Finite Element Analysis and Computational Fluid Dynamics for the Flow Control of a Non-Return Multi-Door Reflux Valve

Abstract

This paper presents a comprehensive analysis of a multi-door check valve using computational fluid dynamics (CFD) and finite element analysis (FEA) to evaluate flow performance under pressure test conditions, with an emphasis on its ability to prevent backflow. Check valves are essential components in various industries, ensuring fluid flow in one direction only while preventing reverse flow. The non-return multi-door reflux valve is increasingly preferred due to its superior backflow prevention, fluid control, and effective flow regulation. Rigorous testing under varying pressure conditions is essential to ensure that these valves perform optimally. This study uses CFD and FEA simulations to evaluate the structural integrity and flow characteristics of the valve, including pressure drop, flow velocity, backflow prevention effectiveness, and flow coefficient. A high-fidelity 3D model was created to simulate the valve’s behavior under various conditions, analyzing the effects of parameters such as the number of doors, their orientation, geometry, and operating conditions. The CFD results demonstrated a significant reduction in backflow and pressure drop across the valve. However, localized turbulence and flow separation near the valve doors, particularly under partially open conditions, have raised concerns about potential wear. The velocity profiles indicated a uniform distribution at full opening with laminar velocity profiles and minimal resistance to flow. The results of the FEA showed that the stresses induced by the fluid forces were below critical levels, with the highest stress concentrations observed around the hinge points of the valve doors. Although the valve structure remained intact under normal operating conditions, some areas may have required reinforcement to ensure long-term durability. Combined CFD and FEA analyses demonstrated that the valve effectively preserves system integrity, prevents backflow, and maintains consistent performance under various pressure and flow conditions. These findings provide valuable insights into design improvements, performance optimization, and enhancing the efficiency and reliability of reflux valve systems in industrial applications.

1. Introduction

Reflux valves are designed to allow fluid to flow in one direction while preventing reverse flow. Multi-door reflux valves are a subtype of these valves that consist of multiple hinged doors that pivot to regulate fluid flow, opening in response to forward flow and then closing when the flow reverses, preventing the backward movement of fluid, ensuring system integrity, safety, and effective fluid control. The design ensures a minimal pressure decrease while maintaining effective sealing. These valves play a vital role in preventing backflow and maintaining system efficiency, and their performance is heavily reliant on their internal geometry and fluid dynamics [1]. Due to its unique design and angled door position, a multi-door backflow valve exhibits superior flow characteristics, including maximum flow compared to other hinged disk valves. The doors’ airfoil design, similar to an airplane wing, minimizes flow resistance while providing stability in the fully open position. Traditionally, the design and optimization of reflux valves are based on experimental tests and empirical equations [2], but recent advancements in CFD and FEA offer a more detailed and efficient approach to studying and improving these valves [3].

The performance of multi-door reflux valves has been investigated by several researchers using experimental and computational methods. Each one of these experts discovered remarkably interesting and unique factors that affect the flow performance of a multi-door valve, as well as what needs to be adjusted on the valve to obtain effective outcomes when the multi-door non-return valves are in use.

Zeng et al. [1] established that the opening angle of the valve gates and the position of the valve in the pipeline greatly influence the flow performance of a three-gate reflux valve under various operating conditions using CFD analysis. Similarly, Chen et al. [4] used CFD models to evaluate the impact of adding additional doors to the valve, finding that this enlarged the flow area, further improved the flow performance of the valve, and decreased the risk of roughness and instability in the fluid motion. Additionally, Liu et al. [5] discovered that the operation of the valve is strongly dependent on the Reynolds number and fluid viscosity. The more the fluid denotes opposition to flow in the valve, the more significant the decrease in the flow coefficient, according to a numerical analysis of multi-door reflux valve at different flow rates and fluid viscosities. Using the CFD method on a four-door non-return valve with different door designs and structures, Song et al. [6] found that the valve’s door shape could improve its flow performance, and this outcome further improved flow characteristics when implementing certain structural shapes.

Researchers also focused on improving the flow performance of non-return multi-port reflux valves. Lee et al. [7] used a genetic algorithm to optimize the shape of a two-door check valve. The optimized valve demonstrated a higher flow coefficient and lower pressure drop compared to the original design, according to their findings. These studies collectively contribute to understanding and improving the performance of multi-door backflow valves. Finally, research reveals that the flow performance of a multi-door check valve can be influenced by various elements, including the number of doors, door geometry, opening angle, fluid characteristics, and Reynolds number. CFD numerical simulations provide important information on how multi-door reflux valves flow and aid in design optimization [8,9,10]. In a study by Ahmadi and Riasi [11], the flow performance of a multi-door reflux valve was evaluated using CFD simulations. The authors found that the valve’s flow coefficient (C_v) (which represents the flow capacity of the valve) increased with the number of doors and the valve’s opening angle. They also observed that the valve’s pressure drop decreased as the number of doors increased. The results of the study suggest that multi-door reflux valves can provide better flow performance than single-door valves.

Xu and Zhang [12] investigated the flow performance of a novel type of multi-door reflux valve with a variable opening angle. They found that these multi-door reflux valves were able to control the reflux flow rate more accurately than a conventional multi-door reflux valve, particularly at low flow rates. They also found that variable-opening-angle multi-door reflux valves had a lower pressure decrease than conventional multi-door reflux valves, which could improve their performance at higher flow rates. The numerical analysis of non-return multi-door reflux valve performance has been the focus of several studies. For instance, Zeng and Luo [13] used CFD to analyze the flow performance of a three-door reflux valve under various operating conditions. Their results showed that the valve’s performance was affected by the Reynolds number, opening angle, and the valve’s position in the pipeline. A more recent study by Li et al. [3] performed a comparative study of different numerical analysis techniques (CFD, FEA, and BEM (Boundary Element Method)) to analyze the flow performance of a multi-door reflux valve. They found that the accuracy and efficiency of the numerical techniques varied depending on the complexity of the valve geometry and the flow conditions.

