Critical Mass Flux Research Articles

A new paradigm in critical flow analysis: Combining Buckingham Pi theorem with neural network for improved predictions in microchannels

Critical flow phenomena are prevalent in many chemical engineering processes, such as microchannel heat exchangers, nuclear safety analysis, jet pump modeling, and industrial systems utilizing subcooled or two-phase pressurized fluids. Understanding the impact of various physical parameters on critical flow and accurately predicting critical flow mass flux is essential in these processes. This article collects extensive experimental data on subcooled water two-phase critical flow and supplements it with additional experimental data from actual micro-cracked channels, constructing a comprehensive benchmark database. The database covers an inlet pressure range of 1.82–16.29 MPa, an inlet subcooling range of 0.3–119.35 K, and a microchannel hydraulic diameter range of 0.09–2.2 mm. By integrating the classical Buckingham Pi theorem with a data-driven active subspace method, the dominant dimensionless numbers in subcooled water two-phase critical flow were identified, addressing some limitations of the Buckingham Pi theorem by ranking the influences of these dimensionless numbers. Based on these dominant dimensionless numbers, the impact of physical quantities on two-phase critical flow was accurately identified, leading to a concise predictive correlation for critical flow mass flux with a mean absolute percentage error of 20.3 % across 1071 experimental data points, outperforming commonly used critical flow models. Furthermore, leveraging the dominant dimensionless numbers improved existing model results, enhancing the Henry-Fauske model’s overall prediction accuracy from a mean absolute percentage error of 47.6 % to 17.8 %. This study outlines a promising path for discovering physical characteristics and mechanisms in data-driven critical flow, facilitating a deeper understanding of critical flow phenomena.

Verification of Delayed Equilibrium Model for the R134a critical flow in a slit

R134a has the advantage of conducting visible critical flow experiments because of the lower temperature and pressure at the critical point than water. Whether the water critical flow model is suitable for predicting the flow rate and the pressure profile of R134a critical flow is unknown. An experiment on the critical flow rate and the pressure profile of R134a critical flow in a slit, mimicking the shape of a crack in the pipe, has been conducted. The dimension of the slit and the subcooling degree at the entrance are changed in the experiment. The Delayed Equilibrium Model (DEM), which is accurate for the water critical flow mass flux in a slit, is verified based on the experiment results. The empirical coefficients in the original DEM are adjusted according to the approximate saturated curve of R134a. The conservative and aggressive approaches to changing empirical coefficients are verified, respectively. For R134a, the ratio of boiling pressure to saturated inlet pressure is determined to minimize the relative error of volume flow rate and pressure profile in the slit with 0.3 mm width. It proves that the aggressive approach is lower in relative errors and differences in relative errors among different slit widths and different subcooling degrees. For the aggressive approach, the abstract value of the relative error of volume flow rate is lower than 20% in most cases. The abstract value of the mean relative error of pressure is lower than 15% in most cases. Besides, the differences in relative errors among different slit widths are not significant, and the differences in relative errors tend to be zero as the subcooling degree increases. DEM is adequate for predicting the volume flow rate and pressure profile for the R134a critical flow in a slit. Nevertheless, the relative error of the volume flow rate should disperse around zero at low subcooling degree, which is not achieved in this research. Further optimization requires more rigorous analytical methods and experiment data to find the best set of empirical coefficients, and the effect of velocity difference may be introduced.

Spontaneous ignition of corrugated cardboard under dynamic high radiant flux

Understanding the response of solid combustibles under high radiant fluxes is critical in predicting the thermal damage from extreme scenarios. Unlike the more moderate radiant fluxes in conventional hydrocarbon fires, extreme events such as strong explosion, concentrated sunlight and directed energy can generate dynamic radiant fluxes at the MW/m2 level, creating a unique threat to materials. This study investigates the pyrolysis and spontaneous ignition behaviors of corrugated cardboard by using both experimental and numerical methods, under 10-cm dynamic high radiant fluxes ranging from 0.2 to 1.25 MW/m2 for 10 s. The spontaneous ignition process at dynamic high radiant fluxes was recorded and quantified. Two ignition modes were found at the critical radiant flux of 0.4 MW/m2, namely hot-gas spontaneous ignition and hot-residue piloted ignition. The latter is not the focus of this paper due to its extremely small probability of occurrence. The research reveals that the increase in flux intensity induces shorter delay times for both pyrolysis and ignition, lower ignition energy density, along with a corresponding rise in the critical mass flux and surface temperature at ignition moment. The simulation results are generally aligned with the experimental findings, despite some divergences may be attributed to model simplifications and parameter assumptions. The work contributes to a deeper insight into material behavior under extreme radiation, with valuable implications for fire safety and hazard assessment.

