Mist Diameter Research Articles

Combined effects of blowing ratio and mist diameter with mainstream turbulence intensity in mist-assisted film cooling

Advanced cooling techniques are essential in modern gas turbines to improve the efficiency of the Brayton cycle by raising the turbine inlet temperature. Mist-assisted film cooling offers an innovative solution for cooling high-temperature gas turbine blades. When mist particles with various momenta are injected through the cooling holes, the interplay between mainstream turbulence intensity (Tu) and mist momentum plays a crucial role in mist-assisted film cooling under high Tu conditions. Hence, this numerical study investigates the relationship between mainstream Tu and mist characteristics for the first time, considering the blowing ratio and mist diameter as controlling parameters. Film effectiveness and particle distribution statistics are analysed to understand their correlation. The results demonstrate that mist-assisted film effectiveness follows the trend of air-only film cooling with varying blowing ratios and Tu; however, the magnitude is amplified. The influence of the mist diameter on film effectiveness is determined by the surface-area-to-volume ratio and Stokes number. These factors impact the sensitivity of particles to Tu and subsequently affect film effectiveness. This study provides a novel quantitative analysis of the combined effect of mainstream Tu and mist on film cooling effectiveness, revealing the correlation between mist and mainstream parameters.HighlightsCombined effect of mainstream turbulence intensity (Tu) and mist characteristics is investigated.High mainstream Tu significantly increases the cooling enhancement induced by mist.Mist-assisted film cooling exhibits similar trends to varying mainstream Tu and blowing ratio.Mist diameter significantly influences the response to Tu, governed by surface-area-to-volume ratio and Stokes number.Small particles demonstrate the highest cooling effectiveness and variation by Tu.

Experimental evaluation of individual effects of water mist spray characteristics on thermal radiation attenuation using twin‐fluid nozzles with full‐cone spray pattern

AbstractIn this study, the effects of water mist spray characteristics on thermal radiation attenuation were experimentally investigated using five types of external and internal mixing twin‐fluid nozzles with a full‐cone spray pattern. To the best of our knowledge, this may be the first attempt to experimentally examine the separate effects of water mist spray characteristics on thermal radiation attenuation. Water and air supply pressures were measured, and their values were 1.3–55.5 and 29.8–316 kPa, respectively. The Sauter mean diameter and volume median diameter of the water mist were measured to be 20–99 μm and 21–108 μm, respectively. The spray angle and width of the water mist were approximately 20° and 110 mm, respectively. The thermal radiation attenuation afforded by the water mist discharged from the twin‐fluid nozzle increased with increasing water and air flow rates and decreasing droplet sizes. Within the experimental range, the thermal radiation attenuation was approximately 6.9%–28.4%. Based on experimental data, the effects of the water flow rate and droplet size on thermal radiation attenuation were examined independently. The dependence of the thermal radiation attenuation on the droplet size was greater than that on the water flow rate.

Flow and heat transfer performance of the channel with different shaped ribs cooled by mist/steam two-phase flow

The flow and heat transfer performance of mist/steam coolant in a straight channel with 45°/60°/75°V-shaped ribs, 45°/60°/75°/90°paralleled ribs and a smooth channel under different working conditions are studied. Based on vortex analysis, for mist/steam coolant, the regions where the Mainstream Secondary Flow Vortexes and the Longitudinal Secondary Flow Vortexes exist simultaneously can achieve better cooling performance. Among all mentioned rib structures, the 45°V-shaped ribbed passage achieves the best cooling enhancement, its sidewall average Nu number ratio is 33.8%–74.0% higher than the 90°paralleled ribbed channel. Although the heat transfer non-uniformity of the channel with 45°V-shaped ribs is not the lowest, it has lower heat transfer non-uniformity than the highest 45°paralleled ribbed channel. For mist/steam coolant, increasing inlet Re number, the sidewalls average Nu number ratio gradually decreases, but their heat transfer non-uniformity increases. As wall heat flux increases, the secondary flow vortexes in the channel does not change but both average Nu number ratio and the heat transfer non-uniformity clearly decreases. Raising mist/steam will not change the secondary flow vortexes structure. Instead, it will obviously increase the average Nu number ratio and heat transfer unevenness. Enlarging the mist diameter decreases the heat transfer performance of the sidewall, but also makes the sidewall heat transfer become less even.

