A Novel Inlet Guiding Structure for Pressure-Loss Reduction in Gas–Liquid Cyclone Separators

Abstract

Gas–liquid cyclone separators are an efficient and emerging method for air removal in hydraulic systems, yet often suffer from excessive pressure loss. A novel contracting inlet guiding structure is proposed to minimize hydraulic losses. This study adopts a comprehensive methodology combining theoretical modeling, computational fluid dynamics (CFD) using the Reynolds Stress Model (RSM), and experimental validation. A theoretical pressure-loss model incorporating the diminishing-returns effect of the contraction angle was established. Simulations revealed that increasing the contraction angle reduces energy dissipation by improving the uniformity of the tangential-velocity field. Based on the balance between pressure-loss reduction and degassing potential, a contraction angle of 11° was identified as the optimal design and experimental tests on a prototype confirmed the validity of the numerical model. The results demonstrate that, compared to the conventional straight tangential inlet, the optimized inlet reduces the pressure loss by approximately 30% under rated conditions. The experimental–numerical discrepancy decreases significantly with flow rate, achieving a relative error of approximate 10% at the design flow rate. These findings provide a theoretical basis and practical guidance for the low-energy design of hydraulic cyclone separators.

1. Introduction

Hydraulic transmission and control systems are widely used in engineering equipment, marine power systems, and advanced manufacturing owing to their high power density, fast response, and capability to operate under harsh conditions [1,2,3,4]. Hydraulic oil is the primary medium for the operation of the hydraulic system. In practical operation, hydraulic oil contamination can significantly impair system reliability. Engineering statistics indicate a strong correlation between oil contamination and hydraulic system failures, with more than 75% of failures attributed to hydraulic oil contamination [5]. Among various contaminants, gaseous pollutants are one of the dominant types. Hydraulic oil typically contains 8–12% dissolved gas, which can be readily released from solution and form bubbles under pressure fluctuations, thereby aggravating cavitation and further inducing performance degradation, noise, vibration, and efficiency loss [6,7,8]. With the continuing trend toward high-pressure, compact systems, conventional gravity-based degassing methods are increasingly constrained by limited separation efficiency and poor compactness [9]. Consequently, cyclone separation has become an important approach for hydraulic oil deaeration and purification, combining compactness, high efficiency, and inline degassing capability [10,11].

Gas–liquid cyclone separators achieve phase separation with different density through swirling flow fields. To ensure high separation efficiency, a sufficiently strong swirl intensity is required. However, a strong swirl also increases energy consumption. Pressure loss is an important manifestation of the energy expenditure associated with swirl and becomes a critical performance metric of cyclone separators. Extensive studies have investigated cyclone pressure-loss characteristics. Hoffmann and Stein [12] decomposed the pressure loss into inlet local losses, main-body swirl losses, and outlet-related losses. However, the research conducted by Vermande Paganel et al. [13] focusing on hydrocyclones showed that purely empirical formulas often become inaccurate when geometric scales deviate from the calibration range. Furthermore, Durango-Cogollo et al. [14] demonstrated that internal flow distributions strongly affect pressure-drop prediction, suggesting that a single empirical expression is insufficient to represent loss redistribution under complex disturbances. Consequently, analyzing the location of pressure loss in the cyclone separator and establishing corresponding pressure-loss prediction models have become the mainstream approach in correlational studies. For instance, the vortex-finder configuration [15,16,17] and the underflow-orifice geometry [18] have been identified as key factors modulating local losses. These studies suggest that synthesizing a total pressure-drop model from component-wise analyses is more beneficial for structural optimization than directly fitting the total pressure loss.

From a broader viewpoint of geometric effects, the main-body structure influences cyclone pressure loss primarily by modifying the flow field distribution; accordingly, some studies have examined the effects of main diameter and length on pressure-drop characteristics [9,11,19,20]. Nevertheless, under practical operating constraints and limited installation space, the tunable range of main-body parameters is often restricted. By contrast, the inlet structure directly determines the inlet local loss and governs swirl establishment and the initial angular-momentum input, thereby exerting a substantial influence on main-body dissipation and the overall pressure loss. In cyclone-related review studies, the inlet is commonly regarded as one of the most designable and pressure-drop-sensitive components [12].

Existing studies on inlet-oriented pressure-drop reduction have formed diverse technical routes, including inlet angle regulation, multi-inlet arrangements, axial inlets, and inlet-adjacent guiding/locally reconstructed structures. Juengcharoensukying et al. [21] investigated the coupled effects of inlet angle and vortex-finder geometry and indicated that the inlet significantly alters the near-inlet recirculation structure and swirl establishment process, thereby changing the spatial distribution of energy dissipation and the overall pressure-drop response. For gas–liquid cyclone separators, Ghasemi et al. [22] proposed a numerical optimization scheme and showed that separator performance is highly sensitive to inlet geometry, with inlet modifications typically affecting both inlet local losses and swirl establishment efficiency. For multi-inlet cyclones, Barua et al. [23] systematically assessed the effects of inlet height and width and found that inlet geometry not only changes local resistance but also significantly affects total pressure loss by modulating angular-momentum input and turbulence intensity. From the perspective of inlet–body synergy, Raeesi et al. [24] emphasized that inlet design should be evaluated within a holistic flow-organization framework in two-phase separation cyclones, because inlet parameters couple with main-body geometry and local-loss reduction must be aligned with global pressure-drop optimization. For axial-inlet hydrocyclones, Qiu et al. [25] reported that axial-inlet structural parameters directly control swirl formation and internal flow distribution, implying higher sensitivity and potentially larger design benefits for inlet optimization in this configuration. Consistently, Xiong et al. [26] revealed interaction effects between inlet velocity and apex diameter, indicating that inlet optimization should be assessed jointly with key geometric parameters. In studies of miniaturized gas–liquid cyclones, Dehnavi and Adelpour [27] showed that, at small scales, inlets and local structures become more dominant in determining performance and pressure loss, and optimization benefits depend more strongly on parameter matching. In addition, Chen et al. [28] proposed an optimized overflow-slit structure and validated its effectiveness through experiments and numerical analyses, demonstrating the feasibility of controlling pressure loss by reconstructing near-inlet flow paths and redistributing high-dissipation regions via localized structural redesign. Overall, inlet-oriented pressure-drop reduction mechanisms can generally be summarized into two pathways: (i) directly reducing the inlet local loss coefficient; and (ii) promoting rapid formation of the swirling field to reduce dissipation in the main section. However, the benefit of different inlet schemes is highly sensitive to parameter combinations and operating ranges, and thus should be integrated with a pressure-drop theoretical model to enable an interpretable design and optimization methodology. The key findings and reported pressure-loss mechanisms from the above studies are summarized in Appendix A.

