Non-dimensional Heat Release Rate Research Articles

Effect of ambient wind on horizontal flame spread over discrete multi-column fuel arrays

The flame spread behaviors of discrete charring fuels are significantly influenced by ambient wind. This paper studied the horizontal flame spread characteristics of discrete birch rod arrays under ambient wind experimentally and theoretically. Here, seven kinds of array spacings (denoted by S, 7–19 mm) and four kinds of wind speeds (denoted by U, 0.5–2.0 m/s) were designed to develop 28 experiments. The experimental results show that the flame inclination angle decreases as wind speed increases. The non-dimensional flame length and the non-dimensional heat release rate are also found to be correlated, and two ignition modes under the action of ambient wind were differentiated. The flame spread rate and wind speed have a linear relationship based on experimental data. The ratio of wind speed to fuel loading is introduced to further examine the variation of flame spread rate. In this article, a heat transfer model is established by simplifying discrete flame spread process and incorporating both radiative and convective heat transfer. A prediction model for flame spread rate is presented, which aligns well with the experimental results. Finally, the mass loss rate under the ambient wind is discussed.

Experimental study on the flame merging and temperature profile produced by two pool fires beneath the curved ceiling

Compared to single-source fires in tunnels, double-source fires may exhibit more intricate flame merging behavior and higher flame burning rates due to their interaction, thereby escalating the risk of fire propagation within the tunnel. In this investigation, a 1:10 scale model of a horseshoe-shaped tunnel test site was deployed to conduct experiments on lateral double-source fires, scrutinizing flame merging behavior, probability prediction models, and temperature characteristics of tunnel ceiling smoke gas by varying the oil pool size and double-source spacing. Findings from the study suggest that flame merging behavior within the tunnel is contingent upon double-source spacing and heat release rate (HRR), manifesting in three distinct forms: complete merging, intermittent merging, and complete separation. Through the introduction of non-dimensional heat release rate and non-dimensional fire source spacing, a piecewise function has been devised to forecast the probability of flame merging for both fire types. Furthermore, a predictive model for the maximum temperature rise along the longitudinal centerline of a horseshoe tunnel was formulated, drawing from established theoretical frameworks.

Flame extension length and temperature profile beneath ceiling induced by endwall-attached fire inside compartment with lateral openings

This study experimentally investigated the fire characteristics of endwall-attached fire within the long-narrow compartment, including the flame extension and temperature profile. Experiments were conducted in a reduced scaled compartment featuring multiple lateral openings. Results show that the previous models of flame extension length and temperature rise in the literatures, whether for sidewall fires in tunnels or central fires in compartments with lateral openings, cannot predict the experimental data in this study. A new correlation is proposed for the flame extension length based on non-dimensional heat release rate. The longitudinal temperature profile generated by endwall-attached fires in compartment can be classified into three distinct regions related to the position of the lateral opening: temperature rapid decrease region, temperature slow decrease region, and backflow region at the end of the compartment. A model for the maximum temperature rise and a piecewise equation based on single exponential function for temperature decay profile are proposed, and these equations effectively correlate the experimental data. The findings of this study can deepen the understanding of fire dynamics within similar building structures and have value for the fire hazard assessment.

Experimental study and newly proposed correlations for maximum ceiling gas temperature rise in tunnel fires with natural ventilation

As a critical factor in tunnel fire safety, previous research on model predictions of the maximum ceiling gas temperature rise under natural ventilation has not demonstrated consistent results. These discrepancies are commonly attributed to variations in tunnel dimensions and materials. To address this issue, an experimental investigation utilizing heptane pool fires with different dimensions was conducted in a model-scale tunnel. The results show that the burning rate increases with an increasing aspect ratio of the fire source for the selected diameter range of 0.078–0.169 m. The flame length was characterized using a modified diameter of the fire source considering the air entrainment, and found that the non-dimensional flame length is 2.4 times the 2/5th power of the non-dimensional heat release rate. Finally, incorporating the concept of flame virtual origin, two different forms of correlations were developed to quantify the maximum ceiling gas temperature rise under different impingement conditions of the fire plume, and the coefficients were determined as 0.065 and 0.215 by numerous experimental results from different studies. The newly proposed models demonstrate good applicability to the fire sources with different dimensions, especially for the rectangular fire source with a large aspect ratio, thus solving the problem of insufficient accuracy of classical models under this condition.