Numerical study of swirl cooling enhancement by adding mist to air: Effects of droplet diameter and mist concentration

Swirl cooling with air/mist mixture coolant is a promising heat transfer method, for which the combined influence of swirl and mist should be clearly understood. In this work, numerical simulations on the swirl cooling performance of the leading edge of a turbine vane using mist/air mixture and air are implemented for comparative study. The Eulerian-Lagrangian particle tracking method is adopted to investigate the two phase cooling. The coolant air impacts tangentially the inner surface of the circular swirl chamber through two rectangular nozzles, and the mists with different concentrations (5%, 10%, and 20%) and droplet diameters (1 μm, 2.5 μm, 5 μm, 7.5 μm, and 10 μm) are included to explore their effects on the cooling performance. The results demonstrate that the circumferentially-averaged Nusselt number, Nucir, increases with the increase of mist concentration, and this effect becomes prominent when the droplet diameter increases. For droplet diameter of 10 μm and mist concentration of 20%, Nucir can increase by 12.6% to 309.7% as compared to pure air. In addition, the empirical correlations of the global-averaged Nusselt number, and friction coefficient to the mist diameter and mist concentration are given for the first time. It is concluded that the thermal performance factor, which can be used to evaluate comprehensively the cooling characteristics, increases with the increase of mist concentration and droplet diameter. The empirical correlations and thermal performance evaluation provide the basis for further theoretical analysis of the cooling performance using air/mist mixture.

Generation of ash particles from different lube oil mists

Ash and soot particles are generated during engine combustion and are deposited in particulate filters. In order to understand the basic processes that occur in a particulate filter during the filtration process the particles have to be generated quickly and replicably. In this study, fundamental investigations are conducted on the generation of ash particles independently of an engine to produce a defined aerosol. The formation of ash particles from engine oils with differences in sulfate ash content (SAC; 0.7%, 2.6%, 4.5%) as well as the variation of process parameters (oil temperature, nozzle volume flow) are investigated. The ash particles are produced by nebulizing engine oil and a subsequent thermal conversion in a furnace. The SAC of the oil does influence the ash particles that are generated. With the increase of the SAC, the ash mass flow and the number weighted median diameter increase. Raising the nozzle volume flow as well as the oil temperature leads to an increase in total number concentration and mass flow of the ash particles. The number median diameter of the oil mist and ash particles decrease with the increase of oil temperature and nozzle volume flow. For the fast loading of a particulate filter, the SAC of the oil should be 4.5%. The oil temperature and nozzle volume flow should be set at 30 °C and 6 L·min−1. In conclusion, the ash generation method can be used for the rapid loading of a particulate filter.

Effects of Discharge Area and Atomizing Gas Type in Full Cone Twin-Fluid Atomizer on Extinguishing Performance of Heptane Pool Fire under Two Heat Release Rate Conditions in an Enclosed Chamber

In this study, the effects of discharge area and atomizing gas type in a twin-fluid atomizer on heptane pool fire-extinguishing performance were investigated under the heat release rate conditions of 1.17 and 5.23 kW in an enclosed chamber. Large and small full cone twin-fluid atomizers were prepared. Nitrogen and air were used as atomizing gases. With respect to the droplet size of water mist, as the water and air flow rates decreased and increased, respectively, the Sauter mean diameter (SMD) of the water mist decreased. The SMD of large and small atomizers were in the range of approximately 12–60 and 12–49 μm, respectively. With respect to the discharge area effect, the small atomizer exhibited a shorter extinguishing time, lower peak surface temperature, and higher minimum oxygen concentration than the large atomizer. Furthermore, it was observed that the effect of the discharge area on fire-extinguishing performance is dominant under certain flow rate conditions. With respect to the atomizing gas type effect, nitrogen and air appeared to exhibit nearly similar extinguishing times, peak surface temperatures, and minimum oxygen concentrations under most flow rate conditions. Based on the present and previous studies, it was revealed that the effect of atomizing gas type on fire-extinguishing performance is dependent on the relative positions of the discharged flow and fire source.

