lecture8 - MECH 6251/498D MECH 7221 Idealized Rocket Design...

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1 MECH 7221 Idealized Rocket Design and Analysis • Real nozzle design for optimal performance • Nozzle contour and shape Objectives Reading assignment: Sutton and Biblarz Chapter 6 NERVA Nozzle Testing
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2 In designing a rocket, we are given A *, P o and P as main design parameters. The desired goal is to design a nozzle such that the exit pressure, P e , closely matches the ambient pressure P . complete expansion inside the nozzle It can be shown using variational calculus on the thrust relationship that given a pressure ratio P /P o the optimal nozzle performance occurs when: = p p A A exit throat exit gvie to adjusted is Optimal Nozzle Exit pressure has a dramatic effect on nozzle performance
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3 Effect of Back Pressure
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4 Exhaust Plume Pattern
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5 For optimal condition may also require that nozzle expands to very large area ratios If the nozzle is not probably contoured Flow separation Losses
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6 Optimal Nozzle Contours • Optimum nozzle configuration for a particular mission depends upon system trades involving performance, thermal issues, weight, fabrication, vehicle integration and cost. http://www.k-makris.gr/RocketTechnology/Nozzle_Design/nozzle_design.htm Length
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7 Flow Field Characteristics
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8 Nozzle • Reduce the nozzle length (hence weight)
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9 Conical Nozzle • Easier to manufacture – for small thrusters • Exit velocity is not all in the desired direction Nozzle Divergence Correction Coefficient • Here λ is the “thrust efficiency”, defined as ratio of actual to ideal thrust accounting for flow divergence. ε Is the nozzle area ratio (ratio of exit area to throat area).
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10 Nozzle Divergence Correction Coefficient • Quasi-1-D analysis assumes exit flow leaves parallel to longitudinal axis of the nozzle this rarely happens in reality!! θ nozzle
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11 Nozzle Divergence Correction Coefficient • Look at mass flow across spherical exit surface dS = r sin[ φ ] d ψ× Rd φ= R 2 sin[ ] d d ψ m = ρ exit V exit 0 θ 0 2 π dS = 2 exit V exit 0 0 2 R 2 sin[ ] d d ψ= 2 πρ exit V exit R 2 1 cos[ ] {}
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12 Nozzle Divergence Correction Coefficient • Look at axial momentum flow across spherical exit surface dS = r sin[ φ ] d ψ× Rd φ= R 2 sin[ ] d d ψ F axial = M axial = ρ exit V exit 2 0 θ 0 2 π cos[ ] dS = exit V exit 2 0 0 2 R 2 sin[ ]cos[ ] d d ψ= 2 πρ exit V exit 2 R 2 1 cos 2 [ ] {} 2 = πρ exit V exit 2 R 2 sin 2 [ ]
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13 Nozzle Divergence Correction Coefficient dS = r sin[ φ ] d ψ× Rd φ= R 2 sin[ ] d d ψ F axial m V exit = πρ exit V exit 2 R 2 sin 2 [ θ ] 2 exit V exit R 2 1 cos[ ] {} V exit = exit V exit 2 R 2 sin 2 [ ] 2 exit V exit 2 R 2 1 cos[ ] = sin 2 [ ] 21 cos[ ] = sin 2 [ ]1 + cos[ ] cos[ ] 1 + cos[ ] = sin 2 [ + cos[ ] cos 2 [ ] = sin 2 [ + cos[ ] 2s i n 2 [ ] = 1 2 1 + cos[ ]
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14 Nozzle Divergence Correction Coefficient F axial m V exit = 1 2 1 + cos[ θ ] {} ≡ λ Actual Momentum Thrust Momentum Thrust of idealized Nozzle T hrust = λ m V exit + A exit P exit P [] Application of Correction Factor
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15 Nozzle Divergence Correction Coefficient Typical
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16 Conical nozzle
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lecture8 - MECH 6251/498D MECH 7221 Idealized Rocket Design...

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