# Effects of Nanoparticle Enhanced Lubricant Films in Thermal Design of Plain Journal Bearings at High Reynolds Numbers

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## Abstract

**:**

_{2}nanoparticle with different volume fraction percentages are used. The parameters that are changed to evaluate the performance of the bearing include volume fraction percentage of the nanoparticle, type of lubricant, and rotational speed. Based on the results, for all different lubricant types, the dissipation power, average shear stress, and temperature rise are increased with augmenting the rotational speed. By increasing the rotational speed from 500 to 1500 rpm, the average shear stress increases by more than 100%, 120%, and 130% for DTE 26, DTE 25, and DTE 24 lubricant types, respectively. Moreover, by increasing the rotational speed from 500 to 1500 rpm, the dissipation power, and temperature rise are increased around 600% and 800%, respectively. Furthermore, increasing nanoparticles volume fraction from 0% to 10%, increases all parameters by approximately 10% for all lubricant types and in all rotational speeds.

## 1. Introduction

_{2}, Al

_{2}O

_{3}, CuO, etc. can significantly influence several aspects of journal bearing performance such as thermodynamic characteristics and tribological performance [20].

_{2}. For evaluating the performance of this lubricant, different types of oils including DTE 24, DTE 25, and DTE 26 are considered. Moreover, the nanoparticle volume fractions of 0%, 5%, and 10% and rotational speeds of 500, 1000, and 1500 rev/min are examined to study the behavior of nanoparticle additive to the lubricant.

## 2. Mathematical Problem

#### 2.1. Governing Equations

#### 2.2. Lubricant Film Thickness in Bearings

#### 2.3. Reynolds Equation

_{i}, y

_{j}) on the meshed domain of the problem as shown in Figure 3; N

_{x}and N

_{y}are the number of sampling points in the x and y directions of the field variable domain. Assuming the viscosity of the lubricant fluid to be varied in Equation (4) and re-applying the rules of the GDQ method, the following equation is derived to extract the values of thermal pressure created at different points of the lubricant fluid film:

#### 2.4. Thermophysical Properties

#### 2.5. Energy Equation

## 3. Numerical Algorithm

## 4. Results and Discussions

_{2}is added to enhance the performance of the lubricant.

_{2}) volume fraction percentage and lubricant types. As DTE 26 lubricant has higher viscosity compared to the other two lubricants, the average shear stress for this lubricant is much higher. It is clearly observed that the average shear stress has a monotonic increasing trend in all cases. Moreover, the increasing trend is a linear function of rotational speed increments. It can be observed that for all different lubricant types, the rotational speed has a direct relationship with the increase of average shear stress. By increasing the rotational speed from 500 to 1500 rpm, the average shear stress increases by more than 100% for the DTE 26 lubricant type. This criteria is even higher for other lubricant types indicating slightly more than 120% and 130% increment for DTE 25 and DTE 24 lubricant types, respectively. Despite showing different values, increasing nanoparticles increases the average shear rate by approximately 10% for all cases. That is clearly observed since at higher nanoparticle volume fractions, the inter-particle interactions result in higher shear stress values.

_{2}) volume fraction percentage and lubricant types. The dissipation power also increases monotonically with the increment of rotational speed, but it shows an exponential trend in contrast to that of average shear stress. Similar to the previous figure, the rotational speed has a direct increasing relationship with the dissipation power. The increase rate is found to be much higher than that of the average shear stress showing an increase in the order of approximately 600% from 500 to 1500 rpm for the DTE 26 lubricant type. The increase rate is almost similar for different lubricant types, in contrast to what is observed for the average shear stress. Similar to what is observed in Figure 10, increasing nanoparticles volume fraction increases the average shear rate by approximately 10% for all lubricant types and in all rotational speeds.

_{2}) volume fraction percentage and lubricant types are shown in Figure 12. This figure shows an exponential trend for the increase of temperature as the rotational speed increases. This can be quantified by approximately 800% factor of increase from 500 to 1500 rpm for the DTE 26 lubricant type. The increase rate is almost similar for different lubricant types, in contrast to what is observed for the average shear stress.

