1.2 SJ Modeling
1.2.1 A Round SJ in Quiescent Environment
An SJ emanating from a round orifice in a quiescent environment could exhibit axial or spherical symmetry (Krishnan and Mohseni 2009b) depending on the properties of the jet and generating actuator. If the jet is coming out of a long cylindrical tube, one expects an axially symmetric flow, and if the jet is exiting a large cavity through a small and thin orifice, a spherical symmetry is expected.In this section,modeling of an SJ as an axisymmetric or a spherical jet is considered.
1.2.1.1 Axisymmetric SJs in Cylindrical Coordinates
Schlichting (1933) offered a similar solution to the axisymmetric boundary layer equations
for the case of free incompressible CJ.This is the case for the far field of an axisymmetric jet
emanating from a small orifice into a similar fluid at rest (Figure 1.5). At far distances from
the orifice, the jet appears to issue from a point source of momentum in the jet direction.
In this section, a summary of the Schlichting solution for a CJ, both laminar and turbulent,
is offered and then it is extended to the case of SJs.
The far field of a CJ may be imagined to be generated by a continuous point source
of momentum in an infinite incompressible fluid. It is admissible to describe
the mean velocities in the CJ by boundary layer equations. In seeking a self-similar solution to
the boundary layer equations, the streamwise pressure gradient is assumed to be zero,
whereupon a closed form solution for a laminar jet exists (Schlichting 1933). Following
along these lines, it is hypothesized here that the mean velocity field of an SJ may be
modeled as a laminar free jet, along with the use of a virtual viscosity coefficient obtained
empirically for an SJ.
- Synthetic Jets Kamran Mohseni, Rajat Mittal Published by CRC Press