Realizable k-ε Model-Based Gradual-Radius Volute Tongue on Aerodynamic Performance and Noise of Multi-Wing Centrifugal Fan

Abstract

The multi-wing centrifugal fan is an important part of air conditioning systems, particularly in the automotive domain. Due to the compact structure and short blade passage of the fan, it may reduce the aerodynamic performance and generate noise. As a key part of the multi-wing centrifugal fan, the volute tongue has an important impact on the aerodynamic performance and noise of the multi-wing centrifugal fan. In this paper, the volute tongue of a multi-wing centrifugal fan is modified for air conditioning systems, and a novel gradient-radius volute tongue is designed. Specifically, a simulation calculation model for the multi-wing centrifugal fan is developed based on the Realizable k-ε turbulence model and the Ffowcs Williams–Hawkings (FW-H) equation. The simulation results are analyzed, and the reliability of the proposed method is assessed by comparing the total pressure efficiency and noise levels with the corresponding experimental measurements. Subsequently, the aerodynamic performance and noise characteristics of the gradient-radius volute tongue are investigated, with particular attention given to variations in the flow field, pressure pulsation, and noise before and after the modification. The results indicate that the gradient-radius volute tongue effectively attenuates the pressure pulsations arising from the interaction between the volute and the airflow, thereby reducing the tongue-region noise. Compared with the original fan, a noise reduction of 3.5 dB is achieved through the implementation of the gradient-radius volute tongue.

1. Introduction

The air conditioning fan is a crucial component in air conditioning systems. Its aerodynamic performance directly determines the user experience of the air conditioner and influences its energy consumption. Additionally, the fan noise significantly impacts in-vehicle comfort. Abundant research shows that when the air conditioning system operates under high load, the noise level inside the vehicle can exceed 60 dB. Prolonged exposure to this high noise state harms people’s health and reduces vehicle driving safety [1]. Thus, optimizing the aerodynamic performance of the air conditioning fan and reducing its noise are essential. These improvements not only enhance the overall performance of the air conditioning system but also create a more comfortable and safe in-vehicle environment. In contrast to other fan types, the multi-wing centrifugal fan offers distinct advantages, chief among them being its compact structure and substantial air volume delivery capacity. Owing to these favorable attributes, it has found extensive application within the air-conditioning domain. Nevertheless, the multi-wing centrifugal fan is also characterized by a relatively short blade passage and a small blade wrap angle. These inherent structural features give rise to suboptimal working efficiency of the fan, thereby resulting in significant energy consumption within the air conditioning system [2]. The generation of fan noise is closely related to the flow field. Aerodynamic noise is the primary type of fan noise, and some scholars have conducted research in this regard. Lighthill et al. [3] propose the Lighthill equation, which serves as the fundamental equation of aeroacoustics. Frowcs et al. [4], building on the previous research, put forward the FW-H equation, which solved the problem of sound generation by moving objects in fluids. Goldstein et al. [5] supplement the FW-H equation, breaking through the original assumption in the FW-H equation that the propagation medium velocity of the noise source is zero. Sundstrom et al. [6] extended the FW-H method to non-zero velocity flow situations such as rotational stall in centrifugal compressors and achieved quantification of the acoustic source distribution and propagation characteristics. The proposal of basic equations of aeroacoustics has provided a crucial foundation for subsequent theoretical studies on fan noise, enabling understanding of noise to develop from qualitative to quantitative.

Noise has a direct impact on the aerodynamic performance of fans. Thus, researching the noise within fans and the associated flow fields is of particular significance. Powell et al. [7] elucidate the relationship between turbulence and acoustic energy, indicating that in unsteady fluid flows, aerodynamic sound is generated as a result of the movement of vortices and vorticity. In a slightly compressible fluid, vorticity can be regarded as inducing the entire flow field, and this property can be utilized to evaluate the sound radiation formula. The framework of this theory facilitates the estimation of flow-induced sound based on vorticity. Lowson et al. [8] employ the Fourier series expansion method to derive the discrete noise model of the rotating impeller as well as the discrete noise model of the mutual interference between the blade and the guide vane. This model can also serve to guide the aerodynamic design of fans. Amiet et al. [9] derive the expression of blade wake noise by taking the pressure pulsation on the trailing edge surface of the blade as the input, thereby further enriching the blade noise theory. Wang et al. [10] drew inspiration from the swimming characteristics of carps in the C-shaped starting posture and carried out a bionic design of the blade. Through the application of the reverse engineering method, Bionic Equal Thickness Blades (BETBs) inspired by the C-shaped starting mid-arc of carp are designed and optimized. Based on the comparison between the numerical and experimental results of the fan’s aerodynamic performance, the Optimal Bionic Equal Thickness Blade (O-BETB) is obtained. When the O-BETBs are applied to the original fan, the flow rate increases by 6.8% and the noise decreases by $0.5$ dB(A). Mao et al. [11] compute the unsteady flow field inside the centrifugal fan and use the results to identify the location and type of the primary aerodynamic noise sources within the fan. Additionally, by means of time-domain and frequency-domain analysis methods, the distribution characteristics of the amplitude and frequency of the pressure pulsation can be obtained in the flow field. By comparing these results with the noise test findings, a technique is proposed that can effectively provide information for fan noise reduction design without directly solving the sound field. Furthermore, the selection of an appropriate turbulence calculation model is crucial for accurately determining the fan flow-field information when calculating fan noise. In this regard, some scholars have conducted relevant research. Liu et al. [12] utilize the Large Eddy Simulation (LES) method [13] to calculate the internal flow field of the centrifugal fan. The results indicated that the vortex sound theory can predict noise more accurately than the acoustic analogy method, and the results are closer to the experimental values. Dai et al. [14] simulate the aerodynamic noise of a small, high-speed centrifugal fan for aerospace applications using a variety of turbulence models. The results demonstrate that the LES model, which can be applied to the noise reduction design of this type of fan, is in the best agreement with the experimental results. The volute tongue is an important part of a multi-wing centrifugal fan. Under the high-speed drainage of the impeller, the gas is discharged into the pipeline connected to the volute tongue through the volute collection, flow diversion, and pressure expansion. The volute tongue can effectively prevent the gas from circulating into the volute tongue, and the structural parameters of the fan have the greatest influence under the rated flow rate [15]. Turbulence and eddy flow are important factors that affect the noise of the fan and directly affect the aerodynamic performance of the fan. The turbulence calculation model has a general understanding of the noise flow in the fan, but the structure of the fan directly affects the formation and change of turbulence and eddy flow, and the rationality of the fan structure is strictly required.

