Week 7 - Simulating Fluid Sloshing effect inside a Gear-box

Geometry:

The view of a fluid volume geometry:

Click on the plane < and select split tool < click on remove the region, then it seems like a split body. The yellow highlighted area is what we want, so copy the area and paste it into the new design, then we will get the 2D view.

2D view:

Mesh:

Mesh grid size = 2mm.

No. of nodes = 17089.

Setup:

Multiphase modes < vol of fluids < select implicit < ok, model < k-epsilon < realizable < enhance wall treatment for getting more accurate values < ok < tick on transient time and on gravity < y = -9.81 < ok < for mark and adapt cells we have to calculate the gearbox enclosure and enter the values.  

The total height of the gearbox enclosure: 135mm.

20% of gearbox enclosure: 0.2*135 = 27mm (from bottom)

30% of gearbox enclosure: 0.3*135 = 40.5mm (from bottom)

In the mark/adapt cells we have to take the left-hand side bottom corner values are X and Y min values and right-hand top corner values are X and Y max values.

20% immersion:

 30% immersion:

User defined < functions < compiled < open rate.c UDF < build < load. Now open setting up domain < dynamic mesh < and tick on the mesh methods < setting < zone name < rigid body < left gear < motion UDF left motion < create < right gear < motion UDF right motion, gravity x = 0.115 < create < close < display zone motion < preview < ok .

Now open solving < select hybrid method < click on initialize < patch < phase < engine oil and n-heptane < select vol fraction =1 < select hexahedral < patch.

Postprocessing < contour < phases < vol fraction < fuel < select all < display < create < solve < create animation and run the calculation.

20% immersion:

30% immersion:

Case 1: Engine oil

I) 20% immersion:

https://www.youtube.com/watch?v=O0uyCc8VazY&ab_channel=Harsha

30% immersion:

 https://www.youtube.com/watch?v=K8S8pNVZ18E&ab_channel=Harsha

Case 2: n-heptane(`C_7h_16`)

 I) 20% immersion:

 https://www.youtube.com/watch?v=iY7Ysn3q0SE&feature=youtu.be&ab_channel=Harsha

II) 30% immersion:

 https://www.youtube.com/watch?v=awTNndc-V3g&feature=youtu.be&ab_channel=Harsha

Part 2:

Sloshing effect:

In fluid dynamics, slosh refers to the movement of liquid inside another object (which is, typically, also undergoing motion). Strictly speaking, the liquid must have a free surface to constitute a slosh dynamics problem, where the dynamics of the liquid can interact with the container to alter the system dynamics significantly. 

Important examples include propellent slosh in spacecraft tanks and rockets (especially upper stages), and the free surface effect (cargo slosh) in ships and trucks transporting liquids (for example oil and gasoline).  However, it has become common to refer to liquid motion in a completely filled tank, i.e. without a free surface, as "fuel slosh".

Extensive mathematical and empirical relationships have been derived to describe liquid slosh. These types of analyses are typically undertaken using computational fluid dynamics and finite element methods to solve the fluid-structure interaction problem, especially if the solid container is flexible. Relevant fluid dynamics non-dimensional parameters include the Bond number, the Weber number, and the Reynolds number.

Slosh is an important effect for spacecraft, ships, and some aircraft. Slosh was a factor in the Falcon 1 second test flight anomaly and has been implicated in various other spacecraft anomalies, including a near-disaster with the Near-Earth Asteroid Rendezvous satellite.

Dynamic meshing:

A Mesh is a network that is formed of cells and points. It can have almost any shape in size and is used to solve partial differential equations. Each cell of mesh represents an individual solution of the equation. Solving the entire object without dividing it into smaller pieces can be impossible because of the complexity that is within the object so we require mesh to solve the object.

Types of Meshing:

1. Sliding/Moving Mesh: The mesh model allows you to set up a problem in which separate zones move relative to each other. The motion can be translational or rotational. Example: Take 2 trains passing through a tunnel.    

2. Dynamic Mesh:  The mesh model allows you to move the boundaries of a cell zone relative to other boundaries of the zone and to adjust the mesh accordingly. The boundaries can move rigidly with respect to each other, such as pistons moving inside an engine cylinder or a flap deflecting on an aircraft wing.

An important special case of dynamic mesh motion is called the sliding mesh in which all of the boundaries and the cells of a given mesh zone move together in a rigid-body motion. In this situation, the nodes of the mesh move in space, but the cells defined by the nodes do not deform. Furthermore, mesh zones moving adjacent to one another can be linked across one or more non-conformal interfaces. As long as the interfaces stay in contact with one another, the non-conformal interfaces can be dynamically updated as the meshes move, and fluid can pass from one zone to the other. 

