Extended Abstracts of The Second Pacific Rim Thermal Engineering Conference December 13-17, 2019, Maui, Hawaii, USA
PRTEC-24140
EVALUATION AND ANALYSIS OF ACTIVE NUCLEATION SITE DENSITY
MODELS IN BOILING
Achref Rabhi1,∗, Rebei Bel Fdhila1,2
1Mälardalen University, School of Business, Society & Engineering, P.O. Box 883, SE-721 23 Västerås,
Sweden
2ABB AB, Corporate Research, SE-721 78 Västerås, Sweden
ABSTRACT
Computational Fluid Dynamic (CFD) models employed to simulate thermohydraulic flows where boiling is occurring, require the knowledge of several parameters that are crucial for the flow prediction. It has been shown in several publications that the active nucleation site density (ANSD) is one of the key parameters that has strong influence on the simulation accuracy. This work which aims to evaluate the main used ANSD models, takes place within a larger project frame dedicated to improving the prediction of subcooled boiling using both measurements and CFD simulations. Existing empirical and semi-empirical ANSD correlations are generally formulated and validated solely against a restricted range of experimental conditions. This limits their validity domain and justifies their re-evaluation undertaken in this publication. 3D CFD simulations are performed to investigate subcooled flow boiling heat transfer and evaluate ANSD models by comparing the flow results to our own published measurements in Kromer 2015 and Kromer et al. 2016. The selected measurements consist of temperature values at three axial positions situated on the heated wall center-line of a vertical mini-channel water model (400mm x 100mm x 3mm) at atmospheric pressure and heated from one side. The reviewed ANSD models are implemented in the open-source finite volume CFD code OpenFOAM in order to benchmark them versus temperature measurements and identify the parameters that are affecting most the accuracy of the predictions. The results show that the axial wall temperature is underestimated by all the tested models. However, the models based on a mechanistic or experimental approach, Benjamin & Balakrishnan 1997 and Hibiki & Ishii 2003, that take into account the heated wall surface and material characteristics e.g. density, thermal conductivity, specific heat and roughness, provide much better results with a temperature difference of 4°C compared to more than 10°C for the others.
KEYWORDS: Active nucleation site density, Subcooled boiling, Minichannel, Computational fluid dynamics, Model evaluation
1. INTRODUCTION
Cooling in industry is important to avoid exceeding the maximum temperatures at which an electric/electronic device or a process can operate without being degraded, destroyed or ageing faster than intended. Cooling is needed to provide the appropriate process or product quality while minimizing energy consumption and environmental impact. An ever-increasing power density drives the need for more effective cooling and particularly two-phase cooling.
Subcooled flow boiling has been of particular interest since it can provide intensive cooling for a heat flux exceeding 100 W cm−2[1]. The nucleate boiling region is characterized by the formation of vapor bubbles at certain preferred location known as "nucleation sites" [2]. The ANSD is one of the key parameters in nucleate boiling. The numerical prediction of boiling flows requires several parameters of boiling heat transfer, such ANSD, bubble departure diameter, bubble departure frequency...
Many investigators studied the ANSD in pool boiling and in convective flow boiling conditions. Most of the proposed correlations relate the ANSD to the liquid thermophysical properties and the wall superheat. One of the first known correlations was proposed by Gaertner and Westwater [3], where they estimated the ANSD by
counting the number of holes in a deposited nickel layer, and linked it to the heat flux applied to the surface. Cornwell and Brown [4], Krepper et al. [5] and Yang et al. [6] correlated directly the ANSD to the wall superheat, based on their experimental data. One of the most known and widely used ANSD correlation in CFD was proposed by Lemmert and Chawla [7].
Other attempts were made by several investigators to relate the ANSD to the boiling parameters, the fluid and heated surface thermophysical properties and the heated surface material characteristics. Johov [8] linked the critical cavity diameter to the saturation temperature, the wall superheat, the latent heat of vaporization and the liquid-vapor surface tension, and proposed an empirical correlation for the ANSD valid for low pressure. Kocamustafaogullari and Ishii [9] proposed a correlation for the ANSD where they supposed that it is influenced by the surface conditions and the thermophysical properties of the fluid. Wang and Dhir [10] and Basu et al. [11] included the effect of surface tension on the ANSD. One of the most relevant studies that relates the ANSD to the wall superheat, the thermophysical properties of the working fluid and the heated surface, and the surface roughness was proposed by Benjamin and Balakrishnan [2]. Other investigators as Hiesh et al. [12] and Chang et al. [13] related the ANSD to dimensionless numbers, such as the boiling number, the Reynolds number and the Jacob number.
