Strouhal Number Research Articles

Flow and noise control of a cylinder using grooves filled with porous material

In the present numerical study, we propose a new passive flow control mechanism at the Reynolds number of 3900. The novel method benefits from making grooves in the cylinder wall while the grooves are filled with porous materials of a specific permeability. According to the literature survey, while the porous medium is potentially an effective noise control method, it has serious drawbacks, mainly significant pressure drop. In the present study, instead of a porous coating, porous fillers are introduced offering substantial reduction of the noise level, in addition to managing the hydrodynamic parameters. To find a suitable design for the grooves and porous fillers, a systematic parametric study is performed on the number, sequence and size of the grooves, as well as the porous fillers' permeabilities. Based on the results, the newly proposed method dominated the traditional full porous coating by limiting the turbulent kinetic energy (TKE). The results of the parametric study indicated that grooves at an angle of 90° relative to the front stagnation point reduced the overall sound pressure level (OASPL) by 1.25 dB; meanwhile, the high-intensity TKE region shrunk. Further reductions were achieved by deeper grooves and porous fillers, as the drag coefficient, the lift coefficient, the Strouhal number, and the OASPL reduced up to 40.2%, 27.4%, 10.6%, and 3 dB, respectively. The proposed passive control method will be helpful for various industrial applications of cylinders through rigorous control of aerodynamic parameters and the noise level.

Effects of surface roughness on the drag coefficient of spheres freely rolling on an inclined plane

An experimental investigation identifying the effects of surface roughness on the drag coefficient ( $C_{D}$ ) of freely rolling spheres is reported. Although lubrication theory predicts an infinite drag force for an ideally smooth sphere in contact with a smooth wall, finite drag coefficients are obtained in experiments. It is proposed that surface roughness provides a finite effective gap ( $G$ ) between the sphere and panel, resulting in a finite drag force while also allowing physical contact between the sphere and plane. The measured surface roughnesses of both the sphere and panel are combined to give a total relative roughness ( $\xi$ ). The measured $C_{D}$ increases with decreasing $\xi$ , in agreement with analytical predictions. Furthermore, the measured $C_{D}$ is also in good agreement with the combined analytical and numerical predictions for a smooth sphere and wall, with a gap approximately equal to the root-mean-square roughness ( $R_q$ ). The accuracy of these predictions decreases for low mean Reynolds numbers ( $\overline {Re}$ ), due to the existence of multiple scales of surface roughness that are not effectively captured by $R_{q}$ . Experimental flow visualisations have been used to identify critical flow transitions that have been previously predicted numerically. Path tracking of spheres rolling on two panels with different surface roughnesses indicates that surface roughness does not significantly affect the sphere path or oscillations. Analysis of sphere Strouhal number ( $St$ ) highlights that wake shedding and sphere oscillations are coupled at low $\overline {Re}$ but with increasing $\overline {Re}$ , the influence of wake shedding on the sphere path diminishes.

Fluid dynamics of a flapping wing interacting with the boundary layer at a flat wall

In this paper, we consider the fluid dynamics of a flapping wing interacting with a boundary layer developed at a no-slip flat wall. Direct numerical simulations are carried out via implementing the non-iterative immersed boundary-lattice Boltzmann method, over a Reynolds number range of 10≤Re≤1000, for a fixed Strouhal number of St = 0.3 and for a given symmetric plunging and pitching flapping motion. The interactions between the wing and the boundary layer are modulated by varying the mean distance of the wing to the wall H0. The results indicate that the presence of the boundary layer at the wall amplifies the fluctuations in both lift and drag due to the boundary layer separation, in contrast to the pure ground effect. This separation also leads to the decrease in both average lift and average drag over one flapping cycle when H0 is low. When it comes to the flow patterns in the wake, it generally gets more complex for a low H0 and/or a high Re. Secondary vortices can be observed for Re≥500 in the present configuration, which either evolve by themselves or interact with the vortices in the wake while being convected downstream and dissipated via viscosity. In the end, a dynamic mode decomposition analysis is performed to explore further the flow structures in the wake. One observes the sheltering effect of the boundary layer that the vortices in the wake are prevented from penetrating the boundary layer, while this effect will not hold if the vortex intensity is sufficiently high, such as the low order mode of the case for Re≥1000 in this study.