The Dynamic mesh model in ANSYS fluent can be used to model flows where the shape of the domain is changing with time due to motion on the domain boundaries. This model can be applied to both single and multiphase flows. And you need to provide a starting volume mesh and a description of the motion of any moving zones in the model. 

Three groups of mesh motion methods are available in ANSYS Fluent to update the volume mesh in the deforming regions subject to the motion defined at the boundaries:

1. Smoothing Methods: 

 when smoothing is used to adjust the mesh of a zone with a  moving and/or deforming boundary, the interior nodes of the mesh move, but the number of nodes and their connectivity does not change. In this way, the interior nodes "absorb" the movement of the boundary. 

In smoothing, we have 3 methods they are: 

• Spring/Boundary/Laplace layer: For this method, the edges between any two mesh nodes are idealized as a network of interconnected springs. we can use the spring-based method to update any cell or face zone whose boundary is moving. 
• Diffusion: This smoothing method is an alternative method for the spring method. It is available for all element types, and you can use it to update any cell zone. It is computationally more expensive than the spring smoothing method, but likely results in better mesh quality. 
• Linearly elastic solid: This method supports triangular and quadrilateral elements in 2D and tetrahedral, wedge, hexahedral, and pyramid cells in 3D. It cannot be applied for deforming cell zone contains polyhedral cells. In such cases, the diffusion smoothing method is recommended.  

  2. Dynamic Layering:

We can use this method to split or merge cells adjacent to any moving boundary if all cells adjacent to the moving face zone are either wedges or hexahedra even though the cell zone may contain mixed cell shapes. The cell layers must be completely bounded by one-sided face zones, except when the sliding interface is used.  

3. Remeshing Methods: 

When the boundary displacement is large compared to the local cell sizes, the cell quality can deteriorate or the cell can become degenerate if only mesh smoothing is used.  This will invalidate the mesh (for example, result in negative cell volume).

To circumvent this problem, ANSYS Fluent agglomerates(collect into a grp) cells that violate the skewness or size criteria and locally remeshes the agglomerated faces or cells. If the new cells or faces satisfy the skewness criterion, the mesh is locally updated with the new cells. Otherwise, the new cells are discarded and the old ones retained.     

Example of dynamic mesh:

 Piston moving inside an engine cylinder, Gearbox, Flexible artery wall responding to the pressure pulse from the heart.

UDF(user defined function):

A UDF is a function provided by the user of a program or environment, in a context where the usual assumption is that functions are built into the program or environment.

                          or

A  UDF is a function that you program that can be dynamically loaded with the ANSYS FLUENT solver to enhance the standard features of the code. These UDFs are written in the c programming language. At the beginning of the UDF file, we can find udf.h(#include "udf.h") of the source code file, which allows definitions for define macros and other functions to be included during the process. 

The UDF used in this project is shown below:

#include "udf.h"

DEFINE_CG_MOTION(right_motion, dt, vel, omega, time, dtime)
{
	vel[0] = 0.0;
	vel[1] = 0.0;
	vel[2] = 0.0;

	omega[0] = 0.0;
	omega[1] = 0.0;
	omega[2] = 2.0e2; /* [rad/s]*/
}
DEFINE_CG_MOTION(left_motion, dt, vel, omega, time, dtime)
{
	vel[0] = 0.0;
	vel[1] = 0.0;
	vel[2] = 0.0;

	omega[0] = 0.0;
	omega[1] = 0.0;
	omega[2] = -2.0e2; /* [rad/s]*/
}

In the above UDF, two functions are defined. The first one belongs to the right gear and the second function belongs to the left gear. Both the gears rotate with a uniform angular velocity of 200 rad/s. 

Errors in the simulation:

1) 'Dynamic mesh failed' error: This error occurs due to the inappropriate setting of smoothing, meshing, and remeshing. In the below dynamic mesh figure only smoothing and remeshing are enable. Layering was disabled because the geometry was in 2D. 

2) 'Negative cell volume detected' error: This error occurs due to the distance moved by a cell per timestep is greater than the cell size in the dynamic region. This error can be resolved by changing the dynamic mesh settings which are shown in the 'Dynamic mesh fail' error.  

Conclusion:

The sloshing effect is less in the engine oil while compared with n-heptane. The reason for the highest sloshing effect is less viscosity and more immersion. The engine oil is having more viscosity than the n-heptane. And the engine oil with 30% immersion is more suitable for the gearbox among the above all cases.