CJDetonationAnalysisILect19ME525SP2011

CJDetonationAnalysisILect19ME525SP2011 - ME 525: Combustion...

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School of Mechanical Engineering, Purdue University ME 525: Combustion Lecture 19: Detonations and Deflagrations: Chapman-Jouguet Analysis Prof. Robert P. Lucht Room 87, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana Email: Lucht@purdue.edu Phone: 765-494-5623 March 22, 2011 1/28
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School of Mechanical Engineering, Purdue University Lecture Topics • Qualitative differences between detonations and deflagations. • Derivation of the Rankine-Hugoniot relations. • Properties of the Hugoniot curve. 2/28
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School of Mechanical Engineering, Purdue University Detonations and Deflagrations: Qualitative Comparison Consider a 1-D planar combustion wave propagating in a very long duct with constant area. The combustion wave can either be a deflagration (subsonic u 1 ) or a detonation (supersonic u 1 ). Detonations are discussed in detail in Kuo, Principles of Combustion, 2 nd Edition, 2005. In frame of reference attached to this combustion wave: Unburned u 1 Burned u 2 1 , P 1 , T 1 2 , P 2 , T 2 3/28
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School of Mechanical Engineering, Purdue University Detonations and Deflagrations: Qualitative Comparison Typical values for detonations and deflagrations are shown above (Kuo, Table 4.1, p. 357). 4/28
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School of Mechanical Engineering, Purdue University Derivation of the Rankine-Hugoniot Relation Consider the conservation equations applied to control volume surfaces far removed from the combustion wave so that dT/dx = 0 and du/dx = 0. Conservation of mass:   11 2 2 1 constant uu m    Conservation of momentum:  22 1 2 2 2 2 Pu P u  Conservation of energy: 2 2 3 hu h u 5/28
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School of Mechanical Engineering, Purdue University Derivation of the Rankine-Hugoniot Relation We also have the ideal gas equation of state:   22 2 2 4 PR T The four equations can be reduced to one equation in two unknowns, the Rankine- Hugoniot relation. There are four equations but five unknowns: 2 1 2 ,, , , PT u u 6/28
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School of Mechanical Engineering, Purdue University Derivation of the Rankine-Hugoniot Relation Combine Eqns. (1) and (2) to give the Rayleigh line relation:    22 11 2 2 21 1 1 2 2 12 2 2 2 2 5 uu PP u u mw h e r e m u u m          7/28
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School of Mechanical Engineering, Purdue University Derivation of the Rankine-Hugoniot Relation Now we will work with Eqn. (5) to derive some expressions that will be useful for later analysis of detonation and deflagration waves. Derive an expression for u 2 - u 1 : From Table 4.1 in Kuo we can see that for a detonation 2 > 1 , while the reverse is true for a deflagration. Thus the sign of u 2 - u 1 will be negative for a detonation and positive for a deflagration.
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CJDetonationAnalysisILect19ME525SP2011 - ME 525: Combustion...

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