Fluid Mechanics and Energy Transport BIEN 301 Lecture 15 Compressible Flows Continued – Isentropic Flow Juan M. Lopez, E.I.T. Research Consultant LeTourneau.

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Presentation transcript:

Fluid Mechanics and Energy Transport BIEN 301 Lecture 15 Compressible Flows Continued – Isentropic Flow Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer Louisiana Tech University

Isentropic Flow Area Changes (White 9.4) Flow can be considered one-dimensional when: There is a no slip condition at the wall dh/dx << 1 and h(x) << R(x) V = V(x), reacts to changes in area The 1D approximation: p(x)V(x)A(x) = dm/dt = constant 2/6/2007 BIEN 301 – Winter 2006-2007

Isentropic Flow Differential form of continuity for area-dependent 1D flow: This simple relationship helps us predict the behavior of a compressible fluid in a 1D flow situation. 2/6/2007 BIEN 301 – Winter 2006-2007

Isentropic Flow Ma < 1 Ma > 1 dV < 0 dp > 0 Subsonic Diffuser dV > 0 dp < 0 Supersonic Nozzle dA > 0 dV > 0 dp < 0 Subsonic Nozzle dV < 0 dp > 0 Supersonic Diffuser dA < 0 2/6/2007 BIEN 301 – Winter 2006-2007

Isentropic Flow More relationships 2/6/2007 BIEN 301 – Winter 2006-2007

Isentropic Flow Ideal Gas Area Change The previous equation helps us to identify a maximum mass flow (choking condition) for compressible, isentropic flows: 2/6/2007 BIEN 301 – Winter 2006-2007

Isentropic Flow Eq’s 9.48a-d Provide good relationships for the mach number at different area relationships. We will be skipping the sections on shock waves. Read them for your own edification-the material is good, the pictures are quite interesting 2/6/2007 BIEN 301 – Winter 2006-2007

Blood Flow From these equations to blood flow is quite a ways. However, I wanted to be sure we had the foundations before we saw a true blood flow solution worked out. Here is a full blood flow solution for pulsatile flow. Poiseuille flow is utilized. 2/6/2007 BIEN 301 – Winter 2006-2007

Isentropic Flow Converging and Diverging Nozzles A few examples 2/6/2007 BIEN 301 – Winter 2006-2007

Chapter 9 Homework DUE 2/22/2007 P9.11 P9.43 P9.78 P9.88 EC: P9.114 Due with the Ch. 7 and Ch. 8 HW. 2/6/2007 BIEN 301 – Winter 2006-2007

Remember Study Session tomorrow night Project Questions – Office hours today, tomorrow, and during the study session Report format is required on the final projects. Projects due Thursday! 2/6/2007 BIEN 301 – Winter 2006-2007

Questions? 2/6/2007 BIEN 301 – Winter 2006-2007