**4. Results and discussions**

#### **4.1 Gaseous-phase area reproducibility**

#### *4.1.1 Under flooded lubrication conditions in the journal bearing*

In this study, four types of calculations were calculated to clarify the effects of vapor pressure and surface tension. Results of (i) analysis of the volume fraction *F* distribution of oil and (ii) experimental visualization under flooded lubrication conditions are depicted in **Figure 5**. The red color in **Figure 5(i)** indicates the phase of complete oil, whereas the blue color indicates that of complete gas. Further, the solid and dotted black lines perpendicular to the circumferential direction of the bearing indicate the maximum and the minimum clearance, respectively. The 0° means the position of the most upper part of the bearing and the oil-filler port of the bearing exists at this position. The black arrow means the rotational direction and, consequently, the main flow direction of lubrication oil is the same.

In this study, we have presented the results for the surface of the rotating shaft. Moreover, in **Figure 5(ii)** of the experimental result, the yellow areas represent the gaseous phase, and the remaining areas indicate the oil film. The conditions of these calculations and experiment are as shown below. The rotational speed was *n* = 3500 rpm. The volume of oil supply was *q* = 2.6 cm<sup>3</sup> /s, the eccentricity ratio *ε* = 0.54, and the attitude angle *ϕ* = 72.9°. These values are based on the experimental result.

In the case of VOF and VOF with surface tension as shown in **Figure 5(i-a, i-b)**, the volume fraction around the side end of the bearing decreases between 270° and 135°, and the volume fraction of the remaining area is approximately 1, which means complete oil. Around the oil-filler port, the volume fraction is most decreased. In the case of VOF with vapor pressure as depicted in **Figure 5(i-c)**, the volume fraction around the side end of the bearing slightly decreases between 300 and 100°. The range of the volume-fraction decrease in this case is smaller than that observed in the case of VOF alone or in the case of VOF with surface tension. On the other hand, in the case of VOF with vapor pressure and surface tension as shown in **Figure 5(i-d)**, the volume fraction around the bearing side end is approximately 1 between 300 and 0°. This tendency is quite different from other cases. Moreover, between 0 and 135°, the value of volume fraction decreases, and the decreased area which means the gaseous-phase area is wider than that of VOF with vapor pressure shown in **Figure 5(c-1)**. The tendency found in **Figure 5(i-d)** of the gaseous-phase area is also found in the experiment. Therefore, it is concluded that **Figure 5(i-d)** is in good agreement with the experiment compared with the other cases.

#### **Figure 5.**

*Comparison of calculation and experimental results under flooded lubrication conditions ([1] partially modified). (i) Calculation results and (ii) Experimental result.*

#### *4.1.2 Under starved lubrication conditions in the journal bearing*

The calculation results of oil volume fraction and experimental visualization result under starved lubrication conditions are depicted in **Figure 6**. Further, the volume of oil supply under this condition was *q* = 0.5 cm3 /s, the eccentricity ratio was *ε* = 0.76, and the attitude angle was *ϕ* = 71.5°.

between them, striped bands of oil are observed. Additionally, the volume of fraction in the vicinity of the bearing center between 0 and 120° is zero, and this range is observed to be the full air phase. From the above results, it is found that the

*Comparison of calculation and experimental results under starved lubrication conditions ([1] partially*

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil…*

*DOI: http://dx.doi.org/10.5772/intechopen.92421*

In the case of VOF with vapor pressure and surface tension as shown in **Figure 6(i-d)**, the tendency of the gaseous-phase area is in good agreement with that of the experiment shown in **Figure 6(ii)**. On the other hand, other calculation results which are shown in **Figure 6(i-a–c)** are very different from the experiment. The differences are more clear than the case of the flooded lubrication condition. Therefore, it is important to consider both vapor pressure and surface tension in the case of starved lubrication conditions especially. From these results, we were interested in the oil-film rupture shape at the end of the wedge side in the case of

**Figure 8** depicts the calculation and experimental visualization results of the oil-

film rupture under starved lubrication conditions. It is found that the volume fraction near the moving shaft surface is one, and the value is decreasing gradually as approaching the bearing surface in the case of VOF with vapor pressure, as shown in **Figure 8(i-a)**. This tendency is the same as the model of the Coyne and Elrod which define the gas–liquid boundary between the bearing gap. However, in this case, the strong fluctuation is found between the boundaries of the volume

gaseous phase changes before and behind of oil-filler port.