Glowing and piloted flaming ignition of vertical wood exposed to power-law thermal radiation

Fire hazards are dangerous to human life and property safety. Fire accidents occur frequently in wood-frame villages all over the world. In this paper, glowing and flaming ignition of vertical wood heated by five power-law heat fluxes (HF) is experimentally studied using a self-built apparatus. Comparative ignition tests with and without piloted ignitor were performed, and some crucial variables were collected, encompassing surface and in-depth temperatures, mass loss rate, and ignition time. A 1D numerical model was developed to simulate experimental results and determine temperature-dependent thermodynamics of wood by inverse modelling. The results showed that ignitor induced flaming ignition, whereas absence of ignitor enabled only glowing ignition. Flaming ignition was preceded by flash ignition. Surface temperatures of flaming ignition were well predicted by numerical model. However, the predictive accuracy declined when modelling in-depth temperatures due to cracks in char layer. Three stages were identified in both ignition modes: a preheating stage, a water evaporation stage, and a pyrolysis stage. The numerical model underestimated mass loss rates due to additional heating contributed by flash ignition and char cracks. Critical temperature and critical mass flux were comparatively analyzed, and the former was used in assessing ignition time. Measured ignition times were well estimated by an analytical correlation. The numerical model accurately predicted flaming ignition times but overpredicted glowing ignition times due to char cracks. The proposed model can contribute to the fire safety retrofitting of historic buildings and minimize human casualties and property damage.

A comparative study of plain and enhanced helical microfin evaporator tube with drift flux-based entropy generation model for R32 and R410A refrigerants

In the present paper, a comparative study is carried out to assess the relative thermodynamic performance of plain and helical microfin evaporator tubes with two new emergent refrigerants, R32 and R410A. An entropy generation analysis is performed based on the drift flux model for two-phase forced convective boiling flow, and the comparison of the enhanced tube to the plain one is done quantitatively. A critical value of relevant parameters, i.e., mass flux, tube diameter, length, heat flux, inlet quality, and operating pressure, are identified, below or above which the enhanced tube is observed to be thermodynamically more favourable than the plain tube. The study reveals that by increasing the tube diameter from 8 mm to 14 mm, the critical mass flux increases from 335 kg/m2s to 495 kg/m2s for R32 and 394 kg/m2s to 565 kg/m2s for R410A, respectively, below which the enhanced tube performs better. The helical microfin tube exhibits a better performance below a critical mass flux from 412 kg/m2s to 374 kg/m2s for R32 and 492 kg/m2s to 443 kg/m2s for R410A when tube length increases from 1 m to 5 m. The critical inlet quality, below which the enhanced tube is observed to be superior, shifts to a lower value (0.29 to 0.16 for R32 and 0.44 to 0.26 for R410A), increasing the mass flux from 400 kg/m2s to 500 kg/m2s. However, the enhanced tube shows a better performance above a critical operating pressure, which increases from 11.4 bar to 16.9 bar for R32 and 9.3 bar to 13.4 bar for R410A, with increasing the mass flux from 400 kg/m2s to 500 kg/m2s. The enhanced tube performs better below a critical mass flux which increases from 336 kg/m2s to 461 kg/m2s for R32 and 399 kg/m2s to 489 kg/m2s for R410A when the heat flux is increased from 8 kW/m2 to 15 kW/m2. The overall parametric study with two emergent refrigerants enables one for effective selection of the helical microfin evaporator tube for a suitable range of relevant parameters.

