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26 4. METHODS 4.2. Turbulence When the flow reach a certain Reynolds number the flow goes from being laminar to turbulent. The Reynolds number is defined as Re = U · L (4.6) υ where U is a characteristic velocity scale, L is a characteristic length scale and υ is the kinematic viscosity. Reynolds number is a dimensionless number that describes the ratio between the inertial forces and the viscous forces. This means that for low Re-number, the viscous forces are the predominant, and for high Re-number, the inertial forces are dominant. For a pipe flow, the characteristic velocity is the bulk velocity and a typical length scale is the pipe diameter. With these characteristic quantities, a laminar pipe flow will become turbulent when the Re-number exceeds a certain value which depends on the particular set-up; i.e. approximately 2000 or larger, c.f. Carpinlioglu & Gundogdu (2001). One may define a critical Re-number based either on theoretical (stability analysis) arguments or empirical data as is the case for the pipe flow. Flows with Re-number larger than the critical Re-number, does not necessarily imply that it is a fully developed turbulent flow. Turbulent flows are characterized by being time dependent and 3-dimensional where the flow at each location can be described by a mean velocity and a fluctuating part. Since the fluctuating part is irregular, only statistical methods can be used to characterize and quantify the flow properties. Another feature of turbulent flow is that the viscous forces dissipate the turbulent kinetic energy into heat. The turbulent flow consists of eddies with different length scales, where the largest eddies are the most energetic ones. The large eddies have velocity and length scales of the same order as the mean flow. The large eddies are unstable and break up into smaller eddies. These smaller eddies in turn drive even smaller eddies, until the scales where viscous dissipation becomes important. In this way, energy is transferred from the larger scales to the smaller scales. Small eddies are by nature independent of the boundary conditions and therefore have a universal and isotropic character. The larger eddies are characterised by the particular flow and these eddies carry most of the turbulent kinetic energy. In the range between the energy bearing eddies and the small eddies, in the dissipative range, one finds a range of eddies (scales) that are dependent only of inertia and therefore one talks about the inertial subrange. The dominating part of turbulence production takes place in the energy containing range, while almost all dissipation occurs in the dissipation range. The transfer of energy from larger to smaller scales occurs mainly in the inertial subrange.PDF Image | Numerical computations of the unsteady flow in a radial turbine
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