*modified). (i) Calculation results and (ii) Experimental result.*

starved lubrication conditions as shown in **Figure 7**.

fraction.

**201**

**Figure 6.**

From these results, it is found that the volume-fraction distribution and gaseous area under starved lubrication differ from the results under flooded lubrication. In the case of VOF, the volume fraction as shown in **Figure 6(i-a)** is one which means a complete oil phase at the minimum clearance of 180°, and the range of the decrease of volume fraction increases for the remaining ranges. In a wide range of around the side end of the bearing, the volume fraction decreases compared to that of the flooded lubrication conditions.

In **Figure 6(i-b)**, in the case of VOF with surface tension, a similar tendency is observed in the case of VOF. In contrast, from **Figure 6(i-c)**, the volume fraction increases at the side end of the opposite wedge side, and the volume fraction between 0 and 130° decreases at a greater rate than that observed in the cases of VOF and VOF with surface tension. Further, the volume fraction of the opposite wedge is observed to moderately decrease between 180 and 295°.

On the other hand, in the case of VOF with vapor pressure and surface tension shown in **Figure 6(i-d)**, the different tendency is observed. The volume fraction in the vicinity of bearing centerline and side end decreases from 270 to 0°, and

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil… DOI: http://dx.doi.org/10.5772/intechopen.92421*

#### **Figure 6.**

*4.1.2 Under starved lubrication conditions in the journal bearing*

volume of oil supply under this condition was *q* = 0.5 cm3

wedge is observed to moderately decrease between 180 and 295°.

was *ε* = 0.76, and the attitude angle was *ϕ* = 71.5°.

*modified). (i) Calculation results and (ii) Experimental result.*

*Computational Fluid Dynamics Simulations*

of the flooded lubrication conditions.

**Figure 5.**

**200**

The calculation results of oil volume fraction and experimental visualization result under starved lubrication conditions are depicted in **Figure 6**. Further, the

*Comparison of calculation and experimental results under flooded lubrication conditions ([1] partially*

From these results, it is found that the volume-fraction distribution and gaseous area under starved lubrication differ from the results under flooded lubrication. In the case of VOF, the volume fraction as shown in **Figure 6(i-a)** is one which means a complete oil phase at the minimum clearance of 180°, and the range of the decrease of volume fraction increases for the remaining ranges. In a wide range of around the side end of the bearing, the volume fraction decreases compared to that

In **Figure 6(i-b)**, in the case of VOF with surface tension, a similar tendency is observed in the case of VOF. In contrast, from **Figure 6(i-c)**, the volume fraction increases at the side end of the opposite wedge side, and the volume fraction between 0 and 130° decreases at a greater rate than that observed in the cases of VOF and VOF with surface tension. Further, the volume fraction of the opposite

On the other hand, in the case of VOF with vapor pressure and surface tension shown in **Figure 6(i-d)**, the different tendency is observed. The volume fraction in the vicinity of bearing centerline and side end decreases from 270 to 0°, and

/s, the eccentricity ratio

*Comparison of calculation and experimental results under starved lubrication conditions ([1] partially modified). (i) Calculation results and (ii) Experimental result.*

between them, striped bands of oil are observed. Additionally, the volume of fraction in the vicinity of the bearing center between 0 and 120° is zero, and this range is observed to be the full air phase. From the above results, it is found that the gaseous phase changes before and behind of oil-filler port.

In the case of VOF with vapor pressure and surface tension as shown in **Figure 6(i-d)**, the tendency of the gaseous-phase area is in good agreement with that of the experiment shown in **Figure 6(ii)**. On the other hand, other calculation results which are shown in **Figure 6(i-a–c)** are very different from the experiment. The differences are more clear than the case of the flooded lubrication condition. Therefore, it is important to consider both vapor pressure and surface tension in the case of starved lubrication conditions especially. From these results, we were interested in the oil-film rupture shape at the end of the wedge side in the case of starved lubrication conditions as shown in **Figure 7**.

