# Flow and Noise Characteristics of Centrifugal Fan in Low Pressure Environment

^{*}

## Abstract

**:**

## 1. Introduction

^{3}, which is only about half of that in the plain area [1,2]. However, from the sea level to the elevation below 85,000 m, the volume ratio of the main gases such as nitrogen and oxygen is basically the same at each altitude. So, the relative molecular mass of air remains basically unchanged. Density is proportional to atmospheric pressure at a given temperature [3,4]. When the temperature is constant, molecular concentration and air density increase with an increase of pressure [5]. The characteristics of air flow and noise change correspondingly in the application of vehicle fan and air conditioning fan. The flow rate, static pressure, axial power, efficiency, rotational speed, noise, and other performance parameters of the fan are all related to the physical properties of the air, so the flow and noise characteristics of the fan will inevitably be affected by the change of environmental pressure.

## 2. Analysis of the Influence of Low-Pressure Environment on Noise Characteristics of Centrifugal Fan

#### 2.1. Simplification of Air Flow in Centrifugal Fan

- The blades are infinitely thinner than axial thickness of fan, and the trajectory of fluid completely coincides with the blade profile;
- The fluid is ideal, that is, the flow loss in the fan caused by uneven velocity field due to viscosity is not considered;
- The flow is considered to be incompressible, axisymmetric, and steady;
- The gravitational potential energy of the air inside the fan is neglected.

#### 2.2. Noise Analysis of Centrifugal Fan in Low Pressure Environment

_{f}):

_{f}is average flow rate (u

_{f}).

^{0.5}[14], in which k is the volumetric modulus of elasticity of the medium.

_{H}/P

_{0}= ρ

_{H}/ρ

_{0}, in which it can be seen that the sound pressure P is also in a linear relationship with the air density.

## 3. Experimental Study

#### 3.1. Fan Testbed

#### 3.2. Uncertainty in Experiments

^{3}/s and 5427 Pa, respectively.

_{i}(i = 1,2, …, n), and δv

_{i}(i = 1, 2, … n) represents the uncertainties of variables v

_{i}. After calculation, the uncertainties of mass flow rate is 0.212%, the fan pressure head is 0.257%, the fan efficiency is 0.97%, and the average uncertainties of the main parameters are less than 1%. The relationship between R and v

_{i}is shown in Table 1. In the table, ε is blade displacement coefficient; D is blade diameter; b is width of blade; v

_{r}is the radial component of the absolute velocity; ρ is air density; D

_{o}is diameter of outlet; D

_{i}is diameter of inlet; S

_{r}is radial blade clearance; g is gravitational acceleration; u is peripheral speed; v

_{u}is the axial component of the absolute velocity. Therefore, it can be considered that the testbed can meet the requirements of fan test accuracy.

#### 3.3. Experimental Results and Analysis

_{v}.

_{tF}, i.e.,:

_{1}and P

_{2}are the static pressure at the inlet and outlet; u

_{f1}and u

_{f2}are the average flow rate at the inlet and outlet, and r is the rotating radius of the blade.

_{f}of the medium of the fan in unit time can be expressed as

^{3}/s to 9.4 m

^{3}/s, and the fan average power varies from 16 kW to 92.8 kW. It can be found that with the same speed of fan and with the decrease of volume flow rate, the total pressure of the fan and the power consumed by the fan increase gradually.

## 4. Simulation Study

#### 4.1. Grid Division and Definition of the Boundary

#### 4.2. Governing Equations

- Mass conservation equation

- 2.
- Momentum conservation equation$$\left.\begin{array}{l}\frac{\partial \left(\rho {u}_{1}\right)}{\partial \tau}+div(\rho {u}_{1}\cdot U)=div(\mu grad{u}_{1})-\frac{\partial p}{\partial x}+{S}_{u}\\ \frac{\partial \left(\rho {u}_{2}\right)}{\partial \tau}+div(\rho {u}_{2}\cdot U)=div(\mu grad{u}_{2})-\frac{\partial p}{\partial y}+{S}_{v}\\ \frac{\partial \left(\rho {u}_{3}\right)}{\partial \tau}+div(\rho {u}_{3}\cdot U)=div(\mu grad{u}_{3})-\frac{\partial p}{\partial z}+{S}_{w}\end{array}\right\},$$
_{1}, u_{2}, and u_{3}are the components of the velocity vector in the X, Y, and Z directions, and S_{u}, S_{v}, S_{w}are the generalized source terms.