Tracking the Nearfield Evolution of an Initially Shallow, Neutrally Buoyant Plane Jet Over a Sloping Bottom Boundary

AbstractUnderstanding coastal plane jets which occur when a body of water discharges into an ocean or a lake through a channel or outlet is important, since they play a significant role in sediment, nutrient, and pollutant exchange. This study investigates the nearfield of initially shallow, neutrally buoyant plane jets, bounded by a free surface and a sloping bottom (Sloping Bottom Jet; SBJ) that issue into a laterally unconfined quiescent ambient both experimentally and numerically, and compares them with a plane jet flowing over a horizontal bottom (Horizontal Bottom Jet; HBJ). Results revealed that, different from the HBJ, the width and centerline velocity of SBJ decrease near the mouth. The SBJ width gradually increases after that as the transverse longitudinal velocity profile progressively transforms from a “top‐hat” into a Gaussian distribution. Once the Gaussian distribution is established, both jets diverge and centerline velocity decreases. Shear layers are generated on the sides of both jets with Kelvin Helmholtz‐type Coherent Structures (KHCS) developing inside. KHCS produce periodic velocity fluctuations with a Strouhal number of ∼0.079 and contribute significantly to momentum exchange and turbulent kinetic energy production. Since the thickness of the SBJ increases longitudinally, the vertical extent of KHCS also increases. When the two shear layers meet and merge at the centerline, they cause a flapping motion of the jet. This location is closer to the jet mouth for SBJs than for the HBJ. These findings demonstrate that a sloping bottom modifies the flow field from quasi‐2D for the HBJ to strongly 3D for SBJs.

On the study of the pitch angular offset effects at various flapping frequencies for a two-dimensional asymmetric flapping airfoil in forward flight

This article explores the aerodynamic performance of a two-dimensional elliptical airfoil undergoing sinusoidal heaving and asymmetric pitching motions in forward-flight conditions for the Strouhal number (St) range of 0.1–0.6. The study employs numerical simulations and water tunnel experiments to investigate the effects of non-zero pitch angular offset angles (θoffset) while maintaining a fixed Reynolds number of 5000 and an effective angle of attack amplitude of 15° at the pivot location. The θoffset is varied from −15° to +15° at 5° intervals. The present research shows that these parameters significantly impact the leading-edge effective angle of attack, flow velocity, and the formation of high-pressure regions, which are crucial factors in thrust and lift generation throughout the flapping cycle. Moreover, the pitch angle determines whether the resultant force favors thrust or lift. It is observed that the cyclic time-averaged lift consistently increases with θoffset, surpassing symmetric cases (θoffset = 0°). Conversely, the cyclic time-averaged thrust is lower for non-zero θoffset values. Increasing St enhances both cyclic time-averaged thrust and lift up to the respective critical Sts, after which their performance declines. Notably, the critical St of cyclic time-averaged lift exceeds that of cyclic time-averaged thrust; interestingly, their values are invariant with θoffset. Moreover, in the conditions where thrust efficiency maximizes, lift efficiency attains a minimum value and vice versa. So, depending upon the application, one needs to suitably select the pitch angular offset and flapping frequency to maximize thrust or lift performance.

Hydrodynamics and propulsion of a hydrofoil undergoing leading-edge pitching and traveling wave-based surface undulation

We numerically study the fluid–structure interaction of a free-stream flow across a hydrofoil pitching at its leading edge with superimposed traveling wave-based surface undulations. We utilize an in-house code that employs the sharp interface immersed boundary method and consider a constant pitching amplitude θ0 = 5°, a constant local amplitude-to-thickness ratio AL=0.15, and wave number K = 20 of surface undulation. We compare the effect of surface undulation on a pitching hydrofoil with that of a hydrofoil undergoing pure pitching or experiencing pure surface undulation. The findings reveal that surface undulation on the pitching hydrofoil increases thrust on the hydrofoil. The onset of asymmetry in the vortex street occurs at a lower pitching Strouhal number (St) due to the early formation of a vortex dipole. In addition to the presence of an asymmetric inverse von Kármán vortex street, higher pitching frequencies reveal re-deflection of the asymmetric inverse von Kármán vortices. We quantified dynamics of vortex dipole to explain the occurrence of asymmetric and re-deflected reverse von Kármán vortex street. Furthermore, the analysis reveals an optimum combination of St and phase speed that yields higher propulsive efficiency, as both motions compete in generating thrust. A linearly superimposed scaling analysis for the time-averaged thrust of the combined motion is also presented. The computations and scaling are found to be in good agreement.

