Plots of Fluid Flow Data Profile plots- A profile plot indicates how the value of a scalar (or vector can be plotted but only the magnitude) property varies along some desired direction in the flow field (pressure, temperature and density). Vector plots- A vector plot is an array of arrows indicating the direction and magnitude of a vector property at an instant in time

Vector Plots 2- dimensional flow field ; turbulent and unsteady, Long time average is plotted. a) Streamlines, b) velocity vector, close up view of the separated flow region

Contour Plots A contour plot shows curves of constant values of a scalar property or magnitude of a vector property at an instant in time. Isocontour plots are generated for pressure, temperature, velocity magnitude, species concentration, properties of turbulence etc. Contour line-simple curves indicating various levels of the property Filled contour plot- filled with different colors. Pressure is highest at thefront face

Types of Motion a) Translation b) Rotation c) Extensional strain (linear strain) d) Shear Strain Velocity= rate of translation Angular velocity =rate of rotation Linear strain rate Shear strain rate

Vorticity and Rotationality Vorticity is a measure of rotation of a fluid particle and is equal to twice the angular velocity of a fluid particle. Rotation of fluid elements is associated with wakes, boundary layers, flow through turbomachinery (fans, turbines, compressors etc.) and flow with heat transfer. The vorticity of a fluid element can not change except through the action of viscosity, non-uniform heating (temperature gradient)

Vorticity For a two-dimensional flow in the xy-plane, the vorticity vector always points in the z or –z direction. In this illustration, the flag-shaped fluid particle rotates in the counterclockwise direction as it moves in the xy-plane; its vorticity points in the positive z- direction as shown. Contour plot of the vorticity field ζz due to flow impinging on a block, as produced by CFD calculations; only the upper half is shown due to symmetry. Dark regions represent large negative vorticity, and light regions represent large positive vorticity.

Reynolds Transport Theorem (RTT) In thermodynamics and solid mechanics we often work with a system (also called a closed system), defined as a quantity of matter of fixed identity. In fluid dynamics, it is more common to work with a control volume (also called an open system), defined as a region in space chosen for study. The size and shape of a system may change during a process, but no mass crosses its boundaries. A control volume, on the other hand, allows mass to flow in or out across its boundaries, which are called the control surface. A control volume may also move and deform during a process, but many real world applications involve fixed, non-deformable control volumes.

System vs Control Volume Two methods of analyzing the spraying of deodorant from a spray can: (a) We follow the fluid as it moves and deforms. This is the system approach—no mass crosses the boundary, and the total mass of the system remains fixed. (b) We consider a fixed interior volume of the can. This is the control volume approach—mass crosses the boundary.

(RTT) Most principles of fluid mechanics are adopted from solid mechanics, where the physical laws dealing with the time rates of change of extensive properties are expressed for systems. In fluid mechanics, it is usually more convenient to work with control volumes, and thus there is a need to relate the changes in a control volume to the changes in a system. The relationship between the time rates of change of an extensive property for a system and for a control volume is expressed by the Reynolds transport theorem (RTT), which provides the link between the system and control volume RTT is named after the English engineer, Osborne Reynolds (1842–1912), who did much to advance its application in fluid mechanics.