CFD Simulation and Experimental Investigation of Water Distribution Patterns in Transitional Attack

Abstract

Transitional attack represents a pivotal tactic in modern firefighting, whose efficacy is profoundly contingent upon the impact characteristics of water streams and their subsequent distribution patterns. This study integrates computational fluid dynamics (CFD) simulations with experimental validation to develop a momentum decomposition model for jet impingement on a ceiling. The model analyzes the dominant mechanisms of tangential spread and normal rebound on water distribution and optimizes water application strategies. Theoretical analysis reveals that upon ceiling impact, the normal velocity component of the stream undergoes rapid attenuation, causing the flow to be predominantly governed by tangential diffusion. This phenomenon results in an asymmetrically elliptical ground distribution, characterized by a significant concentration of water volume at the terminus of the diffusion path, while wall boundaries induce further water accumulation. A comparative analysis of the stream impact process and water distribution demonstrates a high degree of concordance between experimental and simulation results, thereby substantiating the reliability of the proposed model. Numerical simulations demonstrate that an increased jet angle markedly improves both coverage area and flux density. Higher water pressure enhances jet kinetic energy, leading to improved distribution uniformity. Appropriately extending the horizontal projection distance of the water jet further contributes to broadening the effective coverage. The parametric combination of a 49° jet angle, water pressure of 0.2–0.25 MPa, and a relative horizontal distance of 1.5–2.0 m is identified as optimal for overall performance. This research provides a scientific foundation and practical operational guidelines for enhancing the efficiency and safety of the transitional attack methodology.

1. Introduction

In fire suppression operations, the properties of firefighting water jets are critical determinants of both operational efficiency and firefighter safety. Transitional Attack, as a key tactical approach, facilitates rapid modulation of the fire environment through exterior stream application, thereby establishing conditions conducive to subsequent interior offensive operations. This tactical concept was first introduced by the Colorado Springs Fire Department (CSFD) in 2002, defined as “an interim firefighting mode involving rapid suppression via a straight stream directed at the ceiling from the exterior, followed by a transition to interior attack”. Subsequently, Schwarz and Wheeler [1] experimentally validated the efficacy of this tactic in retarding fire development and maintaining thermal equilibrium, while also delineating its applicable conditions and limitations.

This body of work refined the definition of the tactic to “the application of water from an exterior position into the fire compartment through openings such as doors or windows prior to entry, to achieve rapid flame knockdown, reduce interior temperatures and thermal hazards, and thus enhance the safety of subsequent interior offensive operations.” Operationally, FSRI emphasizes the use of a straight, stationary, and intermittent stream pattern to maximize water delivery into the fire compartment while minimizing air entrainment. The stream should be directed at the ceiling at a steep angle, allowing the water to impact, atomize effectively, and cover a larger area. This mechanism facilitates a “reset” of the thermal environment within the fire compartment, which acts to delay or prevent the occurrence of rollover and flashover. Consequently, a critical temporal window is created, enabling the safe initiation of interior firefighting operations [2,3].

Some studies have focused on the impact of the transitional attack on human thermal exposure. Traina [4], in a comparative analysis of thermal injury risk to firefighters and potential occupants under different firefighting tactics, reported a higher fractional effective rate of heat exposure (FER) in non-fire areas on the second floor compared to the first floor in a two-story residential structure. The study further demonstrated that applying an exterior stream to the second floor could significantly reduce this thermal exposure hazard for occupants. In a related work, Horn G P. [5] compared the post-attack thermal conditions inside a structure following a direct interior attack versus a transitional attack. Their findings indicated that the transitional attack yields a more pronounced reduction in average compartment temperature and results in an average decrease of approximately 0.5 °C in the skin temperature measured at firefighters’ necks.

Extensive research has been conducted by scholars on the characteristics and distribution patterns of firefighting jets, primarily focusing on their motion mechanisms and breakup processes in air. For example, Miyashita et al. [6] developed a three-dimensional simulation model using the Moving Particle Semi-implicit (MPS) method to predict the trajectory of high-flow fire monitor jets, correlating it with operational parameters such as flow rate and pressure. Based on breakup theory, Sugawa et al. [7] employed the MPS method to evaluate the planar distribution characteristics of water jets, proposing a quantitative assessment methodology validated through small-scale experiments. Andres Valencia [8] established a model for jet trajectory and internal structure in quiescent air based on one-dimensional Euler equations, revealing the phenomenon wherein a portion of the jet atomizes and is transported along the trajectory. Through Computational Fluid Dynamics (CFD) simulations, FA Ponziani [9] reproduced the droplet dynamics and deposition patterns of firefighting jets in an open environment. BE Salyers [10] investigated the atomization mechanism of straight-stream jets, identifying that shear forces induced by high Weber numbers drive the breakup of the water column, a process captured using chromographic imaging techniques.

Research indicates that the transitional attack serves as a critical tactic in modern fire suppression for controlling fire development, with its effectiveness largely contingent upon the impact dynamics and dispersal patterns of water jets [11]. Despite this recognition, persistent gaps remain in the understanding of the underlying physical mechanisms, particularly concerning momentum partitioning during impact and water distribution under wall confinement. This is especially pertinent in compartment fire scenarios involving ceilings and walls, where the spatial redistribution of water due to boundary effects has not been systematically quantified. Moreover, prevailing models often rely heavily on empirical assumptions and lack integration with experimental data within a coherent theoretical framework, which consequently constrains their predictive accuracy and general applicability.

To address these research gaps, this study integrates computational fluid dynamics (CFD) simulations with experimental validation to develop a momentum-decomposition model for water-jet impingement on ceilings. The model aims to disentangle the contributions of two primary mechanisms governing post-impingement water distribution: tangential spreading along the surface and normal rebound. Controlled experiments are conducted to quantify the influence of adjacent wall boundaries and to map the water distribution directly beneath the impingement point, thereby assessing the model’s predictive accuracy. This work seeks to address a fundamental gap in the current understanding of jet dynamics during the transitional attack phase, paving the way for more precise and scientifically informed firefighting tactics. The specific objectives of this study are

(1)

To establish a momentum-decomposition model for ceiling jet impingement, clarifying the key physical mechanisms responsible for water distribution.

