2 Basic Laws EAS 4101 S10

# 2 Basic Laws EAS 4101 S10 - EAS 4101, S11 University of...

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EAS 4101, S11 University of Florida 1/11/11 1/11 Section 2, Basic Laws 2 Basic Laws 2.1 Reference Frames and Control volumes Before proceeding to the governing laws, we need some background information on which reference frames and control volumes to use for our analysis 2.1.1 Ground Fixed Coordinate System In the Ground-Fixed Coordinate system, the air vehicle is flying at a constant velocity into a mass of air at rest or possessing some wind speed. o Since the ground is not accelerating, this is a inertial reference frame. o An example is watching an airplane fly overhead.

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EAS 4101, S11 University of Florida 1/11/11 2/11 Section 2, Basic Laws 2.1.2 Vehicle Fixed Coordinate System In the Vehicle-Fixed Coordinate system, the air is flowing over the stationary vehicle. o An example is observing an airfoil in a wind tunnel. o An unsteady Gallilean transformation of the governing equations from the ground- to vehicle-fixed coordinate systems is invariant, therefore we can use the vehicle-fixed system for analysis purposes. o The vehicle-fixed coordinate system thus possesses steady flow 2.2.1 Definitions of Regions (CV’s) Control region or volume: any closed region bounded by a surface (control surface). In general, regions (or volumes) are either open (mass and energy transfer occurs), closed
EAS 4101, S11 University of Florida 1/11/11 3/11 Section 2, Basic Laws (no mass transfer, but energy transfer occurs), or isolated (no mass transfer, no energy transfer). Here is another classification of 3 types of regions: 1. Fixed Region: control surface (CS) doesn’t move, but is fixed in space i.e. nozzle (mass and energy transfer across CS may occur, so it is an open control volume) Fixed region Figure 1 Example of fixed region: nozzle (Foss 1982). 2. Material Region: control surface moves with the local fluid velocity and always contains the same material i.e. gas bubble rising in liquid (no mass transfer across CS, but there can be energy transfer: closed system!) V  expansion V circulation V Figure 2 Example of material region: CS around an expanding, moving gas bubble in a liquid (Foss 1982). 3. Arbitrary Region: moves and deforms (Example: open balloon exiting air and shrinking) (May, but not required, to have mass transfer. Example: control surface that expands and rises with the gas but doesn’t circulate with the gas . There can be mass and energy transfer, but the CS does not move with the gas.)

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EAS 4101, S11 University of Florida 1/11/11 4/11 Section 2, Basic Laws Arbitrary region U  Figure 3 Example of arbitrary region: deflating balloon (Foss 1982). 2.2 Conversation Laws All conservation laws (continuity, momentum, …) come from Lagrangian method of description (LMOD). We must use obtain tools to transform the equations to the Eulerian method of description (EMOD).
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## This note was uploaded on 09/05/2011 for the course EAS 4101 taught by Professor Sheplak during the Spring '08 term at University of Florida.

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2 Basic Laws EAS 4101 S10 - EAS 4101, S11 University of...

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