when you stir fluid in a beaker of fluid, how is the motion on the fluid by the stirring rod calculated? the fluid is represented using smoothed particle hydrodynamics lagrangian method so that I can look at fluid as a bunch of spheres interacting with each other through a sort of force field. so now I try to add stirring motion into this, and so far I only have collision detection implemented using penalty force, and the results do not reflect the stirring motion because the fluid particles do not get dragged by the stick at all. how should the stirrind rod transfer its motion into the pool of spheres and drag the fluid with it?
This is not the way to model the fluid mechanics of a stirring rod in a fluid. You should be using continuum fluid dynamics, and treating the material as a Newtonian fluid (viscous fluid). The boundary condition with any solid is zero velocity difference at the boundary (the so-called non-slip boundary condition). This is a routine problem for computational fluid dynamics software. The equations solved are the Navier Stokes equations.
can you link me to the procedure to approach this problem? I realized too that this must be solved in the Navier Stokes equation, not just simple collision detection like walls and stuff, but I don't know how the forces work in that perspective since I am pretty new to fluid mechanics myself. thx
To get some good background on fluid mechanics, see Transport Phenomena by Bird, Stewart, and Lightfoot. This is not an elementary problem to solve. The computational fluid dynamics people first started getting solutions to problems like this (and ones with more complicated industrial stirrers) only about 20-30 years ago. You have a moving boundary, which is always hard to handle. You are interested in getting the load on the stirrer. They calculate that. All the detailed mathematics is done by the software, using the finite element method. One of the things it calculates (among many) is the stress tensor at the stirrer surface. It then properly integrates the stresses to get the load. I suggest you google computational fluid dynamics software if you are really serious about doing this problem. There may also be articles in the literature by people who have already solved similar problems. I'm sure that the CFD software vendors would be happy to accommodate you, but it probably won't be cheap.
thing is, I already have SPH program, is there no reasonable way to add the effects of the stirring force into my numerical solution? my lagrangian navier stokes equation is already much simplified. the momentum equation has 3 terms, pressure, viscosity, and external force. surely there must be a way to describe the force the stirring rod applies to the fluid at that location in that velocity and acceleration.
To get a first approximation to the force, you might consider the solutions available for flow past an infinite cylinder. This is the same as the solution for movement (at constant speed) of a cylinder through a stationary fluid. The drag force on a cylinder is presented in the literature in terms of the drag coefficient as a function of the Reynolds number. Google drag on a cylinder.
just wondering, is there any place where I can find existing force data on fluid stirring? I have a force sensor but it won't register anything under a newton. stirring water won't even beat the noise values, so I am hoping there are existing data I can use as reference