Fire Dynamics Simulator Software Research Articles

A dynamic risk assessment model for evacuation in healthcare facilities during fire scenarios

Evacuation is a critical procedure for safeguarding individuals during a fire incident within a healthcare facility. Assessing the risk associated with the evacuation process is instrumental in enhancing emergency decision-making and developing contingency strategies. Evacuation, a dynamic process, poses challenges in accurate risk evaluation using conventional static quantitative risk assessment (QRA) techniques. This study introduces a dynamic QRA approach to precisely evaluate the evacuation risk to individuals in healthcare settings during a fire. The dynamic event tree methodology is initially utilized to determine the evolving probabilities of various fire scenarios, considering the equipment failure and repair rates. Subsequently, data on fire products and the evacuation of individuals under different fire scenarios are gathered through simulations conducted with Fire Dynamics Simulator (FDS) and Pathfinder software. In addition, this research proposes a dynamic incapacitation model to calculate the consequences of fire, incorporating changes in individuals' locations and the fire products surrounding them during evacuation to accurately estimate the casualty risk. Lastly, the dynamic scenario probability was integrated with the average incapacitation probability for all individuals, introducing the concept of a fire evacuation safety time window to comprehensively assess hospital fire evacuation risk. The findings revealed that the dynamic quantitative risk analysis (DQRA) approach more effectively captures the influence of fire products on the evacuation risk compared to static methods. Specifically, the peak incapacitation probability in a hospital fire reached 0.85, with firefighting equipment, especially the sprinkler system, reducing this risk by over 97% and decreasing evacuation time by 45%. In addition, the risk of fire evacuation in hospitals reaches a critical threshold in the fourth year, enhancing the repair rate of the firefighting system postpones the risk's escalation to a critical threshold until the fourteenth year.

The Use of Fire Dynamics System (NIST) in Determining The Architecture of Educational Spaces for Children and Young People

Objective: This study aims to investigate the potential of the Fire Dynamics Simulator (FDS) software, developed by the National Institute of Standards and Technology (NIST), as a tool to assess and improve Fire Safety (FS) in educational environments, specifically in the classrooms of CEFET in Araxá (MG), Brazil. Theoretical Framework: The research is based on the importance of fire safety in educational environments, highlighting the vulnerability of children and young people. Concepts of fire behavior, smoke propagation, and thermal conditions in buildings are addressed. Method: The methodology adopted for this research involves detailed computer simulations using FDS to analyze different fire scenarios. The simulation results were validated with the PyroSim software. Data collection was conducted through these simulations, generating robust empirical data that support the review and development of specific regulations. Results and Discussion: The results indicate that FDS is an important ally in promoting fire safety in educational buildings. The simulations showed the effectiveness of FDS in predicting fire behavior, smoke propagation, and thermal conditions, helping to prevent and minimize potential damages. The discussion contextualizes these results, highlighting the need for accurate empirical data to strengthen Brazilian fire safety legislation. Research Implications: The practical and theoretical implications of this research are discussed, providing insights into how the results can be applied to positively influence legislation, optimize architectural designs, and promote safety guidelines in educational institutions in Brazil. Originality/Value: This study significantly contributes to the advancement of knowledge and practices in FS. The originality of the research lies in the application of FDS for simulations in educational environments, offering a robust tool for evaluating and improving fire safety.

Numerical simulation and safety assessment of fires in historic timber structures based on fire load investigation

Historic timber structures face substantial fire loads and complex fire risks. Subsequent renovations and utilization may influence their fire safety performance. Therefore, accurately predicting indoor fire development in historic buildings and assessing their fire safety performance is crucial. Numerical fire simulation is currently at the forefront of analyzing and assessing fire risks in historic buildings. However, there is a shortage of globally accessible historic building fire data. This paper proposes a method to determine fire scenarios, peak heat release rates, and development curves of indoor fires in wooden historic buildings through a fire load investigation. Using the Guangzhou ancestral hall as an example, PyroSim fire dynamics simulation software is employed to calculate fire development and assess the available safe evacuation time. The simulation results are subsequently input into the Pathfinder evacuation simulation software to ascertain the required safe evacuation time for indoor occupants. A comparative assessment is conducted to evaluate the fire safety performance before and after the renovation of historic buildings. The research findings indicate that installing closed glass curtain walls in the courtyards of ancestral hall buildings in Guangzhou accelerates the infiltration of smoke during fires, leading to rapid fire spread and long-distance ignition, significantly reducing the time available for safe evacuation. Therefore, when renovating and utilizing the ancestral hall buildings in Guangzhou, the installation of ventilation and smoke extraction systems should be prioritized to slow down fire development. Additionally, controlling the number of indoor occupants is an effective management measure to mitigate fire damage in historic buildings.