Based on the above research status, this study is motivated by hydraulic oil deaeration applications. To promote rapid swirl establishment, the conventional straight tangential inlet provides a strong tangential velocity at the entrance, which leads to a considerable inlet-related pressure loss. This local inlet pressure loss is particularly in hydraulic systems, where the high viscosity of hydraulic oil amplifies system backpressure and increases system energy consumption. Nevertheless, quantitative design guidance that links inlet geometry to inlet-related pressure loss remains limited for hydraulic oil degassing. In this context, we develop a pressure-loss model that accounts for the inlet-duct geometry and propose a contracting guided inlet segment, aiming to mitigate the inlet local-loss mechanism without modifying the cyclone main-body geometry, while preserving stable swirl establishment. The proposed design is validated by simulations and pressure-loss experiments.

2. Materials and Methods

2.1. Cyclone Separator Structure

The gas–liquid cyclone separator primarily consists of an overflow pipe, tangential inlet, vortex chamber, conical section, and underflow pipe. A schematic of the internal and outer swirling flow patterns in the straight tangential multi-inlet cyclone separator is shown in Figure 1.

The gas–liquid cyclone separator was designed based on the target working conditions. Considering the operating conditions of the hydraulic system, the continuous hydraulic oil phase is treated as incompressible under the investigated temperature and pressure range. Therefore, the operating condition is specified by the volumetric flow rate, consistent with common hydraulic practice. The dispersed gas phase is characterized by the prescribed inlet gas volume fraction, and an equivalent mass-flow representation can be obtained by density conversion without affecting the pressure-loss trends. Based on typical hydraulic operating conditions, the rated volumetric flow rate was set to 20 L/min in this study. The inlet hydraulic diameter was determined using empirical correlations. The prototype separator adopts a multi-inlet configuration with straight tangential inlets arranged uniformly around the cylindrical section. A rectangular-inlet cross-section was selected as the baseline design. Previous studies have reported that rectangular inlets can enhance tangential-momentum input and strengthen the vortex, and can lead to improved separation performance [29]. However, rectangular inlets may also be associated with a higher inlet-related pressure loss, which motivates the inlet-loss reduction addressed in this study. The dimensions of the fluid domain in the gas–liquid cyclone separator are shown in Figure 2, and the structural parameters of the fluid-domain model are listed in

Table 1. Structural parameters of the straight tangential inlet cyclone separator.

Boundary Type	Numerical Size
Diameter of the vortex chamber D, mm	30
Width of the rectangular inlet b, mm	3
Height of the rectangular inlet h, mm	6
Diameter of the overflow pipe Don, mm	10
Diameter of the underflow pipe Ddown, mm	5
Length of the cylinder section Hcy/mm	16
Length of the upper conical section Hco1/mm	25
Length of the lower conical section Hco2/mm	60
Diameter at the intersection of the large and small conical sections Dco/mm	16

.

2.2. Inlet Pressure-Loss Model

2.2.1. Inlet Pressure-Loss Composition

The overall pressure loss of a cyclone separator can be decomposed into local structural losses and flow-induced dissipative losses. The dissipative losses are essential for maintaining separation performance and are therefore difficult to reduce directly through structural optimization. By contrast, the inlet local loss constitutes a major component of the cyclone pressure loss. The inlet structure is generally regarded as one of the most designable elements and one of the most pressure-drop-sensitive components. Accordingly, optimizing the inlet configuration can significantly reduce the overall pressure loss of the cyclone separator [30]. The composition of the pressure losses associated with the inlet section is illustrated in Figure 3.

For a conventional straight tangential inlet, the incoming fluid experiences intense impingement and friction as it enters the inlet duct, leading to a rapid change in the flow state. When the inlet passage is treated as a combination of a short straight duct and local fittings, the pressure loss from the inlet entrance to the location where the flow discharges into the cylindrical section of the cyclone chamber consists of: (i) the inlet-pipe linear loss, ΔP₁, and (ii) local losses in the transition zone between the inlet pipe and the main body, ΔP₂. In the development of the flow field of the cyclone, the sudden expansion imparts angular momentum to the incoming flow and facilitates rapid formation of the swirling field, which is important for separation. Therefore, to avoid significant adverse impact on the separation performance, the optimization is thus focused primarily on reducing the losses within the inlet pipe. This study mainly focuses on the impact of the inlet-pipe structure. Therefore, the inlet pipe linear loss, ΔP₁, is the primary optimization metric.

2.2.2. Straight Tangential Inlet

For the straight tangential inlet, the inlet passage can be idealized as a constant-cross-section rectangular short duct. Because the inlet duct is short under the installation constraints of hydraulic systems, the flow is typically hydrodynamically developing. The apparent-friction formulation based on short-duct/fully developed asymptotic blending is adopted. The pressure loss across the rectangular-inlet short duct is expressed as

$$∆P_{sc}=f_{Dsc}{\displaystyle \frac{L}{D_h}}{\displaystyle \frac{\rho u_{in}^2}{2}}$$

(1)

where $L$ is the length of the inlet passage, $D_h$ is the hydraulic diameter of the rectangular duct, $u_{in}$ is the cross-sectional mean velocity, $\rho$ is the density of the hydraulic oil, and ${f_D}_{sc}$ is the apparent Darcy friction factor accounting for hydrodynamic development. The hydraulic diameter of a rectangular duct $D_h$ is given by

$$D_h={\displaystyle \frac{2bh}{b+h}}$$

(2)

where $b$ and $h$ denote the width and height of the passage at section e, respectively.

For a straight tangential inlet, the inlet duct is a constant-cross-section rectangular channel. The mean velocity $u_{in}$ in the inlet passage is determined by the total volumetric flow rate and the number of inlets:

$$u_{in}={\displaystyle \frac{Q_{in}}{n{A}_e}}={\displaystyle \frac{Q_{in}}{nbh}}$$

(3)

The flow regime in the inlet passage can be identified with the Reynolds number as follows:

$$\mathrm{R}\mathrm{e}={\displaystyle \frac{\rho u_{in}{D}_h}{\mu }}$$

(4)

To quantify the developing-flow effect in a short duct, a dimensionless length is introduced:

$$L^{+}={\displaystyle \frac{L}{\mathrm{R}\mathrm{e}{D}_h}}$$

(5)

For fully developed laminar flow of an incompressible Newtonian fluid in a smooth, straight rectangular duct of constant cross-section, Shah and London [31] expressed the Poiseuille number as a function of the ratio of the shorter side to the longer side of the duct. In the present inlet duct, the ratio of the width $b$ and height $h$ is 0.5 based on Table 1. The flow in the inlet duct remains in the laminar regime under the investigated operating conditions, as indicated by the Reynolds number defined in Equation (4). Therefore, the $Po$ can be evaluated as

$$Po=24\left(1-1.3553{\displaystyle \frac{b}{h}}+1.9467{{\displaystyle \frac{b}{h}}}^2-1.7012{{\displaystyle \frac{b}{h}}}^3+0.9564{{\displaystyle \frac{b}{h}}}^4-0.2537{{\displaystyle \frac{b}{h}}}^5\right)$$

(6)

To simultaneously cover the short-pipe effect and the flow field development effect within the same framework, the asymptotic stitching idea proposed by Muzychka and Yovanovich was adopted [32]. The short-pipe limit and the fully developed flow field limit were combined. The calculation methods for both are as follows:

$${\left(f_F\mathrm{R}\mathrm{e}\right)}_{short}={\displaystyle \frac{3.44}{\sqrt{L^{+}}}},{\left(f_F\mathrm{R}\mathrm{e}\right)}_{fd}=Po$$

(7)

By substituting the inlet width b and height h into the correlation, $Po$ is obtained as approximately 15.56 and the friction factor ${f_D}_{sc}$ can be obtained as

$$f_{Dsc}={\displaystyle \frac{4}{\mathrm{R}\mathrm{e}}}{\left[{\left({\displaystyle \frac{3.44}{\sqrt{L^{+}}}}\right)}^n+15.56^n\right]}^{1/n}$$

(8)

where $n$ is the blending exponent and is usually set to 2 in engineering estimations.

