Parametrization of the fire-smoke exhaust system for a large and high-rise atrium in Shanghai through salt-bath experiment

Abstract

Present specifications in Building Codes in China lack design parameters for smoke exhaust for large and high-rise atrium in buildings. An investigation of natural smoke filling and parametrization of fire-smoke exhaust in an atrium building in Shanghai was conducted based on salt-bath experiment, due to dynamic analogy between thermal smoke movement in air and brine dispersion in water. To obtain a small, scaled-down version of an atrium with a high polyfoam fire up to 1 MW, the brine-bath experiment was conducted with calcium chloride for small strength fire in small-space rooms, to demonstrate the natural smoke filling within the atrium. The interface height and filling time derived was highly comparable to those obtained by empirical equations. The results of computational fluid dynamics simulations agreed well with the salt-bath experiments. The evacuation time was also calculated with a dimensionless interface height of 0.2 to determine whether there was sufficient time for occupants to escape. The smoke filling process under mechanical smoke exhaust was also investigated by experiments, to parametrize the fire smoke exhaust system in the atrium. The optimal smoke exhaust level, natural and mechanical make-up level were determined and were recommended as the design parameters for the construction of atrium in buildings.

Keywords

Atrium Fire smoke exhaust Salt-bath experiment Similarity theory Interface height Computational fluid dynamics simulations

Introduction

In modern buildings, atria have been increasingly popular and attractive due to the high-open space and the well-lit covered environment in enclosed areas. However, the further development of the atrium has been a challenge to the fire protection technology. Traditional buildings are constructed based on the concept of floor-to-floor compartmentation. The remarkable features and the confirmed stack effect of the atrium make it significantly different from a small enclosure in fire detection, control and extinction.^1–4 In most atria, the smoke is often exhausted through the roof by natural or mechanical exhaust system whose objective is to drive the smoke out and increase the escape time in case of a fire.⁵ However, it is difficult to manage the smoke movement through conventional smoke exhaust systems in atria, especially with the restriction of complying with the existing prescriptive fire codes.⁶ Therefore, a deep understanding of smoke movement and pursuit for feasible and practical design parameters are of great importance for the occupants to evacuate from the atrium in case of a large strength fire.

Two common means are used to study atria: numerical simulations and physical experiments.

Numerical modelling is one of the fastest developing areas in fire safety science. Many studies on atria have been done by establishing computing fire models including large-eddy simulation (LES) models (applied to simulation software fire dynamic simulator (FDS)), zone models,⁷ field models⁸ and self-developed models.⁹ These fire models aim at investigating the smoke filling process,⁶ the smoke temperature inside the atrium,¹⁰ the impact of different locations of the fire source,¹¹ the effectiveness of the smoke exhaust system,^6,11,12 as well as the influence of the geometrical parameters of the atrium.¹² Although the numerical fire models seem to be able to provide plausible and incredible scenarios, there are still some issues when considering the hypotheses in the entire process of fire modelling. The selection of the parameter values and the input data required by the software program are crucial factors affecting the modelling accuracy. Furthermore, the computing models can hardly provide good predictions in situations involving multiple fuel packages as they can only deal with one single fuel. As for FDS, the most common software used in fire simulations, some studies have shown that the FDS code cannot be used to simulate fires in small ventilated compartment.^13,14 Verification and revision work has to be done to test the accuracy and the feasibility of the computing fire models.

An alternative method to study the smoke movement is to conduct physical experiments including full-scale burning tests, reduced-scale burning tests and salt-bath tests. Chow et al.^15–17 carried out a series of full-scale burning experiments in the atrium at the Hong Kong Polytechnic University and University of Science and Technology, China (PolyU/USTC Atrium Project), which was specially constructed for atrium smoke movement investigation. The authors mainly focused on the effect of ventilation systems,¹⁵ the natural smoke filling process¹⁶ and the impact of the make-up air.¹⁷ Lai et al.¹⁸ measured the influence of the natural ventilation on smoke layer descent, and the results indicated that a room with a natural ventilation shaft could control the smoke layer in a fire better than rooms without a shaft. Fong et al.¹⁹ studied the thermal smoke layer environment under the ceiling space of an atrium using two scaled models with various shapes, and found that the configuration of the ceiling would directly affect the maximum height of the smoke layer. Fang et al.²⁰ conducted a scaled-down experiment to demonstrate the early fire movement and pointed out that the thermally stratified environment could intensify the temperature and the velocities of a fire plume until it terminated at a certain height. Previous studies,^15–20 including full-scale and reduced-scale experiments, have made great achievements in studying a fire case in atria. However, there are many questions about the use of these two methods. The fire dynamics in one building is not necessarily the same as that in another, especially for atria with complex construction. Although many full-scale studies have been conducted in state key laboratory, such as the PolyU/USTC Atrium project,^15–20 it remains unjustifiable to apply the general findings to a certain specific building. Besides, studies on atria through full-scale facilities are too expensive to be implemented. Reduced-scale facilities may be economical to study smoke filling process in a large atrium. However, when a real fire takes place, the similarities between the reduced-scale building and its corresponding prototype building would be difficult to preserve.²¹ Additionally, the fire size cannot be too big when using the full-scale or reduced-scale facilities because of potential fire hazards to researchers and damage to indoor decoration. Furthermore, many fire detectors would respond to a threshold, which may give false alarm solely due to the increase in particle density in the air. There are also difficulties in installing detectors given the vast size of the full-scale or reduced-scale facilities.

