Simulation Study of the Capture and Purification Performance of Exhaust Fume Systems in Chinese Commercial Kitchens—Case Study in Tianjin

Abstract

A Chinese commercial kitchen fume exhaust (CCKEF) system mainly consists of a wall-mounted canopy hood, air duct and terminal electrostatic purifiers, the capture and purification performance of which should be guaranteed to obtain satisfactory indoor and outdoor air environment in engineering applications. However, few studies have focused on the operation performance of CCKEF systems. This study was aimed at providing a simulation method to investigate the operation performance of such systems. The simulation model of a representative CCKEF system was established using CFD software and validated with measured temperature, air velocity and purification efficiency with a deviation within 10%. The validated model was used to predict the indoor air environment and purification efficiency of the CCKEF system under different working conditions. The results showed that the temperature of transfer air from adjacent rooms had a greater impact on the thermal environment of the cooking area than the surface temperature of stoves. The exhaust air volume had a significant influence on both the indoor air environment and purification efficiency. CCKEF system was suggested to be operated at the optimum airflow according to the simultaneous coefficient of stoves as the energy consumption of the system can be saved by 3.75%.

1. Introduction

Chinese cooking, which is characterized by stir-frying and braising, can produce large amounts of heat and cooking fumes during the cooking process, especially in Chinese commercial kitchens (CCKs), where there is intensive cooking equipment and a large volume. Cooking pollutants are not only harmful to the productivity and health of employees in CCKs [1,2] but are also a significant source of atmospheric particulate matter [3,4]. An efficient CCK fume exhaust (CCKEF) system is required to capture and purify pollutants to guarantee that the indoor air environment and outdoor emissions meet the relevant requirements of current standards [5,6,7,8].

At present, many studies have been carried out on the capture or purification performance of cooking fumes in kitchens. In terms of the capture performance, the hood type and its geometric features, the supply air distribution strategy, exhaust air volume and airflow disturbances had significant effects on hood capture efficiency [9]. Zhao et al. [10] studied the impact of hood shape, side panel and exhaust duct arrangement on hood capture performance through CFD simulations. Wang et al. [11] numerically investigated the influence of the exhaust hood position on ultrafine particles and found that it did not significantly reduce the concentration of ultrafine particles. Zhou et al. [12], Lu et al. [13], Chen et al. [14] and Liu et al. [15] indicated that the use of air curtains could effectively increase exhaust performance in terms of both pollutants and heat. Lv et al. [16] and Song et al. [17] investigated factors that affect the function of the air curtain range hood, such as the exhaust rate, air curtain velocity, slot width and angle. The results showed that the exhaust rate was the main factor affecting the performance of the air curtain range hood. Lal Pal and Netam [18] carried out a numerical investigation of the temperature distribution and exhaust gas motion under different natural make-up air conditions and showed that the ventilation condition of windows and doors has a direct impact on temperature distribution and particle motion. Lv et al. [19] and Mahaki et al. [20] investigated the effect of disturbing the airflow caused by humans walking on the performance of a range hood in a residential kitchen. They found that the capture efficiency had a decrement of 0.5 under the most unfavorable conditions, and an air curtain could prevent the effect induced by humans walking with a smaller increment in air volume.

With regard to the purification of cooking fumes, the technologies used in the catering industry in China currently include mechanical separation, filtration, washing and absorption and electrostatic deposition [21]. The electrostatic deposition is the most common technology, with the proportion of terminal two-stage electrostatic purifiers used to purify cooking fume in Chinese commercial kitchens as high as 98.04% [22]. The influence of structural (diameter, spacing and quantity of corona wire) and operating (applied voltage and airflow velocity) parameters on the performance of a two-stage electrostatic precipitator were widely investigated. Gao et al. [23] studied the effects of geometric size, voltage parameters and working conditions on the dust-removal performance of a two-stage electrostatic precipitator. The results showed that for particles with large size, the dust removal performance was proportional to the particle diameter and inversely proportional to the inlet wind speed. Li et al. [24] studied the effects of various parameters on the collecting efficiency of a two-stage electrostatic module for oil mist particles and found that the degree of influence from high to low was as follows: the voltage applied to the precharger, the heteropolar distance of the precharger, the velocity, the heteropolar distance of the collector, the voltage applied to the collector, the length of the collector plate and the length of the precharger grounding plate. Zhu et al. [25] investigated the factors influencing the removal of PM_2.5 in a two-stage electrostatic precipitator.

A literature review showed that most of the previous studies on the capture and purification of cooking fume mainly focused on certain parts of the kitchen fume exhaust system. For example, studies on the capture of cooking fumes mainly considered the kitchen and hood part and investigated the kitchen indoor air environment or the capture efficiency of the hood, while studies on the purification of cooking fume considered the purifier module and explored the factors affecting purification efficiency. This kind of research was helpful in optimizing the design parameters of local structures. However, in practical application, the Chinese commercial kitchen fume exhaust (CCKEF) system encompasses the kitchen, exhaust hood, air duct and purifier. Compared with simplified local kitchen exhaust hood or purifier modules, the airflow characteristics in a complete CCKEF system are more complicated, which may result in capture and purification performance that is inconsistent with the design requirements of each module. Therefore, the operation performance of the CCKEF system should be examined. However, there have been few related studies.

A previous survey study conducted by Zhang et al. [22] showed that the proportions of wall-mounted canopy hood, rectangular air duct and terminal electrostatic purifier used to capture, transport and purify the cooking fume in Chinese commercial kitchens were 94.12%, 100% and 98.04%, respectively. That is to say, most of the CCKEF systems were composed of wall-mounted canopy hoods, rectangular air ducts and terminal electrostatic purifiers. In order to study the actual operating performance of such systems, this study developed a simulation method. First, a geometric model of a representative CCKEF system, including kitchen stoves, personnel, exhaust hood, air duct, terminal electrostatic purifier and make-up air, was established and discretized with an unstructured grid using CFD software. The types of boundary conditions were determined based on the literature and actual measurement. The MHD potential model with generalized convection diffusion equation was coupled with the RNG k-ε turbulence model and species transport model to calculate the steady-state continuous-phase flow, temperature, pollutants and electric fields. After calculation convergence, the DPM model in the Lagrange frame was introduced to track the particles entrained in the gas phase and calculate the purification efficiency of the purifier. In order to verify the accuracy of the model, the temperature, air velocity and purification efficiency of the CCKEF system were measured at several measurement points. The validated model was used to predict the indoor air environment and purification efficiency of the CCKEF system under different working conditions (simultaneous coefficient of stove, surface temperature of stoves, replacement air parameters and exhaust air volume) to understand the actual operation of the case system and offer suggestions for improvement.