(2)

To analyze the respective effects of tangential spreading and normal rebound on water distribution, validating the model through integrated CFD simulations.

(3)

To investigate the effects of jet angle, water pressure, and nozzle horizontal distance on water distribution characteristics, and to propose optimized water deployment strategies for transitional firefighting operations based on hydraulic distribution patterns.

2. Materials and Methods

2.1. Theoretical Model

To provide a mechanistic understanding of the kinetic behavior of water jets upon ceiling impact during transitional attack operations, a simplified theoretical model is developed in this section. This model decomposes the jet motion into normal and tangential components, with the objective of quantifying the effects of initial water jet parameters such as impact angle and velocity, as well as ceiling surface characteristics, including roughness, on the water spread range and the resulting floor distribution pattern. The model provides a theoretical foundation for subsequent experimental validation and numerical simulation analysis.

2.1.1. Model Assumptions

In a transitional attack, a water jet from a fire hose enters a compartment through a window. After impinging on the ceiling, the jet follows a tangential trajectory along the ceiling surface and subsequently descends to the floor due to gravitational force. A conceptual depiction of the jet impingement and rebound effect is shown in Figure 1. The derivation of the theoretical model is based on the following assumptions:

Regarding the jet parameters, the kinetic energy is supplied by the nozzle outlet pressure $P_0$. The initial jet velocity is given by $v_0=\sqrt{2P_0/\rho }$, and the flow is treated as steady. The ceiling is modeled as a rigid, smooth, and non-absorbent surface. This smooth-surface assumption implies minimal flow resistance during tangential spreading, leading to an extended coverage area. The compartment walls define the hydraulic boundary, confining the spread and generating a rebound effect. Consequently, the final water distribution on the floor is determined by the combined influence of the ceiling spread pattern and these boundary conditions.

2.1.2. Initial Jet Motion and the Instant of Ceiling Impact

Applying Newton’s laws of motion and the equations of oblique projectile motion [12,13], and with the assumptions of negligible air resistance and viscosity and a constant jet velocity, the horizontal range and the tangential and normal velocity components during the initial phase of jet motion are derived. The initial velocity components of the fire hose jet in the tangential and normal directions are given by $v_x=v_0\cos \theta$ and $v_y=v_0\sin \theta$, respectively.

The condition for the jet to impact the ceiling at a height $H_c$ is described by the oblique projectile trajectory equation:

$$H_c=H+\mathrm{t}\mathrm{a}\mathrm{n}\theta -{\displaystyle \frac{g{L}^2}{2v_0^2{\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta }}.$$

(1)

Solving Equation (1) for the horizontal travel distance $L$:

$$L={\displaystyle \frac{v_0^2{\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta }{g}}\left(-\mathrm{t}\mathrm{a}\mathrm{n}\theta +\sqrt{{\mathrm{t}\mathrm{a}\mathrm{n}}^2\theta +{\displaystyle \frac{2g(H_c-H)}{v_0^2{\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta }}}\right).$$

(2)

At the moment of ceiling impact, the velocity components of the water stream in the tangential and normal directions are expressed as

$$v_{x,c}=v_0\cos \theta , v_{y,c}=v_0\sin \theta -{\displaystyle \frac{gL}{v_0\cos \theta }}.$$

(3)

The corresponding resultant impact velocity is

$$v_c=\sqrt{v_{x,c}^2+v_{y,c}^2},$$

(4)

where $v_0$ is the initial jet velocity, $v_x$ is the tangential velocity component, $v_y$ is the normal velocity component, $H_c$ is the ceiling height, $H$ is the nozzle height, $\theta$ is the inclination angle of the jet, $L$ is the horizontal travel distance to impact, $v_c$ is the resultant velocity at ceiling impact, $v_{x,c}$ is the tangential velocity component at impact, and $v_{y,c}$ is the normal velocity component at impact.

2.1.3. Modeling of Post-Impact Jet Behavior upon Ceiling Strike

The interaction between a water jet and a solid boundary is governed by momentum transfer and energy dissipation. Upon striking the ceiling, the component of velocity normal to the surface undergoes rapid decay due to the inelastic nature of the impact. This post-impact normal velocity $v_n^{\prime }$ is modeled as

$$v_n^{\prime }=-C_r{v}_c\sin \varphi ,$$

(5)

where $C_r$ denotes the coefficient of normal restitution. For practical water streams impacting typical building surfaces, $C_r$ approaches zero, implying a nearly complete loss of normal momentum. Consequently, the subsequent transport of water is dominated by its initial tangential motion.

The tangential velocity component is retarded by surface friction. Assuming a linear drag model, where the frictional force is proportional to the instantaneous tangential velocity, the governing differential equation is

$${\displaystyle \frac{d{v}_t}{dt}}=-\alpha v_t.$$

(6)

Here, $\alpha$ is a phenomenological damping coefficient encapsulating the effects of surface roughness and fluid properties. The solution to Equation (6), with the initial condition $v_t\left(0\right)=v_c\cos \mathrm{\varnothing }$, the tangential velocity as an exponentially decaying function of time is

$$v_t\left(t\right)=v_c\cos \varphi \cdot e^{-\alpha t}.$$

(7)

Integration of Equation (7) provides the horizontal travel distance $x_t\left(t\right)$ of the water front along the ceiling:

$$x_t(t)={\displaystyle \frac{v_c\cos \varphi }{\alpha }}(1-e^{-\alpha t}).$$

(8)

The theoretical maximum spread, corresponding to the asymptotic limit of Equation (8) as time $t\to \mathrm{\infty }$, is therefore,

$$x_t^{max}={\displaystyle \frac{v_c\cos \varphi }{\alpha }}.$$

(9)

This model establishes a direct relationship between the jet’s impact conditions $\left(v_c,\mathrm{\varnothing }\right)$, the surface interaction parameter $\alpha$, and the resultant water distribution pattern on the ceiling.

