*Numerical Investigation of Rising Vapour Bubble in Convective Boiling Using an… DOI: http://dx.doi.org/10.5772/intechopen.96303*

the other hand, is going through a series of interesting shape evolution, as such, it is considered to compare against Clift et al. [19] shape regimes. A series of instantaneous bubble status points were considered, and their corresponding *Re* were calculated using bubble velocity obtained from the ISM simulation for comparison. With the increase of bubble velocity and it corresponding higher *Re*, the bubble was deforming from spherical to ellipsoidal to wobbling shape regimes. **Figure 12** demonstrates the bubble shapes obtained from the ISM simulation have excellent

Bubble shapes obtained in the ISM simulation were also compared with Kamei and Hirata's [32] experimentation and found to be a good agreement – see **Table 6**. The condensing bubble was keeping its spherical shape because of small size and high surface tension forces during its rise. **Table 6** also shows the comparison of shapes with past numerical works (Zeng et al. [33] and

Likewise growing bubble, the rise velocity of condensing bubbles is different from adiabatic bubbles [8]. For continuous reduction in bubble size (i.e. volume) in subcooled boiling flow condition, bubble rise velocity and shape are also always changing. From **Figure 13**, it is evident that with the increase of liquid Subcooling bubble rise velocity continues to increase. The findings are consistent with [8] numerical results. The deviation is the result of different test setups; however, **Figure 13** overall indicates the trends of higher the liquid Subcooling higher the bubble rise velocity. Bubble buoyancy force decreases for continuous reduction of bubble volume. The drag force is also reduced for smaller bubble frontal area; however, the resulted net effect is positive buoyancy force acting upwards, and the

*Bubble shape validation with Clift et al. [19]. Test case:* Db0 *= 4 mm,* ΔTsub *= 25 °C, Eötvös number,*

Eo = *2.55 (adapted from [31]). All bubbles are on the same scale for comparison.*

agreement with Clift et al. [19] shape regimes.

*Heat Transfer - Design, Experimentation and Applications*

bubble rise velocity increases continuously.

Samkhaniani and Ansari [34]).

*3.2.2.3 Velocity*

**Figure 12.**

**136**

**Flow Velocity [m/s] Simulation Time,** *t* **[ms]**

*DOI: http://dx.doi.org/10.5772/intechopen.96303*

*Numerical Investigation of Rising Vapour Bubble in Convective Boiling Using an…*

**0.05** [N/A]

**0.1** [N/A] [N/A]

**0.3** [N/A] [N/A] [N/A)

*Condensing bubble shape comparison for various fluid flow velocity [*Dbo *= 2 mm,* ΔTsub *= 5 °C]. All bubbles*

**0**

**Table 7.**

**Figure 15.** *Temperature models.*

**Figure 16.**

**139**

*2 mm bubble condensation rates [*Dbo *= 2 mm,* ΔTsub *= 5* °*C].*

*are on the same scale for comparison.*

**0 1.5 3 4.5 6**

**Figure 13.** *3 mm bubble rise velocity comparison with Jeon et al. [8]. (as demonstrated in [31]).*

### *3.2.2.4 Effects of fluid flow and varying temperature fluid field*

Effects of fluid flow and varying temperature fluid field on bubble condensation were also investigated. With the increase of fluid flow velocity, the bubble was condensing at a higher rate (see **Figure 14**). This is because the relative bubble velocity increases for same-directional (positive) fluid flow velocity resulting in the higher mass transfer or mass loss from the bubble (see Eq. (18)–(19)). **Table 7** depicts the effects of fluid flow velocity on the bubble shape. With a rapid mass loss for a higher fluid flow field, the bubble was deforming at a higher rate and becoming unstable with relatively shorter life span.

For varying temperature fluid field, two models were considered: (i) linear and (ii) exponential – see **Figure 15**. The Linear model can be applied to thermal stratification of hot water tanks and the natural systems, such as lakes and ponds. The exponential model is more suitable for the convective boiling application and hence was applied to current numerical study. Because of the computational domain and the relative higher heat transfer coefficient (*h*) value for convective boiling condition (*h* = 8,000 W/m<sup>2</sup> °*C* was used in **Figure 15**), the temperature of fluid field is rapidly achieving the liquid bulk-temperature. As a result, the effects of varying temperature field, in this instance, were minimal on both condensing bubble size and shape. See **Figure 16** and **Table 8**.