2. Numerical Simulation Methodology

2.1. Geometric Model and Grid Generation

2.1.1. Geometric Model

Based on the actual dimensions and layout of the exhaust fume system of a canteen kitchen in Tianjin, the geometric model of the representative CCKEF system, including kitchen stoves, lamps, personnel, exhaust hood, air duct and terminal electrostatic purifier together with make-up air was established in this paper using CFD software.

The case kitchen was a large cooking room, with length, width and height of 8.1, 8.6 and 3.0 m, respectively. The kitchen was located in the interior of the building, without exterior doors or windows, and was connected to a dining area and a preparation area through two doors (door 1: 1.4 m × 2.0 m; door 2: 1.4 m × 3.0 m). The cooktop was 5.7 m long, 1.2 m wide and 0.74 m above the ground, and it consisted of four cauldron stoves (S1 to S4 from left to right) and one stockpot (S5) located in a line against the wall. All burners used natural gas, consuming five cubic meters per hour. The cauldron stove had a rectangular combustion exhaust vent 0.35 m × 0.12 m in size. During cooking, there were often three chefs standing about 0.10 m in front of the cooktop. The kitchen was equipped with six 130 W lamps and a 3.6 m × 0.74 m × 0.8 m shelf in the middle of the kitchen. The refrigerators and washing basins were located far from the working area, so they had little effect on the indoor flow field and were not considered when modeling. The exhaust fume system was composed of a wall-mounted canopy hood, terminal two-zone static purifier, rectangular duct, centrifugal fan and mechanical make-up air. The dimension of the canopy hood was 5.74 m in length, 1.2 m in width and 0.5 m in height, and it was located against the wall on three sides. The vertical distance between the front lower edge of the hood and the cooktop was 1.06 m. There were three suction vents 0.46 m × 0.24 m in size connecting the hood and air duct. The size of the outlet was 1.03 m × 1.0 m. The air diffusers (1.2 m × 1.2 m) of the mechanical make-up air system were located on the ceiling, 1.2 m from the edge of the exhaust hood.

The structures of the stoves, personnel and electrostatic purifier were relatively complex, so they were reasonably simplified when modeling. Cauldron stoves and stockpots were simplified to cylinders with diameters of 850 mm and 350 mm and a height of 60 mm. Three cooks were simplified to rectangular block models (1.7 m height, 18% head ratio, 40% upper body proportion, 42% lower body proportion) [11]. The geometric model of stoves and personnel is shown in Figure 1a. The model of the electrostatic fume purifier was simplified, as shown in Figure 1b. The diameter of the wire plate was 10 mm, with 45 mm between plates all around. The length of the collecting plate in the collection region was about 650 mm, with 45 mm between plates on both sides. The geometric model of the CCKEF system is displayed in Figure 1c.

2.1.2. Grid Generation

The geometric model was discretized by unstructured grids using Workbench software. In order to increase the calculation accuracy, local grid refinement was applied around the stoves, lamps, human bodies, exhaust hood and fume purifier. The number of grids was critical to the simulation results. A coarse grid might lead to a larger discretization error. However, the over-refined mesh would enlarge the computation expense. Thus, a proper grid resolution should be conducted to achieve the balance between the computation expense and computational accuracy. The computational grid is shown in Figure 2.

A grid independence test was carried out using three meshes with 200,000, 350,000 and 600,000 cells. The calculated average air temperature and air velocity at three suction vents shown in Figure 1c under different grid numbers is displayed in Figure 3. As shown, the calculated average air velocity and temperature of the solution with 350,000 grid cells were consistent with that of 600,000 grid cells. By considering the balance between the computation expense and computational accuracy, the 350,000 cell mesh was chosen for the simulation.

2.2. Definition of Materials and Boundary Conditions

2.2.1. Materials

In Chinese commercial kitchens, the flowing fluid is a complex mixture of gas (VOCs and exhaust gases) and solid (particles). In this paper, to investigate the kitchen indoor air quality, benzene (C₆H₆) and CO₂ were considered to represent the VOCs in cooking fume and combustion exhaust gas, respectively. The oil particles were dispersed in the gas phase. Firstly, cooking emissions can result in human exposure to both coarse particles (2.5–10 μm) and ultrafine particles (UFPs) (<0.1 μm) [26]. In order to understand the volume-based size distribution during the Chinese cooking process, Gao et al. [27] indicated that the typical Chinese-style cooking process, such as frying, can be simplified as a 2 min oil heating stage, and they found that the volume frequency of fume particles in the range of 1.0–4.0 μm accounts for nearly 100% of PM 0.1–10 μm with the mode diameter around 2.5 μm during the heating stage. Secondly, the purification performance of electrostatic purifiers is also often evaluated by the removal efficiency of PM2.5 in the literature [25,28]. As a result, PM_2.5 was selected as the representative cooking particulate in this study. As the surrounding temperature near the gas stove was quite high, the Boussinesq approximation was not suitable for buoyancy-driven flows with large density differences in the flow field inside the kitchen. The incompressible ideal gas equation was applied to obtain the variation in fluid density with different temperatures in this study according to Equation (1).

$${\rho }_f=\frac{PM}{nRT}$$

(1)

where ${\rho }_f$ is the density of fluid [kg/m³]; P is the pressure [Pa]; M is the mass of fluid [kg]; n is the amount of substance [mol]; T is the temperature [K]; R is a constant, 8.314 [J/(mol·K)].

