Chapter08

Chapter08 - Compressible Flow Compressible Flow z When...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Compressible Flow Compressible Flow z When density variations cannot be ignored, we are dealing with a compressible flow – An aircraft cruising faster than 30% of the speed of sound – Flow in a standard combustion reciprocating engine – Flow in rocket engines – Flow in gas- or steam-turbine engines – Flow of traffic on a large highway z We will examine one-dimensional compressible flows, including… – Isentropic flow, Laval nozzle – Normal shock waves – Fanno flow, which includes viscous effects – Rayleigh flow, which includes heat-transfer Classification Classification z With regard to compressibility, we classify flows according to Mach Number… z The various compressible-flow regimes are… z Virtually all liquid flows are incompressible…not so with gases The M 2 column is relevant because most compressible-flow algebraic expressions involve M 2 Example: Density in a low-speed flow is Thermodynamic Properties of Air Thermodynamic Properties of Air-- 1 1 z We will deal mostly with air, which obeys the perfect-gas law where R is the perfect-gas constant… z Air is calorically perfect so that where specific heats c p and c v are constant and given by with Thermodynamic Properties of Air Thermodynamic Properties of Air-- 2 2 z As we found in Chapter 7, the entropy of a perfect, calorically-perfect gas follows from Gibbs’ equation so that z Thus, for isentropic flow… z All of these thermodynamic relations are valid for temperatures as high as 2000 K Speed of Sound Speed of Sound-- 1 1 z Consider an acoustic wave, i.e., a weak wave moving though a fluid, where weak means z Using a Galilean transformation, it is a simple exercise to compute the speed of sound An acoustic wave moves at the speed of sound, a Speed of Sound Speed of Sound-- 2 2 z The flow in this reference frame is steady and we use a stationary control volume so that mass conservation is z So, for constant cross-sectional area (out of the page) z Dropping the (very-small) quadratic term yields Æ Speed of Sound Speed of Sound-- 3 3 z Ignoring body forces and viscous effects, the equation for x-momentum conservation simplifies to z Evaluating the integrals, a little algebra yields z Before dropping the quadratic term, mass conservation is ρ a = ( ρ + ∆ ρ )( a – ∆ u ) , so that z Simplifying, we have Æ Speed of Sound Speed of Sound-- 4 4 z Recall from above that so that which, in the limit ∆ ρ → , is z Pressure, like all thermodynamic state variables, is a function of two other state variables, so that this is a partial derivative z Since an acoustic wave is isentropic, we conclude that ← Subscript s means the derivative is taken with s held constant Speed of Sound Speed of Sound-- 5 5 z As noted when we summarized thermodynamic properties of air, p = A ρ γ for isentropic flow, so that z Therefore, the speed of sound of a perfect gas is z Example: Compute the speed of sound of air on a summer day when T = 95 o F = 554.67 o R and on a winter day when...
View Full Document

This note was uploaded on 10/12/2009 for the course AME 309 at USC.

Page1 / 40

Chapter08 - Compressible Flow Compressible Flow z When...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online