Study of the effect of virtual mass force on two-phase critical flow

Abstract Critical (choked) flow is a highly concerning phenomenon in safety analysis for nuclear energy. The discharge mass flow rate prediction is crucial for engineering design and emergency response in case of nuclear accidents. Unfortunately, the critical flow is difficult to predict especially when the two-phase flow exists. The accuracy is based on a deeper understanding of the complex phenomenon of critical flow. The influence of virtual mass force on the two-phase critical flow was seldom concentrated on owing to the lack of suitable critical flow models for studies in detail. This study is based on a developed 6-equation two-phase critical flow model. It is confirmed that the virtual mass force contributes to the stability and convergence of the critical flow simulation and it will impact not only the critical mass flux but also the thermal hydraulic parameters along the discharge duct. The magnitude depends on the geometry of the discharge duct and the upstream condition. It is larger when the duct is longer and the pressure is lower. Furthermore, the virtual mass force for each flow regime was studied in detail with a sensitivity study. The results show that the most sensible condition for the virtual mass force is annular flow along a long tube under relatively low pressure. The future work is to develop a correlation of virtual mass force for critical flow specifically since the correlations in the literature were developed under general two-phase flow process conditions.

Study on supercritical CO2 critical flow through orifices under power cycle operating conditions

For prediction of critical flow occurring under supercritical carbon dioxide (S-CO2) condition, one-dimensional (1-D) analytical critical flow models are evaluated in this study. Specifically, homogeneous equilibrium model (HEM) and a newly proposed non-equilibrium model are evaluated. The new non-equilibrium model adopts Moody’s slip ratio for mechanical non-equilibrium and a newly proposed correlation of supercooling for thermal non-equilibrium. For evaluation of the models over various thermodynamic states, S-CO2 critical flow experiment through an orifice is conducted to supplement and expand a range of previously published S-CO2 critical flow experiment data. From the evaluation results with the expanded S-CO2 critical flow experiment database, the new non-equilibrium model shows better prediction performance than HEM in terms of the prediction of critical mass flux and critical pressure. For practical applications, discharge coefficients for each 1-D analytical critical flow model are suggested for the orifice geometry.

Smouldering organic waste removal technology with smoke emissions cleaned by self-sustained flame

Smouldering is slow, low-temperature and flameless, and has been potentially regarded as an alternative for organic waste removal technology. However, as an incomplete combustion process, toxic smoke and pollution from the smouldering are significant concerns that limit its popularization. This work applies a newly developed smouldering-based waste removal technology to investigate the removal of coffee waste, wood waste, and organic soil (simulated sludge) via using a flame to clean smouldering emissions at different airflow velocities (3–24 mm/s). Once ignited from the top, the smouldering front first propagates downwards where a stable flame situated above could be piloted and sustained to purify the smouldering emissions until the smouldering front reached the bottom of the fuel bed. The efficiency of pollution mitigation was demonstrated by significantly lower CO and VOCs emission after purification by self-sustained flame. The equivalent critical mass flux of flammable gases required for igniting the smouldering emissions is 0.5 g/m2∙s, regardless of the fuel type. The smouldering temperature, propagation rate and burning flux all increase with the airflow velocity but are also slightly sensitive to the type of waste. This work enriches strategies for the clean treatment of smouldering emissions and promotes an energy efficient and environmentally friendly method for organic waste removal.

Geometric and thermodynamic considerations of saturated and slightly subcooled water flow through nozzles

• Deviation from equilibrium is recognized as a manifestation of rapid depressurization events including Rapid Phase Transitions, Boiling Liquid Expanding Vapor Explosions, and flow of saturated and slightly subcooled liquids through converging nozzles and sudden contractions. • Non-equilibrium effects are attributed to nozzle geometry and the pressure driving force for saturated and slightly subcooled liquid flow through nozzles and sudden contractions. • Bubble nucleation theory is used to estimate the deviation from equilibrium and single-phase flow methods are used to estimate the critical mass flux when rapid vaporization occurs at the nozzle throat. It is well known that homogeneous equilibrium methods for calculating the mass flux of initially subcooled or saturated liquids in short nozzles under-predict the measured values and various methods for estimating non-equilibrium effects have been presented in the past. It is shown in this paper that acceleration effects at the entrance of converging nozzles due to changing cross-sectional area and approach to thermodynamic saturation pressure at the point of maximum fluid acceleration can be the most significant causes of non-equilibrium. By properly accounting for non-equilibrium due to the fluid acceleration, single-phase flow methods can be used to estimate the pressure loss and mass flux in nozzles when rapid vaporization occurs at the nozzle throat. For these cases, choking occurs due to the rapid vaporization while the difference between the inlet pressure and choking pressure determines the nozzle mass flux.