Hsu [14] proposed the first known semi-theoretical model to determine the maximum and minimum radii of a of a cavity in a heated surface, in order to be activated and nucleation can occur. Yang and Kim [15] proposed a mathematical model for the ANSD based on a statistical approach, where they assumed that the cavity radius and cone angle could fit the Poisson and the normal distribution, respectively. This latter model was improved by Hibiki and Ishii [16] and later by Wang and Podowski [17]. By studying the flow over a bubble attached to a channel wall, Kandlikar et al. [18,19] developed a correlation for the range of active nucleation cavities radii, where the thermal boundary layer close to the heated surface is accounted for.
In this paper, a 3D CFD model where we implemented several ANSD correlations was developed to simulate the experiment performed by Kromer et al. [20,21].
2. NUMERICAL METHODOLOGY
2.1 Model description A two-fluid Eulerian approach is used to model subcooled nucleate boiling flow. The governing equations have been extensively described in many works, e.g. [22–24]. The model consists of three transport equations for each phase, mass, momentum and energy, and was implemented in the open-source finite volume CFD code "OpenFOAM", based on its Eulerian two-phase solver "reactingTwoPhaseEulerFoam". The turbulence is modeled using the standard k − ε model. Each transport equation has a source term that represents the interfacial transfer accounting for the phase change, the energy exchange and the forces exerted on each phase. The drag force and the turbulent dispersion force are modeled following [25] and [26] respectively. The implemented boiling model was based on RPI wall heat flux partitioning model [27].
The input parameters such as bubble departure diameter and release frequency are taken from [9] and [28] respectively because they have been validated and often implemented in numerical simulations. However, they are not fully validated for the conditions of interest in this work and will represent the main limitation to a wider conclusion of the results. An experimental investigation will soon start, to study the interaction between the main boiling characteristics and the ANSD for the subcooled boiling case.
In order to evaluate and analyse the ANSD, we implemented four models besides the one of Lemmert and Chawla [7] which is already existing in the standard OpenFOAM solver.
2.2 Active nucleation site density models and correlations The major known and used ANSD are:
Lemmert and Chawla [7] and Kurul and Podowski [27]. This model was first developed based on experiments on pool boiling of saturated water. They reported that the nucleation site density depends on the local wall superheat by assuming that vapor is trapped in conical cavities that exist on the heated surface before any nucleation could occur. The proposed the following correlation:
NaL−C = (n∆Tsu p)
m (1)
where ∆Tsu p is the wall superheat, and n and m are empirical constants determined experimentally. [27]
proposed the same model as (1) but with different constants, NaK − P.
Benjamin and Balakrishnan [2]. The authors investigated experimentally the ANSD during pool boiling of saturated pure liquids at low and moderate heat fluxes using high speed imaging . They studied the effect
of the surface-liquid interaction and the surface roughness Ra on the ANSD. They proposed the following
correlation valid for stainless steel and aluminum, and for a variety of working fluids, as distilled water, carbon tetrachloride, n-hexane and acetone:
NaB−B = 218.8Pr 1.63
l ∆T
3
su pγ−1θ−0.4 (2)
where Prl is the liquid Prandtl number, γ = pκwρwCpw/(κlρlCpl) is the surface-liquid interaction parameter and θ = A + B(RaP/σ) + C(RaP/σ)2is the dimensionless surface roughness parameter, with κ is the thermal
conductivity, ρ is the density, Cp is the specific heat capacity, P is the system pressure, σ is the surface
tension, A, B and C are constants evaluated experimentally and the subscripts l and w denotes wall and liquid respectively.
Hibiki and Ishii [16]. In their work, the authors proposed a mechanistic ANSD model based on their assump-tions concerning the size and cone angle distribution of cavities that are present on the surface:
NaH −I = Nn 1 − exp − θ 2 8µ2 exp λ0ρgif g 2σTsat ∆Tsu p − 1 (3) where Nnis the average cavity density on the heated surface, and µ and λ0are statistical parameters, θ is the
liquid-vapor contact angle, if gis the latent heat of vaporization and Tsat is the saturation temperature.
Chang et al. [13]. The authors studied experimentally subcooled flow boiling heat transfer and bubble char-acteristics of FC-72 on micro-pin-finned silicon chip flush-mounted on the bottom of a horizontal rectangular channel. Among their findings a correlation for smooth surfaces:
NaC = 65 dbC
Bo0.87Re−0.15l Ja0−0.05 (4)
where dbC is the bubble departure diameter, correlated by the same authors [13], Bo is the boiling number, Rel is the liquid Reynolds number and Ja0is a modified Jacob number based on the inlet subcooling.
