NUMERICAL AND EXPERIMENTAL MODELING OF PROPAGATION OF LONGITUDINAL FRACTURES IN MULTI-STAGE HYDRAULIC FRACTURING WITH VISCOUS FLUID

The experimental and numerical modeling of curvilinear propagation of hydraulic fractures driven by viscous fluid is implemented. The trajectories of simultaneous growth of 2-5 fractures from the boundary of a circular opening are presented in plane elasticity. The influence of the fluid viscosity on the fracture trajectory is analyzes. The causes of initiation of main fracture and shut-down of other fractures are revealed. The attempts are made to find such conditions that simultaneous growth of a few main fractures is possible by varying lengths and orientation angles of initiation fractures in the external nonuniform field of compression. The experimental modeling of hydraulic fractures was carried out using blocks made of concrete and organic glass. There were 3 to 5 initiation fractures. The influence of the breakdown fluid viscosity on the number of the main fractures is illustrated. Hydraulic fracturing with a plastic material allowed simultaneous growth of 3 and 4 fractures within a block. The experimental modeling data and the calculation results are compared.

Numerical Investigation of Nonisothermal Cavitating Flows on Hydrofoils by Means of an Extended Schnerr–Sauer Model Coupled With a Nucleation Model

This work aimed to investigate cavitating flows of water, liquid hydrogen, and nitrogen on hydrofoils numerically, using the open source code openfoam. The Eulerian homogeneous mixture approach has been used, consisting in a mass transfer model, which is based on the combination of a two-phase incompressible unsteady solver with a volume of fluid interface tracking method. Thermal effects have been introduced by means of the activation of energy equation and latent heat source terms plus convective heat source term. The dependency of the saturation conditions to the temperature has been defined using Antoine-like equations. An extended Schnerr–Sauer model based on the classical nucleation theory (CNT) has been implemented for the computation of the interfacial mass transfer rates. In order to investigate the nucleation effects, an extension of the CNT has been considered by coupling the population balance equation (PBE)/extended quadrature-based method of moments with the computational fluid dynamics (CFD) model, which has been defined in combination with a transport equation for the nuclei density. Results showed that nucleation determined a nonuniform field of nuclei density so as to produce a reduction of the temperature drop inside the vapor bubbles, as well as a warmed wake downstream the vapor cavity. Unsteady computations also revealed an influence of the nucleation on the dynamics of the vapor cavity and the bubble detachment.