The blades on the impeller hit the surrounding gas medium, which will cause the surrounding gas to produce pressure pulsation and thus generate noise. The main reason for this is that the boundary layer on the blade surface is seriously separated during the rotation process, and then the eddy flow is generated. The shedding of eddy flow will cause large pressure pulsation, and the impeller blades periodically squeeze and beat surrounding air particles. Finally, it is reflected on the adjacent fan’s volute tongue, so the volute tongue becomes the main generating position of fan noise [16]. Liu et al. [17] use Particle Image Velocimetry (PIV) to study the velocity distribution characteristics of the centrifugal fan used for air conditioning along the height of the blade and find that the asymmetry of the volute structure has a greater influence on the airflow velocity, which is reflected by the larger velocity gradient near the volute tongue. On both sides of the volute with larger flowable space, the airflow velocity is evenly distributed. Zhang et al. [18] are concerned about the uneven generation and distribution of fan tracer particles under large flow rates and propose a method of indoor pre-dissemination of tracers to capture the flow at the fan inlet with high resolution. Kawasaki et al. [19] use PIV technology to measure the flow situation near the volute tongue, which is basically consistent with the simulation results. There is a large turbulence loss near the volute tongue, that is, the structure of the volute tongue is the key factor affecting the aerodynamic performance of the fan. Younsi et al. [20] use numerical methods to study the changes of unsteady flow and noise in forward-bending centrifugal fans with different structural parameters, and by comparing with the test results the relationship between pressure pulsation on the volute wall and far-field noise is highlighted. Rong et al. [21] use numerical methods to study the flow situation in the blade channels before and after blade surface grooving and find that the grooving treatment could effectively inhibit the boundary layer separation on the blade surface, and the separation loss in the blade channel is reduced, but the grooving treatment will slightly reduce the effect of the volute tongue on preventing air return. Morinushi et al. [22] compare forward-bending centrifugal fans with different structural parameters and find that the impeller’s working efficiency is the highest when the radius of the volute tongue is $0.08$ times. Liu et al. [23] effectively reduce the overall noise of the fan by increasing the clearance between the impeller and the volute tongue and reduce the sound pressure level under the blade frequency by 15 dB. The results show that the volute tongue clearance is closely related to the noise of the centrifugal fan. Cheong et al. [24] use the mixed CAA method to analyze the contribution degree of the volute tongue region to the noise of centrifugal fans, and the results show that the region between the blade outlet and the spiral casing generated more noise than the region between the blade outlet and the spiral casing outlet. Therefore, the gap between the impeller and the volute tongue could be focused on as the main location for noise reduction. In addition to the volute tongue, the volute profile will affect the flow characteristics of gas in the fan and then affect the aerodynamic performance and noise. Therefore, more scholars have begun to pay attention to the role of volute profile in improving the performance of fans. Zhou et al. [25] highlight that due to the asymmetric structure characteristics of the volute, the airflow at the inlet of the volute is unevenly distributed, so the volute profile is redesigned according to the flow distribution at the inlet, effectively improving the performance of the centrifugal fan. Zhang et al. [26] modify the volute profile of the forward-bending centrifugal fan, taking into account the influence of gas viscosity, and the test showed that the noise of the fan is reduced by 1.1 dB, especially in the low frequency band. This study provides a new idea for volute design closer to the real situation. Li et al. [27] take the spiral angle of the starting and ending position of the volute profile as the design parameter to optimize the structure of the volute. The numerical simulation results show that the efficiency of the fan decreases slightly and the noise of the fan decreases. On the contrary, on the basis of fully studying the flow around the volute tongue by means of experiment and simulation, some scholars have made great improvements to the structure of the volute tongue. Liu et al. [28] design a concave volute tongue and apply it to a multi-wing centrifugal fan of a range hood (Figure 1). Its effect is verified through experiments and simulations, and the results show that the volute tongue design can reduce the noise of the fan by about $1.7$ dB. In addition, the concave volute tongue can increase the flow area of the fan outlet, so the flow rate of the fan is increased. Therefore, in the design, the flow area near the tongue should be appropriately increased to improve the flow quality of the volute. Dong et al. [29] apply the profile structure of the leading edge of the owl wing to the volute tongue of a multi-wing centrifugal fan and conduct numerical simulation of the fan model with different volute tongue installation angles under different flow conditions. The research shows that the design could improve the aerodynamic performance of the fan under different flow rates. Liu et al. [30] apply the wave front structure of humpback whale flippers to the optimal design of the volute tongue of a multi-wing centrifugal fan, establish a three-dimensional wave front airfoil with different wave direction angles, and propose an optimal design method for the volute tongue optimization. The results show that when the wave direction angle is ${45}^{\circ }$, the generation of separation vortex and the shedding of wake vortex can be effectively inhibited, which is helpful to reduce the noise. The static pressure recovery coefficient is about 5% higher than the original fan, the air volume is $5.16$% higher, and the noise is reduced by $0.6$ dB. The results show that a reasonable volute tongue radius and spiral angle can improve the gas flow state near the volute tongue, reduce the influence of eddy flow and reflux on aerodynamic performance, and improve the performance of the centrifugal fan. Therefore, the design of the volute tongue structure plays an important role in affecting the aerodynamic performance and noise of the fan.

