Numerical Investigation on Vortex Structure and Aerodynamic Noise Performance of Small Axial Flow

The details of unsteady flow field in small axial fans are described and the relationship between the internal flow characteristics and aerodynamic noise of small axial flow fans are explored in the manuscript. Firstly, the broadband noise model is introduced to calculate the distributions of broadband noise sources in fan’s internal flow field, and further fan’s internal flow characteristics affecting broadband noise sources are analyzed by the main distributions of broadband noise sources. Secondly, the unsteady characteristics of vortex structure in fan’s internal flow field are analyzed by large eddy simulation, and FH-W acoustic model is introduced to calculate aerodynamic noise affected by the unsteady characteristics of vortex structure. Finally, monitoring points are set up near and far field of small axial fans, at which sound pressure level and spectral characteristics are analyzed. The results show that broadband noise sources are mainly distributed at the tip clearance close to blade trailing edge and one third of chord length of blade trailing edge of small axial fans. The maximum sound power of broadband noise sources at the tip clearance is greater than that at blade trailing edge. Sound power level of broadband noise near one third of blade chord length of blade trailing edge is first increasing and then decreasing when the distance between radial planes and the center of fan hub increases. Fan’s internal flow characteristics affecting broadband noise sources are the tip leakage vortex and the trailing edge vortex shedding. The tip leakage vortices at the leading edge of blade tip first integrate and then break down, while vortex cores of the trailing edge vortex shedding gradually move from blade hub to one-third of blade chord length and then move to far field within a one-seventh of the rotation cycle. Within a flow passage of fan rotation period, sound pressure level of the monitoring points is relevant to the unsteady feature of vortex structure and the main bands of aerodynamic noise of monitor points are irrelevant to the unsteady feature of vortex structure, relating to the distance between the monitor points and fan. With the above distance increasing, the main bands of aerodynamic noise are widened and moved from the low bands to high bands. All conclusions in the paper will provide significant references for reducing the noise of small axial flow fans.


Introduction
Increasing concern about noise from electrical devices has led to increasing demand for quieter cooling fans.With the increasing of small axial fans released on the market, it is difficult to judge which ones have better acoustical performance.The present study is focused on the mechanism of sound generation due to unsteady behavior of vortex flow of fan internal flow field.Actually fan's internal flow field has a great influence on aerodynamic noise [1][2][3].Powell [4] proposed vortex sound theory reveal the relationship between vortex of the internal flow field and sound, and point out that sound should be produced under the conditions of existence of the vortex when the flow rate is very low.Sound was only generated in the flow field with the region of vortices changed over time.OU-yang Hua et al. [5] studied the flow field of low speed axial fans with different setting angle by PIV and CFD simulation, and analyzed the relationship between inner flow field of fan and noise radiation based on vortex sound theory of low speed homentropic flow, and then predicted aerodynamic noise of fan.It was shown that aerodynamic noise of low speed homentropic flow was mainly induced by stretch and breakdown of vortex in flow.To uniform inflow aerodynamic noise source of low speed axial fan was major caused by blade trailing edge vortex shedding and tip vortex noise, moreover intension of preceding noise source is highly large than the latter.
Nevertheless, few references had elaborated the vortex formation mechanism and flow characteristics of the internal flow field of small axial flow fan whose diameter is less than 200 mm.The main distributions of aerodynamic noise sources and the effect of vortex structure on fan aerodynamic noise were still not very clear, and further study had to be carried out.The commercial FLU-ENT software is used in this article.The unsteady characteristics of vortex structure in fan internal flow field are analyzed by large eddy simulation.Broadband noise model is introduced to calculate the distributions of broadband noise sources in fan internal flow field, and FH-W acoustic model is introduced to calculate aerodynamic noise affected by the unsteady characteristics of vortex structure.The results will provide a useful reference about further optimizing noise characteristics of the fan.