## 5. Conclusions

- Temperature on the bearing surface increases monotonically along the z coordinate under specific loading.
- Maximum and minimum pressure on the bearing surface under specific loading is occurred at the middle cylinder. Moreover, these maximum and minimum pressure points are adjacent to each other.
- Distribution of velocity vectors under specific loading is uniform both in magnitude and direction while the rotation is on the counter clock-wise direction.
- Total gap height between the bearing and journal surface is constant along the z coordinate for a specific position on the cylindrical coordinate due to uniform distribution of specific load.
- For all different lubricant types, the rotational speed has a direct relationship with the increase of the average shear stress. By increasing the rotational speed from 500 to 1500 rpm, the average shear stress increases by more than 100%, 120%, and 130% for DTE 26, DTE 25, and DTE 24 lubricant types, respectively. Increasing nanoparticles enhances the average shear rate by approximately 10% for all cases.
- Dissipation power increases with the rotational speed. By increasing the rotational speed from 500 to 1500 rpm, average shear stress increases around 600% for all lubricant types. Increasing nanoparticles volume fraction increases the average shear rate by approximately 10% for all lubricant types and in all rotational speeds.
- By increasing the rotational speed from 500 to 1500 rpm, the temperature rise increases around 800% for almost all lubricant types.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

R | Journal radius, $m$ | ${N}_{x}$ | Number of sampling points in the x direction |

t | Solid thickness, $\mathrm{m}$ | ${N}_{y}$ | Number of sampling points in the y direction |

H | Journal height, $\mathrm{m}$ | $Q$ | Flow rate, ${\mathrm{m}}^{3}{\mathrm{s}}^{-1}$ |

c | Clearance between the journal and the bearing, $\mathrm{m}$ | ${u}_{s}$ | Slip velocity, ${\mathrm{m}\mathrm{s}}^{-1}$ |

$\phi $ | Nanoparticle volume fraction | $\lambda $ | Thermal conductivity, ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ |

$V$ | Fluid velocity vector, ${\mathrm{m}\mathrm{s}}^{-1}$ | $\nu $ | Kinematic viscosity, $\mathrm{cSt}$ |

$P$ | Pressure, $\mathrm{Pa}$ | $T$ | Temperature, K |

$\mu $ | Dynamic viscosity, ${\mathrm{kg}\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$ | $\tau $ | Viscous stress tensor, $\mathrm{Pa}$ |

$h$ | Gap function, $\mathrm{m}$ | ${a}_{conv}$ | Convection coefficient, ${\mathrm{Wm}}^{-2}{\mathrm{K}}^{-1}$ |

${C}_{m}$ | Minimum radial clearance | ${T}_{amb}$ | Ambient temperature, K |

${X}_{j}$ | Position of the journal center in the static equilibrium state | Subscripts | |

${Y}_{j}$ | Position of the journal center in the static equilibrium state | $b$ | Base fluid |

${C}_{P}$ | Specific heat capacity, ${\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ | $sn$ | Solid nanoparticles, |

$\omega $ | Rotor angular velocity, ${\mathrm{rad}\mathrm{s}}^{-1}$ | $f$ | Fluid (oil) |

$U$ | Linear velocity of the rigid rotor, ${\mathrm{m}\mathrm{s}}^{-1}$ | s | Solid (pad and rotor) |

${A}_{i,k}^{\left(1\right)}$ | Weight coefficients matrices for the first-order derivatives of the pressure distribution | $feed$ | Feeding oil |

${B}_{j,l}^{\left(1\right)}$ | Weight coefficients matrices for the first-order derivatives of the pressure distribution | $ir$ | Inner bearing surface |

${A}_{i,k}^{\left(2\right)}$ | Second-order weight coefficients matrices for the pressure distribution | $or$ | Outer bearing surface |

${B}_{j,l}^{\left(2\right)}$ | Second-order weight coefficients matrices for the pressure distribution | $ex$ | Outflow bearing surface |

$\rho $ | Density, ${\mathrm{kg}\mathrm{m}}^{-3}$ | $dr$ | Outer radius of the groove region |

${C}_{P}$ | Specific heat capacity, ${\mathrm{J}\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ | $in$ | Inlet |

$b$ | Slip length, $m$ | $cr$ | Critical |

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**Figure 1.**(

**a**) Computational domain of oil film and (

**b**) schematic of bearing, journal, and lubricant.

**Figure 3.**The position of sample nodes on the problem domain in order to determine the temperature and pressure distribution at different points of the lubricant film.

**Figure 6.**Fluid temperature in degree Celsius versus spatial position on the bearing surface for the test-case under 7 kN specific loading, rotating at 1500 rpm with 10% of nanoparticle volume fraction in DTE 26.

