THE PHYSICAL ORIGIN OF SEVERE LOW-FREQUENCY PRESSURE FLUCTUATIONS IN GIANT FRANCIS TURBINES

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1527-1530 ◽  
Author(s):  
R.-K. ZHANG ◽  
Q.-D. CAI ◽  
J.-Z. WU ◽  
Y.-L. WU ◽  
S.-H. LIU ◽  
...  
Keyword(s):  
Swirling Flow ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Francis Turbine ◽  
Navier Stokes ◽  
Physical Origin ◽  
Navier Stokes Equation ◽  
Power Stations ◽  
Hydraulic Turbines ◽  
Hydrodynamic Stability Theory

The physical origin of severe low-frequency pressure fluctuation frequently observed in Francis hydraulic turbines under off-design conditions, which greatly damages the structural stability of turbines and even power stations, is analyzed based on the hydrodynamic stability theory and our Reynolds-averaged Navier-Stokes equation simulation (RANS) of the flow in the entire passage of a Francis turbine. We find that spontaneous unsteady vortex ropes, which induce severe pressure fluctuations, are formed due to the absolute instability of the swirling flow at the conical inlet of the turbine's draft tube.

scholarly journals Effect of Air Injection on the Internal Flow Characteristics in the Draft Tube of a Francis Turbine Model

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1182
Author(s):  
Seung-Jun Kim ◽  
Yong Cho ◽  
Jin-Hyuk Kim
Keyword(s):  
Flow Rate ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Air Injection ◽  
Low Flow ◽  
Francis Turbine ◽  
Navier Stokes ◽  
Vortex Rope

Under low flow-rate conditions, a Francis turbine exhibits precession of a vortex rope with pressure fluctuations in the draft tube. These undesirable flow phenomena can lead to deterioration of the turbine performance as manifested by torque and power output fluctuations. In order to suppress the rope with precession and a swirl component in the tube, the use of anti-swirl fins was investigated in a previous study. However, vortex rope generation still occurred near the cone of the tube. In this study, unsteady-state Reynolds-averaged Navier–Stokes analyses were conducted with a scale-adaptive simulation shear stress transport turbulence model. This model was used to observe the effects of the injection in the draft tube on the unsteady internal flow and pressure phenomena considering both active and passive suppression methods. The air injection affected the generation and suppression of the vortex rope and swirl component depending on the flow rate of the air. In addition, an injection level of 0.5%Q led to a reduction in the maximum unsteady pressure characteristics.

The Mechanism of Movement and Calculation of Blood Balance in the Flow Channel From the Left Atrium to the End of the Aorta

2020 ◽  
Author(s):  
E. Talygin ◽  
G. Kiknadze ◽  
A. Gorodkov
Keyword(s):  
Exact Solution ◽  
Left Atrium ◽  
Swirling Flow ◽  
Practical Importance ◽  
Sufficient Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Mechanisms Of Formation ◽  
Formation And Evolution ◽  
General Relations

Abstract Today, there are a lot of works studying the mechanisms of formation and evolution of self-organizing tornado-like jets of viscous fluid. In these works, the exact solution of the Navier-Stokes equation for such a class of flows are obtained, the geometry of the generating surface for that flows is established and the necessary and sufficient conditions for the formation and evolution of such swirling jets are formulated. However, important aspects of the mechanics of such flows remain unclear — the structure of the boundary layer, the shape of streamlines in general form, the structure of such flows under a pulsating flow regime, and others. After obtaining the exact solution, attempts were made to obtain relations for streamlines in the corresponding projections. However, due to computational complexity, streamlines were constructed only for regions far from the axis of the swirling flow evolution. In this work, an alternative method of calculating streamlines was used, which made it possible to obtain general relations for these lines at each point in space. Expressions for streamlines contain easily computed functions, which simplifies their practical use Based on the expressions for streamlines, expressions were formulated declaring the conservation of the mass of the swirling blood flow from the left atrium to the aorta and the balance of the medium was calculated. The results of this work are of great theoretical and practical importance. On the one hand, the established expressions for streamlines allow a better study of the mechanisms of formation and evolution of swirling flows in the axial region. On the other hand, obtaining quantitative ratios for the balance of blood in the heart and aorta allows a more accurate study of the mechanics of blood circulation.

