Biomedical Engineering Reference
In-Depth Information
3.3. Mach Number
Mach number plays an important role for high-speed flows. Mach number
on the surfaces of the rotor was found using FLUENT. For all the geometries
of the rotor at the rotational speeds of half-million rpm, one million and two
million rpm, the Mach number is within the subsonic regime, with only a few
spots exceeding a Mach number of 1. For rotating speed below two million,
the subsonic assumption is well justified. However, for higher rpm, the
transonic and supersonic flow regimes need to be taken into consideration.
Using Fluent: Mach number on the surfaces of the rotor was determined
using CFD software. FLUENT needs the user to specify the flow as subsonic,
or supersonic flow as input. Fluent does not require that specification before
the calculation. The regime of the flow (subsonic, transonic, or supersonic)
comes as part of the solution. The geometry of the rotor with three inlets,
inclined at 45 degrees with three inlets and a housing was created and the
mesh was created. Volume elements considered for the mesh were
approximately 600,000. The ideal gas, air, was considered as the fluid and the
k-epsilon turbulence method was used for modeling turbulent flow. An inlet
boundary condition, with a pressure of 60 psi was considered at three inlets. At
the outlet, outlet boundary condition with a pressure of zero was considered.
The rotor was defined as a moving wall with no-slip boundary condition, with
an angular speed of two million rpm along its axis. For the remaining surfaces
of the geometry, a default no-slip stationary wall boundary condition was
applied.
For this compressible flow, a coupled implicit scheme was considered for
the solution. The maximum number of iterations for the convergence control
for the solver was specified as 4500 and the target residual for the convergence
criterion was specified as 1e-6. The governing equations such as continuity,
momentum, energy equations, and equation of state were solved by FLUENT
and the Mach number at various zones was determined. Figure 12 shows the
variation of Mach number at three inlets, outlet, and on the rotor surface for
the rotational speed of the rotor of two million rpm. From the figure it can be
observed that the maximum value of Mach number is 0.96 and the minimum
value is 0.01. At the inlets and on the surfaces of the rotor, the Mach number is
significantly less than 1 and at the outlet, the value is 0.96. From the results it
can be said that only at the outlet, the flow is transonic, as the velocity of the
flow is maximum at the outlet because of zero pressure condition. At the inlets
and on the rotor surfaces, the flow is found to be subsonic.