2.2.2. Boundary Conditions

In order to study the actual operating performance of the CCKEF system, the boundary conditions were defined reasonably according to the literature and actual situations and included three parts: (1) kitchen: envelope including ceiling, walls and floor, lamps, personnel, cooktop and stoves; (2) exhaust fume system: exhaust hood, exhaust air duct, electrostatic purifier and outlet; and (3) make-up air: door 1, door 2, mechanical fresh air inlet and supply air duct.

As for the kitchen part, exterior walls can be defined as the wall boundary with constant temperature [29], while the ceiling, interior walls and floor were often set as adiabatic walls [30,31]. The lamps were set as wall boundaries with a heat flux of 130.6 W/m². The body surface of cooks in a residential kitchen was previously defined as a wall boundary with a heat flux of 27.7 W/m² [11], 50 W/m² [13], or 58.15 W/m² [14] or with a constant temperature of 32 °C [16], 31 °C [32], or 30 °C [29]. In this paper, the metabolic rate of cooking personnel in the commercial kitchen was set as 115 W/m² [7]. The cooktop was set as an adiabatic wall boundary [15]. The particulate boundary of the above was “reflect”. The boundary condition of stoves was a difficult point in the simulation of the CCKEF system, as the cooking process is very complex and difficult to simulate accurately. The boundary conditions of stoves given in the literature were not uniform (

Table 1. Boundary conditions of stoves given in the literature.

Position	Type	Pollutant	Detail Parameters	Reference
Emit	Mass-flow inlet	Aerosol particle	Release rate = 3.3 × 10−7 kg/s; T = 210 °C	[33]
Stove burner	Mass-flow inlet	CO2	Release rate = 4.7 × 10−3 kg/s; T = 127 °C; Mass fraction = 100%	[30]
Boiler	Velocity inlet	Water vapor	V = 2 m/s; T = 70 °C	[14]
Pot (exterior)	Wall	-	T = 120 °C	[15]
Pot (top)	Wall	-	T = 310 °C
Emit	Velocity-inlet	Ultrafine particles	V = 0.1 m/s; T = 210 °C	[11]
Pollutant/heat source	Mass-flow inlet	CO2	T = 1400 K; Release rate = 1.28 × 10−3 kg/s	[13]
Pot (exterior)	Wall	-	T = 100 °C	[29]
Pot (top)	Mass-flow inlet	PM2.5	Release rate = 10−7 kg/s; T = 100 °C
Pot	Velocity inlet	SF6	V = 0.29 m/s; T = 100 °C; Mass fraction = 10%	[19]
Gas burner	Velocity inlet	Exhaust gas	V = 1.714 m/s; T = 1200 K	[18]
Pot	Velocity inlet	-	V = 0.161–0.192 m/s; T = 200–300 °C	[31]

).

In this paper, the boundary condition of stoves was determined based on the type of stove according to the heat and mass transfer process. In CCKs, cauldron stoves, frying stoves and stockpots are commonly used, the heat and mass transfer processes of which are shown in Figure 4. As displayed, the burner of a cauldron stove is located inside the cooktop. The heat of combustion is directly transferred to the pot to heat the oil and ingredients. Cooking fumes are generated from the top surface, and exhaust gas is discharged from a special smoke outlet. For a frying stove or stockpot, the burner is located above the cooktop. The heat of combustion is partly transferred to the pot and partly exchanged with the air near the burner through convection. The heat transferred to the pot is used to heat the food. The exhaust gas from the burner is discharged into the air.

As indicated in Table 1 and Figure 4, the top surface of cauldron stoves is regarded as the source of cooking fume. Spherical particles with a diameter of 2.5 um are released from the top surface with an estimated emission rate and temperature of 0.12 mg/s and 70 °C, respectively [32]. The particle boundary of the top surface of cauldron stoves was “escape”. The exterior surface of cauldron stoves was set as a wall boundary condition, and the temperature was set with the measured value. The smoke outlet of the burner was considered as a mass-flow inlet with a velocity of 0.012 kg/s, and the flue gas fractions were calculated as 9.2% CO₂, 18.3% H₂O and 72.5% N₂. The temperature of exhaust gas was set with a measured value. The top surface of frying stoves or stockpots was also regarded as a source of thermal plumes, while the exterior surface (smoke outlet) was set as the mass-flow inlet. The boundary parameters were similar to those of the cauldron stove. The radiation heat transfer between the stove and the human body can increase the human shell temperature directly. However, this paper mainly focused on the distribution of indoor air temperature in the kitchen, which is mainly determined by convective heat transfer. In addition, the area of the stove surface is small compared with the kitchen volume. Therefore, radiation heat exchanges were not included in this paper [29].

For the exhaust fume system and make-up air parts, the boundaries of the exhaust hood, ESP plates and air duct were set as adiabatic and non-slip wall boundary conditions [34]. The voltage of the ESP collecting plate and wire plate was set as 5 and 25 kV, and the other wall boundaries were regarded as insulation. The particulate boundary of the collecting plate and wire plate was “trap”, and that of the others was “reflect” [34]. A reverse velocity-inlet was imposed at the discharge outlet [11,13,17,31]. A pressure-outlet boundary condition was imposed at the doors and fresh air inlet [11,16]. Fluent could automatically treat them as pressure-inlet boundaries if the velocity vectors are pointed inside there. Zero-gauge pressure was given at all pressure-outlet boundaries. The boundary conditions of the turbulence specification were specified by the intensity and hydraulic diameter. The particulate boundary of outlet and doors was “escape”.

The boundary condition types and parameters for the case CCKEF system are shown in

Table 2. Boundary conditions for case CCKEF system.