2.1.4. Distribution Pattern of Water on the Ground

The subsequent distribution of water on the ground is governed by the ballistic trajectory of droplets after their detachment from the ceiling. Under the assumption that air resistance is negligible, the vertical motion of a droplet is governed solely by gravitational acceleration $g$.

Consequently, the time $t_f$ required for a droplet to fall from a ceiling height $H_c$ is derived from the kinematic equation for free fall:

$$t_f=\sqrt{{\displaystyle \frac{2H_c}{g}}}.$$

(10)

The total horizontal displacement $x_g$ of a droplet on the ground, measured from the point of jet-ceiling impact, results from the sum of its sliding distance along the ceiling $x_t$ and the horizontal travel during its free fall. The horizontal velocity at the moment of detachment, $v_t\left(t_f\right)$, persists during the fall (in the absence of horizontal forces). Therefore, $x_g$ is expressed as

$$x_g=x_t+v_t\left(t_f\right)\cdot t_f.$$

(11)

Analysis of Equations (10) and (11) reveals the mechanism behind the non-uniform ground distribution. Following the ceiling impact, droplets detach continuously over time. Early-detaching droplets retain a higher tangential velocity $v_t$ but have a limited ceiling sliding distance $x_t$. Late-detaching droplets experience greater velocity decay due to friction, resulting in a lower $v_t\left(t_f\right)$, but benefit from a longer cumulative sliding distance $x_t$.

The interplay between these two competing effects—decreasing horizontal velocity and increasing sliding distance with later detachment times—produces a concentration of impact points. Specifically, the majority of droplets land within a confined region near the terminus of the ceiling flow path, where the product in Equation (11) is optimized. This leads to a ground water distribution pattern that is characteristically non-symmetric and elliptical, with the highest water density localized at the far end of the wetted ceiling area.

2.1.5. Effect of Wall Boundary Conditions

The post-collision dynamics of water droplets at vertical wall boundaries govern the resultant water distribution on the floor. When a droplet moving along the ceiling reaches a wall, it undergoes an impact with the surface. Under the assumptions of rigid walls and one-dimensional, inelastic collisions, the component of the droplet’s velocity tangential to the wall is reversed and attenuated. The post-impact reflection velocity, $v_t^{\prime }$, is described by

$$v_t^{\prime }=-\gamma v_t,$$

(12)

where $v_t$ denotes the tangential velocity immediately prior to impact, and $\gamma$ is the boundary reflection coefficient ($0\le \gamma \le 1$).

This formulation implies that the droplet’s momentum normal to the wall is dissipated with each impact, as its velocity is scaled by the factor $\gamma$. Consequently, repeated collisions progressively deplete the droplet’s kinetic energy, preventing it from migrating far from the wall. Subsequently, under the influence of gravity, these energy-diminished droplets descend. Their impact locations on the ground therefore exhibit a statistically higher probability density in the immediate proximity of the wall base. This mechanism leads to a pronounced accumulation of water mass adjacent to the room boundaries, manifesting as a zone of elevated water concentration on the floor near the walls.

2.1.6. Analysis of Mathematical Modeling Results

Analysis of the mathematical model reveals the following key behaviors of water jet interaction with a ceiling. Upon impact, the normal component of the droplet velocity decays rapidly, causing the subsequent water flow to be dominated by tangential spreading along the ceiling surface. The extent of this tangential spread is determined by the initial jet velocity $v_0$, the impact angle $\theta$, and the ceiling roughness coefficient $\alpha$. The resultant water distribution on the floor assumes an asymmetric elliptical pattern. The water mass is predominantly concentrated in the terminal region of the ceiling spreading path, corresponding to the area where droplets lose momentum and fall under gravity. Furthermore, indoor boundary conditions constrain the overall diffusion range and induce localized water accumulation adjacent to the walls. The ceiling material significantly influences the distribution outcome. For a smooth ceiling, the reduced tangential resistance allows for wider droplet dispersion, leading to a broader floor distribution with increased water accumulation in peripheral areas. Conversely, a rough ceiling imposes greater resistance to tangential spreading, which contracts the dispersion range. This results in a more concentrated floor pattern, with a higher water mass deposited closer to the initial impact point directly below.

2.2. Experimental Study

To validate the theoretical model and establish a reliable benchmark for CFD simulation, this section presents a full-scale experimental design. The objective of this experimental study is to capture the dynamic evolution of water jets impacting the ceiling and to quantitatively measure the spatial distribution of water flux on the floor. These results provide essential experimental data for defining boundary conditions and validating the results of subsequent CFD simulations.

2.2.1. Experimental Site and Setup

The experimental investigations were performed in a Compartment Fire Behavior Training (CFBT) facility, designed to simulate realistic structural fire environments. A platform for conducting transitional fire attack maneuvers was erected externally, positioned at a fixed horizontal distance of 1.0 m from the compartment window. A firefighting nozzle was mounted on this platform at an elevation of 0.5 m above ground level. The nozzle was secured using a dedicated angular fixture to ensure a consistent water discharge angle of 45° throughout the testing procedure. The configuration of this transitional attack platform is illustrated in Figure 2.

To closely emulate actual fireground conditions during transitional attack operations, the equipment selected conforms to the standards for frontline firefighting units. This included a 65 mm diameter solid-bore nozzle and a matching 65 mm diameter fire hose, both of which comply with the Chinese National Standard GB 8181-2015 (Fire Fighting Water Monitors) [14]. Photographs of the nozzle and hose are provided in Figure 3 and Figure 4, respectively. All experiments utilized a solid-stream jet (straight stream) configuration, maintained at a constant operating pressure of 0.2 MPa.

2.2.2. Data Acquisition

To enable clear visualization of the water jet trajectory and the detailed evolution of its interaction with the ceiling, two synchronized imaging techniques were employed. A digital single-lens reflex (DSLR) camera (Canon Inc., Tokyo, Japan), mounted on a fixed platform, was used in high-speed burst mode to capture the overall jet dynamics. Simultaneously, the transient process of jet impingement and ceiling flow was recorded in real-time using a DJI Osmo Pocket 3 digital video camera (Da-Jiang Innovations, Shenzhen, China), (20 MP, 5312 × 2980 resolution, standard frame rate of 120 fps). The configurations for these optical measurements are shown in Figure 5 and Figure 6.

