Evaluation of cavitation phenomena in three-way globe valve through computational analysis and visualization test | Scientific Reports

Scientific Reports volume 14, Article number: 21919 (2024) Cite this article

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A three-way valve has a multi-port structure with three openings, which allows control of the fluid direction. However, owing to the complicated trim shape of the internal flow, an irregular fluid flow occurs, which hinders precise fluid flow control. In severe cases, cavitation induces mechanical damage owing to abrupt changes in the fluid direction. In this study conducted a computational fluid dynamics (CFD) analysis was performed to estimate the localized cavitation around the bottom plug of the three-way valve. To quantify localized cavitation, the percentage of cavitation (POC) was derived using the vapor volume fraction (VVF). The POC, defined by the cavitation occurrence zone with VVF > 0.5 divided by the volume of the cavitation danger zone, was 34.90%. Cavitation at this POC level could cause mechanical damage; therefore, a size optimization was performed. The lengths of the optimized waist and tail regions of the bottom plug were obtained wherein the POC level decreased by 19.06%. In addition, experiments were conducted using a flow visualization test setup. The experimental results were quantified into the POC employing the image gradients method, and the results were in good agreement with the CFD analysis.

A three-way valve is widely used for multi-directional switching of working fluids. It features a multi-port structure consisting of three openings allowing control of fluid direction without any additional devices1. However, due to the complicated trim shape of the internal flow path in the multi-port, irregular fluid flow occurs, leading to significant changes in the velocity and pressure of the working fluids. These present challenges in precise fluid flow control and may result in mechanical damage due to strong impacts such as cavitation bubble collapse during abrupt changes in the fluid direction2,3. Therefore, it is necessary to investigate the flow characteristics occurring within the flow field of the three-way valve and to parameterize the complicated trim shape to improve internal fluid flow issues accordingly.

Previous studies investigating the internal fluid flow characteristics resulting from the complicated trim shape of the three-way valve are as follows. Lisowski et al.4 estimated the fluid flow forces acting on the spool of a three-way valve in a hydraulic drive system and evaluated the operational characteristics of the system. They proposed a spool shape by deriving the dynamic fluid flow forces generated by changes in fluid flow direction using computational fluid dynamics (CFD) analysis and evaluated the accuracy of the CFD analysis through experiments. Brilianto et al.5 proposed orifices with different fluid flow path shapes for a three-way globe valve applied in facilities of combined cycle power plants and estimated the internal fluid flow characteristics using CFD analysis. They interpreted through experiments that the proposed orifices improved issues such as vibration and noise while maintaining the mass flow rate of the existing model.

The studies mentioned above were conducted to maintain a certain flow rate while addressing internal fluid flow issues through calculations of fluid flow forces occurring during changes in fluid flow direction of the three-way valves, and also through case studies on various shapes of fluid flow paths. Particularly in the case of three-way valves with a bottom plug, abrupt changes in the fluid flow field can occur depending on the shape and dimensions of the bottom plug, and in severe cases, cavitation bubble collapse can occur6. Elgamal et al.7 and Jin et al.8 estimated the effects of bottom plug shape on flow characteristics according to variations in the flow opening ratio of the fluid flow path and evaluated cavitation phenomena using CFD analysis. However, validation of the CFD analysis results through experiments has not been conducted. Research on cavitation occurrence according to the shape and dimensions of the bottom plug is still lacking. Therefore, when designing a three-way valve, it is essential to thoroughly investigate the flow characteristics around the bottom plug, where the flow path changes abruptly. Furthermore, it is necessary to quantitatively evaluate cavitation, minimize it through the size optimal design of the bottom plug's shape and dimensions, and experimentally verify these improvements.

In this study, CFD analysis was conducted to evaluate the flow characteristics around the bottom plug when opening the flow path for a three-way valve. Particularly, a multi-phase fluid dynamics analysis was performed to numerically determine the cavitation phenomena occurring locally around the bottom plug, and the vapor volume fraction (VVF) was extracted as a result. The extracted VVF was used to derive the percentage of cavitation (POC) to quantitatively assess the localized cavitation phenomena. The size optimal design was carried out on the shapes of the bottom plug to reduce cavitation, and the specimens reflecting the optimized shapes were manufactured. Subsequently, experiments using the specimens installed in the flow test equipment and flow visualization test set-up were conducted, and the obtained experimental results were quantified into the POC using an image gradients method. The results obtained from the experiments were compared with the results numerically obtained from the multi-phase fluid dynamics analysis.

