MomEnergyConsvEqnsLect14ME525SP2011

# MomEnergyConsvEqnsLect14ME525SP2011 - ME 525: Combustion...

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ME 525: Combustion Lecture 14: Momentum and Energy Conservation Equations for Reacting Flows Prof. Robert P. Lucht Room 87, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana mail: [email protected] Email: [email protected] Phone: 765-494-5623 School of Mechanical Engineering, Purdue University February 24, 2011 1/19

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Lecture Topics • Momentum conservation equation. • Energy conservation equation. • Shvab-Zeldovich form of the energy equation. School of Mechanical Engineering, Purdue University 2/19
Momentum Conservation ost general form of momentum onservation: vv v vvv yz D      Most general form of momentum conservation: xyz Dt t x y z Pg        For Newtonian fluids:  v 2 2v 3 x xx x   v v y x xy yx x   School of Mechanical Engineering, Purdue University yx  3/19

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Momentum Conservation The x-component of the momentum equation becomes:  vv 2 2v 3 xx D P Dt x x x       v v y z x g yy xz x z      For steady 1-D planar flow, neglecting friction and body rces we obtain: forces we obtain: v v0 x d dP across flames (neglect KE change) x dx dx School of Mechanical Engineering, Purdue University 4/19
Energy Conservation – One-Dimensional Form School of Mechanical Engineering, Purdue University 5/19

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Energy Conservation – One-Dimensional Form The energy equation for flames will be analyzed gy q y under the following assumptions: Steady state No radiation heat transfer No shaft work or viscous dissipation Potential energy is negligible Constant area duct • With these assumptions, the 1-D energy equation becomes: v v xx x dQ d dh m x dx dx     School of Mechanical Engineering, Purdue University dx  6/19
Energy Conservation – One-Dimensional Form Q d h  v v xx x dQ dh m dx dx dx     0 0 0 School of Mechanical Engineering, Purdue University 7/19

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## This note was uploaded on 12/27/2011 for the course ME 525 taught by Professor Lucth during the Fall '11 term at Purdue.

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MomEnergyConsvEqnsLect14ME525SP2011 - ME 525: Combustion...

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