Comparative Analyses of Dynamic Characteristics of Gas Phase Flow Field Within Different Structural Cyclone Separators

Abstract

The gas phase flow field inside a cyclone separator is crucial to the particle separation process. Previous studies have paid attention to the steady-state characteristics of the gas phase flow field, while research on its dynamic characteristics remains insufficient. Meanwhile, cyclone separators often adopt different structural forms according to the process requirements, the evolution laws of the dynamic characteristics flow field within them are still not well understood. Therefore, in this study, a hot-wire anemometer (HWA) was employed to measure the instantaneous tangential velocity of the gas phase flow fields within different structural cyclone separators (cylinder type, cylinder–cone (no hopper), and cylinder–cone (with hopper)). Comparative analyses and discussions were conducted regarding the dynamic characteristic distribution rules of the flow field in the time domain and the frequency domain. The results revealed that the dimensionless tangential velocity distributions of different types of cyclone separators all conformed to the Rankine vortex structure. The instantaneous tangential velocity fluctuated with low frequency and high amplitude, and the low-frequency velocity fluctuation exhibited a transfer behavior along the radial direction. Compared with the cylinder–cone-type cyclone separator, the tangential velocity in the cylinder-type cyclone separator fluctuated more greatly, and its quasi-periodic behavior was also more obvious. The time-averaged tangential velocity, the tangential velocity fluctuation intensity (S_d), and the dominant fluctuation frequency all had obvious attenuation along the axial direction in the cylinder-type cyclone separator, while the above-mentioned parameters had no attenuation along the axial direction in cylinder–cone-type cyclone separators. Additionally, the backflow from the hopper of the cylinder–cone-type cyclone separator (with hopper) led to an increase in the instantaneous tangential velocity fluctuation intensity of the local flow field near the dust outlet, as well as the occurrence of the “double dominant frequencies” phenomenon.

1. Introduction

As an important type of gas–solid separation equipment, the cyclone separator is widely utilized in chemical industry, environmental protection, energy, and other fields [1,2,3]. The cyclone separator uses the supergravity centrifugal flow field formed by the swirling airflow for gas–solid separation, and its flow field characteristics have a significant impact on the gas–solid separation process. Therefore, research on the flow field has always been the focal point in improving the separation performance of the cyclone separator. Moreover, it serves as the foundation for analyzing the gas–solid separation process and establishing the gas–solid separation mode [4,5]. Although the structure of the cyclone separator is simple, the flow field within it is highly complex and exhibits strong dynamic characteristics. The dynamic characteristics of its flow field have a significant impact on the separation efficiency and equipment performance [6,7,8]. However, the current research on the dynamic characteristics of the swirling flow is neither deep nor systematic enough, thus affecting people’s understanding of the gas–solid separation process inside the cyclone separator.

In recent years, researchers have utilized a variety of techniques to investigate the dynamic characteristics of the flow field within cyclone separators, including experimental measurements, computational fluid dynamics (CFD) simulations, and theoretical analysis. Among them, experimental measurement is one of the relatively effective approaches for investigating the dynamic characteristics of the flow field within cyclone separators. Measurement of flow field velocity is mainly achieved by means of a laser Doppler velocimeter (LDV) [9,10,11], particle image velocimetry (PIV) [12,13,14], and hot-wire anemometer (HWA) [15,16,17] to measure the distribution of velocities in all directions within the cyclone separator. These studies have provided valuable insights into the behavior of the flow field, which mainly included the swirling flow within the cyclone separator that exhibits unstable characteristics, the existence of a precessing vortex core (PVC), the quasi-periodic fluctuation characteristics of the velocity, etc. Regarding pressure measurement, high-precision pressure sensors were applied to measure the pressure changes within the cyclone separator. Researchers have revealed that the instantaneous pressure fluctuations present a certain regularity, which provides some assistance in explaining the dynamic characteristics of the cyclone separator’s flow field [18,19]. In addition, some numerical simulations based on CFD were adopted to analyze the dynamic characteristics of the flow field within the cyclone separator. These simulations elaborate on details such as the velocity and pressure distributions within its internal flow field, thereby providing crucial assistance in understanding the dynamic characteristics of the flow field [20,21,22].

