Air Entrainment Research Articles

Heat transfer and mathematical model of flame geometry of rectangular-shaped pool fire in longitudinal ventilation tunnel

Fire is one of the most serious threats in operation of the tunnel. The thermal radiation disaster of fire is dependent on flame height and inclination angle which are affected by the longitudinal ventilation. The coupling effect of aspect ratio of rectangular container (n = 1, 2, 4, 8, 16) and longitudinal wind on flame geometry of heptane pool fire are revealed. The flame height decreases with an increase in the wind, while the inclined angle increases in longitudinal winds of 0–2.49 m/s. The variation of flame geometry is interpreted using the mechanical equilibrium of horizontal inertial force and gas uprising buoyancy induced by liquid fire. According to air entrainment theory and heat feedback theory, the flame height and inclined angle of rectangular-shaped fire change with characteristic scale ratio (n+1n) in mathematics. The measurements of flame height and inclined angle are analyzed and several quantitatively mathematical equations incorporating heat release rate, characteristic scale ratio, non-dimensional burning rate, non-dimensional air flow are proposed. The predicted results of flame geometry are fully validated by experimental measurements. The current finding is convenient for establishing radiation model of pool fire in air-blown condition.

Resistance of Concrete with Crystalline Hydrophilic Additives to Freeze–Thaw Cycles

The study explores the hypothesis that crystalline hydrophilic additives (CA) can enhance concrete’s resistance to freeze/thaw cycles, crucial for assessing building durability. Employing EU standards, the research evaluates concrete resistance through standardized European freeze/thaw procedures. Monitoring concrete slabs exposed to freezing in the presence of deionized water and in the presence of 3% sodium chloride solution, the study measures surface damage and relative dynamic modulus of elasticity. Additionally, it assesses internal damage through monitoring of relative dynamic modulus of elasticity on cubes and prisms submerged in water and exposed to freezing/thawing. The pore spacing factor measured here aids in predicting concrete behavior in freeze/thaw conditions. Results suggest that the standard air-entraining agent offers effective protection against surface and internal damage due to freeze/thaw cycles. However, the CA displays potential in enhancing resistance to freeze/thaw cycles, primarily in reducing internal damage at a 1% cement weight dosage. Notably, a 3% replacement of cement with CA adversely affects concrete resistance, leading to increased surface and internal damage. The findings contribute to understanding materials that can bolster concrete durability against freeze–thaw cycles, crucial for ensuring the longevity of buildings and infrastructure.

Paste, aggregate, or air? That is the question.

The Ambassador Bridge between Detroit, Michigan, and Windsor, Ontario, has served for almost 100 years as North America's busiest international border crossing. But in 2025, the Ambassador will be replaced by the new Gordie Howe International Bridge. The Gordie Howe is a cable-stayed bridge, with two massive 220 m tall concrete piers on opposite banks of the St. Claire River, a single clear span of 853 m, and 42 m of clearance over this busy waterway. To ensure durability in this harsh freeze-thaw environment, air-entrained concrete is specified throughout. And, to ensure the quality of air entrainment, the ASTM C 457 Procedure C, Contrast Enhanced Method is employed. While a similar automated microscopic approach has been in use for well over a decade according to EN 480-11 Determination of air void characteristics in hardened concrete, this is the first large-scale application of automated air void assessment in North American infrastructure. According to the ASTM Procedure C, the air void characteristics are determined through digital image processing, while the paste content may be determined by either mix design parameters, manual point count, or 'other means'. Of these three options, point counting is used for Gordie Howe; but in parallel, during each point count, the digital image coordinates and phase identifications for each evaluated stop are recorded. This allows for training of a neural network, for automated determination of paste content, as demonstrated here.

Dispersion and Spatial Distribution of Air Voids or Microspheres in Assessing Frost Resistance of Concrete

Abstract The standard spacing factor developed by Powers is typically used to evaluate the quality of the air void system in hardened concrete, but it does not always correlate with durability of the concrete. Several air void spacing equations, which are also applicable when polymeric microspheres are used in place of air entrainment, have been proposed because of the need for a more robust and comprehensive basis to evaluate the quality of the air void system. However, the spacing parameters provided by the various proposed equations, when used as sole measures in predicting the frost resistance of concrete, do not seem to do any better than the standard spacing factor. Dispersion and spatial distribution have been shown to be effective ways of describing air void or microsphere systems in hardened concrete because they have been quantified to establish criteria to assess the frost resistance of concrete. In this paper, dispersion and distribution factors are further elaborated upon to explain how they characterize zones that are protected by air voids or microspheres in the concrete. Criteria to assess the durability of concrete under rapid cycles of freezing and thawing based on the dispersion and distribution factors are linked to the exposure classes defined in the ACI 318 Code and in the recently proposed Unified Durability Guidance in ACI Committee Documents.

