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January 8, 1999, 03:09 
particle trajectory calculation

#1 
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Let be a particle droped in a 2D flow without speed. The speed of the flow is initialy on the x direction and then the velocity change (direction and magnitude). Is there ananlytical solution for this problem? Where can I find some references about this subject?


January 8, 1999, 13:57 
Re: particle trajectory calculation

#2 
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So,initially the location of the particle is known, and the relative velocity is also known and is in xdirection. From this and the particle diameter, and Reynolds number you can compute the drag force acting on the particle. ( you need this formula for drag coefficient on a sphere at different Reynolds number , and you need to do some searching to look for this formula on your own. not me!) Then you can use Newton's 2nd law to compute the particle motion for a small time step delta t. You do this for the motion in xdirection and the motion in ydirection. ( the force in ydirection is the gravitational force.) F=m*a, m is the mass of the particle, and F is the component of force in either x or ydirections, a is the acceleration=dV / dt. Now you have dV=a*dt, you can pick a small dt to compute your dV, that is the change in velocity at the end of dt. The velocity is then V(t+dt)=V(t) + dV. At this point the particle should move to a new location defined by x(t+dt)=x(t) + V,in xdirection * dt, y(t+dt)=y(t) + V,in ydirection * dt. Since the particle will have both V,x and V,y velocity components, make sure to find the relative velocity and the direction so that the proper drag force can be computed ( this is also the direction of the relative velocity). In ydirection, the force acting on the particle is m*g + F,y . m*g is the gravitational force which is roughly constant and F,y is the component of the darg force in ydirection which depends on the relative velocity at time t and t=dt and so on..


January 28, 1999, 17:15 
Re: particle trajectory calculation

#3 
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Here are some publications that cover the problem (I assume you are interested in the behavior of small particles): 1Tchen,C.M. Mean Value and Correlation Problems Connected with the motion of Small particles suspended in a turbulent flow, Diss. TH Delft, 1947 2Millikan,R.A. The general law of a small spherical body through a gas, Phys Review, Sec.Ser.,Vol. 22,No.1, 1923 3Allen,M.D., Raabe,O.G. Reevaluation of Millikans Oil drop datafor the motion of small particles in air, J.Aerosol Sciences, Vol13,No.6,1982 4Kurz,R., Experimentelle und theoretische Untersuchungen an gleichfoermig und ungleichfoermig geteilten Turbinengittern, Diss UBw Hamburg, 1991.
Hope this helps! 

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