Therefore, salt-bath experiment (or brine-water modelling)²² has been selected to study the smoke movement and filling process. The method can display the fire smoke movement well owing to the dynamic similarity between the thermal smoke in air and salt-water in clean water. Linden et al.²³ used the method to study the fluid mechanics of natural ventilation and established analytical work. Chen et al.²⁴ developed a new technique, known as electrolytically generated fine hydrogen bubbles, to demonstrate the buoyancy-driven ventilation air-flows in buildings by means of salt-bath modelling. Compared to other means mentioned above, salt-bath experiment is an economic, straightforward and suitable way to study the smoke movement.

Research objectives

The atrium studied in this paper is 60 m high with crescent cross-section. Given the cost and complexity of fire tests, studies on the smoke movement in such an atrium using the full-scale or the reduced-scale facilities would be difficult if not impossible. In this work, a salt-bath system with a new salt was established as a new method to study this atrium, instead of using full-scale or reduced-scale facilities. Additionally, the fire dynamics simulator version 5 (FDS5) was used in the paper, which was developed by the National Institute of Standards and Technology (NIST) of the USA, and has been widely applied in the fire case. This study consisted of four parts:

The similarity theory between air flows and brine flows was analysed, followed by a determination of the reduced-scale factor, a selection of the salt solution, for the salt-bath experiment and calculation of drainage and water supply levels.

A series of salt-bath experiments were conducted to demonstrate the smoke filling process in the atrium and to parametrize fire smoke exhaust. The result without operating the smoke exhaust system was verified by the empirical equation.

Experimental results were analysed to provide suggestions for the real design.

Computational fluid dynamics (CFD) simulation was conducted, and the results were compared with those of the experiments.

This paper describes a new method to obtain the parameters for the design of the smoke exhaust system in large and high-rise atrium.

Salt-bath experiment

The atrium building used

The atrium selected which is regarded as the research model is located in Shanghai, China, whose shape and size can be seen from Figure 1. Both the exterior and interior building envelopes of the atrium are full glass curtain walls. The interior wall separates the atrium from the office floors. Mechanical exhaust fans are installed on the roof, and mechanical make-up air diffusers are located close to the floor along the interior wall.

This atrium is large and high rise. Similar to other atrium buildings, fire safety in this atrium is one of the major concerns especially when the atrium is linked to the office floors, given the circumstances of the interior wall breakage at high temperature in the event of a fire. For security, the extreme case scenario should be investigated to conduct studies on smoke filling process and predict the smoke layer interface height with or without operating the smoke exhaust system.

At present, there are two codes to quantify the smoke exhaust level in China, namely the Shanghai Engineering Construction Standard-Civil Building Smoke Control Code (DGJ08-88-2006)²⁵ (Shanghai local fire code for short) and the Code for Fire Protection Design for Tall Buildings (GB 50045-95-2005)²⁶ (the national fire code for short).

According to the Shanghai local fire code,²⁵ smoke exhaust level is determined by calculation through equation (5.2.5) or Table 5.2.3. The specification clause 8.4.2.3 of the national fire code²⁶ requires that smoke exhaust level is calculated through different air changes referring to the atrium volume. Both building fire codes explicitly stipulate that the level of the mechanical make-up air should be no less than 50% of that of the exhaust smoke.

However, these two fire codes are both lacking in detailed consideration of all the factors regarding the smoke exhaust level for a specified atrium. The determination of the smoke level according to the Shanghai local fire code²⁵ is based on two parameters, namely the fire size and the clear height, without considering the geometry of the atrium. Quite to the contrary, the determination of the smoke level based in the national fire code²⁶ requires the geometry and the size of the atrium due to its referring to the atrium volume, but does not take into consideration the fire size and clear height.

Considering that both fire codes have some deficiencies as mentioned above, a new calculation method to take into account all factors influencing the smoke exhaust level would be desirable. In this study, the salt-bath experiment has been developed as a new method to conduct studies on a large and high-rise atrium in Shanghai.

Theory of salt-bath experiment

Reduced-scale salt-bath experiments can be applied to represent the thermal buoyancy effect in air due to water being much denser and having a lower viscosity than air. In fact, brine diffuses in water much less than heat in air which will enforce the dynamic similarity between the smoke in air and brine in clean water.

Fundamental to the operation of ventilation are buoyancy-driven thermal plumes. In the prototype building, the increased temperature emanating from a point heat source produces buoyancy forces in the vicinity of the source. In the salt-bath system, buoyancy is a force produced by local density difference between incoming brine and the (ambient) fresh water in a fluid subject to gravity, which can be thought of as a reduced gravity force. The strength of a buoyancy source is named the buoyancy flux B, which is defined as the product of the buoyancy and the volume flux B_f in the prototype building. For a source of brine in fresh water, the buoyancy flux B_m is defined as the product of the buoyancy and the volume flux of brine at the source.

