Superheated Immiscible Liquids Neville Rebelo, Huayong Zhao*, - PowerPoint PPT Presentation

Evaporation of A Liquid Nitrogen Droplet in Superheated Immiscible Liquids Neville Rebelo, Huayong Zhao*, Francois Nadal, Colin Garner Wolfson School of Mechanical, Electrical and Manufacturing Engineering Loughborough University, United Kingdom, LE11 3TU Email: H.Zhao2@lboro.ac.uk Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 1 Cryogenic Heat and Mass Transfer (CHMT 2019)

Outline  Background and Motivation  Experimental Methodology  Results  Conclusion and future work Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 2 Cryogenic Heat and Mass Transfer (CHMT 2019)

Cryogenic Energy System Motivation ： more sustainable and clean energy system for transportation Chemical → Mechanical Heat → Mechanical Gasoline/Diesel ： 42-46 MJ/kg Liquid nitrogen (77K – 300K): 0.74 MJ/kg Liquified Natural Gas ： 50 MJ/kg Advantage ： 1. zero-emission ； 2. efficient in Electrical → Mechanical recovering low-grade heat or refrigeration ； Lithium-ion battery: 0.32-1.07 MJ/kg Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 3 Cryogenic Heat and Mass Transfer (CHMT 2019)

Liquid nitrogen system – heat and mass transfer Approach 2 ： Direct Injection Approach 1: Indirect Injection H. Clarke et. al (2010) Technical requirement ： Technical requirement ： effective Fast evaporation process How? systematic thermal management Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 4 Cryogenic Heat and Mass Transfer (CHMT 2019)

Experimental Methodology - Setup Optical system and Test section Vacuum Insulated Drop Injector liquid nitrogen diffuser foam insulation test cell iris LED LN2 drop high speed camera 1 solenoid valve condenser Condenser to vacuum pump high speed Electrical Feedthrough camera 2 Orthogonal-view high-speed backlit imaging system nitrogen drop N. Rebelo et al., Evaporation of liquid nitrogen droplets in superheated immiscible liquids, Int. J. Heat Mass Trans. , 143, 2019 Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 5 Cryogenic Heat and Mass Transfer (CHMT 2019)

Experimental Methodology – post-processing Vapour layer Droplet b) Side view a) Front view 3D Ellipse Edge detection reconstruction detection Randomized Alpha Shape Fitting Sobel / Canny filters Hough Transform Measured ： 𝑊 𝑒𝑠𝑝𝑞 , 𝑊 𝑐𝑣𝑐𝑐𝑚𝑓 , 𝐵 𝑒𝑠𝑝𝑞 & 𝐵 𝑐𝑣𝑐𝑐𝑚𝑓 𝜍 𝑕 ∆𝑊 𝑐𝑣𝑐𝑐𝑚𝑓 ℎ 𝑔𝑕 ⇒ Derived parameter ： Equivalent radius 𝑠 = 3×V 𝐵 ， heat flux ሶ 𝑅 = ∆𝑢.𝐵 𝑒𝑠𝑝𝑞 Main assumption: 1. Smooth ellipsoid with aspect ratio close to unity (Bo ≤ 4 & 𝑆𝑓 ≤ 9) 2. Increase in the sensible heat in the vapour layer << latent heat during evaporation Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 6 Cryogenic Heat and Mass Transfer (CHMT 2019)

Results – 𝑈 𝑐𝑣𝑚𝑙 = 294 𝐿 • The initial droplet size (v 0 ) has the dominant effect – larger droplet lead to more rapid growth • Other fluid properties, e.g. viscosity and surface tension could have minor but noticeable effect Fig. Bubble volume ( 𝑊 𝑐 ) growth for a nitrogen droplet in (a) Propanol; (b) methanol; (c) Pentane; (d) hexane Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 7 Cryogenic Heat and Mass Transfer (CHMT 2019)

Results – Scaling analysis Assume 1) diffusion-controlled evaporation of the droplet and negligible droplet heating: 2 = 𝑠 0 2 − 𝛽𝑢 𝐸 2 -law 𝑠 𝑒 Where 𝑠 𝑒 - radius of the droplet at time 𝑢 ; 𝑠 0 Methanol is the initial radius; Hexane Pentane Further assume 2) quasi-steady vapour phase; Propanol 3) vapour phase behaves as ideal gas; White – 294 K 4𝜆 Grey – 303 K 4) vapour pressure and temperature are uniform 𝜆 Black – 313 K 5) Negligible effect of vapour confinement −𝟐 𝒆𝑾 𝒄 Eq. 1 1 ⇒ 𝒘 𝒑 𝒆𝝊 = 𝝀; Fig. Rescaled experimental data based on Eq. (1) 𝜍 𝑒 𝑆 ത 3 𝑈 𝛽𝑢 Where 𝜆 = 𝑁 𝑂2 𝑄 𝑏 ; 𝜐 = 2 ; Eq. (1) with 𝜆 ′ = 4𝜆 fits experimental 2 𝑠 𝑝 𝑑 𝑞 𝑈 𝑐 −𝑈 𝑒 data well, except for the pentane data 𝛽 = 2𝑙 𝑐 𝜍 𝑒 𝑑 𝑞 ln 1 + ℎ 𝑔𝑕 1 - N. Rebelo et al., Evaporation of liquid nitrogen droplets in superheated immiscible liquids, Int. J. Heat Mass Trans. , 143, 2019 Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 8 Cryogenic Heat and Mass Transfer (CHMT 2019)

