Flash atomisation and droplet size

Generally, systematic increase of the liquid temperature beyond its saturated temperature at prevailing condition, i.e. 𝑇 > 𝑇𝑠𝑎𝑡, leads to the formation of smaller droplets. Void

development accelerates the flow and increases disturbances inside and outside of the liquid element. Reitz (1990) conducted a photographic study of flash atomisation and observed that the atomising jet could be subdivided into an intact inner core and its surrounding small ligaments. It was concluded that flashing reduces the size of the inner core as well as the size of the surrounding droplets.

Wiener (1958) highlighted flashing as the principal mechanism of atomisation of pressurised liquids. The phenomenon is caused by abrupt pressure drop and subsequent heat transfer between the liquid and gas phases during a very brief period of time. The process is assumed to be adiabatic as well as mass transfer dominant. Wiener (1958) calculated the percentage of propellant 12 vaporised at 21 °C during primary atomisation of a spray actuation event (actuator press and fire), using a simple adiabatic heat balance equation:

𝑚_𝑓(%) = 𝑐𝑝𝑙(𝑇𝑙− 𝑇𝑤𝑏)

ℎ_𝑙𝑔 × 100 ‎2-29

Where 𝑚𝑓(%) is the flashed mass of the propellant represented in percentage. 𝑇𝑙 and 𝑇𝑤𝑏

are the initial liquid temperature and wet bulb temperature, respectively and 𝑐𝑝𝑙 is the heat

capacity of liquid. Calculation showed that for propellant 12 at 21 °C, 27% of its mass can turn into vapour.

The idea of flash atomisation of a jet as a result of liquid nucleation was brought forward by Brown and York (1962). The proposed process involved regular generation of low pressure

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eddies due to the geometrical imperfections inside the nozzle. These eddies create regions with low pressure leading to bubble formation. The bubbles are then carried downstream regions by the flow. Eventually the jet breaks up due to the gradual growth of the bubbles. Brown and York (1962) used photographic counting methods to derive an empirical correlation linking the droplet mean diameter D10 (m), to the Weber number and

temperature of the flow in the expansion chamber (space with enlarged volume across flow path) for water and propellant 11:

𝐷₁₀ = (4220 − 9.3𝑇𝑒𝑐

𝑊𝑒_𝑔 ) × 10−6 ‎2-30

In this equation 𝑇𝑒𝑐 (K) is the expansion chamber temperature.

Theoretical work to predict droplet size produced by flashing was carried out by Sher and Elata (1977). The work considered the formation process of spray from a pressurised can containing propellant as the working fluid. The process was described as rapid growth of bubbles as the can releases propellant into the atmosphere. Continual growth results in adjacent bubbles touching each other, forming larger void volume and fragmenting the liquid. The geometric arrangement of bubbles was assumed to be a close packed array. Hence vapour and liquid volume fraction are π/6 and 1 − π/6, respectively. At this point, regime change is assumed to take place and the energy contained in the exploding bubbles will be partly transformed into droplet surface energy. It was also assumed that droplets follow a log-normal distribution. Using these assumptions, an expression was derived to relate mean spray droplet size to fluid thermo-physical properties and flow parameters:

𝐷𝑑 = 𝛼𝜎 𝜌𝑙 [ ℎ_𝑙𝑔2 _𝑝̅2_𝑀2 𝐶𝑝𝑙𝜌𝑙𝑇̅3𝑅′2𝐷𝑡ℎ0.5 ] 4 exp (−2.5 ln2_𝜎 𝑔) Ψ4_(Δ𝑝)4 ‎2-31

Where = 1.266/𝜂𝑚2/3 , in which 𝜂 is the fraction of bubble energy which transforms into droplet surface energy and 𝑚 is the volume density of vapour nuclei. 𝑝̅ and 𝑇̅ are the absolute average values inside and outside the pressurised can. 𝑀 is the molecular weight of the propellant and Ψ is assumed to be 1. 𝐷𝑡ℎ is the thermal diffusion coefficient. 𝑅′ is the

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distribution. Eventually Δ𝑝 is the pressure difference. Comparison of the model results against measured droplet size did not show a very good match against the observation. The main difficulty of the model was a priori determination of the many of the parameters required by equation ‎2-31. It should also be mentioned that experimentation showed that the nozzle configuration had no significant effect on droplet size. The nozzle diameter does not explicitly appear in equation ‎2-31; the nozzle throat only acts as a space for nucleation and bubble growth.

Solomon et al. (1985) investigated the droplet size issued from twin-orifice system, using propellant 11 and Jet A/dissolved air. The emitted mass flow rate from the valve and spray orifices were estimated with the locally homogeneous model (LHM) and separated flow model (SFM). The flow model was linked to a droplet size correlation adopted from the work done by Lefebvre (1980), which was originally derived for pre-filming airblast atomisers. The model predictions of droplet size showed reasonable agreement with the measured data obtained by laser diffraction particle sizer. By comparing the results of propellant 11 (flashing case) and Jet A/air (non-flashing case), It was found that flashing generally increased the atomisation quality judged by reduced droplet size.