Considering the above problems, this paper establishes a simulation calculation model of a multi-wing centrifugal fan with a gradient-radius volute tongue based on the Realizable turbulence model and the FW-H equation. The fan flow field adopts a Realizable turbulence model, which adapts to the flow field of rotating machinery to obtain an accurate internal flow of the fan, and fan noise is solved by the acoustic analogy method. Based on the FW-H equation, the sound field information obtained from the flow field calculation is input into the far-field wave equation, and the noise data of the measuring point is obtained by integration. Then, the fan is modeled and numerically simulated, and the calculation results are analyzed. The reliability of the simulation method is verified by comparing the performance data of the fan obtained by the test. Then, the tongue structure of the fan is adjusted; the gradient-radius volute tongue is designed; and the pressure analysis, flow loss analysis, and noise analysis of the fan basin before and after optimization are carried out. Compared with the prototype fan, the noise of the fan decreases by 3.5 dB, which is beneficial to the noise reduction of the fan during operation.

The structure of this paper is organized as follows: Section 2 presents the calculation equations related to the aerodynamic performance of the fan and carries out the modeling and numerical simulation, Section 3 designs the gradient-radius volute tongue structure and analyzes how the fan aerodynamic performance changes, and Section 4 concludes this study.

2. Flow Field and Noise Calculation of Multi-Wing Centrifugal Fan

During the operation of the fan, the conversion of mechanical energy and static and dynamic pressure energy of air is involved, and there are flow separation, laminar flow to turbulent flow conversion, vortex generation and fragmentation, and other phenomena accompanied by noise generation. Therefore, relevant theories and calculation methods are elaborated in this chapter. At the same time, based on the main working part of the automobile air conditioning fan, the geometric model of the multi-wing centrifugal fan is established and the grid is divided, and the gradient-radius volute tongue structure is proposed. The accuracy of the simulation calculation is verified by comparing the simulation results with the test results, and the influence of the gradient-radius volute tongue structure on the internal flow of the fan is highlighted. It is convenient to carry out the subsequent analysis based on simulation and the optimization of the gradient-radius volute tongue.

2.1. Calculation Method of Fan Flow Field

2.1.1. Basic Equation of Fan Flow Field Calculation

In this paper, the multi-wing centrifugal fan is an automobile air conditioning fan, and the internal flow field can be regarded as an incompressible flow with constant temperature and density, regardless of gas gravity. According to relevant theories of fluid mechanics, the basic equations of fan flow field calculation include the equation of motion (N-S equation) and the mass conservation equation, as in [31]:

$$\left\{\begin{array}{c}\nu {\nabla }^2{u}_i-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial x_i}}={\displaystyle \frac{\partial u_i}{\partial t}}+u_j{\displaystyle \frac{\partial u_j}{\partial x_j}},\hfill \\ {\displaystyle \frac{\partial u_i}{\partial x_i}}=0,\hfill \end{array}\right.$$

(1)

where $\rho$ denotes the gas density, p denotes the gas pressure, $u_i$ denotes the velocity in the $x_i$ direction, and $\nu$ denotes the kinematic viscosity coefficient.

2.1.2. Turbulence Model for Fan Flow Field Calculation

Turbulence is a type of flow state in fluids, typically characterized by the random movement of fluid micro-turbules. The micro-turbules pulsate at a high frequency in all directions, and their trajectories are disordered. In numerical calculations, the Reynolds number Re is commonly used to distinguish between laminar and turbulent flows. The gas flow in the fan duct is mostly turbulent. Therefore, before conducting the simulation calculation, it is necessary to select an appropriate turbulence model to reduce the computational cost while ensuring the most accurate simulation of the actual flow.

(1)

Standard k-ε model based on the Reynolds Averaged Navier–Stokes method

The Reynolds Averaged Navier–Stokes (RANS) method homogenizes the N-S equations, converting the transient fluctuating momentum into averaged equations, thereby avoiding the direct solution of the N-S equations and significantly reducing the computational cost. It is suitable for solving most engineering problems. The representation of the turbulent viscosity in the standard k-ε model is

$$\begin{array}{c}\hfill {\mu }_t=\rho C_{\mu }\left({\displaystyle \frac{k^2}{\epsilon }}\right),\end{array}$$

(2)

where $C_{\mu }$ is the empirical constant, and $\epsilon ={\displaystyle \frac{\mu }{\rho }}\left({\displaystyle \frac{\partial {\overline{u}}_i^{·}}{\partial x_k}}\right)\left({\displaystyle \frac{\partial {\overline{u}}_i^{·}}{\partial x_k}}\right)$ is the turbulence dissipation rate.