Experimental investigation on the characteristics of the shock wave emitted by the cavitation bubble near the air bubble

This study explores the mitigation of cavitation damage in hydraulic engineering through air entrainment. The primary aim is to experimentally analyze the shock wave characteristics emitted by cavitation bubbles adjacent to air bubbles affixed to a tube nozzle. The schlieren optical system is utilized to visualize the shock wave, while a hydrophone measures its pressure. Experiments are conducted on cavitation bubbles induced by the spark-generated method in the vicinity of air bubbles, varying the dimensionless distances and sizes of the air bubbles. The results indicate that (1) The introduction of an air bubble noticeably changes the morphology, kinematic behavior, and shock wave features of the cavitation bubble. (2) Four distinct shock wave patterns are identified based on the quantity and shape of the shock wave, with variations in the cavitation bubble's collapsing behavior and shock wave characteristics across different patterns. (3) The dimensionless distance γ and size δ exert significant influence on the shock wave's quantity, pressure peak, shape, and energy. With γ decreases or δ increases, the shock wave quantity increases while the shock wave intensity decreases. This investigation of the interaction between cavitation bubbles and air bubbles is essential for elucidating the mechanism through which air entrainment mitigates cavitation damage.

Accurate assessment of land–atmosphere coupling in climate models requires high-frequency data output

Abstract. Land–atmosphere (L–A) interactions are important for understanding convective processes, climate feedbacks, the development and perpetuation of droughts, heatwaves, pluvials, and other land-centered climate anomalies. Local L–A coupling (LoCo) metrics capture relevant L–A processes, highlighting the impact of soil and vegetation states on surface flux partitioning and the impact of surface fluxes on boundary layer (BL) growth and development and the entrainment of air above the BL. A primary goal of the Climate Process Team in the Coupling Land and Atmospheric Subgrid Parameterizations (CLASP) project is parameterizing and characterizing the impact of subgrid heterogeneity in global and regional Earth system models (ESMs) to improve the connection between land and atmospheric states and processes. A critical step in achieving that aim is the incorporation of L–A metrics, especially LoCo metrics, into climate model diagnostic process streams. However, because land–atmosphere interactions span timescales of minutes (e.g., turbulent fluxes), hours (e.g., BL growth and decay), days (e.g., soil moisture memory), and seasons (e.g., variability in behavioral regimes between soil moisture and latent heat flux), with multiple processes of interest happening in different geographic regions at different times of year, there is not a single metric that captures all the modes, means, and methods of interaction between the land and the atmosphere. And while monthly means of most of the LoCo-relevant variables are routinely saved from ESM simulations, data storage constraints typically preclude routine archival of the hourly data that would enable the calculation of all LoCo metrics. Here, we outline a reasonable data request that would allow for adequate characterization of sub-daily coupling processes between the land and the atmosphere, preserving enough sub-daily output to describe, analyze, and better understand L–A coupling in modern climate models. A secondary request involves embedding calculations within the models to determine mean properties in and above the BL to further improve characterization of model behavior. Higher-frequency model output will (i) allow for more direct comparison with observational field campaigns on process-relevant timescales, (ii) enable demonstration of inter-model spread in L–A coupling processes, and (iii) aid in targeted identification of sources of deficiencies and opportunities for improvement of the models.