All of the conducted research and analyses clearly show that a multi-door non-return valve’s flow performance is strongly controlled and influenced by several factors and elements on each design principle of the valve. In some cases, access to relevant data, such as detailed valve specifications, operational conditions, and performance metrics has been restricted and unavailable to researchers. Without data to guide valve specification and evaluation decisions, researchers continually face challenges related to process variation, undermining the credibility and generalizability of the conclusions drawn. Therefore, a prognostic solution is needed to address this predicament.

This research presents a numerical study of the flow performance of a non-return multi-door reflux valve, locally designed and constructed in South Africa at AVK Valves, to examine the effect of different valve configurations on flow distribution, with the aim of improving the efficiency and reliability of its design under various operating conditions. The methodology for analyzing the valve flow performance includes (i) the creation of a 3-dimensional model of the valve to accurately represent geometry and flow dynamics, (ii) employing the FEA to assess the mechanical stresses and structural integrity of the valve components under operational conditions, and (iii) Using CFD simulations to analyze the fluid (water) flow characteristics, pressure distribution, and potential flow issues within the valve.

The results of this investigation will shed light on the behavior and functionality of non-return multi-door reflux valves, helping to identify potential problem areas that could be addressed to improve its overall effectiveness and to develop a rapid decision tool for valve selection and design that will help manufacturers justify the cost of valve replacement, ultimately improving their systems’ efficiency and reliability.

The structural system being studied and the underlying presumptions are covered in Section 2. In Section 3, the valve flow characteristics are described. Section 4 offers a description of the CFD flow analysis for each specific set of parameters. Section 5 presents the valve’s flow performance results from CFD, while Section 6 is a general summary of flow characteristics and CFD results. This article concludes with viewpoints in Section 7.

2. Working Principle of Non-Return Multi-Door Reflux Valve

A multi-door reflux valve is a valve with multiple hinged doors that open and close depending on the direction of fluid flow. The valve consists of a centerpiece housing with multiple ports with moveable doors sealed to the seat surface. The valve design includes a top cover and shaft stops for the lower, middle, and upper doors. The doors are counterweight-loaded to close automatically when there is no flow or reverse flow direction. The angled position of the door is crucial to minimize flow resistance and minimize water column inversion. The off-center pivot of the angled doors counteracts the closing force, ensuring no slamming or minimal slamming depending on the speed of the column reversal. The valve provides simultaneous control of flow direction in multiple ports, making it useful in applications requiring the control or separation of multiple process streams. The valve design considers the threshold pressure required for door movement and closure. Regular maintenance is necessary for proper operation, including inspecting doors for wear, cleaning debris, and adjusting counterweight tension to maintain the desired opening and closing characteristics, as shown in Figure 1.

2.1. Structural Analysis

Structural analysis is primarily concerned with the prevention of yielding and brittle failure. Exceeding the yield strength can cause permanent deformation, which is unacceptable for applications as it would compromise the safety of the valve and irreversibly deform and damage all components of the valve. Therefore, all subsequent calculations of the margin of safety will be performed using the yield strength as a point of reference together with the ultimate tensile strength or fracture strength.

2.1.1. Valve Pressure Testing and Simulation Setup

Pressure testing is a vital aspect of ensuring the functionality and reliability of non-return multi-door reflux valves. The valve is constantly subjected to pressure differentials during its operational lifespan, and pressure testing is instrumental in verifying its structural integrity and performance durability. The ability of a valve to maintain its sealing capacity under various pressure conditions is crucial in preventing catastrophic failures in fluid systems. The FEA simulations aimed to identify potential areas of stress concentration, deformation, and failure points to ensure the valve’s reliability to withstand operational pressures and compliance with safety standards in real-world applications. The SolidWorks 2022 Simulation software is utilized for conducting the FEA pressure testing. The valve model, created with accurate geometrical and material properties, is meshed to ensure an optimal balance between accuracy and computational efficiency. Material properties, such as tensile strength, yield strength, and elasticity, are assigned based on the actual material used in the valve’s construction.

Figure 2 presents the procedure flow chart for the FEA simulation. It begins with the input data, which progresses through a series of essential steps. First, to analyze the flow performance of the valve using FEA, we must solve the governing equations that describe fluid flow and structural behavior, including the assumptions made during the analysis. Next, we define the valve’s structural geometry and material properties to accurately represent the entire system. Following this, we apply boundary conditions and loads that simulate real-world scenarios, enabling a thorough assessment of the structural response. The subsequent step involves mesh generation, which breaks down complex geometries into finite elements for analysis. Throughout the simulation, the FEA solver uses these inputs to generate output factors. Finally, post-processing is conducted to examine and interpret the results, focusing on deformation and induced stresses that could lead to valve failure.

• FEA Governing Equations

The FEA of a non-return multi-door reflux valve requires some computational effort and expertise but offers an advanced tool to determine stresses and strains within the fluctuating valve with significant accuracy compared to the real situation. The basic equations for FEA simulation are derived from the equations of solid mechanics and then expressed as three-dimensional Cartesian coordinates expressed in the following form [14].

$${\displaystyle \frac{\partial {\sigma }_{xx}}{\partial x}}+{\displaystyle \frac{\partial {\sigma }_{xy}}{\partial y}}+{\displaystyle \frac{\partial {\sigma }_{xz}}{\partial x}}+f_x=0$$

(1)

$${\displaystyle \frac{\partial {\sigma }_{yx}}{\partial x}}+{\displaystyle \frac{\partial {\sigma }_{yy}}{\partial y}}+{\displaystyle \frac{\partial {\sigma }_{yz}}{\partial x}}+f_y=0$$

(2)

$${\displaystyle \frac{\partial {\sigma }_{zx}}{\partial x}}+{\displaystyle \frac{\partial {\sigma }_{zy}}{\partial y}}+{\displaystyle \frac{\partial {\sigma }_{zz}}{\partial x}}+f_z=0$$

(3)

where σ_ij are the stress tensor components, f_x, f_y, and f_z are the vector components of the body force. To ensure that the deformation components are consistent and give rise to a continuous displacement field without overlap in the deformed material, the 3D material compatibility conditions for deformation are expressed as follows [15]:

$${\displaystyle \frac{{\partial }^2{\epsilon }_{xx}}{\partial y^2}}+{\displaystyle \frac{{\partial }^2{\epsilon }_{yy}}{\partial x^2}}=2{\displaystyle \frac{{\partial }^2{\epsilon }_{xy}}{\partial x\partial y}}$$

