1. Introduction
With the rapid economic development, people have put forward new requirements for the ventilation and air-conditioning system. At the same time, the COVID-19 pandemic has further raised people’s attention on this [
1,
2]. Building electrical energy accounts for a large proportion of total energy consumption [
3,
4], and ventilation and air-conditioning systems are important energy-consuming sections, accounting for about 40% of building energy consumption [
5]. Fan is an important component of ventilation and air-conditioning system. The improvement in fan performance can reduce electricity consumption by itself, which is considerable in some ventilation use and help increase the efficiency of refrigeration system to decrease even more electric energy cost. Therefore, research on developing ventilation equipment with high efficiency, energy-saving and low noise has grown increasingly important [
6].
From the user’s point of view, the multi-blade centrifugal fan has the characteristics of small space occupation and low noise. These two unique advantages make it widely used in air conditioning, ventilation, building ventilation and other industries [
7]. However, its low efficiency has always limited the market promotion of this type of fan [
8]. Noise and energy consumption problems in existing multi-blade centrifugal fan designs have grown increasingly problematic as modern demands for energy conservation and emissions reduction have intensified [
9]. As the main working component of a building ventilation system, improving the efficiency of the fan can reduce the energy consumption of the entire system [
10]. The increase in fan efficiency may also reduce the fan noise, which significantly affects users’ experience on building ventilation and air conditioning systems [
11].
As the power component of the multi-blade centrifugal fan, the aerodynamic performance and the acoustic characteristics of the fan were impacted by the impeller [
12]. Multi-blade centrifugal fans usually have 60 blades, so by adjusting the structure of the blades, the performance of the fan can be greatly improved [
13,
14]. In the conventional design, the blade profile of the multi-blade centrifugal fan is polynomial (and usually single) in the middle arc. The air performance of single arc blades is generally poor [
15]. However, optimizing the design of the multi-segment curve of the blade profile may improve aerodynamic performance, the efficiency and acoustic characteristic of the fan.
Many previous scholars have attempted to optimize the design of multi-blade centrifugal fan blades. In selecting multi-blade centrifugal fan airfoil, Zuo [
16] explored a single-arc blade type multi-blade fan and a double-arc blade type multi-blade fan to find that the aerodynamic characteristics of the former are inferior to those of the latter. A double-arc blade type multi-blade fan with a larger arc radius shows favorable aerodynamic characteristics and low noise. Recently, researchers have developed bionic designs on a leaf (blade) surface, leading-edge and trailing edge by extracting the unique noise-reducing characteristic structure produced by natural organisms during evolution [
17,
18]. Liu [
19] found that the A-level noise of non-smooth structured bionic blades, striped surface bionic blades and bionic serrated leading-edge blades are all lower than those of prototype blades.
Early fluid machinery blade parameterization techniques mainly centered on the bump function method [
20], which is convenient for airfoil design but requires approximately 10 control parameters. As the upper and lower surfaces are modified, the design volume grows excessive and it is difficult to intuitively reflect the influence of a single parameter on the design result. Deng et al. [
21] proposed a new parametric airfoil design method based on the Bessel curve and developed it into a generalized form of adjustable shape parameters. The Bessel function addition was found to improve the local control ability over the position of the front and rear edges of the airfoil, which is very important in regards to the blade design. Zuo [
22] developed the airfoil disturbance function designed by Hicks-Henne to investigate the multi-parameter and multi-objective optimization function in the airfoil optimization process; they proposed airfoil optimization design ideas accordingly. In order to improve aerodynamic performance of the range hood, Yang [
23] used a dual-arc profile in the multi-blade centrifugal fan.
The above methods provide effective optimization results, but no previous researcher has fully considered the practical applicability of single-arc blade parameterization. These methods also tend to have an excess of design variables, which complicates the optimization process. At the same time, the reliability of the above method in practical engineering problems has not yet been verified. Therefore, there is still room for improvement. In the present study, the classical airfoil of the existing multi-blade centrifugal fan is fitted by linear superposition of four shape functions based on the Class Shape Transformation (CST) function, which has not been reported yet to the author’s knowledge. Design variables are established based on the perturbation function concept.
The Q35 fan, usually is used in building ventilation, is chosen for study in this work. The shape function coefficient of the disturbance CST function is used as a design variable to parameterize the blades. Using the experimentally validated CFD model, performance results of fans with different blade CST parameters are obtained. The RBF model is used to fit the coupling relationship between the CST parameters of the sample model and the numerical simulated performance value. The Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used to complete the optimization process. After the optimized impeller is analyzed by numerical simulation, its prototype is fabricated and verified by air performance and noise testing. This optimization method is also applicable to the blade airfoil optimization of other types of wind turbines and lays the basis for the optimization of building systems and heating ventilation and air conditioning (HVAC) systems that use wind turbines as their main power equipment.