Numerical simulation of methane explosion suppression by ultrafine water mist in a confined space

This numerical study focused on the heat transfer process between the ultrafine water mist and explosion flame, and the suppression mechanism of ultrafine water mist and the effect of mist parameter on methane explosion. Hence, a three-dimensional numerical model for methane explosion suppression by ultrafine water mist was established. Large eddy simulation and partially premixed combustion models were used to determine the explosion flow field characteristics and methane explosion process, respectively. The Euler-Lagrange equation was used to solve the continuous and discrete phases, and the coupling calculation was realized by alternately solving these two phase models. In addition, the validity of the numerical model and calculation method was verified by the experimental results. Mist vaporization, heat transfer between the gas and liquid phases, and influencing factors (including the mist diameter (d), mist velocity (v), and mist concentration (QMist)) were analyzed quantitatively. The results indicate that heat exchange mainly occurs in the reaction zone, and the heat exchange rate can be affected by the mist parameters, which further affects the temperature inside the vessel. Moreover, the vapor pressure generated from mist vaporization is an important component of the explosion pressure in the closed vessel, and it is comprehensively affected by the mist vaporization rate and temperature. Simultaneously, the mist parameters are also the key influencing factors for the above process.

Combined effects of obstacle and fine water mist on gas explosion characteristics

Abstract Combined effects of obstacles and fine water mist on a methane-air explosion of a semi-closed pipe were investigated experimentally. In this study, the diameter of the water mist, the location, and the number of obstacles was considered. The results demonstrated that 5 µm water mist present a significant suppression affected while 45 µm shows a slight promotion effected on a gas explosion of the condition without obstacles. In the presence of an obstacle, however, the inhibitory effect of 5 µm water veils of mist dropped significantly during flame propagation, and the effect of 45 µm water veils of mist changed from the enhancement of inhibition, and its inhibitory effect was significant. The inhibitory effect of 45 µm water veils of mist on gas explosion weakened firstly and then enhanced with the increasing distance between obstacle location from the ignition location as well as in several obstacles.

Evaluation of the suppression effect on the flame intensification of ethanol fire by N2 twin-fluid water mist containing KQ compound additive

Water mist is one of the important substitutes of halon fire extinguishing agents with the advantages of clean and environmental protection. However, there will be a short time of flame intensification in the fire extinguishing progress of water mist, which threatening the safety of surrounding combustibles and fire fighters. The main objective of this study is to assess the suppression performance of N2 twin-fluid water mist containing KQ compound additive (composed of 6% fluorine surfactant and K2CO3) on ethanol pool fire, and analyze the suppressing mechanism on the flame intensification phenomenon. Experimental results showed that: the fire extinguishing time of several fire extinguishing agents from low to high was N2 twin-fluid water mist containing KQ compound additive < N2 twin-fluid water mist containing potassium additives < N2 twin-fluid water mist < N2 twin-fluid water mist containing 6% fluorine surfactant < air twin-fluid water mist. Comparing to air twin-fluid water mist, there was no obvious intensification phenomenon of flame in the initial extinguishing stage with N2 twin-fluid water mist containing KQ compound additive, and the suppression effect on the fire was improved significantly. N2 played a pre-inerting role, which could increase the specific heat of the mixture and dilute the concentration of oxygen, resulting in reducing the flame intensity and flame buoyancy. Meanwhile, comparing to potassium salt solution, the compound additive of KQ solution reduced the droplet diameter of water mist, which fastening the generation rate of K ions; and leading to smaller turbulence disturbance on flame caused by water mist. Therefore, the physical and chemical fire extinguishing effects were both improved. Moreover, compound additive KQ reduced the potassium salt concentration by 50 %, hence reduced the corrosion of chemical additives. This research will improve the fire extinguishing efficiency and reliability of water mist fire extinguishing technology.

Experiments and numerical simulation on the suppression of explosion of propane/air mixture by water mist