(4)

$${\displaystyle \frac{{\partial }^2{\epsilon }_{yy}}{\partial z^2}}+{\displaystyle \frac{{\partial }^2{\epsilon }_{zz}}{\partial y^2}}=2{\displaystyle \frac{{\partial }^2{\epsilon }_{yz}}{\partial y\partial z}}$$

(5)

$${\displaystyle \frac{{\partial }^2{\epsilon }_{zz}}{\partial x^2}}+{\displaystyle \frac{{\partial }^2{\epsilon }_{xx}}{\partial z^2}}=2{\displaystyle \frac{{\partial }^2{\epsilon }_{zx}}{\partial z\partial x}}$$

(6)

where ε_ij is the component of the strain tensor. For linearly elastic isotropic materials, the relationship is given as follows [16]:

$${\sigma }_{ij}=C_{ijkl}{\epsilon }_{kl}$$

(7)

For isotropic materials, the constitutive relation is simplified to the following:

$${\sigma }_{ij}=\lambda {\delta }_{ij}{\epsilon }_{kk}+2\mu {\epsilon }_{ij}$$

(8)

where C_ijkl is the fourth-order stiffness tensor, λ is the Lamé parameters, δ_ij is the Kronecker delta, which has a value of one when i = j and zero if i is not equal to j; ε_kk is the volumetric strain component and μ is the shear modulus.

$$\lambda ={\displaystyle \frac{E\nu }{\left(1+\nu \right)\left(1-2\nu \right)}}$$

(9)

$$\mu ={\displaystyle \frac{E\nu }{2\left(1+2\nu \right)}}$$

(10)

where E is the Young’s modulus, and $v$ is Poisson’s ratio. The FEA governing equations are described in the context of a mesh of finite elements. This means that the displacement field within an element is approximated by shape functions N_i and nodal displacements u_i at any point: x, y, and z. The displacement field u and the strain–displacement matrix B are employed to establish the strain component $\epsilon$ [15].

$$\mathrm{u}={\displaystyle \sum _{i=1}^n{N}_i}{\mathrm{u}}_i$$

(11)

$$\epsilon =B\mathrm{u}$$

(12)

Using the constitutive matrix D and the strain displacement matrix B, the stiffness matrix K_e can be formulated in the following form [17]:

$$K_e={\displaystyle {\int }_{V_e}{B}^{T}DBdV}$$

(13)

The stiffness matrices of each element are assembled into a global stiffness matrix K, and the global system of equations can be expressed as [18]:

$$K\mathrm{u}=f$$

(14)

where f is the global force vector.

• Geometry

The assumptions for FEA modeling are as follows: 1. the stress–strain relationship is assumed to remain within the elastic limit. 2. The valve material is homogeneous and isotropic. 3. The valve is fixed at the flanges, with all degrees of freedom constrained to prevent displacement. 4. Deformations do not change the original geometry of the valve during simulation. 5. The hydrostatic pressure is constant and applied uniformly during the simulation. 6. The applied pressure assumes ideal conditions, excluding any dynamic fluctuations.

The 3D CAD model of the non-return multi-door reflux valve is created by SolidWorks, representing the accurate geometry of the valve as shown in Figure 3a. The scenario involves a non-return multi-door reflux valve subjected to line pressure, similar to a Shell under Internal Pressure. The focus is on determining the wall thickness of the shell, crucial for safety. Following the ASME B16.34 standard [16], the minimum inside diameter for a DN1400 PN17.5 Valve body is specified as 1395 mm, but it is maintained at 1400 mm to comply with both standards and customer requirements. The design of the Inlet, Outlet, and Top flanges adheres to the ASME B16.5 standard. Equations from ASME B16.34 (Table VI–1) [18] are used to calculate the minimum wall thickness for a DN1400 PN17.5 valve for a diameter ranging from 100 < ID ≤ 1500:

$$t_m(PN17.5)=[(0.0163\times ID+4.7]\times 1.7=46.8\mathrm{mm}$$

(15)

where ID = 1400 mm is the actual inside diameter of the valve body. Therefore, the minimum wall thickness to be maintained as per ASME B16.34 is as follows:

$$T_s=t_m(PN17.5)+CA=50\mathrm{mm}$$

(16)

where CA = 3 mm is the corrosion allowance of 3.0 mm per side. The thickness of the body shell under internal pressure can be determined using the following formula [16]:

$$W_{bs}={\displaystyle \frac{1.7\times P\times ID}{S\times E-0.6\times P}}+CA=35.5\mathrm{mm}$$

(17)

where P = 3500 kPa is the maximum hydrostatic test pressure applied in the body, S = 258.3 MPa is the maximum allowable stress, and E = 1 is the joint efficiency of cylindrical shells.

• Boundary conditions

Appropriate boundary conditions are applied to simulate real-world scenarios. The valve is constrained at fixed points to represent its mounting points, and pressure loads are applied to simulate fluid pressure variations during operation. The simulation aims to capture the stress distribution, displacement, and deformation of the valve components under these conditions.

The valve body is fixed on both flange areas as depicted in Figure 3b,c because the valve flanges are fastened with the pipe flanges, thus all the degrees of freedom of the valve body are arrested.

• Material properties

The material properties in

Table 1. Material properties [18].

Properties	Value	Units
Material	Ductile Iron AS1831 Gr.450-10	-
Elastic modulus	169	GPa
Poisson’s ratio	0.28	-
Shear modulus	77	GPa
Mass density	7100	kgm−3
Tensile strength	450	MPa
Yield strength	310	MPa
Thermal coefficient	1.1 × 10−5	/K
Thermal conductivity	75	W/(m·K)
Specific heat	450	J/(kg·K)
Material damping ratio	206,800	-

such as tensile strength, yield strength, Poisson’s ratio, and modulus of elasticity are defined based on the actual material specifications used in the valve’s construction.

