the coherent vortical structures in the draft tube of hydraulic turbine is studied for two partial load operating points. POD enables to identify the eigen modes, which compose the flow field and rank the modes according to their energy. Swirling flow fields are decomposed, which provides information about their streamwise and crosswise development and the energy transfer among modes. Presented methodology also assigns frequencies to the particular modes, which helps to identify the spectral properties of the flow with concrete mode shapes. Thus POD offers a complementary view to current time domain simulations or measurements.

Spatio-temporal description of the cavitating flow behavior around NACA 2412 hydrofoil

Spatio-temporal description of the cavitating flow around hydrofoil with 8 degrees incidence using proper orthogonal decomposition (POD) is presented. POD is a suitable tool, which provides information not only about the flow dynamics, but also about relevance of different flow structures. POD also enables to track energy transport within the domain and energy transfer among the eigenmodes of the flow field. Analysis documents change of the flow structure for decreasing cavitation number, which can be most likely attributed to sheet/cloud cavitation transition.

Reduced order model of draft tube flow

Swirling flow with compact coherent structures is very good candidate for proper orthogonal decomposition (POD), i.e. for decomposition into eigenmodes, which are the cornerstones of the flow field. Present paper focuses on POD of steady flows, which correspond to different operating points of Francis turbine draft tube flow. Set of eigenmodes is built using a limited number of snapshots from computational simulations. Resulting reduced order model (ROM) describes whole operating range of the draft tube. ROM enables to interpolate in between the operating points exploiting the knowledge about significance of particular eigenmodes and thus reconstruct the velocity field in any operating point within the given range. Practical example, which employs axisymmetric simulations of the draft tube flow, illustrates accuracy of ROM in regions without vortex breakdown together with need for higher resolution of the snapshot database close to location of sudden flow changes (e.g. vortex breakdown). ROM based on POD interpolation is very suitable tool for insight into flow physics of the draft tube flows (especially energy transfers in between different operating points), for supply of data for subsequent stability analysis or as an initialization database for advanced flow simulations.

The swirl turbine

In the article is introduced the new type of the turbine - swirl turbine. This turbine is based on opposite principle than Kaplan turbine. Euler equation is satisfied in the form gHηh = −u2vu2. From this equation is seen, that inflow of liquid into the runner is without rotation and on the outflow is a rotation of liquid opposite of rotation of runner. This turbine is suitable for small head and large discharge. Some constructional variants of this turbine are introduced in the article and theoretical aspects regarding losses in the draft tube. The theory is followed by computational simulations in Fluent and experiments using laser Doppler anemometry.

Dynamics of the cavitating flow downstream of the orifice plate

Orifices with varying number of holes, but with the same flow cross-sections were tested in a cavitation circuit. Static characteristics, in term of loss coefficients, were measured in a range of non-cavitating and cavitating regimes. Since cavitating flow has very rich dynamics attention was also paid to spectral properties, especially in the cavitating regime. Data evaluated from several pressure transducers placed downstream of the orifice and for different orifice types are presented and discussed. Marked differences in both static and dynamic characteristics are observed between single-hole and multi-hole orifices.Orifices with varying number of holes, but with the same flow cross-sections were tested in a cavitation circuit. Static characteristics, in term of loss coefficients, were measured in a range of non-cavitating and cavitating regimes. Since cavitating flow has very rich dynamics attention was also paid to spectral properties, especially in the cavitating regime. Data evaluated from several pressure transducers placed downstream of the orifice and for different orifice types are presented and discussed. Marked differences in both static and dynamic characteristics are observed between single-hole and multi-hole orifices.

Spatio-Temporal Description of the Swirling Flow in Hydraulic Turbine Draft Tube

Highly swirling ow leaves runner of the hydraulic turbine, which is operated o the best e ciency point. Instability of the swirling ow results in so called vortex rope. Rotating vortex rope is a source of pressure pulsations, causes structural loads, vibrations and noise. Proper orthogonal decomposition (POD) provides a spatio-temporal description of the draft tube swirling ow and proves that only a very limited number of the ow eigenmodes is necessary to describe the ow dynamics. Construction of the reduced order model (ROM), which is derived by projection of Navier-Stokes equation onto POD basis forms a suitable state equation for the draft tube ow control. This paper presents a review of POD application to draft tube ows and a proposal of extension to ROM and closed loop ow control.

Analysis of novel low specific speed pump designs

Centrifugal pumps with very low specific speed present significant design challenges. Narrow blade channels, large surface area of hub and shroud discs relative to the blade area, and the presence of significant of blade channel vortices are typical features linked with the difficulty to achieve head and efficiency requirements for such designs. This paper presents an investigation of two novel designs of very low specific speed impellers: impeller having blades with very thick trailing edges and impeller with thick trailing edges and recirculating channels, which are bored along the impeller circumference. Numerical simulations and experimental measurements were used to study the flow dynamics of those new designs. It was shown that thick trailing edges suppress local eddies in the blade channels and decrease energy dissipation due to excessive swirling. Furthermore the recirculating channels will increase the circumferential velocity component on impeller outlet thus increasing the specific energy, albeit adversely affecting the hydraulic efficiency. Analysis of the energy dissipation in the volute showed that the number of the recirculating channels, their geometry and location, all have significant impact on the magnitude of dissipated energy and its distribution which in turn influences the shape of the head curve and the stability of the pump operation. Energy dissipation within whole pump interior (blade channels, volute, rotor- stator gaps) was also studied.

Combination of a Particle Swarm Optimization and Nelder–Mead Algorithm in a Diffuser Shape Optimization

This work focuses on the optimization of a hydraulic turbine diffuser, which is located behind the runner of the swirl turbine. The present paper extends our work in shape optimization using direct methods (namely Nelder–Mead method) and stochastic methods (namely Particle swarm optimization) coupled with CFD simulations. Both methods have their own advantages and disadvantages. Present work focuses on a combination of particle swarm optimization (at the beginning of the algorithm) and Nelder–Mead algorithm (NMA) (at the end of the algorithm). The diffuser will serve as the test case to demonstrate efficient coupling of the mathematical optimization procedure and CFD simulation. The main goal of this test problem is set to maximize the coefficient of pressure recovery c p, which is the main parameter to judge the proper design of the draft tube. Results obtained with this new method will be discussed and their advantages/disadvantages summarized.

Investigation of the Cavitation Within Venturi Tube: Influence of the Generated Vortex

The main scope of the paper is evaluation of the experimental results and comparison of the dynamics of the vortex affected cavitating flow with the dynamics of purely axial flow within the Venturi nozzle. The analysis of the high-speed records with the sampling frequency of 20,000 images per second will be presented. Records will be analyzed using the proper orthogonal decomposition (POD) and spectral analysis of the pixel intensity within the selected region of images. These analyses will be done for the wide range of regimes for the both experimental configurations (with and without the swirl generator). Analysis of the pressure pulsations and vibrations will be utilized for the verification of the results. The cavitation patterns affected by the presence of the vortex will be described and compared with the case of axial inflow. The analysis of the experimental data will be complemented with the numerical computations of the chosen regimes carried out using the OpenFoam v1606+ and its multiphase interPhaseChangeFoam solver.