The velocity of fluid flow increases when a working fluid encounters a narrow section of fluid flow path such as an orifice. After passing through the narrow section where acceleration is added, the velocity immediately reaches its highest value, known as the vena contracta9. At the vena contracta, despite the high velocity of fluid flow, there is a corresponding decrease in pressure. When the pressure drops below the saturated vapor pressure of the working fluid, cavities are formed, a phenomenon known as cavitation, in which the liquid transitions into a gas. Subsequently, these cavities move to areas where the pressure exceeds the saturated vapor pressure, which collapse rapidly, and cause noise and vibration10. These can lead to mechanical damage such as erosion and pitting. Such problems not only hinder the regulation of flow rate but also shorten the lifespan of valves. Therefore, during the initial design stage, accurate predictions of cavity occurrence through various evaluation techniques should be performed to minimize cavitation.

Various cavitation indices have been proposed by international organizations and committees, such as the IEC (International Electrotechnical Commission), ISA (International Society of Automation), and VDMA (Machine and Equipment Manufacturer Association). However, there is currently no international standard for predicting mechanical damage. Instead, many valve manufacturers define the beginning of cavitation as the pressure drop exceeding 2% from the straight line of the flow coefficient curve, denoted as Kc, and predict it as the mechanical damage due to cavitation. Additionally, the cavitation is quantified using a cavitation index σv according to the regulations recommended by ISA-RP75.23-199511. This index is obtained from the pressure difference between the inlet and outlet of pipelines, where the occurrence and intensity of cavities are inversely proportional to σv, and indicates that higher σv reduces cavity occurrence and intensity.

The cavitation indices mentioned above are applied as evaluation indicators for macroscopic cavitation affecting the entire pipelines. However, they are not suitable for use as indicators to evaluate cavitation occurring locally in the fluid flow path of the valves. Therefore, the percentage of cavitation (POC) was introduced for the quantitative evaluation of the local cavitation phenomena. The cavitation occurrence can be presented by the vapor volume fraction (VVF), which refers to the ratio of the volume occupied by vapor, Vvapor, to the total volume of a given element, Vone element , and expressed as shown in Eq. (1). The Vvapor can be calculated using a multi-phase fluid dynamics analysis based on the computational fluid dynamics (CFD).

In general, cavitation occurrence is defined when the VVF reaches 10−5. However, it is rational to consider cavitation with a VVF of 0.5 or higher as potentially causing mechanical damage12. The POC is defined as the cavitation occurrence zone with VVF > 0.5 divided by the volume of the cavitation danger zone, as shown in Eq. (2). This allows for the quantification of locally occurring cavitation and expression as a percentage, which enables to indicate the potential for the mechanical damages to pipelines.

Based on a previous study13 on CFD analysis, it was determined that if the POC exceeds 30%, it will cause mechanical damage to pipelines.

In this study, the cavitation occurring around the bottom plug of a three-way valve was quantitatively evaluated using a commercial software of ANSYS CFX14. The compressible Navier–Stokes equation is generally used for the CFD analysis. However, in cases involving multi-phase fluid flows where bubbles occur, additional turbulence stress terms should be considered. Therefore, the Reynolds-Averaged Navier–Stokes (RANS) equation15, as shown below, was utilized,

where \(\rho_{m}\) is the mixture density, \(\overline{{u_{i} }}\) is average velocity component, \(P\) is pressure, \(r_{\alpha }\) is phase volume fraction, \(g_{i}\) is gravity component, \(\tau_{ij}\) is stress tensor component, \(u^{\prime}_{i}\) is Fluctuating velocity component, and \(M_{i}\) is external force component.

The Eddy viscosity model can be described by assuming that Reynolds stresses are related to the mean velocity gradients and turbulent viscosity. This can be expressed like Newtonian laminar flow as follows:

Here, \(\mu_{t}\) represents the turbulent viscosity or eddy viscosity coefficient, which is calculated using the SST (Shear Stress Transport) turbulence model in this study. The SST model16 is based on a combination of the k-ε model17 and Wilcox's k-ω model18. The turbulent viscosity was calculated according to Frank model19 as follows:

where \(k\) is kinetic energy and \(\omega\) is turbulence frequency.