**Figure 8** depicts the calculation and experimental visualization results of the oilfilm rupture under starved lubrication conditions. It is found that the volume fraction near the moving shaft surface is one, and the value is decreasing gradually as approaching the bearing surface in the case of VOF with vapor pressure, as shown in **Figure 8(i-a)**. This tendency is the same as the model of the Coyne and Elrod which define the gas–liquid boundary between the bearing gap. However, in this case, the strong fluctuation is found between the boundaries of the volume fraction.

**Figure 7.** *Oil-film rupture position.*

**Figure 8.**

*Calculation and experimental results of the oil-film rupture under starved lubrication [1]. (i) Comparison of calculations and (ii) Experimental visualization result.*

> conditions **Figure 9(b)**. **Figure 9(i)** indicates the calculation results in volume fraction, **Figure 9(ii)** indicates the calculation results in velocity distribution, and **Figure 9(iii)** indicates the experimental visualization results. These figures depict the view from the front. The dash-dotted lines indicate the surface of symmetry. From **Figure 9(i-a)**, under flooded condition, the oil phase is observed throughout the structure of the oil-filler port and the oil-supply groove. Furthermore, from

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil…*

*DOI: http://dx.doi.org/10.5772/intechopen.92421*

**Figure 9.**

**203**

*Results of inner flow on the oil-filler port [1].*

**Figure 9(ii-a)**, it is observed that the velocity vectors are directed from the

close to the experimental results under the flooded lubrication conditions.

entrance surface of the oil-filler port to the oil-supply groove and bearing clearance in strong momentum. Hence, it is considered to be a less gaseous phase in the bearing clearance under flooded conditions. Here, the comparison between the analytical and experimental visualization results shows that the obtained results are

On the other hand, under starved lubrication conditions as shown in **Figure 9(i-b)**, it is observed that the gaseous phase exists in the major area of the oil-filler port whereas the oil exists around the inlet of oil-filler port and at the upper center area of oil-supply groove. Further, from the velocity vector result of **Figure 9(i-b)**, it is found that the oil

In the case of VOF with vapor pressure and surface tension as shown in**Figure 8(i-b)**, a two-phase flow exhibits a similar tendency as that exhibited by VOF with vapor pressure shown in **Figure 8(i-a)**. However, the interface between the oil film and gaseous phase is smoothly curved with an increase in clearance. From these results, it is confirmed that our proposed 3D CFD calculation model considering the vapor and the surface tension can reproduce the oil-gas boundary and it is in good agreement with the experiment shown in **Figure 8(ii)**.

### **4.2 Inner flow difference on the oil-filler port**

From the abovementioned results, we focused on the inner state of the oil-filler port, because the gaseous area around the oil-filler port including the supply groove was large especially under the starved lubrication conditions.

**Figure 9** depicts the results at a cross section of the oil-filler port in the case of under flooded lubrication conditions of **Figure 9(a)** and under starved lubrication *The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil… DOI: http://dx.doi.org/10.5772/intechopen.92421*

**Figure 9.**

In the case of VOF with vapor pressure and surface tension as shown in**Figure 8(i-b)**,

*Calculation and experimental results of the oil-film rupture under starved lubrication [1]. (i) Comparison of*

From the abovementioned results, we focused on the inner state of the oil-filler port, because the gaseous area around the oil-filler port including the supply groove

**Figure 9** depicts the results at a cross section of the oil-filler port in the case of under flooded lubrication conditions of **Figure 9(a)** and under starved lubrication

a two-phase flow exhibits a similar tendency as that exhibited by VOF with vapor pressure shown in **Figure 8(i-a)**. However, the interface between the oil film and gaseous phase is smoothly curved with an increase in clearance. From these results, it is confirmed that our proposed 3D CFD calculation model considering the vapor and the surface tension can reproduce the oil-gas boundary and it is in good agreement with the

experiment shown in **Figure 8(ii)**.

