Mass Flow at the Mid-Plane in a closed container

In summary, the conversation is about designing a cylindrical can with a temperature difference and understanding the fluid movement within the can. After conducting a simulation, the individual wants to calculate the mass flow in the transverse plane to determine the amount of liquid movement. They discuss using a surface integration method to evaluate the mass flow and ask for suggestions. The expert suggests dividing by 2 to get the up flow and down flow.
  • #1
c.teixeira
42
0
Hi there.

I am designing a type cilindrical can full of a fluid, with a temperature difference between the top and bottom. Now, after the simulation of the free convection phenomenom in COMSOL, I wanted to understand the effect of varying the temperatures, to the "fluid movement" (fluid flow/convection) that occurs within the can. To do so, I calculated the mass flow in the transverse plane ( the mid-plane[at the same distance from the top and bottom]): [itex]\dot{m}[/itex] = [itex]\int\int\rho*w*dA[/itex].

The results I got for the mass flow were = 0. As there is no mass sink or source within the can, the mass flow had indeed to be zero unless it was compressing part of the liquid, and "creating" vacuum in another part of the can. So basically, the amount of mass that flows trough the mid-plane to the top is equal to the mass that flows trough the mid-plane to the bottom. However, what is relevant for my work, is to understand "how much liquid movement" occurs in the can. In order to do so, what do you think would be the most suitable surface integration I could use?
I tough about evaluating the following surface integral: [itex]\dot{m}[/itex] = [itex]\int\int\rho*\sqrt{w^{2}}*dA[/itex].
In this case, the fluid crossing the plane of integration in direction to the bottom( with negative w) would count as positive mass flow. do you think this is a reasonable solution? do you have any sugestions?

Here is a sketch to make it more clear:
PF_sketch.png




c.teixeira
 
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  • #3
Your method should work just fine. Just divide by 2 to get the up flow and the down flow.
 

What is mass flow at the mid-plane in a closed container?

Mass flow at the mid-plane in a closed container refers to the movement of mass through the center plane of a closed container. This can occur due to differences in pressure, temperature, or concentration between the two sides of the mid-plane.

Why is mass flow at the mid-plane important?

Understanding mass flow at the mid-plane is important for various industrial and scientific applications. It can help in optimizing processes, such as in chemical reactions, and in designing efficient systems, such as in heat exchangers.

What factors affect mass flow at the mid-plane?

The main factors that affect mass flow at the mid-plane are the pressure difference, temperature difference, and concentration difference between the two sides of the mid-plane. Additionally, the size and shape of the container, as well as any obstructions in the flow path, can also impact the mass flow.

How is mass flow at the mid-plane calculated?

Mass flow at the mid-plane can be calculated using principles of fluid mechanics, such as Bernoulli's equation and the continuity equation. These equations take into account the various factors that affect mass flow and can provide an accurate estimation of the flow rate.

Can mass flow at the mid-plane be controlled?

Yes, mass flow at the mid-plane can be controlled by manipulating the factors that affect it. For example, the flow rate can be increased by increasing the pressure or temperature difference between the two sides of the mid-plane. Similarly, the flow rate can be decreased by decreasing these factors.

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