To measure the water volume distribution, a grid of 72 collecting cups (arranged in 6 rows × 12 columns) was positioned directly beneath the jet impingement area to ensure full coverage of the spray region, as illustrated in Figure 7. Each cup measured 18.1 cm × 18.1 cm in cross-section. The mass of water collected in each cup was determined using an electronic balance, and the corresponding volume was calculated by dividing the mass by the density of water (taken as 1 g/mL), as expressed in Equation (13):

$$V_{ml}={\displaystyle \frac{m_l}{\rho }},$$

(13)

where $V_{ml}$ is the volume of water, $m_l$ is the measured mass of water, and $\rho$ is the density of water.

2.2.3. Experimental Procedure

Based on observations from multiple preliminary experiments through slow motion video playback, a stable impingement point of the water jet was formed within 0.5 s, and the spatial water distribution pattern on the ground reached a dynamic equilibrium, indicative of a quasi-steady state, after approximately 1.0 to 1.2 s. Given the considerable volume of experimental data, the complexity of operational procedures, and the significant computational resources required for subsequent computational fluid dynamics simulations, a water jet duration of 1.5 s was selected for the formal experiments to ensure complete capture of the flow development while maintaining experimental efficiency.

The experiment was executed as follows. Prior to each test, the door and windows of the experimental compartment were opened. The fire pump and all data acquisition instruments were then activated and calibrated. The DSLR and digital video cameras were positioned at their predefined locations, and the measurement grid was placed at the designated points beneath the impingement zone. An experimenter, operating the water discharge device, initiated the jet. Water discharge was maintained for a precisely timed period of 1.5 s, during which all data were recorded. Following each experimental run, the measurement instruments were re-zeroed. This sequence constituted one complete trial. To account for experimental variability and reduce random error, three independent trials were conducted, and the results from these trials were averaged for analysis.

2.3. Numerical Simulation Study

The numerical simulations in this study were conducted using the commercial CFD software ANSYS Fluent (2022). To capture the characteristics of the water-air two-phase flow, the Volume of Fluid (VOF) multiphase model coupled with the RNG k-ε turbulence model was employed.

2.3.1. Geometric Model

A full-scale (1:1) computational model was constructed based on the dimensions of the CFBT container and the experimental water discharge platform. The external planar dimensions of the compartment are 6000 mm in length and 2750 mm in width, with corresponding internal dimensions of 5823 mm and 2573 mm. The compartment features two openings: a 1000 mm-long window and an 890 mm-long door. The water discharge nozzle was positioned outside the window at a height of 0.5 m above the ground. Detailed compartment dimensions are illustrated in Figure 8. To quantify water distribution on the floor, a grid of 72 uniformly distributed water collection points, labeled 1 through 72, was defined within the interior space, ensuring coverage of the entire floor area as shown in Figure 9.

2.3.2. Mesh Generation

The geometric models for the free jet flow field of the firefighting nozzle and the transitional attack flow field were constructed using SolidWorks (2022) and ANSYS SpaceClaim (2022). The tail section of the free jet model features a progressively tapered, focused geometry. Discretization of this region required finer mesh elements to accurately capture the flow features. Conversely, the transitional attack flow field exhibits a regular, large-area geometry. Applying the same fine mesh resolution across this entire domain would lead to a prohibitive increase in computational expense. To address this, a hybrid meshing strategy was adopted: the two flow regions were modeled separately in SolidWorks, assembled, and then the unified fluid domain was extracted in SpaceClaim. A Body of Influence (BOI) region was defined to encapsulate the free jet zone for subsequent local mesh refinement, as illustrated in Figure 10.

ANSYS Fluent Meshing was utilized for grid generation. The surface mesh, comprising triangular elements, is presented in Figure 11. Local refinement was applied to the nozzle region with a minimum element size of 1 mm, while a coarser maximum size of 32 mm was specified for the outer flow field. The resulting surface mesh contained a minimum of 307,442 elements. The corresponding volume mesh, composed of hexahedral cells, is shown in Figure 12. The BOI method was employed to apply local refinement to the nozzle and the initial jet development region, maintaining a minimum cell size of 1 mm. The maximum cell size in the outer domain was set to 64 mm. The final volume mesh consisted of no fewer than 2,316,281 cells.

2.3.3. Boundary Conditions and Solver Settings

The water jet inlet was specified as a pressure-inlet boundary condition. The total pressure at this inlet was assigned based on experimentally measured values. The volume fraction of the water phase was set to unity, with a turbulence intensity of 3% and a hydraulic diameter of 65 mm prescribed. All outlets, including the room doorway, windows, and the ambient region surrounding the firefighting nozzle, were defined as pressure-outlet boundaries with a static pressure corresponding to the standard atmospheric pressure (101,325 Pa). A no-slip condition was applied to all solid walls, utilizing the solver’s default settings.

For the solver configuration, the pressure term was discretized using the PRESTO scheme. A first-order upwind discretization scheme was employed for the remaining governing equations to ensure robust convergence behavior while maintaining acceptable accuracy. Under-relaxation factors were adjusted dynamically to improve solution stability and convergence rates. The convergence criterion for the scaled residuals of all solved equations was set to 10⁻⁶ to ensure high solution precision.

To ensure the accuracy and stability of the numerical simulation, the following solver settings and numerical models were implemented. The time step was controlled adaptively based on the global Courant number to accurately capture the gas–liquid interface within the VOF framework. The solver dynamically adjusted the time step at each iteration to maintain a maximum Courant number below 0.5. The initial time step was set to 1 × 10⁻⁵ s. The total physical simulation time for all cases was set to 1.5 s, which was sufficient to fully capture the entire process of jet development from entry into the compartment, impingement on the ceiling, and subsequent spreading along the floor until a quasi-steady distribution was established. The Volume of Fluid (VOF) model was employed to track the macroscopic interface between water and air. This approach is well-suited for simulating large-scale flow behaviors such as impact, rebound, and liquid film spreading, which are central to the study of water distribution during transitional fire attack. The Geo-Reconstruct scheme was used for high-resolution interface reconstruction. Turbulence and droplet breakup phenomena including primary and secondary breakup of the water jet were modeled using the RNG k–ε turbulence model. This model effectively captures shear layer instabilities and turbulent momentum and energy exchange, thereby implicitly representing the turbulent fluctuations responsible for jet breakup. Surface tension effects were incorporated in the VOF model, with the air–water surface tension coefficient specified as 0.072 N/m.