Yang et al. [6]. This work is based on an experimental study of subcooled flow boiling of water at atmospheric pressure, in a vertical upward narrow channel where copper is the heated surface. Based on their experimental results, the authors proposed the following model:
NaY = 0.28∆T 2.66
su p (5)
2.3 Case set up and experimental data The subcooled boiling flow experiment of Kromer et al. [20] and Kromer [21] is modeled using CFD based on OpenFOAM. The investigated domain is a narrow rectangular vertical channel of 400 mm height, 100 mm width and 3 mm depth heated from one side and operating at atmospheric pressure. The heated body is in aluminum and the channel front side is in polycarbonate to ensure transparency. The arithmetic average surface roughness for this material at this experiment was equal to Ra= 0.634 µm. Water is flowing upward with a mass flux equal to 134.2 kg m−2s−1at 90°C. Cartidridges
were used to heat the aluminum plate generating a 5 W cm−2heat flux. Thermocouples were used to measure the heated surface temperature, placed at the external surface along the center-line of the minichannel, at axial distances of 221 mm, 281 mm and 336 mm from the inlet. These temperature measurements will be compared with the CFD results of the simulation where the ANSD models are implemented.
3. NUMERICAL RESULTS AND DISCUSSION
Figure1 represents the heated surface computed temperature, obtained for all reported ANSD models. The CFD model underestimates the temperature by more than 10°C when NaY, NaL−C, NaK − P and NaC are used. However, better results are obtained for NaH −I and NaB−B with approximately 4°C difference with the experimental results. The ANSD model represented by NaH −I gives the best temperature predictions. This can be explained by the fact that this model takes into account the liquid and surface thermophysical properties, the contact angle, the liquid-vapor surface tension and the wall superheat. NaB−Btakes into account the liquid and the surface thermophysical properties, in addition to the surface roughness and also provides a successful temperature prediction. Figure2represents the void fraction axial distribution at the mid-plane near the heated surface. A lower void fraction is estimated by NaH −I and NaB−B. Figure3shows the volume fraction contours in the narrow channel estimated with three ANSD models. It shows that the Onset of Nucleate Boiling (ONB) starts approximately 100 mm from the channel inlet for NaH −I and NaB−B, however, it starts much earlier for the other ANSD models. Figure4shows a 3D representation of the void fraction in the channel for NaH −I. The first part of the channel between inlet and line A consists of single phase forced convection. The ONB occurs
Fig. 1 Heated surface temperature computed by the 3D model.
Fig. 2 Void fraction axial distribution near the heated surface.
Fig. 3 Volume fraction contours in the minichan-nel near the heated surface for each ANSD model.
Fig. 4 3D representation of the void fraction in the channel.
just after line A and the vapor continuous to be produced intensely to cover the entire channel depth at line B and beyond.
The simulation model includes a bubble coalescence and break-up model based on a transport equation of the interfacial area implemented in OpenFOAM. This allows us to identify the bubble size evolution, small size at the beginning of the two-phase bubbly region and substantially larger near the line B in Fig. 4, where the flow seems to become unstable due the massive generation of vapor as observed in Kromer’s experiment.
4. CONCLUSION
A 3D CFD simulations were conducted to model subcooled nucleate boiling flow in a rectangular narrow channel. The model solves conservation equations of mass, momentum and energy for each phase and a transport equation for the interfacial area concentration to address the phenomena of bubble break-up and coalescence. The boiling was modeled using RPI partition and the main five ANSD models are implemented. The numerical predictions of the channel surface temperature of the ANSD models are compared to measure-ments of Kromer et al. [20, 21]. It was shown that both models that take into account the majority of the process characteristics, fluid, surface and material, Benjamin and Balakrishnan [2] and Hibiki and Ishii [16] agree successfully with the experimental data with 4°C of absolute accuracy. The trend to an unstable flow that has been observed at the top of the experimental channel seems to be also encountered in the vapor fraction profiles. This shows that the simulation model has reached some degree of maturity and can be used further to investigate other complex flow situations and address sensitivity analysis of some key parameter necessary to model the boiling.
ACKNOWLEDGEMENTS
The authors gratefully acknowledge ABB AB, Westinghouse Electric Sweden AB and the Swedish Knowledge Foundation (KKS) for their support and would like to particularly thank Prof. Jean-Marie Le Corre and Prof. Henryk Anglart for their contributions and evaluation of the current work.
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