scholarly journals Physiologic blood flow is turbulent

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Khalid M. Saqr ◽  
Simon Tupin ◽  
Sherif Rashad ◽  
Toshiki Endo ◽  
Kuniyasu Niizuma ◽  
...  
Keyword(s):  
Blood Flow ◽  
Stokes Equation ◽  
Initial Conditions ◽  
Hydrodynamic Instability ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Frequency Spectra ◽  
Hydrodynamic Stability Theory

Abstract Contemporary paradigm of peripheral and intracranial vascular hemodynamics considers physiologic blood flow to be laminar. Transition to turbulence is considered as a driving factor for numerous diseases such as atherosclerosis, stenosis and aneurysm. Recently, turbulent flow patterns were detected in intracranial aneurysm at Reynolds number below 400 both in vitro and in silico. Blood flow is multiharmonic with considerable frequency spectra and its transition to turbulence cannot be characterized by the current transition theory of monoharmonic pulsatile flow. Thus, we decided to explore the origins of such long-standing assumption of physiologic blood flow laminarity. Here, we hypothesize that the inherited dynamics of blood flow in main arteries dictate the existence of turbulence in physiologic conditions. To illustrate our hypothesis, we have used methods and tools from chaos theory, hydrodynamic stability theory and fluid dynamics to explore the existence of turbulence in physiologic blood flow. Our investigation shows that blood flow, both as described by the Navier–Stokes equation and in vivo, exhibits three major characteristics of turbulence. Womersley’s exact solution of the Navier–Stokes equation has been used with the flow waveforms from HaeMod database, to offer reproducible evidence for our findings, as well as evidence from Doppler ultrasound measurements from healthy volunteers who are some of the authors. We evidently show that physiologic blood flow is: (1) sensitive to initial conditions, (2) in global hydrodynamic instability and (3) undergoes kinetic energy cascade of non-Kolmogorov type. We propose a novel modification of the theory of vascular hemodynamics that calls for rethinking the hemodynamic–biologic links that govern physiologic and pathologic processes.

Generation of Twin Vortex Rope in the Draft-Tube Elbow of a Francis Turbine During Deep Part-Load Operation

2021 ◽  
Author(s):  
Mohammad Hossein Khozaei ◽  
Arthur Favrel ◽  
Toshitake Masuko ◽  
Naoki Yamaguchi ◽  
Kazuyoshi Miyagawa
Keyword(s):  
Linear Correlation ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Model Tests ◽  
Francis Turbine ◽  
Deep Part ◽  
Swirl Number ◽  
Vortex Rope ◽  
Part Load

Abstract This paper focuses on the generation of twin vortex rope in the draft-tube elbow of a Francis turbine at deep part-load operation through analyzing the results of model tests along with numerical simulations. Model tests, including pressure fluctuations measurements, are conducted over 10 speed factors. By considering the frequency of the pressure fluctuations with respect to the swirl intensity at the runner outlet, the part-load operating range is divided into three regimes, with two clear transitions between each occurring at swirl numbers 0.4 and 1.7. For operating conditions with a swirl number S>0.4, a linear correlation between the frequency of the precessing vortex core and the swirl number is established. During deep part-load regime (S>1.7), low-frequency pressure fluctuations appear. Their frequency feature another linear correlation with the swirl number. Unsteady CFD simulation of the full domain is performed to elucidate the generation mechanisms of the low-frequency fluctuations. By tracking the center of the vortical structures along the draft-tube, generation of three vortices in the elbow responsible for the pressure fluctuations at the lowest frequency is highlighted: the main PVC hits the draft-tube wall in the elbow resulting in its break down into three vortices rotating with half the rotational speed of the PVC. Two of the vortices rotate with opposite angular position, constituting a structure of twin vortices. The periodic rotation of these three vortices in the elbow induces the low-frequency pressure fluctuations.

Excitation Models for Buffeting of Cylinder Bundles in Parallel Flow

2006 ◽  
Author(s):  
Radu Pomiˆrleanu
Keyword(s):  
Swirling Flow ◽  
Spectral Characteristics ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Parallel Flow ◽  
Rod Bundles ◽  
Wall Pressure Fluctuations ◽  
Flow Geometry ◽  
Model Predictions ◽  
Selection Of

In this paper, the effect of several models representing the state of the art in wall-pressure fluctuations statistics were applied to the geometry of square rod bundles with P/D = 1.33, and used together with the random vibration theory to yield the spectral characteristics of rod vibration. Comparison of model predictions with experimental data representing rod acceleration allowed the selection of Efimtsov model as better suited for the rod bundles flow geometry and low frequency range. Further assimilating the mixing-vanes induced swirling flow as a disturbance to the parallel flow, two corrections were proposed based on comparison of measured vibration characteristics of vaned and vaneless bundles.