A theoretical model for predicting the size of droplets in a superheated water spray due to thermal fragmentation was presented by Razzaghi (1989). The atomisation process is divided into three consecutive stages. The first stage is formation of primary droplets as a result of aerodynamic breakup. The size of the droplet at this stage was assumed to be proportional to the wavelength of instability on liquid surface. The duration of primary droplet formation is considered to be sufficiently short for conditions to be adiabatic (i.e. no heat exchange with the surrounding air), so the droplet and jet temperatures are identical. Consequently, the primary droplets will be superheated. The second stage in Razzaghi’s model is nucleation and growth of vapour cavities inside the superheated droplets. The criterion of flashing inception is based on the non-dimensional degree of superheat adopted from the experimental work of Bushnell and Gooderum (1968):

38 𝑇_𝑙− 𝑇_𝑠𝑎𝑡

𝑇_𝑙 ≥ 0.1 ‎2-32

Where 𝑇𝑙 is superheated liquid temperature. Further growth of the bubble inside the

droplet leads to thinning of the surrounding liquid film up to a point where the bubble bursts. In the final stage, after bubble bursting the remaining mechanical energy (due to the stretched liquid film) and thermal energy in the liquid are partly transformed into surface energy through which “tertiary droplets” with smaller size are formed. The number of tertiary droplets is determined by uniform random number generator algorithm within the range of 1 to 10. This mechanism is illustrated in Figure ‎2.2.

Figure ‎2.2 Schematic of primary, secondary and

tertiary droplets formed as a result of thermal fragmentation adapted from (Razzaghi, 1989)

The results showed that the average droplet size increases from 6 µm to 14 µm as the discharge pressure decreases from 10 MPa to 2.5 MPa. A similar trend was observed when the initial temperature was reduced from 550 K to 475 K.

Park & Lee (1994) studied the effect of the internal flow pattern inside a spray nozzle on the behaviour of the flashing spray, by examining photographs of sprays from circular transparent nozzles of superheated water. The internal flow regime appeared to respond to increases in superheat level by changing from bubbly to slug flow and subsequently to annular flow regime. It was also observed that by increasing the degree of superheat, finer and more uniform droplet sizes were produced. At low superheat levels, a large intact core

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region was observed, where the droplets are mainly formed around the edges of the spray. Further increase of superheat degree at the prevailing pressure resulted in a more violent bubble growth process. Subsequently, bubble collision and coalescence inside the nozzle formed liquid slugs. Discharging of these slugs at the nozzle exit caused rearrangement into stretched ligaments and then disintegration into fine droplets. Further increase in superheat resulted in the formation of a vapour core and thin liquid annulus moving along the walls of the nozzle, which is termed the annular flow regime. As the fluid is released out of the nozzle it disintegrates into fine droplets.

Domnick & Durst (1995) carried out experimental work using phase Doppler particle analysis, laser Doppler anemometry and laser sheet visualisation to study the behaviour of flashing flow of propellant 12 while moving through a constriction (see Figure ‎2.3). It was observed that, due to the generation of low pressure recirculation zones near the entry to the constriction, liquid nucleation and growth of bubbles were initiated. The volume of this recirculation zone increased as a result of continued bubble growth until it reached a threshold where after it collapsed. The fluid in the recirculation zone was periodically transported by the mean flow towards the nozzle exit leading to periodic bubble cloud generation. It was observed that flashing preferentially takes place along the walls of nozzle geometry.

Figure ‎2.3 Schematic of flashing flow through a constriction based on the work of (Domnick and Durst, 1995)

flow streamlines

recirculation region (nucleation)

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Yildiz et al. (2002, 2004, 2006) conducted a series of studies of flashing jet characteristics as a function of initial conditions with relevance to sudden release of liquefied gases into the ambient environment. By employing optical diagnostic techniques such as particle image velocimetry (PIV), Phase Doppler Anemometry (PDA) and high-speed imaging (HSI) the mean droplet diameter, breakup pattern and spatial velocity distributions of HFA134 flashing jets were investigated. The measured droplet size was found to be directly correlated with the degree of superheat. Interestingly, it was also reported that the droplet centreline velocity did not depend on degree of superheat. The influence of upstream pressure was also investigated and it was shown that this parameter had a direct relationship with jet velocity and inverse relationship with the mean droplet size. In terms of breakup pattern, for the same initial pressure and superheat, it was concluded that a jet that emerges from a larger nozzle shows a more explosive breakup pattern. It was also observed that increase of the degree of superheat up to 6.4 °C changed the breakup pattern from slow expansion to violent shattering.