(2)

Realizable k-ε model

The Realizable k-ε model has supplemented the equation of turbulent dissipation rate based on the standard k-ε model, which can more accurately describe the turbulent characteristics inside the fan. Moreover, the Realizable k-ε model performs better in the calculation of flow separation and rotational flow.

Considering that the work of this paper is about the structural optimization design of the fan, a large amount of calculation work is required. To ensure a certain level of calculation accuracy and reduce the calculation cost, the Realizable k-ε model will be selected for numerical simulation in the subsequent work.

2.2. Calculation Method of Fan Noise

2.2.1. Basic Equation of Fan Noise Calculation

The mechanism of discrete noise is that the blades of the fan periodically beat the surrounding air particles when moving, so that the air pressure produces periodic pulsation and spreads to the surrounding area, especially in the vicinity of the volute tongue, where the flow path is extremely narrow. The structure of the volute tongue is subject to the periodic impact of the impeller flow, resulting in high noise. The frequency of discrete noise $f_{\mathrm{discrete}}$ is related to the rotation speed of the impeller and the number of blades [32]:

$$\begin{array}{c}\hfill f_{\mathrm{discrete}}={\displaystyle \frac{nz}{60}}i,\end{array}$$

(3)

where n denotes the speed, z denotes the number of blades, $i=1,2,\dots ,$ denotes the harmonic serial number, and $i=1$ denotes the fundamental frequency. The fundamental frequency (blade frequency) of the fan in this paper is 2871 Hz.

Broadband noise is reflected in a large number of vortices generated by unsteady flows such as boundary layer shedding, turbulent boundary layer gas turbulence, jet wake, etc., during the operation of the fan. The curl of these vortices changes with time and position, resulting in associated pressure pulsation and noise.

Based on the generation mechanism of aerodynamic noise, it can be considered to adjust the blade layout and optimize the shape of the volute tongue to reduce the impact of the outflow on the volute structure and reduce the discrete noise. By improving the shape of the blade and volute, the steady flow of air is promoted to restrain the generation of vortices and reduce the broadband noise.

2.2.2. Turbulence Model of Fan Noise Calculation

In this paper, the acoustic analogy method is used to solve the measuring point noise of a centrifugal fan in automobile air conditioning. Based on the FW-H equation as in [33], the acoustic analogy method inputs the sound field information obtained from the flow field calculation into the far-field wave equation and obtains the far-field sound information through integration regardless of the influence of the flow field, that is, the noise data of the fan at the measurement point. The FW-H equation is shown as

$$\begin{array}{c}\hfill \left({\displaystyle \frac{1}{c_0}}{\displaystyle \frac{{\partial }^2}{\partial t^2}}-{\displaystyle \frac{{\partial }^2}{\partial x_i^2}}\right)p={\displaystyle \frac{{\partial }^2}{\partial x_i\partial x_j}}{T}_{ij}-{\displaystyle \frac{\partial }{\partial x_i}}\left[p_{ij}{n}_j\delta \left(f\right)\right]+{\displaystyle \frac{\partial }{\partial t}}\left[{\rho }_0{v}_j{n}_j\delta \left(f\right)\right],\end{array}$$

(4)

where p denotes the far-field sound pressure, $T_{v}ij$ denotes the Lighthill stress tensor, $v_j$ denotes the flow rate, $n_j$ denotes the normal vector of the object surface, and $\delta \left(f\right)$ denotes the $\delta$ function distribution.

2.3. Geometric Model and Fluid Domain Meshing of Multi-Wing Centrifugal Fan

The multi-wing centrifugal fan is the core working component of automobile air conditioning. The volute tongue is the key component of the multi-wing centrifugal fan, which has great influence on the aerodynamic performance and noise of the fan. Therefore, in this section, a three-dimensional model of the multi-wing centrifugal fan for automotive air conditioning is established, the mesh is divided, and a gradient-radius volute tongue structure is proposed. The rationality of the simulation setting is verified according to the comparison results between the test and the simulation calculation, which lays a foundation for subsequent research on the influence and causes of the structure on the aerodynamic performance and noise of the fan and the improvement of the design.

2.3.1. Modeling and Numerical Simulation of Multi-Wing Centrifugal Fan

The impeller, as the energy conversion component of the core of the fan, rotates at high speed inside the volute, causing the air to be inhaled. In this process, the impeller relies on its own mechanical operation characteristics to effectively transform the mechanical energy into the kinetic energy of the gas and then drives the gas to flow in the fan system. The volute is responsible for guiding the gas from the fan outlet into the air conditioning pipe, during which a part of the dynamic pressure energy is converted into static pressure energy due to the diffuser effect. Therefore, the performance of the fan mainly depends on the shape of the impeller and volute.

A three-dimensional model of the multi-wing centrifugal fan for automotive air conditioning in this paper is shown in Figure 2, and the key structural parameters and working parameters are shown in

Table 1. Parameters of multi-wing centrifugal fan.

	Parameters	Values
Structure parameter	Entrance blade angle	${90}^{\circ }$
	Outlet blade angle	${139}^{\circ }$
	Volute tongue radius	13 mm
	Number of blades	41
Working parameter	Rotating speed of the vane	4202 r/min
	Rated flow	500 m3/h
	Import and export extension section	200 mm

. In order to make the flow of import and export fully develop and reduce the influence of boundary effect, the import and export sections are both extended.