Generic flame extension model development based on machine learning for NPPs fire hazard analysis (FHA)

Abstract In enclosed fire situations, the flame interacts with ceiling and its length extension take place, altering the fire severity significantly. Fire safety analysis demand a generic flame extension model. A generic reliable model is not available as the construct of flame itself had wide variation in literature. The present paper aims to develop a Machine Learning (ML) based generic model of non-dimensional flame extension as a function of non-dimensional Heat Release Rate (HRR). The non-dimensional scaling reduces the number of parameter and also provide a generic nature. Literature review was utilized to collect the data from various open literature sources. This eliminates the limitations of individual correlations and gives a best optimized model which is valid for a wide range of flow regimes and conditions as compared to a specific correlation. Various simple ML models are compared for their performance against test data and a MARS based model was finally recommended. The MARS model was tested against the data which was not used in training and also against the other reported correlation. The developed model has performed well against the test data and marked improvement over other reported correlation as a better optimized performance over an extended range of non-dimensional range. The results of the model were also conservative as compared to another model in the most of the practical requirement of NPPs. A Large Eddy Simulation (LES) based CFD code FDS was also used to generate the flame extension data for demonstrating conservative nature of the ML model.

Experimental study on flame geometric of horizontal jet fire inpinging a facing wall and side wall

This work focuses on investigating the characteristics of restricted horizontal jet fire caused by fuel leakage as a pipeline or tank fracture. The study aims to quantify the effect of the exit velocity and nozzle-facing wall distance on the flame height and width, as well as developing a new non-dimensional heat release rate, Q*n , to better characterize the flame geometry. The study conducted three nozzle-facing wall distances (0.05 m, 0.10 m, and 0.15 m) with varying fuel ejection speeds from 1.04 m/s to 6.25 m/s. Results show that the flame height and width increase with both the nozzle-facing wall distance and fuel ejection speed. The sidewall constrains the air entering into the fire plume, which pushes the flame closer to the sidewall. A new non-dimensional heat release rate, Q*n , was proposed on the basis of plate-nozzle distance, that the flame height and width fit well with the 1/4 and 2/5 power of Q*n , respectively. The global model was developed for flame size under multiple restrictions. The findings of this study are crucial in improving our understanding of the restricted horizontal jet fire accidents caused by fuel leakage and can aid in developing measures to minimize potential casualties and economic losses.

Temperature evolution, flame behavior and extinction inside compartment with a ceiling vent under the ambient wind

This article presents an experimental and CFD simulation investigation and analysis on temperature evolution and flame behavior inside compartment with a ceiling vent under ambient wind. Experiments were conducted employing a reduced-scale model containing a cubic fire compartment with a ceiling vent under the external wind generated by a wind tunnel. The temperature of windward and leeward inside compartment as well as the flame behavior were recorded for various vent dimensions, heat release rates and wind speeds for a total of 720 test conditions. Results show that there are two types of fire behavior regimes inside the compartment for relatively small- (Bernoulli flow regime) or large vents (oscillatory exchange flow regime). With a relatively small vent, the flame is located at the center of compartment and the temperatures of windward and leeward are almost the same with or without the ambient wind. Then the flame turns to extinct due to lack of oxygen with increasing of fuel supply. However, with a relatively large vent, there is a flame transition from windward to leeward accompanied by the transition of temperature distribution with increasing of fuel supply when subject to ambient wind. Such extinction and transition mechanisms are interpreted by the aid of CFD simulation of global equivalence ratio and flow/oxygen field inside compartment. The critical heat release rate for the occurrence of flame transition decreases with raising wind speed while increases with vent size. Their complex dependence is found to be well represented in terms of a non-dimensional heat release rate as a function of the wind Froude number, employing the vent area-equivalent characteristic diameter as length scale. These new findings facilitate the understanding of the compartment fire evolution with a ceiling vent subject to ambient wind.