In the ANSYS CFX, the growth of vapor bubbles in water is evaluated using the Rayleigh-Plesset equation. Therefore, the present study was used the Rayleigh-Plesset equation to calculate the growth of bubbles. Considering the uniform approximation for multi-phase fluid flow, it was assumed that the vapor bubbles, when generated and moving in the fluid flow, had uniform velocity fields with a continuous phase and non-slip velocity. In the case of multi-phase fluid flow where cavitation occurs, only two phases, that is, water and vapor, were considered, and the following mass transfer equation was utilized:

where \(\mathop {M_{v} }\limits^{ \cdot }\) is the mass transfer rate (\({\text{kg}} \cdot {\text{m}}^{ - 3} \cdot {\text{s}}^{ - 1}\)) and the subscripts l and lv denote liquid and liquid–vapor, respectively.

When these terms of the mass transfer equation are applied to the Rayleigh–Plesset equation, it is expressed as follows20,

where RB represents the radius of the bubbles, σ is the surface tension coefficient, Psat is the saturated vapor pressure, P is the fluid pressure, and ρl is the fluid density. Ignoring both the second-derivative terms with respect to the radius of the bubble and surface tension coefficient, the derivative term of the radius of the bubbles can be obtained:

Therefore, the mass transfer rate for a single bubble can be expressed as follows:

where \({\text{m}}_{{\text{B}}}\) is mass of vapor and \(\rho_{v}\) is density of vapor.

When there are \(N_{B}\) bubbles, the vapor volume fraction can be expressed as follows:

The total interphase mass transfer per unit volume owing to cavitation is expressed by the following equation according to Sauer model21 and Zwart model22, which includes both the growth and collapse of bubbles19:

To consider the pressure fluctuations of the turbulent flow affecting the saturated vapor pressure, the critical pressure of the fluid, Pv, was estimated in terms of the turbulent energy as follows:

where \(P_{turb.}\) denotes the pressure term due to turbulence.

Substituting the previously described Rayleigh–Plesset equation into the above equation, the change in the radius of the bubbles over time can be derived as the following equation, which also facilitates the consideration of cavitation occurrence owing to turbulence.

A three-way valve was used in this study, and its cross-sectional views presenting its components and flow paths are shown in Fig. 1. The valve comprises mainly a bonnet, body, stem, top plug, and bottom plug. The stem with the top and bottom plugs moves up and down to switch the flow paths. When the top plug is open, as shown in Fig. 1a, the fluid flow direction is linear such as a relatively simple straight flow path. However, when the bottom plug is open, as shown in Fig. 1b, the flow direction bends at a right angle, creating a curved flow path. In this case, the working fluid flows around the bottom plug, and the flow characteristics change depending on the shape of the bottom plug. Particularly, as the working fluid passes around the bottom plug, abrupt changes in fluid flow cross-sectional area lead to excessive turbulence and even cavitation occurrence.

Cross-sectional view showing components and flow paths of three-way valve.

The flow characteristics were expected to be mainly influenced by the shape of the bottom plug, especially in the case of the curved flow path when the bottom plug was open. Therefore, the shape of the bottom plug needed to be parameterized, and multi-phase fluid dynamics analysis for each parameter should be performed. However, the complicated trim shape of the internal flow path caused problems such as drastically increased computational time and low convergence of numerical results in the multi-phase fluid dynamics analysis. The complicated trim shapes that do not affect cavitation were removed, and a simplified model demonstrating similar flow characteristics was created as shown in Fig. 2. Although there were differences in the numerical results obtained from the full model considering the complicated trim shapes and the simplified model, the POC obtained by using Eq. (2) for two models were 48.01 and 50.00, respectively, with a difference of about 3%. To investigate the flow characteristics around the bottom plug more closely, it was divided into upstream region (UR), bottom plug region (BR), and downstream region (DR). BR was further subdivided into head region (HR), waist region (WR), and tail region (TR). The sizes of the detailed shapes of the bottom plug for the simplified model were as follows: the outer and inner diameters of stem was 10 and 7 mm, respectively. Lengths of UR, BR, and DR were 15 mm each, and lengths of HR, WR, and TR were 8, 6.5, and 7 mm, respectively.