Besides investigating the basic flow field characteristics of cyclone separators, researchers also concentrated on the influence of various structural parameters on the dynamic characteristics of the flow field. For example, alterations in the inlet structure [23,24], dust outlet structure [7,25], vortex finder structure [26,27], and cone structure [28] have led to variations in characteristics such as the velocity distribution, pressure distribution, and swirling flow swing of the flow field. The cyclone separator frequently adopts different structural forms to meet the process requirement. Nevertheless, research on the evolution laws of the dynamic characteristics of the flow field within cyclone separators of different structures is insufficient. Therefore, in this study, the HWA was employed to measure the instantaneous tangential velocities within different structural cyclone separators. The distribution characteristics and evolution laws of the dynamic characteristics of the flow fields inside the cyclone separators were comparatively analyzed from two aspects of the time domain (waveform, standard deviation) and the frequency domain (dominant frequency, power spectral density) for the measured data. The results presented will provide a valuable reference for the design, optimization, and operation of the cyclone separator.

2. Experiments

2.1. Experimental Setup

The experimental setup built for this study, shown in Figure 1, consists of three parts: cyclone separation system, power system, and measuring system. The cyclone separation system is the main part of the experimental setup, which consists of the experimental cyclone separator and the upstream and downstream transmission pipeline. A butterfly valve installed on the downstream line was used to adjust the system air volume. The experiment was carried out under negative pressure conditions in order to alleviate the difficulties of sealing and the interferences of fan operation. Therefore, the power system was located at the end of the experimental setup, consisting of a centrifugal fan (9-19A, Blower Inc., Zhangqiu, China) and an inverter. The maximum air volume of the fan is 2062 m³/h, which corresponds to the maximum inlet velocity of the cyclone separator used in this experiment of 38.3 m/s. The inverter was used to adjust the speed of the fan smoothly. The measurement system consisted of a hot-wire anemometer (IFA300, TSI Inc., Seattle, WA, USA), a Pitot tube, and a coordinate frame. The hot-wire anemometer was used to measure the instantaneous velocity of the cyclone separator, with an accuracy of 0.0001 m/s. The Pitot tube was used to measure the inlet velocity, with an accuracy of 0.01 m/s. The coordinate frame was used to adjust and fix the hot-line probe during the measurement process.

2.2. Cyclone Separator Geometry

Reverse cyclone separators with a single volute inlet were adopted as the foundation for dynamic measurement experiments. For easy observation and measurement, all the cyclone separators were made of transparent plexiglass with a thickness of 10 mm. In order to compare and analyze the characteristics and laws of the gas phase flow field of different structural cyclones, three types of cyclone separators (cylinder type, cylinder–cone type (no hopper), and cylinder–cone type (with hopper)) were selected for the experiment. The reference planes for cyclone separators were set up on the horizontal plane parallel to the upper edge of the entrance. The origin was defined as the intersection of the geometric centerline of the vortex finder and the reference plane, and the positive direction was downward. The experimental cyclone separator geometric dimensions are detailed in Figure 2 and

Table 1. Geometric properties of cyclone separators.

Geometric Parameter (mm)	Cylinder Type	Cylinder–Cone Type (No Hopper)	Cylinder–Cone Type (With Hopper)
Cylinder diameter (D)	300	300	300
Vortex finder diameter (dr)	110	110	110
Rectangular entrance (a × b)	178 × 84	178 × 84	178 × 84
Vortex finder height (S)	178	178	178
Cylindrical body height (H)	1090	430	430
Cone height (Hc)	—	660	660
Dust outlet diameter (De)	—	—	130
Hopper size (Dh × Hh)	—	—	220 × 230

.