2.3.4. Design of Numerical Simulation Cases

A one-factor-at-a-time (OFAT) experimental design was employed to establish the simulation cases, with the objective of systematically examining the effects of three key operational parameters: the nozzle elevation angle, the supply pressure, and the horizontal standoff distance from the window opening. These parameters were assessed for their influence on the jet dynamics and the subsequent water distribution pattern on the compartment floor. In consideration of computational resource limitations, each transient simulation was configured with a physical time duration of 1.5 s. This duration was selected as a compromise to make efficient use of available resources while being sufficient to capture the complete process of jet impingement, breakup, and final droplet deposition. For all cases, the nozzle was positioned at a fixed height of 0.5 m above the floor. The complete matrix of simulation cases for the transitional attack study is detailed in

Table 1. Simulation Case Setup for Transitional Attack Water Jet.

Controlling Factor	Case No.	Horizontal Distance from Window (m)	Nozzle Pressure (MPa)	Jet Elevation Angle (°)
Jet Elevation Angle	1	1.0	0.20	41
	2	1.0	0.20	45
	3	1.0	0.20	49
	4	1.0	0.20	53
	5	1.0	0.20	57
Nozzle Pressure	6	1.0	0.10	53
	7	1.0	0.15	53
	4	1.0	0.20	53
	8	1.0	0.25	53
	9	1.0	0.30	53
Horizontal Distance	10	0.5	0.20	63
	5	1.0	0.20	57
	11	1.5	0.20	46
	12	2.0	0.20	38
	13	2.5	0.20	33

.

3. Results

3.1. Observation and Analysis of Water Jet Experimental Results

Based on the experimental methodology outlined previously, this section conducts a systematic analysis of the dynamics of water jet impingement on the ceiling and the consequent water distribution patterns. The primary objective is to characterize the actual diffusion morphology, spread range, and interaction patterns with wall boundaries of the water jets. These findings provide direct experimental evidence for evaluating the water distribution effectiveness in transitional attacks.

Figure 13 presents experimental imagery of a water jet impacting a ceiling under the conditions of a supply pressure of 0.2 MPa, a nozzle standoff distance of 1.0 m from the window, and an elevation angle of 45°. The jet, ejected from the nozzle at high velocity, forms a coherent and stable stream with significant kinetic energy concentration and strong directionality. Upon impingement, the jet’s concentrated momentum generates a localized high-pressure zone at the impact point, leading to a partial reflection of the water. At this point, the jet’s kinetic energy resolves into two orthogonal components: a normal component responsible for the vertical rebound of water droplets, and a tangential component that drives the flow and spreading of water along the ceiling surface. A visible mist dispersion zone forms around the impact point, indicative of energy conversion into turbulence and the subsequent atomization of the water column into fine droplets. In the subsequent rebound and dispersion phase, the weak normal component results in limited vertical droplet rebound, with droplets descending under gravity. Conversely, the dominant tangential component facilitates rapid radial flow and film formation across the ceiling, as evidenced by the distinct, continuous horizontal water path observed in the figure.

The water distribution was evaluated using the water flux index. Water flux is defined as the volume of water droplets passing through a unit area per unit time, as expressed in Equation (14). Under the experimental conditions, with a collection cup area of 0.032761 m² and a duration of 1.5 s, the water flux was calculated based on the equivalent area and time interval, with results expressed in cm³:

$$J={\displaystyle \frac{V_{ml}}{A\times t}},$$

(14)

where $J$ denotes the water flux, $V_{ml}$ represents the volume of water collected in the cup, $A$ is the cross-sectional area of a single collection cup, and $t$ indicates the duration of the jet.

The distribution of water flux in the experiment is analyzed below. The spatial distribution of the water flux was analyzed statistically. Data from three parallel experimental trials were used to compute the sample mean, $\overline{x}$, and the sample standard deviation, $s$, which quantify the central tendency and dispersion of the measurements, respectively. These were calculated using the following standard formulas:

$$\overline{x}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n x_i,$$

(15)

$$s=\sqrt{{\displaystyle \frac{1}{n-1}}{\sum }_{i=1}^n (x_i-\overline{x}{)}^2},$$

(16)

where $x_i$ is the i-th data point in the sample, $\overline{x}$ is the sample mean, $s$ is the sample standard deviation, and $n$ is the total sample size.

The results are presented in Figure 14. The error bars, which represent the variability, fall within a range of approximately ±5% of the mean values. This relatively small dispersion confirms that the triplicate measurements exhibit good precision and reproducibility.

Figure 15 and Figure 16, respectively, present a schematic diagram and a contour plot of the water flux distribution. It is observable from the figures that the water flux is predominantly concentrated in the region proximate to the wall (within the range of X = 0~0.3 m), exhibiting a distinct concentrated distribution along the Y-axis. The maximum water flux is between 160 cm³ and 230 cm³, with the distribution characterized by localized areas of high flux. Experimental measurements determined that the water density directly beneath the impact point accounts for merely 10–15% of the total volume. This indicates that the majority of the water flow propagates horizontally along the ceiling post-impact, forming a relatively concentrated and confined distribution band.

