TRANSIENT SIMULATION OF FLUID SLOSHING EFFECT INSIDE A GEARBOX BY VARYING LUBRICATING FLUID AND GEAR IMMERSION LEVELS

TRANSIENT SIMULATION OF FLUID SLOSHING EFFECT INSIDE A GEARBOX BY VARYING LUBRICATING FLUID AND GEAR IMMERSION LEVELS USING ANSYS FLUENT

1. AIM

Our aim is to simulate Fluid Sloshing Effect inside a Gearbox by varying lubricating fluids and gear immersion levels using ANSYS FLUENT.

2. THEORY/EQUATIONS/FORMULAE USED

Mesh Generation   

The flow domain is discretized into a mesh. The mesh generation involves defining the structure and topology and then generating a mesh on that topology. Currently all cases involve multi – block, structure mesh, however, the Mesh blocks may be abutting, contiguous, non – contiguous and overlapping. The Mesh should exhibit some minimal Mesh quality as defined by measures of orthogonality (especially at the boundaries), relative Mesh spacing (15% to 20% stretching is considered a maximum value), Mesh skewness, etc. Further the maximum spacing should be consistent with the desired resolution of important features.

Dynamic Meshing

As the name suggests, the computational mesh will not be the same instead it can change during computation. The dynamic mesh is used to simulate problems with boundary motion. As per the problem, both the gear teeth are in motion and are defined by UDF.

There are three schemes for dynamic meshing in ANSYS Fluent, namely, smoothing, layering, and Re-meshing. These schemes are used individually or in combination as per the requirement of the problem. Dynamic meshing is used in problems such as check valves, store separations, etc.  

Dynamic meshing consists of three steps: determining the dynamic mesh method, specifying modes with mesh methods, and defining the meshing zones. Smoothing and Re-meshing schemes are used for our problem. These schemes provide instant mesh deformation capabilities.

Common Errors that occurs in this Simulation

1. Dynamic Mesh Failed
2. Negative Cell Volume Detected

These errors occur when the displacement/ motion of boundaries per time step are large compared to the local cell size due to which the quality of cell reduces and dynamic mesh fails. It produces the negative cell volume error, known as non-physical cell.  Negative Volume may also occur due to overlapping of nodes.  

So, Re-meshing settings are done in order to maintain the quality of mesh such as skewness by manually defining the maximum and minimum length scale. The defined parameters are taken as upper and lower limits of cell size as the mesh is more sensitive in our problem due to the gear motion.

Fluid Sloshing Effect

The fluid slosh means the irregular movement of fluid inside a container with a splashing sound. The fluid is partially filled in the container for the slosh to happen. The slosh is caused due to disturbances to the fluid. Depending on the type of fluid of disturbance and container shape the fluid experiences different types of motion such as rotational, planar, non-planar, periodic, chaotic, etc.

Examples of fluid sloshing are fuel in a tank, coffee in a mug, etc. The fluid sloshing effects have negative impact as it affects the stability and performance of the containers. It can cause deformation, spillage in case of open containers.

Sloshing effect normally involves the hydrodynamic pressure (gravity), forces, moments, natural frequency, etc. of the free liquid surface. But for our problem we are looking the lubrication efficiency i.e., whether the liquid is moving along the gears and the covering all the teeth’s.  

Use of User Defined Functions (UDF)

Certain functions which are already present may not be always useful for our problem. So the user can provide a function as per the requirement. It is done using any programing language. For our problem the angular velocity of left and right gear in clockwise and anti-clockwise direction are defined respectively. 

Problem – Fluid Sloshing Effect

Transient state simulation of Fluid Sloshing Effect inside a Gearbox by varying lubricating fluids and gear immersion levels to study the lubrication efficiency of gear teeth’s using dynamic mesh. Also the gear motion is defined by a UDF.  

Calculation - Transient Flow Simulation

UDF for Gear Motion

Angular Velocity, ω - 200 rad/s

                                                     ω = 2πN/60, where N = Number of rotation per minute

                                                                                 N = 1910.83 rpm

So number of rotations per second = 31.83. Therefore, for one rotation it takes 0.03 sec.

It’s computationally expensive to compute all 1910.83 rotations, so due to limited computational power the computation is done for 1 sec.

                                              For 1 sec, Time step = 0.0001 & Total number of time steps = 1000

We can achieve more than 3 rotations.      

Fluids chosen for the problem – Engine Oil, n-heptane (c7h16)

Gear Teeth Immersion Levels

    3. PROCEDURE

• In the process, firstly the 2D flow domain is created from the available 3D Geometry in SpaceClaim by extracting the fluid volume and splitting the body.
• Surface Meshing is done and all the boundaries are named respectively. Also checked the mesh quality is good enough to carry out the simulation.
• Material, solver type, the initial and boundary condition, suitable turbulence model are defined as per the problem.
• The User Defined Function (UDF) is loaded to define angular velocity of both left and right gear motion and the dynamic mesh settings are done.
• In the current problem 4 cases are defined by varying the fluid material and the gear teeth immersion levels.
• Contour for phases with volume fraction of engine oil and n-heptane on the flow domain is initiated in order to visualize the lubricating efficiency. Finally the animation is also added to study the overall behavior after the simulation is converged.