Simulation of Fire Evacuation in a Naturally Ventilated Bifurcated Tunnel

The natural wind velocities in tunnels under different natural conditions are distinct, and the longitudinal ventilation velocity significantly impacts the evacuation environment. This paper examines the evacuation conditions and strategies under varying wind velocities in bifurcated tunnels. Using Fire Dynamics Simulator (FDS) and Pathfinder software, the fire development and evacuation of three distinct longitudinal positions in a bifurcated tunnel are simulated. The simulation results demonstrate that the evacuation conditions for disparate fire sources at varying wind velocities are markedly disparate. In consideration of the construction cost and the maximization of evacuation capacity, the width of the evacuation doors at the three locations should be set to 2 m, 1.5 m, and 1.5 m, respectively. Furthermore, an analysis of the safety of individual personnel through Fractional Effective Dose (FED) revealed that directing evacuees towards the upstream of the fire after the fire is detected can significantly reduce individual personnel injuries while ensuring the overall success of the evacuation.

A critical analysis of the influence of architecture on the temperature field of RC structures subjected to fire using CFD and FEA models

The temperature–time-heating curve describes the dynamics of a fire in a room. A variety of factors related to the architecture and the thermal properties of the furniture influence the temperatures. The reinforced concrete (RC) structures of the buildings are designed for the case of fire with standardized curves that ignore the real fire temperatures. In this study, a group of individual rooms were solved numerically to understand the thermal cross-sectional field in RC structures based on real fire curves. The fire dynamics of the room were defined by a computational fluid dynamics (CFD) model solved with the Fire Dynamics Simulator (FDS) software. A finite element analysis (FEA) model was created for the RC structures and solved using Abaqus software. A typical RC ribbed slab on the roof of the room was considered. The structure was heated according to the real and standardized fire curves. The real fire temperatures were up to 70 % lower than those predicted by the standard. The results show how safe the buildings are from fire-induced collapse.

BUILT‐UP COLD‐FORMED STEEL‐LIGHTWEIGHT CONCRETE (CFS‐LWC) COMPOSITE BEAMS SUBJECTED TO ELEVATED TEMPERATURES

AbstractCold‐formed steel (CFS) products are extremely versatile and can be used in multiple applications. Recent experiments tests by the authors have shown that mobilising composite action within systems comprising cold‐formed steel beams and lightweight concrete is feasible and can lead to substantial improvements in structural performance. However, their behaviour subjected to elevated temperatures has yet to be investigated; this is, therefore, the focus of the present study. The results of two tests on CFS‐LWC beams at ambient and elevated temperatures are reported. A numerical modelling study using fire dynamics simulator (FDS) software is then described in which the temperature development was successfully replicated.

Effect of Door Openings on Train Fire Scenarios within a Subway Depot

It is challenging to control smoke in the case of a train fire occurred in the subway depot with a complex internal structure. In this paper, the effect of door opening state on smoke behavior characteristics induced by subway depot fire scenario was investigated. A series of numerical simulation were conducted by Fire Dynamics Simulator (FDS) software. Three key parameters were analyzed corresponding to the temperature, visibility and CO concentration for evaluating smoke propagation respectively. Results show that temperature distribution and CO concentration at 2 m height inside the train with train door opening state are lower than those with the train door closed. However, visibility at 2 m height inside the train shows the opposite trend. The results can provide reference in the ventilation system design and emergency evacuation scheme for the subway depot.