Simplified model for CFD analysis and detailed shape of bottom plug.

To evaluate the flow characteristics around the bottom plug, the multi-phase fluid dynamics analysis was carried out using the commercial software ANSYS CFX 2023 R1. In the pre-processing, 230,000 tetrahedral elements were generated in the bottom plug region (BR), and 120,000 hexahedral elements were created in the pipeline including regions of upstream and downstream. Additionally, for accuracy in the calculations, more than 10 prism elements were adopted near the walls using tetrahedral elements, and all grid points were generated to ensure that the value of y + was below 1 on whole wall surfaces. Figure 3 shows the results of the grid convergence test to estimate changes of the inlet averaged pressure and the solver running time regarding to different grid sizes. When the grid size decreased, the inlet averaged pressure gradually decreased, while the solver running time required for convergence of the numerical results increased significantly. Considering both the accuracy of the numerical results and the required solver running time, a grid size of 0.7 mm was selected.

Results of grid convergence test.

For the condition of the curved flow path when the bottom plug was open, the working fluid was taken into account of phases of water and vapor, and the boundary conditions are given by a mass flow rate of 6.5 kg/s at the inlet and atmospheric pressure at the outlet. The temperature of the working fluid was 25 ℃, and the saturated vapor pressure of water was set to 3167 Pa.

Figure 4 shows the results of the multi-phase fluid dynamics analysis calculated by Eq. (9), which are represented by the vapor volume fraction (VVF) expressed in Eq. (1). Contour plots of VVF distributed around the bottom plug, presented in volume rendering and cross-sectional views, are shown in Fig. 4a. These demonstrate a significant increase in cavitation in both of the tail region (TR) and downstream region (DS) of the bottom plug, which indicates a wide area with VVF > 0.5. This could lead to initial mechanical damage to the pipeline, and higher intensity of cavitation was expected. To quantitatively evaluate the intensity of cavitation, the TR was divided into 70 sections in the x–y plane starting from the beginning point of TR, and the VVF values of each section were averaged. The averaged values are then presented in the z-direction, as shown in Fig. 4b. The VVF values sharply increase in the z-direction, which maximum value is up to 0.9. The percentage of cavitation (POC), which was calculated by dividing the cavitation occurrence zone with VVF > 0.5 into the volume of the cavitation danger zone, as shown in Eq. (2), is obtained as 34.90%. This is consistent with other research13 indicating that a POC above 30% causes mechanical damage to the pipeline. The cavitation with this POC level could cause mechanical damage to the bottom plug, so that a size optimization of the bottom plug should be performed to reduce the cavitation.

Results of VVF obtained by multi-phase fluid dynamics analysis.

In the results obtained from the multi-phase fluid dynamics analysis in Chapter 3, it was confirmed that the POC is 34.90%, indicating the occurrence of cavitation around the bottom plug, which could cause mechanical damage to the pipeline. Especially, the cavitation occurred rapidly from the tail region after the working fluid passed through the bottom plug region. Therefore, the length of waist region (WR) and tail region (TR) were parameterized to perform a size optimal design for the reduction of the cavitation. Since the inner diameter of the pipeline cannot be changed, it was fixed to 7 mm, and the lengths of WR and TR for the initial simplified model were 6.5 and 7 mm, respectively.

The length of the design variables WR and TR, selected for the parametric study of size optimal design, were varied from 1.5, 3.5, 6.5, 9.5, 12.5 mm and 1, 4, 7, 9, 13 mm, respectively. The POC for each parametric study was quantitatively evaluated. Figures 5 and 6 show the distribution of VVF and the change in POC obtained from the multi-phase fluid dynamics analysis regarding to the changes in shape parameters.

VVF and POC regarding to WR (TR = 7 mm).

VVF and POC regarding to WR (WR = 6.5 mm).