**Figure 7.**

**Figure 8.**

**202**

*Oil-film rupture position.*

*Computational Fluid Dynamics Simulations*

**4.2 Inner flow difference on the oil-filler port**

*calculations and (ii) Experimental visualization result.*

was large especially under the starved lubrication conditions.

conditions **Figure 9(b)**. **Figure 9(i)** indicates the calculation results in volume fraction, **Figure 9(ii)** indicates the calculation results in velocity distribution, and **Figure 9(iii)** indicates the experimental visualization results. These figures depict the view from the front. The dash-dotted lines indicate the surface of symmetry.

From **Figure 9(i-a)**, under flooded condition, the oil phase is observed throughout the structure of the oil-filler port and the oil-supply groove. Furthermore, from **Figure 9(ii-a)**, it is observed that the velocity vectors are directed from the entrance surface of the oil-filler port to the oil-supply groove and bearing clearance in strong momentum. Hence, it is considered to be a less gaseous phase in the bearing clearance under flooded conditions. Here, the comparison between the analytical and experimental visualization results shows that the obtained results are close to the experimental results under the flooded lubrication conditions.

On the other hand, under starved lubrication conditions as shown in **Figure 9(i-b)**, it is observed that the gaseous phase exists in the major area of the oil-filler port whereas the oil exists around the inlet of oil-filler port and at the upper center area of oil-supply groove. Further, from the velocity vector result of **Figure 9(i-b)**, it is found that the oil flows from the top surface of the oil-filler port to the oil-supply groove along the walls whereas outer air flows into the oil-filler port through the oil-supply groove. One of the main causes of these flows is considered due to the surface tension of oil and air, and the effects appear to be significant especially in the case of starved lubrication.

Furthermore, oil is supplied from the oil-supply groove to the bearing, thereby causing the occurrence of the gaseous phase at the center of the bearing of the wedge side of the journal bearing under starved lubrication conditions.

The same tendencies are confirmed from the experimental visualization results of **Figure 9(iii)**.

#### **4.3 Influence of surface tension in the journal bearing**

In the previous section, it is confirmed that considering the surface tension to calculate the gaseous-phase areas accurately in journal bearings especially under starved lubrication is important. In the next step, we considered the influence of surface tension on journal bearing from the viewpoint of Weber number *We*. The Weber number is expressed in the following equation:

$$\mathcal{W}\_{\varepsilon} = \frac{\rho U^2 H}{\sigma} \tag{9}$$

**Figure 10** depicts the calculation result of the Weber number *We* against the oil flow rate. The continuous line indicates the value, whereas several plots indicate the value in other studies of journal bearings under the starved lubrication conditions [3, 26, 27]. Focusing on the continuous line, the Weber number *We* drop below 1

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil…*

surface tension in the internal flow of the oil-filler port becomes too large to ignore. Moreover, it is found that the Weber number *We* of another research of journal bearing under starved lubrication is remarkably smaller than one. Therefore, it is concluded that the cause of surface tension influence is related to supply velocity

In this section, the thermal CFD analysis in journal bearing under two kinds of lubrication conditions is discussed. In our previous study [3, 4], it was found that the supply oil quantity affects the journal bearing stability, and the critical oilsupply quantity of transition state is determined. Therefore, two types of oil-supply quantity, one is transition state and the other one is starved lubrication condition, were selected in this chapter. The conditions of supply quantity and journal center positions are shown in **Table 3**. These conditions were decided by the experiment.

**Figure 11** shows the thermal CFD analysis results under two conditions of supply oil quantity. **Figure 11(i)** indicates the volume-fraction distribution of oil under both conditions. The red color means full oil and the blue color means full air. **Figure 11(ii)** indicates the analytical results of the temperature distribution of bearing. From **Figure 11(i-a)**, under transition condition, the volume fraction of the wedge side becomes zero at the side end. Thus, these areas are the gaseous phase. Moreover, the volume fraction increases at the centerline of bearing. On the other hand, the volume fraction of the inverse wedge side decreases with increasing of clearance. From **Figure 11(ii-a)**, the temperature slightly rises caused by the shear friction, but it is found that the temperature is almost 40°C at the full area of the bearing. Thus, it is found that the heat quantity by the shear friction is small in the

On the other hand, from **Figure 11(i-b)**, the volume fraction of the wedge side increases at the center of bearing, while it is zero around the side end. The volume fraction of the inverse wedge side decreases with increasing of clearance, while it becomes zero around the oil-filler port. From **Figure 11(ii-b)**, it is found that the temperature around the oil-filler port is about 38°C while it decreases compared to the temperature of supply oil. Moreover, the temperature of the around centerline

**Figure 12** shows the theoretical results of temperature distribution on the transition region and starved conditions at the point of centerline under (a) transition

/s, and the influence of

approximately under the amount of supply oil of 4 cm3

*DOI: http://dx.doi.org/10.5772/intechopen.92421*

from the oil-filler port.