Effect of water mist on minimum ignition energy (MIE) and lower and upper flammability limits (LFL and UFL) of C3H8–air mixtures were investigated by experiments and numerical simulation. Ignition experiments were performed in a combustion tube. Polydisperse water mist with a Sauter mean diameter of D32 = 21 µm was generated by a piezoelectric atomizer. Mixture was ignited by an exploding wire heated instantaneously by electrical discharge. Ignition probability follows the cumulative probability distribution function of energy density, i.e., energy per unit volume of the wire. Water mist increases minimum ignition energy density (MIED) defined at 50% ignition probability when the equivalence ratio φ < 1.0 and φ > 1.3. However, for 1.0 < φ < 1.3, the suppression effectiveness was scarcely observed. In numerical simulation, water mist was assumed to be an imaginary ideal gas and evaporation process was expressed by a chemical reaction. Ignition energy is added in the flame kernel at the center and the flame propagates spherically if ignited. This model can predict MIE of the mixture without water mist reasonably. MIE increases nonlinearly with the mass fraction of water mist Y0 and flammability range narrows. At Y0 = 0.146 and beyond, the mixture of any φ becomes unable to be ignited. Relative suppression effectiveness factors Se and Ss are newly introduced for experiments and simulation, respectively. Comparison of Se with Ss shows that the water mist is not so effective as expected by simulation. The life time of a droplet before evaporation is much longer for the water mist of D32 = 21 µm than the residence time in the flame, and only a part of water mist can evaporate in the flame zone. To make full use of the suppression potential of water mist, the mist diameter should be sub-5 µm.

Flow and heat transfer characteristics of mist/steam two-phase flow in the U-shaped cooling passage with 60 deg. ribs

The flow and heat transfer characteristics of mist/steam coolant in U-shaped gas turbine cooling passage are studied in this paper. The mist/steam mass ratio and mist diameter are carefully analyzed with the numerical method. The results show that the heat transfer of the ribbed-wall gradually increases with the increasing of mist/steam mass ratio. Under the condition of water mist diameter = 10 μm, as mist mass ratio increases from 2% to 10%, the averaged Nusselt number of the First Flow Passage increased by 60.13% and the Second Flow Passage increased by 112.5%. The evaporation rate and surviving time of mist can be controlled by controlling the mists diameter. Larger mist diameter is not always good for enhancing the heat transfer of the ribbed walls. When mist/steam = 8%, as for the First Flow Passage and the Second Flow Passage, water mists of 10 μm diameter has higher average Nu number of ribbed wall than mists of 5 μm, 15 μm and 20 μm. The improvement of the heat transfer performance obtained from the evaporation of the water mist is bound to the increasing of the heat transfer non-uniformity of the heated walls.

Effect of droplet characteristics on heat transfer of mist/air cooling in a pin-finned channel

Effects of droplet characteristics of mist/air cooling on heat transfer for three pin-fin structures are investigated. The round-tip pin-fin structure is newly proposed with partial detachment from one endwall with a round-shaped tip structure. A flat-tip pin-fin with partial detachment and a traditional pin-fin with full attachment serve as references. Reynolds-averaged Navier-Stokes equations and the shear-stress-transport turbulence model are applied. Influences of initial mist temperature, initial mist diameter and initial mist velocity are analyzed in the Reynolds number range 15,000 to 50,000. The round-tip pin-finned channel has highest heat transfer coefficient and lowest pressure loss among the structures. Heat transfer enhancement increases first gradually and then decreases sharply with increasing initial mist diameter but an optimal diameter exists for the highest Nusselt numbers. Nusselt number decreases monotonically with increasing initial mist temperature. Droplet movement and heat transfer are nearly independent of initial mist velocity.

Experimental research on explosion suppression affected by ultrafine water mist containing different additives.

The suppression effects of pure ultrafine water mist and 5% mass fraction alkali metal (NaCl, Na2CO3, KHCO3, KCl and K2CO3) solutions ultrafine water mist on methane explosion were conducted under five mist concentrations in a sealed visual vessel. Mist diameters of different additive solutions were measured by a phase doppler particle analyzer. Pressure data and dynamic flame pictures were recorded respectively by a high-frequency pressure sensor and a high-speed camera. Results indicate that alkali metal compound can enhance the suppression effect of ultrafine water mist and it was related to the additive type. The suppression order of alkali metal compound for methane explosion was K2CO3>KCl > KHCO3>Na2CO3>NaCl. Meanwhile, additive radicals can obviously affect explosion intensity and it mainly reflected in the reduction of explosion pressure under different mist conditions (K+>Na+, Cl- >HCO3-). The pressure generated from combustion wave accelerating propagation underwent two accelerating rises and was affected by additive type and mist amount. The effect of additive type on explosion intensity (maximum explosion overpressure (ΔPmax), two peak values of pressure rising rate) was similar with flame propagation velocity and were decreased evidently with increasing mist concentration. The enhancement in explosion suppression was due to the combination of improved physical and chemical effects.