Fan Prototype
A small axial fan RF24S9225H is selected as a study prototype in the paper, as shown in Figure 1.The impeller diameter is 84 mm, the impeller thickness is 18 mm, hub ratio is 0.39, tip clearance is 1.5 mm, number of blades is 7, blade stagger angle is 46.9˚, and the rated rotating speed is 3000 r/m, rated air volume is 0.010 kg/s, rated air pressure is 37.25 Pa.

Mesh and Computational Domain
To make the air flow more fully, the arrangement of fan flow field should be reasonable.The center of fan hub is set as the coordinate origin and the length of outlet extension is 400 mm, whose diameter in the computational domain is 200 mm, as shown in Figure 2.Meanwhile, the computational region is divided into 4 parts, nonstructural grid (tetrahedral T-grid) is used in rotating fluid area and surrounding pipeline, while structural grid (hexahedral cooper mesh) is used in the regions of front channel and back channel, as shown in Figure 3.The total grid positions are 2.86 × 10 6 for fan prototype.The degree of twist of the grid is predominantly between 0.1 -0.5.The inlet boundary condition is set as a given flow rate, for the outlet the total pressure is taken as a boundary condition.The solid walls such as vane surfaces and hub satisfy the no-slip condition in the computational domain.

Numerical Calculation
The Mach number of the airflow is under 0.3, hence, the   fluid is regarded as incompressible.Large eddy simulation (LES) can accurately simulate the turbulent field because it can accurately calculate not only the large scale turbulent fluctuation, but also the small scale turbulent fluctuation with the appropriately closed model [6].In this paper, the steady flow field with standard k-ε turbulence model is the initial solution to the unsteady flow field with the large eddy simulation.The filtered N-S equations with finite volume method are adopted.S-L model with simulating sub-grid scale effects is applied and PISO algorithm to solve the coupling of velocity and pressure is used [7].Momentum equation is calculated by the second order central difference scheme.The second order implicit scheme is used as time advance, and time step of unsteady-state calculation is set to 2 × 10 −5 s.
The noise prediction can be carried out only when the statistically steady-state solution was acquired in large eddy simulation of the unsteady flow field [8].FW-H equation based on Lighthill acoustic analogy theory is used to simulate sound production and dissemination when the noise is predicted [9].The equation expression is: In the formula: i u is the fluid velocity component along the i x direction, n is the fluid velocity components perpendicular to the plane f = 0, i is the surface velocity component along the i u v x direction, n is the surface velocity components perpendicular to the plane are the Heaviside function and Diracdelta function respectively: Noise spectrum distribution from the axial fan is acquired after the source data has been obtained in time domain integration and then fast Fourier transform (FFT) processing has been applied.Time step of noise calculation is set to 2 × 10 −5 s and cutoff frequency of noise calculation is 20 Hz.
When the monitoring point is set up at 1 m away from the central axis of the impeller along fan outlet, sound pressure level of aerodynamic noise by the numerical calculation is 32.6 dB, compared with 33 dB noise index of fan prototype from fan factory, and the difference is less than 1 dB.It is proved that the numerical calculation method of fan aerodynamic noise is feasible.