Position	Type	Parameters
		Velocity	Temperature	Mole Fraction	Particle	Electric Potential
Envelop/counter	Wall	No slip	Adiabatic	-	Reflect	Insulation
Lamps	Wall	No slip	130.6 W/m2	-	Reflect	Insulation
Personnel	Wall	No slip	115 W/m2	-	Reflect	Insulation
Pot(top)	Wall	No slip	Measured value	0.2% C6H6, 99.8% H2O	Escape	Insulation
Pot(exterior)	Wall	No slip		-	Reflect	Insulation
Smoke outlet	Mass flow inlet	0.012 kg/s	Measured value	9.2% CO2, 18.3% H2O, 72.5% N2	Escape	$\frac{\partial \mathrm{V}}{\partial \mathrm{n}}$ = 0
Hood/duct	Wall	No slip	Adiabatic	-	Reflect	Insulation
Wire plate	Wall	No slip	Adiabatic	-	Reflect	25 kV
Collecting plate				-	Trap	5 kV
Other plates				-	Reflect	0 kV
Outlet	Reverse velocity-inlet	Measured value	-	-	Escape	$\frac{\partial \mathrm{V}}{\partial \mathrm{n}}$ = 0
Door 1/door 2/Fresh air inlet	Pressure-inlet	0	Measured value	23.1% O2, 76.9% N2	Escape	$\frac{\partial \mathrm{V}}{\partial \mathrm{n}}$ = 0

.

2.3. Numerical Methods

2.3.1. Calculation Process

In order to evaluate the operating performance of the CCKEF system, the air velocity, temperature and pollutant concentration distribution in the kitchen and the particle purification efficiency of the electrical purifier should all be calculated. Therefore, the turbulence model, species transport model, MHD model and DPM model were combined in this paper. As the fluid in the kitchen ventilation system was in a turbulent state and contained curved near-wall flows and swirl flow at the elbow and electrostatic purifier, the flow field was computed with a three-dimensional, steady-state RNG k-ε model combined with buoyancy effect and standard wall function. The temperature distribution was determined by solving the energy equations. The concentration of gas pollutants was predicted by solving the species transport equation. After the flow field calculation converged, the MHD model was opened. A generalized convection diffusion equation was employed to describe the electric potential distribution and the ion migration induced by corona discharge in the purifier. After obtaining the convergence solution of the steady flow field and electric field, the DPM model in the Lagrange frame was opened to track the movement trajectory of particles and calculate the number of particles captured by the purifier.

2.3.2. Governing Equation

For convenience, the main equations used in the mathematical model are described as follows.

Continuity equation:

$$\frac{\partial \left(\rho u\right)}{\partial x}+\frac{\partial \left(\rho v\right)}{\partial y}+\frac{\partial \left(\rho w\right)}{\partial z}=0$$

(2)

Momentum equation:

$$\nabla ·\left(\rho u\mathit{u}\right)=-\frac{\partial p}{\partial x}+\frac{\partial {\tau }_{xx}}{\partial x}+\frac{\partial {\tau }_{yx}}{\partial y}+\frac{\partial {\tau }_{zx}}{\partial z}+F_x$$

(3)

$$\nabla ·\left(\rho v\mathit{u}\right)=-\frac{\partial p}{\partial y}+\frac{\partial {\tau }_{xy}}{\partial x}+\frac{\partial {\tau }_{yy}}{\partial y}+\frac{\partial {\tau }_{zy}}{\partial z}+F_y$$

(4)

$$\nabla ·\left(\rho w\mathit{u}\right)=-\frac{\partial p}{\partial z}+\frac{\partial {\tau }_{xz}}{\partial x}+\frac{\partial {\tau }_{yz}}{\partial y}+\frac{\partial {\tau }_{zz}}{\partial z}+F_z$$

(5)

Energy equation:

$$\nabla ·\left({\rho }_f\mathit{u}T\right)=\nabla ·\left(\frac{k}{c_p}grad\left(T\right)\right)+S_T$$

(6)

Concentration equation:

$$\nabla ·\left({\rho }_f\mathit{u}{c}_s\right)=\nabla ·\left(D_{s}grad\left({\rho }_f{c}_s\right)\right)+S_s$$

(7)

Turbulent energy equation:

$$\nabla ·\left({\rho }_f\mathit{u}k\right)=\nabla ·\left({\alpha }_k{\mu }_{eff}gradk\right)+G_k+{\rho }_f\epsilon$$

(8)

Dissipation rate equation:

$$\nabla ·\left({\rho }_f\mathit{u}\epsilon \right)=\nabla ·\left({\alpha }_{\epsilon }{\mu }_{eff}grad\epsilon \right)+\frac{\epsilon }{k}\left(C_{1\epsilon }{}^{*}{G}_k-C_{2\epsilon }{\rho }_f\epsilon \right)$$

(9)

$${\mu }_{eff}=\mu +{\mu }_t$$

(10)

$${\mu }_t={\rho }_f{C}_{\mu }\frac{k^2}{\epsilon }$$

(11)

$$C_{1\epsilon }{}^{*}=C_{1\epsilon }-\frac{\eta \left(1-\eta /{\eta }_0\right)}{1+\beta {\eta }^3}$$

(12)

$$\eta ={\left(2E_{ij}·E_{ij}\right)}^{1/2}\frac{k}{\epsilon }$$

(13)

$$E_{ij}=\frac{1}{2}\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)$$

(14)

where u is the fluid velocity vector and u, v, w is the component of the velocity vector in the x, y, z direction [m/s]; μ is the dynamic viscosity of the gas [Pa·s]; P is the pressure [Pa]; ${\rho }_f$ is the mass density of fluid [kg/m³];$F$ is the body force [N]; $c_{s }$ is the component volume fraction;$S_{T }$ is the heat source term; $S_{s }$ is the mass source term; $D_{s }$ is the mass diffusion coefficient of the component;$C_{\mu }$ = 0.085; ${\alpha }_k$ = ${\alpha }_{\epsilon }$ = 1.39;$C_{1\epsilon }$ = 1.42; $C_{2\epsilon }$ = 1.68; ${\eta }_0$ = 4.38; $\beta$ = 0.012.