Accordingly, the inlet-duct pressure-drop model for the straight tangential inlet can be written as

$$∆P_{sc}={\displaystyle \frac{2\mu L{u}_{in}}{D_h^2}}{\left[{\left({\displaystyle \frac{3.44}{\sqrt{L^{+}}}}\right)}^2+P{o}^2\right]}^{0.5}$$

(9)

2.2.3. Contracting Guided Inlet

The tapered inlet structure is shown in Figure 4. The tapered inlet pipeline is a rectangular pipeline with a single-sided contraction, and its cross-sectional area will change as the inlet pipeline develops.

Because the contracting inlet introduces a contraction angle $\alpha$, the inlet duct height remains constant while the inlet width gradually decreases along the streamwise direction. The inlet width at the entrance $b_0$ is given by

$$b_0=b+L\mathrm{t}\mathrm{a}\mathrm{n}\alpha$$

(10)

The inlet width is assumed to decrease linearly along the streamwise direction. With the entrance of inlet pipe taken as the origin and the contraction direction defined as the positive $\mathit{x}$-axis, the local width $b\left(x\right)$ is given by

$$b\left(x\right)=b_0-x\mathrm{t}\mathrm{a}\mathrm{n}\alpha$$

(11)

The local mean velocity $u\left(x\right)$ is

$$u\left(x\right)={\displaystyle \frac{Q\left(x\right)}{hb\left(x\right)}}$$

(12)

The hydraulic diameter $D_h\left(x\right)$ is

$$D_h\left(x\right)={\displaystyle \frac{2hb\left(x\right)}{h+b\left(x\right)}}$$

(13)

The local Reynolds number is defined by

$$\mathrm{R}\mathrm{e}\left(x\right)={\displaystyle \frac{\rho u\left(x\right)D_h\left(x\right)}{\mu }}$$

(14)

The dimensionless length based on the local flow condition is introduced as

$$L^{+}={\displaystyle \frac{L}{\mathrm{R}\mathrm{e}\left(x\right)D_h\left(x\right)}}$$

(15)

The short-pipe limit and the fully developed flow field limit can be modified as follows:

$${\left(f_F\mathrm{R}\mathrm{e}\right)}_{short,con}={\displaystyle \frac{3.44}{\sqrt{L^{+}\left(x\right)}}},{\left(f_F\mathrm{R}\mathrm{e}\right)}_{fd,con}=Po\left({\displaystyle \frac{b\left(x\right)}{h}}\right)$$

(16)

Based on Equation (9), the equivalent frictional loss within the inlet duct for the contracting inlet can be expressed as

$$∆P_{con}={\int }_0^L{\displaystyle \frac{2\mu u\left(x\right)}{D_h(x{)}^2}}{\left[{\left({\displaystyle \frac{3.44}{\sqrt{L^{+}\left(x\right)}}}\right)}^2+Po{\left({\displaystyle \frac{b\left(x\right)}{h}}\right)}^2\right]}^{0.5}dx$$

(17)

2.2.4. Inlet-Pipe Pressure Drop

To compare the inlet-pipe pressure loss between the contracting inlet and the straight tangential inlet, theoretical calculations were performed for the straight tangential inlet and for contracting inlets with different contraction angles, based on Equations (8) and (17). The results are compared in Figure 5.

Figure 5 shows the overall trend of the inlet-pipe pressure loss as a function of the contraction angle. It can be seen that the inlet-pipe pressure loss generally decreases with increasing contraction angle; however, the rate of reduction gradually diminishes, exhibiting a clear diminishing marginal return.

2.3. Numerical Simulation

2.3.1. Meshing

Three-dimensional models of the cyclone separators were constructed according to the structural configuration in Figure 2 and the parametric cases listed in Table 1. The meshes were generated using the Fluent Meshing module in ANSYS Workbench 2024R1. Local refinement was applied at the inlet, the overflow pipe, the underflow orifice and the junctions of different sections to better resolve strong gradients in pressure and velocity. The resulting mesh is illustrated in Figure 6.

A grid independence study was carried out to verify that the numerical results are not sensitive to mesh resolution. Three unstructured meshes with different global element sizes were generated: 1.00 mm (coarse mesh), 0.80 mm (medium mesh), and 0.64 mm (fine mesh). For all three meshes, the same meshing strategy was applied, and the computational domain and boundary conditions were kept identical.

Three representative quantities were selected as indicators of mesh sensitivity: (i) the area-weighted static pressure at the inlet, $p_{in}$, representing the overall pressure loss; (ii) the mixture volume flow rate at the overflow outlet, $Q_{mixo}$, characterizing the hydraulic split between the overflow and underflow; and (iii) the domain-averaged gas volume fraction, $a_g$, representing the overall gas content in the separator. The mesh parameters and the corresponding values of these quantities are listed in

Table 2. Grid independence verification.

Serial	Global Element Size h/mm	Total Cells N	${\mathit{p}}_{\mathit{i}\mathit{n}}$/Pa	${\mathit{Q}}_{\mathit{m}\mathit{i}\mathit{x}\mathit{o}}$/m3/s	${\mathit{a}}_{\mathit{g}}$/−
1	1	294,595	30,993.93	$2.65456\times 10^{-4}$	0.07193
2	0.8	496,942	31,254.74	$2.65217\times 10^{-4}$	0.07226
3	0.64	844,541	31,684.96	$2.65443\times 10^{-4}$	0.07218

.

When the mesh is refined from 1.00 mm to 0.80 mm, the inlet-averaged pressure and the domain-averaged gas volume fraction change by about 0.83% and 0.46%, respectively. Meanwhile, the mixture volume flow rate at the overflow outlet varies by only 0.09%, indicating that the overflow hydraulic throughput is already weakly dependent on the mesh. Further refinement from 0.80 mm to 0.64 mm reduces the differences between the two meshes to 1.36% for the inlet pressure, 0.11% for the gas volume fraction, and 0.09% for the overflow mixture flow rate. Overall, the monitored quantities show a consistent convergence behavior with mesh refinement.