Experimental study on the effect of sound waves on the heat transfer characteristics of heated pipes

This study has experimentally investigated the heat transfer characteristics of a heated steel pipe (diameter = 20 mm) placed horizontally in a vertical experimental cylindrical pipe under longitudinal sound waves. The ranges of sound parameters used in this study are as follows: sound frequency f = 210–1000 Hz, and sound pressure level SPL = 125–135 dB. The heat transfer coefficient and Nusselt number of the cross- section of the heated pipe are used to describe the influence of different sound parameters on the heat transfer behavior of the heated pipe. The results show that under the action of low-frequency strong sound wave (f < 230 Hz), the distribution of local Nusselt number of heated pipe decreases (0-90°) at first and then increases (90-180°), while under the action of high-frequency strong sound wave (f > 500 Hz), the distribution of local Nusselt number first increases and then decreases. The relative Nusselt number decreases exponentially with the increase of the Strouhal number. In addition, the oscillating flow induced by sound waves is greatly influenced by the natural convection. The local enhancing or weakening effects of strong sound waves with different parameters on the heat transfer in a hot steel pipe are related to the characteristics of local flow.

The research on flow-induced vibration of compact curved tube bundles subjected to liquid cross flow

This paper presents a series of dynamic tests and analyses on single and compactly bundled straight and curved tubes subjected to liquid cross flow. The purpose of this research is to study the flow-induced vibration behavior of compact curved tube bundles, with particular interest in their differences to those of the straight tubes. Both modal and dynamic response tests are performed with tube structures of different bending radius and pitch-diameter ratios. Based on the test results, the vortex shedding phenomenon and Strouhal numbers of single straight tube and single curved tube are analyzed in this paper, and so are the fluid-elastic instability phenomenon and Connors constant of straight tube bundles and curved tube bundles. The test results and analysis conclusions provide valuable assessment tool for the design of helically coiled tube bundles commonly used in steam generators or heat exchangers.

The wake characteristics and hydrodynamic forces of a near-wall circular cylinder with the splitter plate

Flow around a near-wall circular cylinder with the splitter plate is numerically performed at Reynolds number of 500, with the objective of investigating the wake characteristics and hydrodynamic forces. Five gap ratios [Formula: see text] and [Formula: see text] (G is the gap between the lower surface of the cylinder and the wall, D is the diameter of the cylinder) are selected, and the splitter plate length [Formula: see text] ranges from 0 to [Formula: see text]. The flow characteristics of an isolated cylinder with the splitter plate are investigated first for comparison, and four wake flow modes are observed, which include 2S mode ([Formula: see text]), P+S mode ([Formula: see text]), 2S+S mode ([Formula: see text]) and 2P mode ([Formula: see text]). As [Formula: see text] increases from 0 to [Formula: see text], the mean drag coefficient ([Formula: see text]) is decreased, and there is a slight increase of [Formula: see text] for [Formula: see text]. In addition, the cases of [Formula: see text] and [Formula: see text] produce a very significant reduction of drag, and the [Formula: see text] is reduced by as much as [Formula: see text] and [Formula: see text], respectively. The wake characteristics and hydrodynamic forces of a near-wall cylinder with the splitter plate are investigated in detail, and five wake regimes are observed, which include the wake vortex merging regime I, merged vortex attaching regime II, steady flow regime III, wall shear layer elongation regime IV and upper shear layer attaching regime V. For [Formula: see text], the wake vortex shedding is suppressed. For [Formula: see text], the Strouhal number (St) is decreased as [Formula: see text] increases from 0 to 1.0, and there is an increase of St at [Formula: see text]. At [Formula: see text], the St of the near-wall cylinder is larger than that of the isolated cylinder, and the increase in St is affected by the deflected gap flow. What is more, the hydrodynamic characteristics are affected by the wall. For [Formula: see text], the variations of [Formula: see text] with [Formula: see text] are similar to that of the isolated cylinder. It is found that the cases of [Formula: see text] and [Formula: see text] still produce a significant reduction of drag for [Formula: see text], and the [Formula: see text] is increased for all cases of [Formula: see text] as [Formula: see text] increases.

