Predicting Critical Heat Flux With Multiphase CFD: 4 Years in the … · 2018. 8. 2. · PREDICTING...

PREDICTING CRITICAL HEAT FLUX WITH MULTIPHASE CFD: 4 YEARS IN THE MAKING

Emilio Baglietto, Etienne Demarly, Ravikishore Kommajosyula Department of Nuclear Science and Engineering

Massachusetts Institute of Technology Cambridge, MA 02139, USA

ABSTRACT Advancement in the experimental techniques have brought

new insights into the microscale boiling phenomena, and provide the base for a new physical interpretation of flow boiling heat transfer. A new modeling framework in Computational Fluid Dynamics has been assembled at MIT, and aims at introducing all necessary mechanisms, and explicitly tracks: (1) the size and dynamics of the bubbles on the surface; (2) the amount of microlayer and dry area under each bubble; (3) the amount of surface area influenced by sliding bubbles; (4) the quenching of the boiling surface following a bubble departure and (5) the statistical bubble interaction on the surface. The preliminary assessment of the new framework is used to further extend the portability of the model through an improved formulation of the force balance models for bubble departure and lift-off.

Starting from this improved representation at the wall, the work concentrates on the bubble dynamics and dry spot quantification on the heated surface, which governs the Critical Heat Flux (CHF) limit. A new proposition is brought forward, where Critical Heat Flux is a natural limiting condition for the heat flux partitioning on the boiling surface. The first principle based CHF is qualitatively demonstrated, and has the potential to deliver a radically new simulation technique to support the design of advanced heat transfer systems.

INTRODUCTION A large-scale effort is ongoing at MIT on the development of advanced meso-scale modeling for Multiphase Computational Fluid Dynamics (M-CFD). The overall approach is based on the well-known time and space averaged Eulerian-Eulerian, two-fluid model, which represents today the most amenable framework for engineering application. The key to accurate simulations is therefore contained in the closure relations for mass, momentum and energy terms in the governing equations, for both the phase-to-phase and wall-to-flow aspects. Extensive assessment of the existing closures [1][2][3][4][5] has already demonstrated their very limited applicability, and the need for more general and robust physics based methods. In order to address this complex challenge, a multipronged

approach is leveraged at MIT, and graphically presented in Fig. 1, leveraging a schematic representation of a boiling channel in a nuclear reactor to identify the different boiling regimes.

Figure 1: MIT Multiphase Flow Boiling Model.

The activities include the development of momentum closures for high void fraction regimes, hydrodynamic and turbulence closures for bubbly flow, and boiling heat transfer. Among the numerous objectives, one challenge stands out and has driven the overall approach: deliver an accurate representation of the physics at the boiling wall, with the specific aim of challenging the prediction of Critical Heat Flux (CHF). The work has largely been driven by the recent advancement in experimental techniques, which have brought tremendous new insights into the microscale boiling phenomena and provide the base for a new physical interpretation to be incorporated in the CFD closures. This paper focuses on describing the novel approach and the tight interaction with the experimental activities to drive and incorporate new discoveries towards a truly predictive method to describe the thermal crisis limit. The boiling heat transfer predictions are assessed against the experimental measurements first, to demonstrate the increased generality and accuracy of the model. The discussion then concentrates on the statistical

Proceedings of the ASME 2017 Fluids Engineering Division Summer Meeting FEDSM2017

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representation of the surface physics, introducing and qualitatively demonstrating the validity of the heat transfer representation and the consistency of the postulated CHF mechanism.