2.3. Measuring Method

2.3.1. HWA System

Although measurement methods such as LDV and PIV are non-contact measurement techniques, both of them require relatively high light transmittance and a certain concentration of tracer particles during the measurement process. Due to the separation effect of the swirling flow in the cyclone separator on the tracer particles, the concentration of tracer particles in the central area of the cyclone separator is relatively low, which makes it not easy to obtain high-frequency velocity fluctuations [29]. HWA is a contact measurement technique that has a certain impact on the measured flow field, and the flow field with particles cannot be measured because the hot-wire probe is prone to damage. However, compared with the size of cyclone separators, the size of the probe (2.5 mm in diameter in this study) is relatively very small, and its influence on the strong swirling flow field can be ignored. In addition, HWA has the advantages of simple operation, small volume, and high spatial and temporal resolution, which is suitable for measuring high-frequency velocity fluctuations within the cyclone separator [30,31].

The operation of the HWA is shown in Figure 3. The basic principle of the constant-temperature hot-wire anemometer is thermal equilibrium [32]. A heating current is passed through the wire to keep its temperature constant (constant-temperature type). When the velocity changes, the heat transfer of the wire changes accordingly. The lost heat is supplemented by the current, and thus the electrical signal changes. Through the calibration of the hot-wire probe, the corresponding relationship between the change in the electrical signal and the magnitude of the velocity can be established, achieving the measurement of the flow field [33]. Therefore, the hot-wire probe needs to be calibrated to ensure the accuracy of the measured velocity before measurement. Generally, the calibration of the hot-wire probe is carried out in a standard wind tunnel. The calibration device and calibration curve of the probe are shown in Figure 4. Judging from the calibration curve, the velocity data of the standard wind tunnel measured by the probe has a high degree of agreement with the data calculated through voltage, with an average error of 0.034%. Moreover, after the velocity becomes greater than 7 m/s, the measurement error is basically very small. Therefore, the calibrated hot-wire probe can accurately collect the gas velocity of the flow field in the cyclone separator.

2.3.2. Measuring Process

The air volume of the experimental system was adjusted using the butterfly valve and a Pitot tube was used to measure the inlet velocity. A constant inlet velocity was set at 6.8 m/s (the corresponding Reynolds number (Re) is 137,837, calculated based on the inlet velocity (V_i) and the cyclone cylinder diameter (D), Re = $\rho V_{\mathrm{i}}D/\mu$ [10]) for all experiments in this study.

The instantaneous velocity of the gas phase flow field within cyclone separators was measured by HWA. The tangential velocity V_t (the core component for the three-dimensional swirling flow) was selected as the interest parameter to characterize the flow field dynamic characteristic. Therefore, the hot-wire probe must be arranged vertically with the tangential velocity during the measurements. The arrangement of measurement sections and measurement points is illustrated in Figure 2. 4 Measurement sections were set at different axial positions Z₁–Z₄ (z/D = 1.23, 1.93, 2.52, 3.30) in the separation space, and six measurement points with different r/R were arranged along the radial direction (spanning 0° to 180°) of each measurement section. The sampling frequency was set to 1000 Hz and the sampling time was 10 s.