Assessment of Agent Avoidance Behavior in the Face of Fire Hazards

ABSTRACT An assessment approach is proposed to assess the injury consequences of evacuation in the face of fire hazards, taking into account the spatial-temporal distribution of fire hazards and the time-varying location of agents. In this study, the diffusion process of fire hazards is simulated first using the fire dynamics simulator (FDS version 6.7.7) software, and an assessment approach is proposed, when fire hazards including toxic gases, thermal radiation, high temperature, and extinction coefficient are considered. Then, a novel fire avoidance model based on the modified social force model is proposed, and the impacts of heat release rate and soot yield on the injury consequences are discussed. The results demonstrate that an increase in heat release rate leads to an increase in the temperature and radiation values near the fire source, which directly raises the injury consequences. Soot yield primarily affects environmental visibility and thus the agent’s evacuation speed, which in turn affects the exposure time in fire hazards and injury consequences. Finally, the proposed fire avoidance model is compared with the existing radiation repulsive force model and the interaction force model between agents and fire. It is concluded that the proposed fire avoidance model can present a more reasonable fire avoidance behavior with significantly less cumulative injuries than the existing fire avoidance models.

Влияние скорости воздушного потока на тепловое излучение от углеводородного пожара в резервуаре для хранения нефти

Purpose. The article assesses the effect of air flow velocity on the intensity of thermal radiation from a fire in a vertical steel tank with a floating roof of 65 000 m3 capacity (VSTWFR-65000) with crude oil. The indicators of hazardous fire factors - open flame, smoke and temperature at different wind speeds – have been studied. Methods. The method of numerical modeling in the Fire Dynamics Simulator software package, as well as the method of processing the obtained research results have been used in the study. Findings. The dependence of the flame inclination angle at different air flow speeds has been obtained. The simulation results have been shown: smoke distribution at different wind speeds, as well as temperature change at a distance from the fire source depending on the air flow velocity. Research application field. The results of the study can be used in the development of design documentation for measures to ensure fire safety of a tank farm with floating roof tanks, as well as in adjusting fire extinguishing plans. Conclusions. Based on the simulation results it has been found that with an increase in the air flow velocity the intensity of thermal radiation initially increases and then decreases. It has been found that at an air flow velocity of 9 m/s the maximum thermal radiation reaches 23.43 kW/m2 at the nearest point of the adjacent tank in the projection from the central axis of the burning tank. At an air flow velocity of 6.5 m/s the temperature at the top of the adjacent tank reaches 176 °C, and at 9 m/s – 426 °C, which is higher than the autoignition temperature of oil, which is within 222–256 °C, there by creating a threat of fire spread. The study has defined the maximum distances from the burning VSTWFR-65000 for the safe presence of people, amounting to 47.3; 48.9; 50.2; 53.4; 55.7; 56.8; 59.4 m for wind speed of classes 0, 1, 2, 3, 4, 5 and 6 respectively.

Fire Hazard Analysis on Different Fire Source Locations in Multi-Segment Converging Tunnel with Structural Beams

To investigate the fire risk in a complex tunnel with varying cross-sections, sloped structures, and dense upper cover beams, this study considered four fire source positions: the immersed tube section, confluence section, highway auxiliary road section, and four-lane sections of the main line. It also considered four beam spacings: 1 m, 1.8 m, 3.6 m, and 7.2 m. The Fire Dynamics Simulation Software FDS was utilized to create a comprehensive tunnel model. The analysis focused on temperature and visibility changes at a 2 m height under a 20 MW fire condition for different fire source positions. These changes were then compared with critical danger values to assess the safety of evacuating personnel within the tunnel. Subsequently, this study proposed corresponding emergency rescue strategies. The findings indicated that when the beam grid spacing exceeded 3.6 m, the upper dense beam gap showed a robust smoke storage capacity, leading to a reduced distance of high-temperature smoke spread. However, this increased smoke storage disrupted the stability of the smoke layer, resulting in a heightened smoke thickness. The location of the ventilation vent at the entrance of the immersed tunnel section caused a non-uniform ventilation flow under the girder, deflecting the smoke front towards the unventilated side and decreasing visibility in the road auxiliary area. In comparison to scenarios without a beam lattice, the presence of a beam lattice in the tunnel amplified fire hazards. When the beam lattice spacing was 3.6 m or greater, the extent of the hazardous environment, which is unfavorable for personnel evacuation, expanded. With the exception of the scenario where the fire source was located in the highway auxiliary roadway, all other conditions surpassed 150 m, which is roughly one-third of the tunnel length. Consequently, more targeted strategies are necessary for effective evacuation and rescue efforts.