Fluctuating characteristics of air-mist mixture flow with conjugate wall-film motion in a compressor of gas turbine

A feasible method of injecting water mist into the air can improve the operation performance of gas turbine. This study aims to develop a deeper understanding of aerodynamic characteristics of fluctuating quantities and its influence caused by air-mist two phase flow with conjugate the liquid film. The effect of various mist injection conditions on transient characteristics of compressor was investigated by the frequency attribute analysis. The results show that the film attached to the blade surfaces will aggravate the aerodynamic fluctuation. Notably, the fluctuating quantities, such as pressure, temperature, mass flow, flow loss and compression work, center on the lower frequency region, indicating that the dominant component of disturbance source appears a weak fluctuation because of unevenly distributed flow field after mist injection. Within the range of 0.5–5% mist concentrations and 1–9 μm mist diameters, mist injection can weaken the fluctuation of pressure and tip leakage flow, meanwhile the fluctuations of temperature and entropy increase are a good improvement in large mist ratio or small mist size. However, the fluctuation reduction is marginal as mist concentration and particle size increase. Therefore, the fluctuation characteristics in the compressor can be controlled by manipulating mist injection conditions.

Extinguishment of counterflow diffusion flame stabilized in turbulent airflow by polydisperse water mist

In the present study, the effect of turbulence on extinguishment of counterflow diffusion flame by polydisperse water mist was investigated experimentally. A counterflow methane-air diffusion flame was stabilized in the forward stagnation region of a porous cylinder. Water mist was supplied by a pressure-type atomizer. Uniform turbulence was produced in the airflow by a grid. Mist characteristics were measured by a phase Doppler particle analyzer and turbulence properties by a hot wire anemometer. For laminar flames, the critical stretch rate at extinguishment decreases with the mass fraction of water mist and the extinguishment is not affected by the Sauter mean diameter D32 even when D32 is as large as 70 µm. Turbulence reduces significantly the critical bulk (mean flow) stretch rate at extinguishment. Effect of turbulence on extinguishment is relevant to the turbulence stretch rate, which is the inverse of the Kolmogorov time scale. Sum of the bulk stretch rate and the turbulence stretch rate is the total stretch rate that actually exerts on turbulent flame. If the relative turbulence intensity v’/V is as low as 0.06 and D32 is smaller than 30 µm, extinguishment of turbulent diffusion flame is expressed uniquely by the total stretch rate, which coincides with that of laminar flame. On the other hand, for large water mist, D32 > 30 µm or high turbulence intensity, v’/V = 0.10, non-uniformity of mist dispersion appears, of which scale is of the order of integral scale of turbulence. The locally extinguished flame by a spot of dense water mist is reignited by surrounding flame and the suppression effectiveness of water mist is deteriorated when the turbulence intensity is high or the mist diameter is large.

Effect of droplet characteristics and rotation speed on the flow and heat transfer characteristics of mist/air cooling in a rotating ribbed two-pass rectangular channel

The flow and heat transfer characteristics of mist/air cooling in the rotating ribbed two-pass rectangular channel are numerically investigated using the CFD software ANSYS-CFX. In this article, a comparison in heat transfer performance between the mist/air cooling and the air-only cooling is performed. Additionally, the effect of the initial mist diameter, temperature, velocity and the channel rotation speed on the mist/air cooling performance is analysed. The results show that the droplet flow distance and Nusselt number of the mist/air cooling increase as the initial mist temperature decreases. In addition, as the initial mist diameter decreases, the diameter of mist on the whole channel decreases, resulting in the higher heat transfer, whilst the mist concentration also decreases, leading to the lower heat transfer. Therefore, there is an optimal initial mist diameter which makes the heat transfer performance best. Nevertheless, the droplet movement and heat transfer performance of mist/air cooling are nearly insensitive to the initial mist velocity. It is also noted that the Coriolis force increases with the channel rotation speed, causing the flow deflection becomes more obvious. Consequently, as the channel rotation speed increases, in the first passage the averaged Nusselt number on the trailing wall increases, and that on the leading wall decreases, while the trend in the second passage is reversed.