Governing equations for the buoyancy-driven flows

Salt-bath experiment (or brine-water modelling)²² can be used to demonstrate the fire smoke movement due to the dynamic similarity. The typical parameters in the two flows are defined by equations (1) to (4), as follows

Typicalvelocityscaleofprototype : u f = (Q c g / (ρ f 0 C p T 0 H f)) 1 / 3

(1)

where the subscripts f and m are on behalf of values of the prototype building and values of the salt-bath model, respectively; H_f is the typical length of the prototype; H_m is the typical length of the salt-bath model; C_p is the convection section of the fire size (kW); ρ_f0 is the density of fresh air at the room temperature (kg/m³); ρ_mo is the density of fresh water at the room temperature (kg/m³); Q_c is the smoke exhaust level (m³/h); M₀ is mass flux of smoke at the source (kg/h); T₀ is the ambient temperature (K); g is the gravitational acceleration (m/s²).

Typicaltimeofprototype : τ f = H f / u f

(3)

Typicaltimeofmodel : τ m = H m / u m

(4)

Through dimensionless analysis using the above typical parameters H_f_, u_f and τ_f, governing equations (including mass-conservation equation, momentum-conservation equation and temperature-distribution equation) for the smoke plume flow brought about by temperature difference produced by the heat source which is emanating from a point source of buoyancy are described by equation (5), as follows (assuming the smoke fluid is incompressible)

where U_i is the dimensionless velocity of horizontal coordinate axis and U_j is the dimensionless velocity of vertical coordinate axis; X_i is the dimensionless length of horizontal coordinate axis and X_j is the dimensionless length of vertical coordinate axis; t is the dimensionless time; P is the dimensionless pressure; Θ is the dimensionless temperature and

Θ = Δ T / T 0

; Re is the Reynolds number; Pe is the Peclet number; Fr is the Froude number; k_i = (0, 1, 0).

Through dimensionless analysis using the above typical parameters H_m_, u_m and τ_m, governing equations (including mass-conservation equation, momentum-conservation equation and density-distribution equation) for the brine plume emanating from a point source of buoyancy due to the density difference between the incoming brine and the (ambient) fresh water are described by equation (6), as follows (assuming the brine fluid is incompressible)

where C is the dimensionless density and

C = Δ ρ / ρ mo

.; the other corresponding symbols were defined above.

Dimensionless criterion quantities are defined by equations (7) to (12), as follows

Fr f = \sqrt{\frac{u_{f}^{2}}{gH f}}

(7)

Fr m = \sqrt{\frac{u_{m}^{2}}{gH m}}

(8)

Re f = \frac{u f H f}{v f}

(9)

Re m = \frac{u m H m}{v m}

(10)

Pe f = Re f P r

(11)

Pe m = Re m Sc

(12)

where

ν f

is kinematic viscosity of smoke (m².s⁻¹);

ν m

is kinematic viscosity of brine (m².s⁻¹); Pr is Prandtl number; Sc is Schmidt number in Equations (9) to (12).

By comparing equation (5) with equation (6), the equations are almost the same. In other words, salt-bath experiments²² can be used to simulate the thermal buoyancy-driven flows in buildings in a real fire situation provided that the values of Re, Fr and Pe in the prototype and salt-bath model are equal correspondingly.

Determination for similarity criteria

Criteria numbers referring to these two flow states including Re, Fr and Pr (Sc) are listed in Table 1.

Table 1.

Criteria numbers.

Criteria numbers	Smoke flow	Brine fluid
Reynolds	$Re f = u f H f / ν f$	$Re m = u m H m / ν m$
Froude number	$Fr f = u f / \sqrt{gH f}$	$Fr m = u m / \sqrt{gH m}$
Peclet/Schmidt number	$P e f = Re f ⪻ = u f H f / D φ f$	$P e m = Re m Sc = u m H m / D φ m$

where D_ϕf is diffusivity of heat in air (m²/s); D_ϕm is diffusivity of brine in water (m²/s) in Table 1.

Reynolds (Re) and Peclet (Pe) numbers are dimensionless quantities to compare inertia forces with friction forces, and inertia forces with diffusion forces, respectively.

If the values of Re and Pe remain large, the flow can be considered to be independent of the molecular properties (viscosity and diffusion) of the fluid. Based on previous studies,^27,28 the magnitude of Reynolds number for brine flows (Re_m) is in the order of 10⁴, and that for the smoke flows (Re_f) is in the order of 10⁵, which means that both the brine and smoke flows are turbulent flows when Re is at such magnitude. Assuming that the Re number is sufficiently large, both flows are independent of the Re number, and therefore, the similarity relation between the two flows holds. In addition, the ratio of Re_f/Re_m should not exceed the number 20.²⁹ Therefore, unequal Re_f and Re_m numbers would not affect the similarity between the two flows as long as both flows enter the turbulent region and the ratio of Re_f/Re_m is no greater than 20.

Pe_f number and Pe_m number are the product of Re number and Pr number, and the product of Re number and Sc number, respectively. Pr and Sc are the physical properties of the fluids which demonstrate the temperature distribution filed in a prototype and concentration distribution filed in its corresponding salt-bath model, respectively. When the flows enter the turbulent region, the value of Pr is almost close to Sc number, and their numerical difference can be ignored.²⁹ According to the analysis above and equations (11) and (12), the requirements for Pe numbers can be removed for turbulence-dominated flows at sufficiently large Re numbers.

Froude (Fr) number, which is used to compare inertia forces with buoyancy forces, is another dimensionless parameter required to be identical to ensure the dynamic similarity between the model and its prototype.