Distributions of Broadband Noise Sources
In order to clarify the distributions of broadband noise sources in fan's internal flow field, broadband noise model is introduced after the stability of steady calculation [10].Sound power level distributions of broadband noise in the surface of fan's flow field are calculated by broadband noise model, as shown in Figure 4.It can be seen from Figure 4 that the maximum sound power is distributed in the rotating fluid area of fan flow field.Figure 5 shows sound power level of broadband noise of meridian plane (X = 0 mm).It can be seen from Figure 5 that sound power level of broadband noise is mainly concentrated in the rotating fluid area of fan's internal flow field, where sound power level close to the outlet is the greater than that of other regions.According to the results of Figures 4 and 5, broadband noise sources are  In order to clarify the distributions of broadband noise sources in the rotating fluid area of fan's internal flow field, sound power level distributions of broadband noise of different revolution surfaces and meridian plane are analyzed respectively.Figure 6 shows sound power level contour of broadband noise of meridian plane (Y = mm).It can be seen from Figure 6 that the maximum sound power is distributed in the tip clearance region and blade trailing edge region of the rotating fluid area and the maximum sound power at the tip clearance region is greater than that at blade trailing edge region.
Figure 7 shows sound power level contour of broadband noise of revolution surfaces (R = 24 mm and R = mm).It can be seen from Figure 7(a) that the maximum sound power is distributed in blade trailing edge region, while the maximum sound power is concentrated in tip  Figure 8 shows sound power level contour of broadband noise of radial planes (Z = −8 mm, −9 mm and −10 mm).It can be seen from Figure 8 that the maximum sound power is distributed near radius R = 24 mm, which means broadband noise sources in blade trailing edge region are mainly concentrated in 1/3 of blade chord length.As we can see from Figures 8(a)-(c), the sound power level of broadband noise near radius R = 24 mm is first increasing and then decreasing when the distance between radial planes and the center of fan hub increases.

Internal Flow Characteristics
Due to the conclusions of Section 3.1 that broadband noise sources are mainly distributed in the tip clearance region and blade trailing edge region of fan rotating fluid area, the internal flow characteristics of the above regions are analyzed.Take the sections X = 0 mm and X = 3 mm along the axial direction respectively, and two pieces of tip clearance regions can be obtained in the section X = 0 mm, while a piece of blade tip clearance regions and a piece of the trailing edge regions can be obtained in the section X = 3 mm, as shown in Figure 9.
Figure 10 shows velocity streamlines for the axial sections X = 0 mm and X = 3 mm.It can be seen from Fig- ure 10 that the tip leakage vortex is the internal flow characteristics of the tip clearance region, and blade trailing edge vortex shedding is the internal flow characteristics of blade trailing edge region.
Figure 11 shows vorticity magnitude contour for the axial section X = 3 mm.It can be seen from Figure 11 that maximum vorticity magnitude is distributed in the tip clearance region and blade trailing edge region of the rotating fluid area.Thus the internal flow field flow characteristics affecting aerodynamic noise are the tip leakage vortex and blade trailing edge region.

The Unsteady Characteristics of Vortex
The unsteady characteristics of the tip leakage vortex and blade trailing edge vortex shedding are analyzed, which   It can be seen from Figure 12 that the tip leakage vortices at the leading edge of blade tip are integrated from t = 0.018648 s to t = 0.018768 s, and the number of vortex cores gradually decrease from 2 to 1.The vortex energy of blade tip is gradually enhanced during this time.However, the tip leakage vortices are broken down from t = 0.018768 s to t = 0.018788 s, and the number of vortex cores gradually increase from 1 to 2. The vortex energy of blade tip is gradually weakened during this time.Vortex cores of blade trailing edge vortices gradually move from blade hub to one-third of blade chord length contributes to describing the viscous flow details and variation patterns of the internal flow characteristics.As blade number of fan is 7 and it is the axial symmetrical structures, so the unsteady characteristics of the vortices are only analyzed in 1/7 of the rotation cycle.Due to a rotation period T = 0.02 s, velocity streamlines of 5 different moments are sampled within the one-seventh rotation cycle respectively (t = 0.018648 s, t = 0.018688 s, t = 0.018728 s, t = 0.018768 s, t = 0.018788 s). Figure 12 shows velocity streamlines at different times within a one-seventh of the rotation cycle.   1 that sound pressure level is reduced from t = 0.018648 s to t = 0.018788 s at monitoring point 1, which is consistent with the variation of vortex energy of blade trailing edge vortex shedding during this time.
Since monitoring point 1 is set up at the main distribution region of blade trailing edge vortex shedding, aerodynamic noise of monitoring point 1 can be considered relating to blade trailing edge vortex shedding.And so on, aerodynamic noise of monitoring point 2 can be considered relating to the tip leakage vortex.
Figure 13 shows power spectral density distributions of monitoring point 1, monitoring point 2 as well as monitoring point 3 in the different moments.It can be seen from the figure that sound pressure level of monitoring points is relevant to different sample time and the main bands of aerodynamic noise of monitoring points are irrelevant to different sample time, relating to the distance between the monitoring points and fan.With the above distance increasing, the main bands of aerodynamic noise are widened and moved from the low bands to high bands.Since the unsteady feature of vortex structure is related to different sample time, sound pressure level of the monitoring points is relevant to the unsteady feature of vortex structure and the main bands of aerodynamic noise of monitor points are irrelevant to the unsteady feature of vortex structure according to Figures 12 and 13.