**Figure 14.** *Bubble condensation rates for various fluid flow velocity [*Dbo *= 2 mm,* ΔTsub *= 5 °C].*

*Numerical Investigation of Rising Vapour Bubble in Convective Boiling Using an… DOI: http://dx.doi.org/10.5772/intechopen.96303*

#### **Table 7.**

*3.2.2.4 Effects of fluid flow and varying temperature fluid field*

*Heat Transfer - Design, Experimentation and Applications*

*3 mm bubble rise velocity comparison with Jeon et al. [8]. (as demonstrated in [31]).*

ing unstable with relatively shorter life span.

**Figure 13.**

**Figure 14.**

**138**

ble size and shape. See **Figure 16** and **Table 8**.

*Bubble condensation rates for various fluid flow velocity [*Dbo *= 2 mm,* ΔTsub *= 5 °C].*

Effects of fluid flow and varying temperature fluid field on bubble condensation

For varying temperature fluid field, two models were considered: (i) linear and

(ii) exponential – see **Figure 15**. The Linear model can be applied to thermal stratification of hot water tanks and the natural systems, such as lakes and ponds. The exponential model is more suitable for the convective boiling application and hence was applied to current numerical study. Because of the computational domain and the relative higher heat transfer coefficient (*h*) value for convective boiling condition (*h* = 8,000 W/m<sup>2</sup> °*C* was used in **Figure 15**), the temperature of fluid field is rapidly achieving the liquid bulk-temperature. As a result, the effects of varying temperature field, in this instance, were minimal on both condensing bub-

were also investigated. With the increase of fluid flow velocity, the bubble was condensing at a higher rate (see **Figure 14**). This is because the relative bubble velocity increases for same-directional (positive) fluid flow velocity resulting in the higher mass transfer or mass loss from the bubble (see Eq. (18)–(19)). **Table 7** depicts the effects of fluid flow velocity on the bubble shape. With a rapid mass loss for a higher fluid flow field, the bubble was deforming at a higher rate and becom-

*Condensing bubble shape comparison for various fluid flow velocity [*Dbo *= 2 mm,* ΔTsub *= 5 °C]. All bubbles are on the same scale for comparison.*

**Figure 15.** *Temperature models.*

**Figure 16.** *2 mm bubble condensation rates [*Dbo *= 2 mm,* ΔTsub *= 5* °*C].*

**4. Summary**

good agreement.

**Nomenclature**

*Roman*

**Conflict of interest**

The authors declare no conflict of interest.

*a* Thermal diffusivity, m<sup>2</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.96303*

*cp* Specific heat, kJ/kg°C

*Eo* Eötvös number, *Fo* Fourier number, *g* Gravity, m/s<sup>2</sup>

*Ja* Jacob number,

*Nu* Nusselt number, p Pressure, Pa

*Re* Reynolds number,

*ΔTsub* Liquid subcooling, °C *ΔTsuper* Liquid superheat, °C *Ub* Bubble rise velocity, m/s *Uter* Bubble terminal velocity, m/s

*Vb* Bubble volume, m<sup>3</sup>

*α* Volume fraction *β* Bubble History

*ρ* Density, kg/m3

*μ* Dynamic viscosity, kg/ms

*σ* Surface tension force, N/m

*t* Time, s

*Greek symbols*

**141**

The InterSection Marker (ISM) – a new type of 3D interface tracking method was used to simulate the evaporative growth and condensation of a rising vapour bubble due to convective boiling conditions. The ISM method's ability to calculate interfacial area more accurately than conventional VOF methods proved it an ideal candidate for multi-phase flow simulations involving heat and mass transfers across the interface. During the simulation, the predicted vapour bubble properties such as size, shape and velocity were compared against the past works and found to be in

*Numerical Investigation of Rising Vapour Bubble in Convective Boiling Using an…*

/s

/m<sup>3</sup>

°C

s

*aif* Interfacial area between phases per unit volume, m<sup>2</sup>

*hif* Interfacial (convective) heat transfer coefficient, W/m2

*Cz* Location of bubble centre in the z-direction *Db* Sphere-equivalent Bubble Diameter, m

*Sheat* Interfacial heat transfer source term, W/m3 *Smass* Interfacial mass transfer source term, kg/m<sup>3</sup>

*Ustb* Evaporating bubble velocity in the stable regime, m/s

*hfg* Enthalpy for vaporisation, kJ/kg

*kl* Thermal conductivity, W/m°C

### **Table 8.**

*Condensing bubble shape comparison for varying temperature field [*Dbo *= 2 mm,* ΔTsub *= 5* °*C]. All bubbles are on the same scale for comparison.*
