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Chapter 4: Fluid Kinematics

Fluid Kinematics deals with the motion of fluids without necessarily considering the forces and moments which create the motion. Two ways to describe motion are Lagrangian and Eulerian description. Lagrangian description of fluid flow tracks the position and velocity of individual particles. (eg. Brilliard ball on a pooltable.) | Chapter 4: Fluid Kinematics Overview Fluid Kinematics deals with the motion of fluids without necessarily considering the forces and moments which create the motion. Lagrangian Description Two ways to describe motion are Lagrangian and Eulerian description Lagrangian description of fluid flow tracks the position and velocity of individual particles. (eg. Brilliard ball on a pooltable.) Motion is described based upon Newton's laws. Difficult to use for practical flow analysis. Fluids are composed of billions of molecules. Interaction between molecules hard to describe/model. However, useful for specialized applications Sprays, particles, bubble dynamics, rarefied gases. Coupled Eulerian-Lagrangian methods. Named after Italian mathematician Joseph Louis Lagrange (1736-1813). Lagrangian Description Eulerian Description Eulerian description of fluid flow: a flow domain or control volume is defined by which fluid flows in and out. We define field variables which are functions of space and time. Pressure field, P=P(x,y,z,t) Velocity field, Acceleration field, These (and other) field variables define the flow field. Well suited for formulation of initial boundary-value problems (PDE's). Named after Swiss mathematician Leonhard Euler (1707-1783). Example: Coupled Eulerian-Lagrangian Method Forensic analysis of Columbia accident: simulation of shuttle debris trajectory using Eulerian CFD for flow field and Lagrangian method for the debris. Acceleration Field Consider a fluid particle and Newton's second law, The acceleration of the particle is the time derivative of the particle's velocity. However, particle velocity at a point at any instant in time t is the same as the fluid velocity, To take the time derivative of, chain rule must be used. ,t) Acceleration Field Since First term is called the local acceleration and is nonzero only for unsteady flows. Second term is called the advective acceleration and accounts for the effect of the fluid particle moving to a new . | Chapter 4: Fluid Kinematics Overview Fluid Kinematics deals with the motion of fluids without necessarily considering the forces and moments which create the motion. Lagrangian Description Two ways to describe motion are Lagrangian and Eulerian description Lagrangian description of fluid flow tracks the position and velocity of individual particles. (eg. Brilliard ball on a pooltable.) Motion is described based upon Newton's laws. Difficult to use for practical flow analysis. Fluids are composed of billions of molecules. Interaction between molecules hard to describe/model. However, useful for specialized applications Sprays, particles, bubble dynamics, rarefied gases. Coupled Eulerian-Lagrangian methods. Named after Italian mathematician Joseph Louis Lagrange (1736-1813). Lagrangian Description Eulerian Description Eulerian description of fluid flow: a flow domain or control volume is defined by which fluid flows in and out. We define field variables which are functions of space and