In conclusion, when flows resulted from a salt-bath model are similar to those in its corresponding prototype, the Froude number is required to be identical, and the Reynolds number is expected to be sufficiently large to make both flows enter the turbulent region. Besides, the value of Re_f /Re_m cannot be greater than 20.

Determination of reduced scale

As for the time corresponding to the actual fire scene and the salt-bath experiment, the relation between t_f and t_m is as defined by equation (13)

t f / t m = R 1 / 2

(13)

where R is the reduced scale (H_f/H_m).

According to the UK Chartered Institute of Building Services Engineers TM19, Relationships for Smoke Control Calculations,³⁰ the convection section of the fire size can be determined by equation (14)

Q c = Q 0 / 1.5

(14)

In order to specify the reduced scale, the dimensionless variables u_f, B_f and B_m are defined by equation (15), as

Thebuoyancyfluxofprototype : B f = \frac{Q c g}{ρ f 0 C p T 0}

(15)

Typical velocity scale of prototype is defined by equation (16), as

u f = (B f / H f) 1 / 3 = (Q c g / (ρ f 0 C p T 0 H f)) 1 / 3

(16)

The buoyancy flux of salt-bath model is defined by equation (17), as

B m = Q m 0 g (Δ ρ / ρ 0)

(17)

Typical velocity scale of model is defined by equation (18), as

u m = (B m / h m) 1 / 3 = (Q m 0 g Δ ρ / (ρ 0 H m)) 1 / 3

(18)

where Q_m₀ is volume flux of brine at the source (m³/h);

Δ ρ

is the density difference between incoming brine and the (ambient) fresh water.

Typical velocity scale of prototype equation (16) and typical velocity scale of model equation (18) were substituted into equations (7) and (8), respectively. As elucidated above, the similarity between the salt-bath model and its corresponding prototype requires that Froude number (Fr_m) for the model be equal to its counterpart (Fr_f) as given in equation (19) for the prototype

Fr f = Fr m

(19)

Consequently, equation (20) is derived

\frac{B_{f}^{2}}{B_{m}^{2}} = \frac{H_{f}^{5}}{H_{m}^{5}}

(20)

Substituting equations (15) and (17) into equation (20) gives equation (21)

Q 0 \frac{Δ ρ}{ρ m 0} = \frac{Q c / ρ f 0 C p T 0}{(\frac{H f}{H m}) 5 / 522}

(21)

Substituting typical velocity scale of prototype equation (16) and typical velocity scale of model equation (18) into equations (9) and (10) respectively, the relation of Re_f/Re_m is given by equation (22) below

\frac{Re f}{Re m} = (\frac{B f}{B m}) 1 / 133 (\frac{H f}{H m}) 2 / 233 (\frac{ν m}{ν f})

(22)

Substituting equation (20) into equation (22) gives equation (23)

\frac{Re f}{Re m} = (\frac{H f}{H m}) 3 / 322 (\frac{ν m}{ν f})

(23)

Equation (23) shows that the value of Re_f/Re_m is only related to the reduced scale (H_f /H_m) due to the ν_f and ν_m being constant. Substituting ν_f = 1.506 × 10⁻⁵ m²/s, ν_m = 1.006 × 10⁻⁶ m²/s and Re_f /Re_m = 1 into equation (23) gives equation (24)

H f / H m = 6.074

(24)

The reduced scale (H_f /H_m) from Equation (24) cannot be applied to research on large and high-rise atria (e.g. the atrium is 60 m high) considering the feasibility and economic reasons. An Re_f/Re_m value of 1 is not appropriate for a large space, especially for a large and high-rise atrium.

Figure 2 shows that the mass flux varies with the reduced scale (H_f/H_m). Figure 3 shows that the values of Re_f, Re_m and Re_f /Re_m vary with the reduced scale (H_f /H_m). As the reduced scale (H_f /H_m) increases, the salt water mass flux and Re_m decrease (Figures 2 and 3), while the value of Re_f /Re_m increases (Figure 3). As mentioned in the previous section, the value of Re_f/Re_m should not exceed 20. Therefore, substituting the maximum upper bound value 20 into equation (23) gives H_f/H_m ≤ 44.75. From Figure 2, the reduced scale of the prototype would be 44.75, and the considerable reduction of the salt water mass flux can be achieved. In this paper, the reduced scale (H_f/H_m) is assigned as 50, which is a round number close to 44.75 within the limits of error.

Selection of the salt solution

Table 2 lists the saturated density of five salt solutions at room temperature, 20℃. The density of LiBr is the highest, followed with FeCl₃, CaCl₂, NaCl, and KCl. As shown in Figure 4, the larger the fire strength is, the greater the salt water volume flux would be for a particular salt solution and that the higher the salt water density, the smaller the salt water volume flux for a given fire strength. In other words, high-concentration salt solution can effectively reduce the outlet flux of the salt water and the volume of the salt water tank. Considering that the saturation concentration of the KCl solution is too low and the FeCl₃ solution is hazardous to the environment, the two salt solutions would not be discussed further. Table 3 shows the relationship between the volume flux of the chosen saturated brine (CaCl₂, LiBr and NaCl) and the fire strength under the reduced scale of 50. For a given fire scenario, the volume flux consumption of the NaCl solution is the largest, nearly twice as much as the CaCl₂ solution and three times as much as the LiBr solution. In fact, the NaCl solution is the traditional salt used for the salt-bath model, but the salt solution is not suitable for simulating large size fires due to its low saturated density. In order to reduce the volume flux of brine at the source and the volume of the salt water tank when simulating large size fires, high-concentration CaCl₂ and LiBr salts are good candidates for this study. However, because the LiBr salt is much more costly than the CaCl₂ salt, the CaCl₂ salt was chosen as the final salt for the salt-bath experiment in this study.