3. Results and Discussion

3.1. Time Domain Characteristics of Flow Field Within Different Types of Cyclone Separators

3.1.1. Dimensionless Time-Average Tangential Velocity

Figure 5 shows the time-average tangential velocity profiles of different types of cyclone separators. The dimensionless tangential velocity (${\overline{V}}_{\mathrm{t}}/V_{\mathrm{i}}$) distributions were largely in line with the Rankine vortex structure, which consists of an internal rigid vortex and an outer quasi-free vortex [34]. Since the diameter and vortex finder diameter of the three types of cyclone separators are the same, the interface between the rigid vortex and the quasi-free vortex is about r/R = 0.21, which is less than the diameter of the vortex finder (d_r/D = 0.367). All three have in common that the dimensionless time-average tangential velocity (${\overline{V}}_{\mathrm{t}}/V_{\mathrm{i}}$) in the rigid-vortex region gradually increased as the radial position moved towards the wall, while it gradually decreased in the quasi-free-vortex region. The difference is that the tangential velocity within the cylinder-type cyclone separator significantly attenuated along the axial direction, while had almost no attenuation along the axial direction within the cylinder–cone-type cyclone separators. This is mainly because the frictional loss between the swirling airflow and the wall surface in the cylinder-type cyclone separator led to a decrease in the rotation intensity. However, in the cylinder–cone-type cyclone separator, the rotation intensity was basically unchanged and even slightly enhanced under the action of the cone. However, the tangent velocity distribution had some difference at section Z₄ (z/D = 3.30) for cylinder–cone-type cyclone separator with a hopper or not. This is mainly because of the increase in the velocity fluctuation intensity near the dust outlet region caused by the backflow from the hopper.

3.1.2. Instantaneous Tangential Velocity

Figure 6 shows the curve of the instantaneous tangential velocity over time (5–6 s within 10 s sampling time) for different axial sections within three types of cyclone separators. At each measuring section, the instantaneous tangential velocity fluctuated continuously over time. The magnitude of velocity fluctuation was relatively small at higher r/R ratios near the wall. As the radial position moved towards the geometric center, the magnitude of fluctuation gradually increased and exhibited a certain quasi-periodic fluctuation behavior, especially more obvious at lower r/R ratios near the central region. Take the cylinder-type cyclone separator as an example. At the measuring point with r/R = 0.92 near the wall on the Z₁ (z/D = 1.90) section, the fluctuation range of the instantaneous tangential velocity was less than 4 m/s. However, at the measuring point near the center with r/R = 0.12, the fluctuation range increased to approximately 12 m/s, and the fluctuation curve showed certain quasi-periodic characteristics. Comparing the fluctuation ranges of the instantaneous tangential velocities within the cylinder-type cyclone separator and the cylinder–cone-type cyclone separator, the fluctuation range of the cylinder-type cyclone separator was larger on the same axial section. This is mainly because as the conical space gradually decreased in the cylinder–cone-type cyclone separator, it had a certain restrictive effect on the fluctuation of the instantaneous velocity. It is worth noting that at the Z₄ (z/D = 3.30) section near the dust outlet in the cylinder–cone-type cyclone separator (with hopper), the fluctuations of the instantaneous tangential velocities at all radial measuring points were relatively large, which was caused by the fluid backflow from the hopper.

The waveform analysis in the time domain is simple and intuitive, and the signal waveform can be used to analyze the flow characteristics. The data of the measuring points r/R = 0.12 near the center on two axial sections (z/D = 1.23 and z/D = 3.30) of three types of cyclone separators were selected as the analysis samples. Figure 7 shows the measurement data curves in the interval from 5.4–5.6 s and the sinusoidal fitting curves for the data. The local waveform curves and fitting results showed that the instantaneous tangential velocity contained not only high-frequency and low-amplitude irregular fluctuations, but also low-frequency and high-amplitude quasi-periodic fluctuations. The sine waveforms at different sections of the cylinder-type cyclone separator fit well with the measured data. For cylinder–cone-type cyclone separators, there were certain differences between the fitting curves of the cylindrical part and the measured data, and the section at the lower end of the conical part fit well. However, the Z₄ (z/D = 3.30) section of the cylinder–cone-type cyclone separator (with hopper) showed a higher fluctuation frequency. The above waveform analyses showed that the sine characteristics of the low-frequency velocity fluctuations in the cylinder-type cyclone separator are obvious, while in the cylinder–cone–type cyclone separators they are slightly weakened. Considering that the velocity fluctuations in the cyclone separator were caused by the swing of the rotation center [7], this indicated that the swing trajectory of the rotation center of the swirling flow in the cylinder-type cyclone separator was closer to a circle, and the degree to a circle in the cylinder–cone-type cyclone separator was varied at different axial positions.

