COMPUTATIONAL FLUID DYNAMIC ANALYSIS OF SLOSHING EFFECT OF LUBRICANT INSIDE GEARBOX CASING USING VOLUME OF FLUID APPROACH.

PROJECT TITLE : COMPUTATIONAL FLUID DYNAMIC ANALYSIS OF SLOSHING EFFECT OF LUBRICANT INSIDE GEARBOX CASING USING VOLUME OF FLUID APPROACH.

OBJECTIVE AND AIM :

Cases to be solved:-

1. 20% Immersion, Fluid - Engine oil

2. 30 % Immersion, Fluid - Engine oil

3. 20% Immersion, Fluid - n-heptane-liquid(c7h16)

4. 30 % Immersion, Fluid - n-heptane-liquid(c7h16)

Running all the cases for the same simulation time.

1. What is dynamic meshing and where the dynamic meshing is useful? Give other examples and describe the advantage and disadvantages of dynamic meshing.

2. What is sloshing and explain whether the sloshing effect is good or bad for any applications?

3. What is UDF? Explain the usage of UDF.

INTRODUCTION : Like other types of rotating equipment, gearboxes rely on lubrication to reduce friction and provide cooling for optimal operation and life. Gearbox manufacturers provide recommendations for the type of lubrication to be used and the typical lubrication intervals, but the actual gearbox lubrication requirements depend on the environmental conditions the gearbox is exposed to, whether it is properly maintained, and whether it experiences overloading.

There are several methods for lubricating a gearbox, with the most common being grease lubrication, oil splash, and forced oil.

Grease lubricationis suitable for low-speed operation, but it provides less cooling than oil, and is not recommended for continuous-duty or heavily loaded applications, even at low speeds. With any lubrication, using the proper quantity of lubricant is important, and this is especially critical with grease. Using too little lubrication prevents an adequate lubrication film from forming, but too much lubrication – especially grease – adds viscous drag and results in power loss.

Oil splash lubrication is often used for helical, spur and bevel gearboxes. This method is also referred to as an oil bath, because it uses a reservoir is filled (or partially filled) with oil. As the gears rotate, they dip into this oil bath and splash the oil onto the other gears and bearings. But if the gear teeth are fully submerged, a condition known as “churning” occurs.

Essentially, churning is when the gears or bearings must work harder to “push through” the lubricant. A good analogy is walking along the edge of the water at the beach. Walking through ankle-deep water is relatively easy, but if you move to knee-deep water, walking requires much more effort.

The effectiveness of oil splash lubrication is heavily dependent on the speed of the gears. A common rule of thumb is that a tangential speed of at least 3 m/s is required in order for splash lubrication to be effective.

Forced oil lubrication is preferred for high-speed applications, and includes methods such as oil mist, oil spray, and oil drop. In the oil mist method, oil is atomized so that it saturates all areas of the gears and other internal components. In contrast, the oil spray method applies oil lubricant directly to the gears and other components, but this method is not always effective, as high centrifugal forces affect the direction of the oil spray.

The oil drop method pumps, or “drops,” oil directly onto the surfaces where it’s needed. A pump takes lubrication from a reservoir and delivers it to the gears and/or bearings via an internal piping system. This method can often be found in conjunction with the splash (aka oil bath) method, where some components may be difficult to reach via oil splash.

Regardless of the lubrication method used, the right type of lubrication is critical to gearbox performance. And of the parameters involved in selecting a lubricant, viscosity is the most important.

A lubricant with a viscosity that is too high for the application (i.e. the lubricant is too “thick”) won’t flow sufficiently as the gear teeth engage to protect mating surfaces and provide cooling. But lubrication with a viscosity that’s too low won’t provide a sufficient film thickness to prevent metal-to-metal contact between the mating surfaces.

Hence, sloshing can be described as the movement of a fluid contained inside another object(which may or may not be moving). Such motions are characterized by "interial waves" and plays significant role in some phenomena. Extensive mathematical and empirical relationships have been derived to describe liquid slosh. These types of analyses are typically undertaken using CFD and to solve the fluid-solid interaction problem.

Sloshing in road tank vehicles

Liquid sloshing strongly influences the directional dynamics and safety performance of highway tank vehicles in a highly adverse manner. Hydrodynamic forces and moments arising from liquid cargo oscillations in the tank under steering and/or braking maneuvers reduce the stability limit and controllability of partially-filled tank vehicles. Anti-slosh devices such as baffles are widely used in order to limit the adverse liquid slosh effect on directional performance and stability of the tank vehicles.

Sloshing of water in oceans can cause the ship some instability.

Sloshing or shifting cargo, water balalst, or other liquid (e.g., from leaks or fire fighting) can cause disastrous capsizing in ships due to free surface effect; this can also affect trucks and aircraft.

From perspective of gear box lubrication, sloshing becomes important because it is responsible for lubrication of oil over entire volume of the gear box. If there is no sloshing then the efficiency of the gear lubrication will decrease.

Considering the fact that, working of the gears inside the gearbox mainly depends upon the kind of lubrication they receive, it becomes very important to know how the fluid interacts with the gears while they are in motion. This is very challenging because to replicate this problem in ANSYS Fluent, the mesh needs to be dynamic. The CFD model will then might help us to optimize the gear lubrication so that they work in a more efficient way and lasts long.

The 2D CAD Model:

This model is meshed with 0.003m size elements. Capture Proximity option is turned on to capture small regions and mesh them. The method employed is All Triangles method to make the mesh less stiffer. As it would be with the structural elements(quads) .

