For the purpose of automatic generation control (AGC), a portion of the propeller hydro-turbine units in China is adjusted to operate within a restricted range of 75%-85% load using computer-controlled AGC strategies. In engineering applications, it has been observed that when a propeller hydro-turbine unit operates under off-design conditions, a large-scale Vortex rope would occur in the draft tube, leading to significant pressure fluctuations. Injecting air into the draft tube to reduce the amplitude of pressure fluctuations is a common practice, but its effectiveness has not been proven on propeller hydro-turbine units. In this study, a CFD model of a propeller hydro-turbine was established, and 15 cases with different guide vane openings (GVO, between 31° and 45°) under unsteady conditions were calculated and studied. Two air admission measures were introduced to suppress the Vortex rope oscillation in the draft tube and to mitigate pressure fluctuations. The reason for the additional energy loss due to air admission was then explained by the entropy production theory, and its value was quantified. This study points out that when injecting air, it is necessary to first consider whether the air will obstruct the flow in the draft tube. Finally, based on simulation and experimental data under various load conditions, pressure fluctuation analysis (based on fast Fourier transform, FFT) was conducted to assess the effectiveness of air admission measures. This study can provide an additional option for balancing unit efficiency and stability when scheduling units using an AGC strategy.

In this paper, fluid flow in Francis turbine draft tube is simulated with and without water injection condition in unsteady state using actual and straight diffuser geometry of draft tube. Also a new method for selecting nozzle diameter for injection is proposed. Simulation is carried out using Fluent software and k-ε and SST k-ω turbulence models in the straight and actual geometries of the draft tube, respectively. In two considered geometries, results of proposed method for selecting the nozzle diameter, which is based on the ratio of the total loss to the pressure recovery factor, have been compared with the method used in the previous researches, which was based on the total loss calculation. Inlet boundary conditions and validation are based on the experimental data. Results show that selecting nozzle diameter is depended on the geometry of the draft tube, and using the ratio of total loss to pressure recovery factor approach for selecting nozzle diameter will improve the size of selected nozzle diameter up to 33%, velocity fluctuations up to 16. 3% and pressure fluctuations amplitude up to 19% in draft tube.

The hydraulic turbines, especially Francis turbines, frequently run at part load (PL) conditions to meet the dynamic energy needs. The flow field at the runner exit changes significantly with a change in the operating point. At PL, flow instabilities such as the Rotating Vortex rope (RVR) form in the draft tube of the Francis turbine. The present paper compares the features of the velocity and vorticity field of the Francis turbine draft tube at the best efficiency point (BEP) and PL operations using the Proper Orthogonal Decomposition (POD) of the 2D-PIV data. The POD analysis decomposes the flow field into coherent and incoherent structures describing the spatiotemporal behavior of the flow field. A visual representation of the coherent structures and the turbulent length scales in the flow field is extracted and analyzed for BEP and PL, respectively. The study highlights the salient features of the draft tube flow field, which differentiate the BEP and PL operation. The fast Fourier transform of the temporal coefficients confirms the presence of RVR frequency (0.29 times the runner frequency) at PL. The phase portraits of different modes elucidate the relationship between different harmonics of the RVR frequency at PL.

Intense pressure pulsations, which are caused by the Vortex rope in the runner cone and the draft tube of pump-turbines, result in vibrations and noise under partial load conditions in turbine mode and also reduce the machine’s efficiency. The most common method for reducing these fluctuations is injecting air through the shaft. This method has some disadvantages such as, negative influence on efficiency, high cost, and technical difficulties. In the present paper, the concept of locating grooves on the conic surface of runner has been investigated. In this regard, the runner and the draft tube geometry have been designed according to the specifications and the accessible information of Siah-Bishe project. Afterwards, the 3-dimensional flow field has been solved numerically, using Ansys CFX package. The numerical results have been verified by investigating their independency from grid size and comparing the results with experimental ones. Maximum difference between the proposed and the existing design’s performance is than 2 percent. The results indicate that locating grooves on the conic surface of the runner results in an increase in the flow velocity beneath the runner cone. Moreover, pressure pulsations have been decreased and the low-pressure area at the beginning of the draft tube shrank. The maximum amount of decrease in pressure pulsations has been recorded in two opening positions of the guide vanes (lower than 60% and more than 90% of design point). In addition, maximum efficiency drop in the revised design is less than 0.3 percent. Furthermore, because of the rotational direction change in the pump mode, the magnitude of the tangential velocity is increased.

Annular Vortex tube is a Vortex tube which allows the hot flow pass again over the hot tube. It is introduced for first time in this work. Hot Flow is not allowed to exit after passing conic valve in annular Vortex tube, but it is redirected over hot tube. This back flow absorbs heat from outer wall of hot tube. To study temperature separation which occurs in an annular Vortex tube; the performance of this type of Vortex tube has been experimentally tested and compared with the performance of a typical Vortex tube. Inlet test pressure is 4 bars and natural gas is being used as working fluid. For both type of Vortex tubes, ratio of length to diameter of tube is 10. Cold oriice diameter of Vortex generator is set to 6.4 mm. It was observed that redirecting hot flow over the hot tube in annular Vortex tube improves cooling efficiency up to 24% respect to a typical Vortex tube at the maximum temperature difference. The results show that cold mass fraction in which the coldest temperature occurs is lower for annular Vortex tube comparing with a typical Vortex tube.