• Load application

The valve is subjected to a range of loading conditions, simulating different pressure scenarios encountered during operation. Pressure loads are incrementally applied to the internal surfaces of the valve body to simulate varying operational pressures. This included normal operating pressures, sudden pressure surges, and emergency shutdown pressures to assess the valve’s robustness under varying conditions. During the working condition of the valve, the maximum allowable working pressure of the fluid medium 1750 kPa acts as the load, but as per the standard specifications [19], during the hydrostatic body shell test, the load is calculated by multiplying the 20 °C working pressures by 2. Therefore, the hydrostatic test pressure of 3500 kPa is applied to the internals of the valve body housing, as shown in Figure 3d.

• Meshing application

As presented in Figure 3e,f, a meshing strategy is employed to discretize the geometry into smaller elements, ensuring an accurate representation of the valve’s complex structure. The mesh density is optimized to balance accuracy and computational efficiency.

Table 2. FEA meshing information [20,21].

Mesh Type	Solid Mesh
Mesher used	Blended curvature-based mesh
Jacobian points for high-quality mesh	16
Maximum element size	224.712 mm
Minimum element size	9.48611 mm
Mesh quality	High
Total nodes	958,226
Total elements	619,334
Maximum aspect ratio	126.28
Percentage of elements\with aspect ratio < 3	94.3
Percentage of elements\with aspect ratio > 10	0.67
Percentage of distorted elements	0
Number of distorted elements	0
Time to complete mesh (hh:mm:ss)	00:01:13

describes the specifications of the mesh types used in the finite element analysis of the valve structure. The curve-type meshing technique, which takes into account the geometry of curvatures, produces a network with smooth edges and precise appearances. Jacobian points serve as benchmarks to assess the quality of each element of the mesh. Although increasing the maximum element size can reduce computational costs, it can negatively impact accuracy. Conversely, the benefits of a smaller minimum element size include higher spatial resolution, allowing for a more detailed representation of fine features and accurate reproduction of geometric features within the domain.

2.1.2. Primary Result of Stress and Deformation Analysis

After applying the boundary conditions, a structural analysis was performed and the FEA pressure test results revealed several key findings, as shown in Figure 4a–d. The stress distribution across the valve body is analyzed, and high-stress concentrations are identified, particularly around critical areas such as hinges and sealing surfaces.

The maximum stress is 206 MPa on the valve inlet body and 103 MPa on the outlet body (Figure 4a,b). Deformation patterns under different pressure loads are observed in Figure 4c,d. Excessive deformation in specific regions indicates potential weaknesses or points of failure, but in this case, the maximum deformation is 0.413 mm on the valve inlet body and 0.391 mm on the valve outlet body, which is well within the safety limit (Figure 4c,d). The graphical representation of the arrows in Figure 3 provides a clear indication of where the pressures are applied and where the model is held in place, the red arrows indicate the uniformly distributed applied pressure, and the green arrows indicate a fixed-end constraint showing that the valve cannot move at these points.

3. Flow Characteristics

Analyzing the flow performance of non-return multi-door reflux valves is complex due to the dynamic nature of fluid flow and the intricate valve design. In this study, the valve flow coefficient and the valve loss coefficient are numerically estimated to evaluate the overall performance of the valve to understand how it behaves under different conditions, including varying flow rates and fluid properties. The minimum pressure needed to open the valves is calculated using first principles and system analysis. The system’s velocity is inputted into a CFD model to determine pressure loss across the valve. This pressure loss is then paired with the system volumetric flow rate to determine the valve flow coefficient, C_v, plotted against time. The valve flow coefficient and valve loss coefficient are numerically calculated to assess the valve’s performance under various conditions, including flow rates and fluid properties, which align with experimental data in [22].

3.1. Valve Flow Coefficient

The valve flow coefficient is influenced by factors such as valve type, valve diameter, valve opening rate, and operating fluids. This coefficient, determined by the differential pressure between upstream and downstream, is a crucial factor to take into account when analyzing the operation of the valve [23]. The valve flow coefficient is defined by the following equation:

$$C_v=Q\sqrt{{\displaystyle \frac{SG}{\Delta P}}}$$

(18)

where $C_v=0.066$ (obtained from Equation (6)) is the flow coefficient, Q = 4.62 m³/s (obtained from the equation where Q = Area of valve nominal bore 1400 mm × inlet flow velocity) represents the flow rate, $SG$ is the specific gravity of water (SG = 1), and $\Delta P=4.9\mathrm{kPa}$ is the pressure drop at DN1400 valve fluid inlet velocity of 3 m/s. The Inlet pressure into the valve is 1750 kPa while the average operating outlet pressure is 1755 kPa.

The combination of a high flow rate with low-pressure drop normally sets the upper design flow coefficient of the valve and hence, the valve body size. A low flow rate with a high-pressure drop normally sets the valve’s lower design flow coefficient and propensity for cavitation or flashing. The ratio of a valve’s maximum to minimum controllable C_v is called the valve’s range ability, C_v ratio, or turndown. The higher the rangeability number, the more precisely the valve can control the fluid flow [24].

3.2. Valve Head Loss Coefficient

When fluid flows through a valve in a piping system, the internal components of the valve disrupt the flow and cause additional losses due to flow separation and mixing. A partially closed valve (10% open) causes the greatest pressure drop due to the decrease in flow among the system configurations. The relationship between pressure difference, fluid density, and average fluid velocity is represented by the valve loss coefficient. The valve head loss coefficient, $K_v=0.076$, is defined in the following equation [25]:

$$K_v=1.156C_v$$

(19)

3.3. Reynolds Number Implication

The Reynolds number is a crucial parameter in valve behavior, determining whether fully developed flow conditions lead to laminar or turbulent flow. Effective lengths for laminar and turbulent flow are calculated, and an increase in Reynolds number causes the flow to transition from laminar to turbulent within a specific range [26].

$${\Re }_e={\displaystyle \frac{\rho VDN}{v}}$$

(20)

where ${\Re }_e$ is Reynolds number, $v=1.002\times {10}^{-3}\mathrm{Pa}·\mathrm{s}$ is the dynamic viscosity, V = 3 m/s is flowing velocity, $\rho =998.2{\mathrm{kg}/\mathrm{m}}^3$ is density, and DN = 1400 mm represents the nominal diameter of the valve. The calculated Reynolds number at the inlet for water at room temperature of 20 °C is of magnitude ${\Re }_e=4.184\times {10}^6$ indicating turbulent flow.