**4.4 Temperature analysis**

case of the transition region.

*Specifications of calculation conditions [2].*

**Table 3.**

**205**

*4.4.1 Oil-film temperature and volume fraction*

on the bearing is smaller compared around the side end.

where *U* represents the speed and *H* represents representative length.

In the Weber number *We*, the meaning of the numerator is the fluid inertia force and that of the denominator is the surface tension. Generally, it is known that if *We* is less than one, the influence of surface tension is strong.

First, we examined the surface tension influence on bearing clearance. In this case, it was assumed that the representative speed *U* is the peripheral speed of moving the journal surface. Since the rotational speed is high, the Weber number extremely exceeds, and the influence of surface tension is negligible. This result is reasonable. Because many previous studies have been neglected, the surface tension effect and the reliability have been verified. However, as mentioned above, it is found that the influence of surface tension on gaseous-phase areas under starved lubrication is significant. Therefore, we focused on the internal flow of the oil-filler port. As the representative speed, the internal flow speed which is determined from supply oil flow rate was used.

**Figure 10.** *Relation between the Weber number and amount of supply oil [1].*

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil… DOI: http://dx.doi.org/10.5772/intechopen.92421*

**Figure 10** depicts the calculation result of the Weber number *We* against the oil flow rate. The continuous line indicates the value, whereas several plots indicate the value in other studies of journal bearings under the starved lubrication conditions [3, 26, 27]. Focusing on the continuous line, the Weber number *We* drop below 1 approximately under the amount of supply oil of 4 cm3 /s, and the influence of surface tension in the internal flow of the oil-filler port becomes too large to ignore.

Moreover, it is found that the Weber number *We* of another research of journal bearing under starved lubrication is remarkably smaller than one. Therefore, it is concluded that the cause of surface tension influence is related to supply velocity from the oil-filler port.

#### **4.4 Temperature analysis**

flows from the top surface of the oil-filler port to the oil-supply groove along the walls whereas outer air flows into the oil-filler port through the oil-supply groove. One of the main causes of these flows is considered due to the surface tension of oil and air, and the

Furthermore, oil is supplied from the oil-supply groove to the bearing, thereby causing the occurrence of the gaseous phase at the center of the bearing of the wedge side of the journal bearing under starved lubrication conditions.

The same tendencies are confirmed from the experimental visualization results

In the previous section, it is confirmed that considering the surface tension to calculate the gaseous-phase areas accurately in journal bearings especially under starved lubrication is important. In the next step, we considered the influence of surface tension on journal bearing from the viewpoint of Weber number *We*. The

*We* <sup>¼</sup> *<sup>ρ</sup>U*<sup>2</sup>

In the Weber number *We*, the meaning of the numerator is the fluid inertia force and that of the denominator is the surface tension. Generally, it is known that if *We*

First, we examined the surface tension influence on bearing clearance. In this case, it was assumed that the representative speed *U* is the peripheral speed of moving the journal surface. Since the rotational speed is high, the Weber number extremely exceeds, and the influence of surface tension is negligible. This result is reasonable. Because many previous studies have been neglected, the surface tension effect and the reliability have been verified. However, as mentioned above, it is found that the influence of surface tension on gaseous-phase areas under starved lubrication is significant. Therefore, we focused on the internal flow of the oil-filler port. As the representative speed, the internal flow speed which is determined from

where *U* represents the speed and *H* represents representative length.

*H*

*<sup>σ</sup>* (9)

effects appear to be significant especially in the case of starved lubrication.