Table 2.

The solubilities and saturated densities of five types of salt at temperature of 20℃.

Salt types	KCl	NaCl	CaCl₂	FeCl₃	LiBr
Solubilities (g/100 g)	34.4	36	74.5	86.9	111.2
Saturated densities (kg/m³)	1344	1360	1745	1869	2112

Table 3.

The volume flux of saturated brine varying as the fire strength under the reduced scale 50.

Salt type	Volume flux (m³/s)
Salt type	1 MW	2.1 MW	5 MW	10 MW
NaCl	2.95 × 10⁻⁴	6.2 × 10⁻⁴	1.48 × 10⁻⁴	0.574
CaCl₂	1.43 × 10⁻⁴	2.99 × 10⁻⁴	0.713 × 10⁻⁴	0.277
LiBr	0.955 × 10⁻⁴	2.01 × 10⁻⁴	0.478 × 10⁻⁴	0.186

Salt-bath experiment system

Introduction of the system

The system consists of four main components: a large fresh water reservoir, a scaled atrium model, a salt water tank of high static pressure, a fresh water tank of high static pressure. The large fresh water reservoir (marked ‘2’ in Figure 5(a)) has the dimensions of 2.0 m (long) × 1.0 m (wide) × 1.8 m (high). A large-scaled atrium model (marked ‘1’ in Figure 5(a)) was submerged in the reservoir with a clearance of 60 mm above the top plane of the reduced-scale model to ensure stable pressure environment in the model. The scaled atrium model was 1.2 m high made from transparent Perspex. The shape of the cross-section was crescent with 1.5 m long inner arc and 1.82 m long outer arc as can be seen from Figure 5(b). Two boxes, namely salt-water storage tank, marked ‘4’ in Figure 5(a), and fresh-water storage tank, marked ‘6’ in Figure 5(a), were auxiliary facilities to supply salt water and fresh water to the salt water tank of high static pressure and fresh water tank of high static pressure with water pumps. The drainage tank, marked ‘7’ in Figure 5(a) was used to drain water with water pumps from the scaled building model to simulate mechanical smoke exhaust in the large high atrium. The layout of salt-bath experimental system and photos of the salt-bath laboratory room are shown in Figures 6 and 7(a).

Figure 7(b) shows the test system of online digital conductivity meter. Four test holes were arranged evenly on the top plane of the scaled model (Figure 5(b)), and four probes were placed at the dimensionless heights where h/H_f = 0.21, 0.37, 0.74, 1.00, respectively. Before the experiment, brine water with different densities was confected. The density of the salt water and the electrical conductivity were measured by densitometer and the online digital electrical conductivity meter, respectively. The relationship of the salt water density and the electrical conductivity was developed in this study. It can be expressed as equation (25)

ρ m = 3.71163 \times 10 - 5 \times Ec 3 - 0.00747 \times Ec 2 + 1.02812 \times Ec + 990.73222

(25)

where Ec is the electrical conductivity (ms/cm);

ρ m

is the salt water density.

During the experiment, the measured conductivity was sent to a computer for statistical analysis of the brine water density.

The brine water was coloured by the dye to make this scaled building model produce an inverted image of what would happen when a heat source drives a flow in the large and high-rise atrium with mechanical smoke exhaust. The volume of water reservoir, which is marked ‘2’ in Figure 5(a), is large enough, so the ambient fluid density can be assumed constant throughout the experiment. To ensure consistency when making the analogy between air and brine flows, the source inlet on the top was on the same level as the heat source, and the brine water outlet for simulating smoke exhaust was on the same level as the smoke exhaust fan on the bottom of the salt-bath model.

Main test parameters were as follows: the density of source salt water, the salt water volume flux through the openings, the fresh water volume flux through the inlet, the density distribution in the scaled model during the experiment, the drain water volume flux through the outlet and interface height.

Quantities of drainage water and supply water

The schematic for the determination of the drainage and supply water level is shown in Figure 8. The air changes and water changes are the same, in $τ f$ time, and the corresponding $τ m$ time is based on the similarity principle. The relational expression is as described by equations (26) and (27):

\frac{Q f \times τ f}{H_{f}^{3}} = \frac{Q m \times τ m}{H_{m}^{3}} = N

(26)

Q m = Q f \times H_{m}^{3} / H_{f}^{3} \times τ f / τ m = Q f \times R - 3 \times \sqrt{R}

(27)

where N is air changes (/h);

τ f

is typical time of prototype (H_f/u_f₎;

τ m

is typical time of model (H_m/u_m); Q_f is the smoke exhaust level (m³/h); Q_m is the drainage water level (m³/h);

τ f

is typical time of prototype (H_f/u_f₎;

τ m

is typical time of model (H_m/u_m).

