Numerical Simulation of Random Cavitation Suppression Based on Variable NACA Airfoils

In order to suppress the cavitation of an airfoil under random operating conditions, a deformable covering was constructed in the cavitation prone area of the NACA0012 airfoil. By sensing the pressure difference between the inner and outer sides of the airfoil, the covering of the airfoil can be changed adaptively to meet the requirement of suppressing random cavitation of the airfoil. The simulation results show that the cavitation influence range of the airfoil with a shape memory alloy covering can be reduced by more than 70%, and the cavitation is well reduced and suppressed. Moreover, the backflow near the wall of the airfoil was reduced under random working conditions. When the maximum bulge deformation of the covering was between 3–6 mm, the airfoil produced a cavitation range only on the covering surface of the airfoil, and there was no cavitation erosion on other parts. This method with locally variable airfoil to suppress cavitation provides a good reference value for other hydraulic machinery to suppress cavitation.

Indecomposable branched coverings over the projective plane by surfaces M with χ(M) ≤ 0

In this work, we study the decomposability property of branched coverings of degree [Formula: see text] odd, over the projective plane, where the covering surface has Euler characteristic [Formula: see text]. The latter condition is equivalent to say that the defect of the covering is greater than [Formula: see text]. We show that, given a datum [Formula: see text] with an even defect greater than [Formula: see text], it is realizable by an indecomposable branched covering over the projective plane. The case when [Formula: see text] is even is known.

Simplifying branched covering surface-knots by an addition of 1-handles with chart loops

A branched covering surface-knot over an oriented surface-knot [Formula: see text] is a surface-knot in the form of a branched covering over [Formula: see text]. A branched covering surface-knot over [Formula: see text] is presented by a graph called a chart on a surface diagram of [Formula: see text]. For a branched covering surface-knot, an addition of 1-handles equipped with chart loops is a simplifying operation which deforms the chart to the form of the union of free edges and 1-handles with chart loops. We investigate properties of such simplifications.

Natural Convective Heat Transfer From a Horizontal Rectangular Isothermal Element Imbedded in a Plane Adiabatic Surface With a Parallel Adiabatic Covering Surface

Natural convective heat transfer from a horizontal flat rectangular isothermal heated element imbedded in a flat rectangular adiabatic surface has been numerically studied. The surface of the heated rectangular element is in the same plane as the surface of the surrounding adiabatic material. A rectangular flat horizontal adiabatic surface is mounted parallel to and at a relatively short distance from the heated element. The heated element is facing upwards with the covering surface above the element. For the conditions considered laminar, transitional, and turbulent flows can occur. The flow has been assumed to be steady. Constant fluid properties have been assumed except for the density change with temperature which gives rise to the buoyancy forces. This was dealt with using the Boussinesq approach. To obtain the solution, the commercial CFD solver ANSYS FLUENT© was used to numerically solve the governing equations. The k-epsilon turbulence model was employed with account being taken of buoyancy force effects. The effects of the dimensionless distance of the rectangular covering surface from the heated rectangular element and of the ratio of the side lengths of the rectangular element on the variation of the Nusselt number with Rayleigh number have been examined.