In the ESP, the electrostatic field caused by the corona discharge process was solved with Poisson’s equation and current continuity equation, which are expressed as follows.

$${\nabla }^2\left(-{\epsilon }_0\phi \right)={\rho }_{ion}$$

(15)

$$\nabla ·\left({\rho }_{ion}\left(k_{ion}\mathit{E}+\mathit{u}\right)-D_i\nabla {\rho }_{ion}\right)=0$$

(16)

where φ is the electric potential [V]; ε₀ is the permittivity of free space, 8.85 × 10⁻¹² [C²/(N · m²)];${\rho }_{ion}$ is the ion charge density [C/m³], E is the electric field strength [V/m], u is the fluid velocity [m/s], $k_{ion}$ is the mobility of ions, and $D_i$ is the ion diffusion coefficient.

The corona onset electric strength on the electrode surface can be calculated according to Peek’s law using the equation.

$$E_w=3.1\times {10}^{6}m\delta \left(1+0.03/\sqrt{\left(\delta r\right)}\right)$$

(17)

where $E_w$ is the electric field strength of discharge wire surface [V/m];$m$ is the dimensionless surface parameter; r is the wire radius [m]; δ is the relative density compared with the standard condition, with the value set to 1 at 273 K and 0.1 MPa.

Particle charging is an integral process in ESP, which occurs once particles enter the ionization zone. There are actually two mechanisms by which particles become charged in an ESP: field charging and diffusion charging. For particles with a diameter greater than 2 um, field charging takes hold. The particles are assumed to be charged and saturated in a short time after entering the ionization zone. The saturation charge was calculated as follows:

$$q_s=\frac{3{\epsilon }_r\pi {\epsilon }_0}{{\epsilon }_r+2}{d}_p^2{E}_w$$

(18)

where $q_s$ is the saturation charge [C]; ${\epsilon }_0$ is the permittivity of free space, 8.85 × 10⁻¹² [C²/(N · m²)];${\epsilon }_r$ is the relative permittivity of the particles [C²/(N · m²)];$d_p$ is the diameter of the particles [m]; $E_w$ is the electric field strength [V/m].

The oil particles entrained in the gas phase were tracked by the DPM method in the Lagrange frame. The equation for particle motion can be described as follows [35].

$$\frac{d{\mathit{u}}_p}{dt}=\frac{3C_d\rho }{4{\rho }_p{d}_p}\left|\mathit{u}-{\mathit{u}}_p\right|\left(\mathit{u}-{\mathit{u}}_p\right)+\frac{6q_p\mathit{E}}{\pi {\rho }_p{d}_p^3}$$

(19)

$$C_d=\left\{\begin{array}{c}\frac{24}{C_c{R}_e}, R_e<0.1\\ \frac{24\left(1 + 0.15R_e^{0.687}\right)}{R_e}, 0.1<R_e<800\\ 0.44, R_e\ge 800 \end{array}\right.$$

(20)

where $R_e$ is the Reynolds number of fluid; $C_d$ is the coefficient of fluid drag; $C_c$ is the Cunningham correction factor; ${\rho }_{f }$ is the mass density of airflow [kg/m³]; ${\mathit{u}}_p$ is the particle velocity [m/s]; $\mathit{u}$ is the fluid velocity [m/s]; $d_p$ is the particle diameter [m]; ${\rho }_p$ is the mass density of particle [kg/m³]; $q_p$ is the particle charging.

2.3.3. Details of the Computational Method

The finite volume method (FVM) was applied to transform the differential equations described above into discrete equations. A second-order upwind scheme was used for differential derivatives. The semi-implicit method for the pressure-linked equations (SIMPLE) algorithm was adopted to couple the pressure and velocity fields to provide accurate gas phase parameters, while discretized equations were solved by the least squares cell-based method. Under-relaxation factors of 0.3 for pressure, 0.7 for momentum, 0.8 for k and ε, 0.9 for electrical potential and 1 for energy and the pollutant were used for the convergence of all variables. The convergence criteria were set as follows: residuals for both velocity and continuity reaching 10⁻⁴, and energy residual reaching 10⁻⁶.

3. Field Measurement

In order to verify the accuracy of the model in this paper, the temperature and air velocity of multiple measurement points and the system purification efficiency were tested during peak cooking hours (10:55–11:05) on three typical working days. The layout of the measurement points is displayed in Figure 5.

As shown in Figure 5, the measurement points A1–A3 were 0.1 m from the edge of the cooktop and 1.5 m above the ground, and they were used to measure the temperature and air velocity of the kitchen cooking area. Points B1–B5 were 1.6–4.0 m from the cooktop and 1.0 m above the ground, and they were used to measure the temperature and air velocity of the kitchen zone far from the stoves. Points C1–C3 were located at the edge of the cooktop and 0.75 m above the ground to measure the temperature and air velocity of the control point of the exhaust system. Points D and E were located on the pot surface and the burner smoke outlet, and they were used to measure the temperature of the pot surface and exhaust gas, respectively. Points F1–F3 were located at the suction vents connecting the hood and air duct to measure the temperature, air velocity and fume concentration at the suction vents. Point G was used to measure the temperature and air velocity of the hood opening. Points H1 and H2 were located at the doors to measure the temperature of transfer air from adjacent rooms. Point I was located at the discharge outlet to measure the exhaust air rate, temperature and discharge fume concentration. Point J was located outside the building without direct sunlight, 0.5 m from the exterior wall and 1.5 m above the ground, to measure the outdoor temperature.

The air temperature and velocity of the measurement points in the kitchen (points A and B) and outside (point I) were measured by a self-recording temperature instrument and hot-wire anemometer. The temperature of points D and E were measured through a thermocouple. The air velocity and temperature of measuring points C, F, G, H, and I were measured by a hot-wire anemometer. The cooking fume concentration at points F and I were measured by an infrared spectrophotometer (GB18483, 2001). The average of test results during peak cooking hours (10:55–11:05) was taken as the final value of each measurement point and the measurement error (U) was calculated by the following formula.

$$U=s/\sqrt{n}$$

(21)

where s is the standard deviation and n is the sample number. Field test pictures of typical parameters are shown in Figure 6. The test results are given in

Table 3. Measured temperature and air velocity at measurement points.