To quantify the remaining discretization error, the Grid Convergence Index (GCI) was evaluated between the fine and medium meshes [33]. The refinement ratios are $r_{12}=r_{23}=1.25$ between the fine, medium and coarse meshes. For the GCI evaluation, the ratio $r_{23}$ was used. Considering that the inlet-duct flow is laminar and its pressure loss is dominated by viscous friction, the convection terms were discretized using a first-order upwind scheme. The first-order spatial accuracy $p=1$ was adopted in the GCI calculation to provide a conservative estimate of the numerical uncertainty. The safety factor $F_S=1.25$ was adopted. For a generic monitored quantity $\varphi$, the GCI between the fine (${\varphi }_3$) and medium (${\varphi }_2$) meshes is defined as

$$\mathrm{G}\mathrm{C}{\mathrm{I}}_{23}=F_S{\displaystyle \frac{\left|{\varphi }_3-{\varphi }_2\right|}{{\varphi }_3\left(r_{23}^p-1\right)}}$$

(18)

The relative differences between two successive meshes were computed as

$${∆}_{12}={\displaystyle \frac{\left|{\varphi }_1-{\varphi }_2\right|}{\left|{\varphi }_2\right|}}\times 100\%$$

(19)

$${∆}_{23}={\displaystyle \frac{\left|{\varphi }_2-{\varphi }_3\right|}{\left|{\varphi }_3\right|}}\times 100\%$$

(20)

On this basis, the relative differences between grids and the GCI values for the three monitored quantities are summarized in

Table 3. Relative differences between grids and Grid Convergence Index (GCI) between the fine and medium meshes.

Quantity	${∆}_{12}$	${∆}_{23}$	GCI
$p_{in}$	0.83	1.36	6.8
$Q_{mixo}$	0.09	0.09	0.45
$a_g$	0.46	0.11	0.55

.

The GCI values are approximately 0.25% for the domain-averaged gas volume fraction, 3.02% for the inlet-averaged pressure, and 0.19% for the overflow mixture volume flow rate. These results indicate that the medium mesh with a global element size of 0.80 mm already provides solutions sufficiently close to those of the fine mesh, especially for the overflow hydraulic throughput and the overall gas content, while maintaining a substantially lower computational cost. Therefore, the 0.80 mm mesh was used in all subsequent simulations as a compromise between numerical accuracy and computational efficiency.

To ensure adequate near-wall resolution, boundary-layer inflation was applied to all wall boundaries using a smooth-transition scheme. Specifically, five inflation layers were generated with a growth rate of 1.2, and the inflation was restricted to wall surfaces only to maintain mesh quality in the core flow region. This near-wall refinement strategy was designed to be compatible with the enhanced wall treatment (EWT) adopted in the turbulence modeling. For the selected mesh, the area-weighted average wall y+ on the body surface is approximately 0.36, with a maximum of about 1.23 and a minimum of about 0.02, indicating that the first-cell height provides sufficient resolution within the viscous sublayer for the present simulations.

2.3.2. Mathematical Model

In this study, the swirling gas–liquid two-phase flow in the cyclone separator was simulated using ANSYS Fluent 2024R1. Considering that the hydraulic oil contains a non-negligible amount of dispersed gas and the gas phase is distributed throughout the domain, the Eulerian–Eulerian multiphase model was adopted to describe the interpenetrating continua of the liquid and gas phases. This formulation solves the phase volume fraction field and the corresponding phase-averaged conservation equations, making it suitable for predicting statistically steady macroscopic flow characteristics and pressure-drop performance in gas–liquid cyclone separators. The gas content in the present hydraulic oil is 10% and the dispersed gas is distributed throughout the oil, which is well suited to the Eulerian–Eulerian model [34]. Compared with the interface-resolving methods that are more conducive to analyzing the flow state of multiphase flow cross-sections and the Euler–Lagrange method for tracking the trajectory of bubbles, this study focuses more on predicting the stable pressure-drop characteristics and macroscopic phase distribution under statistically steady conditions, rather than tracking the trajectory of individual bubbles. For these reasons, the Eulerian–Eulerian approach was adopted in this work.

Within the Reynolds-averaged Navier–Stokes (RANS) framework, the continuity and momentum equations for the mixture flow can be written in a standard form as

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_i\right)}{\partial x_i}}=0$$

(21)

$${\displaystyle \frac{\partial \left(\rho U_i\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_i{U}_j\right)}{\partial x_j}}=-{\displaystyle \frac{\partial P}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\mu \left({\displaystyle \frac{\partial U_i}{\partial x_j}}+{\displaystyle \frac{\partial U_j}{\partial x_i}}\right)\right]-{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)$$

(22)

where $U_i$ is the mean velocity component, $P$ is the mean pressure, and $\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ is the Reynolds stress tensor.

The flow inside cyclone separators is characterized by strong swirl, pronounced streamline curvature, and turbulence anisotropy. Under such conditions, the Reynolds Stress Model (RSM) is widely adopted in CFD studies of cyclone separators and is generally considered more appropriate than isotropic eddy-viscosity closures, because it directly solves transport equations for the Reynolds stresses and can better represent anisotropic turbulence and swirl-dominated vortex structures [14,15]. Other two-equation eddy-viscosity RANS models including the standard k-ε model and re-normalization group k-ε model assume isotropic turbulence and may be less reliable for strongly swirling flows with pronounced anisotropy, which has been compared in previous research [14]. Large-eddy simulation can resolve more unsteady structures but requires transient simulations and substantially higher mesh and time-step requirements, which is not economical for the present multi-case parametric study focused on mean pressure drop. Therefore, the steady RANS framework with RSM was selected as a balance between modeling fidelity and computational cost.

A representative transport equation for the Reynolds stresses $\overline{u_i^{\prime }{u}_j^{\prime }}$ is written as

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)+{\displaystyle \frac{\partial }{\partial x_k}}\left(\rho U_k\overline{u_i^{\prime }{u}_j^{\prime }}\right)=P_{ij}+{\mathsf{\Phi }}_{ij}-{\epsilon }_{ij}+{\displaystyle \frac{\partial }{\partial x_k}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_R}}\right){\displaystyle \frac{\partial \overline{u_i^{\prime }{u}_j^{\prime }}}{\partial x_k}}\right]$$

(23)

where $P_{ij}$ is the production term, ${\mathsf{\Phi }}_{ij}$ is the pressure–strain term, ${\epsilon }_{ij}$ is the dissipation tensor, and the last term represents the combined molecular and turbulent diffusion. The production term is commonly expressed as

$$P_{\mathit{i}\mathit{j}}=-\rho \left(\overline{u_i^{\prime }{u}_k^{\prime }}{\displaystyle \frac{\partial U_j}{\partial x_k}}+\overline{u_j^{\prime }{u}_k^{\prime }}{\displaystyle \frac{\partial U_i}{\partial x_k}}\right)$$

(24)

For engineering applications, the dissipation tensor is often approximated as isotropic:

$${\epsilon }_{ij}={\displaystyle \frac{2}{3}}\rho \epsilon {\delta }_{ij}$$

(25)

In the present simulations, the linear pressure–strain formulation was adopted to close ${\mathsf{\Phi }}_{ij}$. In addition, the wall-reflection effect was activated to improve the near-wall stress redistribution in rotating and swirling flows.