3.2. Comparative Analysis of Simulation and Experimental Results

A comparison between the simulation and experimental results was conducted to validate the accuracy and reliability of the CFD model in predicting both the jet morphology after water impingement on the ceiling and the resulting water distribution on the ground. The comparison was performed under consistent experimental conditions, including a jet angle of 45°, water pressure of 0.2 MPa, and a horizontal distance of 1.0 m between the water nozzle and the window. The comparative analysis between the CFD simulations and experimental measurements is focused on the region of jet interaction with the ceiling, as the jet pressure, injection angle, and nozzle position were predefined by the experimental setup, which captured the post-impingement flow dynamics. Figure 17 presents a comparative visualization of the transitional firefighting attack process. The temporal evolution of the flow field, as revealed by both methods, is analyzed as follows:

• At t = 0.3 s, corresponding to the initial jet development phase, the flow is characterized by a coherent, high-momentum stream. Minimal flow dispersion is observed upon entry into the compartment, with propagation predominantly aligned with the jet trajectory and absent of significant backflow or splashing.
• At t = 0.5 s, subsequent to ceiling impingement, the primary flow transitions into a radially spreading film along the ceiling surface. Concurrently, a downward-directed component emerges due to splash and rebound. The simulation captures this expanding distribution, illustrating the initial reflection and dispersion mechanisms.
• At t = 0.7 s, further propagation and attenuation of the ceiling film occur. The flow distribution area increases while its local intensity diminishes. Gravity-driven descent of water along the wall becomes evident. The close agreement between the simulated and experimental flow patterns at this stage validates the numerical model’s fidelity.
• At t = 0.9 s, the ceiling film achieves its maximum lateral extent as the jet’s kinetic energy is largely dissipated. The distribution assumes a fan-shaped morphology, with flow accumulation prominent near the ceiling-wall junction and minor drainage towards the floor.
• At t = 1.1 s, a quasi-steady flow distribution is established under continuous injection, marked by maximal spatial coverage and an energy balance between incoming and draining flow. Pronounced backflow and dispersion are evident in both datasets, with significant water accumulation persisting in the vicinity of the impingement zone.

As shown in the comparative visualization of Figure 18, a strong agreement is observed between the experimental records and simulation results regarding the post-impingement dispersion and rebound dynamics of the jet. The numerical model accurately reproduces the spatial distribution and temporal evolution of the water flow, showing remarkable consistency with the experimental observations and thereby confirming its reliability and predictive accuracy. Furthermore, the simulation successfully captures critical experimental flow features, including the gravity-driven falling film and the actual spreading pattern. Notably, at t = 0.9 s and t = 1.1 s, the model distinctly represents the pronounced lateral spreading along the ceiling surface and the consequent backflow phenomenon, which aligns closely with the physical experiment.

Figure 18 illustrates the simulated water flux distribution. The results indicate a pronounced concentration of water on the wall side aligned with the jet direction, consistent with the distribution pattern shown in Figure 15. Measurable water collection was observed in all five sampling cups positioned closest to the wall. The water flux density exhibits a gradual decline from the wall side toward the window side, with a maximum recorded value of 226 cm³ among all cups. A comparative analysis of the simulated and experimental water flux contour plots is presented in Figure 19. The primary dispersion width of the water flow is approximately 0.428 m, with flux densities ranging from 23 to 230 cm³. The agreement between the experimental data and simulation results confirms that the numerical model effectively captures the impingement and subsequent spreading dynamics of the water stream during the transitional attack phase, thereby validating the model’s reliability.

3.3. Analysis of Simulation Results on Influencing Factors of Water Distribution in Transitional Attack

Following the validation of the CFD model’s reliability, this section employs parametric simulations to systematically investigate the influence mechanisms of three key influencing factors: water jet angle, water pressure, and water jet horizontal position on water distribution patterns. The objective of this analysis is to quantify the effects of these parameters on the water flux, coverage area, and distribution uniformity. The findings provide a scientific basis for optimizing water distribution strategies in transitional attack.

3.3.1. Effect of Water Jet Angle

Simulation results for water flux distribution under varying jet inclination angles are presented in Figure 20. The data indicate that the jet angle is a critical parameter governing the spatial water flux pattern. At lower angles (41°, 45°), water delivery is concentrated in the central zone of the side walls, resulting in restricted coverage. An intermediate angle of 49° promotes a more balanced distribution. The widest coverage and highest flux density are achieved at larger angles (53°, 57°), with the 57°configuration proving most effective. A clear trend is observed whereby increasing the jet angle enhances both the overall coverage area and the flux density. Consequently, the high-flux zones evolve from localized concentration at shallow angles to a more extensive distribution across the side walls and the region forward of the jet at steeper angles. The spatial influence of the jet angle is further detailed in the contour plot of Figure 21. For the smaller angles (41°, 45°), the water distribution is relatively diffuse, with confined high-flux regions primarily centered near X ≈ 3 m, corresponding to an insufficient coverage width. As the angle increases to 49°, the flow exhibits significant focusing, forming a pronounced and expanded high-density core in the central region, which denotes improved uniformity favorable for transitional attack. With a further increase to 53° and 57°, the high-flux region demonstrates substantial longitudinal (Y-direction) extension. The distribution becomes more uniform, and the total coverage area increases markedly. The 57° condition attains the peak flux density and maximum coverage.

In summary, increasing the jet angle is an effective strategy for improving the uniformity and coverage capacity of the water distribution. An angle approximating 49° offers an optimal compromise between flow concentration and spatial coverage. For scenarios demanding rapid, expansive coverage, a larger angle such as 57° is recommended.

3.3.2. Influence of Water Pressure

The simulated water flux distributions under varying water discharge pressures are presented in Figure 22. A progressive increase in pressure from 0.1 MPa to 0.3 MPa induces notable alterations in both the magnitude of the peak flux and its spatial configuration. Under the low-pressure condition of 0.1 MPa, a subdued peak flux (approximately 25 cm³) is observed. The high-flux zone remains localized near the jet core, exhibiting a constrained distribution pattern indicative of inadequate kinetic energy. Elevating the pressure to the 0.15–0.2 MPa range results in a substantial augmentation of the peak flux (75–88 cm³). Concurrently, the high-value region undergoes longitudinal and lateral expansion, extending toward door and window peripheries, with a concomitant improvement in distribution uniformity. At higher pressures of 0.25–0.3 MPa, the peak flux exceeds 100 cm³. The high-flux region becomes extensively developed and homogeneous, signifying the full conversion of pressure into kinetic energy. This state yields the maximum spatial coverage and throw distance, representing the optimal condition for overall water application. The contour plots in Figure 23 further elucidate the pressure-dependent spatial characteristics of the water flow. At lower pressures, the insufficient kinetic energy of the jet leads to a restricted and non-uniform distribution of the rebound flow, compromising effective coverage of the target area. In contrast, medium pressure levels promote a marked improvement in both the uniformity of the distribution and the areal extent of coverage. Under high-pressure conditions, the flow achieves an optimal kinetic energy state, characterized by a high peak flux and a uniform spatial pattern. The resultant rebound flow forms a widespread and consistent water curtain. This configuration is advantageous not only for the rapid suppression of large-scale fires but also for enhancing heat extraction from the fire environment. Therefore, increasing the water discharge pressure is a critical operational parameter for optimizing flow distribution and augmenting firefighting and cooling efficacy.

