lectures-chapter9

lectures-chapter9 - 650:460 Aerodynamics Chapter 9 Prof....

Info iconThis preview shows pages 1–8. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 650:460 Aerodynamics Chapter 9 Prof. Doyle Knight Tel: 732 445 4464, Email: doyleknight@gmail.com Office hours: Tues and Thur, 4:30 pm - 6:00 pm and by appointment Fall 2009 1 Compressible Flow Assumptions Inviscid Steady Irrotational Isentropic (and therefore barotropic) From Kelvins Theorem, the flow is irrotational if the flow upstream of any aerodynamic body is irrotational and p = p ( ). This latter condition is satisfied if we assume the flow is isentropic. This implies that there are no shock waves. 2 Compressible Flow Bernoullis Equation Conservation of momentum bracketleftbigg vector v t + ( vector v ) vector v bracketrightbigg = p where is the gradient operator p = p x vector i + p y vector j + p z vector k and vector i , vector j and vector k are the unit vectors in the x-, y- and z-directions. 3 Compressible Flow Bernoullis Equation Vector identity ( vector v ) vector v = ( 1 2 vector v 2 ) vector v where = vector v is the vorticity. Substitute into the conservation of momentum vector v t + ( 1 2 vector v 2 ) + 1 p = 0 since the vorticity is assumed zero everywhere. Since the fluid is assumed barotropic 1 p = parenleftbiggintegraldisplay dp parenrightbigg 4 Compressible Flow Bernoullis Equation Since the fluid is assumed irrotational vector v = and thus vector v t = t = parenleftbigg t parenrightbigg Therefore the conservation of momentum is bracketleftbigg t + 1 2 vector v 2 + integraldisplay dp bracketrightbigg = 0 and thus t + 1 2 vector v 2 + integraldisplay dp = f ( t ) where f ( t ) is a function of time only. 5 Compressible Flow Bernoullis Equation For isentropic flow p p o = parenleftbigg o parenrightbigg and thus integraldisplay dp = ( 1) p Thus, the integral of the conservation of momentum is t + 1 2 + ( 1) p = f ( t ) This is the compressible Bernoulli equation . 6 Compressible Flow Equation for Take the inner product of vector v with the conservation of momentum parenleftbigg vector v vector v t + vector v ( vector v ) vector v parenrightbigg = vector v p Identity vector v ( vector v ) vector v = vector v ( ( 1 2 vector v 2 ) vector v ) = vector v ( 1 2 vector v 2 ) since = vector v = 0 by assumption....
View Full Document

This note was uploaded on 01/24/2012 for the course MECHE 343 taught by Professor Professor during the Spring '11 term at Carnegie Mellon.

Page1 / 38

lectures-chapter9 - 650:460 Aerodynamics Chapter 9 Prof....

This preview shows document pages 1 - 8. Sign up to view the full document.

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