Determination of heat transfer process in vertical cable tunnels of nuclear power plants under real fire conditions

The object of the study was heat and mass transfer processes occurring in vertical cable tunnels. The problem to be solved was the definition of process mechanisms in the inner space of the tunnel. For this, field tests were conducted, mathematical models were created, and computational experiments were conducted to establish specific parameters that affect the temperature regime of a fire in a vertical cable tunnel of a nuclear power plant. The dynamics of temperature changes with known geometric parameters and fire load were determined, and the adequacy of mathematical models built in the Fire Dynamics Simulator software was investigated and computational experiments were carried out. It has been proven that they consist in determining the temperature regime in a vertical cable tunnel of a nuclear power plant with known technical and geometric parameters. Such studies have practical applications in the field of safety of nuclear power plants and the development of new technologies in this field. An important conclusion of these studies is the possibility of determining the fire resistance of building structures of vertical cable tunnels of nuclear power plants with the selection of the most severe temperature regime, according to the conducted field test. This means that research results can be used in practice in designing and evaluating the safety of such objects. The conducted research established that the temperature in the inner space of the tunnel can reach values from 1200 to 1400 ℃. The following factors influence the maximum temperature value and the maximum time to reach the maximum temperature in the fire cell: fire load, height and area of the tunnel. With a lower fire load, the maximum temperature in the vertical cable tunnel of the nuclear power plant was 75 % lower. Therefore, the results of these studies have a direct practical application in the field of safety of nuclear power plants and can be used to improve and develop new technologies in this field

Thermal Hydraulics Simulation of a Water Spray System for a Cooling Fluid Catalytic Cracking (FCC) Regenerator

Olefins are crucial building blocks for petrochemical industry, serving as raw materials for the production of various products such as plastics, synthetic fibers, detergents, solvents, and other chemicals. In FCC, heavy petroleum feedstocks are injected into a catalytic cracking unit, where they are mixed with a catalyst. The catalyst aids in breaking down the large hydrocarbon molecules into smaller fragments, including olefins like Propylene and Ethylene. These polymerization reactions occur at high temperatures. They demand that heat removal occurs as quickly as possible in order to control the reactor temperature and to avoid “hot spots” in the Regenerator or localized oxidation reactions (and to avoid creep rupture of the regenerator steel cladding). The cooling of the regenerator cladding surface can be achieved by impinging water droplets (spray), ejected from a spray nozzle. Spray cooling can provide uniform cooling and handle high heat fluxes in both a single phase and two phases. This research provides a thermal hydraulic design of regenerator spray cooling systems. In the framework of this research, Fire Dynamics Simulator (FDS) software was applied in order to simulate the temperature field and the water vapor mass fraction. A COMSOL Multiphysics finite element code was used in order to calculate the temperature field inside the regenerator cladding. The calculated surface temperatures and heat transfer convective coefficient, obtained using FDS software, were validated successfully against COMSOL numerical results and previous results in the literature. The numerical simulations were carried out for two cases. The first case was carried out at a distance of 0.5 m, and the second case was carried out at a distance of 0.2 m. A grid sensitivity study was carried out on the FDS model. Numerical integrations were carried out over time in order to calculate the average temperatures. The difference between these four average temperatures, calculated by applying different grids, is less than 7.4%. The calculated surface temperatures and heat transfer convective coefficient were validated successfully against COMSOL numerical results and previous research. It was shown that the calculated temperatures decrease in the second case. The water spray system managed to cool the steel wall more effectively as the water spray system approaches the steel cladding.

Fire Effect and Performance of Bridge Pylon Columns under Construction

The fire effect and performance of bridge pylons under construction were investigated via an analysis conducted on two types of pylons with different wall thicknesses. Three fire scenarios, namely internal fire, external ring fire, and external side fire, were established for a 40 m high section of the bridge pylon under construction. The distribution of fire smoke and temperature was obtained using fire dynamics simulation software for different fire scenarios. In addition, a finite element simulation was performed using the thermal–mechanical coupling method to obtain the temperature, stress, and deformation of the columns. The simulation results demonstrate that the average temperature of the internal fire is higher. The chimney effect extends the height range of temperature influence. In the vertical direction, the temperature decrease curve for the internal fire follows a single negative exponential function, while the external fire adheres to a double negative exponential function. The thickness of the temperature influence in the bridge pylon is extended by heating to approximately 200 mm. The stress value considering the thermal expansion coefficient is nearly 27.5 times that without the expansion coefficient, while the deformation value increases by 1 to 8 times. In conclusion, the calculations of the coupled expansion coefficient are helpful in improving the fire safety of bridge pylons.