3.3.3. Influence of Water Jet Horizontal Position

Figure 24 illustrates the effect of the distance between the water gun and the window on the spatial distribution of water flux. As this distance increases from 0.5 m to 2.5 m, the peak water flux gradually declines from approximately 83 cm³ to about 58 cm³, while the uniformity of its spatial distribution improves markedly. Under the extremely close distance of 0.5 m, the excessive kinetic energy of the jet results in a steep rebound angle, causing the flux to be highly concentrated near the window and adjacent wall areas. This leads to a highly non-uniform distribution prone to creating “firefighting blind spots.” When the distance is increased to 1 m–1.5 m, the peak flux decreases (to 74.7 cm³–66.4 cm³), and the high-flux zone begins to diffuse toward the center and sides of the room, enhancing distribution uniformity. With a further increase in distance to 2 m–2.5 m, the peak flux continues to decrease. However, the water flow achieves its widest coverage and most uniform spatial distribution, with a significant reduction in areas of high flux concentration. These results indicate that the distance of the water gun from the window necessitates a trade-off between peak flux magnitude and distribution uniformity. A position too close causes concentrated distribution and incomplete coverage, whereas an excessive distance reduces the overall flux level. Comprehensively, a distance in the range of 1.5 m to 2 m can maintain a certain flux intensity while achieving relatively optimal spatial coverage uniformity, offering valuable guidance for practical firefighting to avoid blind spots and ensure effective cooling.

The results from Figure 25 demonstrate that the horizontal distance from the water gun to the window is a key parameter controlling the spatial distribution characteristics of the jet after ceiling rebound. As the distance increases, the coverage area and distribution uniformity of the water flow improve, but the peak flux concomitantly decreases. At excessively short distances, the steep incident angle of the jet concentrates kinetic energy in the vicinity of the window opening, failing to convert effectively into horizontal dispersion, which limits coverage and creates uneven distribution. Appropriately increasing the distance optimizes the incident angle, enhancing the conversion efficiency of kinetic energy on the ceiling and thereby expanding the coverage area. However, when the distance becomes too large, the kinetic energy decay of the jet in air intensifies, leading to a significant reduction in the flux entering the compartment. Although the distribution may be uniform, the overall cooling intensity can be compromised. Therefore, practical application requires balancing peak flux against distribution uniformity, with an optimal distance range existing to achieve effective and balanced spatial coverage.

4. Discussion and Conclusions

This section integrates theoretical, experimental, and simulation results to provide a comprehensive analysis. First, it discusses the dynamic evolution of water jet impingement and subsequent rebound, the characteristics of water distribution patterns, and optimization strategies derived from key operational parameters. Finally, it synthesizes these multi-dimensional findings and the underlying physical mechanisms to draw conclusions, to identify the study’s limitations, and to suggest promising directions for future research.

4.1. Discussion

4.1.1. Evolution of Water-Jet Impingement and Rebound

Based on experimental and simulation results, the post-impact evolution of a ceiling-striking water-jet can be described through four consecutive phases:

(1)

Formation of the impact zone. The kinetic energy of the jet is rapidly dissipated near the impact point, causing a local pressure rise and generating both reflected and radially spreading flows. This zone is characterized by highly turbulent flow and represents the region of peak energy dissipation.

(2)

Decay of the normal rebound. Water rebounding vertically loses momentum quickly under the influence of gravity and air resistance. Only a small fraction of droplets retain sufficient kinetic energy to travel downward, which accounts for the limited water reflection observed at ground level during transitional fire-attack operations.

(3)

Dominance of tangential spreading flow. After impact, the tangential momentum component becomes predominant due to ceiling constraint. This leads to a spreading flow along the ceiling surface, which gradually develops into a thin water film or a field of fine droplets.

(4)

Atomization of water. A portion of the impacting water is atomized into fine droplets under the high impingement force. These droplets promote evaporation and cooling, thereby contributing to temperature reduction and smoke dilution in the fire environment.

4.1.2. Water Distribution Characteristics of Fire Suppression Jet Flows

The post-impact water distribution resulting from a ceiling-striking fire suppression jet is characterized by three principal features: local concentration, radial spreading, and strong directionality.

(1)

Localized concentration. The water density flux is highest in the immediate vicinity of the impact point, indicating a highly concentrated flow distribution. This concentration occurs because a substantial fraction of the jet’s initial kinetic energy is dissipated at the primary impact zone, thereby limiting its capacity for immediate radial expansion.

(2)

Constrained radial spreading. The water flow propagating along the ceiling surface exhibits radial spreading, the rate of which is constrained by both the ceiling’s surface roughness and the fluid’s viscosity. The eventual coverage area is strongly influenced by key parameters, including the jet’s impact angle, its initial kinetic energy, and the thermophysical properties of the ceiling material.

(3)

Directional flow dominance. The flow demonstrates pronounced directionality, with the majority of water forming a confined horizontal film along the ceiling. Only a minor fraction of the flow is redirected back toward the injection opening (e.g., a window) or undergoes significant vertical rebound.

4.1.3. Optimization Strategy for Transitional Attack Water Distribution Based on Hydraulic Distribution Patterns

Based on CFD simulation results regarding hydraulic distribution patterns, this study proposes optimization strategies for water distribution under pure water jet conditions. These strategies aim to enhance the efficiency of transitional attack operations while balancing operational safety and effectiveness.

