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Unformatted text preview: Fluids – Lecture 11 Notes 1. Introduction to Compressible Flows 2. Thermodynamics Concepts Reading: Anderson 7.1 – 7.2 Introduction to Compressible Flows Definition and implications A compressible ﬂow is a ﬂow in which the ﬂuid density ρ varies significantly within the ﬂowfield. Therefore, ρ ( x, y, z ) must now be treated as a field variable rather than simply a constant. Typically, significant density variations start to appear when the ﬂow Mach number exceeds 0.3 or so. The effects become especially large when the Mach number approaches and exceeds unity. The figure shows the behavior of a moving Lagrangian Control Volume (CV) which by definition surrounds a fixed mass of ﬂuid m . In incompressible ﬂow the density ρ does not change, so the CV’s volume V = m/ρ must remain constant. In the compressible ﬂow case, the CV is squeezed or expanded significantly in response to pressure changes, with ρ changing in inverse proportion to V . Since the CV follows the streamlines, changes in the CV’s volume must be accompanied by changes in the streamlines as well. Above Mach 1, these volumetric changes dominate the streamline pattern. V V Lagrangian control volume Lagrangian control volume volume decreases −p +p volume constant (Incompressible) increasing pressure −p +p increasing pressure Incompressible Compressible Many of the relations developed for incompressible (i.e. low speed) ﬂows must be revisited and modified. For example, the Bernoulli equation is no longer valid, 1 p + ρV 2 negationslash = constant 2 since ρ = constant was assumed in its derivation. However, concepts such as stagnation pressure p o are still usable, but their definitions and relevant equations will be different from the low speed versions....
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05