The dissipation rate $\epsilon$ was obtained from a standard transport equation:

$${\displaystyle \frac{\partial \left(\rho \epsilon \right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho U_k\epsilon \right)}{\partial x_k}}={\displaystyle \frac{\partial }{\partial x_k}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_k}}\right]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{P}_k-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}$$

(26)

where $k=\overline{u_i^{\prime }{u}_i^{\prime }}/2$ and $P_k$ denotes the production of turbulent kinetic energy. The detailed numerical schemes, boundary conditions, and solver settings are provided in Section 2.3.3.

2.3.3. Boundary Conditions and Solver Setting

As described in Section 2.3.2, this study employed the RSM to conduct steady-state simulation for turbulence closure and the Eulerian–Eulerian approach for gas–liquid two-phase flow. The flow was assumed to be incompressible and isothermal, and heat transfer between the fluid and the wall was neglected. Wall boundaries were treated as no-slip walls. The pressure–velocity coupling was handled by the Phase-Coupled SIMPLE algorithm. Gradients were computed using the least-squares cell-based method. To ensure numerical stability under the conditions of two-phase strong swirling flow, the pressure term is discretized using a second-order scheme, while the convective terms in the momentum, volume fraction, turbulent kinetic energy, dissipation rate and Reynolds stress transport equations are discretized using a first-order upwind scheme. The near-wall region was resolved using enhanced wall treatment (EWT). A velocity inlet was specified at the inlet, and both the overflow and underflow outlets were set as pressure outlets with a gauge pressure of 0 Pa. Convergence was assessed using both scaled residuals and monitored integral quantities. The scaled residual target was set to 1 × 10⁻⁵ for the governing equations, which is a widely adopted tolerance for steady Reynolds-averaged simulations of internal flows. In addition to residuals, the iteration was continued until the monitored pressure drop between the inlet and outlets and the outlet flow rates became stable, and the overall mass imbalance was sufficiently small. Besides the typical viscosity condition of hydraulic oil, supplementary simulations at 293.15 K were conducted to reflect the experimental ambient conditions and to strengthen the scientific validity of the measurement–simulation comparison. The main operating conditions and numerical settings are summarized in

Table 4. Numerical parameters of the simulation.

Parameter	Value
Hydraulic oil type	No. 46 hydraulic oil
Temperature, K	313.15, 293.15
Density, kg/m3	850
Dynamic viscosity (313.15 K), Pa·s	0.0391
Dynamic viscosity (293.15 K), Pa·s	0.106
Gravity acceleration, m/s2	9.81
Gas content	10%

.

2.3.4. Case Matrix

In Section 2.2.3, the inlet-pipe pressure losses of the straight inlet and the tapered inlet were compared. Considering the diminishing-return characteristic of pressure-loss reduction with increasing contraction angle, five representative angles (7°, 9°, 11°, 13°, and 15°) were selected for the simulation case matrix. These cases were used to examine the consistency between the theoretical trend and the numerical predictions and to identify a reasonable contraction-angle range for subsequent optimization. The groups are shown in

Table 5. Simulation groups.

Group	Contraction Angle
1	0°
2	7°
3	9°
4	11°
5	13°
6	15°

.

Based on the selected representative angle and the baseline straight inlet, additional simulations were conducted over multiple flow-rate conditions to cover the operating range of the experimental test rig. Furthermore, to eliminate the potential interference of inlet cross-sectional variation and to quantify geometric sensitivity, one-factor perturbation analyses were performed for the inlet width and inlet height under the representative contraction-angle condition. This case design provides a structured basis for the subsequent result interpretation and inlet-structure optimization.

2.4. Pressure-Loss Test Rig

Due to the small structural dimensions of the gas–liquid cyclone separator, the experimental model was fabricated by hollowing out acrylic blocks. This design facilitates the observation of the gas–liquid phase distribution within the separator and aids in validating the numerical simulation results of the internal flow field. In the present study, two physical prototypes were manufactured and tested, including a baseline straight tangential inlet and a tapered inlet with a contraction angle of 11°. Other angles were evaluated numerically, and the 11° configuration was selected for fabrication based on the combined consideration of pressure-drop reduction and flow field constraints discussed in Section 3. The experimental model, secured with bolts and nuts, features sealing rings placed in the annular groove between the two acrylic blocks for sealing purposes. The inlet modules are shown in Figure 7 and the cyclone separator prototype is shown in Figure 8.

The pressure-loss testing platform for the gas–liquid cyclone includes a three-phase asynchronous motor, pressure sensors, a hydraulic oil tank, an air pump, a system control valve group, a flowmeter, and the test prototype. The system schematic diagram of the testing platform is shown in Figure 9.

The components corresponding to the labels in Figure 9 are as follows:

1.

Three-phase asynchronous motor,

2.

Axial piston variable pump,

3.

Relief valve,

4.

Flowmeter,

5.

Air source,

6.

Pressure sensors,

6.1.

Pressure sensor,

6.2.

Pressure sensor,

7.

Cyclone test prototype,

8.

Throttle valve,

9.

Filter,

10.

Hydraulic oil tank.

Pressure sensors were connected to the inlet and outlet of the cyclone separator prototype to collect pressure data. The pressure sensors can display the pressure loss of the oil cyclone separator, and the installation positions of the pressure sensors are shown in Figure 10. A throttle valve was used to regulate the system flow rate, and a filter was employed to remove solid contaminants. In this study, the pressure loss $∆P$ was defined as the differential pressure between the pressure tap upstream of the inlet duct and the pressure tap at the underflow orifice, thereby representing the total pressure loss of the cyclone prototype under a given operating condition. A differential-pressure transmitter (XSENR/PCM series, model PCM950, Suzhou Xuansheng Instument Technology Co., Ltd., Taicang, China) was used for pressure-drop measurement, with a full-scale range of 0–3 MPa and an accuracy grade of 0.075%. The pressure signal was recorded by a data-acquisition unit at 20 Hz.

The gas–liquid cyclone separator prototype was connected to the test system. Pres-sure sensors were connected to the inlet and outlet of the cyclone separator, and the device was started with the overflow valve fully open. The overflow valve was adjusted to set the flowmeter reading to the rated flow rate of 20 L/min. The pressure signal was sampled at 20 Hz and time-averaged over a 1 min steady window. The reported value corresponds to the averaged reading. The tapered inlet block was then replaced, and the above procedure was repeated. Before data logging, the system was allowed to reach a steady state, judged by stabilized readings of both the flow rate and differential pressure. To improve repeatability, each operating condition was measured three times and the mean value was reported.