Evaluation of flame geometry of horizontal turbulent jet fires in reduced pressures: A numerical approach

Accidental releases of hydrocarbons can result in jet fires, which have the potential to escalate accidental events to catastrophes. The geometry and size of a jet flame are vital parameters deciding the potential of the flames to trigger such a series of accidental events called domino effects. In this study, Computational Fluid Dynamics (CFD) simulations on horizontal turbulent jet fires are carried out using Fire Dynamics Simulator (FDS®). The results are validated with previous experimental results. Eight different fuel exit velocities ranging between 27.5 and 125 m/s, and 5 different ambient pressures: 0.6, 0.7, 0.8, 0.9 and 1 atm, are used for studying two main flame geometrical parameters: jet flame length and flame area. The simulation results obtained for the flame lengths are found to be higher in reduced pressure cases. In the present study, the classic correlation proposed by Quintiere and Grove is extended to reduced pressure conditions by refining the ‘air entrainment strength (C)’ values. These air entrainment strength constants were found to have a linear relationship with the ambient pressures. In addition, it is revealed that low ambient pressure conditions can also result in higher jet flame areas. The previously established relationship between the flame area and the non-dimensional heat release rate (i.e.AF∼Q*4/5) is also verified with the present obtained results, with an introduced proportionality constant (k) showing linear variations with the ambient pressure.

Study of elevated- and ground pool fire flame horizontal lengths in cross airflows: Air entrainment change due to Coandă effect

The present study investigates experimentally the flame horizontal lengths of elevated pool fires and compares with those of ground pool fires in cross airflows. This, as a fundamental problem considering air entrainment and combustion structure change due to Coandă effect resulted from ground at leeward side, has not been quantified but is of practical significance. Experiments were performed employing both elevated- and ground square propane pool fires of various heat release rates in cross airflows from 0∼3.0 m/s with 224 test conditions in all. The overall flame horizontal length could be physically divided into two parts: 1) cross flow momentum-dominated length (base-drag part, Lm); 2) buoyancy-dominated length (plume-like part, Lb). Both the Lm and the overall flame horizontal length showed to be significantly larger for a ground pool fire than those of an elevated one, due to the ground constraint effect on air entrainment at leeward side (Coandă effect). Lb/(u2/g) or Lm/(u2/g) of elevated fires is proportional to that of ground fires. Large eddy simulations for two representative fire scenarios were further conducted utilizing an in-house version of FireFOAM. The purpose of the simulations was to uncover the underlying physics of combustion and flow structures observed in the experiment. Finally, a model was proposed based on analysis of air entrainment, momentum- and buoyancy effects, which described well the overall flame horizontal lengths of both elevated- and ground pool fires generally as a function of non-dimensional heat release rate, normalized volumetric air entrainment and Froude numbers using Lm and Lb as length scales. This work provides new observation and basic quantification on elevated- and ground pool fire flame horizontal lengths considering air entrainment change due to Coandă effect in wind.

Characteristic studies of diffusion flame tilt angle and length in a branched tunnel fire under the effect of airflow

ABSTRACT The reduced scale experiments were conducted to investigate the LPG flame geometry in branched tunnel fire under different airflow velocities to better comprehend the diffusion flame characteristics in narrow – long space with multiple entrance. Five different heat release rates varied from 1.72 kW to 5.18 kW were considered. The flame tilt angle and flame length were measured and correlated. Results show that the flame tilts downward to multiple entrance direction (ramp and mainline) under natural ventilation, which is mainly related to the asymmetry tunnel cross-section dimensions between fire source two sides. The experiments presented three different flame tilting conditions under different heat release rates and airflow velocities due to the dominance of buoyancy force or inertial force. The flame tilt angle is correlated using the nondimensional heat release rate and Froude number, and the predictions by proposed correlation agree reasonably well with the experimental data. The flame length increases with the heat release rate and elongated by airflow. The empirical model for dimensionless flame length are developed both under natural and longitudinal ventilation.

