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MAE 4262: ROCKETS AND MISSION ANALYSIS

MAE 4262: ROCKETS AND MISSION ANALYSIS. Conservation Equations and Examples Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk. CONSERVATION OF MASS. This is a single scalar equation Velocity doted with normal unit vector results in a scalar

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MAE 4262: ROCKETS AND MISSION ANALYSIS

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  1. MAE 4262: ROCKETS AND MISSION ANALYSIS Conservation Equations and Examples Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

  2. CONSERVATION OF MASS • This is a single scalar equation • Velocity doted with normal unit vector results in a scalar • 1st Term: Rate of change of mass inside CV • If steady d/dt( ) = 0 • Velocity, density, etc. at any point in space do not change with time, but may vary from point to point • 2nd Term: Rate of convection of mass into and out of CV through bounding surface, S • 3rd Term (=0): Production or source terms • Last equation arises from vector equation: Vintertial = Vrelative + Vcontrol surface Relative to CS Inertial

  3. MOMENTUM EQUATION: NEWTONS 2nd LAW Inertial Relative to CS • This is a vector equation in 3 directions • 1st Term: Rate of change of momentum inside CV or Total (vector sum) of the momentum of all parts of the CV at any one instant of time • If steady d/dt( ) = 0 • Velocity, density, etc. at any point in space do not change with time, but may vary from point to point • 2nd Term: Rate of convection of momentum into and out of CV through bounding surface, S or Net rate of flow of momentum out of the control surface (outflow minus inflow) • 3rd Term: • Notice that sign on pressure, pressure always acts inward • Shear stress tensor, t, drag • Body forces, gravity, are volumetric phenomena • External forces, for example reaction force on an engine test stand • Application of a set of forces to a control volume has two possible consequences • Changing the total momentum instantaneously contained within the control volume, and/or • Changing the net flow rate of momentum leaving the control volume

  4. HOW ALL ROCKETS WORKS F Chemical Energy Rocket Propulsion (class of jet propulsion) that produces thrust by ejecting stored matter • Propellants are combined in a combustion chamber where chemically react to form high T&P gases • Gases accelerated and ejected at high velocity through nozzle, imparting momentum to engine • Thrust force of rocket motor is reaction experienced by structure due to ejection of high velocity matter • Same phenomenon which pushes a garden hose backward as water flows from nozzle, gun recoil • Examples to come in next lecture: mass, momentum and derivation of Rocket Equation QUESTION (Hill and Peterson, Chapter 1, p.3): Could a jet or rocket engine exert thrust while discharging into a vacuum (with not atmosphere to “push against”)? Thermal Energy Kinetic Energy

  5. SOLID ROCKET MOTOR ANALYSIS: MASS CONSERVATION • How does the exhaust velocity vary with, • Changes in density as the solid propellant burns? • Regression velocity of the solid grain? • Cross-sectional area of the grain relative to the exit area? http://www.fofweb.com/Subscription/Science/Sc/ffdsptech2530b.jpg

  6. SOLID ROCKET MOTOR CROSS-SECTION http://www.aerospaceweb.org/question/propulsion/rocket/solid-rocket2.jpg

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