Experimental Evidence of Hydroacoustic Pressure Waves in a Francis Turbine Elbow Draft Tube for Low Discharge Conditions

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Jorge Arpe ◽  
Christophe Nicolet ◽  
François Avellan
Keyword(s):  
Pressure Fluctuation ◽  
Swirling Flow ◽  
Draft Tube ◽  
Flow Direction ◽  
Pressure Fluctuations ◽  
Operating Conditions ◽  
Hydropower Plant ◽  
Francis Turbine ◽  
Scale Model ◽  
Vortex Rope

The complex three-dimensional unsteady flow developing in the draft tube of a Francis turbine is responsible for pressure fluctuations, which could prevent the whole hydropower plant from operating safely. Indeed, the Francis draft tube is subjected to inlet swirling flow, divergent cross section, and the change of flow direction. As a result, in low discharge off-design operating conditions, a cavitation helical vortex, so-called the vortex rope develops in the draft tube and induces pressure fluctuations in the range of 0.2–0.4 times the runner frequency. This paper presents the extensive unsteady wall pressure measurements performed in the elbow draft tube of a high specific speed Francis turbine scale model at low discharge and at usual plant value of the Thoma cavitation number. The investigation is undertaken for operating conditions corresponding to low discharge, i.e., 0.65–0.85 times the design discharge, which exhibits pressure fluctuations at surprisingly high frequency value, between 2 and 4 times the runner rotation frequency. The pressure fluctuation measurements performed with 104 pressure transducers distributed on the draft tube wall, make apparent in the whole draft tube a fundamental frequency value at 2.5 times the runner frequency. Moreover, the modulations between this frequency with the vortex rope precession frequency are pointed out. The phase shift analysis performed for 2.5 times the runner frequency enables the identification of a pressure wave propagation phenomenon and indicates the location of the corresponding pressure fluctuation excitation source in the elbow; hydroacoustic waves propagate from this source both upstream and downstream the draft tube.

Unsteady vortical flow simulation in a Francis turbine with special emphasis on vortex rope behavior and pressure fluctuation alleviation

2017 ◽  
Vol 231 (3) ◽  
pp. 215-226 ◽  
Author(s):  
Xianwu Luo ◽  
An Yu ◽  
Bin Ji ◽  
Yulin Wu ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Pressure Fluctuation ◽  
Swirling Flow ◽  
Draft Tube ◽  
Pressure Fluctuations ◽  
Flow Simulation ◽  
Vortical Flow ◽  
Francis Turbine ◽  
Vortex Rope ◽  
Spiral Vortex ◽  
Baroclinic Torque

Hydro turbines operating at partial flow conditions usually have vortex ropes in the draft tube that generate large pressure fluctuations. This unsteady flow phenomenon is harmful to the safe operation of hydropower stations. This paper presents numerical simulations of the internal flow in the draft tube of a Francis turbine with particular emphasis on understanding the unsteady characteristics of the vortex rope structure and the underlying mechanisms for the interactions between the air and the vortices. The pressure fluctuations induced by the vortex rope are alleviated by air admission from the main shaft center, with the water-air two phase flow in the entire flow passage of a model turbine simulated based on the homogeneous flow assumption. The results show that aeration with suitable air flow rate can alleviate the pressure fluctuations in the draft tube, and the mechanism improving the flow stability in the draft tube is due to the change of vortex rope structure and distribution by aeration, i.e. a helical vortex rope at a small aeration volume while a cylindrical vortex rope with a large amount of aeration. The preferable vortex rope distribution can suppress the swirl at the smaller flow rates, and is helpful to alleviate the pressure fluctuation in the draft tube. The analysis based on the vorticity transport equation indicates that the vortex has strong stretching and dilation in the vortex rope evolution. The baroclinic torque term does not play a major role in the vortex evolution most of the time, but will much increase for some specific aeration volumes. The present study also depicts that vortex rope is mainly associated with a pair of spiral vortex stretching and dilation sources, and its swirling flow is alleviated little by the baroclinic torque term, whose effect region is only near the draft tube inlet.