Points	30 April		30 August		11 September
	T (°C)	V (m/s)	T (°C)	V (m/s)	T (°C)	V (m/s)
A1	31.0 ± 0.16	0.35 ± 0.01	36.2 ± 0.07	0.54 ± 0.02	35.7 ± 0.06	0.48 ± 0.02
A2	29.1 ± 0.12	0.67 ± 0.02	36.4 ± 0.06	0.77 ± 0.03	28.8 ± 0.02	0.57 ± 0.01
A3	28.0 ± 0.10	0.57 ± 0.01	35.3 ± 0.09	0.59 ± 0.01	33.4 ± 0.07	0.48 ± 0.03
B1	25.4 ± 0.05	0.32 ± 0.01	31.4 ± 0.04	0.33 ± 0.02	31.3 ± 0.04	0.22 ± 0.06
B2	25.5 ± 0.11	0.22 ± 0.01	31.3 ± 0.01	0.40 ± 0.003	30.6 ± 0.10	0.18 ± 0.01
B3	23.8 ± 0.02	0.27 ± 0.02	31.0 ± 0.01	0.10 ± 0.01	30.1 ± 0.02	0.16 ± 0.01
B4	25.1 ± 0.03	0.09 ± 0.03	32.9 ± 0.04	0.14 ± 0.08	31.2 ± 0.04	0.18 ± 0.01
B5	23.4 ± 0.02	0.16 ± 0.02	29.8 ± 0.04	0.30 ± 0.005	29.5 ± 0.02	0.25 ± 0.03
C1	32.4	0.55 ± 0.02	35	0.48 ± 0.01	34.6	0.26 ± 0.06
C2	32.9	0.66 ± 0.04	35.2	0.53 ± 0.02	33.1	0.46 ± 0.03
C3	33.3	0.68 ± 0.03	35.8	0.51 ± 0.04	33.5	0.42 ± 0.03
D	/	/	/	/	365.8	/
E	/	/	/	/	339.5	/
F1	35.1 ± 0.75	11.28 ± 0.28	34.48 ± 1.11	11.98 ± 0.14	43.83 ± 1.04	11.95 ± 0.16
F2	35.6 ± 1.67	9.03 ± 0.22	35.08 ± 1.06	9.04 ± 0.13	33.6 ± 0.39	8.69 ± 0.07
F3	36.4 ± 1.97	6.94 ± 0.16	32.75 ± 0.24	6.35 ± 0.13	34.65 ± 0.89	6.60 ± 0.19
G	30.5 ± 0.40	0.35 ± 0.04	32.8 ± 0.18	0.35 ± 0.11	32.7 ± 0.16	0.31 ± 0.01
I	34.6 ± 0.50	4.23 ± 0.20	44.47 ± 0.18	4.73 ± 0.16	39.6 ± 0.08	4.09 ± 0.10
H1	24.1 ± 0.02	0.66 ± 0.01	31.8 ± 0.02	0.69 ± 0.01	30.6 ± 0.02	0.73 ± 0.03
H2	22.3 ± 0.01	0.15 ± 0.02	29.7 ± 0.01	0.31 ± 0.02	29.2 ± 0.02	0.22 ± 0.01
J	27.3 ± 0.07	/	32.5 ± 0.04	/	23.4 ± 0.06	/

and

Table 4. Measured purification efficiency of the CCKEF system.

Date	Cooking Fume Concentration (mg/m3)		Purification Efficiency (%)
	Point F1	Point I
30 April	14.99 ± 0.49	2.59 ± 0.27	82.72
30 August	12.24 ± 0.52	1.81 ± 0.29	85.21
11 September	12.22 ± 0.55	1.74 ± 0.19	85.76

.

The measured temperature values of points D, E, H1, and H2 were used for the temperature boundary conditions of stove surface, smoke outlet, door 1 and door 2, respectively. The measured air velocity of point I was used for the velocity boundary conditions of the outlet. The measured temperature and air velocity of points A1–A3, B1–B5, C1–C3, F1–F3 and G were used to verify the temperature and velocity fields of the CCKEF system. The fume concentration measured at points F1 and I were used to verify the purification efficiency of the system.

4. Results and Discussion

4.1. Model Validation from Experimental Data

4.1.1. Temperature

The comparison of simulated and measured temperature of the measurement points in the kitchen (A1–A3, B1–B5) and exhaust fume system (C1–C3, F1–F3 and G) is shown in Figure 7. It can be seen in the figure that the simulated temperatures of points in the kitchen were slightly lower than the measured values, with a deviation of 10%. The simulated temperatures of points in the exhaust system were closer to the measured values, with deviation generally within 5%.

4.1.2. Velocity

The comparison of simulated and measured air velocity of points in the kitchen (A1–A3, B1–B5) and the exhaust fume system (C1–C3, F1–F3 and G) is shown in Figure 8. As shown, the values of simulated air velocity of points in the kitchen were closer to the measured values, while the simulated air velocity of points in the exhaust system had slightly higher values than the measured values. The deviation in all cases was within 10%.

4.1.3. Purification Efficiency

The simulated and measured purification efficiency of the CCKEF system on three test days is shown in Figure 9.

In engineering applications, grease is deposited in the grease purifier, especially before system cleaning (the case kitchen was cleaned at the beginning of August). Grease accumulation reduces the purification efficiency of the electrostatic purifier. As a result, the measured purification efficiency was as low as 82.72% on April 30 and increased to about 85% on 30 August and 11 September, as shown in Figure 9. The measured purification efficiency of the CCKEF system was lower than the designed value. The simulated purification efficiency was slightly higher than the measured value, with a deviation between 4.86% and 9.28% but close to the designed value.

By comparing the simulated and measured values of air temperature, air velocity at different measurement points and the purification efficiency of the CCKEF system, it was found that the simulated and measured deviations were all within 10%, indicating that the established numerical model can better reflect the actual operation of the system and can be used for performance prediction of CCKEF system in engineering practice.