Conjugate heat transfer analysis of leading edge and downstream mist–air film cooling on turbine vane

Numerical simulations are performed to explore leading edge and downstream film cooling enhancement by application of injecting water mist into the air. The accuracy of numerical simulation program for conjugate heat transfer methodology is verified with the C3X gas turbine vane cooled with leading edge and downstream film holes. The Eulerian–Lagrangian particle tracking method is adopted to investigate the two phase film cooling. The effects of various parameters including mist concentration, mist diameter and mist injection location on the improvement of cooling performance are investigated in this paper. The results show that the average wall temperature reduction at mid span increases from 20K to 48K from 1% to 3% mist ratio, the corresponding average heat transfer coefficient reduction increases from 77Wm−2K−1 to 103Wm−2K−1. Mist cooling can decrease the boundary layer temperature without impact on the mainstream temperature and boundary layer thickness. The degree and the location of cooling performance can be controlled by manipulating the sizes of injected water mist. The superimposition of different mist injection locations can be used to further strengthen the two phase cooling performance.

Effect of low ambient air pressure on spray characteristics of water mist

To investigate the effect of low ambient air pressure on the characteristics of water mist which was injected into a low pressure (<0.1 MPa) environment, the sizes and velocities of the water droplets were measured using Shadowgraph technique. A stainless steel vessel with a diameter of 600 mm and height of 800 mm was designed for simulating low ambient air pressure conditions using a vacuum pump. Ambient air pressures of 0.1, 0.08, 0.06, 0.04, 0.02 MPa, and working pressures of the water mist system of 1.0, 3.0, 4.0 MPa were considered. The results show that, under each certain pressure of water mist system, both of the Sauter mean diameter (d32) and the arithmetic mean diameter (d10) of water mist droplets decrease with decrease of the ambient air pressure from 0.10 to 0.02 MPa. An empirical formula has been developed to express the influence of ambient air pressure on Sauter mean diameter of water mist. In addition, the axial velocities of water mist droplets generated with working pressure of 3.0 MPa and 4.0 MPa decrease following a decrease in ambient air pressure, while there is no obvious variation to the tested results of the cases with 1.0 MPa working pressure.

Numerical Study on the Effects of Ambient Air Pressure on Water Mist Characteristics

Abstract The effects of ambient air pressure on water mist characteristics were investigated with CFD code FDS6.0. The cases with ambient air pressures of 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, 2.0, 2.5 and 3.0 atm, and water mist operating pressure of 1.5 MPa were considered in the numerical simulation, while the validation experiments were conducted with a single orifice nozzle at normal ambient pressure by using a LaVision Particle-Master Shadow system. The results show that the Sauter mean diameter (D32) of water mist decreased and the droplet velocity increased with the decrease of the ambient air pressure in the same location within the spray. Spray contraction phenomenon occurred where the contraction locations were different under different ambient pressures. Some of the results should be helpful for optimising the water mist fire suppression system.

Inhibition of counterflow methane/air diffusion flame by water mist with varying mist diameter

In the present study, the effect of fine water mist on extinguishment of a methane–air counterflow diffusion flame was investigated to understand the underlying physics of fire extinguishment of highly stretched diffusion flame by water mist. Twin-fluid atomizers were used to generate polydisperse water mist of which Sauter mean diameters were 10, 20, 40, and 60μm. When water mist is not added, the critical stretch rate at extinguishment is 439s−1 as compared to the theoretical value of 460s−1. For the case with water mist addition, when the stretch rate is small enough, almost all the water mist evaporates within the flame zone. On the other hand, for high stretch rate case, large mist droplets pass through the flame zone and can reach the stagnation plane. However, no oscillatory motion was found around the stagnation plane. Critical stretch rate at extinguishment decreases monotonously with the mass fraction of water mist independently of the mist diameter within the range of D32 from 10μm to 60μm. On the other hand, with increase in the surface area parameter, the critical stretch rate at extinguishment decreases rapidly and becomes less sensitive at large surface area parameter, of which tendency is qualitatively in good agreement with theoretical predictions. For a constant surface area parameter, the critical stretch rate decreases with mist diameter because the mass fraction of water mist should increase in proportion to the mist diameter to keep the surface area parameter constant. When the water mist evaporates completely in the flame zone as in the present study, the mass fraction of the water mist is the dominant factor for fire extinguishment, rather than the surface area parameter. Therefore, an appropriate combination of stretch rate and water mist mass fraction should be provided to suppress effectively a given fire with a small amount of water mist.