Figure 2.11: Jump in electric field across the interface.

A comparison of the electric field values obtained by solving Eq. 2.51 and that obtain from the exact solution is illustrated in Fig. 2.11. The numerical solu- tion provides the exact values of electric field values in both the media with a smoothening across the interface.

## Effect of Superheat and Electric Field on Saturated Film Boiling

The influence of superheat temperature and applied uniform electric field across the liquid-vapor interface during film boiling has been investigated. The hydrodynamics of bubble growth, detachment and its morphological variation with electrohydrody- namic forces are investigated considering the medium to be incompressible, viscous and perfectly dielectric at near critical pressure. The transition in interfacial insta- bility behavior occurs with increase in superheat, the bubble release being periodic both in space and time. Discrete bubble growth occurs at a smaller superheat whereas vapor columns form at the higher superheat values. Destabilization of in- terfacial motion due to applied electric field, results in decrease in bubble separation distance and increase in bubble release rate culminating in enhanced heat transfer.

A comparison of maximum bubble heights owing to application of different inten- sities of electric field is performed at a smaller superheat. The change in dynamics of bubble growth due to increasing superheat at a high intensity of electric field is studied too. The effect of increasing intensity of electric field on the heat transfer rate at different superheats is determined. The boiling characteristics are found to be influenced significantly above a minimum critical intensity of the electric field.

The contents in this chapter have been published as Pandey, V., Biswas, G., and Dalal, A.,“Effect of superheat and electric field on saturated film boiling”, Physics of Fluids, 2016, vol.

28, pp. 052102-1 – 052102-19 (available online, DOI: http://dx.doi.org/10.1063/1.4948545).

### 3.1 Introduction and Definition of the Problem

The hydrodynamics of film boiling extensively depend on the variation in vapor film thickness along the superheated substrate. The variation in substrate superheat results in changes in the variation of heat transfer rate from solid to the vapor and hence the changes in vapor generation at the liquid-vapor interface. As mentioned in Sec. 1.1.1, the instability at the interface depends on the degree of superheat of the substrate. Therefore, the heat transfer rate and the bubble morphology are also strongly dependent on the magnitude of superheat.

Using the CLSVOF approach, Tomar et al. [160] performed simulations of film boiling, analyzing different modes of bubble growth. They also found the discrete bubble release at lower values of superheat and the columnar growth at higher values of superheat. Study of the frequency of bubble release and the heat transfer analysis was performed using water and R134a as the fluids. The work was extended to multimode analysis [3] of bubble growth and the change in mode of instability from Rayleigh-Taylor to Taylor-Helmholtz with increasing superheat was observed. The nature of interface instability and bubble dynamics with different Jacob numbers was further studied by Hens et al. [161]. They observed the change in flow behavior from laminar to turbulent mode where the periodicity of bubble release was ceased to exist and the columnar structures of bubbles were found interacting and merging with each other.

The numerical simulation of film boiling under the effect of electrohydrodynamic (EHD) forces was performed by Welch and Biswas [162]. The mass transfer model and surface tension model were implemented in CLSVOF algorithm with an electric force term. Tomar et al. [163] also simulated the effect of EHD on film boiling using their method [164] and found an increase in bubble release frequency.

The present analysis utilizes the formulation explained in Chapter 2, to study
the influence of a range of electric fields on the bubble growth rate and heat transfer
characteristics at different degrees of superheat. The interface is initially perturbed
with disturbances of random modes and a random film thickness of small magnitude
iny direction. A time step of∆t = 5.0×10^{−6} s, which is much below the restrictive
capillary time limit is considered in all simulations. A grid dimension of ∆x =
λB/240 has been considered for all the simulations performed.

Single fluid formulation has been followed considering both liquid and vapor phases as incompressible and homogeneous. The physical conditions considered

are at near critical pressure (properties are mentioned in Table 3.1) so that large variation in bubble morphology is brought about by a small increase in the value of superheat. In the bulk vapor or liquid regions, corresponding phase properties are used while at the interface, the properties are calculated using the volume fraction of each phase.

A range of wall-superheats and intensities of electric field have been applied to analyze the changes in interface growth pattern and heat transfer characteristics.

In the CLSVOF algorithm, the jump in interfacial properties across the interface is smoothened in a transition region whose thickness is considered to be δ = 1.5∆x.

The properties of water are taken at near critical pressure, i.e. P = 0.99Psat where the capillary length is ls = p

σ/(ρl−ρv)g = 2.1×10^{−4} m. The value of Beren-
son’s most dominant wavelength [6], λB = 2πp

3σ/(ρl−ρv)g is 0.002275 m. The schematic of the computational domain is shown in Fig. 3.1.

00000000000000000000000000 00000000000000000000000000 11111111111111111111111111 11111111111111111111111111

w = T sat + T _{ sup}

T ∆

Ψ0

A B

VAPOR

H

L LIQUID D C

Figure 3.1: Schematic of the computational domain.

Isolated effects of superheat is shown initially to verify the already observed change in instability-mode from lower to higher superheat and then detailed effects of higher superheats are analyzed. The effect of electric field at a given superheat has been studied, in order to observe the change in interfacial morphology and heat transfer characteristics. The effect of electric field on change in bubble deforma- tion is another focus of the current investigation. Various combinations of electric field intensities and superheats have been deployed to analyze the changes in bub- ble ebullition cycles and variation in heat transfer rates. In this investigation, the

Table 3.1: Properties of water with Tsat = 646 K; Psat = 21.9 MPa; hlv = 276.4 kJ/kg; σ = 0.07 mN/m

Phase ρ (kg/m^{3}) µ(N.s/m^{2}) k(W/m.K) cp(kJ/kg.K) ǫ

Liquid 402.4 46.7 0.5454 2.18 ×10^{2} 7.35

Vapor 242.7 32.38 0.5383 3.52 ×10^{2} 3.71

interface has been captured by CLSVOF approach [144] and the medium has been considered purely dielectric discarding the effect of free charges at the interface.

Dielectrophoretic forces have not been considered.