Parameters and four scenarios of the salt-bath experiment

According to the specification clause 4.2.1 of the Shanghai local fire code,²⁵ the fire size Q₀ in this experiment is 1 MW, of which the conventional part Q_c is 2/3 MW which can be calculated by equation (14). The fire is located at the centre of the atrium floor.

According to the previous section, the reduced scale (H_f /H_m) is 50. The values of Re_f, Re_m, and Re_f/Re_m were, respectively, 2,686,827, 113,765, and 23.6, obtained from equation (19). These values indicate both the smoke flow and brine fluid entered the turbulent region, and the value of Re_f/Re_m was close to 20 within the error range, and the salt water volume flux Q_m₀ was 1.09 m³/h when the density of CaCl₂ solution was 1350 kg/m³.

Four different working conditions with respect to the smoke exhaust level were considered:

Method 1: The smoke exhaust level was calculated based on equation (5.2.5) ( $V = M ρ T / ρ 0 T 0$ ) according to the Shanghai local fire code,²⁵ and the result was 274,579 m³/h.

Method 2: The smoke exhaust level was determined by different air changes and the atrium volume that is explicitly stipulated by the specification clause 8.4.2.3 of the national fire code,²⁶ and the result was 156,124 m³/h.

Method 3: The smoke exhaust level was based on the salt-bath model with the drainage water level ranging from 8.83 to 15.53 m³/h, corresponding to the smoke exhaust level in the prototype building ranging from 156,124 to 274,579 m³/h.

Method 4: The smoke exhaust level was zero. The condition was based on the possibility of smoke control and exhaust system failures, which could verify whether there would be sufficient time for the occupants to evacuate from the building before the operators open the smoke exhaust system manually.

According to both fire codes, the make-up air level was calculated by no less than 50% of smoke exhaust level. In this study, the air supply was determined by 50% of smoke exhaust level considering the fact that the inlets for air supply could be any combination of the doors and windows of the atrium and that the make-up air flow level are not controlled owing to the experimental difficulties. The smoke exhaust level and mechanical make-air level correspondingly to the values of drainage water and mechanical supply water were calculated by equation (27). Parameters for methods 1, 2 and 4 are given by Table 4.

Table 4.

Smoke exhaust parameters through different methods in salt-bath experiments.

Fire smoke exhaust parameters	Method types
Fire smoke exhaust parameters	Method 1	Method 2	Method 4
The smoke exhaust level (m³/h)	274,579	156,124	0
The mechanical air supply level (m³/h)	137,290	78,062	0
The drainage water level (m³/h)	15.53	8.83	0
The supply water level (m³/h)	7.77	4.42	0

Experimental results and discussion

Visual observations and comparison using methods 1, 2 and 3

Smoke filling process with the smoke exhaust system operating

Experiments were initiated by injecting dyed brine water into the reduced-scale model, and the drainage pump and the make-up pump, which simulate the mechanical smoke exhaust fan and mechanical make-up air fan in the prototype building, were operated 16 s later (to reflect the response time of fans in the actual fire scene).

In fact, the brine water movements of methods 1, 2 and 3 are almost the same except for the filling time. Due to page limitation, we selected only a set of photographs (Figure 9) illustrating the brine plume development of method 3 for analysis descriptions. Figure 9 shows a set of photographs illustrating the brine development of the flow and the formation of steady interface height eventually.

As shown in Figure 9 (a) to (i), the brine plume developed as more and more dyed brine fluid entered the box. The transformation from the brine plume in Figure 9 (a) to (c) (before the onset of smoke exhaust fan), to the subsequent brine plume in Figure 9 (d) to (i) (after the onset of smoke exhaust fan) and reddening of fluid above is obvious.

Comparison of three methods and parametric determination for the fire-smoke exhaust system

The predicted and measured values by methods 1 and 2 were plotted in Figures 10 and 11. As predicted, a steady interface state formed when the sum of brine water and make-up fresh water volume inflow is equal to the drainage volume outflow (Figures 10(a) and 11(a)). The density profiles were plotted according to the data measured by the online digital electrical conductivity meter and equation (25). Smoke layer interface was deduced from the density profiles and the visual observations referring to the steel ruler attached vertically to the front wall in the model.

As shown in Figure 10, the dimensionless steady smoke layer interface height h_n determined by method 1 is 0.29; hence, the steady smoke layer interface height h_ns1 = 0.29 × 60 m = 17.4 m, and the result by Method 2 from Figure 11 is 0.15; hence, the steady smoke layer interface height h_ns2 = 0.15 × 60 m = 9.0 m.

A series of salt-bath experiments were conducted based on method 3 with drainage water levels ranging from 8.83 to 15.53 m³/h. Among all the experiments, the dimensionless steady smoke layer interface height and the density distribution used to demonstrate the temperature distribution were ideal when the level of drainage water was 12.45 m³/h as can be seen from Figures 12 and 13. Figures 12 and 13(b) demonstrate that the dimensionless steady smoke interface height h_n by method 3 is 0.20, and the steady smoke layer interface height h_ns3 = 0.20 × 60 m = 12.0 m.