In Fig. 5, the results of the VVF and POC regarding to change of the WR are shown, where the length of TR was fixed to 7 mm. Figure 5a demonstrates the change in the VVF in z-direction of the bottom plug. As the length of the WR increases, the distribution of the VVF decreases, especially the area with VVF > 0.5. The influence of the WR on the POC, calculated by dividing the cavitation occurrence zone with VVF > 0.5 into the volume of the cavitation danger zone, is shown in Fig. 5b. At the shortest WR of 1.5 mm, the POC reaches up to 49.96%, and as WR increases, the POC decreases to below down to 10.55%.

Meanwhile, Fig. 6 shows the variation in VVF distribution and POC regarding to the TR with the fixed WR of 6.5 mm. Similar to the results in Fig. 5, as the length of the TR increases, the area with VVF > 0.5 decreases, and also the POC decreases from 46.86 to 14.27%.

Based on the results obtained from the parametric study considering the WR and TR of the bottom plug, the size optimal design was conducted. The lengths of WR and TR were chosen as design variables, and the range of design variables was determined with consideration for manufacturing feasibility while not affecting other components after dimensional changes. The objective function was the POC, and the optimization problem was formulated to impose boundary conditions satisfying the POC of 30%, which causes mechanical damage to the pipeline due to cavitation.

For the size optimization of the shape design variables, experimental points for each design variable needed for the design of the experiment (DOE) integrated with multi-phase fluid dynamics analysis were derived23. Using the commercial software of JMP24, a regression equation was obtained through stepwise regression analysis to form a response surface model (RSM). To verify the accuracy of the regression equation, the coefficients of determination R2 and adjusted-R2 were found to be 0.89 and 0.86, respectively, which indicate a high adequacy of the obtained regression equation.

The optimal solution for the design variables was obtained using a desirability function. The desirability function, with a range between 0 and 1, evaluates the satisfaction level of the objective function during the process of finding the optimal solution25. A value closer to 1 indicates an ideal optimal solution. The overall desirability function, denoted as D, applies the geometric mean to individual satisfaction values dn for the objective function and constraints, as shown in the following equation. The overall desirability function derived using the Eq. (10) is summarized in Table 1.

Figure 7 shows the RSM and prediction profiler, which approximate the variation in the POC based on two design variables using the embedded artificial neural network model of JMP. Design space exploration was conducted to identify the optimal point. The POC significantly increases as the length of TR increases, while variations in the WR reveal a localized minimum point. The results of the size optimal design for the shape of the bottom plug, obtained through the design space exploration, are the WR and TR of 5.39 and 6.96 mm, respectively, with a minimized POC of 19.06%. The overall desirability function D is 0.97. It means that the obtained optimal solution is close to the ideal value.

Response surface model and prediction profiler of object function regarding to design variables.

The POC of 34.9% in the initial simplified model decreased to 19.06% as predicted through the size optimal design. To validate the optimized POC, the multi-phase fluid dynamics analysis reflecting the optimal design variables of the WR and TR was conducted. Table 2 shows the results, in which the validated POC from the multi-phase fluid dynamics analysis is 17.62%. The validated POC agreed well with the predicted value from the size optimal design within an error of 7.56%.

In order to validate the results from the multi-phase fluid dynamics analysis and the size optimal design, a flow visualization test was conducted. While particle image velocimetry (PIV) is commonly used for flow visualization, in this study, a method employing a high-speed camera was adopted due to the clear identification of cavities within a transparent pipe. The occurrence and intensity of cavities were quantified using images captured through this method. For the flow visualization test, facilities, and measurement equipment compliant with the ISA-RP75.23 standard12 were utilized, where the available diameter range for valve specimens is from 15 to 400 A, with a maximum pump pressure of 15 bar and a reservoir capacity of 6.5 m × 5.5 m × 3.0 m.

Figure 8 shows the setup of the flow visualization test, including test specimens and experimental apparatus. The test specimens were the bottom plugs, one representing the initial model, and the other reflecting the size optimization, as shown in Fig. 8a. In the initial model, the lengths of WR and TR were 6.5 and 7 mm, respectively, while in the optimized model, these dimensions were 5.39 and 6.96 mm, respectively. The test specimens were inserted into a transparent acrylic pipe, and flow visualization was achieved using a high-speed camera with a shutter speed ranging from 5 to 20 µs. Figure 8b depicts the flow visualization test setup. The pressure of the working fluid supplied from the pump was measured using a pressure gauge (PG), and images were captured using the high-speed camera (CA) installed outside of the transparent acrylic pipe where test specimens were inserted. Subsequently, the flow visualization test was conducted while controlling the pump using an electromagnetic flowmeter (EF) to measure the flow rate. The working fluid used was water at room temperature, and the experiment was conducted based on flow rate control, starting from an initial flow rate of 3.5 kg/s and increasing by 1 kg/s increments until reaching a final flow rate of 6.5 kg/s.