3.1.3. Standard Deviation

Standard deviation (S_d) is a standard measure for quantifying the dispersion degree of data distribution and is used to measure the extent to which data values deviate from the arithmetic mean. For the dynamic parameters in a cyclone separator, the tangential velocity V_t at any moment can be expressed as the superposition of the average tangential velocity $\overline{V_{\mathrm{t}}}$ and the fluctuating velocity V_t^’, that is:

$$V_{\mathrm{t}}={\overline{V}}_{\mathrm{t}}+{V_{\mathrm{t}}}^{\prime }$$

(1)

The formula for calculating the average tangential velocity $\overline{V_{\mathrm{t}}}$ is:

$${\overline{V}}_{\mathrm{t}}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{V}_{\mathrm{t}\mathrm{i}}}$$

(2)

If V_ti is the instantaneous tangential velocity at the i–moment, then the standard deviation S_d for any measurement point is:

$$S_{\mathrm{d}}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{\left(V_{\mathrm{ti}}-\overline{V_{\mathrm{t}}}\right)}^2}}$$

(3)

Since the stable component has been removed, S_d of the time-series velocity can be used to characterize the extent to which the instantaneous parameter fluctuation data values deviate from the average value in the cyclone separator and intuitively measure the fluctuation intensity of the fluctuation signal.

Figure 8 shows the S_d of the measurement data at each measuring point of three types of cyclone separators calculated according to Formula 3. For the cylinder-type separator, as illustrated in Figure 8a, in the radial direction of different sections, the S_d in the region near the center was relatively large, and as the radial position approached the wall, the S_d gradually decreased. In the axial direction, as the axial position moved downward, the S_d of the instantaneous tangential velocity gradually decreased. This is because the frictional loss on the wall of the cylinder-type separator had a weakening effect on the swing of the swirling flow, which reduced the fluctuation intensity of the instantaneous tangential velocity. For cylinder–cone-type cyclone separators, as illustrated in Figure 8b,c, in the radial direction, the S_d had the same variation trend as that of the cylinder-type cyclone separator. S_d was relatively large near the center, and as the radial position moved towards the wall, the S_d gradually decreased and tended to be stable. The difference is that, in the axial direction, due to the existence of the cone, which had an enhancing effect on the swirling flow, the S_d of the instantaneous tangential velocity increased as the axial position moved downward and reached the maximum near the bottom. In the cylinder–cone-type cyclone separator (with hopper), the S_d at different radial measurement points on the Z₄ (z/D = 3.30) section near the dust outlet were all relatively large, indicating that the velocity fluctuation intensity in this region was very high, which was caused by the hopper backflow.

Combined with the S_d distribution of the instantaneous tangential velocity and the analysis results of Figure 6 and Figure 7, this showed that the tangential velocity fluctuation intensity inside the cyclone separator was the result of the combined action of the low-frequency fluctuation of the swirling flow and the irregular pulsation of the turbulence itself. Among them, the low-frequency fluctuation of the swirling flow caused by the swing of the swirling flow was the main component. For example, the tangential velocity fluctuation intensity was relatively large near the center of the cyclone separator, the low-frequency fluctuation gradually became less obvious as the radial position moved towards the wall, and the fluctuation intensity was mainly affected by the irregular pulsation of the turbulence itself.

3.2. Frequency Domain Characteristics of Flow Field Within Different Types of Cyclone Separator

3.2.1. Spectral Analyses

Spectral analysis is one of the most widely used methods in dynamic signal processing. Its purpose is to decompose complex time-series waveforms through the Fourier transform (among which the fast Fourier transform (FFT) is the most commonly used tool) into several single-harmonic components for study, so as to obtain information such as the frequency structure of the signal and the amplitude, phase, and energy of each harmonic. Based on the Fourier series and Fourier integral, the power spectral density function in the signal frequency domain can well reflect the essence of the fluctuation signal in the cyclone separator, represent the energy distribution at different frequencies, and be used to analyze the causes of the fluctuation of dynamic parameters in the flow field and the characteristics of transmission, etc. [17].