In order to further analyse the differences in the brine water filling process among the three methods, a systematic experiment was conducted to investigate the dynamic change of the brine water movement by adjusting the drainage water level based on methods 3, 1 and 2 in sequence. Figure 14 shows the results of density with h/H_f = 0.37 and h/H_f = 0.74. The first stage of the experiment was the same as method 3, and the drainage water level was 12.45 m³/h. The densities of both locations remained constant (the density of clear water), in the first 60 s, since it would take some time for the brine water to reach the locations. Roughly between 60 and 300 s, both densities rose, and the curves almost overlapped as the drainage system was working. Roughly between 300 and 700 s, the drainage water level was adjusted to 15.53 m³/h (method 1). As the drainage water level became larger, the level of the brine water exhausted from the tank became larger which resulted in the decline of the two density curves. At about 700 s, the density curves started to rise when the drainage water level was adjusted to 8.83 m³/h (method 2). In view of the aim of the paper, method 1 was based on the Shanghai local fire code and mainly considered the fire size and the clear height; method 2 was determined by the national fire code and emphasized the volume of the object. Method 3 was a trade-off between methods 1 and 2, and combined all the factors of methods 1 and 2 (e.g. the fire size, the clear height, the size and the geometry of the building). Given the needed clear height and the initial fans cost of smoke-exhaust system, the density distribution used to demonstrate the temperature distribution by method 3 in Figure 14 was shown to be more acceptable in the event of evacuation. The dimensionless steady smoke interface height h_n in Figure 12(b) by method 3 would be more suitable for the atrium of the Shanghai Tower, for the steady smoke layer interface height h_ns₂ would be too small in evacuation, and the steady smoke layer interface height h_ns1 would be too large which would incur a huge cost to be used in the design of the smoke exhaust system.

In summary, the salt-bath experiment would be a better method to parametrize fire smoke exhaust system. The optimized parameters of the drainage water level and mechanical supply water level were 12.45 and 6.225 m³/h, respectively. The corresponding parameters of smoke exhaust system are listed in Table 5. The smoke exhaust level and mechanical air supply level determined in this study were recommended as the design parameters applied in the construction of the Shanghai Tower.

Table 5.

Optimized fire smoke exhaust parameters by method 3.

Fire smoke exhaust parameters	The smoke exhaust level (m³/h)	The mechanical air supply level (m³/h)	The drainage water level (m³/h)	The supply water level (m³/h)
Method 3	220,000	110,000	12.45	6.225

Visual observations using method 4 and comparison with empirical equations

Smoke filling process without operating the smoke exhaust system

Photographs in Figure 15 illustrate the brine plume filling process without operating the smoke exhaust system. As shown in Figure 15, the dimensionless dyed brine plume interface height h_n varied as the time t_m and the dimensionless height h_n was 0.2 when t_m was 25 s and t_f was 178 s in Figure 15(f) viewed by the steel ruler attached to the front wall vertically in the model. Based on the obtained results by method 3, the optimized parameters were suggested as the design parameters in the construction of Shanghai Tower. In summary, the ideal dimensionless height h_n was 0.2, which corresponded to the dimensionless height in Figure 15(f). Considering the possibility of smoke control and exhaust system failures, the estimated evacuation time was crucial for the occupants to escape from the building before the operators can open the smoke exhaust system manually. So the estimated evacuation time was estimated to be 178 s in the actual fire scene when the smoke layer interface height descended to the safety dimensionless height of 0.2.

Comparison with empirical equation

Because the evacuation time without operating the smoke exhaust system is a vital parameter to fire safety, this study compared the results obtained from salt-bath experiments with those from the empirical equation.

A plume equation (equation (28)) with a simple two-layer zone model is proposed by Zukoski et al.³¹

where h_s is given by equation (29)

h s = [0.084 (\frac{α g}{ρ 0 c P T 0 A 3}) 1 / 3 \frac{Q 0}{α} 5 / 6 + H_{f}^{- 2 / 3}] - 3 / 2

(29)

where A is cross-sectional area of the atrium (m²); h_s is the smoke layer interface height at the transition into steady burning fire in the atrium (m); h_n is smoke layer interface height normalized as a percentage of ceiling height (%); Q₀ is fire size at steady burning period (kW); t_s is transition time from t²-fire to steady burning fire (s); α is growth factor of unsteady t²-fire (kW·s⁻²).

Parameter values of Q₀, α and t_s are summarized in Table 6. Table 7 compares the plume filling time with the mechanical smoke fan off under two conditions: (1) t_f = 178 s and h_n = 0.2, and (2) t_f = 226 s and h_n = 0.13.

Table 6.

The values of Q₀, α and t_s.

Q₀(KW)	α (kW·s⁻²)	t_s(s)
1000	0.047	$\sqrt{(Q 0 / α)}$ = 146

Table 7.

The plume filling time in different position without mechanical smoke fan working.

A/H ²	h_n	Salt-bath experiment	Equations (28) and(29)
0.22	0.20	t_m = 25 s (t_f = 178 s)	t_f = 170 s
0.22	0.13	t_m = 32 s (t_f = 226 s)	t_f = 182 s

As seen from Table 7, the results obtained from the salt-bath experiments agreed well with those from empirical equations (28) and (29) in different positions of the dimensionless smoke layer interface height for the large and high-rise atrium with the axis-symmetric fire. The comparison shows that the salt-bath system is reliable for studying fire exhaust systems in large and high-rise atria.

In summary, the experimental results indicated that large and high-rise atria have the smoke storage effect to certain extent and can provide 170 s for the occupants to evacuate from the atrium before operators opened the smoke exhaust system manually.