Structure and extinction of reverse smolder waves in the presence of heat losses: A premixed-flame perspective

A reverse smolder wave is structurally analogous to a premixed flame in the sense that the solid fuel and the gaseous oxidizer enter the reaction zone in a co-current manner. Such structural similarity is explored in this work to analytically examine the structural characteristics and extinction properties of planar reverse smolder waves that are driven by a forced oxidizer flow, based on the activation-energy asymptotic method. The analysis covers both the adiabatic condition and the non-adiabatic condition resulting from an external heat loss. Within the framework of the adopted diffusive-thermal model, two distinct reaction regimes are identified, namely the fuel-rich regime and the fuel-lean regime, separated in between by a stoichiometric state, which corresponds to a critical gas mass flux (for the adiabatic condition) or a critical heat loss coefficient (for the non-adiabatic condition). It is found that, under both adiabatic and non-adiabatic conditions, extinction occurs exclusively in the near-stoichiometric fuel-lean regime, in the sense that the values of characteristic quantities at the extinction limit are at most O(ε) away from those at the corresponding stoichiometric state, where ε is a small parameter inversely proportional to the activation energy. It is then demonstrated how this near-stoichiometric character can be exploited to seek a series-form representation of all the quantities characterizing the extinction limit, where the normalized initial oxygen mass fraction and the oxygen Lewis number are identified as two primary control parameters. A close examination of the differences between reverse smolder waves and premixed flames identifies a mechanism that may account for why reverse smolder waves are generally more robust than premixed flames when subjected to heat losses. Further, it is justified that limiting kinetics as a unified bottom-level mechanism can provide a uniform characterization of the extinction conditions of non-adiabatic reverse smolder waves.

Effect of porosity on ignition and burning behavior of cellulose materials

Porosity is one of the important factors to determine the fuel efficiency and the risk of forest combustible fire. In this work, we explore the porosity effect on the ignition phenomena, autoignition limit, and extinction of flaming combustion. The ignition experiment of pine needle and wood powder fuel bed with various porosity was conducted under external radiation at a constant heat flux of 5 ∼ 60 kW/m2. Several ignition phenomena including the cone-piloted flaming ignition, smouldering, smouldering to flaming transition, and no ignition can be obtained. And the pine needle could be burnt out in the flaming state, but the wood powder was easily ignited and presented a short flaming period, such as only 10% mass loss in flaming combustion and 70 ∼ 80% mass loss in smouldering combustion for an 84.67% porosity fuel under the radiant heat flux of 35 kW/m2. The ignition of a larger porosity fuel bed is more difficult, requiring a higher critical heat flux. The measurements suggested that the porosity was important to determine smouldering to flaming transition, but weak affected the smouldering ignition with the critical surface temperature 350 °C to pine needle and 280 °C to wood powder. The porosity has a slight influence on the ignition time and critical mass flux, with an order of magnitude lower than incident heat flux. The fuel with low porosity is more likely to be self-extinguished due to limited oxygen supply, and responds to a higher critical mass flux of flaming self-extinguishing. The proposed heat-transfer analysis explains and well predicted the ignition limit and delay time. This research helps understand the development of biomass burners and forest fire, and the interaction between flaming and smouldering fires.