**4.3 Influence of surface tension in the journal bearing**

Weber number is expressed in the following equation:

is less than one, the influence of surface tension is strong.

*Relation between the Weber number and amount of supply oil [1].*

supply oil flow rate was used.

**Figure 10.**

**204**

of **Figure 9(iii)**.

*Computational Fluid Dynamics Simulations*

In this section, the thermal CFD analysis in journal bearing under two kinds of lubrication conditions is discussed. In our previous study [3, 4], it was found that the supply oil quantity affects the journal bearing stability, and the critical oilsupply quantity of transition state is determined. Therefore, two types of oil-supply quantity, one is transition state and the other one is starved lubrication condition, were selected in this chapter. The conditions of supply quantity and journal center positions are shown in **Table 3**. These conditions were decided by the experiment.

#### *4.4.1 Oil-film temperature and volume fraction*

**Figure 11** shows the thermal CFD analysis results under two conditions of supply oil quantity. **Figure 11(i)** indicates the volume-fraction distribution of oil under both conditions. The red color means full oil and the blue color means full air. **Figure 11(ii)** indicates the analytical results of the temperature distribution of bearing. From **Figure 11(i-a)**, under transition condition, the volume fraction of the wedge side becomes zero at the side end. Thus, these areas are the gaseous phase. Moreover, the volume fraction increases at the centerline of bearing. On the other hand, the volume fraction of the inverse wedge side decreases with increasing of clearance. From **Figure 11(ii-a)**, the temperature slightly rises caused by the shear friction, but it is found that the temperature is almost 40°C at the full area of the bearing. Thus, it is found that the heat quantity by the shear friction is small in the case of the transition region.

On the other hand, from **Figure 11(i-b)**, the volume fraction of the wedge side increases at the center of bearing, while it is zero around the side end. The volume fraction of the inverse wedge side decreases with increasing of clearance, while it becomes zero around the oil-filler port. From **Figure 11(ii-b)**, it is found that the temperature around the oil-filler port is about 38°C while it decreases compared to the temperature of supply oil. Moreover, the temperature of the around centerline on the bearing is smaller compared around the side end.

**Figure 12** shows the theoretical results of temperature distribution on the transition region and starved conditions at the point of centerline under (a) transition


**Table 3.** *Specifications of calculation conditions [2].*

**Figure 11.** *Results of thermal CFD analysis [2].*

**Figure 13** depicts the experimental visualization results of (i) temperature distributions and (ii) results of gaseous-phase visualization. In **Figure 13(ii-a, b)**, there are typically four results which are indicated due to some fluctuation of gaseous-

*/s; (b) Starved* Q *= 0.5 cm<sup>3</sup>*

*/s). (ii) Experimental*

*/s).*

*/s; (b) Starved* Q *= 0.5 cm<sup>3</sup>*

*Results of temperature distributions and gaseous-phase visualizations [2]. (i) Experimental results in*

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil…*

From the results in **Figure 13(i)**, it is found that the same tendencies of temperature distributions are shown between calculation and experiment. As shown in **Figure 13(i)**, the temperatures are almost constant against the bearing angle in the case of transition condition. Hence, the same tendencies of temperature distributions are found between the calculation and the experiment. On the other hand, under the starved lubrication condition, the temperatures are higher against the bearing angle, and the difference of temperature between two bearing positions is found. Here, the temperature at the center of bearing is lower than that of between the center and side despite being closer to outside the edge. Generally, the temperature of the bearing is larger than that of the side. Therefore, the reason could be the

As shown in **Figure 13(ii-a)**, the gaseous phase rarely existed at the center of the

bearing at bearing angles between 0 and 135°. However, the temperatures are almost constant. This is because the friction resistance is not so high due to the

On the other hand, under starved condition shown in **Figure 13(ii-b)**, the gaseous phase exits at the center of the bearing. The gas is considered the inflow air

cooling effect from the visualization results shown in **Figure 13(ii)**.

relatively large amount of oil-film thickness existing in this case.

phase existing under actual rotations.