4.2. Performance Prediction of Case CCKEF System under Various Conditions

4.2.1. Different Surface Temperatures of Stoves

During cooking, there were mainly four flame states, as shown in Figure 10. Changming Fire state (state “a”) means that the stove has been turned on, but the fuel gas valve of the stove is set to the minimum, which is often used in the gap between two sets of cooking to keep the stove at the open status. Thus this section only focuses on the latter three flame states (states “b–d”). Different flame states corresponded to different stove surface temperatures, as shown in

Table 5. Stove surface temperature with different flame status.

Fire Status	Small Fire	Medium Fire	Big Fire
Surface temperature	100 °C	210 °C	365 °C

. This section investigated the air velocity, temperature, pollutant concentration distribution of the kitchen cooking area and the system purification efficiency under different stove surface temperature conditions (T = 100, 200, 365 °C), as shown in Figure 11.

As seen in Figure 11a, the change in stove surface temperature had no effect on the air velocity in the kitchen since the exhaust air volume was constant. Figure 11b shows that the temperature in the head area of the third cook was higher than that of the two other cooks and a thermal fume overflowed from the hood edge near the left side of the third cook. The overflow flowed upward and eventually accumulated at the ceiling. This indicates that the distribution of suction vents connecting the hood and air duct may not be proper, which leads to uneven air distribution around the stoves and cooks. As shown in Figure 11a, there was a vortex area above the head zone of the third cook, and the airflow velocity was small, which could not remove the convective heat effectively. When the surface temperature of the stove increased from 100 to 200 °C, the thermal fume overflow was slightly aggravated, but the overall change in temperature was not significant. The reason for the aggravation of hot smoke overflow with the increase in stove surface temperature can be explained from two aspects. On the one hand, due to the increase in stove surface temperature, the temperature of cooking thermal fumes was increased, and the molecular thermal motion was intensified. On the other hand, the increase in temperature difference between the hot thermal fume and ambient air increases the airflow disturbance and then aggravates the fume spillover. Figure 11c illustrates that some pollutants spilled from the left wall of the exhaust hood due to the nature of the thermal fume flowing against the wall. Figure 11d indicates that the purification efficiency was about 91% when the surface temperature was 100 and 200 °C and increased to 93% when the surface temperature was 365 °C.

4.2.2. Different Simultaneity Coefficient of Stoves

There are generally 4–6 stoves in CCKs, but not all of them are burning at the same time during cooking. By taking the case kitchen with four cauldron stoves and one stockpot as an example, the percentage of simultaneity coefficient of stoves (φ) is shown in

Table 6. The use state of stoves in the case kitchen during brunch cooking.

Number of Stoves Burning	Usage State of Stoves					Simultaneity Factor (φ)	Percentage (%)
	S1	S2	S3	S4	S5
One	Frying	Off	Off	Off	Off	0.2	16.9
Three	Frying	Frying	Frying	Off	Off	0.6	46.1
Four	Frying	Frying	Frying	Stewing	Off	0.8	33.8
Five	Frying	Frying	Frying	Stewing	Stewing	1	3.2

Note: Cooking process during lunch and dinner in canteen-type kitchens is similar, so only the use state of stoves during brunch cooking was surveyed in this paper.

. In this part, the air velocity, temperature and pollutant distribution of the kitchen cooking area at breathing height (in Figure 5, Line a) and the system purification efficiency were studied under four simultaneity coefficient values (φ = 0.2, 0.6, 0.8, 1). The results are shown in Figure 12.

Figure 12a–c shows that the change in simultaneity coefficient of stoves affected the air velocity, temperature and pollutant concentration distribution of the cooking area. When the simultaneity coefficient was 0.2, the temperature of the cooking area near the stove was high at 24–28 °C, while the temperature of other areas was about 24 °C. When the simultaneity usage factor ranged from 0.6 to 1, the temperature of the cooking area with personnel standing was high at 24–30 °C, while that of other areas was about 24 °C. This was because the presence of personnel decreased the air velocity (0.2–0.3 m/s) near the burning stoves, and the generated cooking heat could not be eliminated effectively. Due to its wall-hugging characteristics, the heat plume flowed leftward and upward. The larger the simultaneity coefficient was, the more serious the pollutant spillage. As shown in Figure 12d, the purification efficiency of the electrostatic purifier decreased as the simultaneity coefficient of stoves increased. The purification efficiency also met the requirement of the minimum limit (85%) when all stoves were burning.

4.2.3. Different Scenarios of Natural Transfer Air from Adjacent Rooms

The replacement air of the case kitchen was natural to transfer air from the adjacent rooms, which is common in CCKs. The natural replacement air parameters (NRAP) may be various in different seasons. Therefore, this section predicted the air velocity, temperature and pollutant distribution of the kitchen cooking area and the system purification efficiency based on measured replacement air temperature and velocity (

Table 7. Temperature and velocity of natural transfer air from adjacent rooms in four seasons.

Case		NRAP–1 (Spring)	NRAP–2 (Summer)	NRAP–3 (Autumn)	NRAP–4 (Winter)
1	T1 (°C)	24.4	30.3	25.8	17.9
	V1 (m/s)	0.47	0.41	0.40	0.41
2	T2 (°C)	22.3	29.3	24.3	12.9
	V2 (m/s)	0.46	0.40	0.39	0.51

), and the results are shown in Figure 13.