To validate the accuracy of the simulation model, the pressure difference signals of the gas–liquid cyclone separator with a tapered inlet were collected separately by varying the flow rate of the cyclone separator prototype. When the flow rate was 20 L/min, the flowmeter reading was 1.2 m³/h. Additional tests were conducted at flowmeter readings of 1.1, 1.3, 1.4, and 1.5 m³/h, resulting in five flow-rate points (1.1–1.5 m³/h) in total.

3. Results and Discussion

3.1. Experimental Validation of the Simulation Model

The 11° inlet was selected as a representative prototype design, and the selection rationale is discussed later in Section 3.2.1. Experimental validation was conducted for the cyclone separator equipped with a contracting inlet of 11° under multiple flow-rate conditions, with the flow rate ranging from 1.1 to 1.5 m³/h. Because the pressure loss inside the inlet duct was difficult to measure directly, the overall pressure loss of the cyclone separator was used to provide an indirect validation of the numerical predictions. The oil temperature was maintained at 20 °C to match the ambient conditions. After eliminating external influences introduced by the test-rig connectors, the measured overall pressure loss is denoted as $∆P_T$, while the numerically predicted overall pressure loss is denoted as $∆P_S$. The comparison between experiments and simulations is shown in Figure 11.

As shown in Figure 11, the overall pressure loss increases monotonically with flow rate for both inlet configurations, indicating enhanced energy dissipation under higher momentum input. For the 11° contraction guided inlet, the experimentally measured overall pressure loss rises from 38.97 kPa at 1.1 m³/h to 47.15 kPa at 1.5 m³/h. In comparison, the straight tangential inlet consistently exhibits a heavier pressure loss over the entire flow-rate range, demonstrating the effectiveness of the contracting inlet in reducing system-level hydraulic losses. Simulation predictions reproduce the same monotonic trends for both configurations and capture the relative ranking between the two inlets, suggesting that the numerical model is able to describe the pressure-drop evolution of the tested representative design. Notably, the discrepancy between experiments and simulations is more pronounced at the lower flow rates and decreases as the flow rate increases, implying that measurement uncertainty and unmodeled losses become less influential under higher-flow conditions.

To quantify the discrepancy, the relative error is defined as

$$\epsilon ={\displaystyle \frac{\left|∆P_T-∆P_S\right|}{∆P_T}}\times 100\%$$

(27)

The simulated and experimental overall pressure loss and the corresponding relative errors at each flow rate are summarized in

Table 6. Comparison between experimental and simulated overall pressure loss for the straight tangential inlet and the 11° contracting inlet at 20 °C.

Contraction Angle/Deg	Flow Rate/m3/h	$∆{\mathit{P}}_{\mathit{S}}$/kPa	$∆{\mathit{P}}_{\mathit{T}}$/kPa	$\mathit{\epsilon }$/%
0	1.1	44.38	58.27	23.84
	1.2	46.56	58.71	20.69
	1.3	57.05	64.8	11.96
	1.4	64.03	66.85	4.22
	1.5	71.34	74.57	4.33
11	1.1	30.48	39.99	23.78
	1.2	35.6	39.62	10.15
	1.3	40.48	44.22	8.46
	1.4	46.35	45.51	1.85
	1.5	51.92	50.98	1.84

.

As shown in Table 6, for the 11° contraction inlet, as the flow rate increases, the relative error significantly decreases. At the low-flow-rate end of 1.1 m³/h, the simulation results underestimated the overall pressure loss, and the relative error reached 23.78%. The difference between the experimental results and the simulation results, in the low-speed zone, may mainly be attributed to the following three factors. Firstly, the full-scale range of the differential-pressure transmitter used and the pressure loss at low flow rates may not match well, and the actual pressure loss operates near the lower limit of the sensor range, increasing the measurement uncertainty. Secondly, the wall friction related to swirl and the local losses of the connection components in the low-flow-rate region contribute more significantly compared to those in the swirl chamber. Thirdly, the turbulence model has a good predictive effect on the swirl state. Meanwhile, in the transition region from the inlet to the main body under low-momentum conditions, it may over-predict the attenuation of the swirl intensity, leading to an underestimation of the total pressure loss. Correspondingly, when the flow rate increases, the dominant role of inertial force increases, and the working range of the sensor becomes more precise, resulting in the relative error rapidly decreasing to below 2%. Despite these deviations, the simulations reproduce the monotonic increase in pressure loss with flow rate and correctly capture the relative level of pressure loss, supporting the applicability of the numerical model for analyzing the pressure-drop characteristics of the inlet configuration.

3.2. Simulation Result

3.2.1. Pressure-Loss Characteristics

(1)

Effect of Contraction Angle

The inlet-pipe pressure loss as a function of contraction angle under the rated flow condition is shown in Figure 12.

Figure 12 presents a comparison of the inlet-pipe pressure loss derived from the theoretical model (Equations (9) and (17)) and the simulations across different contraction angles. As shown in the figure, a high degree of consistency is observed between the theoretical predictions and the numerical results, suggesting the reliability of the established mathematical model. Both curves exhibit a monotonic decrease in pressure loss with increasing contraction angle, featuring a distinct diminishing-returns behavior. The reduction is most pronounced in the initial small-angle range, after which the slope gradually flattens. Quantitatively, the pressure loss decreases from 11.58 kPa at 0° to 7.05 kPa at 15°, corresponding to a reduction of 39.2% relative to the baseline. Notably, the theoretical model accurately captures this trend, with the deviation between theory and simulation remaining small across the investigated range. The steep drop when increasing the angle from 0° to 11° yields a significant reduction of approximately 7.4 kPa, whereas a further increase from 11° to 15° yields only a marginal benefit of 0.64 kPa. This strong agreement between theory and simulation confirms that 11° represents a critical inflection point for design optimization.

To further interpret the pressure-loss reduction mechanism in the inlet duct, the mid-height top-view contours of mixture static pressure and the corresponding pressure-gradient magnitude are compared across different contraction angles, as shown in Figure 13 and Figure 14, where a unified scale is used for each figure to ensure visual comparability.

As shown in Figure 13, the straight tangential inlet (0°) exhibits a localized high-static-pressure region near the inlet turning and near-wall transition zone, accompanied by a steep-pressure-gradient band. With increasing contraction angle (7–11°), the pressure transition becomes more gradual and spatially extended, and the extent of localized high-gradient regions is reduced. When the angle is further increased to 13–15°, the changes in the pressure-gradient distribution become less pronounced. To provide a more discriminative visualization of the inlet-duct loss-concentration behavior, the magnitude of the static-pressure gradient is further compared for different contraction angles, as shown in Figure 14, where a unified scale is used for direct visual comparison.