PHYSICS BASED BOILING FRAMEWORK Practically all M-CFD calculations in the literature have adopted a variant of the original heat partitioning approach introduced by Judd and Hwang [6] and adapted by Kurul and Podowski [7], where the total heat flux is computed as the sum of three partitioned components: qtot

′′ = qfc′′ + qe

′′ + qq′′ (1)

The three components originate from a simplified description of pool boiling, shown in Fig. 2. Here the convection term qfc

′′ , describes the removal of heat by single-phase turbulent convection; the evaporation term qe

′′, represents the latent heat contained in the departing vapour bubbles; and the quenching term qq

′′, accounts for the heat transfer to the subcooled liquid that rewets the boiling surface when bubbles depart from the wall. This family of models, usually referred to as “RPI boiling models”, have demonstrated extreme sensitivity to their closure parameters and in particular to bubble departure diameter, bubble departure frequency and active nucleation site density [1][8].

Figure 2: RPI boiling model.

Many attempts have been made to improve the fundamental limitations of the RPI approach, focusing on its main sensitivities, as for example nucleation site density and bubble departure frequency [9][10]. As noted by Cheung et al. [11] however, the review of a large number of formulations has evidenced that no single combination is able to produce reasonable results on a large set of test cases. Yeoh further concluded that a new framework is necessary for the heat flux partitioning model [12]. In order to assemble such a framework, and spearhead a new family of flow boiling models in CFD, all necessary mechanisms have been included, and are schematically represented in Fig. 3 (left). The model explicitly tracks: (1) the size and dynamics of the bubbles on the surface; (2) the amount of microlayer and dry area under each bubble; (3) the amount of surface area influenced by sliding bubbles; (4) the quenching of the boiling surface following a bubble

departure (5) the statistical bubble interaction on the surface.

Figure 3: MIT flow boiling model.

In terms of heat partitioning, the model can be condensed into 4 components, given in Fig. 3 (right): - Forced convection: which, now includes the effect of

bubbles present on the surface - Evaporation: which must account for three separate

contributions, coming from the initial inertial growth of a bubble, the microlayer evaporating during the thermal growth, and the microlayer evaporating under a sliding bubble

- Sliding conduction: which accounts for the heat transfer associated with disturbance of the thermal boundary layer, in addition to that caused by the sliding bubbles themselves, which is included in the evaporation term.

- Quenching: which includes the increased heat removal on the fluid side after a bubble departure, as well as the heat stored in the dry area under the bubble.

Each of the heat partitioning components is evaluated from a mechanistic representation of the underlying physics, which can be illustrated through the mind map in Fig. 4.

Figure 4: Mind-map of MIT flow boiling model.

While all details on the mechanistic closures are available in [14], here we only present a brief description of the model assessment, to evidence the key features and findings. The model



is evaluated against experimental data from the MIT test facility [15] and is compared to a reference wall boiling model which employs the heat partitioning approach by Kurul and Podowski [7], The model was implemented in the commercial code STAR-CCM+ via external C user coding, and implementation details are available in [14]. Results are shown at 2.0 bar (the highest experimental pressure formerly available at MIT) and highest mass flux conditions (representative of industrial heat removal systems), for three different subcoolings, respectively 5, 10 and 15K (Figs. 5-7). The experimental error bars from [15] are related to the in-situ calibration process; the IR camera uncertainty, calibration thermocouple uncertainty and the error in the polynomial fit calibration curve all combine to a total temperature uncertainty of 2.0°C. The complete test matrix is available in [14].

Figure 5. Average heater temperature predictions for a mass

flux of 1250 kg/m2-s, inlet subcooling of 5 K, and at a pressure

of 2.0 bar.


flux of 1250 kg/m2-s, inlet subcooling of 10 K, and at a

pressure of 2.0 bar. Gilman (2017) from [13].


flux of 1250 kg/m2-s, inlet subcooling of 15 K, and at a

pressure of 2.0 bar.