   4. NUMERICAL ANALYSIS (Software used – ANSYS 2018 R1)

• Geometric Model

The 3D geometry of Gearbox is shown in the figure given below.

3D Geometry of flow domain

2D flow domain

• Mesh 

                                                                                              Fig: Baseline Surface Mesh

                                                                                                          Fig: Element Quality

• Solver Set-up

1. The mesh file is imported into the FLUENT software for the analysis of the modeled surface.
2. Once the mesh file is loaded and displayed, it is checked for the units, scale, and mesh.
3. There are two types of numerical solver methods pressure –based and density-based solver. The pressure based solver was used rather than the density based solver as the simulation is for lower Mach number. Absolute velocity formulation, Transient state was used for the analysis as only then the evolution of the flow can be visualized and understand how the lubrication efficiency is achieved at the end.
4. Gravity is checked on with -9.81 on the Y-axis as fluids are under the gravitational pull.

    5. Energy equation was switched off for the analysis as we are not interested in temperature of the system.

    6. K-epsilon turbulence model was used for the analysis with enhanced wall treatment.

    7. The fluid material chosen are Engine Oil, n-heptane c7h16.

    8. Multiphase Model chosen – Volume of Fluid with 2 numbers of Eulerian Phases and Implicit formulations for Volume Fraction parameters.

    9. Phases need to be specified into primary phase as air and secondary phase as engine Oil & n-heptane c7h16 respectively.

    10. User Defined Function (UDF) is loaded to define angular velocity of both left and right gear motion.

     11. Re-meshing settings are done in order to maintain the quality of mesh such as skewness as 0.7 by defining the maximum and minimum length scale. The defined parameters are taken as upper and lower limits for mesh at every iteration.   

    12. The cells are marked by defining the coordinates of Quad for setting the 20 and 30 percent immersion levels.     

    13. Solution methods – SIMPLE Scheme used for Pressure-Velocity coupling and the methods for Spatial Discretization are as per the below image.

    14. Hybrid initialization is done and then zones are patched accordingly.

    15. Contour for phases with volume fraction of Engine Oil and n-heptane on the flow domain is initiated in order to visualize the lubrication of gear teeth during run time and also animations are added for every time-step.

    16. Run the iteration with appropriate time-step size and the number of time-steps.

     5. RESULTS

• CASE 1 - Engine Oil | 20% Gear Immersion | Time – 1 sec (More than 3 Rotations)
• Video Link - https://youtu.be/HEFovkaOo5o

• CASE 2 - Engine Oil | 30% Gear Immersion | Time – 1 sec (More than 3 Rotations)
• Video Link - https://youtu.be/RsalBYQXAQ4

• CASE 3 – n-heptane (c7h16) | 20% Gear Immersion | Time – 1 sec (More than 3 Rotations)
• Video Link - https://youtu.be/dIxHMvAayBM

• CASE 4 – n-heptane (c7h16) | 30% Gear Immersion | Time – 1 sec (More than 3 Rotations)
• Video Link - https://youtu.be/m0YrDVtoAQ4

    6. CONCLUSION

1. The transient state flow simulation of Fluid Sloshing Effect inside a Gearbox is carried out by varying lubricating fluids and gear immersion levels in all 4 cases.
2. In order to visualize such phenomena where we are interested to see how the fluids at different immersion levels travels and lubricates the gear teeth’s, transient state simulations is the best suited option.
3. Initially, the fluid is stagnant at the bottom then slowly rises and fills up the gear teeth’s as it starts moving.
4. We can observe that the fluids with 30% immersion level case is more effective in lubricating as it covers more number of gear teeth’s compared to 20% immersion level case.
5. The animation of all the cases shows that the engine oil is able to form a better/ stable lubrication layer onto the gear teeth’s compared to n-heptane.
6. Also the sloshing of n-heptane is more than the engine oil. This is mainly because of the viscosity of n-heptane being less than the engine oil.
7. Hence we can conclude that the Engine oil with 30% immersion levels is the best suited option for lubrication of gear teeth amongst all other cases.

    7. REFERENCES

1. https://cfd.ninja/ansys-fluent/ansys-fluent-dynamic-mesh/
2. https://www.semanticscholar.org/paper/ASSESSING-SLOSHING-EFFECT-OF-FLUID-IN-TANKER-OF-CAE-Chaudhari-Deshmukh/815e32e9da080113572747531f66e27d2ae8e96f
3. https://www.researchgate.net/profile/Ning-Qin 3/publication/252407768/figure/fig9/AS:392837226090520@1470671101509/Moving-mesh-around-main-foil-and-flaps.png
4. https://en.wikipedia.org/wiki/User-defined_function
5. https://www.cambridge.org/core/books/abs/liquid-sloshing-dynamics/introduction/28590DC3DDD1070D697C8E6024BC289F
6. https://www.matec-conferences.org/articles/matecconf/pdf/2017/21/matecconf_dyn2017_00069.pdf
7. https://www.mr-cfd.com/services/fluent-modules/dynamic-mesh/