Heat transfer characteristics of pulsating flow in a straight channel with rhombic-shaped expanding chamber: A numerical study

ABSTRACT The combination of passive and active heat transfer recovery techniques in channel flows has significant potential in terms of increasing thermal performance. Therefore, this study focused on the numerical examination of the flow and thermal behavior of pulsating flow in a straight duct containing a rhombus chamber. In the context of the study, iterations were solved using the finite volume method (FVM). The study was carried out for different pulsating amplitudes (A: 0.2, 0.4, 0.6, and 0.8), Strouhal numbers (St: 1, 2, 3, 4), and Reynolds numbers (200 ≤ Re ≤ 800). The surfaces other than the adiabatic lengths at the inlet and outlet of the duct were kept constant at Tw = 360 K. Results were compared with the results of the steady flow case. The effects of pulsating velocity and oscillatory parameters on Nusselt number, pressure drop, and performance factor were discussed. Velocity and temperature images were presented for different Reynolds numbers and pulsating components in the channel. The findings revealed that although the pulsating parameters significantly enhanced the heat transfer at increasing Reynolds numbers, they had a fairly low effect on heat transfer at the same Reynolds number. It was observed that at Re = 800, the Nusselt number formed a peak at St = 3 for all tested pulsating amplitudes. For the parameters of Re = 800, A = 0.6, and St = 2, heat transfer and performance factor in pulsating flow increased by 8.96 and 8.22 times, respectively, compared to steady flow conditions.

Flow kinematics model for universal Strouhal number in the separated flow past a bluff body

Flow kinematics model for universal Strouhal number in the separated flow past a bluff body

An experimental investigation on the influence of Strouhal number and amplitude on the flow and heat transfer behavior of synthetic jet impingement

ABSTRACT Here, tests are performed to analyze the effect of Strouhal number (St) and amplitude on thermo-fluid characteristics of synthetic jet (SJ) impingement for varied range of Reynolds numbers (Re = 3000–6000) and three different SJ actuation amplitudes (Vrms = 4, 6, 8 V). The hot wire anemometer and the infrared thermal imaging camera are used to measure the flow velocity and surface temperature, respectively. At a constant amplitude of the SJ actuation, discrete pairs of Strouhal numbers, i.e. low St ( S t L ) and high St ( S t H ), are found to exhibit the same Re. The heat transfer characteristics are expressed in three different regions such as the region of recirculation, the region of high Strouhal number dominance, and the region of low Strouhal number dominance. At lower orifice-to-surface spacings (z/d < 6), the thermal efficacy of SJ with S t H is found to be lower compared to the SJ with S t L . At z/d = 2, SJ with S t H exhibits the decrease in the average Nusselt number upto 53.4% corresponding to S t L at Re = 4000 and 4 Vrms. However, at intermediate spacings (z/d ≥ 6 ), the SJ with S t H tends to outperform the S t L , which may be due to vortex pairing at high St synthetic jets. At larger z/d, the dominance of S t L is reestablished due to matching of the SJ actuation frequency with the natural frequency of a steady jet. Correlations have been proposed for the average Nusselt number at both S t L and S t H as a function of Re, St, and z/d. The results of the study provide information on the selection of the operating frequency of SJ to achieve higher heat transfer at varied orifice-to-surface spacings.

Role of suction/injection on free convective flow in a vertical porous channel with non‐Fourier effects in the presence of periodic boundary

AbstractThe key attention of this work is on the impact of suction/injection on the free convective flow of a viscous fluid passing between two infinite, parallel, vertical and porous plates with non‐Fourier effects. The analysis focuses on a porous channel with boundaries featuring a steady–periodic temperature regime. The governing equations, representing velocity(momentum) and temperature(energy) fields, are well‐stated in dimensional form. Employing a separation technique, the momentum and energy equations are separated into steady and periodic components. On solving, the resulting second‐order ordinary differential equations derived, revealed the expressions for velocity and temperature in dimensionless form. However, the study investigates the influence of various flow parameters used in this work, including suction/injection , heat source/sink , Strouhal number , Prandtl number , and dimensionless relaxation time , on the velocity and temperature distributions. Also not left out is the rate of heat transfer on the flow performance and the skin‐friction coefficient on the plates. The findings are visualized using MATLAB‐generated graphs. An interesting observation found during the course of investigation in that the introduction of suction/injection enhances the flow velocity and fluid temperature within the channel, and they are both seen as declining functions of the Strouhal number, which measures the frequency of periodic heating on the plates. Furthermore, when the suction/injection parameter(s) is being relaxed, this study demonstrates a strong agreement with the findings of Ajibade and Mukhtar.