Development of a PISO-SPH method for computing incompressible flows

2013 ◽  
Vol 228 (3) ◽  
pp. 481-490 ◽  
Author(s):  
Ali Tayebi ◽  
Behzad Ghadiri Dehkordi
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Pressure Fluctuations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Sph Method ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Particle Hydrodynamics ◽  
Incompressible Fluid Flows

A new algorithm is proposed for solving the time-dependent Navier-Stokes equations in a sequential uncoupled manner. The algorithm, known as PISO (Pressure Implicit with Splitting of Operators) is extended to the Smoothed Particle Hydrodynamics (SPH) context (PISO-SPH). The algorithm consists of one prediction and two correction steps, based on a full Navier-Stokes equation, therefore, a modified Poisson equation is derived which makes the algorithm more stable with less pressure fluctuations. The proposed PISO-SPH method is applied to solve a number of benchmark problems including both unsteady and steady state test cases. Comparing the results with analytical solutions and other numerical methods, it is shown that the proposed method is accurate and straightforward for the simulation of incompressible fluid flows.

Flow-Feedback Method for Mitigating the Vortex Rope in Decelerated Swirling Flows

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Constantin Tănasă ◽  
Romeo Susan-Resiga ◽  
Sebastian Muntean ◽  
Alin Ilie Bosioc
Keyword(s):  
Swirling Flow ◽  
Flow Instability ◽  
Pressure Fluctuations ◽  
Water Injection ◽  
Operating Regime ◽  
Experimental Investigations ◽  
Vortex Rope ◽  
Practical Applications ◽  
Wall Pressure Fluctuations ◽  
Hydraulic Turbines

When reaction hydraulic turbines are operated far from the design operating regime, particularly at partial discharge, swirling flow instability is developed downstream of the runner, in the discharge cone, with a precessing helical vortex and its associated severe pressure fluctuations. Bosioc et al. (2012, “Unsteady Pressure Analysis of a Swirling Flow With Vortex Rope and Axial Water Injection in a Discharge Cone,” ASME J. Fluids Eng., 134(8), p. 081104) showed that this instability can be successfully mitigated by injecting a water jet along the axis. However, the jet discharge is too large to be supplied with high pressure water bypassing the runner, since this discharge is associated with the volumetric loss. In the present paper we demonstrate that the control jet injected at the inlet of the conical diffuser can actually be supplied with water collected from the discharge cone outlet, thus introducing a new concept of flow feedback. In this case, the jet is driven by the pressure difference between the cone wall, where the feedback spiral case is located, and the pressure at the jet nozzle outlet. In order to reach the required threshold value of the jet discharge, we also introduce ejector pumps to partially compensate for the hydraulic losses in the return pipes. Extensive experimental investigations show that the wall pressure fluctuations are successfully mitigated when the jet reaches 12% of the main flow discharge for a typical part load turbine operating regime. About 10% of the jet discharge is supplied by the plain flow feedback, and only 2% boost is insured by the ejector pumps. As a result, this new approach paves the way towards practical applications in real hydraulic turbines.

Low Frequency Acoustic Streaming in a Hele-Shaw Cell

2014 ◽  
Author(s):  
Maxime Costalonga ◽  
Hassan Peerhossaini ◽  
Philippe Brunet
Keyword(s):  
Boundary Layer ◽  
Linear Time ◽  
Acoustic Streaming ◽  
Low Frequency ◽  
Navier Stokes ◽  
Viscous Boundary Layer ◽  
Navier Stokes Equation ◽  
Acoustic Frequency ◽  
Hele Shaw Cell ◽  
Streaming Flow

When an acoustic wave propagates in a fluid, it can generate a second order flow which characteristic time is much longer than the period of the wave. Within a range of frequency between 1 and several hundred Hz, a relatively simple and versatile way to generate streaming flow is to put a vibrating object in the fluid. The flow develops vortices in the viscous boundary layer located in the vicinity of the source of vibrations, which in turns leads to an outer irrotational streaming denoted as Rayleigh streaming. Due to that the flow originates from non-linear time-irreversible terms of the Navier-Stokes equation, this phenomenon can be used to move fluids and even to generate efficient mixing at low Reynolds number, for instances in confined geometries. Here we report an experimental study of such streaming flow in a Hele-Shaw cell of 2 millimeters span using long exposure flow visualization and PIV measurements. Our study is especially focused on the effects of acoustic frequency and amplitude on flow dynamics. It is shown that some features of this flow can be predicted by simple scaling arguments, invoking a balance between viscous dissipation in the boundary layer and inertia term, and that acoustic streaming facilitates the generation of vortices.

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