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Drag Force
Compressibility Effect
For high-speed flows with high Mach number, the compressibility
could affect the drag coefficient. Many expressions were suggested in the
literature to account for the effect of gas Mach number on the
drag force. Henderson (1976) suggested two expressions for drag force
acting on spherical particles for subsonic and supersonic flows.
Accordingly, for subsonic flow
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(11) |
where M is the Mach number based on relative velocity,
 , and 
is the molecular speed ratio, where γ is the specific heat ratio. For
the supersonic flows with Mach numbers equal or greater
than 1.75, the drag force is given by
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(12) |
For the flow regimes with Mach number between 1 and 1.75, a
linear interpolation may be used. Carlson and Hoglund (1964) proposed
the following expression:
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(13) |
Droplets
For drag force for liquid droplets at small Reynolds numbers is given as
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(14) |
where the superscripts f and p refer to the continuous fluid and discrete
particles (droplets, bubbles), respectively.
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