In order to independently evaluate the new boiling framework, its validation has been performed without any calibration; rather, all model coefficients were mechanistically selected a priori. Results of the assessment indicate that the new framework already produces improvements in the predictions when compared to the traditional Kurul-Podowski approach. The wall temperature comparison indicated closer agreement for the new model predictions, for all available test conditions, both from a quantitative and qualitative viewpoint. This is particularly promising, since while sensitivity to hard-to-measure parameters still exists, the model has not been adjusted to fit the results. An important outcome of the new consistent framework is a demonstrated improvement in the model robustness. While the traditional approaches do not numerically converge at high heat flux conditions, particularly for small subcoolings, the new model is able to converge at all heat fluxes tested by the experiment. BUBBLE DEPARTURE AND LIFTOFF The sensitivity study performed as part of the overall assessment in [14], demonstrated the improved robustness of the framework, and as expected, its reduced sensitivity to specific closure parameters deriving from the fully mechanistic description. In order to further extend the accuracy and portability of the model to a wide range of flow and heat transfer conditions, a key aspect is related to the accurate prediction of the bubble lifecycle on the surface. As shown in Fig. 8, all contributions to the heat transfer have a direct dependency on the bubble departure diameter, which in the case of the evaporation term is as strong as Dd

3 .



Figure 8. Influence of Departure Diameter (Dd) on heat

partitioning predictions.

Attempts at empirical based correlations [16][17][18] have shown extremely limited applicability. In particular, all models derived their understanding from pool boiling experiments, and assumed that bubbles ‘depart’ directly from the nucleation site to the fluid bulk. As shown in Fig. 3 instead, bubble detachment and departure into the flow follow a more complex path: (1) Departure to Bulk (Dd): bubble departing the nucleation site

into the bulk, as is common in pool boiling and low mass flux scenarios in flow boiling;

(2) Departure by sliding (Dm in Fig. 3): bubble sliding off the nucleation site, as is common in most flow boiling scenarios;

(3) Liftoff (Dl in Fig. 3): the event when a sliding bubble detaches from the heater surface.

The current framework requires estimating all 3 modes of detachment, for which existing correlation are not appropriate. Zeng and Klausner introduced a mechanistic force balance approach [19], which showed great promise to extend the generality and accuracy of the predictions. Several, modifications have been proposed [20][21][22][23][24], and have been calibrated on specific set of test data. Yet, no model captures the three modes of detachment, and all models show poor performance outside their validation range. To this effect, an improved mechanistic approach [25] had to be assembled, with an improved physical representation, to achieve higher portability to a large set of conditions. Review of the existing models indicates a clear bias on water databases, and suggests their main weakness to be the description of the bubble growth. All models leverage the original proposal by Zuber [26], which adopts the presence of a superheated film of liquid surrounding the bubble and fueling the growth. The Zuber approach is represented on the left in Fig 9, in contrast to the more realistic representation of a growing bubble, on the right. In subcooled flow boiling, the growth of the bubble is mostly fueled by the microlayer beneath the bubble, while the subcooled fluid surrounding the bubble is mostly responsible for the effect of condensing the bubble.

Figure 9. Improvements in bubble growth modeling

Both effects are therefore introduced in the mechanistic force balance model: (1) the bubble growth due to microlayer evaporation is

quantified following the approach proposed by Cooper and Lloyd [27];

(2) the condensation of the bubble due to bulk subcooling is modeled using Zuber approach [26].

Figure 10. Improvements in the prediction of Departure and

Liftoff Diameters.

The improvements in predictions of bubble departure diameter, owing to the improved physical representation of bubble growth, are evident in Figure 10 (top). Liftoff diameter predictions remain challenging, due to the sensitivity to the lift force on the bubble, which depends on the relative velocity of the sliding bubble. Existing models adopted rough estimates for the relative velocity from a small set of experimental evidences, which lead to widely varying predictions across experimental



databases (Fig. 10 bottom left). A correlation for sliding bubble velocities was derived here from the database Philipps [15]. The corresponding improvement in the prediction of liftoff diameter are shown in Figure 10 (bottom right), where a more robust applicability is evidenced. SURFACE INTERACTIONS MODELING A crucial innovation introduced is the statistical treatment of bubble interactions on the boiling surface. While models in the literature [26][29] can provide an estimation for the number of available sites for bubbles to nucleate, they do not account for the inevitable interaction between sites, as bubbles start covering the boiling surface at higher heat fluxes. A bubble growing on the surface leads to a zone of influence, represented by the shaded areas in Fig. 11, where the lower local superheat deactivates the available nucleation sites. Sliding bubbles can also merge with other bubbles on the surface leading to their departure. Both mechanisms are characterized in Fig. 8 and are represented by the purple branches in the mind map of Fig. 4.