- 3.
- Energy conservation equation$$\frac{\partial \left(\rho t\right)}{\partial t}+div\left(\rho Ut\right)=div(\frac{\lambda}{{c}_{p}}gradT)-\frac{\partial p}{\partial x}+{S}_{T},$$
_{p}is the specific heat capacity, and S_{T}is the viscous dissipation term.

^{−6}, the numerical simulation results can be considered to converge.

#### 4.3. Simulation Model Verification

#### 4.4. Numerical Calculation Results and Analysis

#### 4.4.1. Pressure Analysis of the Fan under Different Ambient Pressures

_{f}) under different ambient pressure. The figure shows that the outlet pressure head of the fan increases with the increase of flow rate (u

_{f}) but changes little under different ambient pressure. It can be seen that the environmental pressure has little effect on the outlet pressure head of the fan. Although this change is not obvious, it can be found that the outlet pressure head decreases gradually with the increase of ambient pressure.

#### 4.4.2. Noise Analysis under Different Ambient Pressure

^{3}/s at atmospheric pressure. It can also be seen from Figure 11 that although Point 1 is more than twice as far away from Point 2, the sound pressure level differs little at different frequencies. At the same time, for Point 2 in the axial direction, with the continuous increase of frequency (0–50,000 Hz), the sound pressure level gradually decreases and the trend eases. In the radial direction, with the increase of frequency, the variation of sound pressure level fluctuates greatly, which is the smallest when the frequency reaches 5000 Hz. This is because the change in axial pressure is much smaller than the change in radial pressure.

_{0}is the reference sound power, and it is generally taken as 10

^{−2}W. As can be seen from Equation (9), we can obtain that L

_{p}~ lgW. Since the sound power W and the air density ρ are in a linear relationship, namely W ~ ρ, so L

_{p}~ lgρ, it can be seen that the logarithmic relationship of the sound pressure level and the air density is linear.

## 5. Conclusions

- The sound power and sound pressure of the fan are proportional to the air density, while the sound pressure level of the fan is proportional to the logarithm of the air density.
- The total pressure and static pressure of the fan decrease with the decrease of environmental pressure. The total pressure and static pressure of the fan at 60 kPa pressure operating mode decrease by 42.3% and 38.3%, respectively, compared with the normal pressure. The main reason for this phenomenon is the decrease of air density due to the decrease of environmental pressure.
- Under the same working condition (fan rotational speed of 5500 r/min, flow rate of 8.5 m
^{3}/s), the sound pressure level at the two measuring points of the centrifugal fan increases by about 5.8% and 2.8%, respectively, as the ambient pressure increases from 50 kPa to 100 kPa. With the increase of ambient pressure, the sound pressure level of fan noise shows an approximate logarithmic growth trend.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**(

**a**) Power consumption curve of centrifugal fan; (

**b**) Performance characteristic curve of centrifugal fan.

**Figure 6.**Comparison between the experimental and the simulation results of total pressure of the fan.

R | v_{1} | v_{2} | v_{3} | v_{4} |
---|---|---|---|---|

q_{m} | D | b | v_{r} | ρ |

η | D_{o} | D_{i} | S_{r} | |

H | g | u | v_{u} |

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**MDPI and ACS Style**

Zhang, X.; Zhang, Y.; Lu, C.
Flow and Noise Characteristics of Centrifugal Fan in Low Pressure Environment. *Processes* **2020**, *8*, 985.
https://doi.org/10.3390/pr8080985

**AMA Style**

Zhang X, Zhang Y, Lu C.
Flow and Noise Characteristics of Centrifugal Fan in Low Pressure Environment. *Processes*. 2020; 8(8):985.
https://doi.org/10.3390/pr8080985

**Chicago/Turabian Style**

Zhang, Xilong, Yongliang Zhang, and Chenggang Lu.
2020. "Flow and Noise Characteristics of Centrifugal Fan in Low Pressure Environment" *Processes* 8, no. 8: 985.
https://doi.org/10.3390/pr8080985