A Numerical Study of the Irradiated Ignition of Obliquely Oriented Thermally-Deformable Polymer

This study numerically investigates the influence of molten matter dynamics on the gasification and subsequent ignitability of an inclined thermoplastic specimen subjected to localized irradiation heat flux normal to the surface. A thermoplastic material is modeled as a phase change material with predefined solidification and melting temperatures, respectively, and the gasification process is modeled by the Arrhenius law of molten matter. Gas phase kinetics is not considered for simplicity purposes; instead, the onset of ignition of polymer is estimated on the basis of the critical mass flux concept. According to the numerical results, as the inclination angle becomes steeper (toward the vertical angle), the estimated ignition delay becomes shorter, showing ignition is promoted, whereas it is turned to be difficult to occur when inclination angles are above the vertical angle (>90?) having a longer delay time for the onset of gasification. With careful observation, the thermal interaction between the hot molten matter and unmelted (cold) solid is found to play an important role in gasification. The formation of a bulge due to resolidification to suppress the dripping downstream could be the source to promote ignition. By contrast, the hot molten matter is enforced to detach from the unmelted solid and “freely fall-off” to prohibit ignition for inclination angles beyond 90?. This supports the notion that high-enthalpy caused by the external heating is simply lost because of dripping, and there is less chance of catching fire there.

Modeling of lubricant retention in suction lines with R32/PVE oil mixture

Modeling study for predictions of oil retention and critical refrigerant mass flux in compressor suction line was presented in the current work. Three approaches were developed for prediction of oil retention amount in suction line, namely, annular flow model, flow-pattern based method and empirical void fraction model. The annular flow model assumed that annular flow exists as the flow pattern, while the flow-pattern based method described the flow behavior of refrigerant/oil mixture by the flow pattern classifications and double circle model. Based on the proposed models, new correlations of interfacial friction factor and void fraction were established. The experimental data for R32 with coexistence oil PVE68 inside horizontal, vertical and inclined suction lines were used as the foundation and validation of the models. The results showed that all the models display satisfying prediction for oil retention. The flow-pattern based method exhibited the best results, which yielded the mean absolute deviation of 9.35% and captured 87.83% of the data within ±20% error bands. Moreover, two models for prediction of minimum refrigerant mass flux were recommended in order to ensure successful oil return. These models could serve as tools for operation optimization incorporating the lubricant oil effect.

Pyrolysis and autoignition behaviors of oriented strand board under power-law radiation

This contribution addresses a multi-component high order parallel reaction scheme developed for pyrolysis of Oriented Strand Board (OSB), a typical engineered wood product, and its application in estimating autoignition behaviors under power-law heat flux (HF). Thermogravimetric analysis tests were conducted first to parameterize the pyrolysis model by model fitting method. Subsequently, gram-scale autoignition experiments, using five power-law HFs, were implemented in a newly designed apparatus. Thermodynamics of OSB were determined by inverse modelling combining an improved numerical model and the measured surface temperatures and mass loss rates under a moderate HF. The extrapolation capability of the developed model was verified by simulating the remaining experimental measurements at alternative heating scenarios. Both critical temperature and critical mass flux were employed in predicting autoignition times. The results show that the developed pyrolysis model accurately captures the measured mass and mass loss rate collected in TGA tests. Meanwhile, relatively good agreement was found between the simulated and measured surface temperatures and mass loss rates in bench-scale tests despite some minor divergence due to the observed cracks of generated char layer. Furthermore, the uncertainties of the attained kinetic and thermodynamic parameters were quantitatively evaluated by parametric study.

Jet impingement in high-energy piping systems, part I: Characteristics and model evaluation