Flame attachment and downstream heating effect of inclined line fires

Experiments were conducted to quantify downstream heating from inclined fires generated by a 25 cm wide, 5 cm deep gaseous line burner. A variety of orientation angles (θ) and fire heat-release rates (HRR) were employed simulating, at reduced scale, the dynamics of two-dimensional (2-D) inclined flame spread as found in wildland or building fires. The total heat flux q˙f″(x) to a nearly-adiabatic surface ahead of the burner was measured by a water-cooled total heat flux gage at different downstream locations (x). It was found that, with an increase in fire HRR or θ, q˙f″(x) increases. The same is true for both the flame projection length on the inclined surface (Lf,p) and the flame attachment length (La). The location of flame attachment divides a flame into an attachment region (0≤x≤La) and a liftoff region (La<x≤Lf,p). A scaling analysis was performed to correlate the modified non-dimensional heat flux q˙f*(x) and the normalized downstream distance x/La in these two regions as a piecewise power-law function. Lf,p is scaled by a non-dimensional HRR, Q˙θ*=Q˙/(ρ∞cpT∞(gcosθ)1/2D3/2L), together with the angle between a flame and an inclined surface (α). La is well represented by two derived non-dimensional quantities, L/Lf,0 and Lf,p/Lf,0 (Lf,0 is free flame height), based on the analysis of the balance between the buoyancy force of a flame (upward) and the inertial force due to air entrainment (horizontal). The quantitative comparison with previous flame spread tests over inclined PMMA samples demonstrates the effectiveness of the proposed correlations in predicting downstream heating of 2-D flame spread over inclined terrains.

Experimental study of back-layering length and critical velocity in longitudinally ventilated tunnel fire with various rectangular cross-sections

Back-layering length and critical velocity are important parameters in longitudinally ventilated tunnel fires. The present study explored the effects of tunnel aspect ratios on smoke back flow by scale model tests and theoretical analyses. Results show that the increase of the tunnel width will enhance the heat transfer between the smoke and the tunnel boundaries and decrease the smoke layer thickness, reducing the back-layering length and critical velocity. New correlations to predict back-layering length and critical velocity with more comprehensive physical significance were proposed by improving the aspect ratio correction coefficient. The prediction results of the model are in good agreement with the experimental data. The new model indicates that under small fire conditions, non-dimensional critical velocity gradually decreases as the aspect ratio increases and eventually approaches a limiting value, which is the critical velocity without sidewall constraints. The determination of the fire scale relies on the aspect ratio when non-dimensional heat release rate Q* is lower than 0.44. In contrast, the fire is always a large one when Q* is larger than 0.44.

Buoyant turbulent diffusion flame heights of free-, wall- and corner air entrainment conditions: Experiments and global model based on mirror approach

This paper investigates buoyant turbulent diffusion flame height of gaseous fuel combustion in various air entrainment conditions: free-, wall- and corner flames. Experiments are carried out using five square burners with side lengths of 0.3 m, 0.25 m, 0.2 m, 0.15 m and 0.1 m, and five rectangular burners with side dimensions of 0.15 m × 0.3 m, 0.125 m × 0.25 m, 0.1 m × 0.2 m, 0.075 m × 0.15 m, 0.05 m × 0.1 m, to produce corner-, wall- and free flames. The heat release rates (HRR) are in the range of 6.62–26.46 kW for the rectangular burners and 2.21–35.28 kW for the square burners to have 172 experimental conditions comprehensively. It is found that for the same HRR and burner size, the flame height (ℓf) of corner restriction is larger than the flame height of wall flame, and ℓf of wall flame is larger than that of free flame. For a given HRR and air entrainment condition, the flame height decreases with the burner dimension increase. Results also show that the effect of wall or corner on the air entrainment can be represented by the “mirror-approach” with an acceptable deviation (−12.5%~13.5%). At the same time, for free and wall flames, there is a transition of dimensionless flame heights from two-dimensional air entrainment to three-dimensional air entrainment. For corner flame, most of the data fall in the two-dimensional air entrainment condition. Combined with comprehensive data of previous reports together, flame height formulas and critical non-dimensional heat release rates for the transition points are proposed for these three types of air entrainment conditions globally by using the perimeter as the characteristic length scale based on “mirror-approach”.

Experimental study on flame characteristics of double fires in a naturally ventilated tunnel: Flame merging, flame tilt angle and flame height

A series of fire tests was carried out to investigate the diffusion flame characteristics of double fires generated from separated burners in a naturally ventilated tunnel, considering different heat release rates and fire separation distances. The results show that the flame tilt angle, as well as the horizontal projected flame length, first increases with fire separation distance and then remains constant, but the vertical flame length first decreases and then remains constant, which is different from two fires in free spaces where flames do not tilt when the separation distance is relatively long. This difference is caused by the non-dimensional fire induced air flow velocity in the tunnel, which is mainly related to the tunnel cross-section dimensions and burner radius. Three regions can be identified, i.e. flame vertical merging, plume vertical merging and non-merging with flame tilted. The critical flame merging separation distance, estimated by the flame merging probability, is greater than that of two fires in an open environment due to the fire-induced air flows. The merging flame height is lower than that of a single fire with a same heat release rate. A correlation was proposed to estimate flame height of two fires in a tunnel by the modified non-dimensional heat release rate using an air entrainment perimeter as the characteristic length. This work enhances the understanding of diffusion flame behaviors of double fires in naturally ventilated tunnels.