(1)

Optimization of the Jet Impact Angle

• Shallow Angles (41–45°): Jets incident at shallow angles approach the ceiling nearly horizontally. This results in an extended rebound path and a fan-shaped water dispersion pattern, which promotes wide-area coverage suitable for space cooling. A primary limitation is the concomitant reduction in water flux density in the central floor region, thereby weakening direct fire suppression capability in that zone.
• Medium Angle (−49°): An impact angle of approximately 49° generates a moderate rebound path. This configuration yields a favorable compromise, producing a water distribution that is both sufficiently uniform and adequately widespread, effectively balancing coverage with concentration. It is therefore recommended as the default angle for generalized transitional attack operations.
• Steep Angles (53–57°): Near-vertical jet impingement leads to a short rebound path and concentrated water fallout directly beneath the point of impact or window. This creates a region of high water density, optimizing this strategy for the direct suppression of localized, intense fire sources.

(2)

Optimization of the Operating Pressure

• Low Pressure (0.1–0.15 MPa): The low flow momentum at this pressure range results in minimal air entrainment and limited post-impingement dispersion. Consequently, the area of effective water coverage is restricted, making it suitable only for incipient stage or very small-scale fires.
• Medium Pressure (0.2–0.25 MPa): This pressure range provides balanced flow momentum. It ensures effective water dispersion upon ceiling impact, leading to uniform floor coverage. Air entrainment—a critical mechanism for cooling smoke and gases—is also significantly enhanced. This represents the recommended operating pressure for the majority of compartment fire scenarios.
• High Pressure (0.3 MPa): High-pressure operation delivers superior flow momentum, translating to rapid coverage and deeper penetration of the fire plume. However, the associated short rebound path concentrates water in a smaller area. This setting is advantageous when the tactical priority is the rapid knockdown of a well-defined fire.

(3)

Optimization of Water Jet Horizontal Position

• Close Distance (0.5–1 m): Deployment at a close distance focuses the impingement zone, but the shortened rebound path confines the majority of the water to the ceiling layer. This leads to a highly non-uniform distribution on the floor and poor coverage of fire sources remote from the entrance.
• Medium Distance (1.5–2 m): A medium deployment distance allows for optimal development of the jet prior to impingement and a subsequent rebound path that promotes extensive and uniform water distribution across the floor. This position is identified as yielding the best overall performance for most configurations.
• Far Distance (−2.5 m): While maximizing the spatial spread of water, deployment from a far distance is subject to significant jet momentum decay before ceiling impact. This markedly reduces the resulting water density on the floor, rendering the strategy more appropriate for large-volume cooling than for direct fire suppression.

4.2. Conclusions

This study systematically investigates the hydrodynamic characteristics and water distribution patterns of fire hose streams in transitional attack, employing a synergistic approach that integrates theoretical modeling, computational fluid dynamics (CFD) simulations, and experimental validation. The principal conclusions are as follows:

(1)

Regarding the evolution of stream impact and rebound, upon impacting the ceiling, the kinetic energy of the fire hose stream is rapidly dissipated near the impact point, forming both reflected and diffused flows. The normal component of the rebound stream undergoes swift kinetic energy attenuation due to gravity and air resistance, with only a small fraction of droplets retaining sufficient momentum to propagate downward. The majority of the flow propagates along the ceiling surface, exhibiting a distinct diffusive trend. During the impact process, the impulsive force causes atomization, generating fine droplets that are beneficial for fireground cooling.

(2)

In terms of water distribution patterns, the experimental results demonstrate a high degree of concordance with the mathematical model and CFD simulations, thereby substantiating the reliability of the theoretical framework. The water flux density is highest near the impact point, where the distribution is relatively concentrated. A significant portion of the water flows horizontally along the ceiling, forming a relatively concentrated distribution band, with only a small fraction being redirected toward the window or rebounding vertically. Experimental measurements determined that the water density directly beneath the impact point accounts for merely 10–15% of the total volume, indicating that the majority of the water flows horizontally along the ceiling post-impact.

(3)

Concerning influencing factors and optimization strategies, this study proposes water distribution optimization measures under pure water jet conditions based on simulation results of three operational parameters: jet angle, water pressure, and nozzle position. A medium jet angle (approximately 49°) achieves an optimal balance between distribution uniformity and coverage area, making it the recommended angle for most scenarios. A medium working pressure range (0.2–0.25 MPa) ensures effective water diffusion and is recommended as the standard pressure for mainstream firefighting operations. A medium nozzle distance (1.5–2 m) provides the best comprehensive performance in terms of ground coverage and distribution uniformity.

Although this study has made significant progress in elucidating water distribution patterns within transitional attack strategies, several limitations persist, which concurrently delineate trajectories for future research.

Firstly, this study focuses on fundamental theoretical investigations of idealized surfaces, employing a model that assumes a rigid and smooth ceiling. This idealized assumption markedly diverges from the material diversity encountered in real fire scenarios. For instance, surface roughness may increase flow resistance and suppress tangential dispersion, while elevated surface temperatures can enhance droplet evaporation and vapor generation. Such factors are likely to alter jet characteristics and water distribution outcomes. Future work should incorporate material models with varying roughness, hygroscopicity, and thermal response properties, as well as explore more complex architectural geometries. These steps are essential for advancing model development and enabling thorough experimental validation.

Furthermore, this study primarily focuses on the dynamic behavior of water jets and does not incorporate coupled effects such as heat transfer and liquid–gas phase interactions. Subsequent investigations should integrate multiphysics modeling approaches to elucidate the synergistic mechanisms governing water distribution, heat transfer, and smoke transport. Such advancements will provide a more comprehensive basis for evaluating the efficacy of fire suppression tactics.

Finally, the current model predictions are primarily applicable to the hydraulic control phase during transitional fire attack, such as scenarios occurring prior to the onset of intense thermal feedback or where cooling constitutes the primary tactical objective. The applicability of the model under fully developed fire conditions remains to be validated. Extending the model to encompass such scenarios is identified as a critical direction for future research.