$$\mathrm{Effective}\mathrm{Length},L_e\left(Laminar flow\right)=0.06\times {\Re }_e\times DN=351462\mathrm{m}$$

(21)

$$\mathrm{Effective}\mathrm{Length},L_e\left(Turbulent flow\right)=4.4\times {{\Re }_e}^{\left({\displaystyle \frac{1}{6}}\right)}\times DN\times 1.4=78.195 \mathrm{m}$$

(22)

3.4. Valve Head Loss

For turbulent flow conditions through the valve, the head loss is calculated using the Darcy–Weisbach equation [27]:

$$h_f={\displaystyle \frac{fL{V}^2}{2gD}}$$

(23)

where h_f is the head loss (in meters), f is the Darcy–Weisbach friction factor (depends on the Reynolds number), and L = $L_e$ is the effective length of the valve in a turbulent flow state as calculated from Equation (22) ($L_e$ = 78.195 m).

For such a highly calculated Reynolds number, the flow in the valve is turbulent, and appropriate correlations are used to find the friction factor. For turbulent flow, the Colebrook equation is calculated as follows [28]:

$$f={\displaystyle \frac{0.25}{\left[{\log }_{10}\left(\frac{\epsilon /D}{3.7}+\frac{5.74}{{\Re }_e^{0.9}}\right)\right]}}=0.0207$$

(24)

$\epsilon$ = 0.0015 m, is the roughness height of the pipe to valve inlet, and $h_f$ = 0.5304 m.

3.5. Cavitation

A valve controls fluid flow by creating a pressure drop that accelerates the fluid through the narrowest region of the valve. When the valve opens, the fluid decelerates, recovering from some of the pressure drop. When the pressure is lower than the vapor pressure of the fluid, vapor bubbles form, and if the pressure increases above the vapor pressure, cavitation occurs, causing the bubbles to collapse into liquid [29]. Constant cavitation data are used to evaluate the effects of cavitation on valve life. To predict whether cavitation will occur, a cavitation index is calculated as follows [30]:

$$\sigma ={\displaystyle \frac{P_u-P_v}{P_u-P_d}}={\displaystyle \frac{1750\left(\mathrm{kPa}\right)-101.3\left(\mathrm{kPa}\right)}{1750\left(\mathrm{kPa}\right)-1648.7\left(\mathrm{kPa}\right)}}=16.28$$

(25)

where $P_u$ is upstream pressure, $P_v$ is vapor pressure, and $P_d$ is downstream pressure.

The lower the cavitation index value, the more likely cavitation will occur. Manufacturers typically suggest that when σ is less than 2.5, cavitation may occur [31]. Additionally, regardless of the cavitation index, prolonged throttling below 10° valve open is not suggested because highly localized velocities could etch and damage valve seat surfaces.

3.6. Results and Discussion of FEA

The non-return multi-door reflux valve was tested under normal conditions and can withstand higher-than-design pressures during emergency scenarios. The maximum stress experienced inside the valve body was 206 MPa on the inlet and 103 MPa on the outlet, which is within the ASME Section VIII Division 2 [18]. The maximum deformation recorded was 0.413 mm on the inlet body and 0.391 mm on the outlet body, both within the safety limit. However, the yield strength of the valve body material is 310 MPa, indicating that the maximum stress is below the material’s yield strength. The analysis also identified areas for design optimization to improve the valve’s performance. The wall thickness of the reflux valve housing is calculated to be 50.0 mm, meeting ASME B16.34 [18] requirements, and UG 27 of ASME Section VIII Division 1 [18] calculated wall thickness is 35.5 mm. This ensures that the design is safe and can efficiently withstand a hydrostatic test pressure of 3500 kPa. The wall thickness is optimized according to standards, theoretical calculations, and structural analysis, resulting in a high degree of structural stability in the reflux valve housing. The obtained results revealed that the FEA had maximum stress values of 206 MPa at the inlet and 103 MPa at the outlet, while the maximum strain was 0.413 mm and 0.391 mm for the inlet and outlet bodies, respectively.

4. CFD Flow Characteristics

For a thorough assessment of fluid flow patterns, pressure distribution, turbulence intensity, backflow tendencies, and efficiency under various operating conditions, numerical simulation techniques based on mathematical models and algorithms are used in CFD. These techniques offer insights that are frequently costly, time-consuming, or difficult to obtain through physical experiments alone [32]. First, discrete fluid models are created based on the door’s geometry, taking into account mesh quality factors. Subsequently, turbulence models and boundary conditions are assigned, and the planned simulations are performed.

4.1. Methodology

The CFD analysis is conducted using state-of-the-art computational fluid dynamics software. The setup includes a 3D model of the non-return multi-door reflux valve and a virtual closed-fluid circulation system. Key parameters and boundary conditions are defined for the simulations.

• Geometry

The first step involves creating a 3D computer model of the valve and its surroundings. Complex geometries, including the valve doors and housing, are meticulously recreated. The structural and fluid domains of the multi-port check valve are shown in Figure 5. The valve has a diameter of 1400 mm, and the opening angle of the valve varies with the amount of fluid flow, resulting in changes in the angle of the valve. The coordinate of the geometry is oriented in the following way: the x-axis is located in the flow direction, the y-axis is oriented upwards, and the z-axis is located along the rotational axis. When the doors are fully open, the angle is 65.5 degrees and when the doors are fully closed the angle is 0 degrees. The angular velocity is negative when the doors close.

• Dynamic Mesh

In Figure 6, the model has been divided into a mesh to ensure finer resolution near the valve components, accurately capturing the fluid behavior. In fluid–structure interaction, dynamic meshing plays a key role in problem configuration. Therefore, three techniques were applied to update the mesh as the boundary changes: smoothing, superposition, and re-meshing. These methods were used either individually or in combination depending on the mesh movement. We also implemented a user-defined function to enable the flow simulation to perform specific actions, such as describing the valve door movement or controlling boundary conditions in a targeted manner.

Table 3. CFD meshing information [33].