As shown in Figure 14, the straight tangential inlet exhibits concentrated high-pressure-gradient regions in the inlet duct, especially near the turning and near-wall transition zone, indicating a sharp spatial pressure variation that is typically associated with strong local acceleration, shear, and near-wall dissipation. With increasing contraction angle from 7 degrees to 11 degrees, the high-gradient regions are weakened and become more spatially distributed along the duct, suggesting that the pressure recovery and momentum redistribution occur more gradually rather than being concentrated in a short region. When the contraction angle further increases from 13 degrees to 15 degrees, the overall pattern changes only marginally, which is consistent with the diminishing-return behavior in inlet-pipe pressure loss indicated in Figure 12. In combination with Figure 13, Figure 14 provides a clearer mechanistic interpretation that the contracting guided inlet reduces inlet-pipe pressure loss mainly by suppressing localized high-pressure-gradient concentrations within the inlet duct, thereby mitigating inlet-induced non-uniformity and associated hydraulic dissipation.

(2)

Volume Flow Impact Analysis

Based on the angle-sweep results, 11° was selected as a representative contraction angle and compared with the 0° inlet under five flow rates ranging from 1.1 to 1.5 m³/h. The inlet-pipe pressure loss increases monotonically with flow rate for both inlet configurations, while the 11° inlet remains consistently lower across the investigated operating range.

The top-view static-pressure contours for the two inlet configurations at different flow rates are shown in Figure 15.

As shown in Figure 15, increasing the flow rate strengthens the pressure gradients in the inlet duct for both configurations. Under the same flow rate, the 0° inlet exhibits a more localized high-pressure region and steeper pressure gradients near the inlet turning zone, whereas the 11° inlet maintains a smoother pressure transition and a reduced extent of localized high-gradient regions, indicating moderated inlet-induced pressure non-uniformity. To further clarify the inlet-duct loss-reduction mechanism from a three-dimensional flow-organization perspective, the velocity-vector fields of the straight tangential inlet and the 11° contracting guided inlet are compared in Figure 16.

As shown in Figure 16, the straight tangential inlet presents a more abrupt reorientation of the incoming flow near the inlet–chamber transition, where the velocity vectors exhibit a stronger transverse component and a less uniform directional adjustment process. This behavior implies that the momentum redistribution is concentrated in a short region, which tends to promote local shear enhancement and contributes to the formation of steep-pressure-gradient concentrations in the inlet duct. By contrast, the 11° contracting guided inlet introduces a progressive geometric constraint that guides the flow direction more gradually toward the intended tangential entry direction. The enlarged view shows a smoother vector alignment and a more distributed reorientation process along the inlet duct, which is consistent with the weakened high-gradient regions observed in Figure 15. Therefore, Figure 16 provides a three-dimensional flow field explanation supporting that the inlet-pipe pressure-loss reduction is achieved mainly through controlled flow guidance and moderated momentum adjustment within the inlet duct.

Figure 17 compares the inlet-duct pressure loss obtained from the theoretical inlet model and numerical simulation for the straight tangential inlet and the 11° contraction guided inlet.

As shown in Figure 17, for the 0° inlet, the inlet-pipe pressure loss obtained from the simulation increases from 10.37 kPa at 1.1 m³/h to 15.54 kPa at 1.5 m³/h, while the theoretical prediction increases from 10.05 kPa to 15.19 kPa over the same range. For the 11° inlet, the simulated inlet-pipe pressure loss increases from 3.28 kPa to 4.98 kPa, and the theoretical values show a consistent increase from 3.28 kPa to 4.98 kPa. The inlet-duct model is established using classical laminar rectangular-duct correlations as the fully developed reference limit and further incorporates a developing-flow correction for the short inlet pipe, as described in Section 2.2 [31,32]. Therefore, within the investigated operating range, the friction-dominated inlet-pipe component exhibits an approximately linear scaling with the volumetric flow rate. The relative reduction provided by the 11° inlet is therefore approximately 67–69% across the investigated flow-rate range, showing a slight decreasing trend as the flow rate increases, which indicates that additional inlet-loss contributions beyond wall friction become increasingly influential at higher flow rates, and the relative improvement is correspondingly weakened. Overall, the close agreement between the theoretical and simulated results in both magnitude and slope suggests that the inlet-duct model captures the dominant scaling of inlet pressure loss with flow rate for both inlet configurations.

3.2.2. Velocity Flow Field Analysis

(1)

Effect of Contraction Angle

To examine the influence of contraction angle on swirl establishment, the center-plane tangential-velocity contours under different contraction angles are compared in Figure 18.

As shown in Figure 18, the tangential-velocity field at Face II exhibits a typical swirl pattern, featuring an outer high-speed ring and an inner low-speed core. For the straight tangential inlet (0°), the outer high-speed band shows pronounced local intensification and intermittent patches near the inlet-merging region and the near-wall turning zone, accompanied by sharper velocity gradients. These features indicate a stronger azimuthal non-uniformity of tangential momentum at the inlet exit, which is unfavorable for establishing a circumferentially consistent main swirl in the cyclone chamber. With increasing contraction angle to 7°, 9°, and 11°, the circumferential continuity of the high-speed band is noticeably enhanced, the localized intensified patches are weakened, and the transition between the outer ring and the inner core becomes smoother. This suggests that the contracting transition promotes tangential-momentum redistribution prior to entering the cyclone chamber, thereby mitigating tangential-velocity distortion and facilitating a more stable swirl establishment.

To further quantify the flow field mechanism underlying the inlet-duct pressure-drop reduction, a statistical non-uniformity metric, namely tangential-velocity non-uniformity coefficient $C_V$, is introduced to characterize the relative dispersion of velocity on a cross-section, following common practices in quantitative assessments across multiple engineering fields [35,36]. For the tangential velocity at the terminal section B, the non-uniformity index is defined as

$$C_V={\displaystyle \frac{{\sigma }_{V_{\theta }}}{\overline{V_{\theta }}}}={\displaystyle \frac{\sqrt{\overline{V_{\theta }^2}-{\left(\overline{V_{\theta }}\right)}^2}}{\overline{V_{\theta }}}}$$

(28)

where $\overline{V_{\theta }}$ is the area-averaged tangential velocity at the terminal section and $\sigma$ is the corresponding standard deviation. The statistics of $C_V$ for different contraction angles are summarized in Figure 19.

As shown in Figure 19, the tangential-velocity non-uniformity coefficient $C_V$ decreases overall with increasing contraction angle, indicating an improvement in circumferential uniformity at the terminal section, consistent with the contour observations in Figure 15. Notably, the reduction in $C_V$ becomes marginal when the angle is further increased beyond approximately 13°, suggesting a plateauing tendency in tangential-velocity homogenization. Combined with the inlet-pipe pressure-loss results, these findings suggest that the contracting inlet mitigates tangential-velocity distortion near the inlet exit and promotes momentum redistribution prior to entering the cylinder section, thereby contributing to the reduced inlet-pipe pressure loss.

