Optimum Shapes of Supercavitating Hydrofoils at Zero Cavitation Number

Abstract: We investigate the problem of the flow around a supercavitating hydrofoils at zero cavitation number. Making use of formulas for the lift and drag, derived in the work by D. V. Maklakov (J. Fluid Mech, 2011, vol. 687, pp. 360–375), we dtermine the hydrofoil shape that provides the minimum drag coefficient at a given lift coefficient. This ensures the maximum lift-to-drag ratio

Intake rate through openings in the side wall of the duct

© 2020 St-Petersburg State Polytechnical University. All rights reserved. Subject. In technological and general ventilation ducts with a given uniformity of intake is often needed to be designed. The calculation of pressure losses in such ducts is complicated by the lack of reliable information about the characteristics of the flows at the inlet to the intake openings and slots. Intensity of air intake through slot openings located on one and two opposite walls of the duct in a series of sequentially placed slots, which determines the presence of a transit air stream passing by the hole is calculated. The slots are perpendicular to the generatrix panel and can be opposite or offset relative to each other. The presence of a stagnant zone formed when the flow is cut off from a sharp edge at the inlet is taken into account. Methods. The search for a solution is carried out in the framework of ideal fluid jets theory using the Kirchhoff scheme and Chaplygin method of singularities, as well as by the numerical method using Flow3d software package, where the system of equations of plane turbulent motion was ended with "standard" k-e model. Results. The flow rates of the air entering through the slots were found, depending on their width and value of the transit flow. Dependencies for the attached flow with and without flow separation are obtained. The shape of the free streamline separating the jet and vortex zones, the compression coefficients of the jet are determined. Current flow lines are constructed for different values of the geometric parameters of the duct and the hole. Conclusion. Analytical and numerical calculations showed that the kinematics of currents and values of the attached flow rate are very similar, but the size and shape of the stagnant zone are significantly different. A numerical solution gives more physics of stagnant zone formation. It was found that flow separation reduces the associated flow rate. It was also found that the intensity of absorption is minimal with the opposite order of cracks

Modeling of fluid inflow towards multistage hydraulic fractures of infinite permeability using stream tubes

This article is devoted to the problem of a fundamental reduction of the machine time for numerical solution of non-steady state problems of the flow in the vicinity of multistage hydraulic fractures along horizontal wells in a petroleum reservoir. This issue arises when it is necessary to solve inverse problems associated either with the identification of fracture parameters based on the results of their hydrodynamic studies or with their optimization to obtain specified production indicators. As a way to reduce computational costs, we previously proposed replacing the spatial problem of flow in the reservoir with a set of one-dimensional problems along the stream tubes. In this case, the problems for pressure in each fracture are solved taking into account the distributed inflow of reservoir fluid from the stream tubes adjacent to the fracture edges. Decomposition of the spatial problem into a set of one-dimensional problems along the stream tubes reduces the required machine time for numerical simulation of the non-steady state flow by orders of magnitude. The object of this research is the functions of the relative width along the stream tubes distribution and their lengths, which are necessary to calculate the local inflow to the fractures and are the key parameters of the model that determine its accuracy. The parameterization of the functions of length and distribution of the relative width along the stream tubes adjacent to the edges of vertical multistage hydraulic fractures is performed. The well between the fractures is assumed to be non-perforated. The case of fractures of infinite permeability in a homogeneous reservoir is considered, when the problem is reduced to a two-dimensional formulation in a horizontal plane. The results are also applicable without any changes to a stratified heterogeneous formation. Analytical expressions are obtained for the listed properties of stream tubes with a difference between the inner and outer edges of the fractures. For this purpose, analytical solutions of the corresponding model problems are used. An algorithm for the parametrization of stream tubes for the case of fractures differing in length is proposed. The proposed simplification of the spatial model is tested, and the range of values of the initial parameters of the system, which allows for an acceptable level of error of the simplified model for evaluative calculations, is shown