Limits of Fully Turbulent Flow in a Stirred Tank

Publisher Summary This chapter illustrates a new method for scaling velocities in a stirred tank in which the velocity profiles in the bulk of the tank are scaled with the characteristic velocity and length scale in the wall jet that is formed along the baffle of the tank.. Here the limit of fully developed turbulence is defined using the Reynolds number (Re), or the ratio of inertial to viscous forces. Using this Reynolds number the chapter illustrates that fully turbulent flow in the top third of the tank does not exist for Re I = 2 x 10 4 . This is important for design of vessels that have greater height than vessel diameter because the lack of fully turbulent flow means that the velocity profiles will be affected both by the characteristic velocity scale and the fluid viscosity. The chapter also describes some conditions that are required for the characterization of turbulence and the application of computational fluid dynamics (CFD) to conditions in the bulk of the tank. The power number and friction factor are used to define the onset of fully turbulent flow for their respective systems; however, the onset of fully turbulent flow can be more accurately determined using dimensionless velocity profiles. In fully turbulent flow, the dimensionless velocity profiles will collapse to a single similarity profile if the proper characteristic velocity and length scales are used. In the transitional regime, both inertial and viscous forces influence the velocity profiles and similarity no longer holds. The objective of this chapter is to carefully examine the limits of fully developed turbulence in the bulk of a stirred tank.