Introduction

An Introduction to Computational Methods in Fluids by Biringen S., Chow C.-Y.

By Biringen S., Chow C.-Y.

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001DEGREES. 5), respectively M A counter for changing angle θ0 N A counter for time steps PI π T Dimensionless time THETA0 Initial angle between flight path and x -axis, θ0 , radians U, U0 Dimensionless horizontal velocity of glider and its initial value, respectively V, V0 Dimensionless vertical velocity of glider and its initial value, respectively W0 Dimensionless initial velocity of glider X, Y Coordinates of glider X1, Y1 Coordinates of glider for θ0 = −90◦ X2, Y2 Coordinates of glider for θ0 = 180◦ 2 INVISCID FLUID FLOWS All the problems in this chapter are concerned with flows in the absence of viscosity.

Using 40 discrete vortices to replace the vortex sheet does not give accurate results at large values of T , since the constituent vortices are separated far apart. 8 1 (continued) region. Results at later time steps show that the paths of some vortices in that region are contorted, and certain parts of the vortex sheet may become crossed. The computation should actually be terminated before this unrealistic situation has developed. The chaotic motion of the spiral has been found by several authors.

2), they become the equations of motion for an airplane. 6 can be used to simulate taking off, climbing, and other two-dimensional aircraft maneuvers. 1 s. Plot the height (z ) and velocity (v) as a function of time, t. From the plots determine, approximately, a. The maximum speed of the rocket, and the time and height at which it occurs. b. The maximum height the rocket can reach, and the time at which it occurs. c. The time and velocity when the rocket hits the ground. d. Check your results with those that you will obtain by using MATLAB ODE45 solver.

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