As seen in Figure 13a, the natural replacement air temperature had a greater effect on the kitchen indoor air temperature than the stove surface temperature. When the replacement air temperature was 22–26 °C (spring and autumn), the cooking area temperature was in the range of 22–30 °C, meeting the standard temperature requirements (18–32 °C). When the adjacent room temperature was 30 °C (summer), the temperature of the cooking area was within 29–38 °C, exceeding the high limit requirement in many places. When the make-up air temperature was 13–18 °C (winter), the temperature of the cooking area was in the range of 13–20 °C, and many places did not meet the low limit requirements. Therefore, commercial kitchens with only transfer air from adjacent rooms have a poor indoor thermal environment in summer and winter, and air-conditioned air needs to be installed to improve the thermal environment. As shown in Figure 13b, when the exhaust air volume was constant, the change in air velocity distribution of the cooking area under different seasonal scenarios was not obvious. The range of air velocity in the cooking area was 0.2–0.8 m/s, with an average of 0.5 m/s. The air velocity under the NRAP-4 scenario was a little higher, as the replacement air volume from door 2 was larger in the winter due to the higher temperature difference. It was deduced that the indoor air velocity was mainly influenced by the exhaust air volume. Figure 13c showed that pollutants spilled over and the concentration of C₆H₆ in the cooking area exceeded the standard limit (1.49 × 10⁻⁹ kmol/m³) under NRAP-1 (spring) and NRAP-4 (winter) scenarios. Combined with Table 7, the transfer air velocity from adjacent rooms in these two scenarios was higher than in the other two scenarios. High transfer air velocity intensified the airflow disturbances, which was adverse for the hood capture performance, and then led to the overflow of cooking fumes. As seen in Figure 13d, the purification efficiency of the exhaust fume system was higher in summer than in other seasons, which may be due to the higher inlet temperature of the purifier in summer, which is conducive to trapping particles in the electrical purifier.

4.2.4. Different Exhaust Air Volumes

The analysis results in Section 4.2.1, Section 4.2.2 and Section 4.2.3 show that when the system was operated at 11,726 m³/h (65% of the rated air volume), the purification efficiency met the standard requirements while the temperature in the cooking area was beyond the comfort range and pollutants spilled out on the left side against the wall. It was deduced that 11,726 m³/h was not the optimal operating air volume for the case CCKEF system. In this part, the effects of four sets of airflow conditions (50, 65, 80 and 100% rated airflow) on the indoor kitchen environment and the system purification efficiency were studied for three main simultaneous coefficient of stoves values (φ = 0.2, 0.6, 0.8). The results are shown in Figure 14.

As seen in Figure 14, exhaust air volume had a significant effect on the temperature, air velocity, pollutant concentration and system purification efficiency.

When the exhaust air volume was increased from 50% (9000 m³/h) to 100% (18,000 m³/h) of the rated air volume, the temperature in the cooking area decreased by about 4.5 °C, and the C₆H₆ concentration decreased from 8 × 10⁻⁹ to 1.49 × 10⁻⁹ kmol/m³. In the kitchen zone far from the cooking area, the temperature change was smaller, and the C₆H₆ concentration decreased from 3 × 10⁻¹⁶ to 4 × 10⁻¹⁸ kmol/m³ or less. The indoor air velocity increased significantly, with the increased rate of cooking area and kitchen zone far from the cooking area at 69.2% and 50%, respectively. The system purification efficiency decreased from about 93% to about 85%. Considering the indoor environment and system purification efficiency together, when the simultaneous coefficient of stoves was 0.2, and the exhaust air volume was 80% of the rated air volume, the indoor temperature of the kitchen was comfortable, the pollutant concentration met the standard limit, and the purification efficiency was relatively high (90%). When the simultaneous coefficient of stoves was greater than 0.6, the exhaust air volume should be 100% of the rated air volume to keep the indoor temperature comfortable and guarantee the pollutant concentration, as well as the purification efficiency, meet the standard requirements. Therefore, in order to ensure the indoor and outdoor air environments meet the standards required under various working conditions, the case CCKEF system should operate at 100% of the rated air volume. The control of exhaust air volume under three scenarios (scenario a: CCKEF system is operated at constant measured airflow; scenario b: CCKEF system is operated at optimum airflow according to the simultaneous coefficient of stoves; scenario b: CCKEF system is operated at constant rated airflow) is shown in Figure 15.

As shown in Figure 15, in actual operation, the case CCKEF system was operated at 65% of rated airflow constantly (scenario a). The energy consumption of scenario “a” was the lowest among the three scenarios, while the indoor environment was unsatisfactory from the above analysis. If the case CCKEF system was operated at the rated airflow constantly (scenario c), though the indoor and outdoor air environment can be guaranteed, the energy consumption was the highest. By contrast, it was better for the case CCKEF system to operate at the optimum airflow according to the simultaneous coefficient of stoves (scenario b: also called demand control). The demand control of the CCKEF system can not only provide a comfortable indoor environment and eligible purification efficiency but also reduce the system energy consumption by 3.75% compared with the other two scenarios.

5. Conclusions

This study proposed a simulation method to predict the operation performance, including indoor air environment and purification efficiency of the Chinese commercial kitchen exhaust fume (CCKEF) system. The simulation model was validated with measured data with a deviation within 10%. The validated model was used to predict the indoor air environment and purification efficiency of the exhaust system under different working conditions (simultaneous coefficient of stoves, stove surface temperature, make-up air parameters and exhaust air volumes) to understand the actual operation of the case CCKEF system and give suggestions for improvement. The main conclusions are as follows:

(1)

The change in simultaneity coefficient of stoves affected the air velocity, temperature and pollutant concentration distribution of the cooking area near the cooking stoves. Compared with the surface temperature of stoves, the temperature of natural transfer air from adjacent rooms had a greater impact on the thermal environment of the cooking area, and high airflow from adjacent rooms may disturb the hood capture performance. In order to improve the indoor kitchen environment, air-conditioned air was suggested to be introduced into the kitchen in summer and winter;

(2)

The exhaust air volume had a significant influence on both the indoor air environment and purification efficiency. The measured air volume for the case CCKEF system, 65% of the rated air volume, was not the optimal operating air volume. The optimal operating air volume varied with the simultaneous coefficient of stoves, which was 80% and 100% of the rated air volume when the simultaneous coefficient of stoves was 0.2 and greater than 0.6, respectively;

(3)

On the premise of providing a comfortable indoor environment and eligible purification efficiency, the CCKEF system was suggested to be operated at the optimum airflow according to the simultaneous coefficient of stoves as the energy consumption of the system can be saved by 3.75% during the brunch cooking period.