Parameter	Details
SolidWorks Version	SolidWorks 2022
Solver	SolidWorks Flow Simulation (CFD)
Mesh Type	Computational Mesh (CFD)
Global Mesh Size	10 mm
Mesh Refinement Levels	3 Levels (automatic)
Boundary Layer Mesh	5 layers, growth rate = 1.2
Element Type	Tetrahedral
Minimum Element Size	1 mm
Maximum Element Size	15 mm
Mesh Quality Criteria	Skewness < 0.85, aspect ratio < 5
Adaptive Meshing	Yes (based on velocity and pressure gradients)
Advanced Refinement Zones	Yes, near the valve seat and fluid contacts
Number of Elements	2.5 million elements
Number of Nodes	1.8 million nodes
Automatic Mesh Sizing	Automatic with manual refinements
Solver Settings	Steady-state, incompressible flow
Computational Domain	Full 3D domain around the valve
Mesh Symmetry	Full valve simulated
Valve Seat Mesh Density	High-density (Fine mesh)
Inlet and Outlet Mesh Refinement	2–5 mm
Pressure Convergence Criteria	100 kPa
Velocity Convergence Criteria	1 m/s
Turbulence Model	k-ε (k-epsilon)
Gravity Settings	Enabled (based on vertical flow)
Fluid Material	Water
Solid Material	Ductile iron
Mesh Independence Study	Yes, after convergence
Post-Processing Output	Velocity contours, pressure gradients
Wall Treatment	Wall functions or full-resolution
Wall Functions or Full-Resolution	full resolution
Parallel Computing	Yes, enabled (multi-core processor)

outlines the major considerations for setting up a mesh for the CFD simulation of the valve fluid domain structure, to highlight the effect of mesh density on the accuracy of the flow performance predictions. The table includes various aspects related to the mesh setup, such as mesh type, refinement levels, and details specific to SolidWorks for a CFD analysis. The mesh is tailored for high accuracy, especially around areas like the valve seat, where flow separation and backflow are critical.

• CFD Software Numerical Algorithms Input Analysis

Appropriate numerical methods are chosen to solve the governing fluid flow equations, including the Navier–Stokes equations, which describe the behavior of incompressible fluids, ensuring an accurate representation of flow behavior [34]. The fluid domain of the non-return multi-door reflux valve, as depicted in Figure 6, is used for CFD analysis. For the incompressible steady-state analysis of the valve, a turbulence and laminar model is selected. Water is considered as the working fluid and a maximum uniform velocity of 3 m/s is applied at the inlet, with a defined opening condition for the outlet. The walls are fixed with a non-slip condition and a wall roughness of 0.0015 mm. During CFD analysis, different valve opening angles are tested, ranging from a 10% (10 degrees) valve opening to fully open and fully closed positions.

CFD also employs a laminar flow model and turbulence flow model to accurately simulate the flow within the valve. The turbulence model used from SolidWorks CFD simulation is the k-ε (k-epsilon) model, providing a good balance between accuracy and computational efficiency. These models help capture the flow phenomena at various flow rates. The analysis aims to compute and visualize various flow parameters, including velocity profiles, pressure distributions, different flow rates, flow directions, fluid characteristics, and turbulence characteristics. Parameters will be analyzed to identify any issues or inefficiencies in the valve’s operation. These data will be used to optimize the design of the valve for better performance.

• Boundary Conditions

The inlet and outlet boundaries are set to replicate the pressure and flow conditions corresponding to real-world flow analysis and pressure testing scenarios, along with other physical properties, such as the viscosity and density of the fluid. The valve’s operation is also incorporated into the simulation, allowing the doors to pivot in response to the fluid’s direction.

The simulations involve water as a fluid type that is commonly transported in pipelines, and the properties are accurately defined. The fluid is assumed to be incompressible water at 20 °C, with a density of 998.2 kg/m³ and a dynamic viscosity of 0.001003 kg/ms [35]. The inlet boundary condition is set as a velocity inlet, while at the outlet, a pressure boundary condition is used. The inlet boundary condition is also chosen to be a mass flow inlet. The mass flow rate at normal operating conditions will be 3000–5000 kg/s in the experiment [29]. Therefore, the mass flow rate is set to 4500 kg/s in the simulations. Should the pump trip, the mass flow rate through the inlet will start to decrease. The function for approximating the mass flow rate is written in Equation (26).

$$\dot{m}=\rho VA=4618\mathrm{kg}/\mathrm{s}$$

(26)

At the outlet, a pressure boundary condition is used. The operating pressure in the system is set to 1750 kPa and the gauge pressure at the outlet is set to zero, indicating that the absolute pressure in the domain is the same as the operating pressure.

• Valve Positions

The virtual valve is set in various positions to analyze its behavior at different openings for 0° (fully closed), 10° open, 50° open, and 65.5° open (fully open), respectively, as shown in Figure 7 below.

4.2. Flow Performance of Multi-Door Reflux Systems in Preventing Backflow

The study aims to evaluate the performance of multi-door reflux systems in preventing backflow and sealing during various operational conditions. The Fluid Controls Institute (FCI) defines leakage classes using ANSI Standards for measurements. Each class has a unique test procedure and low leakage at a specified operating differential pressure. The leakage class should balance seat leakage, valve cost, and durability. Seat leaks can reduce plant efficiency but may require more expensive valves. For rated applications where seat leakage is nominal and not significantly reduced, a less restrictive class should be used [36]. The CFD simulations provide light on the fluid dynamics in the reflux system, enabling a detailed assessment of the effectiveness of backflow prevention and sealing mechanisms. The sealing mechanisms in multi-door reflux systems are investigated to assess their effectiveness in preventing backflow. Special attention is given to door design, material properties, and contact surfaces to understand how these factors contribute to sealing integrity. To evaluate the effectiveness of backflow prevention, the inlet flow will be on the downstream side, as indicated by red arrows in Figure 8, and the analysis of the effectiveness of multi-door reflux systems in preventing backflow is quantified.