The fan is modeled, simplified, and channel-extracted by SolidWorks 2024, then imported into ANSYS-ICEM 2020 for inspection, repair, and meshing. A hexahedral structure grid (≤3 mm) is used in the inlet and outlet areas, and an unstructured mesh (volute $\le 3$ mm, impeller $\le 2$ mm) mixed with tetrahedrons and a small amount of hexahedrons is used in the volute and impeller basins due to irregular shape. The mesh is connected through a pyramid grid, and key areas such as the volute tongue and impeller blade are enciphered to improve calculation accuracy. The grid structure of the fan is shown in Figure 2, which is divided into the inlet and outlet extension sections and the volute and impeller basins. Each basin realizes data interaction through interface connection.

2.3.2. Boundary Condition Setting and Verification of Mesh Independence

This paper uses the ANSYS-FLUENT solver to conduct numerical simulation calculations for the internal flow field of a multi-blade centrifugal fan. The governing equations for the internal flow are the incompressible form of the Navier–Stokes equations, and the turbulence model adopts the Realizable model. In the steady-state simulation process, the inlet is set as a mass flow inlet, and the outlet is set as a pressure outlet. The pressure field and velocity field are coupled using the Simple algorithm, and the discretization method selects the Second-order Upwind method. The blade passage area adopts the rotating coordinate system, while the remaining passages are static domains. The steady-state calculation is based on the mrf model because the grid does not undergo actual movement. Therefore, the calculation is more stable and faster compared to transient calculation, and it can provide a better initial condition for transient calculation. During the steady-state calculation process, the number of calculation steps is 2000, and the convergence accuracy is ${10}^{-4}$. When calculating the noise of the fan, it is necessary to start non-steady-state calculations and use the FW-H equation to calculate the far-field noise based on the steady-state calculation results. The blade passage area adopts a rotating coordinate system for transient calculations, using a slip-grid approach to ensure the capture of sudden changes in velocity vectors during the coordinate system transformation. In the non-steady-state calculation, the time step is set to $\Delta t=7.93273\times {10}^{-5}$, which is the time for the impeller to rotate by $2^{\circ }$. Each time step involves 20 iterations, and the total number of calculation steps is 420. This ensures that the steady-state calculation errors can be eliminated and the flow field can be fully developed, thereby improving the accuracy of the noise calculation.

To eliminate the influence of the number and quality of the meshes on the calculation results and to minimize the mesh size as much as possible to ensure efficiency, it is necessary to first conduct mesh independence verification. By adjusting the mesh density in the near-wall region, the maximum $y^{+}$ value is controlled at 210. The total pressure and efficiency of the fan are selected as the verification indicators. Eight calculation examples are calculated, and the results are shown in Figure 3. Considering the accuracy and speed of the solution, the mesh division scheme with a mesh quantity of $5.99\times {10}^6$ is selected as the standard for subsequent calculations.

2.3.3. Gradient-Radius Volute Tongue Structure

To prevent the infinite circulation of air in the fan, the clearance design between the volute tongue and the impeller is narrow, resulting in the volute tongue becoming the main source of noise in the fan. In order to reduce the noise, the method of increasing the radius of the volute tongue or increasing the clearance between the volute tongue and the impeller is usually adopted. Increasing the radius can reduce the flow resistance and weaken the interaction between the airflow and the volute tongue. Increasing the gap can reduce the pressure gradient and avoid airflow backflow interfering with fan performance. However, too large a radius or clearance can cause the performance of the fan to deteriorate.

The original fan has a volute tongue structure with constant radius. In this paper, a gradient-radius volute tongue structure is designed (Figure 4). The volute tongue radius on the front disk side is larger, and it is gradually reduced to the volute tongue radius of the original fan (13 mm) along the axis. Considering the complexity of the front side flow, the design adopts large radius and clearance to reduce pressure pulsation and noise. The side flow of the middle and rear disks is improved, and the radius is gradually reduced to maintain the aerodynamic performance of the fan. In addition, the gradient-radius volute tongue structure makes the phase difference of the airflow at different heights on the volute tongue, and the superimposed noise is less than that of the ordinary volute tongue structure, which further reduces the noise of the fan.

2.4. Fan Test and Result Analysis

2.4.1. Aerodynamic Performance Test

The device shown in Figure 5 is used to test the aerodynamic performance of the fan, including the L-shaped pitot tube, pointing rod, differential pressure meter, connecting hose, etc. The test boundary conditions ensure that the environment is in a quiet space without the influence of external airflow and ensure that the connection between the airflow channel and the L-type pitot tube is absolutely sealed. The L-type pitot tube is installed in the extended section of the pipeline, facilitating pressure detection when the air flow rate in the pipeline is relatively stable. Before the test, the gas in the L-type pitot tube is emptied to avoid the influence of residual gas on the airflow. The pressure differential meter is zeroed out before use. The L-type pitot tube is aligned to flow and transfer pressure, and the differential pressure meter is connected with the pitot tube through a joint to measure the static and total pressure of the fan. For the fan studied in this paper, the simulation calculation and test are carried out at a flow rate of 500 m³/h.