Under postulated pipe rupture accidents in nuclear power plants (Loss-of-Coolant Accident or LOCA), jet impingement can occur where the high-energy fluid is discharged and cause damage to the surrounding structures, systems, and components (SSCs). As a part of addressing the potential non-conservatisms in the Standard model ANSI/ANS-58.2 (1988), the current work investigates characteristics of jet impingement in high energy piping systems as in nuclear power plants including pressure distribution within jets, pressure on target, and critical mass flux and performs model evaluation. The pressure prediction using ANSI/ANS-58.2 (1988) as well as critical mass flux models are evaluated using the experimental data available in literature. An organized experimental database with different inlet fluid conditions including subcooled water, saturated water/two-phase (0 ≤ x < 0.7), and saturated steam (x ≥ 0.7) is compiled for data analysis and model evaluation. It is found that a power law can be used to correlate the dimensionless static and stagnation pressures at the center of the free jets, while either a power law or an exponential function can be used to correlate the dimensionless stagnation pressure at the center of the targets in impinging jets. The difference in stagnation pressure between free and impinging jets is negligible for saturated steam and saturated water/two-phase jets, but it is significant for subcooled water jets. From model evaluations, the stagnation pressure within the saturated steam jets can generally be predicted well by the Standard model. Although stagnation pressures at far distances (z* > 3.3) can be underestimated, the dimensionless pressures at these axial locations are below 0.07. For saturated water/two-phase jets, the stagnation pressure can be predicted well using the Standard model for the large-scale test data (D > 0.28 m) but are underestimated at some axial locations for the medium- and small-scale test data (D < 0.15 m). Significant overestimation in stagnation pressure is observed for subcooled water jets with high degree of subcooling, which is because the critical mass flux is overestimated using Homogeneous Equilibrium Model (HEM). For subcooled water jets with low degree of subcooling, HEM underestimates the data. Different from HEM, Henry-Fauske model always overpredicts the experimental data, where the degree of overestimation increases as the degree of subcooling decreases. The critical mass flux for saturated steam jets and saturated water/two-phase jets can be predicted well by isentropic expansion model and HEM, respectively.

Choked liquid flow in nozzles: Crossover from heterogeneous to homogeneous cavitation and insensitivity to depressurization rate

The critical mass flow rate is the maximum flow rate that can pass through a constrained geometry such as a nozzle. For liquid CO2, it has been shown that homogeneous relaxation models systematically underpredict the critical mass flow rate. In this work, we demonstrate that a delay of the phase transition is necessary to reproduce experiments. To analyze this in further detail, two methodologies are presented: (1) the delayed homogeneous relaxation model (Delayed HRM), and (2) the metastable isentrope model (MIM). Delayed HRM is a relaxation model that can readily be incorporated into a spatially distributed description of the fluid flow, e.g. in ejectors. MIM assumes isentropic flow and instantaneous equilibrium up to the limit of metastability, and yields a geometry-independent critical mass flux as the solution of a set of algebraic equations. We compare the two methodologies to available experimental data on the critical mass flow rates of CO2 and H2O through nozzles, finding that they give nearly identical predictions. This suggests that the critical mass flow rate is mostly determined by the achievable degree of metastability before onset of phase change, and is rather insensitive to dynamic variables such as the depressurization rate or the rate of relaxation towards equilibrium. Using the limit of metastability predicted by homogeneous nucleation theory works well at high temperatures, rendering the methodologies completely predictive. They deviate on average 11% from experimental data on CO2, and thus outperform homogeneous relaxation models by a large margin, even when the latter employs several fitted parameters. Especially good agreement was found with experiments that employ a lubrication oil, which is hypothesized to suppress heterogeneous nucleation. The limit of superheat at lower temperatures must be described by heterogeneous nucleation theory. For water and CO2 we find a crossover between homogeneous and heterogeneous nucleation at T≈590 K and T≈285 K respectively. Moreover, the predicted limit of superheat falls on a single curve in the temperature–pressure space of water, and we present an empirical correlation of this curve. By combining this expression with the above methodologies, we obtained an average deviation of 3% with available experimental data on H2O mass flow rates.

Development of a pyrolysis model for poly(vinylidene fluoride-co-hexafluoropropylene) and its application in predicting combustion behaviors