5. Non-Return Multi-Door Reflux Valve’s Flow Performance Results Using CFD

The CFD analysis offered a comprehensive view of the fluid’s behavior within the valve, including velocity profiles, pressure distributions, and shear stresses, aiding in fine-tuning the valve design. Through extensive simulations and analysis, the research study yields valuable glimpses into the flow performance of the multi-port backflow valve under pressure testing conditions and the effectiveness of backflow prevention. Full flow analysis is performed for different door opening angles, 0° (fully closed), 10°, 50°, and 65.5° (fully open), respectively. Some key findings include the following:

5.1. Pressure Distribution Using CFD

The pressure is evenly distributed across the doors, indicating that the valve effectively manages pressure. Maximum pressure in the valve occurs in the upstream flow, while the downstream flow experiences minimum pressure. Arrows in Figure 9a, Figure 10a, Figure 11a and Figure 12a indicate water flow pressure streamlines inside the valve.

The pressure distribution plots in Figure 9, Figure 10, Figure 11 and Figure 12 show a gradual increase in pressure from inlet to outlet as the door opening angle increases, with a greater initial pressure drop at a valve opening angle of 10°, and then a constant pressure drop across the valve. The obstruction of fluid flow through the doors at the seating area and seal arrangement causes this pressure drop, causing an increase in fluid flow velocity.

5.2. Velocity Distribution by CFD

Flow streamlines revealed that the valve maintained a consistent and reliable performance across a range of flow rates, and no significant areas of flow separation or stagnation were observed, confirming its suitability for various operational scenarios, and suggesting that the valve maintains a smooth and controlled flow. The arrows in Figure 13a, Figure 14a, Figure 15a and Figure 16a indicate water flow velocity streamlines inside the valve.

The velocity contours plotted in Figure 13, Figure 14, Figure 15 and Figure 16 reveal that the fluid flow is directed towards the valve doors and partially obstructed by them, causing the formation of a downstream vortex that increases the velocity of the fluid behind the doors. As the flow moves toward the area of the seat–seal arrangement downstream of the valve doors, the velocity rapidly increases until it reaches a maximum downstream of the valve doors. Beyond this point, the speed gradually increases until reaching the outlet boundary condition downstream of the valve doors. The flow velocity decreases as the valve door opening angle increases.

5.3. Pressure Drop Analysis and Flow Reversal Sealing Efficiency

The pressure drop across the valve door ports is shown in the figures above as a function of velocity and valve opening angle. The pressure drop increases rapidly for opening angles of less than 10%. Also, the pressure drop is velocity-dependent and increases as the velocity decreases. The simulations indicated that the pressure drop across the valve remained within acceptable limits and consistent with the experimental findings, even under high-pressure conditions. This suggests that the valve effectively manages flow resistance.

The CFD analysis in Figure 17 demonstrated that the valve effectively prevented backflow, even under high-pressure differentials, thereby ensuring system integrity. The multi-door reflux system demonstrated efficient control over fluid dynamics, with minimal risk of backflow occurring during regular operations. The sealing analysis identified areas of potential improvement in the design, highlighting regions where tighter tolerances or enhanced sealing materials might be beneficial. Leakage paths and pressure differentials across door interfaces are quantified.

The CFD simulations revealed that under normal flow conditions, the DN1400 PN17.5 multi-door reflux valve effectively maintains its sealing integrity. Figure 18 shows that there is no backflow into the upstream side of the valve. Therefore, the valve exhibits no leakage and maintains a tight seal, ensuring efficient flow control in the intended direction. The CFD analysis in Figure 18 also demonstrated that the DN1400 PN17.5 multi-door reflux valve exhibits robust sealing capabilities even under challenging flow reversal conditions. The valve effectively closes off the flow path in the reverse direction, minimizing the risk of backflow and associated operational issues.

5.4. Flow Coefficient (C_v), Flow Visualization, and Valve Positioning

The C_v values remained consistent, highlighting the valve’s ability to maintain stable flow rates under different pressures (Figure 5). CFD allowed for the visualization of fluid turbulence and flow patterns within the valve, helping to identify regions where recirculation or eddies may occur, potentially causing wear and tear on valve components, revealing areas of turbulence and stagnation, which can be critical for valve design optimization. This study highlighted how the valve design minimized turbulence and sedimentation by introducing the multi-door body seat arrangement, ensuring a stable and reliable flow performance, suggesting a reduced risk of clogging and maintenance requirements (Figure 19). This study indicated that the angle at which the doors are positioned affects flow performance. The optimal door positioning for maximum efficiency is identified at the fully open valve doors (Figure 12 and Figure 16).

5.5. Sensitivity Analysis

Variations in valve geometry, material properties, and operating conditions were explored through sensitivity analysis to determine the impact on performance. CFD enabled the sensitivity analysis of design parameters, providing ideas for potential design improvements for improved performance. The position of the valve door was found to have a significant impact on flow characteristics, highlighting the importance of correct positioning and operation, as shown in Table 3 and Figure 19. The CFD analysis also indicated that the valve design reduced clogging and sediment buildup, suggesting potential benefits in lower maintenance requirements. The simulations also provided information on the durability of the valve components. Stress and strain analysis can optimize valve design for extended longevity.

5.6. Results and Discussion of CFD Flow Analysis

The results in

Table 4. Flow characteristics and CFD results.

Parameter	Fully Closed (0°)	10° Open	50° Open	Fully Open (65.5°)
Area, A (m2)	1.54	1.54	1.54	1.54
Flow Rate, Q (m3/s)	4.62	4.62	4.62	4.62
Velocity at Inlet (m/s)	3	3	3	3
Velocity at Outlet (m/s)	2.5	3.11	3.03	3.03
Pressure at Inlet (kPa)	1750	1750	1750	1750
Pressure at Outlet (kPa)	1790	1755	1754	1754
Pressure Drop (kPa)	40	5	6	6
Mass Flow Rate (kg/s)	4610	4610	4610	4610
Flow Coefficient (Cv)	0.016	0.025	0.06	0.066
Head Coefficient (Kv)	0.019	0.029	0.069	0.076
Head Loss (m)	0.034	0.029	0.019	0.017
Reynold Number (Re)	4.3 × 106	4.3 × 106	4.3 × 106	4.3 × 106
Laminar Flow, Le (m)	3.5 × 105	3.5 × 105	3.5 × 105	3.5 × 105
Turbulent Flow, Le (m)	78	78	78	62
Turbulent Energy (m2 s2)	0.494	0.166	0.144	0.032
Turbulence Length (m)	0.045	0.029	0.036	0.039
Turbulent Time (s)	0.399	0.408	0.593	0.627
Cavitation Index (σ)	20.75	48	278.95	338.51
Water Leak Rate (L/min)	0	0	0	0
Response Time (s)	5	8	18	20

show parameters for different valve door configurations, from a fully closed position at 0°, 10°, and 50° to a fully open position at 65.5°.