Synchrotron X-ray phase-contrast imaging of ultrasonic drop atomization

Ultrasonic atomization is employed to generate size-controllable droplets for a variety of applications. Here, we minimize the number of parameters dictating the process by studying the atomization of a single drop pending from an ultrasonic horn. Spatiotemporally resolved X-ray phase-contrast imaging measurements show that the number-median sizes of the ejected droplets can be predicted by the linear Navier–Stokes equations, signifying that the size distribution is controlled by the fluid properties and the driving frequency. Experiments with larger pendant water drops indicate that the fluid–structure interaction plays a pivotal role in determining the ejection onset of the pendant drop. The atomization of viscoelastic drops is dictated by extended ligament formation, entrainment of air, and ejection of drop-encapsulated bubbles. Existing scaling laws are used to explain the required higher input amplitudes for the complete atomization of viscoelastic drops as compared to inviscid drops. Finally, we elucidate the differences between capillary wave-based and cavitation-based atomization and show that inducing cavitation and strong bubble oscillations quickens the onset of daughter drop ejection but impedes their size control.

Air void system and freezing-thawing resistance of concrete composite with the incorporation of thermo-expansive polymeric microspheres

Air-entraining agent (AEA) was first used in concrete in 1930’s to improve freezing – thawing resistance of concrete. After about 90 years of experience, many debates have been raised regarding the benefit of durability improvement using AEA in concrete. Under this circumstance, polymeric microspheres show promising ability to replace the AEA with the purpose of entraining air in concrete. In this study, thermo-expansive polymeric microspheres were added to concrete. As a comparison, concrete specimens with the addition of AEA were also prepared. The air contents of freshly mixed concrete and hardened concrete were characterized. In addition, compressive strength development was measured. Moreover, the microstructure and air-void system of concrete was characterized by multiple methods. Finally, the dynamic modulus of elasticity and scaling of concrete beams after the cyclic freezing–thawing attack were evaluated. It was found that compared with the addition of AEA, adding polymeric microspheres entrained comparable air content in concrete. The void size distribution of polymeric microspheres mixed concrete is finer than that of AEA mixed concrete, which provides comparable freezing–thawing resistance of concrete in the viewpoint of dynamic modulus. However, due to the potential “internal curing” and nucleation effects with the presence of microspheres, the strength of microsphere-mixed concrete is slightly higher than that of plain concrete, and freezing–thawing caused surface scaling of concrete mixed with microspheres is much less severe than that incorporated with AEA.

Molecular dynamics simulations of adsorption behavior of mixtures of surfactant and polymer at C3A/water and Ettringite/water interfaces

In cementitious system, surfactant is used as air-entraining agents, which is often incompatible with other chemical admixtures, such as superplasticizers. The adsorption of surfactants at solid–liquid interface is critical for the bubble stability. The measurement of adsorption properties of surfactant in fresh cement or concrete is very difficult. In this study, classical molecular dynamics simulations is used to analysis the influence of two polymers (call as HPMC and PCA, respectively) on the adsorption behaviors of the two anionic surfactants (call as HSO4 and HPO4, respectively) at the C3A/water and ettringite/water interfaces. At solid/water interface, both of HSO4 and HPO4 molecules form a monolayer with hydrophilic head groups adsorbed on the solid surfaces. After adding polymers, the adsorption conformations are changed to spherical micelle or multilayer. The electrostatic interaction between oxygen atoms of hydrophilic head groups and calcium atoms of solid surface plays a decisive role. Therefore, the value of adsorption energy of HPO4 with more negatively charged hydrophilic head groups is greater than that of HSO4. The adsorption energies of the two surfactants are weakened by the two polymers, but the adsorption energy value of HPO4 is always greater. The influence mechanism of HPMC and PCA is different. The negatively charged PCA has a strongly competitive adsorption with the surfactants. The neutral HPMC has a weak adsorption capacity but it carries many hydroxyl groups to interact with the hydrophilic head groups of surfactants.

Experimental and computational investigation of chaotic advection mixing in laminar rectangular stirred tanks