Pyrolysis and combustion behaviors of poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP), a promising polymer matrix in lithium-ion polymer battery, are experimentally and numerically investigated. A pyrolysis reaction scheme consisting of three high order consecutive reactions was established based on the thermogravimetric analysis (TGA) measurements and parameterized combining a modified numerical model and Genetic Algorithm (GA). The results show that in the heating rate range of 5–20 K min−1 the peak temperature of pyrolysis increases from 739 to 770 K. After deriving the pyrolysis kinetics, the thermodynamics was further determined by inversely modeling the measured mass loss rate in cone calorimeter tests. By fitting the measured heat release rate, the effective heat of combustion of each gaseous component, the global effective heat of combustion (9.56 MJ kg−1) and the flame heat flux (15 kW m−2) were quantitatively estimated. Reliability of the fully developed model was validated by alternative experimental results which were not utilized in parameterization, and good agreement was found. The collected ignition times in cone calorimeter tests were well predicted by the numerical model employing the measured critical mass flux, 2.87±0.32 g m−2 s−1. By invoking the ignition theory proposed for thermally intermediate solid and the measured ignition data, thermal diffusivity of PVDF-HFP, critical heat flux and critical temperature were assessed to be 3.00 × 10−7 m−2 s−1, 17.13–24.34 kW m−2 and 763.34–794.13 K, respectively.

Application of artificial neural network for the critical flow prediction of discharge nozzle

System thermal-hydraulic (STH) code is adopted for nuclear safety analysis. The critical flow model (CFM) is significant for the accuracy of STH simulation. To overcome the defects of current CFMs (low precision or long calculation time), a CFM based on a genetic neural network (GNN) has been developed in this work. To build a powerful model, besides the critical mass flux, the critical pressure and critical quality were also considered in this model, which was seldom considered before. Comparing with the traditional homogeneous equilibrium model (HEM) and the Moody model, the GNN model can predict the critical mass flux with a higher accuracy (approximately 80% of results are within the ±20% error limit); comparing with the Leung model and the Shannak model for critical pressure prediction, the GNN model achieved the best results (more than 80% prediction results within the ±20% error limit). For the critical quality, similar precision is achieved. The GNN-based CFM in this work is meaningful for the STH code CFM development.

Pyrolysis and autoignition behaviors of beech wood coated with an acrylic-based waterborne layer

Pyrolysis and autoignition of beech wood covered with an acrylic-based waterborne coating layer are experimentally and numerically examined. Thermogravimetric Analysis (TGA) tests were conducted first for wood and coating to derive the kinetic parameters combining a numerical model, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Subsequently, bench scale autoignition tests of thermally thick wood and coating-wood composite with varying coating thickness were performed under four radiative heat fluxes. Thermal conductivities and heat capacities of wood, coating and yielded residue were determined by inversely modelling the measured surface and 3 mm in-depth temperatures at a moderate heat flux. Reliability of the fully parameterized model was validated by simulating the collected surface temperatures and mass loss rates at the remaining heating conditions. Meanwhile, the recorded autoignition times were predicted by the model using the measured critical temperature and critical mass flux. The results show that both GA and PSO yield identical accuracy in fitting the TGA measurements, and their average results are adopted. The parameterized model successfully captures the measured surface temperatures and mass loss rates before ignition despite some minor deviations. Application of the coating considerably improves the fire resistance of wood by increasing the critical heat flux, critical temperature, critical mass flux and ignition time. The measured autoignition times are relatively well estimated, and an approximate linear correlation exists between ignition time and coating thickness.

Composite auto-ignition criterion for PMMA (Poly methyl methacrylate) exposed to linearly declining thermal radiation

This contribution experimentally studies auto-ignition of thermally thick PMMA (Poly methyl methacrylate) subjected to linearly declining heat flux (HF) radiated from a cone heater. Thermogravimetric tests (TGA) were conducted to derive the kinetics of PMMA by model fitting method. A numerical model dealing with heat transfer and pyrolysis is utilized to simulate the experimental measurements. Results show that auto- and no-ignition regions are separated by a critical decreasing rate of HF which is quantitively determined by numerical results. Measured surface temperatures are compared with the analytically and numerically estimated ones, and it is found both ignition time and critical decreasing rate are sensitive to critical temperature. These senilities are also confirmed by numerical model through parametric study. In no-ignition region near the critical condition, the maximum mass flux is higher than the measured critical value, 4.26 g/m2s, indicating critical mass flux is not a credible ignition criterion. Measured critical temperature increases with higher initial HF and yields an average value of 641 K. A composite auto-ignition criterion combining both critical mass flux and critical temperature is found valid in estimating ignition time. Meanwhile, the different affecting mechanisms of decreasing HF on auto-ignition between this work and literature is reasonably interpreted.