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Fluid Mechanics and Energy Transport BIEN 301 Lecture 14 Introduction to Compressible Flows

Fluid Mechanics and Energy Transport BIEN 301 Lecture 14 Introduction to Compressible Flows. Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer Louisiana Tech University. Compressible Flow. When density changes become significant, we have compressible flow.

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Fluid Mechanics and Energy Transport BIEN 301 Lecture 14 Introduction to Compressible Flows

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  1. Fluid Mechanics and Energy TransportBIEN 301Lecture 14Introduction to Compressible Flows Juan M. Lopez, E.I.T. Research Consultant LeTourneau University Adjunct Lecturer Louisiana Tech University

  2. Compressible Flow • When density changes become significant, we have compressible flow. • Occurs in flows moving at sufficient speed • Extremely high pressure gradients in compressible fluids (gases, blood) • Most important effects of compressible flows: • Choking • Shock Waves BIEN 301 – Winter 2006-2007

  3. Compressible Flow • Mach Number (White 9.1) • Awesome transitional picture, p. 598 White. • Crossing Mach 1.0, but what is this number? • Fractional portion of speed of sound in a medium • Defined as: BIEN 301 – Winter 2006-2007

  4. Compressible Flow • Mach Regimes • Ma < 0.3 Incompressible Flow • 0.3 < Ma < 0.8 Subsonic Flow • 0.8 < Ma < 1.2 Transonic Flow • 1.2 < Ma < 3.0 Supersonic Flow • 3.0 > Ma Hypersonic Flow • These are only guides, the individual flow scenarios affect how shock waves might develop. BIEN 301 – Winter 2006-2007

  5. Compressible Flow • Specific Heat Ratio • Usually Tabulated for you already • Variations have small effects on compressible flow calculations, so we will stick with air, k = 1.40 for most calculations in this chapter. BIEN 301 – Winter 2006-2007

  6. Compressible Flow • Ideal Gas • Simple state equation we often use to set up boundary behavior calculations. BIEN 301 – Winter 2006-2007

  7. Isentropic Process • Deals with change in entropy • The solved integral for constant cp: BIEN 301 – Winter 2006-2007

  8. Isentropic Process • Setting entropy equal (isentropic) • The solved integral for constant cp reduces to the power law relationship: BIEN 301 – Winter 2006-2007

  9. Speed of Sound • Adiabatic Process • Expanding our control volume analysis to a wave moving through a medium, we can see how friction and heat transfer effects are limited to the interior of the wave (White, Fig. 9.1) • Speed of sound relates the propagation of a pressure pulse of infinitessimal length through a still fluid. • The speed of sound of a fluid is given by: BIEN 301 – Winter 2006-2007

  10. Steady Flow • Adiabatic and Isentropic Steady Flow (White 9.3) • Through these simplifications, we are able to reduce our steady flow to a few simple relationships BIEN 301 – Winter 2006-2007

  11. Rigid Body Motion • Definition (White 2.9) • All particles are in combined translation and rotation, and there is no relative motion between the particles. • Recalling our last lecture, what terms drop out? BIEN 301 – Winter 2006-2007

  12. Steady Flow • Mach Number Relationships BIEN 301 – Winter 2006-2007

  13. Bernoulli’s • The isentropic, adiabatic process is actually a process that can be described via Bernoulli’s. BIEN 301 – Winter 2006-2007

  14. Examples, Homework • Examples for this chapter • P9.10, P9.33 • No homework from this section for next time. • Homework from Ch. 5 will be due next Thursday (will discuss in a minute) BIEN 301 – Winter 2006-2007

  15. Homework, Reports • Due Date: • Remember, last two homework assignments (Ch. 7, Ch. 8), as well as the Individual and Group Projects are due next week: Tuesday, Feb. 13. • Any questions thus far? • I’ll be posting the numerical analysis method file soon BIEN 301 – Winter 2006-2007

  16. Chapter 5 Assignment • Because there is not class on Thursday, we are going to be reading Chapter 5, and answering a few questions (DUE THURSDAY, FEB. 15). • Define “Dimensional Analysis”, and describe how this is important for our work in fluid mechanics. • Describe the Principle of Dimensional Homogeneity (PDH) • Explain the Pi theorem • Explain why nondimensionalization is important for some types of analyses. • Explain the following terms: • Geometric Similarity • Kinematic Similarity • Dynamic Similarity • In as much detail as possible, describe the steps you would consider in designing a test stand to study a scaled-up version of a blood flow obstruction to determine wall shear stresses and stagnation points at the obstruction. • Which of the items above would be most important? • How would you go about ensuring the validity of your scaled-up experiment? • Why would doing this scaled-up test be useful in the first place? BIEN 301 – Winter 2006-2007

  17. Exam 2 and Homework • No curve on exam • Definitely none needed. • Exam worked as planned: • If you have been faithfully doing ALL of your homework and your OWN work without taking ANY shortcuts or giving up on problems in homework, you did very well. • If you did not do well, consider how much of your homework habits may have hindered you. • Rewarded those who have been working extremely faithfully at getting their homework done RIGHT. Offset the cheating that was going on. BIEN 301 – Winter 2006-2007

  18. Remember • No study session tomorrow night. • I’ll be leaving for Houston this afternoon. Will not be available for office hours. You may reach me via e-mail. BIEN 301 – Winter 2006-2007

  19. Flow Visualizations • Came across some amazing flow visualizations (computational and actual video). I’ll post the link on Blackboard. • I’ll play them now while I hand back the exams and homework, and the presenter for today sets up. • After the presentation, I’ll review the exam for anyone that would like to stay behind. • Your grades are recorded in my notebook, I’ll post them to Blackboard later on today. BIEN 301 – Winter 2006-2007

  20. Questions? BIEN 301 – Winter 2006-2007

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