(2)

Volume Flow Impact Analysis

To assess the effect of flow-rate variation, additional comparisons were conducted for the 0° and 11° inlet configurations. The tangential-velocity contours in the inlet region at different flow rates are presented in Figure 20.

As shown in Figure 20, increasing flow rates lead to an overall increase in the tangential-velocity level for both inlet configurations. The intensity and spatial coverage of the peripheral high-speed band both increase, reflecting the direct role of increased inlet momentum input in promoting swirl establishment. Nevertheless, a persistent difference in the tangential-velocity distribution is observed between the two inlets across all flow-rate points. Specifically, the 11° contracting inlet consistently exhibits a more continuous annular high-speed band and a smoother velocity-gradient distribution, while the localized acceleration near the transition and turning region is comparatively attenuated. In contrast, the 0° inlet more readily develops coexisting localized intensification and attenuation regions, with more concentrated high-gradient zones, indicating that the tangential-velocity consistency is more sensitive to flow-rate variation.

From a mechanistic perspective, increasing flow rate strengthens inertial effects associated with the inlet jet and near-wall turning, thereby intensifying local velocity gradients. The contracting inlet provides a smoother geometric transition and facilitates tangential-momentum redistribution prior to entering the cyclone chamber, which helps maintain circumferential continuity of the high-speed band and mitigates the amplification of inlet-region velocity distortion under varying flow rates. This suggested that the contracting inlet can improve robustness of tangential-velocity distribution against flow-rate fluctuations. This observation is consistent with the pressure-drop results, indicating that the loss-suppression effect of the contracting inlet is not limited to a single rated condition but remains effective within a practical operating flow-rate range.

3.2.3. Gas Volume Fraction Distribution

Numerous studies have indicated that optimizing cyclone pressure-drop performance may adversely affect separation performance. To avoid excessive degradation of separation capability while reducing pressure loss using the contracting inlet, this section compares the gas volume fraction distributions among different contraction angles. The gas volume fraction contours for different contraction angles are shown in Figure 21.

As shown in Figure 21, for all contraction angles, gas preferentially accumulates in the upper region of the cyclone and near the overflow passage, forming a gas-rich zone, while the overall distribution pattern remains similar. With increasing contraction angle, the gas-rich region near the top cover becomes more pronounced, suggesting a weakened swirling effect and an enhanced short-circuit flow. This change is unfavorable for overall separation performance and indicates that the pressure-drop improvement achieved by the contracting inlet is accompanied by a certain penalty in separation-related flow features.

To provide a consistent quantitative assessment, corresponding to Figure 21, a threshold of 20% gas volume fraction was selected to define the gas-rich region, and the volume of gas-rich region was evaluated separately within the main body and within the overflow pipe. The gas-rich regions of overflow pipe and main body were extracted. Among them, the gas-rich region in the overflow pipe represents the gas accumulated within the discharge pathway and indicates the tendency of gas removal through the overflow. By contrast, a large gas-rich region in the main chamber reflects gas holdup that is not promptly evacuated, which may imply a potential deterioration in separation behavior. The variations in these gas-rich volumes with contraction angle are presented in Figure 22.

As shown in Figure 22, the gas-rich volume in the main body exhibits a slight overall increasing trend with increasing contraction angle. In conjunction with Figure 18, the increase in gas-rich volume in the main body does not fully correspond to the development of a central gas core; instead, part of the gas tends to accumulate near the top cover and becomes difficult to discharge. Regarding the overflow pipe, the straight tangential inlet shows the largest gas-rich volume inside the overflow pipe, indicating a stronger gas separation effect compared with the contracting-inlet cases. This further confirms that while the contracting inlet reduces the inlet-pipe pressure loss, it also induces a certain reduction in gas–liquid separation performance.

While the main objective of this study was to reduce pressure loss, the separation performance, as the core performance of the gas–liquid swirl separator, is an important consideration factor. It is worth noting that in the contraction inlet section, the volume of the gas-rich area of the overflow pipe at 11° is relatively high, which further indicates that its gas aggregation model has not significantly deteriorated. Combining previous theoretical predictions and simulation analyses, the benefit of significantly reducing pressure loss is considerable when ensuring a certain separation capacity. Further considering the analysis results of the non-uniformity coefficient of the tangential velocity, this angle can promote a more uniform and stable swirling field, achieving the goal of reducing energy consumption while ensuring the core separation function. Taking all these into account, 11° was selected as the optimized angle for experimental verification.

4. Conclusions

This study addressed the energy-loss issue of a cylindrical–conical gas–liquid cyclone separator for hydraulic applications by targeting the inlet duct as the primary optimization object. A contracting guided inlet was proposed and an inlet-pipe pressure-loss model was established. Through a contraction-angle sweep, multi-flow-rate simulations, and prototype tests, the pressure-loss reduction effectiveness and its dependence on operating conditions were systematically evaluated. The main conclusions are as follows.

• The contracting guided inlet effectively reduces the inlet-related pressure loss. The pressure loss decreases overall as the contraction angle increases, while the marginal benefit diminishes at larger angles. In the experiments, the 11° configuration reduces the overall pressure loss by 18.28–23.59 kPa over the flow-rate range from 1.1 m³/h to 1.5 m³/h, corresponding to a reduction of 31.37–32.52% relative to the straight tangential inlet.
• Considering pressure-loss reduction and flow field constraints, a contraction angle of 11° was selected as the representative design for detailed operating-condition verification and prototype testing. Among the investigated contraction-angle cases, the 11° configuration achieves a pronounced pressure-loss reduction while maintaining acceptable gas-phase distribution characteristics, and therefore serves as a suitable representative design for multi-flow-rate comparisons and experimental validation.
• The multi-flow-rate tests show that the overall pressure loss increases monotonically with flow rate, and the simulations reproduce the same trend. For the 11° inlet, the relative error decreases from 23.78% at 1.1 m³/h to below 2% at 1.4–1.5 m³/h. For the straight tangential inlet, the relative error decreases from 23.84% at 1.1 m³/h to about 4.22–4.33% at 1.4–1.5 m³/h, which supports the applicability of the numerical approach for capturing the pressure-drop evolution across the investigated flow-rate range.
• An engineering implication is that inlet-structure optimization should be guided by a combined criterion that includes pressure-loss reduction, the diminishing-return knee behavior, and flow field constraints. Optimization should not rely solely on increasing the contraction angle, because an overly large angle may yield limited additional pressure-loss reduction and increase the risk of unfavorable flow structures.

Future work can be extended in two directions. One direction is to conduct a coupled evaluation and optimization of pressure loss and separation performance by introducing short-circuit-flow intensity and gas-phase distribution metrics as constraints, thereby developing more general inlet-design guidelines. The other direction is to expand the validation range and geometric combinations to cover different oil viscosities and inlet gas volume fractions, and to supplement direct or indirect measurements of inlet-duct local losses where feasible, so as to improve the transferability and engineering applicability of the model and conclusions.