Research On The Problem Of Flow Around A Cylinder With Complex Boundary

The irrotational motion of non-viscid and incompressible fluid is an idealized simple model.It is a simplification of real fluid motion under certain conditions.It can give many useful results and is more complicated for research.Laying the foundation for the phenomenon of flow is of great practical significance to its research.According to the flow characteristics of the irrotational motion of the non-viscid and incompressible fluid,we can obtain the motion characteristics of the flow field by solving the Laplace equation of the velocity potential function.If the fluid moves in a plane,we can also solve the Laplace equation of the stream function.Since the velocity potential function and the stream function of the plane and irrotational motion of non-viscid and incompressible fluid satisfies the Laplace equation,and the Cauchy-Riemann condition is satisfied between the two,the velocity potential function and the stream function can form an analytical function.This paper uses conformal mapping to transform the outer area of the object with complex boundaries to the outer area of the cylinder,and then obtains the complex potential function of the flow field according to the flow characteristics of the plane irrotational motion of non-viscid and incompressible fluid and then uses the complex method to get the velocity potential function and stream function.According to the definition of velocity potential function and stream function,we can draw the streamline diagram and equipotential diagram of the flow field,and combine the pressure coefficient diagram to analyze the velocity and pressure distribution of the flow field.The results are consistent with the actual situation.This paper studies the non-viscid and incompressible uniform fluid which flows around an elliptic cylinder,a cylinder with a pair of symmetrical plates and a cylinder with two pairs of symmetrical plates.What's more,this paper researches on the influence of singularity pairs of fluid mechanics such as point sinks and point vortices on the flow field around a cylinder.The main contents are as follows:The first chapter introduces the research background,significance and status quo of the flow around movement,as well as the main research methods and content of this article.The second chapter introduces the basic equations satisfied by non-viscid and incompressible fluid in plane and irrotational motion.The third chapter studies the flow around an elliptic cylinder,and uses the inverse transformation of the famous Joukowski transformation to single-valued and conformally maps the outer area of the elliptic cylinder on the physical plane to the outer area of the cylinder on the mathematical plane.And then we obtain the complex potential function of the flow around the elliptic cylinder,come to get the velocity potential function and stream function.When the semi-long and short semi-axes of the ellipse are equal,the flow form degenerates into a classic flow around a cylinder.When the short axis degenerates to 0,the flow degenerates to the flow around the plate.The fourth chapter studies the problem of flow around a cylinder with a pair of symmetrical plates,by a conformal mapping of non-rational function type which transforms the outer area of the cylinder with a pair of symmetrical plates on the physical plane to the outer area of the cylinder on the mathematical plane,come to obtains the complex potential function.And then we use the complex variable method to obtain the velocity potential function and stream function.This flow form can be degenerated into the classic flow around a cylinder and a plate.The fifth chapter studies the problem of flow around a cylinder with two pairs of symmetrical plates.By a non-rational functional conformal mapping,the outer region of the cylinder with two pairs of symmetrical plates on the physical plane is transformed to the outer area of the unit cylinder on the mathematical plane.The complex potential function is obtained,and then the velocity potential function and stream function are obtained by the complex variable method.When the radius of the cylinder degenerates to 0,the flow pattern degenerates to the flow around the cross plate.The flow can also be degenerated to flow around a cylinder and a plate.Finally,the influence of the singular points of hydrodynamics such as point sinks and point vortices on the flow field around a cylinder is studied.According to the circle theorem,the complex potential function of the flow field is obtained,and then the velocity potential function and stream function are obtained by the complex variable method.The study found that the effect of point sinks or point vortices on the flow field around a cylinder is related to the distance between them and the cylinder.