Effects of Flow Pulsation and Surface Geometry On Heat Transfer Performance in a Channel with Teardrop-Shaped Dimples Measured by Transient Technique

Abstract This study focuses on the heat transfer performance of a pulsating flow over a channel surface with teardrop-shaped dimples. Heat transfer measurements were performed by a transient technique with compensation of three-dimensional heat conduction under a bulk Reynolds number of 25,000. Seven types of surfaces with the teardrop-shaped dimples were examined, where dimple arrangement (in-line/staggered) and inclination angle (0-60 deg) were varied. A pulsating flow with the Strouhal number of 0.15 was generated by vibrating a rubber film section on the channel wall using a vibration generator. The pulsation amplitude was evaluated by calculating the root-mean-square value of the phase averaged velocity. Two conditions of the pulsation amplitudes were examined (0.09 and 0.12 of mean velocity). The results showed that the surface-averaged Nusselt number and friction factor for the pulsating flow increased from those for the steady flow. The highest increases of the surface-averaged Nusselt number and heat transfer efficiency index appeared in the 30deg in-line arrangement, and those were 16.1% and 9.8%, respectively, at most as compared with the steady case. Due to the flow pulsation, the local Nusselt number was enhanced at the leading-edge region of the dimples, and supplementary RANS/URANS results showed that the flow separation size was shrunk by the flow pulsation there.

Flow Dynamics of a Dodecane Jet in Oxygen Crossflow at Supercritical Pressures

In advanced aeropropulsion engines, liquid fuel is often injected into the combustor at supercritical pressures, where flow dynamics are distinct from the subcritical counterpart. Large-eddy simulation, combined with real-fluid thermodynamics and transport processes of a liquid N-dodecane jet in oxygen crossflow, is presented at different supercritical pressures and jet-to-crossflow momentum flux ratios (J). Various vortical structures are discussed in detail. The results show that, with the same velocity ratio of 0.75, the upstream shear layer (USL) is absolutely unstable at high supercritical pressure (J=7.1) and convectively unstable at low supercritical pressure (J=13.2), consistent with the empirical criterion at subcritical pressures (Jcr≈10). While decreasing J to 7.1 at low supercritical pressure, however, the USL remains convectively unstable, manifested by the variable dominant Strouhal number of the USL along the upstream jet trajectory. Such abnormal behavior can be attributed to the real-fluid effect induced by strong density stratification at low supercritical pressure, under which an inflection point in the upstream mixing layer renders a large density gradient and tends to stabilize the USL. Linear stability analysis further verifies these findings. The analysis of spatial mixing deficiencies reveals that the mixing efficiency is enhanced at a higher J.

Effects of Flow Pulsation and Surface Geometry on Heat Transfer Performance in a Channel With Teardrop-Shaped Dimples Investigated by Large Eddy Simulation

Abstract Large eddy simulation was performed to investigate heat transfer performance of a pulsating flow over teardrop-shaped dimples. A total of six geometries of dimpled surfaces were examined for dimple arrangements of in-line/staggered/original and dimple inclination angle of 0–60 deg. Pulsating flows were generated by sinusoidally varying the volume-averaged velocity. The pulsation frequency and amplitude were changed for the Strouhal number of 0–0.60 and the root-mean-square velocity amplitude normalized by the bulk flow velocity of 0–0.14. The results showed that the surface-averaged Nusselt number and friction factor were larger for the pulsating flow case than for the steady flow case. The surface-averaged Nusselt number ratio and the friction factor increased with the Strouhal number up to the Strouhal number of 0.30. For the Strouhal number larger than 0.30, they decreased with the Strouhal number or stayed almost constant. Consequently, the heat transfer efficiency index increased with the Strouhal number. The increase in the local Nusselt number ratio due to the flow pulsation was observed at the leading-edge region of the dimples. The results of the streamlines near the dimple showed that the swirling separation bubble was located closer to the leading-edge region due to the pulsation, which resulted in the increase of the absolute values of the turbulent heat flux and the local Nusselt number ratio.

