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Unformatted text preview: AA311: Atmospheric Flight Mechanics Lecture 11 Dr. Laszlo Techy University of Washington Department of Aeronautics & Astronautics October 27, 2011 Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Compressibility P38 video. Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Compressibility Early aircraft went slow. The incompressible flow approximation is valid at low speed. As speed increases, the incompressible assumption fails. World War II fighter aircraft approached the speed of sound in steep dives. A bow shock formed ahead of the wings leading edge. The bow shock disrupted the air flow over the control surfaces, causing a loss of control. Dive brakes were added to slow aircraft down in dives to avoid what was called, at the time, “compressibility.” Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Speed of sound Transmission of sound in a gas is related to the intermolecular collisions inside the gas. When some disturbance is created (say due to an explosion), the energy that is released is transferred through these intermolecular collisions to neighboring molecules. These energized molecules transfer some of their kinetic energy to other neighboring molecules, and the process continues. Therefore, it intuitively makes sense that the speed of sound should be somewhat related to the mean molecular velocity (or equivalently, the temperature) inside the gas. Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Speed of sound a 2 = dp d ρ Recall p 2 p 1 = ρ 2 ρ 1 γ In general, a region within the free stream that is free of shock waves can be considered isentropic. p 2 ρ γ 2 = p 1 ρ γ 1 = const = c p ρ γ = c Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Speed of sound p ρ γ = c a 2 = dp d ρ = d ( c ρ γ ) d ρ = c γρ γ 1 a = r γ p ρ Using the equation of state, p /ρ = RT , we have a = p γ RT Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Mach number Recall the definition of Mach number M = V a The flow can be categorized into very different regions using the Mach number: If M < 1, the flow is subsonic . If M = 1, the flow is sonic . If M > 1, the flow is supersonic . Transonic : 0 . 8 ≤ M ≤ 1 . 2. Hypersonic : M > 5. Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Compressibility and Mach number 1 Recall the gravityfree version of Euler’s equation: dp = ρ VdV . From a 2 = dp d ρ , we have a 2 d ρ = ρ VdV . From the definition of Mach number M = V / a , we have d ρ ρ = M 2 dV V . So, if M < . 3, then a relative change in density will be less then 10% of the relative change in velocity (0 . 3 2 = 0 . 09). Dr. Laszlo Techy AA311: Atmospheric Flight Mechanics Airspeed Measurement for Subsonic Compressible Flow Recall the definition of enthalpy: h = e + pv ....
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 Fall '09
 Fluid Dynamics, Aerodynamics, Mach number, Shock wave, Atmospheric Flight Mechanics, Dr. Laszlo Techy

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