Comparison with numerical simulation

FDS code

Simulations were performed for the salt-bath experiment with method 3. The CFD code used in this study was FDS5 developed by NIST (https://www.nist.gov/) of the USA and is widely used for simulating fire-driven fluid flow. The FDS code uses the LES approach to describe the turbulence of the flow. The post-processor Smokeview of FDS can display the output of the simulations, including almost all the physical parameters, like temperature, velocity, visibility, etc.

FDS model

The computational model was established according to the physical dimensions of the atrium of the Shanghai Tower (Figure 16). The fire size was 1 MW and the fire area 1 m × 2 m. The fire was located at the centre of the floor to mimic the axis-symmetric flames. The smoke detectors with the limitation of 0.200%/m were placed in the 24th, 29th and 34th floors to detect the smoke density (Figure 17(a)). Mechanical exhaust vents were installed on the roof and mechanical air supplement inlets on the floor with flow rates of 220,000 and 110,000 m³/h, respectively (Figure 17(b)).

Taking accuracy and the computing time into consideration, a system of 120 × 80 × 120 cube grids with the size 0.5 m × 0.5 m × 0.5 m was determined for the CFD simulation in the atrium.

Results of FDS simulation

The formation processes of the smoke layer are described in Figure 18. The smoke particles moved upward in the initial period and kept going upward in the subsequent time. As shown in Figure 18 (b) to (f), a smoke layer gradually formed due to the upward and horizontal movement of the smoke particles. When the smoke production rate is equal to the ventilation rate, a steady venting state would be reached, meaning that a steady smoke layer would be formed (Figure 18(f)). The height of the blue line in Figure 18 is 12 m, which was set according to the salt-bath experiments. Based on the simulation results, the steady smoke layer interface height could be deemed as 14–16 m referring to the blue base line.

The dynamic temperature profile is described in Figure 19. To a large and high-rise atrium, roughly between 0 and 100 s, the hot smoke moved upward with the entrainment of the ambient air. In Figure 19 (b) to (f), the smoke kept going upward with the smoke exhaust fan operating, and the temperature was greater in the upper space. The temperature distribution was steady in the atrium, and the highest temperature was no more than 180℃ in Figure 19(f). According to the Fire Engineering Principles for the Design of Buildings,³² the temperature was safe for the occupants to escape. So the selected parameters from the salt-bath experiment, which were recommended for the smoke exhaust system of Shanghai Tower, were reliable.

Considering the fact that the smoke nearby the wall in reality would subside due to the lower wall temperature, and to simulate the heat transfer through walls as well as the vertical temperature gradient in the atrium along the height; minuscule difference is acceptable between the results of the salt-bath experiment and the FDS simulation.

Conclusion

This paper questioned the soundness of the design parameters for the smoke exhaust system for atria as specified in two existing fire codes in China with an emphasis on a specific large and high-rise atrium. The results are also applicable to the design of smoke exhaust system for other atria. The parameters of the smoke exhaust system should be optimized to reduce the initial cost on the premise of the occupants’ safety, instead of being determined only based on the national and regional fire codes in China. The main conclusions of this study are as follows.

The similarity theory between the smoke in air and brine in water was analysed. The equality relationship between the Fr numbers in the salt-bath model and its corresponding prototype is recommended as the primary consideration for keeping the similarity between the two kinds of flows. Meanwhile, the value of Reynolds number should be large enough to ensure that both the brine and smoke flows enter the turbulent region and the value of Re_f/Re_m cannot exceed 20. In addition, the reduced scale (H_f /H_m) should be determined based on the similarity theory and similarity criteria.

A new salt solution, CaCl₂, which has a high saturated density and is more suitable for studying large strength fire in an atrium, was applied to the salt-bath experiments.

The salt-bath experiments were validated to enable the parametrization of the fire smoke exhaust in the atrium of Shanghai Tower. A set of parameters were suggested as the design parameters in the construction of the atrium building.

The evacuation time without operating the smoke exhaust system was verified by the empirical equation. The experiment result showed reasonable agreement with that from the empirical equation. The optimized parameters of the smoke exhaust system obtained by the salt-bath experiment can effectively ensure the occupants to evacuate in case of a large strength fire.

The smoke layer interface height of the FDS simulation is in good consistency with that of the salt-bath experiment.

This study is limited in scope, because the fire type, size, and location are specified to the smoke exhaust system in one atrium in Shanghai Tower. However, the methodology and results of this study are extendable for studies on other types of atria (e.g. the shopping complexes). Other analogous models can be established by applying the methodology, such as the determination of similarity criteria and the reduced scale of height, selection of the salt solution and establishment of the salt-bath system. Moreover, the salt-bath experiment can make up for the deficiencies of other methods for studying the smoke filling process in large and high-rise atria. Compared with other methods, the salt-bath experiment has unmatched advantages in terms of economy, manoeuvrability, reliability and integrity. This paper provides a universal method to study the smoke exhaust system in high and large atria.

Footnotes

Acknowledgements

The authors wish to thank Mr. Tianheng Song for his contribution to the construction of the salt-bath system.

Authors’ contribution

All authors contributed equally to the preparation of this manuscript.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and /or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was funded by Shanghai Committee of Science and Technology (Grant No. 09dz1207704).

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