CFD simulations indicated a maximum pressure drop of 40 kPa, with a constant flow rate of 4.62 m³/s in different valve configurations. The flow coefficient (C_v) increased from 0.016 when the valve was closed to 0.066 at a valve opening of 65.5°, demonstrating efficient flow management. Additionally, the cavitation index remained above safety limits, with a value of 338.51, reducing the risk of cavitation and ensuring the durability of the valve. It was observed that increasing the valve opening angle resulted in decreased flow velocity and higher pressure differentials, but that too large angles caused flow instabilities and potential valve damage. Higher fluid velocities correlated with increased flow rates through the valve; however, at extremely high speeds, turbulence intensified, leading to pressure fluctuations and potential cavitation. Additionally, changes in operating pressure influenced valve dynamics, with higher pressure differentials resulting in faster response times and accelerating the wear of valve components, which was experimentally validated in [22].

6. Results and Discussion on Non-Return Multi-Doors Reflux Valves

SolidWorks CFD software plays a critical role in valve design by accurately simulating fluid velocity and pressure and handling complex geometries and boundary conditions. It enabled changes in fluid characteristics and valve geometry to be evaluated without the need for physical prototypes, reducing the need for bench testing and shortening design cycles. The software provides a clear visualization of flow behavior inside the valve, and its results were used to calculate pressure and velocity vectors at valve angles ranging from 0° to 65.5°, in 10° increments. These vectors were then applied to Equation (18) to determine the valve flow coefficients. The main findings of the CFD analysis summarizing the parameters for various valve shutter configurations are presented in Table 4 and predict the following information:

• Both the flow coefficient (C_v) and the load coefficient (K_v) increase with the percentage of the valve door opening, while the pressure loss decreases as expected for the design requirements of check valves.
• The pressure drop across the valve doors, plotted as a function of speed and valve opening angle, increases rapidly for opening angles less than 10% and is dependent on speed, increasing as speed decreases.
• The pressure distribution plots reveal a gradual pressure drop from the inlet to the outlet, with a larger drop across the valve due to flow obstruction at the seat–seal arrangement, which also increases fluid velocity.
• The velocity plot indicates that fluid flow is directed toward the partially obstructed valve doors, forming a downstream vortex that increases fluid velocity behind the doors.
• The Mach number remains below 0.3, and the cavitation index is within the safe zone, indicating that no cavitation occurs in the valve. The Reynolds number, greater than 4000, confirms turbulent flow through the valve.

Under turbulent conditions, the valve strength is primarily determined by its ability to resist forces generated by the chaotic motion of the fluid, such as pressure fluctuations and vortices [22]. Therefore, an FEA-optimized valve design is essential to withstand these forces, thus avoiding structural failures, leaks, or premature wear.

Key factors to consider in selecting and designing a valve for turbulent flow include the following:

The valve structure is constructed from AS1831 Gr.450-10 ductile iron, which offers a high tensile and yield strength, providing the durability and corrosion resistance needed to withstand the forces exerted by the fluid as well as potential erosion or corrosion caused by turbulent flow. The valve is robustly designed with sufficient wall thickness and reinforcement in critical areas to endure fluid forces and vibrations.

The valve is pressure-rated based on its ability to resist the forces associated with fluid flow. The valve trim, including the doors, seat, and internal body profile, is specially designed to reduce turbulence and minimize pressure drop across the valve. Additionally, flow control considerations are meticulously taken into account to ensure the valve operates within its design limits, supporting a maximum flow velocity of 10 m/s and a maximum operating pressure of 3500 kPa.

The study revealed important information about the structural and flow performance of the multi-door reflux valve. Finite element analysis (FEA) demonstrated that the valve’s maximum stress values of 206 MPa at the inlet and 103 MPa at the outlet are well below the yield strength of the material, ensuring the structural integrity of the valve under high-pressure conditions. The maximum deformation of 0.413 mm (inlet) and 0.391 mm (outlet) were within the permissible limits, confirming the robustness of the valve design. On the flow side, computational fluid dynamics (CFD) analysis confirmed a pressure drop of 40 kPa and a steady flow rate of 4.62 m³/s across different valve openings, which aligns with industry standards for pressure and flow management. The flow coefficient (C_v) increased significantly from 0.016 when fully closed to 0.066 at the 65.5° valve opening, indicating optimal performance with minimal backflow risks. Additionally, the cavitation index of 338.51 suggests minimal cavitation risk, contributing to the long-term durability of the valve. These combined results confirm that the valve is structurally sound and operates effectively under a variety of operating conditions. The study also recommends strengthening specific stress-prone areas and addressing turbulence issues to ensure long-term operational reliability. Finally, experimental validation is encouraged to further verify the results of FEA and CFD.

7. Conclusions

The study presented in this paper proposes a comprehensive analysis of a multi-door check valve using computational fluid dynamics (CFD) and finite element analysis (FEA) to evaluate its flow performance under pressure conditions. The performed analysis demonstrated that the valve effectively reduces backflow and maintains system integrity, particularly under varying pressure and flow conditions. The CFD results indicate a consistent flow profile with minimal resistance when the valve is fully open, although turbulence and pressure drops occur near the seat–seal arrangement under partially open conditions. FEA simulations show that the valve can withstand operational pressures without significant deformation, although stress concentrations near the hinge points suggest that material reinforcements may be necessary for long-term durability. However, the main limitation of the proposed technique lies in its reliance on simulated environments, which may not capture all the dynamic and fluctuating conditions encountered in practical applications. The potential for localized wear in areas of high turbulence could impact the long-term functionality of the valve and should be addressed in future research. Furthermore, experimental validation should be performed using a wider range of fluid types, pressures, and operating conditions, in addition to CFD and FEA results, to confirm the accuracy of the simulated models and provide a more comprehensive understanding of valve performance.