Real-time evacuation route optimization in the fire scenarios of cruise ships

The optimization of evacuation routes for evacuees in fire scenarios on cruise ships directly affects evacuation efficiency. A time-varying equivalent weight Dijkstra algorithm (TVEWDA) is proposed, combining a fire dynamics simulator (FDS) to find optimal evacuation routes in case of a sudden cruise ship fire. First, the FDS software is used to simulate a cruise ship's single and multi-source fire scenarios. Second, the Dijkstra algorithm using only distance between nodes is improved by considering the effects of CO concentration, visibility, and temperature. The evacuees’ speed is taken into consideration within the TVEWDA. The effects of congestion are considered in the evacuees’ moving speed. Finally, the TVEWDA and a cruise ship evacuation network model are integrated to develop a real-time evacuation route optimization model. Simulation results show that the evacuation time achieved by the TVEWDA is 22% shorter than that of the Dijkstra algorithm using only distance between nodes and 11% shorter than that of an improved social force model in the multi-source fire scenario. This approach is well-suited to guide the evacuation of cruise ship evacuees in the event of single-source or multi-source fires, effectively ensuring the safety of passengers and the preservation of their property.

An engineering model for the pyrolysis of materials

Accurately representing the time dependent heat release rate of fuels is critical to performance-based design in fire safety applications. Existing simplified models either use average pyrolysis rates at different heat fluxes or do not account for the change in burning behavior at higher heat transfer rates. This paper presents the theoretical basis of a scaling-based pyrolysis model, S-Pyro. The model is based on the concept of maintaining the shape of a reference heat release rate per unit area curve but scaling the magnitude and time based on a dynamic thermal exposure. The model has been implemented in the computational fluid dynamics software Fire Dynamics Simulator (FDS). The model is validated with solid-phase only and multi-phase simulations of cone calorimeter experiments. The solid-phase simulations evaluated the capability of the model to predict the heat release rate per unit area of 149 materials tested at heat fluxes other than the reference flux. Multi-phase simulations of bench-scale fire experiments with a single material, Canada Pine and Spruce plywood, were used to evaluate the performance of the pyrolysis model in FDS. The model uncertainty was lower for high heat release rate materials, with the model uncertainty approaching the experimental uncertainty at higher burning rates.

An open-source software framework for the integrated simulation of structures in fire

The traditional methods to understand the development of elevated temperature in a structure, and also the associated structural response, are not representative of realistic fire scenarios. To provide a more accurate and realistic reflection of the fire development, the current paper develops a generic middleware which interfaces between the computational fluid dynamics (CFD) software Fire Dynamics Simulator (FDS) and the finite element (FE) analysis software OpenSees. This framework enables a fully integrated simulation of a realistic fire scenario including the heat transfer through the structure and the resulting thermo-mechanical response. The proposed framework is open-source and freely available and therefore can be used and further developed by researchers and practicing engineers and customised to their requirements. This paper shows validation against two sets of experimental results and one real fire incident. A number of different types of thermal boundary conditions such as gas temperatures and heat fluxes, are obtained from the CFD analysis and are then used in the subsequent heat transfer and thermo-mechanical analysis. The primary advantage of this computational tool is that it provides consultants and designers with the means to undertake large-scale projects requiring performance-based fire engineering solutions.

Adapted FLASHCAT methodology to model horizontal cable tray fires using computational fluid dynamics

Nuclear power plants (NPPs) have an extensive network of electrical cables and associated trays to support daily operations. As electrical cables have combustible mass, their presence adds to the fire load in such plants. Thermal stress from cable fires can cause cable failures and spread fire to other redundant cables or other equipment, jeopardizing the safe operation of NPPs. Assessing the heat release rates (HRR) of cable fires is critical for the nuclear industry as HRR regulates the thermal stress in the surrounding of a fire and other fire products that can damage the facility. This paper presents a computational fluid dynamics-based method to model the HRR of such cable fire. The method is partly based on the FLASHCAT model (modified and adapted here) and the surface temperature ignition model of the Fire Dynamics Simulator (FDS) software. The simulation set up with validation objective replicates an experiment of OECD PRISME 3 program in which cables arranged over two horizontal trays are burnt. HRR obtained from the simulation had peak HRR underestimated by 4%, and the time to reach peak HRR overestimated by 5%. The result is encouraging as it provides confidence in using the method outlined in the paper.