The phenomenon of chaotic advection mixing in laminar stirred tanks, particularly when handling high-viscosity fluids, represents a common and challenging issue in various chemical and biochemical industrial processes. The effectiveness of these mixing processes is often constrained by the stretching, folding, and squeezing of fluid particles. Previous research efforts have predominantly concentrated on the design and/or optimization of impellers and operation modes to increase the stretching and folding of fluid particles. However, the mechanism of triggering chaos through the squeezing of fluid particles remains comparatively less explored. This study endeavors to address the intricate problem of laminar mixing by proposing the utilization of unbaffled rectangular stirred tanks. Via a combined approach of experimental and computational investigations, we illustrate that the implementation of rectangular stirred tanks yields significant improvements in chaotic mixing within laminar flow regimes. This type of tank not only enhances the convective transport of fluids but also distorts or completely eliminates the segregation regions by squeezing. Remarkably, as the tank L/W ratio increases from 1 to 2.5, the observed asymptotic area coverage from a frontal perspective escalates from approximately 55 % to about 85 %. Concurrently, the dimensionless mixing time decreased significantly from 1950 to 350. Of particular note, macroscopic homogeneous mixing is observed in stirred tanks with L/W ratios of 2 and 2.5 at Re = 29, with dimensionless mixing times of 550 and 350, respectively. This work highlights the potential of rectangular stirred tanks as a simple and cost-effective system for laminar mixing applications. Furthermore, it also hints at the broader applicability of the approach in various industrial mixing contexts, such as the suspension of floating granules, entrainment of air, and others.

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.

Airborne Transmission of SARS-CoV-2: The Contrast between Indoors and Outdoors

COVID-19 is an airborne disease, with the vast majority of infections occurring indoors. In comparison, little transmission occurs outdoors. Here, we investigate the airborne transmission pathways that differentiate the indoors from outdoors and conclude that profound differences exist, which help to explain why SARS-CoV-2 transmission is much more prevalent indoors. Near- and far-field transmission pathways are discussed along with factors that affect infection risk, with aerosol concentration, air entrainment, thermal plumes, and occupancy duration all identified as being influential. In particular, we present the fundamental equations that underpin the Wells–Riley model and show the mathematical relationship between inhaled virus particles and quanta of infection. A simple model is also presented for assessing infection risk in spaces with incomplete air mixing. Transmission risk is assessed in terms of aerosol concentration using simple 1D equations, followed by a description of thermal plume–ceiling interactions. With respect to this, we present new experimental results using Schlieren visualisation and computational fluid dynamics (CFD) based on the Eulerian–Lagrangian approach. Pathways of airborne infection are discussed, with the key differences identified between indoors and outdoors. In particular, the contribution of thermal and exhalation plumes is evaluated, and the presence of a near-field/far-field feedback loop is postulated, which is absent outdoors.

Experimental study of peripheral fuel injection for higher performance in diesel engines

In conventional diesel combustion (CDC), a centrally located multi-hole injector supplies fuel radially outwards. This study introduces and explores the concept of peripheral fuel injection (PeFI) to supply fuel from multiple locations on top of the combustion chamber using several single-hole injectors. The PeFI concept is designed to eliminate flame-wall and jet-wall interactions, and, ideally, to produce independent flames without any interference. PeFI is also intended to increase air entrainment in the near field and thus, reduce equivalence ratio at the lift-off length and subsequent soot formation. PeFI reduces wall heat transfer compared to CDC although this feature is not considered in the present study. The two methods of fuel injection are compared in a non-reacting optical chamber via high-speed imaging of the jets. N-heptane fuel at 1500 bar supply pressures is injected into a test chamber filled with nitrogen at engine relevant ambient densities of 23.0 and 18.5 kg/m3. Four configurations are trialed including a six-hole central injector and six, single-hole PeFI injectors with holes oriented at a layout angle, defined as the angle between the center of the fuel jet and chamber radius, of 0°, 15°, and 30°. Flow visualizations show jet-to-jet interactions at small layout angles for PeFI, but little to no jet-to-jet (or jet-wall) interference as the layout angle increases to 30°. Image analysis reveals that PeFI provides faster rate of injection, longer jet penetration length, greater width near the jet tip, and larger jet volume compared to those for the central injector. Overall, results demonstrate the potential of PeFI to simultaneously improve fuel efficiency and reduce emissions in diesel engines.

The effect of the compound slope spillway on air entrainment and total kinetic energy using computational fluid dynamics

Abstract The spillway is a hydraulic structure used for managing discharge, dissipating energy, and aeration purposes. The objective of this CFD analysis was to compare the ways in which water moved over various slanted spillways. Both the turbulence and the air–water interface were located using the volume of fluid (VOF) technique and a realizable k-model. Five different spillway models with varying slopes (normal = 30°, compound1 = 20° and 39°, and compound2 = 39° and 20°) were modelled and simulated in ANSYS Fluent. Computational data have been compared to the experimental results, and the findings were astonishing – the CFD model precisely captured the all-important flow facets. The numerical model pinpointed the inception point that occurred due to changes in slope and structure. In comparison to the normal slopes of (30°) and the compound slopes of (39°/20°), the surge in the location of the inception point was around 58%. The results of the research indicate a significant increase in turbulent kinetic energy as a result of the introduction of the compound slope. The study conducted has effectively achieved a crucial objective of the project, which is to enhance the operational efficiency and reliability of the spillway under diverse flow conditions.