**Figure 7.**Pressure contours on the (

**a**) cylindrical view and (

**b**) extended two-dimensional (2D) planar view on the bearing surface for the test-case under 7 kN specific loading, rotating at 1500 rpm with 10% of nanoparticle volume fraction in DTE 26.

**Figure 8.**Velocity vectors on the bearing surface for the test-case under 7 kN specific loading, rotating at 1500 rpm with 10% of nanoparticle volume fraction in DTE 26.

**Figure 9.**Total gap height in micrometers between the bearing and journal surface for the test-case under 7 kN specific loading, rotating at 1500 rpm with 10% of nanoparticle volume fraction in DTE 26.

**Figure 10.**Variation in average shear stress as a function of rotational speed for different nanoparticle (TiO

_{2}) volume fraction percentage and lubricant types; the test-case is simulated under 7 kN specific load.

**Figure 11.**Variation in dissipation power in kW as a function of rotational speed for different nanoparticle (TiO

_{2}) volume fraction percentage and lubricant types; the test-case is simulated under 7 kN specific load.

Parameter | Value | Unit | Description |
---|---|---|---|

Number of pads | 6 | - | Number of pads |

R | 0.03 | M | Journal radius |

T | 0.051 | M | Solid thickness |

H | 0.05 | M | Journal height |

c | 0.00003 | M | Clearance between the journal and the bearing |

Lubricant | $\rho \left(kg/{m}^{3}\right)$ | 855 |

${\lambda}_{f}\left(\frac{W}{mK}\right)$ | 0.13 | |

${\mathrm{C}}_{Pf}\left(\frac{J}{kgK}\right)$ | 2035 | |

Solid | ${\rho}_{s}\left(kg/{m}^{3}\right)$ | 7800 |

${\lambda}_{s}\left(\frac{W}{mK}\right)$ | 47 | |

${\mathrm{C}}_{Ps}\left(\frac{J}{kgK}\right)$ | 434 |

Domain | Position | Boundary Condition |
---|---|---|

Pad | ||

Top (Fluid-Solid interface) | Continuity of heat flux and temperature | |

Bottom/ Outer surface/ Inner surface | $\left\{\begin{array}{c}{a}_{conv}=100\frac{W}{{m}^{2}K}\\ {T}_{feed}=50\xb0C\\ {Q}_{feed}=0.00025{m}^{3}/s\end{array}\right.$ | |

Inlet Side/Outlet Side | Adiabatic | |

Fluid | ||

Inlet/Inner side | Zero relative pressure, $\frac{\partial V}{\partial n}=\frac{\partial T}{\partial n}=0$ | |

Outer side/Outlet | Zero relative pressure, $\frac{\partial V}{\partial n}=\frac{\partial T}{\partial n}=0$ |

**Table 4.**Different mesh resolution and correspondence relative error percentage with respect to exact solution.

Mesh Resolution | Number of Elements | Relative Percent Error in Pressure Calculation |
---|---|---|

Coarser | 64 | 183.22 |

Coarse | 276 | 78.4 |

Normal | 812 | 18.66 |

Fine | 1180 | 2.17 |

Finer | 5724 | 0.53 |

Extremely fine (Exact) | 16,212 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Abdollahzadeh Jamalabadi, M.Y.; Alamian, R.; Yan, W.-M.; Li, L.K.B.; Leveneur, S.; Safdari Shadloo, M.
Effects of Nanoparticle Enhanced Lubricant Films in Thermal Design of Plain Journal Bearings at High Reynolds Numbers. *Symmetry* **2019**, *11*, 1353.
https://doi.org/10.3390/sym11111353

**AMA Style**

Abdollahzadeh Jamalabadi MY, Alamian R, Yan W-M, Li LKB, Leveneur S, Safdari Shadloo M.
Effects of Nanoparticle Enhanced Lubricant Films in Thermal Design of Plain Journal Bearings at High Reynolds Numbers. *Symmetry*. 2019; 11(11):1353.
https://doi.org/10.3390/sym11111353

**Chicago/Turabian Style**

Abdollahzadeh Jamalabadi, Mohammad Yaghoub, Rezvan Alamian, Wei-Mon Yan, Larry K. B. Li, Sébastien Leveneur, and Mostafa Safdari Shadloo.
2019. "Effects of Nanoparticle Enhanced Lubricant Films in Thermal Design of Plain Journal Bearings at High Reynolds Numbers" *Symmetry* 11, no. 11: 1353.
https://doi.org/10.3390/sym11111353