Simplified 1D Model Other main assumptions: 1. Negligible droplet heating 2. Inviscid vapour phase 3. Quasi-steady temperature profile at each time step 𝑆 0 𝑒𝑆 𝑐 ( Pe = 𝑒𝑢 ∈ [0.2, 1.1] so not fully justified) 𝐸 4. Negligible convection Fig. Geometrical configuration used for the model Each time step ( 𝜀𝑢 ): 2 𝑟 4𝜌𝑠 𝑒 𝑒𝑈 ∇ 2 𝑈 = 0 → 𝑈 𝑠 → 𝑟 = 𝑙 𝑐 𝑒𝑠 → 𝑒𝑜 = ℎ 𝑔𝑕 𝑁 𝑂2 𝑒𝑢 𝑆 𝑐 𝑠 2 𝑄 𝑐 𝑁 𝑂2 2𝜏 𝑚 4𝜌 𝑄 𝑐 = 𝑄 𝑚 + 𝑆 𝑐 ; 𝜍 𝑐 𝑠 = → 𝑜 = 𝑆 𝑄 𝑐 ׬ 𝑈 𝑠 𝑒𝑠 𝑠 𝑒 𝑆𝑈 𝑠 2 2 𝑆 𝑐 𝑠 2 𝑆 2𝜏 𝑚 𝑠 𝑒 2𝜏 𝑚 𝑆 𝑐 2𝜏 𝑚 ⇒ 𝑒𝑆 𝑐 = 4𝜌 𝑒𝑜 + 𝑄 𝑚 + 𝑈 𝑒 𝑒𝑠 𝑒 / 𝑄 𝑚 + 𝑈 𝑐 − 𝑈 𝑠 𝑒𝑠 2 ׬ 𝑠 𝑒 𝑆 𝑐 𝑆 𝑐 𝑆 𝑐 Fig. Pressure due to inertial ( 𝑄 𝑗 ), 𝑆 𝑐 𝑢 + 𝜀𝑢 = 𝑆 𝑐 𝑢 + 𝑒𝑆 𝑐 ; 𝑠 𝑒 𝑢 + 𝜀𝑢 = 𝑠 𝑒 𝑢 + 𝑒𝑠 𝑒 viscous ( 𝑄 𝑤 ) and capillary ( 𝑄 𝑡 ) Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 9 Cryogenic Heat and Mass Transfer (CHMT 2019)

Results – Model vs Experiments 1/4 5/4 [1] 3𝑙 𝑐 𝑈 𝑐 −𝑈 𝑒 𝜈 𝑐 𝜀 = 𝑠 𝑒 4ℎ 𝑔𝑕 𝜍 𝑐 𝜏 𝑒 𝑏 2 • 𝑙 eff = 1.6 × 𝑙 𝑐 fits experimental data well 𝑙 eff - a simple way to compensate for the effects due to the mobilities of droplet and the quasi- steady state assumption [1] Biance et al. Phys. Fluids, 15:1632-1637, 2003 Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 10 Cryogenic Heat and Mass Transfer (CHMT 2019)

Results – Heat flux during evaporation 𝜍 𝑐 ℎ 𝑔𝑕 𝑒𝑊 𝑐 𝑟 𝑐 = 𝐵 𝑐 𝑒𝑢 Normalised using the droplet surface area: 𝑟 𝑒 ~25 W cm −2 Pool boiling: 𝑟 𝑡 ~ 6.5 W cm −2 ഥ Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 11 Cryogenic Heat and Mass Transfer (CHMT 2019)

Key Conclusions 1. Evaporation rate of liquid nitrogen droplets in an immiscible superheated liquid can be scaled well by the 𝐸 2 - law. The effect of droplet confinement and mobility requires a higher coefficient ( 4𝜆 ) compared to the classic quasi-steady state isothermal diffusive evaporation process. 2. Correction for the effect of droplet confinement and mobility can be made by a simplified 1D quasi- steady state model with an ‘effective thermal conductivity’ 𝑙 eff = 1.6𝑙 𝑐 3. The assumption of quasi-steady state is not fully justified and further improvement of the model will require a transient multi-dimensional model, which could be difficult to implement in practical application. 4. The evaporation rate of the liquid nitrogen droplet in a superheated fluid is limited by the insulation vapour layer. More efficient practical application will require ways to destabilize the vapour layer. Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 12 Cryogenic Heat and Mass Transfer (CHMT 2019)

Results – Effect of Bulk Liquid Temperature LN 2 droplet evaporating in methanol LN 2 droplet evaporating in Propanol Similar droplet size; Increased bulk Same bulk temperature temperature Increased bulk temperature Larger droplet ≫ Increased bulk temperature Larger droplet • Higher growth rate in hotter bulk liquid, but the initial droplet size can still be important, or sometimes dominant, for the growth rate Evaporation of Nitrogen Droplets in Superheated Immiscible Liquid Page 13 Cryogenic Heat and Mass Transfer (CHMT 2019)