2. Studied Equipment: The Original Multi-Blade Centrifugal Fan
The research object of this study, as mentioned above, is the Q35 single-suction multi-blade centrifugal fan (
Figure 1) commonly used in the ventilation system. Its rated speed is 880 rpm. Measured at the design working point, the air volume of the multi-blade centrifugal fan is 16.8 m
3/min, its total pressure efficiency is 40.0% and its noise level is 54.05dB. The profile and thickness of the blade could influence the feature of the aerodynamic performance and the acoustic characteristics of the fan. The optimization of this shape can greatly improve the overall performance of the fan, including flow rate, efficiency, noise level and others. The main structural parameters of the fan impeller are listed in
Figure 2 and
Table 1.
The whole optimization process is shown in
Figure 3. The CST function fits the blade, then several groups of blade design samples are established after the perturbation range of the shape function is determined. By establishing the RBF model of the variables and the response, the NSGA-II algorithm was used to solve the RBF model. At the same time, after verifying the feasibility of replacing experiments with numerical simulations, the sample database for the training of the RBF model is calculated by CFD numerical method. After obtaining an optimized airfoil, the results were analyzed via proofing verification and analysis of the numerical simulation.
3. Parameterization the Centrifugal Fan Blade Based on CST Function
Kufan and Bussoletti proposed using a Class Function and a Shape Function (CST function) to represent the geometric shape of an aircraft. This parametric representation method uses the Class Function and the Shape Function to represent the airfoil. It is highly accurate and requires few parameters, making it intuitive and convenient when managing important design parameters such as a leading-edge airfoil radius. The CST method is mainly used to parameterize airfoils in the aviation and military fields and has shown good curve-fitting capabilities [
24,
25]. Multi-blade centrifugal fan airfoil designs are mostly based on traditional concepts. An improved CST function was applied here to parameterize the multi-blade centrifugal fan blade:
where
C(
x/
c) is the class function of the leaf shape;
N1 and
N2 indicate the type of leaf shape. When
N1 = 0.5,
N2 = 0.5, the category function is expressed as an elliptical airfoil with a round nose and round tail. When
N1 = 0.75,
N2 = 0.75, the category function is represented as a Sears-Haack body, as shown in
Figure 4 below.
S(
x/
c) is the shape function of the airfoil,
controls the curve shape of the airfoil from the leading edge to the trailing edge, and
is the thickness of the trailing edge of the airfoil, which can be determined according to the design requirements. The airfoil of the multi-blade centrifugal fan can be considered to have no trailing edge, so the thickness is 0;
c is the chord length of the airfoil. The Q35 fan blade airfoil was decomposed by the CST parameter using a third-order Bernstein polynomial in this study.
N1 and
N2 were fixed at 0.75 and 0.75 to obtain a curve that is close to the original impeller.
During the entire optimization process, the parameterization of the blade profile centerline is the most important. The parameterized blade profile centerline has fixed endpoints M1 and M2 so that the blade chord length
L remains unchanged.
Figure 5 shows the Schematic diagram of CST function superimposed blade forming. The value of
n in Formula (5) not only determines the number of functions in the curvature distribution but also ensures smooth adjustment of key points of the leaf shape. An oversize
n value, however, creates an increase in the number of design variables that complicates the optimization process. If the value of
n is too small, the leaf shape cannot be adjusted effectively. After many comparisons,
n = 3 was found to allow the CST function to be expressed as the sum of four divided subfunctions (
Figure 5).
Figure 6 shows the blade structure of a multi-blade centrifugal fan. The CST parameterization method was used to fit the airfoil of the multi-blade centrifugal fan to validate the proposed method. The fitting curve is shown in
Figure 7. The fitted values of the initial airfoil parameters are shown in
Table 2, where the fitting error is less than 1%.
The design goal, in this case, is to optimize the blade profile, so it needs to be adjusted based on prototype line fitting. This approach reduces the modified sample space so that the optimized solution can be obtained quickly when performing multi-objective optimization.
With reference to the CST fitting parameters of the existing airfoil, the parameters were adjusted to obtain a more suitable airfoil. The variation range of the design variable (
vi) is shown in
Table 3.
7. Conclusions
A multi-objective multi-blade centrifugal fan optimization design was developed in this study using the disturbance CST function. Numerical simulation and experimental analyses were conducted to test its feasibility and effectiveness. The conclusions of this work can be summarized as follows:
(1) Aerodynamic performance and noise tests on original and optimized fans showed consistent characteristic curves between them. The total pressure and efficiency of the total pressure fan were effectively improved in different working environments. At the design working point, the air volume increases by 1.4 m3/min while total pressure efficiency increases by 3.1% and low-frequency noise is markedly reduced. As the main working component of a building ventilation system, improving the efficiency of the fan can reduce the energy consumption of the entire system and noise reduction can significantly improve user comfort.
(2) The disturbance CST function was applied to the optimal design of multi-blade centrifugal fan blades, and the feasibility of coupling the CST function and multi-objective genetic algorithm in the parametric blade design was validated. The entire proposed optimization design requires relatively few design variables. It provides a way of thinking for the energy-saving design of the ventilation system. The optimization process is simple and effective; the proposed method has certain engineering application value. In the longer term, this method provides a feasible method for the design of fluid machinery blades, such as compressors, pumps or wind turbines.