The aspect ratio, skewness and the orthogonal quality for the mesh are shown below which are in good agreement for a well defined mesh:

All the edges of the left gears are selected(279) and named as left gear and the same is done with the right gear so that it becomes easy to implement the user defined function.

ANSYS Fluent 19.3(academic version) is used to computationally solve this problem. A User Defined Function or UDF is used to rotate both the gears. The command is written in C++ format. A compiled function is selected to open the command file and then the library is built and loaded in Fluent. In order to load and build the library in Fluent, the Workbench shortcut and the C++ 64 bit command prompt shortcut are kept in one folder. Workbench is opened from within there.

USER DEFINED FUNCTION:

A user-defined function, or 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. For example, you can use a UDF to define your own boundary conditions, material properties, and source terms for your flow regime, as well as specify customized model parameters (e.g., DPM, multiphase models), initialize a solution, or enhance postprocessing.

UDFs are written in the C programming language using any text editor and the source code file is saved with a .c extension (e.g., myudf.c). One source file can contain a single UDF or multiple UDFs, and you can define multiple source files.

UDF can be used for implementing expressions like variable density or velocity boundary condition inlet as a function of length, etctera. This allows the user to define the input variables according to their need and requirement and not what is provided by ANSYS. Any external or internal source term can be implemented using UDF. One can add new material modeling as per the necessity,like,visco-elastic modeling. This becomes very handy in industrial usage and research fields.

Here in this project I have used a UDF to implement the rotary motion of the gears.

#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]*/
}

The code which is shown above provides rotation to the gears. This code used a header file "udf" where the functions shown above are already defined. This function is used to rotate a dynamic zone with respect to the CG of that zone. It takes six arguments.

First argument is the name of the udf.

Second argument is a pointer.

Third argument is the linear velocity.

Fourth argument is the angular velocity.

Fifth and sixth arguments are time and time step respectively which are not defined in this particular problem.

0 1 2 defines the x y and z co-ordinates of the axes.

The linear velocity is zero in all the directions for both the gears.The geometry is in the x-y plane,hence, omega is given in the z direction. The value of omega is 200 radian/second and it is positive for one gear and, to make rotation possible, negative for the other gear.

Details of the Numerical Methodology:

Transient solver to see how the fluid-gear interaction changes as a function of time.

Pressure based with Absolute velocity formulation.

Gravity - Enabled

Turbulence Model -

K-epsilon method

Standard

Standard Wall Treatment

Multiphase Model - Volume of Fluid(Implicit Method) with Implicit body force formulation.

Fluid materials - Engine oil and n-heptane liquid

Dynamic Meshing -

Smoothing and Remeshing as the mesh methods.

Spring/laplace/Boundary layer type of smoothing.

Other mesh settings:

The solid zones(left and right gears) are assigned to the UDF function. Both the gears are rigid and their centres are allocated by putting the corresponding x and y co-ordinates.

Once, this is done, new cells are registered to make sure that the fluid is fillled to a certain height from the gearbox bottom. The co-ordinates of the new regions are given as shown below and saved.

The immersion height is calculated based upon the total height of the casing from the base. Total height - 135mm

20% immersion - 27mm from base

30% immersion - 40.5mm from base

20% immersion

30% immersion

A Hybrid Initialization is used and the new region marked is patched with water.

The simulation is made to run for 0.1s of flow time in which the gears have rotated 3 full rotations since, it takes 0.03s approximately to complete one full rotation base on the angular velocity alloted to them.

Time step size as 1e-4.

DYNAMIC MESHING:

This meshing interface allows to model those phenomena where the boundary move relative to another boundary in that zone. Since, there is relative movement, we cannot go with the usual rigid mesh because it wont be able to capture the ongoing phenomena and the results will be garbage. Hence, dynamic meshing is adopted. These phenomena include gear motion, turbomachines, vortex shedding(oscillation of the parent body),etctera.

The mesh can either be a rigid mesh or a deformable mesh. The cell domains are updated with respect to time. 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. The new position of the cells depends upon the updated position of the boundaries after every time step.

Best example which highlights the need for dynamic meshing is the blood flow in artery, where your artery wall is flexible. To get the reaction of artery wall on blood flow by giving some flexibility to it. We need dynamic meshing where meshing parameters changes with time depending on the flow behaviour.

The dynamic meshing with its advatages is computationally costly as the mesh is redefined after every time step. Also, the modeling is complex. When the geometry under consideration is itself complex then applying dynamic meshing becomes a challenge.

RESULTS:

Residuals plot for 20% Immersion for Engine Oil:

Animation :

Residuals plot for 20% Immersion for n heptane liquid:

Animation :

Residuals plot for 30% Immersion for Engine Oil:

Animation :

Residuals plot for 30% Immersion for n heptane liquid:

Animation :

CONCLUSION

• After observing the sloshing effect produced by gear motion, we can clearly see that 30% immersion gives more effective sloshing effect reaching every gear teeth.
• Now, taking into consideration any of the immersion rate, the engine oil takes more time to come back to the base via casing walls as compared to n-heptane liquid. This can be validated by the fact that engine oil is much more denser than the n-heptane liquid. Its viscosity is also higher than that of n-heptane liquid.
• The combined effects of these two factors might also lead to drag production on the gears while they are in motion causing loss in transmission power. Hence, engine oil should not be preferred as a lubricant.
• The other factors that must be kept in mind while lubricant selection is heat dissipative capacity, mobility, thermal resistance,etc.