Conclusions
The internal flow field of small axial fans has a great influence on aerodynamic noise.The relationship between the internal flow characteristics and aerodynamic noise of small axial fans is analyzed through the introduction of broadband noise model and the FW-H model.The following conclusions are drawn: 1) Broadband noise sources are mainly distributed at the tip clearance close to blade trailing edge and onethird of chord length of blade trailing edge of small axial fans.
2) The maximum sound power of broadband noise sources at the tip clearance is greater than that at blade trailing edge.Sound power level of broadband noise near one-third of blade chord length of blade trailing edge is first increasing and then decreasing when the distance between radial planes and the center of fan hub increases.
3) Fan internal flow characteristics affecting broadband noise sources were the tip leakage vortex and the trailing edge vortex shedding.The tip leakage vortices at the leading edge of blade tip first integrate and then break down, while vortex cores of the trailing edge vortex shedding gradually move from blade hub to one-third of blade chord length and then move to far field within a one-seventh of the rotation cycle.
4) Within a flow passage of fan rotation period, sound pressure level of the monitoring points is relevant to the unsteady feature of vortex structure and the main bands of aerodynamic noise of monitor points are irrelevant to the unsteady feature of vortex structure, relating to the distance between the monitor points and fan.With the above distance increasing, the main bands of aerodynamic noise are widened and moved from the low bands to high bands.

Figure 4 .
Figure 4. Sound power level distributions of broadband noise on the surface of fan's internal flow field.

Figure 5 .
Figure 5. Sound power level of broadband noise of Meridian plane (X = 0 mm).mainly distributed in the rotating fluid area of fan's internal flow field.In order to clarify the distributions of broadband noise sources in the rotating fluid area of fan's internal flow field, sound power level distributions of broadband noise of different revolution surfaces and meridian plane are analyzed respectively.Figure6shows sound power level contour of broadband noise of meridian plane (Y = mm).It can be seen from Figure6that the maximum sound power is distributed in the tip clearance region and blade trailing edge region of the rotating fluid area and the maximum sound power at the tip clearance region is greater than that at blade trailing edge region.Figure7shows sound power level contour of broadband noise of revolution surfaces (R = 24 mm and R = mm).It can be seen from Figure7(a) that the maximum sound power is distributed in blade trailing edge region, while the maximum sound power is concentrated in tip

Figure 6 .
Figure 6.Sound power level contour of broadband noise of meridian plane (Y = 0 mm).

Figure 7 .
Figure 7. Sound power level contour of broadband noise of revolution surfaces.(a) R = 24 mm; (b) R = 45 mm.clearance region close to blade trailing edge from Figure 7(b).Figure8shows sound power level contour of broadband noise of radial planes (Z = −8 mm, −9 mm and −10 mm).It can be seen from Figure8that the maximum sound power is distributed near radius R = 24 mm, which means broadband noise sources in blade trailing edge region are mainly concentrated in 1/3 of blade chord length.As we can see from Figures8(a)-(c), the sound power level of broadband noise near radius R = 24 mm is first increasing and then decreasing when the distance

Figure 9 .
Figure 9.The sections X = 0 mm and X = 3 mm along the axial direction.

Figure 11 .
Figure 11.Vorticity magnitude contour for the axial section X = 3 mm.

Table 1 .
It can be seen from Table