Reduced Pressure Effect On The Flame Length Of Elevated N-Heptane Fires In An Aircraft Cargo Compartment

ABSTRACT This paper investigates the influence of reduced pressure on flame characteristics of elevated n-heptane fires in an aircraft cargo compartment, including the flame height driven by the weak plume and flame extension length driven by the strong plume, in order to provide theoretical support to the fire detection and surface material design. A series of elevated n-heptane pool fire experiments were carried out in a full-size simulated aircraft cargo compartment at different atmospheric pressures (70 kPa, 80 kPa, 90 kPa, 100 kPa). Results show that the experimental data of flame height and flame extension length at normal pressure agree well with Heskestad and Quintiere & Grove models, however, which cannot predict these flame characteristics of elevated fires. As the fire source elevates gradually, the flame height and flame extension length increase. Then modified flame height and flame extension length models at normal pressure were established by considering the elevated height effect. Furthermore, due to reduced pressure effect on the air entrainment into the fire plume, the flame height and flame extension length increase with the decreasing pressure. New flame height and flame extension length correlations applicable to the reduced pressure conditions were proposed by introducing a reduced pressure coefficient and modified nondimensional heat release rates.

Comparison of particulate-matter emissions from liquid-fueled pool fires and fire whirls

Abstract In-situ burning (ISB) is one of the most effective means of removing oil spilled over open water. While current ISB practices can eliminate a large fraction of the spilled oil, they still result in significant airborne emissions of particulate matter. ISBs are classified as large, free-buoyant pool fires, from which black smoke consisting of particulate matter (PM, soot) emanates as a plume. An experimental investigation of soot emissions from pool fires (PF) and fire whirls (FW) was conducted using liquid hydrocarbon fuels, n-heptane and Alaska North Slope (ANS) crude oil, in fuel pools 10 − 70 cm in diameter. Burning attributes such as burning rate, fuel-consumption efficiency, and emissions of PM, unburned hydrocarbons, carbon dioxide, and oxygen consumption were measured. For both fuels and all pool diameters, compared to PFs, FWs consumed fuel at a higher rate, had lower post-combustion residual mass and PM emission rates. Collectively, these resulted in consistently lower PM emission factors (EF PM ) for FWs at all scales. For FWs, EF PM decreased linearly with a nondimensional quantity defined as the ratio of inverse Rossby number to nondimensional heat-release rate. These results show that the addition of ambient circulation to free-burning PFs to form FWs can increase burning efficiency, reducing both burning duration and EF PM across length scales. The reduction in EF PM with increasing influence of circulation is attributed to a feedback loop of higher temperatures, heat feedback, burning rate and air-entrainment velocity, which in turn contributes to maintaining the structure of a FW. Boilover was observed for fires formed with ANS crude oil at the 70 cm scale, although the overall EF PM was not affected significantly. This investigation presents a foundation to evaluate the detailed mechanisms further, such that appropriate configurations can be developed help minimize the environmental impact of ISBs.

An experimental study on flame envelope morphologic characteristics of downward-orientated buoyant turbulent jet fires

