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With the advancements of numerical upstream and central difference methods in modeling the subsonic and supersonic flows in different paths including the flow inside turbine blades, employing the numerical CUSP technique in the Jameson’s finite volume method can simultaneously benefit from the positive features of both mentioned methods. The novelty of this paper is first, improving Jameson’s finite volume method in modeling a 2D supersonic flow between the blades of a steam turbine using the CUSP method, and second, defining the most optimum control function mode using the Marquardt-Levenberg inverse method and by accounting for the mass conservation equation. By considering the importance of the shock regions in the blade’s surface suction side, the focus of the mentioned method is on this part which results in the significant improvement of the pressure ratio in Jameson’s finite volume method. The results of the first combined method (Jameson and CUSP) at the shock region of the blade’s suction surface desirably agree with the experimental data, and a decrease of numerical errors at this region is resulted. Furthermore, the results of the second combined method (Jameson, CUSP and inverse method) shows that in comparison with original Jameson’s method and the first combined method, by average, the conservation of mass condition is improved 15% at the shock region of the blade’s suction surface.

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Dry Steam flow at blade passages of steam turbines' low pressure stages occurs due to rapid expansion, delay in condensation and the condition of supercooled dry steam and finally after nucleation and condensation shock, phase change from vapor to liquid droplets occurs which is called two-phase or wet steam flow. In this paper, the aim of developing finite-volume flow of wet Jameson is considered for the first time in two-dimensional study by using the advantages of CUSP's numerical method. In this paper, equations governing the formation of liquid phase are combined with equations of survival and by using CUSP's numerical approach in Jameson's finite-volume method (the integrated method) the positive features of both of these methods can be simultaneously used in the modeling of two-phase flow. To calculate nucleation, the classical equation of nucleation with appropriate correction and also Lagrangian solution for growth of droplets are used in integrated method. Additionally, condensation shock effect on the pressure distribution and the droplet size has been calculated and compared with experimental data. Given the importance of areas of shocks on the suction surface of the blade, the focus of integrated method is shifted to this area. The results of integrated two-phase model are examined in subsonic and supersonic flow output .In the shock area on suction surface blade, using the CUSP's method (the integrated method) shows a better coverage in predicting attributes of flow in target area in comparison with the experimental data by a reduction of 20 percent in numerical errors.

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Condensing flow in nozzle and stationary blades of steam turbine has always been the subject of many studies. Due to the lack of precise relationship between surface tension and small droplet radius, the radial dependence of surface tension has been ignored in calculations and surface tension of flat surface instead of droplet surface tension is used. Gibbs-Tolman-Koenig-Buff equation expressing the radial dependence of surface tension that Kalova provides as a relationship of changes in surface tension versus radius of the surface by fitting response from the exact solution of GTKB equation. The aforementioned relationship is known as Kalova surface tension equation. The present study considers the effect of the Kalova surface tension correction on nucleation and droplet growth in condensing flows in an ultrasonic Laval nozzle. Since Tolman coefficient (δ) is an important parameter in Kalova surface tension equation, by fitting response from Tolman equations a correlation for Tolman coefficient temperature changes suggested for the first time. Kalova Surface tension in addition to the direct impact of the droplets crisis radius, to obtain droplet free energy crisis is also impressive that the impact of both them in the modified classical nucleation equation have been studied for the first time. The results of analytical modeling one-dimensional adiabatic supersonic flow with applying the Kalova surface tension correction and using the proposed equation for Tolman coefficient temperature changes indicate an improvement to the 12% in radius of the droplets and 5% in pressure distribution in the region of condensation shock.

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The supercooled steam in low pressure turbines creates the nucleation phenomenon. In most modeling approaches, to reduce the computation time a monodispersed model is used. However, experimental evidence even on one dimensional condensing flow demonstrates the existence of droplets with several sizes. In this paper to develop the modeling of the droplets more realistic, a polydispersed model is used along with the one dimensional HHL Riemann solver. In this study, a simple method is proposed for polydispersed model in Eulerian-Eulerian method. In this scheme, first, a number of elements are considered in the nucleation region and the droplets formed in each of the elements are put into a group. Then the new droplets formed in consecutive elements are distributed based on the ratio between the number of droplets in each group available for merging constrained by having the same number of groups. These groups grow individually until the end of the nozzle and each group has their own wetness, temperature, number of droplets and radius. Based on the results of the proposed polydispersed, the nucleation rate and the number of droplets are found to be more than the results of the monodispersed model, but the average droplet radius is less, with 10% differences is closer to the empirical radius of the Moore nozzle. The pressure distributions for both models have good agreement with experimental data, but in overall, the results of the proposed polydispersed method is significantly closer to experimental results especially with regards to the droplet radius.

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The circular hydraulic jump usually forms when a liquid jet impinges on a horizontal flat plate. However, under certain conditions of fluid viscosity, volume flow rate and obstacle height downstream of the jump, the flow changes from super-critical to sub-critical and hydraulic jump changes shape from circular to polygonal. Despite the phenomenon of the hydraulic polygon jump has observed about two decades, the experimental relationship has not been presented to estimate the number of sides of hydraulic polygon jumps. The size and number of sides of a polygonal hydraulic jump depend on various factors such as fluid volume flow rate, jet diameter, fluid height downstream of the jump, and fluid physical properties; in other words, they depend on the dimensionless numbers of Reynolds, Weber, and Bond. Hence, in this study Taguchi analysis, as a Design of Experiment method, was used to investigate the effect of volume flow rate, jet diameter and obstacle height downstream of the jump on the number of the sides of a polygon hydraulic jump and Linear and nonlinear relationships was proposed for estimating the number of the sides of a polygonal hydraulic jump in terms of the above mentioned parameters.

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