lec14 - Aerodynamics Lecture 14 Non-lifting Flow Over...

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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.1 Lecture 14 Aerodynamics Potential Flow: Source Panel Method AE311 Aerodynamics Manoj T. Nair IIST
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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.2 Agenda 1 Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method 2 Flow Over a Circular Cylinder
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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.3 The Source Panel Method I Till now we had obtained bodies like Rankine oval and circular cylinder - both non-lifting and lifting These were obtained by combining the elementary flows However these shape are of no practical use the method is indirect - we didn’t know the shape a priori Can we have a direct method? - a method which can obtain arbitrary shape defined by us i.e., we define an arbitrary body, and solve for distribution of singularities which in combination with freestream will produce flow over a given body One such technique is called the source panel method Such techniques have been used in the aircraft industry since late 1960s
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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.4 The Source Panel Method II Imagine that we have infinite no. of line sources placed side by side The strength of each of these line source is infinitely small These side by side line sources form a source sheet In the side view, the line sources are all perpendicular to the screen
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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.5 The Source Panel Method III Let s be the distance measured along the source sheet in the edge view Let λ = λ ( s ) be the source strength per unit length along s The strength of a single line source Λ was defined as the volume flow rate per unit depth, m 2 / s Strength of the source sheet λ ( s ) is the volume flow rate per unit depth per unit length of the sheet, m / s
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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.6 The Source Panel Method IV The strength of the infinitesimal portion ds of the sheet is λ ds This small section is treated as a distinct source of strength λ ds Consider P ( x , y ) in the flow located at a distance r from ds
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Aerodynamics Non-lifting Flow Over Arbitrary Bodies: The Source Panel Method Flow Over a Circular Cylinder 14.7 The Source Panel Method V This section of source sheet induces an infinitesimal small potential d φ at P d φ = λ ds 2 π ln r The complete velocity potential at P
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