Total pressure of the fan can be expressed by

$$\begin{array}{c}\hfill P_{\mathrm{total}}=P_{\mathrm{total},\mathrm{out}}-P_{\mathrm{total},\mathrm{in}}.\end{array}$$

(5)

Fans, during the operation process, due to the friction between the rotating impeller and the air, flow separation, eddy flow, and other reasons, cause energy loss; improving the efficiency $\eta$ is one of the work contents of fan optimization design:

$$\begin{array}{c}\hfill \eta ={\displaystyle \frac{P_{\mathrm{total}}{Q}_v}{M\omega }},\end{array}$$

(6)

where $Q_v$ denotes the flow rate, M denotes the impeller torque, and $\omega$ denotes the impeller speed.

To verify the accuracy of the simulation calculation results, the total pressure and efficiency of the fan under different flow rates are selected as the judging criteria, and the comparison results of the two are shown in Figure 6. As can be seen from Figure 6, the calculation results can better reflect the working state of the fan. The maximum errors of total pressure and efficiency are 2.1% and 9.6%, respectively, both of which are less than 10%. The average error in total pressure and efficiency is 12 Pa and 1.7%. For the prototype multi-blade centrifugal fan with a rated working flow of 500 m³/h, the working condition error in total pressure and efficiency is 5 Pa and 1.2%. The positions with large errors are in the flow rate of the fan when it is not to working normally, and the two are more compatible within the normal flow rate range of the fan, indicating that the simulation model is reasonable. It can reflect the working characteristics of the fan more accurately and can be used for the calculation and analysis of the flow field and noise, as well as the optimization and improvement of the structure.

2.4.2. Analysis of Simulation Results of Fan Flow Field

For ease of expression, the velocity cloud image, the static pressure cloud image, the turbulent kinetic energy cloud image, and the volute static pressure cloud image can be obtained for the middle section of the impeller of a multi-wing centrifugal fan in Figure 7.

According to Figure 7, in the narrow position near the volute tongue, because the volute tongue prevents most of the airflow from infinite circulation in the impeller basin, only a small amount of gas returns to the impeller basin through the volute tongue and interferes with the main stream flowing from the blade canal, resulting in difficult normal flow of air in this area and low speed, which degrades the performance of the fan. In addition, the volute tongue is very close to the rotating impeller, and the accelerated airflow has an obvious periodic impact on the volute tongue, which makes the volute tongue part become one of the main sources of fan noise.

Furthurmore, the static pressure reached a peak of $216.7$ Pa near the volute tongue, forming a clear pressure gradient. In the process of changing from axial flow to radial flow, different flow conditions in different sections perpendicular to the axis lead to unsteady interference between the airflow and the volute tongue. Moreover, the asymmetry of the impeller structure in the axial direction leads to different flow conditions of the blades in different sections, which is manifested as non-uniform distribution of static pressure along the axis of the volute tongue. The maximum value of static pressure near the volute tongue appeared in the middle and upper part of the volute tongue, and the minimum value appeared in the lower part of the volute tongue, with a difference of 500 Pa. The turbulent kinetic energy reflects the inevitable dissipation of turbulent energy during fan operation. As can be seen from Figure 7, there is almost no flow separation in the blade channel located between ${300}^{\circ }$ and ${360}^{\circ }$, that is, the flow situation in this region is good and the energy loss is small. In the whole basin, the turbulent kinetic energy near the volute tongue is high, which proves that the flow in this region is complex and is the main location of noise generation.

According to the above analysis of the simulation results of the fan, the volute tongue is the main part of the fan to produce noise, and the study of the gradient-radius volute tongue is of great significance to improve the flow in the fan.

3. Analysis of Influencing Factors of Aerodynamic Performance and Noise of Fan

Based on the theoretical analysis, test, and simulation calculation above, this chapter proposes the parameter scheme of the gradient-radius volute tongue and studies the aerodynamic performance and noise changes of the fan by adjusting different parameter schemes and the causes. In order to ensure that the study parameters vary within a reasonable range and avoid the deterioration of the flow field inside the fan, which may lead to performance degradation and noise increase, this paper made reference to relevant literature and fan design manuals, as in [34], and finally determined the scheme shown in

Table 2. The research parameter selection scheme.

Parameter	Scheme
gradient-radius Lateral radius (Max radius) $R_{\max }$ (mm)	13 (original), 16, 19, 22, and 25

.

Due to the asymmetry of the axial flow field of the fan along the blade wheel, in order to facilitate the analysis of the flow field and noise characteristics at different heights along the axis after the structural parameters are changed, three cross sections are divided, which are, from top to bottom, side section of the front disk (75 mm), middle section (50 mm), and side section of the rear disk (25 mm). The angle division rule is used in the analysis of flow field and sound field. The fan section division is shown in Figure 8.

3.1. Fan Basin Pressure Analysis

The volute plays a role in transforming the gas dynamic pressure energy into static pressure energy, so the static pressure can directly reflect the influence of the gradient-radius volute tongue structure adjustment on the volute workability. Figure 9 shows the cloud diagram of the static pressure-flow line distribution of each section of the volute tongue fan basin with different gradient-radius. When the radius of the volute tongue on the front disk side is increased, the static pressure near the volute outlet decreases compared with that of the original fan, and the decrease becomes more obvious with the increase, but the static pressure distribution at the outlet is more uniform. The high static pressure area is mainly concentrated in the vicinity of the volute tongue near the outlet, which is conducive to weakening the unsteady flow caused by the pressure gradient, reducing the noise, and improving the flow quality of the fan.