Bubble Defect Generation Mechanism in Slot Die Coating of High-Viscosity Fluids.

Slot die coating is a widely used technique for the production of high accuracy films. One of the main challenges in slot die coating processes is determining the optimal range of operating parameters to prevent defects, such as bubbles, in high-viscosity films. In this study, both simulation and experimental methods were used to investigate the changes in the upstream meniscus under various coating parameters. Two types of air entrainment processes were considered, dominated by fluid inertia and viscous force. The formation of anticlockwise and clockwise vortex flows near the bottom of the upstream meniscus was found to alter the apparent dynamic contact angle of the upstream meniscus, leading to fluctuations in the apparent dynamic contact angle within a range of 70°-75° to 135°-140°. These fluctuations eventually resulted in air entrainment. This research is important for improving the quality and efficiency of slot die coating processes.

Construction potential of rice husk ash as eco-friendly cementitious material in a low-water demand for self-compacting concrete

Self-compacting concrete (SCC) is a special mix design that offers advantages, such as high flowability and better compaction. Combining it with natural pozzolans through partial replacement influences considerably the filling and passing abilities, and segregation resistance, while generating high-strength performance. A low water-to-binder ratio (w/b) leads to a dense, non-porous, and durable SCC, but its desired workability is difficult to obtain. Hence, the addition of chemical admixtures, such as superplasticizers (SP) and air-entraining agents (AEA) may resolve this issue. Moreover, the incorporation of rice husk ash (RHA) as supplementary cementitious material (SCM) in an alkali environment promotes enhanced stability and workability, as well as avoiding any bleeding or segregation problems. RHA also improves the concrete’s microstructure owing to its highly reactive fine silica. However, there is limited evidence reported on the effects of RHA on SCC’s overall flowability, pozzolanic reactions, and microstructural analyses. Here the synergistic effects of RHA on the rheological performance, strength development, pozzolanic activities, and microstructural characterization of fresh and hardened SCC were reported. The study showed that while the filling ability, passing ability, and segregation resistance of fresh mixture all conform to the threshold values, the recorded compressive strength of the hardened samples was highest in SC-09 at 90-day cured samples. The mix proportion of this sample includes a low w/b ratio of 0.35 and 15% RHA replacement, with optimized rheological performance and pozzolanic activities. It was observed in the sample’s microstructure that the silica particles chemically reacted with CH, promoting CSH gel products. The disappearance of dicalcium silicate (C2S) and tricalcium silicate (C3S) in diffractograms was observed and replaced by CSH gel, which plays a key role in strength formation. IR spectral bands at ∼765 and ∼464 cm−1 indicated the amorphous silica phase of the RHA-SCC samples, while the spectral band relation of RHA and the samples showed a high degree of reaction of RHA upon mixing. The surface morphology images proved a highly dense matrix in 15% RHA replacement. Observed pores and cracks were lessen compared to samples with 0–10% RHA, which verified the construction potential of RHA in an optimized amount. While the sulfate and seawater performance tests indicated a low mass loss and high relative strength occurred to samples with 15% RHA replacement when immersed to both solutions, signifying that the addition of RHA in concrete leads to better chemical attack resistance compared to OPC alone due to the highly reactive silica of RHA.

Sea spray emissions from the Baltic Sea: comparison of aerosol eddy covariance fluxes and chamber-simulated sea spray emissions

