Could you please help: All other things being equal, will fluid flow start up times be shorter in incompressible fluids or compressible fluids?
Start up time is defined here as the time elapsed when average velocity of a fluid rises from rest to within 1% of its steady state value with the sudden imposition of a pressure gradient in a pipe.
Thanks in anticipation of the help.
First, if the steady state value is 1 m/s, then 1% of it is 0.01 m/s. If the steady state value is 100 m/s, then 1% of it is 1 m/s. This is quite different. In adition, it depends on how you start up the flow: slowly or fast by opening a valve for instance.
Second, if the compressibility of the fluid does play a role, then you should consider the fluid as to be of compressible. The assumption of incompressible fluid is then no more correct. This is particular important, if you have a long pipe. The fluid at the rest in a long pipe cannot be started up equally (1% of steady state value then has no any meaning). You have to conduct the transient computations. The assumption of incompressible fluid in this case may be total wrong (depend on what your computational purpose is).
I hope, this could help you a bit.
Regards
you cannot compare the two flow conditions....in incompressible flows, the pressure equation is elliptic and produces immediately (at t=0) pressure gradient everywhere in the flow (according to the infinite sound velocity propagation). Pressure gradient also force velocity everywhere immediately. I suggest to consider the Reynolds number that can be seen as the ratio between diffusive and convective characteristics times. If the flow field has a steady state, it will be reached at a non-dimensional time of the Re number order.
@Filippo: So is there a simple, heuristic, dimensional start-up time equation for compressible flows (time in seconds)? Can you refer me to an equation in an article I could read? All I have seen are for incompressible flows (e.g. equation 26 and 32 of Patience and Mehrotra 1989) and the seeming lack of literature for compressible flow start up times is very disturbing.
I think that, for compressible flow, the better way is to consider the convective characteristic time due to the characteristic flow velocity and the wave propagation time due to the sound velocity. For a finite value of the sound velocity, their ratio is the Mach number.
Is there a heuristic equation I can use? Any article containing a simple equation? Consider you were teaching an undergrad student, which equation would you give?
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