By Greitzer E.M., Tan C.S., Graf M.B.
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Extra info for Internal flow
This leads to expressions for the equations of motion in integral (control volume) as well as differential form. 1 The rate of change of quantities following a ﬂuid particle To describe what happens at a ﬁxed volume or point in space we must inquire how the time rate of change for a particle can be described in a ﬁxed coordinate system. For deﬁniteness we take Cartesian coordinates x, y, z, and ﬂuid velocity components ux , uy , and uz . Suppose that c is some property of the ﬂuid and we visualize a ﬁeld of values of c continuously distributed throughout space.
The ﬂows addressed can be broadly characterized as follows: (1) There is often work or heat transfer. Further, this energy addition can vary between streamlines, with the result that there is no “uniform free stream”. Stagnation conditions therefore have a spatial (and sometimes a temporal) variation which must be captured in descriptions of the component behavior. (2) There are often large changes in direction and in velocity. For example, deﬂections of over 90◦ are common in ﬂuid machinery, with no one obvious reference direction or velocity.
2) There are often large changes in direction and in velocity. For example, deﬂections of over 90◦ are common in ﬂuid machinery, with no one obvious reference direction or velocity. Concepts of lift and drag, which are central to external aerodynamics, are thus much less useful than ideas of loss and ﬂow deﬂection in describing internal ﬂow component performance. Deﬂection of the non-uniform ﬂows mentioned in (1) also creates (three-dimensional) motions normal to the mean ﬂow direction which transport mass, momentum, and energy across ducts and channels.