For a long time, many efforts have been taken on improving gas turbine performance to increase the propulsive force and keep the chamber walls cool. In this regard, implementation of cyclonic and Vortex engines have been proposed. According to increasing in the engine efficiency and keeping the chamber walls cool, the bidirectional Vortex flow which is exited in the Vortex engine, makes researchers more interested in it. In the Vortex engine, due to its specific geometry, two Vortex layers are established. The combustion occurs in the inner Vortex layer, while the outer layer protects the walls from excessive heat transfer. The Vortex engine with gas fuel and oxidizer has been manufactured in laboratory scale at Virginia Institute of Technology and it is under investigation. Practical usage of the Vortex engine, with both liquid and solid fuels, has its own significance. Investigation and analysis of the flow field in such a chamber have been conducted in different research centers during last five years. The significant results of these studies are the analytical and numerical solution of the flow field by applying many simplifying assumptions. Selecting proper materials, determining the engine dimensions, designing injector plate, and some other parameters in engine manufacturing process require the flow field to be modeled in the combustion chamber which needs the governing equations to be solved. For investigating of the flow field in the Vortex engine, the mass conservation, momentum conservation, and energy equations have to be solved. If the flow is turbulent, the equations become more complicated and many assumptions are needed to simplify the problem. Note that, by assuming the flow to be incompressible, the energy equation becomes segregated from the other equations. At the first stage, the goal of this project is to investigate the previous analytical solution and modify it to become compatible with other numerical and experimental results, provide numerical solution of the governing equations with the least possible assumptions, and compare the obtained numerical and analytical results with each other. Since the governing equations are non-linear and the flow is turbulent, it is impossible to solve the problem analytically in details. The flow will be simulated with respect to the result of numerical solution and applying the conventional methods and the results will be presented. It is to be noted that, if the fuel is liquid, modeling the spray combustion in a two-phase (gas-liquid) flow field is required, which will be described in this project as well. According to the flow field analysis, the propulsive and aero-dynamical results of the engine will be available, which are required to determine the designation parameters and manufacturing of the Vortex engine test rig. Afterwards, by establishing the fundamental requirements for installing the appropriate test rig for the Vortex engine, manufacturing of this test rig with its accessories will be described in details. The obtained results of this project, including the flow field investigation, test rig designation and implementation, are the first steps to achieve mass production of the Vortex engine with both liquid and gas fuels which, according to its innovation and efficiency, has its own significance.

To investigate the dynamics of droplet-Vortex interactions in particle-laden Karman Vortex street flows, the simulations were carried out by using Euler-Lagrange approach, which was validated by the available experiments and numerical results. Then, the particle dispersion and the dimensionless frequency (Strouhal number) of the wake flow were analyzed to evaluate the particle-Vortex interactions. The particle dispersion was statistically analyzed from both time and space dimensions and the different instantaneous dispersion patterns were explained by the relative slip velocity. Two independent scaling parameters, Stokes number StL and particle-fluid mass loading ratio Φ were revealed, and the particle mean square displacement and the Strouhal number were modelled by using these two scaling parameters, respectively. Finally, the characteristic lengths of the particle-laden wake flow were researched, and the Strouhal number physical model was developed based on the oscillating fishtail model. The results indicated that, firstly, StL and Φ, which constitute a dominant scaling group, can characterize the dynamics of droplet-Vortex interactions in wake flow. Particles gradually separate from the Vortex with the increase of StL due to the centrifugal effect, and the Vortex intensity and regularity get worse with the increase of Φ, which further disperses the droplets for their momentum exchange with irregular Vortex structures. Secondly, the length of the formation region and the width of the free shear layer diffuse are the two simultaneous characteristic lengths of the Strouhal number in oscillating wake. The proposed Strouhal number model gives a physical basis for the frequency determination, and the predicted errors are within ±1. 5% error bands with mean absolute percentage error of 0. 67%.

The main objective of this article is to establish a new model and find some Vortex axisymmetric solutions of finite core size for this model. We introduce the hydrodynamical equations governing the atmospheric circulation over the tropics, the Boussinesq equation with constant radial gravitational acceleration. Solutions are expanded into series of Hermite eigenfunctions. We find the coefficients of the series and show the convergence of them. These equations are critically important in mathematics. They are similar to the 3D Navier-Stokes and the Euler equations. The 2D Boussinesq  equations preserve some important aspects of the 3D Euler and Navier-Stokes equations such as the Vortex stretching mechanism. The inviscid 2D Boussinesq equations are known as the Euler equations for the 3D axisymmetric swirling flows.This model is the most frequently used for buoyancy-driven fluids, such as many largescale geophysical flows, atmospheric fronts, ocean circulation, clued dynamics. In addition, they play an important role in the Rayleigh-Benard convection.