*temperature distributions ((a) Transition Q = 3.7 cm<sup>3</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.92421*

*visualization results of gaseous-phase region ((a) Transition Q = 3.7 cm<sup>3</sup>*

**Figure 13.**

**207**

**Figure 12.**

*Analytical results in temperature distributions [2]. (a) Transition* Q *= 3.7 cm3 /s and (b) Starved* Q *= 0.5 cm3 /s.*

and (b) starved lubrication conditions. From **Figure 12(a)**, the temperature elevation in the bearing clearance against the supply oil temperature which is 40°C is not so high. In addition, there is a little difference from 22.5 to 90°. On the other hand, from the results for the starved lubrication condition, as shown in **Figure 12(b)**, the temperature distributions are extremely different from those of the oil transition conditions. The temperature distributions of the starved lubrication condition increase with an increasing bearing angle after 135°, and the highest temperature area is found around the bearing angle of 250°. This is because the minimum clearance around the bearing angle of 250° decreases and the share friction resistance of oil film rises in the starved lubrication conditions. The temperature difference of the bearing center is found from 22.5 to 90° same as the transition region; however, the amount of difference is larger than that of transition region. Moreover, in the low-temperature region, the value of temperature is lower than the supply oil temperature of 40°C.

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil… DOI: http://dx.doi.org/10.5772/intechopen.92421*

#### **Figure 13.**

*Results of temperature distributions and gaseous-phase visualizations [2]. (i) Experimental results in temperature distributions ((a) Transition Q = 3.7 cm<sup>3</sup> /s; (b) Starved* Q *= 0.5 cm<sup>3</sup> /s). (ii) Experimental visualization results of gaseous-phase region ((a) Transition Q = 3.7 cm<sup>3</sup> /s; (b) Starved* Q *= 0.5 cm<sup>3</sup> /s).*

**Figure 13** depicts the experimental visualization results of (i) temperature distributions and (ii) results of gaseous-phase visualization. In **Figure 13(ii-a, b)**, there are typically four results which are indicated due to some fluctuation of gaseousphase existing under actual rotations.

From the results in **Figure 13(i)**, it is found that the same tendencies of temperature distributions are shown between calculation and experiment. As shown in **Figure 13(i)**, the temperatures are almost constant against the bearing angle in the case of transition condition. Hence, the same tendencies of temperature distributions are found between the calculation and the experiment. On the other hand, under the starved lubrication condition, the temperatures are higher against the bearing angle, and the difference of temperature between two bearing positions is found. Here, the temperature at the center of bearing is lower than that of between the center and side despite being closer to outside the edge. Generally, the temperature of the bearing is larger than that of the side. Therefore, the reason could be the cooling effect from the visualization results shown in **Figure 13(ii)**.

As shown in **Figure 13(ii-a)**, the gaseous phase rarely existed at the center of the bearing at bearing angles between 0 and 135°. However, the temperatures are almost constant. This is because the friction resistance is not so high due to the relatively large amount of oil-film thickness existing in this case.

On the other hand, under starved condition shown in **Figure 13(ii-b)**, the gaseous phase exits at the center of the bearing. The gas is considered the inflow air

and (b) starved lubrication conditions. From **Figure 12(a)**, the temperature elevation in the bearing clearance against the supply oil temperature which is 40°C is not so high. In addition, there is a little difference from 22.5 to 90°. On the other hand, from the results for the starved lubrication condition, as shown in **Figure 12(b)**, the temperature distributions are extremely different from those of the oil transition conditions. The temperature distributions of the starved lubrication condition increase with an increasing bearing angle after 135°, and the highest temperature area is found around the bearing angle of 250°. This is because the minimum clearance around the bearing angle of 250° decreases and the share friction resistance of oil film rises in the starved lubrication conditions. The temperature difference of the bearing center is found from 22.5 to 90° same as the transition region; however, the amount of difference is larger than that of transition region. Moreover, in the low-temperature region, the value of temperature is lower than the

*/s and (b) Starved* Q *= 0.5 cm3*

*/s.*

*Analytical results in temperature distributions [2]. (a) Transition* Q *= 3.7 cm3*

supply oil temperature of 40°C.

