Simulating Fluid Sloshing effect inside a Gear-box

Aim: - To perform and visualize the sloshing effect of lubricant in a Gear box Model.

Objective: -

1. To discuss the fluid Sloshing effect and its implication on the model.
2. To describe Dynamic meshing and its application along with use of UDF in the model.
3. To simulate the sloshing effect in the gear Box using Following fluids/lubricants –
4. 20% Immersion, Fluid - Engine oil.
5. 30% Immersion, Fluid- Engine oil.
6. 20% Immersion, Fluid-n-heptane (C₇H₁₆).
7. 30% Immersion, Fluid-n-heptane (C₇H₁₆).

Theory: -

Fluid Sloshing –

In fluid Dynamic, slosh refers to the movement of liquid inside another object. It is motion of fluid having free surface in partially filled objects such as lubricant in gear box/transmission drive, propellent in space crafts, Cargo slosh in ship and truck etc.

The motion of fluid in the closed body can interact with the shell and alter the system dynamics. Depending upon the condition it has both pro and cons. In lubrication purpose it helps in lubricating the inner body efficiently, while when transporting fluids such as oil and gas in containers, the sloshing effect adversely affects the balance of the vehicle.

Dynamic Meshing –

It means that the computational does not remains same but keeps on changing during the computations. It allows boundary to move from one cell zone to other. The boundary can move rigidly with respect to one another in translational or rotational motion.

There are three different Dynamic Mesh Method in ANSYS Fluent.

Mesh Methods:

• Smoothing – It is basically used to adjust the mesh the zone with a moving/deforming boundary, internal nodes of the mesh move but the number of nodes and their connectivity remains constant. Here the internal nodes absorb the movement of the boundary.

• Layering – It is used to split/merge the cells that are adjacent to any moving boundary. But it should satisfy the two conditions; 

1. All the cells adjacent to the moving face zones are either wedges or hexahedral even if the cell zone contain mixed cell shapes. 
2. The cell layers must be completely bounded by one-sided face zones, except when sliding interfaces are used.

• Remeshing – If the boundary displacement is large when compared to the local cell sizes, the cell quality can become degenerate if only the mesh smoothing is used. This will show in the negative cell volumes and consequently it will lead to the convergence problems when the solution is updated to the next time step.

Applications –

1. Moving of piston in cylinder
2. flaps on wings motion in Aerodynamic simulations.
3. Movement of Elastic wall of balloon or rubber.
4. Heart tissue wall during blood pump simulation.
5. Turbomachinery simulation, etc.

User Defined Function (UDF) –

A UDF is basically a C program or a C function that can be dynamically loaded with ANSYS FLUENT to enhance its standard features. It uses predefined macros and functions to access FLUENT solver data and to perform other tasks. These are executed as interpreted or compiled functions.

UDF can be used for a number of applications like:

1. Customize boundary conditions
2. Material property definitions
3. Adjust computed values on a once-per-iteration basis
4. Initialize with a previous solution
5. Execute at the end of an iteration
6. Upon exit from ANSYS FLUENT
7. Enhance post-processing

In this program we are using a UDF to simulate motion to both the gear having angular velocity 200 rad/s and clockwise/anti clockwise motion to respective gear.

Case Setup: -

Geometry –

Gearbox Model                                                                        Gearbox split view

Gearbox fluid volume                                                             Gearbox Fluid Volume split view

2-D view on the section Plane

Two regions are also created and their co-ordinate are used to Mark the region Of 20 % and 30 % o Total height respectively

Meshing –

Method – Triangles

Global mesh size = 1 mm           

Capturing proximity and curvature ON

Number of Node =   15992                                                Number of elements = 28506

Element Quality

Fluent setup

• Pressure based solver and Absolute velocity is used.
• Transient-state Calculation is performed.
• Gravity is enabled in negative Y axis.
• Dynamic Meshing is used in Domain Ribbon

• Two regions are created for 20 and 30 percent, so as to Patch it with lubricant in Adapt<

• A UDF is Compiled to give rotational motion To Gears. Following is the Code for UDF

#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]*/

}

• Multiphase Model is turned on along with Volume of Fluid and number of Eulerian phases is chosen as 2 and Implicit scheme is selected.
• K-ɛ Realizable with Enhanced Wall function.
• Fluid Used:
  • Air: density = 1.225 kg/m³     Viscosity = 1.7894e-5 kg/m-s  
  • Engine Oil: density = 889 kg/m³     Viscosity = 1.06 kg/m-s
  • n-Heptane (C₇H₁₆): density = 684 kg/m³     Viscosity = 0.000409 kg/m-s                                                                                                                                 
• Hybrid Initialization is done and appropriate fluid is patched to desired region marked.
• Time step = .0001 of iteration = 1000   Max iteration/time step = 20

Results: -

Residue Plots –

Case 1:  20% Immersion, Fluid - Engine oil.                                           Case 2:  30% Immersion, Fluid - Engine oil.

Case 3:  20% Immersion, Fluid - n-Heptane (C₇H₁₆).                                          Case 4:  30% Immersion, Fluid - n-Heptane (C₇H₁₆).

Animations:

Case 1:  20% Immersion, Fluid - Engine oil.

 <iframe src="https://www.youtube.com/embed/3xzZZPw4jYA?enablejsapi=1&origin=https://skill-lync.com" allowfullscreen="allowfullscreen"></iframe>

Case 2:  30% Immersion, Fluid - Engine oil.

<iframe src="https://www.youtube.com/embed/JimYSwMVcBU?enablejsapi=1&origin=https://skill-lync.com" allowfullscreen="allowfullscreen"></iframe> 

Case 3:  20% Immersion, Fluid- n-Heptane (C₇H₁₆).

 <iframe src="https://www.youtube.com/embed/_pPrOjbktyc?enablejsapi=1&origin=https://skill-lync.com" allowfullscreen="allowfullscreen"></iframe>

Case 4:  30% Immersion, Fluid - n-Heptane (C₇H₁₆).

 <iframe src="https://www.youtube.com/embed/noXE3kE0MOM?enablejsapi=1&origin=https://skill-lync.com" allowfullscreen="allowfullscreen"></iframe>

Conclusion: -

• 30 % immersion by both the fluid provide sufficient lubrication.
• n-Heptane 30 % immersion provides higher sloshing effect due to low viscosity.
• n-Heptane 30 % immersion give better lubrication due to low density hence remains in contact to tooth better as compared to engine oil which is on the inner walls of housing.
• Sloshing effect only up to a limit is required, above it can reduce its concentration at point of impact.

Error Occurred during Simulation

Dynamic meshing failed: Negative cell volume –

Error encounter due to few missing edges of gear in named selection. The negative cell volume error is displayed when the mesh has been updated in a way to cause a negative cell volume. Factors for causing this error are overlapping nodes and significant mesh motion (relative to cell size) per time step.

Proper selection of edges and giving proper values for maximum length, minimum length and skewness factor in Remeshing (Dynamic Mesh Method) decreases the chance of error.