Page 224 - 48Fundamentals of Compressible Fluid Mechanics

186 CHAPTER 11. EVACUATING AND FILLING A SEMI RIGID CHAMBERS

neglected (only for filling process) the most general equation ideal gas (11.1) reads

N
(11.3)
!
N

When the plus sign is for filling process and the negative sign is for evacuating

process. * *
$

% "
11.2 General Model and Non-dimensioned
It is convenient to non-dimensioned the properties in chamber by dividing them by
their initial conditions. The dimensionless properties of chamber as

>*

>
*

>*

*

(11.4a)

>
*

>*

*
(11.4b)

*

is the characteristic time of the system defined as followed
>
*
@
*
(11.5)
>*
@
*

where*
is the time that will take to evacuate

@

the chamber if the gas in the chamber was in its initial state, the flow rate was at
*
?PO "
N
its maximum (choking flow), and the gas was incompressible in the chamber.
@

Utilizing these definitions (11.4) and substituting into equation (11.3) yields
The physical meaning of characteristic time,*
(11.6)
6

N > >*
where the following definition for the reduced Mach number is added as

@

>

@B
>
> " ?PO

>
>
>
(11.7)
" % "
>*
*
*

*
After some rearranging equation (11.6) obtains the form

?PO
>
N
(11.8)

> >
>
@ ?PO "
>

> *
>
N
>
%
>*
*