**Figure 11.**

**Figure 12.**

**206**

*Results of thermal CFD analysis [2].*

*Computational Fluid Dynamics Simulations*

from the oil-filler port. Hence, it is believed that the oil film at the center position was cooled down by an inflow air. Comparing with it, the position of between center and side, oil phase exists. Therefore, the cooling effect is lower than that of bearing center position.

the oil-supply groove and the side end of bearing cooled the supplied oil and the circulating flow; thus, the temperature of the center of bearing is controlled.

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil…*

In this chapter, using a two-phase flow CFD analysis, the calculation of gaseousphase areas in journal bearings under flooded and starved lubrication conditions was conducted, and the surface tension effect on multiphase flow CFD analysis of

As a result of comparing the calculation results and the experimental results, the VOF calculation considering the surface tension and vapor pressure was observed to

Furthermore, under starved lubrication, the calculation results of the interface of the oil film and gaseous phase during oil-film rupture agree rather well with experimental visualization result if they consider both vapor pressure and surface tension. While using these results, the effect of surface tension was discussed from the viewpoint of the Weber number, and it is concluded that the Weber number is strongly lower than one by using the supply oil speed as the representative speed

Moreover, thermal CFD analysis of a two-phase flow was conducted under two conditions of supply oil, and they were compared with the experiment. As a result, it is believed that in the case of the starved lubrication conditions, the air flowing outside of the oil-supply groove created a circulating flow; thus, the temperature in

It is concluded that the two-phase VOF CFD analysis considering the vapor pressure and surface tension is applicable in reproducing the gaseous phase on the

journal bearing especially generating the gaseous-phase area was studied.

be in good agreement under both lubrication conditions.

**5. Conclusion**

*DOI: http://dx.doi.org/10.5772/intechopen.92421*

and strongly influenced.

the bearing is controlled.

**Conflict of interest**

The authors declare no conflict of interest.

Masayuki Ochiai\*, Fuma Sakai and Hiromu Hashimoto

provided the original work is properly cited.

\*Address all correspondence to: ochiaim@keyaki.cc.u-tokai.ac.jp

Department of Mechanical Engineering, Tokai University, Kanagawa, Japan

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

journal bearing.

**Author details**

**209**

From the abovementioned results, the authors considered that the internal flow of the oil-filler port influenced the temperature characteristics of starved lubrication conditions. Therefore, we focused on the calculation results in the oil-filler port under starved lubrication conditions.

#### *4.4.2 Results in oil-filler port*

**Figure 14** shows the calculation results of the oil-filler port. **Figure 14(a)** indicates the results of the internal oil-filler port at the center of the bearing width of starved lubrication condition. **Figure 14(i-a)** indicates the volume fraction, while **Figure 14(i-b)** indicates the temperature. Moreover, **Figure 14(ii)** indicates the analytical results in the front view of the oil-filler port. From **Figure 14(ii)**, the temperature is high near the shaft, and the volume fraction decreases in that area. From the above, it is considered that the gas phase in this region is a circulating flow. In contrast, the gas phase exists in the wide area in the inside of the oil-filler port, while the temperature of the gaseous phase is smaller than the temperature of supply oil. Moreover, it is found that the temperature of oil is commensurate with the temperature of supply oil or less than. Furthermore, the temperature of the gaseous phase from the bearing clearance is about 40°C at the center of the oil-filler port. In **Figure 14(ii)**, the gaseous phase exists in the wide area in the inside of the oil-filler port as with **Figure 14(i)**, while it exists also in the oil-supply groove. The temperature of gaseous phase around the side end of the oil-supply groove is the same as the ambient atmosphere temperature set on the analysis; thus, it is found that outside air counterflows the oil-supply groove. From these results, in the case of the starved lubrication condition, it is considered that the outside air flows from

#### **Figure 14.**

*Calculation results in the oil-filler port under starved lubrication conditions [2]. (i) Results in the center surface from the view of the side ((a) Volume fraction; (b) Temperature). (ii) Results in the front view ((a) Volume fraction; (b) Temperature).*

*The Multiphase Flow CFD Analysis in Journal Bearings Considering Surface Tension and Oil… DOI: http://dx.doi.org/10.5772/intechopen.92421*

the oil-supply groove and the side end of bearing cooled the supplied oil and the circulating flow; thus, the temperature of the center of bearing is controlled.