According to the flow line distribution on the front panel side, after the static pressure at the outlet drops the air backflow phenomenon caused by the pressure gradient is weakened compared with the original fan, so the interference of the leaf outflow is weakened and the flow loss near the volute tongue is reduced. In the middle disk position, the return flow of the volute tongue in some schemes increases, which is speculated to be because the change of the radius of the volute tongue does not match the exit angle of the original fan blade, resulting in an increased angle between the airflow direction and the volute tongue, and more air is returned to the impeller basin through the volute tongue. At the rear disc position, because the radius of the volute tongue is close to that of the original fan, the flow situation is basically unchanged.

Figure 10 depicts the relationship between radius and total pressure as well as pressure-efficiency, which describes the influence of volute tongue with gradient-radius on aerodynamic performance. According to the change curve of total pressure-efficiency of the fan (Figure 10), although the gradient-radius volute tongue design can reduce the noise of the fan, it will lead to the decrease of the aerodynamic performance of the fan. The aerodynamic performance of the 22 mm scheme is the worst, and the total pressure and efficiency are reduced by $82.94$ Pa and $3.87\%$, respectively. The reason for this is that after improving the structure of the volute tongue, corresponding adjustments are needed, such as other structural parameters of the fan, such as the impeller outlet angle, so as to improve the matching degree between the wind dynamic structure and the static structure and improve the aerodynamic and noise performance of the fan.

3.2. Analysis of Flow Loss in Fan Basin and Around the Tongue

Figure 11 shows the distribution of turbulent kinetic energy with different gradient-radii. According to the $z=75$ mm cloud image, when the radius of the volute tongue on the anterior disk is increased, the turbulence loss at the position of the volute tongue is reduced, and the flow separation phenomenon in the nearby blade canal is significantly weakened, indicating that the mutual interference between the outflow flow and the return flow of the volute tongue on the anterior disk is reduced in the larger flow space, and the flow situation near the volute tongue on the anterior disk is improved. In addition, the increase of the volute tongue clearance also buffers the high-speed airflow in the blade passage, thus reducing the impact on the volute. Although the area of the high turbulent energy area in the upper part of the volute tongue expands along the axial direction of the volute tongue, the area in the transverse section is significantly reduced, and the average value is lower than that of the original fan, indicating that the gradient-radius design has a better performance in the front disk.

According to the turbulent energy cloud diagram of the middle section $(z=50$ mm), the flow position in the middle of the impeller and volute is not significantly improved after adjustment, but the flow loss near the volute tongue is intensified, that is, a high turbulent energy area is formed with the volute tongue as the center and extended to the outlet of the volute and the impeller blade channel, respectively. However, according to Figure 10, the peak value of turbulent energy in the middle of the improved volute is lower than that of the original fan, in which the scheme of $R_{max}=16$ mm is about $0.9$ K lower than that of the original fan, and the scheme of 19 mm is about 3 K lower than that of the original fan. If the value $R_{max}$ continues to increase, the peak value of turbulent energy does not decrease significantly. According to the analysis in the previous section, the reason for this phenomenon is that the improved volute tongue does not match the original impeller, resulting in a new turbulent zone. Therefore, when improving the fan, it is necessary to pay attention to the coordination between multiple parameters in order to achieve the best overall working performance.

Compared with the flow conditions of the posterior disk before and after the improvement, it is found that the high turbulent energy area of the tongue narrowed and the flow loss of the blade channel decreased or even disappeared in the range of 0–${30}^{\circ }$, while the flow condition of the impeller basin in the range of 45–${85}^{\circ }$ deteriorated because the turbulence in the middle region of the impeller extended to the impeller’s posterior disk, causing interference to the inlet air of part of the blade channel. Then, secondary flow is generated in the blade channel, which induces flow separation and interferes greatly with the mainstream. According to Figure 11, different radii of the volute tongue have little influence on the flow near the volute tongue on the posterior disk side, and the turbulent kinetic energy at this position is all within 30 K.

3.3. Pressure Pulsation near the Volute Tongue and Fan Noise Analysis

To obtain pulsation information near the volute tongue, pressure pulsation curves of $P1$ and $P8$ monitoring positions at different heights are drawn, as shown in Figure 12. Since $P1$ is closer to the impeller, there is an obvious pressure amplitude at the blade frequency, while there is a strong interaction between the blade outflow and the volute tongue structure at the M position, so there is also a wide frequency pressure pulsation near the blade frequency. After applying the gradient-radius volute tongue design, the pressure superposition effect near the volute tongue at different heights is weakened, and the amplitude of the wide frequency pressure pulsation is reduced compared with that of the original fan, and the effect becomes more obvious with the increase of the volute tongue design. At the wheel frequency position, increasing the radius of the volute tongue is conducive to reducing the pressure pulsation at the outlet of the volute, among which the scheme of 25 mm has the most obvious effect, and the amplitudes at $P1$–F, $P1$–M, and $P1$–R decrease by about 84 Pa, 60 Pa, and 16 Pa, respectively.

According to the pressure pulsation at the $P8$ position near the volute outlet in Figure 13, the pressure pulsation at this position is mainly under the wheel frequency. Except for $P8$–M, the pressure pulsation at other positions is reduced because the turbulent energy area at the middle outlet of the volute is extended after the change of the volute tongue, which leads to the deterioration of the flow in this area and the increase of the amplitude of the pressure pulsation. For the front and back sides, the amplitude of pressure pulsation decreased to different degrees. Furthurmore, the analysis of the cases with different volute tongue radii in Figure 13 indicates that at the P1 position, which is located near the impeller, both the blade frequency component and the broadband pulsation gradually decrease as the maximum radius of the front disc increases. At the P8 position near the volute outlet, the blade frequency pulsation is suppressed in most cases except for the middle section, with the front disc side being the most sensitive to variations. Among the tested configurations, the scheme with 22 mm exhibits the most effective pulsation attenuation.