Test specimens and test setup for flow visualization.

Figure 9 shows the results of the flow visualization test conducted on the initial and optimized models. For the test condition with a flow rate of 3.5 kg/s, as shown in Fig. 9a, no cavitation was observed in either the initial or optimized models. However, at a flow rate of 6.5 kg/s, cavitation occurred significantly after the TR of the bottom plug in the initial model. This is similar to the multi-phase fluid dynamics analysis results in Fig. 4a of Chapter 3.2. On the other hand, in the optimized model, the occurrence of cavitation is noticeably reduced compared to that in the initial model.

Results of flow visualization test.

To compare the results of the flow visualization test with the multi-phase fluid dynamics analysis, the degree of cavitation was quantified using the image gradients method26. The image gradients method utilizes the vector values of pixels with the greatest change in pixel values within the captured image to detect the boundaries of cavitation occurrence areas by convolving the initial image without cavitation. In this study, Python-script was used to estimate the POC values of cavitation occurrence areas from the images captured by the high-speed camera.

The images captured by the high-speed camera were divided into sequential frames, and the difference values were extracted based on the number of pixels. In this process, areas where pixel values changed abruptly compared to the initial image without cavitation were extracted. Subsequently, the boundaries of the two images, i.e., one with the most cavitation occurrence and the other without cavitation, were extracted using the image gradients method, and the extracted images were adjusted to gray-scale. Meanwhile, the POC was determined based on the frequency of pixels representing values of 128–255 in the gray-scale adjusted images where cavitation occurred with a VVF of 0.5 or higher. These areas were distinguishable to the naked eye.

Figure 10 shows the results obtained from processing images captured by the high-speed camera during the flow visualization test at a flow rate of 6.5 kg/s. It presents the frequency of pixels corresponding to cavitation occurrence areas with a VVF of 0.5 or higher based on the location of the bottom plug TR. The frequency of pixels in the optimized model is significantly lower compared to the initial model. The total pixel frequencies for the initial and optimized models are 31,503 and 20,126, respectively. With the volume of cavitation danger zone corresponding to 99,696 pixels, the POCs for the initial and optimized models observed in the flow visualization test were estimated to be 31.60% and 20.10%, respectively, using Eq. (2). Table 3 presents a comparison of the POCs for the initial and optimized models of the bottom plug obtained from the flow visualization test and multi-phase fluid dynamics analysis at a flow rate of 6.5 kg/s. They exhibit a difference with an error of 12%.

Frequency of pixels obtained by image gradients method regarding to location of bottom plug TR.

The image gradients method introduced for quantifying the results of the flow visualization test focuses on images of the cavitation region at the TR of the bottom plug, as shown in Fig. 9, which can be visually observed. These images are similar to the volume rendering results from the VVF distribution obtained through multi-phase fluid dynamics analysis, as seen in Fig. 4a, but they do not include the cavitation regions present in the cross-section area inside the TR of the bottom plug. The image gradients method has limitations in accurately representing the POC obtained from the multi-phase fluid dynamics analysis, leading to differences between the POC values from the flow visualization test and those from the multi-phase fluid dynamics analysis. Through further research in the future, it will be necessary to introduce measurement techniques to evaluate the volume of bubbles that occur during the flow visualization tests to address these differences.

In this study, multi-phase fluid dynamics analysis was conducted to evaluate the localized cavitation phenomenon occurring around the bottom plug of a three-way valve. Using the vapor volume fraction (VVF) obtained from this analysis, the percentage of cavitation (POC) was determined. Size optimization of the bottom plug shapes was carried out to reduce cavitation. Additionally, the results of cavitation observed through the flow visualization test were compared with those obtained from the multi-phase fluid dynamics analysis.

