A high Reynolds number Newtonian liquid Jet, exiting a two-dimensional channel, Is examined In this study. Fully developed Populously flow, driven by an applied pressure gradient, Is assumed to prevail upstream of the channel exit. Flow is assumed to be laminar, steady and incompressible. A free surface develops as the fluid exits the channel. The resistance of the air on the free surface of the liquid jet can be neglected so that, the shear stress at the channel wall disappears and becomes zero at the free surface.
This stress singularity is a major obstacle in calculating the flow ear the channel exit both numerically and analytically. No exact analytical solution is available for the problem. However, the flow is predicted near channel exit in literature using some approximate analytical methods. High Reynolds number Newtonian Jet contracts downstream of the channel due to the emergence of the normal stress as soon as the fluid detaches Itself from the channel wall.
The effect of inertia on the free surface height and free surface velocity and the flow downstream has been explored. Results obtained are compared with the analytical work of the relevant problem. The computational domain includes the upstream and downstream near the channel exit. Fully developed Policies flow Is used as the boundary condition at the Inlet and zero traction on the free surface at the outlet. The problem is a two phase flow where there are distinct regions for each of the phases.
Multiphase model OF is the most suitable for this specific flow problem. In the OF model, a single set of momentum equations is shared by the fluids, and the volume fraction of each of the fluids in each computational cell is tracked throughout the domain. The tracking of the interface between the phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. For the ‘Goth phase, this equation has the following form: where Is the volume fraction of the q the phase.
The volume fraction equation will not be solved for the primary phase; the primary-phase volume fraction will be computed based on the following constraint: determined by the presence of the component phases in each control volume. In a two-phase system, for example, if the phases are represented by the subscripts 1 ND 2, and if the volume fraction of the second of these is being tracked, the density in each cell is given by In general, for an n-phase system, the volume-fraction-averaged density takes on the following form: All other properties (e. G. Viscosity) are computed in this manner. A single momentum equation is solved throughout the domain, and the resulting velocity field is shared among the phases. The momentum equation in the absence of gravity and other body forces, shown below, is dependent on the volume fractions of all phases through the properties p and p. NUMERICAL PROCEDURE: Gambit (2. 2. 30) has been used to create and mesh the geometry and the problem is solved Fluent 6. 2 (EDP). Geometry: Channel region, radius 0. 05 Channel region, length 0. 1 Air region, radius Air region, length 0. Boundary type: Name Boundary Type Inlet Velocity Inlet Pressure Outlet Wet wall wall Dry wall Axis Solver: Pressure based segregated solver is chosen as solver. Although the flow is steady, it has been treated as unsteady with large time step because of the limitation of the OF model to solve steady state problem. Since, the free surface position is of the remote importance in the present problem, the geometric reconstruction scheme has been used to track the interface between the phases. In Fluent this scheme is considered the most accurate for interface tracking.