Abstract. To compare in situ and laboratory estimates of sea spray aerosol (SSA) production fluxes, we conducted two research campaigns in the vicinity of an eddy covariance (EC) flux tower on the island of Östergarnsholm in the Baltic Sea during May and August 2021. To accomplish this, we performed EC flux measurements for particles with diameters between 0.25 and 2.5 µm simultaneously with laboratory measurements using a plunging jet sea spray simulation chamber containing local seawater sampled close to the footprint of the flux tower. We observed a log-linear relationship between wind speed and EC-derived SSA emission fluxes, a power-law relationship between significant wave height and EC-derived SSA emission fluxes, and a linear relationship between wave Reynolds number and EC-derived SSA emission fluxes, all of which are consistent with earlier studies. Although we observed a weak negative relationship between particle production in the sea spray simulation chamber and seawater chlorophyll-α concentration and a weak positive relationship with the concentration of fluorescent dissolved organic matter in seawater, we did not observe any significant impact of dissolved oxygen on particle production in the chamber. To obtain an estimate of the size-resolved emission spectrum for particles with dry diameters between 0.015 and 10 µm, we combined the estimates of SSA particle production fluxes obtained using the EC measurements and the chamber measurements in three different ways: (1) using the traditional continuous whitecap method, (2) using air entrainment measurements, and (3) simply scaling the chamber data to the EC fluxes. In doing so, we observed that the magnitude of the EC-derived emission fluxes compared relatively well to the magnitude of the fluxes obtained using the chamber air entrainment method as well as the previous flux measurements of Nilsson et al. (2021) and the parameterizations of Mårtensson et al. (2003) and Salter et al. (2015). As a result of these measurements, we have derived a wind-speed-dependent and wave-state-dependent SSA parameterization for particles with dry diameters between 0.015 and 10 µm for low-salinity waters such as the Baltic Sea, thus providing a more accurate estimation of SSA production fluxes.

Three dimensional analysis of the exhalation flow in the proximity of the mouth

The human exhalation flow is characterized in this work from the three-dimensional velocimetry results obtained by using the stereo particle image velocimetry (SPIV) measurement technique on the flow emitted from a realistic airway model. For this purpose, the transient exhalation flow through the mouth of a person performing two different breaths corresponding to two metabolic rates, standing relaxed (SR) and walking active (WA), is emulated and studied. To reproduce the flow realistically, a detailed three-dimensional model obtained from computed tomography measurements on real subjects is used. To cope with the variability of the experimental data, a subsequent analysis of the results is performed using the TR-PIV (time resolved particle image velocimetry) technique. Exhalation produces a transient jet that becomes a puff when flow emission ends. Three-dimensional vector fields of the jet velocity are obtained in five equally spaced transverse planes up to a distance of ▪ from the mouth at equally spaced time instants ▪ which will be referred to as phases (φ), from the beginning to the end of exhalation. The time evolution during exhalation of the jet area of influence, the velocity field and the jet air entrainment have been characterized for each of the jet cross sections. The importance of the use of realistic airway models for the study of this type of flow and the influence of the metabolic rate on its development are also analyzed. The results obtained contribute to the characterization of the human exhalation as a pathway of the transmission of pathogens such as SARS-CoV-2 virus.

Three-dimensional turbulent velocity field and air entrainment of the 22 March 1944 Vesuvius eruption plume

Three-dimensional turbulent velocity field and air entrainment of the 22 March 1944 Vesuvius eruption plume

Research on characteristics of thermal smoke movements of twin fires in a tunnel under reduced pressure

In this study, numerical simulations were conducted to investigate the behavior of thermal smoke movement in tunnels under reduced pressure, with the aim of providing scientific guidance for controlling smoke and heat in the event of tunnel fires. The variables examined included fire spacing (0–6 m), atmospheric pressure (55–100 kPa), and overall heat release rate (6–18 MW). The analysis revealed that the temperature method, which considers relative temperature deviations along tunnel centerlines and on tunnel sidewalls, is effective in identifying the initial position of one-dimensional smoke movement (TY=0 - TY=4.9) / TY=0 ≤ 5 %. It was found that under reduced pressure, the mass of air entrained into the smoke gas per unit time decreased, resulting in a lower mass-flow rate. Specifically, at 100 kPa, the mass-flow rate was approximately 1.4 times higher than at 55 kPa for the same simulation scenario. The effect of fire spacing on the mass-flow rate was found to be weaker compared to pressure, particularly during the non-interaction stage of the fire. The air entrainment coefficient (β) displayed a negative correlation with environmental pressure and positively correlated with fire-heat release rate. In all cases, the β value for dual fire sources in a tunnel ranged from 0.0008 to 0.0022. Finally, a segmented function was developed to forecast the mass-flow rate of thermal smoke, taking into account various factors such as fire source parameters, environmental parameters, and tunnel restrictions.