In the multi-phase fluid dynamics analysis conducted under curved flow conditions of the three-way valve, with water at 25 °C and a flow rate of 6.5 kg/s at the valve inlet, and the VVF was widely distributed from the TR of the bottom plug to the DR. Areas with VVF > 0.5 were also widely observed, indicating an expected high intensity of cavitation.

The POC calculated by dividing the cavitation occurrence zone with VVF > 0.5 obtained from the multi-phase fluid dynamics analysis into the volume of cavitation danger zones was 34.90%. The cavitation with this POC level could cause mechanical damage to the bottom plug.

The lengths of the waist region (WR) and tail region (TR) were parameterized to perform a size optimal design for the reduction of cavitation. The parametric study showed that as both lengths increased, the POC decreased.

The size optimal design was performed, with the POC as the objective function and a boundary condition ensuring the POC remains below 30%. The lengths of WR and TR were chosen as design variables. Consequently, the optimized lengths of WR and TR were determined to be 5.39 and 6.96 mm, respectively, resulting in a decrease in the POC to 17.62% compared to the initial model.

Through a flow visualization test conducted according to the ISA-RP75.23 standard, which considered the curved flow path of the three-way valve, distinct cavitation was observed around the TR of the bottom plug in the initial model. In contrast, in the specimen reflecting size optimization, the occurrence of cavitation was significantly reduced compared with the initial model.

The flow visualization test results were quantified into the POC using the image gradients method. The POCs for the initial and optimized models were 31.60% and 20.10%, respectively. These values agreed with the results obtained from the multi-phase fluid dynamics analysis with an error of 12%.

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Brian, N. Handbook of Valves and Actuators (Roles&Assocoates Ltd, 2007).

Yang, B. S., Hwang, W. W., Ko, M. H. & lee, S. J. Cavitation detection of butterfly valve using support vector machines. J. Sound Vibr. 287, 25–43. https://doi.org/10.1016/j.jsv.2004.10.033 (2005).

Article ADS CAS Google Scholar

Wang, C. et al. Effect of structure parameters on flow and cavitation characteristics within control valve in fuel injector for modern diesel engine. Energy Convers. Manage. 124, 104–115. https://doi.org/10.1016/j.enconman.2016.07.004 (2016).

Article ADS CAS Google Scholar

Lisowski, E., Filo, G., Pluskowski, P. & Rajda, J. Flow analysis of a novel, three-way cartridge flow control valve. Appl. Sci. 13(6), 3719. https://doi.org/10.3390/app13063719 (2023).

Article CAS Google Scholar

Brilianto, R. M., Seong, H. S., Kwak, H. S. & Kim, C. Improvement of 3-way valve for temperature control of gas turbine lube oil in CCPP. Int. J. Precis. Eng. Manufact. 21, 1321–1332. https://doi.org/10.1007/s12541-020-00339-3 (2020).

Article Google Scholar

Saito, K. & Chongho, Y. Prediction of cavitation erosion occurring in a control valve using computational fluid dynamics (CFD). In 15th International Conf. on Fluid Control, Measurements and Visualization (2019).

Elgmal, H., Zeid, A. & Mohsen, Y. A. Effect of control valve plug shape on the fluid flow characteristics using computational fluid dynamics. Int. J. Sci. Eng. Res. 6(12), 654–663 (2015).

Google Scholar

Jin, W. Cavitation generation and inhibition. I. Dominant mechanism of turbulent kinetic energy for cavitation evolution. AIP Adv. 11, 065028. https://doi.org/10.1063/5.0050231 (2021).

Article ADS CAS Google Scholar

Xu, X., Fang, L., Li, A., Wang, Z. & Li, S. Numerical analysis of the energy loss mechanism in cavitation flow of a control valve. Int. J. Heat Mass Transfer. 174, 121331. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121331 (2021).

Article Google Scholar

Eskilsson, C. & Bensow, R. E. Estimation of cavitation erosion intensity using CFD: Numerical comparison of three different methods. In Fourth International Symposium on Marine Propulsors (2015).

ISA–RP75.23, Considerations for evaluating control valve cavitation. In 1995 the International Society of Automation (1995).