Figure 11. Static and sliding surface interaction mechanisms.

Here we mostly concentrate on the static interaction, as a key to the improved model robustness and the starting point for the extension of the model to limiting heat flux condition. Details on the sliding bubbles effects and interaction is available in [14]. The complete Spatial Randomness (CSR) statistical method is leveraged to calculate the probability that a bubble forms underneath a different bubble already present on the heated surface. Figure 11 (bottom right) illustrates the position of a new nucleation site underneath a bubble already formed. The nearest-neighbor method [30][31] is used to determine the probability of one bubble center being within one bubble radius of another nucleation site P = 1 − e−N′′ π(Rd)2 (2) where 𝑅d is the bubble departure radius, obtained from a mechanistic force balance approach. The number of active nucleation sites Na

′′ can then be expressed starting from the available total number of sites. In our case we selected the Hibiki Ishii expression [29] as the most accurate approach, and express

it below as N𝐻𝐼′′ , which then gives

Na

′′ = N𝐻𝐼′′ 𝑒−𝜋𝑅𝑑

2𝑵𝒃" (3)

Here, Nb

′′ represent the fraction of bubbles present on the surface at a certain time instant, and can be computed from the ratio of growth time tg over the total bubble period (= 1/f ), assuming that all bubbles nucleate with a temporally uniform distribution

Nb′′ = (

1

tw+tg) tgN𝑎

′′ = f tgNa′′ (4)

where the bubble growth time is estimated using the growth model by Zuber [26] tg =

π(Rd)2

4b2Ja2ηl (5)

with b set equal to 1.56, and the bubble departure frequency f using the Cole model [32]. An illustration of the effect of using this statistical method is shown in Figure 12. The figure reveals the large effect on the active nucleation site density, and the enforcement of a “realizability” condition, where the active nucleation site density value should not exceed the physical maximum number of bubbles that can fit on the heater surface. This basic conditions is not respected by classic models in literature, as for example the adopted Hibiki-Ishii [29], and explains the inconsistent predictions in literature as the heat flux increases [11] as well as the lack of numerical convergence evidenced on this work.

Figure 12. Static bubble interaction effect on active site

density.

CONSISTENT CRITICAL HEAT FLUX MODELING The statistical interaction introduced in the previous section leads to an interesting observation on the overall boiling heat transfer phenomenon.



1. As the surface temperature increases, more and more sites are activated, which therefore induces all the enhanced heat transfer mechanisms evidenced and modeled in Figs. 3 and 4. This explains the exponential increase in overall heat transfer.

2. However, as more and more sites are activated, the bubbles will start interacting and deactivating new sites, therefore reducing the exponential growth in new bubbles being generated.

3. Finally, the surface will be in saturated balance, where statistically the number of bubbles will not have the possibility to grow. At a certain point the heat transfer mechanisms (in Fig. 3 and 4) will not be able to keep up with the temperature increase, and the total heat flux will reach a maximum.

This heat flux maximum represents a critical condition, where an increase in surface temperature is not balanced by an increase in heat flux enhancement and would results in an exponential temperature increase. This observation leads to a very interesting proposition. While microscopically critical heat flux presents itself as a local occurrence, where the rewetting speed is not able to quench the dry surface efficiently enough, leading to its exponential growth, from a statistical point of view, critical heat flux is a natural consequence of energy balance on the boiling surface. Experimental evidences supporting this observation have also been recently discussed by Jung [33]. Based on this proposition we can therefore express the heat balance in the boiling models and should expect to be able to consistently predict the critical condition on a first principle base.

