[Physics] motion of a fluid in a moving truck

fluid dynamicsnewtonian-mechanicssimulations

I am into a project that simulates a moving truck with a tank holding water inside it, this is example (https://www.youtube.com/watch?v=jqpl4ME6rRY).

I studied the mechanics of the motion of the truck, and the motion of the water inside a static tank.
the problem is the mutual influence between the motion of the fluid and the motion of the truck.
so there are two main problems I am stuck with:

  1. the influence of the motion of the truck to the motion of the fluid inside it.
  2. the influence of the motion of the fluid to the motion of the truck.

You can suppose that the truck moves in a straight line parallel to X-axes, with left and right move only.

for problem 1, as I am using SPH method to simulate the liquid, I am thinking of add the acceleration of the truck to the SPH equation for every fluid particle, I am not sure about it..

for problem 2,
maybe I should compute the pressure force effecting to free surfaces of the truck (getting them from the pressure force of the particles) then add it to the acceleration of the truck, I am not sure also..

I hope my ideas to be correct and to share yours with me.
Thank you.

Best Answer

Since you cannot model the response of the driver, it seems to me you will just have to assume a motion for the truck. (By "the truck", I mean the truck and container but not the fluid itself, the fluid it carries is being treated as a separate subsystem that is subject to the constraints of the motion of its container.) That means part 2 will be limited to finding the forces of the fluid on the truck for given truck motion, rather than solving for the full motion of the center of mass of the system. The SPH can then handle part 1 easily.

So I'd recommend that you select the acceleration of the truck part of the system in advance, call it A(t) to make it a given function of time. The effect of that on the fluid is simple, because you go into the truck frame (to fix the container walls), and just apply a fictitious effective gravity of -mA(t) to any particle of mass m in your SPH. Then run the SPH, and like you say, the pressure at the walls is what will produce forces on the truck. Then you can say for any given A(t), what forces will the truck experience from the fluid, and you can assess how that might feel to the driver, but you can't determine how it will change the movement of the truck (i.e., change A(t)), because you can't know how the driver will respond.

You might also want to consider the drastic differences that will appear if there is any significant amount of air in the container, such that the fluid can slosh back and forth. That would require a two-fluid treatment in the SPH, so it might be too difficult to include.

Related Question