Modelling and Numerical Simulation of a Compartment Fire: Flow Rate Behaviour at Opening

The modelling of fire behaviour in a compartment is the subject of this work. A small-scale experimental study was carried out in a compartment sized 0.5 m × 0.5 m × 0.5 m with a single door with a width of 0.2 m and a height of 0.4 m. The collected results were converted to full-scale results using Froude modelling. The objective of this study was to see how ventilation affects fuel decomposition rate, gas flow rate at the opening and the power generated inside the compartment. This small-scale experimental study allowed us to determine four values of the fuel’s (diesel) mass loss rate, which correspond to four values of the ventilation factor. Numerical simulation using Fire Dynamics Simulator (FDS) software was used to show the gas’ behaviour at the opening and the variation of the power generated inside the compartment. The vertical profiles of the experimental and numerical temperatures were compared. It was found that the dimensions of the opening have a significant influence on the power generated inside the compartment.

Исследование влияния температурного режима пожара на эффективность вспучивающегося огнезащитного покрытия, предназначенного для огнезащиты стальных конструкций

Introduction. The usage of intumescent coating (hereinafter referred to as IC) is justified by the development of a fire protection project, taking into account the data on its fire protection efficiency, estimated under the influence of standard temperature conditions, the usage of which can lead to overestimating the fire resistance margin in the project or underestimating the thermal impact on the steel building structures with IC fire protection in conditions of a real fire. Aims and purposes. The purpose of the study is to evaluate the effect of fire temperature conditions on the effectiveness of IC. To achieve this goal, the following tasks were carried out: a temperature mode of fire in a building under different fire loads by the example of a warehouse building was estimated; experiments to estimate the influence of different heat fluxes, reduced thickness of metal and IC thickness on its effectiveness by the full factor experiment of the type 2 were conducted. Methods. To mathematically simulate real temperature fires, the Fire Dynamics Simulator (FDS) software package, which implements a field (differential) mathematical model, was used. To study the effect of the obtained fire temperature regimes on the effectiveness of IC, experiments were carried out according to the plan of a complete factor experiment type 2. The test specimens were carbon steel metal plates with dimensions of 100 × 100 mm with reduced thickness of 3 and 4.5 mm and painted with 0.25 and 0.5 mm organic-based single-component IC. A radiant heat flux panel with a radiant heat flux density of 10 to 50 kW/m2 was used to assess the effects of heat flux. Results and discussion. In the course of numerical experiments in the FDS software package, it was found that the thermal impact on steel building structures during a fire can differ significantly from the standard temperature regime, both upwards and downwards. The results of the experiment showed that the heating time of the test samples had the greatest influence of the actors under consideration (the value of the heat flux, the reduced thickness of the metal, the thickness of IC) had the value of the heat flux, as the largest absolute value of the regression equation was obtained. Conclusion. The assumption of possible underestimation of the thermal effect under “standard” temperature conditions on the fire resistance of steel building structures with IC fire protection was confirmed by the tests.

Effects of ambient pressure on fire-induced buoyancy driven plume dispersion and re-entrainment behavior in a street canyon

The present study investigated the effects of ambient pressure on fire-induced buoyancy driven plume dispersion and re-entrainment behavior in a street canyon. A series of numerical simulations were conducted adopting Fire Dynamics Simulator software with heat release rate, wind flow velocity and ambient pressure varying. The results show that the fire smoke diffusion characteristics can be divided into four regimes, i.e., buoyancy-dominated regime, transition regime, critical regime and wind-dominated regime. The ambient pressure can influence the smoke diffusion in the street canyon, and the smoke flow patterns under relatively larger ambient pressure are more susceptible to wind flow. The dimensionless ambient pressure P* was introduced to quantify the effect of ambient pressure on critical re-entrainment wind velocity, and a prediction model of critical re-entrainment wind velocity was proposed. Further, considering the influences of ambient pressure and entrainment coefficient, a uniform correlation was proposed to predict the temperature rise ΔT at different heights in the plume region. Besides, the critical Fr number was insensitive to the ambient atmospheric pressure. A good correlation for predicting the critical value of the Fr number was given based on the analyses in this paper.