Kubo, M., Araki, T. & Kimura, S. Internal flow analysis of nozzles for DI diesel engines using a cavitation model. JSAE Rev. 24, 225–261. https://doi.org/10.1016/S0389-4304(03)00034-1 (2003).

Article Google Scholar

Kim, M. J., Jin, H. B., Son, C. H. & Chung, W. J. Numerical analysis on cavitation of centrifugal pump. KSFM J. Fluids Eng. 16(2), 27–34 (2013).

Google Scholar

ANSYS 2023 R2 Capabilities, ANSYS Inc. (2024, accessed on 12 Mar 2024). http://www.ansys.com.

Paik, K. J., Par, H. G. & Seo, J. S. RANS simulation of cavitation and hull pressure fluctuation for marine propeller operating behind hull condition. Int. J. Nav. Archit. Ocean. 5, 502–512. https://doi.org/10.2478/IJNAOE-2013-0149 (2017).

Article Google Scholar

Menter, F. R. Two-equation Eddy-viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605. https://doi.org/10.2514/3.12149 (1994).

Article ADS Google Scholar

Jones, W. P. & Launder, B. E. The calculations of low-Reynolds number phenomena with a two-equation model of turbulence. Zm. J. Heat Mass Transfer 16, 1119 (1973).

Article ADS Google Scholar

Wilcox, D. C. Formulation of the k-ω turbulence model revisited. AIAA J. 46, 2823–2838 (2008).

Article ADS Google Scholar

Frank, T., Lifante, C., Jebauer, S. & Kuntz, M. CFD simulation of cloud and tip vortex cavitation on hydrofoils. In 6th International Conf. on Multiphase Flow (2007).

Fourest, T., Deletombe, E., Dupas, J., Arrigoni, M. & Laurens, J. M. Analysis of bubbles dynamics created by hydrodynamic ram in confined geometries using Rayleigh-Plesset equation. Int. J. Impact Eng. 73, 66–74 (2014).

Article ADS Google Scholar

Sauer, J. & Schnerr, G. H. Unsteady cavitating flow-A new cavitation model based on a modified front capturing method and bubble dynamics. In Proceeding of 2000 ASME Fluid Engineering Summer Conference, Boston, MA (2000).

Zwart, P. J., Gerber, A. G. & Belamri, T. A two-phase flow model for prediction cavitation dynamics. In Proceeding of 5th International Conference on Multiphase Flow, Yokohama, Japan (2004).

Weissman, S. A. & Anderson, N. G. Design of experiments (DOE) and process optimization. Org. Process Res. Dev. 19(11), 1605–1633. https://doi.org/10.1021/op500169m (2015).

Article CAS Google Scholar

JMP, SAS Institute Inc. (2024, accessed 12 Mar 2024). http://www.jmp.com/en_us/home.html.

Candioti, L. V., Zan, M. M. D., Camara, M. S. & Goicoechea, H. C. Experimental design and multiple response optimization using the desirability function in analytical methods development. Talanta. 124, 123–138. https://doi.org/10.1016/j.talanta.2014.01.034 (2014).

Article CAS PubMed Google Scholar

Hui, J. & Liu, C. Motion Blur Identification from Image Gradients. In IEEE Conf. on Computer Vision and Pattern Recognition (2008).

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This study was supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF) (2021R1I1A3042151).

Department of Mechanical Engineering, Dong-A University, Busan, 49315, Korea

Hyo Lim Kang, Hyung Joon Park & Seung Ho Han

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All authors contributed to this work by collaboration. Conceptualization, H.L.K. and S.H.H.; software, H.L.K.; validation, H.J.P., H.L.K. and S.H.H.; formal analysis, H.J.P., H.L.K.; writ-ing—original draft preparation, H.L.K.; writing—review and editing, S.H.H.; supervision, S.H.H. All authors approved the publication.

Correspondence to Seung Ho Han.

The authors declare no competing interests.

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Kang, H.L., Park, H.J. & Han, S.H. Evaluation of cavitation phenomena in three-way globe valve through computational analysis and visualization test. Sci Rep 14, 21919 (2024). https://doi.org/10.1038/s41598-024-72585-8

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Received: 10 June 2024

Accepted: 09 September 2024

Published: 19 September 2024

DOI: https://doi.org/10.1038/s41598-024-72585-8

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