Wake of two tandem square cylinders

The wake of two tandem square cylinders of identical width (d) is experimentally studied, with a view to understanding the dependence of the flow structure, aerodynamics forces and Strouhal number on the centre-to-centre spacing ratio L/d and Reynolds number Re, where L is the distance between the cylinder centres. Extensive measurements are carried out, using hot-wire, particle imaging velocimetry, laser-induced fluorescence flow visualization, surface-oil-flow visualization and surface pressure scanning techniques, for L/d = 1.0 ~ 5.0 and Re ≡ U∞d/ν = 2.8 × (103 ~ 104), where U∞ is the free-stream velocity and ν is the kinematic viscosity of the fluid. The flow is classified into four regimes, i.e. the extended-body (L/d ≤ 1.5–2.0), reattachment (1.5–2.0 &lt; L/d &lt; 2.7–3.2), co-shedding (L/d ≥ 3.0–3.4) and transition (2.7 ≤ L/d ≤ 3.3) where both reattachment and co-shedding phenomena may take place. The mean drag and fluctuating drag and lift exhibit distinct features for different flow regimes, which is fully consistent with the proposed flow classification. Comparison is made between this flow and the wake of two tandem circular cylinders, which provides valuable insight into the profound effect of the flow separation point and the presence of sharp corners on the flow development and classification.

Kinematic analysis of swimming ontogeny in seabass (Dicentrarchus labrax)

Swimming has been investigated in multiple species, but few studies consider the establishment of swimming through ontogeny. This study describes the establishment of cyclical swimming in Dicentrachus labrax, a marine fish from cold, temperate waters. The data were compared with results from previous studies on two subtropical freshwater catfish species (Clarias gariepinus and Corydoras aeneus). The three species have different modes of locomotion each during their adult stage (anguilliform, subacarangiform and carangiform). The swimming of Dicentrarchus labrax was recorded with a high-speed video camera (500 fps) from 0 to 288 hours and from 960 to 2496 hours post-hatching. Three indices, i.e. coefficient of determination (r²), coefficient of variation (CV), and Strouhal number (St), were used to investigate the establishment and efficiency of swimming. Important differences in the timing of swimming establishment were observed between the seabass and the two catfish species. The two catfish species display a sine-shaped swimming mode immediately or soon after hatching, and the efficiency of movement substantially improves during the first days of life. For seabass, however, establishment of swimming is slower during the same developmental period. These differences may be related to a faster developmental rate in the catfishes that allows them to swim rapidly in an intermediate regime flow and to develop the required morphology to establish efficient movements earlier.

Analysis of aerodynamic forces and flow development with the size of square cylinders arranged in equilateral triangle

A two-dimensional in-house code is used to scrutinize the influence of the arrangement of three cylinders and their corresponding dimensions on the behavior of flow around square cylinders arranged in four different combinations. Three square cylinders, C1, C2 and C3, are arranged in an equilateral triangle with the first cylinder C1 positioned upstream while the two remaining cylinders are placed side-by-side downstream. The wake flow patterns, aerodynamic forces and Strouhal number (St) are determined and analyzed for the four-cylinder arrangements in terms of streamlines, iso-vortices and drag and lift coefficients evolutions for steady and unsteady regimes. The numerical outcomes demonstrate that Re values, the different equilateral-triangular arrangements of cylinders, and the dimension variations of each square cylinder have a prominent influence on the flow characteristics.

Experimental study on flow characteristics and burning behavior for fire of flammable gases leakage underwater

The occurrence of subsea pipeline leakage incidents has gradually increased with the rapid development of the offshore oil and gas industry. Research on the fire dynamics of flammable gases leakage underwater is very limited, particularly in understanding the coupling mechanism of flow and combustion on the water surface. This paper presents a systematical investigation on flow characteristics and burning behavior for fire of flammable gases leakage underwater. A series of laboratory-scale fire behavior experiments were conducted through a self-designed experimental platform, consisting of the leakage control module, water tank and measurement apparatus. It was revealed that the leakage flow rate and water depth would influence the flow characteristics and burning behavior significantly. Two different burning conditions were found for the flame burning above the water surface (FBWS), i.e., the stable and self-extinguishing (unstable) burning states. The dimensionless analysis is conducted for the burning conditions, where the critical criterion is developed to distinguish the stable and unstable burning states. The base diameter of stable FBWS is almost 1.6 times of the diameter of bubble plume on the water surface. The flame pulsation frequency and dimensionless flame height (the ratio of height to base diameter of flame) of the stable FBWS are different from thoes of liquid pool fires and gas diffusion fires. Consequently, a correlation between the Strouhal number and the Froude number is correlated. Finally, the correlation between the dimensionless flame height and the dimensionless heat release rate is proposed for the stable FBWS.