Figure 13. Illustration of the dry area, microlayer and area

of influence under bubbles growing on a boiling surface.

Figure 13 can be leveraged to express the total heat transfer in a physically consistent manner. After a bubble appears on the surface, its microlayer (shown in gray) will evaporate, leaving space to a small dry spot (in red) where only vapor is in contact with the surface. Due to the reduced heat transfer, the dry spot temperature can rise to relatively high values in comparison to the average wall temperature. In expressing the total heat transfer of the system, these dry spots must be accounted correctly, as only vapor is available to remove the local heat. In first approximation, based on experimental findings of

Kim and Buongiorno [34][35] we can assume that the radius of the dry spot forming after the evaporation of the microlayer coincides to approximately half the radius of the bubble. Leveraging equations 3-4 for the number of bubble present on the surface, we can then quantify the total dry surface. Therefore, the fraction of dry surface area of the heater Sdry is calculated as shown in Eq. 6 where Adry and Ah are the total dry area and heater area respectively.

Sdry =Adry

Ah=

Nb′′π(

Dd4

)2

Ah (6)

Separating the influence of the dry and wetted surface, and leveraging the new heat partitioning expressed in Fig. 4, the total heat flux is therefore given by:

qtot′′ = (1 − Sdry) × (qfc

′′ + qe′′ + qq

′′ + qsl′′ )

+(Sdry × qgas′′ ) (7)

where q

gas′′ represents the single phase heat transfer to the vapor.

Evaluating the heat flux curve predicted by Eq. 7, for pressure of 1 bar, 10K subcooling and mass flux 500 kg/m2-s produced the curve shown in Fig. 14. Here the CHF is simply obtained as limiting behavior of the heat flux on a boiling surface. As the dry area increases, the saturation of the available nucleation sites limits the amount of heat that can be removed by the wetted surface, which in turns further increases the amount of dry area and leads into the exponential growth of dry surface, observed as CHF.

Figure 14. Illustration of first principle based CHF predicted

by the new heat partitioning model.

CONCLUSIONS AND FUTURE WORK A new and complete modeling framework for investigation of subcooled flow boiling in CFD codes has been developed at MIT. The model provides a consistent representation of all heat



transfer mechanisms observed in flow boiling heat transfer, and mechanistically reproduces them in order to provide greatly improved generality, and reduced the dependency on its closure coefficients. A calibration-free assessment of the model evidences an increased accuracy at all flow conditions, and confirms the robustness of the approach, where contrary to existing closure the simulations converge at all experimentally considered conditions. The assessment and sensitivity studies further underlined the importance of accurately predicting the bubble lifetime on the surface, and a new approach is proposed which demonstrates considerable advancements in the prediction of both departure and liftoff diameters. Starting from the improved representation of the wall, the work focuses on the quantification of bubble interaction, sliding and formation of dry spots, as the key parameters governing critical heat flux (CHF). A new proposition is made, where CHF is evaluated on a first principle base as a limiting condition for the surface heat flux partitioning. A preliminary numerical implementation demonstrates the consistency of the postulated mechanism, where CHF is reached as a self-exciting transition when less heat is removed from the wetted area than is provided by heating of the substrate. Ongoing experimental work at MIT will support the finalization of the new CHF framework and its validation, at a range of mass flow, pressure and subcooling conditions. New experimental methods are in particular being developed to allow quantifying critical modelling aspects, including the dry surface, the heat partitioning and all bubble cycle characteristics including bubble departure diameter and departure frequency.

ACKNOWLEDGMENTS The authors gratefully acknowledge the support by the

Department of Energy Consortium for Advanced Simulation of Light Water Reactors (CASL).

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Predicting Critical Heat Flux With Multiphase CFD: 4 Years in the … · 2018. 8. 2. · PREDICTING...

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