association of PDE and 3d object

shelodn · October 11, 2014, 05:47

Hello, I am in a CFD class, and we are already discussing hyperbolic equations. we finished the elliptical, and supposedly that is what I would use to determine the air forces on an object at subsonic speeds.
This is not for a class project, but just to help me understand a little better. I created the 2d profile of a bottle, and I want to theoretically launch this bottle through the air, nose first. I understand that I need continuity and specifically the material derivative, as well as momentum, to determine the flows around this bottle.
I am struggling with plugging the PDEs learned to the application.
could someone please tell me how I would apply the continuity and momentum equations to the bottle?
more specifically, would the mesh be the bottle, or some arbitrary points around the bottle? and also is there some simpler way to determine the velocity profile to apply in the spatial derivatives in the divergence, or do I need to go all the way down to the velocity potential, and vorticity?
any help greatly appreciated, and I apologize if my questions are confusing. all I'm asking is to be pointed in the right direction.
thanks

DaveyBaby · October 16, 2014, 08:05

Hi, if I have understood your question this might help

You would perform the CFD on the air around the bottle so you would be solving on a mesh in that fluid domain.

To start with, you could essentially draw a large box with a bottle shape missing, apply continuity/conservation of momentum to this fluid domain, while thinking about boundary conditions at the box outer walls and at the interface between the fluid and the bottle surface.

The solution of the NS equations on a suitable mesh (not done by hand!) would give you velocity gradients and hence along with the fluid viscosity would give you viscous stresses up to this fluid/solid interface enabling you to infer the internal stresses at the bottle outer surface (if you are interested in these). In practice, CFD simulations often apply wall functions which give you the velocity gradient near the wall in terms of a normalised velocity and a normalised normal-wall distance.

Kind Regards

October 11, 2014, 05:47	association of PDE and 3d object	#1
shelodn New Member sheldon Join Date: Oct 2014 Posts: 1 Rep Power: 0	Hello, I am in a CFD class, and we are already discussing hyperbolic equations. we finished the elliptical, and supposedly that is what I would use to determine the air forces on an object at subsonic speeds. This is not for a class project, but just to help me understand a little better. I created the 2d profile of a bottle, and I want to theoretically launch this bottle through the air, nose first. I understand that I need continuity and specifically the material derivative, as well as momentum, to determine the flows around this bottle. I am struggling with plugging the PDEs learned to the application. could someone please tell me how I would apply the continuity and momentum equations to the bottle? more specifically, would the mesh be the bottle, or some arbitrary points around the bottle? and also is there some simpler way to determine the velocity profile to apply in the spatial derivatives in the divergence, or do I need to go all the way down to the velocity potential, and vorticity? any help greatly appreciated, and I apologize if my questions are confusing. all I'm asking is to be pointed in the right direction. thanks

October 16, 2014, 08:05	Mesh the fluid not the solid	#2
DaveyBaby Member DaveyBaby Join Date: May 2013 Posts: 46 Rep Power: 13	Hi, if I have understood your question this might help You would perform the CFD on the air around the bottle so you would be solving on a mesh in that fluid domain. To start with, you could essentially draw a large box with a bottle shape missing, apply continuity/conservation of momentum to this fluid domain, while thinking about boundary conditions at the box outer walls and at the interface between the fluid and the bottle surface. The solution of the NS equations on a suitable mesh (not done by hand!) would give you velocity gradients and hence along with the fluid viscosity would give you viscous stresses up to this fluid/solid interface enabling you to infer the internal stresses at the bottle outer surface (if you are interested in these). In practice, CFD simulations often apply wall functions which give you the velocity gradient near the wall in terms of a normalised velocity and a normalised normal-wall distance. Kind Regards