Therefore, before each measurement, the instantaneous velocity at the inlet of the cyclone separator was analyzed by FFT to obtain its power spectral density (PSD) distribution, as shown in Figure 9. The PSD of each frequency component of the instantaneous velocity at the inlet was very small, and there was no dominant frequency. It could be considered that the inlet air was relatively stable and would not affect the analysis of the dynamic characteristics of the swirling flow in the cyclone separator.

Subsequently, spectral analyses via FFT of the instantaneous tangential velocity of each measurement point within three types of cyclone separators were conducted to obtain the distributions of PSD relative frequency, as shown in Figure 10. There was a prominent peak in each frequency spectrum graph of the cylinder-type cyclone separator, and the frequency corresponding to this peak value was the dominant frequency of the tangential velocity fluctuation. In the radial direction, the dominant frequency became gradually less obvious from the position near the geometric center towards the wall. There were slight differences in the dominant frequency values of different axial sections, which were distributed between 15 and 20 Hz. For the cylinder–cone-type cyclone separator, there was a dominant frequency of approximately 21 Hz in each measurement section. In addition, an additional dominant frequency of approximately 55 Hz appeared in the near-center regions of the Z₃ (z/D = 2.52) and Z₄ (z/D = 3.30) sections of the cylinder–cone-type cyclone separator (with hopper). There were dominant frequencies with relatively high PSD in the frequency spectrum graphs of the three types of cyclone separators, indicating that the instantaneous tangential velocity had the characteristic of quasi-periodic fluctuation [20], which also reflected the swing characteristics of the gas-swirling flow. However, it seemed that there were obvious differences in this swing characteristic in different types of cyclone separators.

3.2.2. Discussion of the Dominant Frequency Characteristics

Figure 11 shows the extracted dominant frequency distribution of each measurement point within the different types of cyclone separators. The dominant frequencies of each section of the three types of cyclone separators had basically no obvious change along the radial direction. In the axial direction, the dominant frequency of the cylinder-type cyclone separator gradually decreased as the axial position moved downward, while the dominant frequency of the cylinder–cone-type cyclone separator was basically unchanged with the change of axial position. The dominant frequency distributions indicated that the low-frequency velocity fluctuation in cyclone separators had a transfer behavior along the radial direction. Due to wall friction loss, the low-frequency velocity fluctuation in the cylinder-type cyclone separator had a certain attenuation characteristic along the axial direction. Although the frictional loss still existed in the cylinder–cone-type cyclone separator, the low-frequency velocity fluctuation had basically no attenuation along the axial direction with the enhancement effect of the conical section on the swirling flow.

It is worth noting that there was an additional dominant frequency in the regions near the center of the Z₃ (z/D = 2.52) and Z₄ (z/D = 3.30) sections of the cylinder–cone-type cyclone separator (with hopper). This is because there was an airflow exchange between the cone and the hopper [7]. The airflow from the upstream of the separation space flowed into the hopper along the vicinity of the wall, and then flowed upward from the central region of the hopper into the separation space, as shown in Figure 12. After the swirling flow entered the hopper, it was equivalent to entering a new cyclone system. The diameter of the hopper was smaller than that of the cyclone separator, and a new swing of swirling flow was formed in the hopper, generating a new swing frequency. Eventually, the fluid re-entered the separation space of the cyclone separator along with the upward-flowing air current. Since the upward space gradually expanded, this new swing quickly attenuated and disappeared. Therefore, the additional dominant frequency only existed in the local central region of the lower part of the cone, as shown in Figure 10 and Figure 11.

The PSD magnitudes of the dominant frequency widespread within the experimental cyclone separators were selected for analysis. Figure 13 presents the radial variation curves of the PSD magnitude of the dominant frequency in different sections of three types of cyclone separators. For both cylinder and cylinder–cone types of cyclone separators, the PSD magnitude of the dominant frequency gradually decreased as the radial position moved from the center toward the wall. Moreover, the PSD magnitudes at the measurement points near the center were much higher than those near the wall. This indicated that the influence of the swirling flow swing on the internal rigid vortex region was significantly greater than that on the external quasi-free vortex region. Consequently, the instantaneous tangential velocity fluctuation decreased as the radial position r/R increased, and the low-frequency fluctuation characteristics were more prominent near the central region, as illustrated in Figure 6. Furthermore, the variation trend of PSD magnitudes in different axial sections was consistent with the trend of tangential velocity fluctuation intensity.

