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May 28, 2013, 21:59 
NAvier Stokes and Newton's law coupling

#1 
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sud
Join Date: May 2013
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Hello ppl ,
I am trying to simulate the Navier Stokes Equation for a body falling which starts with some velocity at an altitude . The velocity is not a constant one . It is going to vary for each time step and the height as per newton's law. I wrote code for numerically simulating the NS Equation neglecting body forces . Now i incorporate the body force (rho*g) into it . I need to couple the navier stokes and newton's law together . How do i implement it ? Any suggestions will be of great help . And i m desperately searching things to compete my project . Thanks 

June 3, 2013, 08:50 

#2 
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duri
Join Date: May 2010
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You cannot couple body motion to NS equations because, NS is for flow field. If you add body force to equation it works on fluid and not on the body. You can do it by two ways,
1. Find distance time relation for the body and apply grid motion in unstready flow field. If you are writing your own code, need to correct flux calculations based on wall motion. 2. Find velocity time relation for the body and apply it as inlet condtion. Time varying inlet boundary condition. Thanks 

June 3, 2013, 14:24 

#3 
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Jonas T. Holdeman, Jr.
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Location: Knoxville, Tennessee
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I would expect that you would be working in an accelerating coordinate system where the falling object is stationary. The fluid would be accelerating at rate g minus the result of the drag force. As you say, the fluid would be subject to a body force (rho*g) minus the drag force which you would calculate at each time step from the flow. As the fluid velocity increases the drag force increases until the drag balances the gravitational force. The velocity at which these balance is called the terminal velocity.


June 4, 2013, 12:32 

#4 
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sud
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Thanks Mr. duri . I wrote a code for complete navier stokes equation in viscous supersonic flow long back . Now i wish to simulate the code for any body which is at an altitude of 60km and starts with supersonic velocity and then it gradually drops to zero when it reaches the ground .
I need to extend this navier stokes code to produce the pressure plots throughout the atmosphere as it starts from 60km till ground . you said me to use time dependent boundary condition . But i haven't used it in any of my simulation and i really wanted to do this project. Can you help me out ? 

June 4, 2013, 12:35 

#5  
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sud
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Quote:
I understand what you said . The thing i wanted to do is just to simulate the navier stokes code at all points in the atmosphere coupled with reentry dynamics of the body . how could I proceed ? .. 

June 18, 2013, 04:18 

#6 
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duri
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The easiest way to implement is to use your unsteady code (dual time stepping method is better). Converge solution for initial condition, then solve at minimum one DOF equation and estimate new velocity of body (time integration) and estimate new bc condition.
If you are comfortable with LODI BC's then use them for unsteady BC. 

September 6, 2013, 09:46 

#7  
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sud
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Quote:


September 7, 2013, 01:46 

#8 
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duri
Join Date: May 2010
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I think probably you are talking about multiphase VOF. Its better to try this problem in fluent (probably cfx). It has both vof model and 6dof model and quite easy to setup the solution.


September 15, 2013, 15:26 

#9  
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Quote:
Of course you can !!!! first of all it depends on the size of your object relatively to the size of your mesh cells. first option: your object has a smaller size thant your grid size. 1) solve your navierstokes equations accounting for retroacting force (Two way coupling) 2) compute the fluid forces acting on your solid (drag,lift, magnun safftman forces etc.....) these forces depend on the fluid velocity U. 3) solve newton's law mdV/dt = Summ of all forces (V is the velocity of your object) 4) solve dx/dt=V then you get the new position of your object 5)compute the retroacting force depending on the location of your object which act as source term in NavierStokes equation. This retroacting force may be (summ of all forces) you computed in the newton's law second option your object is much greater that your grid size. I would suggest the use of an Immersed Boundary Method. These kind of methods help the fluid to feel the presence of the obstacle. Many options are available. The newton 's law will tell where the object is in the domain at every time step. Now the forces acting on the object will be computed from the integral over the surface of the object of sigma.n.ds where sigma is the stress tensor = P II + Tau where P is the pressure, II Identity tensor and Tau viscous stress tensor. This can be computed once velocity and pressure are known. Godd luck 

September 30, 2013, 16:13 

#10  
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sud
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Quote:
Thanks in advance .. 

March 6, 2014, 03:42 
Navier stokes streamline vorticity approach

#11 
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Rajashekaran
Join Date: Mar 2014
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Can anyone having the solved example of Streamline Vorticity approach and Navier stoke equation to find the pressure velocity Ux and Uy in 2D.
I found in book only the derivation but i need the solved example for finding pressure and velocity by discritizing and iterative method. Regards K.Rajashekaran 

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