Figure 14 depicts the relationship between the radius and fan noise and describes the influence of volute tongue structure with gradient-radius on fan noise. According to Figure 14, the design of the gradient-radius volute tongue has the effect of reducing the pressure pulses between the volute tongue and the airflow, which can significantly decrease the pressure pulsations generated by the interaction between the volute tongue and the airflow, and reduce the noise at the volute tongue position. Ultimately, this is beneficial for reducing the noise during the operation of the fan. The most effective noise reduction is achieved by the scheme with of 22 mm, and there is a $3.5$ dB reduction in noise compared to the original fan.

3.4. Aerodynamic Noise Test

The aerodynamic noise test of the fan is conducted in a semi-anechoic chamber (Figure 15a–c), where the indoor background noise is significantly lower than that of the centrifugal fan. Figure 15a illustrates the test data acquisition system, which consists of the data acquisition and display unit (upper left), the data processing unit (center), and the experimental monitoring unit (upper right). Figure 15b presents the experimental apparatus, including the expansion pipe, extension section, inlet, mounting hooks, and the test fan. Figure 15c shows the anechoic chamber and monitoring equipment, including the chamber walls, microphone stand, and monitoring devices. The microphone used in the experiment is of the RST1000 model produced by Beijing Renshen Xinpu Company (Beijing, China). Its core specifications include sensitivity of 4 mV/Pa, frequency response range of 20 Hz–40 kHz with an error controlled within ±1 dB; the microphone head adopts a pre-polarized capacitive design, with a polarization voltage of 0 V, a dynamic range of 35–156 dB, a microphone diameter of 6.9 mm, an overall length of 65 mm. The computer used for processing data is equipped with a Windows 10 system and has a storage capacity of 512 GB. The specifications of the microphones used in the laboratory is shown in

Table 3. The specifications of the microphones used in the laboratory.

Core Specifications	Parameters
Microphone model	RST1000
Sensitivity	4 mV/Pa
Frequency response	20 Hz–40 kHz
Error range	±1 dB
Microphone diameter	6.9 mm
Overall length	65 mm

. According to the testing standards provided in [35], a monitoring microphone is placed at a position 1 m away from the fan outlet and at an angle of ${45}^{\circ }$ to reduce the influence of the outflow air and motor noise on the test results.

The results of the fan noise test and simulation are shown in Figure 16. The noise spectrum of the fan has both discrete characteristics and wide frequency characteristics, corresponding to the noise theory of the fan: the blades periodically beat air particles, and the blades periodically impact the inner wall of the volute, which are the main reasons for the discrete noise. The vortex noise caused by flow separation in the impeller region, the “jet-wake” phenomenon near the blade outlet, laminar flow on the wall, and turbulent boundary layer shedding are the main components of vortex noise, which has the characteristics of a wide frequency range.

Comparing the test and simulation results of fan noise, it can be seen that there are some differences between the two. The reasons for the error are as follows: The mechanical noise and electromagnetic noise of the fan are not considered in the simulation, and the fan model is partially simplified before calculation. The maximum error at low frequencies reaches 35%, while the overall average error remains within 20%. Under rated working conditions, the simulated sound pressure level of the fan at the measuring point is $57.75$ dB, and the test sound pressure level is $58.85$ dB, with an error of $1.1$ dB, which is within the acceptable error range.

In general, the trend of the sound pressure level curve of the test and simulation results is basically the same, and the simulation results can better reflect the noise characteristics of the fan. Therefore, the model can be used for the subsequent noise calculation and analysis of the fan, and the rationality of the data simulation theory research on the gradient-radius volute tongue structure is verified. The design of the gradient-radius volute tongue structure can greatly reduce the pressure pulsation caused by the interaction between volute and air flow, and reduce the position noise of the volute tongue, which is conducive to noise reduction during fan operation.

4. Conclusions

This paper discusses the basic equations for calculating the flow field of the fan and the selection of turbulence models; introduces the classification, mechanism, and calculation methods of aerodynamic noise; establishes a geometric model of a multi-blade centrifugal fan and conducts grid division and independence verification; verifies the accuracy of the simulation model through experiments; analyzes the flow field; points out the structures that can be improved; designs a gradient-radius volute tongue structure; compares and analyzes the changes in the flow field, aerodynamic performance, and noise before and after the adjustment; and finally verifies the reliability of the numerical simulation of this structure through aerodynamic noise tests. The main conclusions are as follows:

• The optimized gradient-radius volute tongue structure reduces the pressure pulses between the volute and the airflow and minimizes the noise at the vane position. Compared with the prototype fan, the gradually varying-radius vane results in a 3.5 dB reduction in fan noise.
• Reasonable volute tongue radius and helical inclination can improve the gas flow state near the helical blade, reduce the influence of vortices and backflows on the aerodynamic performance, and enhance the performance of the centrifugal fan. Therefore, the design of the volute tongue structure plays an important role in affecting the aerodynamic performance and noise of the fan, and future research will further refine the range of variation for the tongue radius based on the current study.