4. Conclusions

In this study, a hot-wire anemometer was used to measure the instantaneous tangential velocity of the gas phase flow field within different structural cyclone separators under the same inlet velocity V_i. Comparative analyses and discussions were carried out on the dynamic characteristic distribution rules of the flow field in the time domain and the frequency domain. The main conclusions are summarized as follows:

• The commonalities within the dimensionless tangential velocity distributions of different types of cyclone separators were that the dimensionless time-averaged tangential velocity conformed to the Rankine vortex structure. The differences were that the tangential velocity in the cylinder-type cyclone separator had an obvious attenuation along the axial direction, while had almost no attenuation in cylinder–cone-type cyclone separators. The frictional loss between the swirling flow and the wall caused the rotation intensity to decrease in the cylinder-type cyclone separator, however, the rotation intensity in the cylinder–cone-type cyclone separators remained basically unchanged or even slightly enhanced under the action of the cone.
• The instantaneous tangential velocity distributions, local waveform curves, and sinusoidal fitting results demonstrated that the instantaneous tangential velocity of different types of cyclone separators contained not only high-frequency and low-amplitude irregular fluctuations, but also low-frequency and high-amplitude quasi-periodic fluctuations. Compared with the cylinder–cone-type cyclone separator, the tangential velocity fluctuation of the swirling flow in the cylinder-type cyclone separator was greater, and its quasi-periodic behavior was more obvious, indicating that the swing trajectory of the swirling flow’s rotation center on the section is closer to a circle.
• Structural form had significant impacts on the velocity fluctuation of the swirling flow within the cyclone separator. The S_d of the three types of cyclone separators gradually decreased as the radial position approached the wall. In the axial direction, as the axial position moved downward, the S_d gradually decreased in the cylinder-type cyclone separator, whereas that gradually increased in the cylinder–cone-type cyclone separator. The S_d distributions indicated that the tangential velocity fluctuation intensity inside the cyclone separator resulted from the combined action of the low-frequency fluctuation of the swirling flow and the irregular pulsation of the turbulence itself, among which the low-frequency fluctuation constituted the main component.
• Spectral analysis of the instantaneous tangential velocities within different types of cyclone separators all showed an obvious dominant frequency. The dominant frequencies in each section of the three types of cyclone separators had basically no obvious changes along the radial direction. In the axial direction, the dominant frequency of the cylinder-type cyclone separator gradually decreased (from approximately 20 to 15 Hz) as the axial position moved downward, while that of the cylinder–cone-type cyclone separator remained basically unchanged (approximately 21 Hz). Moreover, an additional dominant frequency (approximately 55 Hz) appeared in the region near the bottom of the cylinder–cone-type cyclone separator (with hopper) due to the influence of the hopper backflow. The dominant frequency distributions suggested that the low-frequency velocity fluctuation in the cyclone separator had a transfer behavior along the radial direction. The low-frequency velocity fluctuation in the cylinder-type cyclone separator had a certain attenuation characteristic along the axial direction, while had basically no attenuation in the cylinder–cone-type cyclone separators.
• Analysis of the power spectral density (PSD) magnitudes of the dominant frequencies within different types of cyclone separators revealed that the PSD magnitude of the dominant frequency gradually decreased as the radial position moved from the center towards the wall. Additionally, the PSD values at the measurement points near the center were substantially higher than those near the wall. This indicated that the influence of the swirling flow swing on the internal rigid-vortex region was significantly greater than that on the external quasi-free vortex region. The variation trend of the PSD magnitude on different axial sections was consistent with the trend of the tangential velocity fluctuation intensity.