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MAE 4261: AIR-BREATHING ENGINES

MAE 4261: AIR-BREATHING ENGINES. Integral Forms of Mass and Momentum Equations January 17, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk. CONSERVATION OF MASS. This is a single scalar equation

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MAE 4261: AIR-BREATHING ENGINES

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  1. MAE 4261: AIR-BREATHING ENGINES Integral Forms of Mass and Momentum Equations January 17, 2012 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 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 A ROCKET 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 Thermal Energy Kinetic Energy

  5. HOW AN AIRCRAFT ENGINE WORKS Chemical Energy Kinetic Energy Thermal Energy • Flow through engine is conventionally called THRUST • Composed of net change in momentum of inlet and exit air • Fluid that passes around engine is conventionally called DRAG Excellent website for how internal components work: http://www.geae.com/education/index.html

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