ISSN 1990-4789, Journal of Applied and Industrial Mathematics, 2018, Vol. 12, No. 2, pp. 355–361.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
V.A. Skorospelov, P.A. Turuk, 2018, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2018, Vol. XXI, No. 2, pp. 93–100.
Geometric Support of Numerical Simulation of Flow
in the Region of the Hydroturbine Spiral Case
V. A. Skorospelov
and P. A. Turuk
Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
Received December 21, 2017
Abstract—Some methods are proposed for geometric simulation of surfaces of the smooth spiral
case and generation of the meshes for numerical simulation of ﬂow.
Keywords: hydraulic turbine, spiral case, turbine stator, ﬁnite-element mesh
In the practice of designing the elements of the ﬂow path of hydroturbines, the methods using
numerical simulation of ﬂows develop actively. This approach allows us to signiﬁcantly reduce the time
and costs of designing hydroturbines due to a signiﬁcant reduction of the volume of model tests. The
main elements of the hydroturbine ﬂow path are: spiral case with stator, guide vane, runner, and draft
tube. Correspondingly, the ﬂow path region is subdivided into the regions of the above elements. The
instruments for geometric support of numerical simulation of ﬂows are aimed at the implementation of
the necessary initial stage of conducting numerical experiments. Their basis is the method of geometric
modeling of surfaces of the ﬂow path elements and the method of the subsequent generation of a ﬁnite
element mesh in the ﬂow region.
In this article, we consider the region of the spiral case and stator (SPC) of the hydroturbine ﬂow
path. The main role of SPC is twisting of the ﬂow that is fed to the entrance of the turbine. In the
practice of hydroturbine engineering, the three types of SPC are used: smooth metal, metal membrane,
and concrete. The technique is proposed for the geometric simulation of a smooth SPC and generation
of meshes in its region. The surface of the smooth SPC (Fig. 1) is divided into the two parts according
to the method of shaping: the input and the main ones.
Fig. 1. The total surface of the smooth SPC and stator.