This study experimentally investigates flame envelope morphologic characteristics of downward-orientated buoyant turbulent jet fires, where the initial jet momentum is opposite to flame buoyancy that an anti-buoyancy jet configuration is naturally formed. Such configuration exists practically in gas leakage jet fires, however, has not been quantified. Experiments were conducted employing four circular nozzles with propane as fuel. The flame downward distance from nozzle outlet, flame length and flame width were measured at various fuel velocities for such downward-orientated jets. The corresponding flame length and width for upward jets were also obtained for comparison. Results showed that the three flame dimensions increased with increasing fuel velocity or heat release rate. The ratio of flame downward distance to flame length correlated well to a dimensionless length scale, ξℓ, representing buoyancy to initial momentum of the jets. The flame width and flame downward distance normalized by nozzle diameter correlated well to non-dimensional heat release rate by 1/2 power and 3/5 power, respectively; and their ratio can be approached by a -1/10 power consequently. The ratio of flame width to flame length of downward jets increased with heat release rates, being much higher than that of upward jets which first increased then plateaued (0.145) finally deceased with increasing heat release rate. Both the flame downward distance and flame length of downward jet showed to be much smaller than flame length of corresponding upward jet. A formula was proposed to correlate flame downward distance as a function of flame Froude number (Frf). The flame downward distance was initially smaller then, however, increased faster and finally turned to be larger than flame length with increasing fuel velocity. The critical turning state as flame downward distance equaling flame length (namely flame upper tip descending to nozzle outlet level) of downward-orientated jet can be represented by ξℓ*=3.4 or Frf*=1.

Experimental study and analysis on the interaction between two slot-burner buoyant turbulent diffusion flames at various burner pitches

This paper investigated the interaction of two slot-burner buoyant turbulent diffusion flames at various burner pitches. Experiments were conducted by employing two identical slot burners (length: 142.5 mm; width: 2 mm) using propane as fuel at various fuel exit velocities. Results showed that with an increase in burner pitch, the interaction of the two flames made a transition from merging to non-merging, resulting in a complex non-monotonic evolution of flame height. An analytical model was developed to characterize the critical burner pitch for flame merging, which was found to be proportional to the free flame height, or have a 2/3 power law dependence on the fuel exit velocity. As a result of their interaction, the flame merging point height increased till the two flames separated with the increase in burner pitch. Meanwhile, the flame height was shown to first decrease, then increase and finally approach the free flame height with the increase in burner pitch. A scaling non-dimensional formula was finally proposed, based on the analysis of the change in air entrainment into the flame from the space between the two burners with burner pitch variation. This proposed formula was shown to well correlate the above transitions based on a newly defined non-dimensional heat release rate using an “effective” entrainment perimeter as a characteristic length, which includes the burner width and length as well as the additional flame base “extension” due to the change in burner pitch.

A Simple Solution of the Smoke Filling Equation

Thirty four years after the enclosure smoke filling equation was first published by Zukoski, Novozhilov found an exact analytical solution for the case of constant fire heat release rate (HRR). This exact solution is fundamentally important in theory, but quite complicated. In this note, a simple solution is reported for the same case. Because of its simple visual appearance, the formula of this solution can be easily calculated on a hand calculator or on a spreadsheet. Comparing with the exact solution, the relative error of this simple solution is from −5 to 5% in the range where the non-dimensional HRR is larger than 0.001 or the non-dimensional smoke layer height is larger than 0.2. This range covers most practical cases.

Flame projection distance of horizontally oriented buoyant turbulent rectangular jet fires

This paper investigated the flame projection distance (defined as the distance from the nozzle exit to the furthest point of the flame in the horizontal direction) of horizontally oriented buoyant turbulent rectangular jet fires. The experiments as well as the correlations reported previously were limited for axi-symmetrical fire sources that are not applicable for non-axi-symmetrical sources. In this work, experiments were conducted using horizontally oriented rectangular nozzles with aspect ratio, n (nozzle length to nozzle width: n= L/W), varied from 1:1 to 71:1 covering the axi-symmetrical, rectangular and linear sources, employing propane as fuel. Results showed that the flame projection distance increased with the heat release rate growth. At the same time, the flame projection distance decreased with the increase of the aspect ratio n for a given nozzle exit area. A non-dimensional function was then derived for the projection distance, in which a characteristic length scale was found in relation to the nozzle length and width, based on the balance of the momentum flux to the buoyancy flux of the projected flame. A new non-dimensional heat release rate was defined based on the proposed characteristic length scale. The data obtained in this work for different aspect ratios, as well as those reported previously for axi-symmetrical sources, were shown to be well correlated by the derived function in two regimes: (1) for relative small non-dimensional heat release rates, the flame projection distance has a 2/3 power dependency on the heat release rate as for a 2-D trend fire; (2) for relative large non-dimensional heat release rates, the flame projection distance has a 2/5 power dependency on the heat release rate as for a 3-D trend fire. The proposed new correlation provides a more general and practical base for estimating the projection distance of horizontally oriented buoyant turbulent jet diffusion flames.