Hybrid computational solvers that integrate Eulerian and Lagrangian methods are emerging as powerful tools in computational fluid dynamics, particularly for external aerodynamics. These solvers rely on the strengths of both approaches: Eulerian methods efficiently handle boundary layers, while Lagrangian methods excel in reducing numerical diffusion in flow convection. Building on our prior development of a two-dimensional hybrid solver that combines OpenFOAM with vortex particle method, this paper extends its application to the complex phenomena of airfoil stall at low Reynolds numbers. Specifically, we examine both static and dynamic stall conditions of a National Advisory Committee for Aeronautics (NACA) airfoil series 0012 (NACA0012) across a wide range of attack angles and oscillation frequencies, comparing our results with established data. The findings demonstrate the accuracy of hybrid Eulerian–Lagrangian solvers in replicating known stall behaviors, underscoring their potential for advanced aerodynamic studies. This work not only confirms the capability of hybrid solvers in accurately modeling challenging flows but also paves the way for their increased involvement in the field of external aerodynamics.
{"title":"Eulerian–Lagrangian hybrid solvers in external aerodynamics: Modeling and analysis of airfoil stall","authors":"R. Pasolari, C. J. Ferreira, A. van Zuijlen","doi":"10.1063/5.0216634","DOIUrl":"https://doi.org/10.1063/5.0216634","url":null,"abstract":"Hybrid computational solvers that integrate Eulerian and Lagrangian methods are emerging as powerful tools in computational fluid dynamics, particularly for external aerodynamics. These solvers rely on the strengths of both approaches: Eulerian methods efficiently handle boundary layers, while Lagrangian methods excel in reducing numerical diffusion in flow convection. Building on our prior development of a two-dimensional hybrid solver that combines OpenFOAM with vortex particle method, this paper extends its application to the complex phenomena of airfoil stall at low Reynolds numbers. Specifically, we examine both static and dynamic stall conditions of a National Advisory Committee for Aeronautics (NACA) airfoil series 0012 (NACA0012) across a wide range of attack angles and oscillation frequencies, comparing our results with established data. The findings demonstrate the accuracy of hybrid Eulerian–Lagrangian solvers in replicating known stall behaviors, underscoring their potential for advanced aerodynamic studies. This work not only confirms the capability of hybrid solvers in accurately modeling challenging flows but also paves the way for their increased involvement in the field of external aerodynamics.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Simultaneously measuring the fluid flow around a flexible structure and the resulting deformations during short-term yet highly dynamic flow events is the focus of this fluid–structure interaction (FSI) study. These scenarios occur when a wind gust impacts a flexible structure, leading to extreme loads and significant deflections. To mimic such gusts, a specifically designed wind gust generator is used within a wind tunnel featuring an open test section. A high-speed particle-image velocimetry system records the flow field, while the digital-image correlation technique captures the structural deformations. That allows us to perform synchronized coupled fluid–structure measurements for a T-structure under wind gust load. The time-resolved measurements are repeated up to 104 times, allowing for phase-averaging of both the flow and the structural data, and to examine the convergence of the statistics. A comprehensive analysis of the instantaneous and phase-averaged data reveals that the flow field in the vicinity of the structure undergoes noticeable changes during the gust impact. The recirculation region behind the T-structures perceptibly increases when the gust hits the structure. A maximum deformation of about 10% of its height is observed during the highly dynamic gust event. Given (1) the availability of synchronously recorded data for both the fluid flow and the structure deformation, (2) the simplicity of the structure's geometry, and (3) the moderate Reynolds number of about 4×104, this case also serves as a well-suited benchmark test case for evaluating simulation methodologies for strongly coupled, highly dynamic FSI problems.
{"title":"Synchronous high-speed measurements of a flexible structure under wind gust load","authors":"M. Breuer, Torben Neumann","doi":"10.1063/5.0215724","DOIUrl":"https://doi.org/10.1063/5.0215724","url":null,"abstract":"Simultaneously measuring the fluid flow around a flexible structure and the resulting deformations during short-term yet highly dynamic flow events is the focus of this fluid–structure interaction (FSI) study. These scenarios occur when a wind gust impacts a flexible structure, leading to extreme loads and significant deflections. To mimic such gusts, a specifically designed wind gust generator is used within a wind tunnel featuring an open test section. A high-speed particle-image velocimetry system records the flow field, while the digital-image correlation technique captures the structural deformations. That allows us to perform synchronized coupled fluid–structure measurements for a T-structure under wind gust load. The time-resolved measurements are repeated up to 104 times, allowing for phase-averaging of both the flow and the structural data, and to examine the convergence of the statistics. A comprehensive analysis of the instantaneous and phase-averaged data reveals that the flow field in the vicinity of the structure undergoes noticeable changes during the gust impact. The recirculation region behind the T-structures perceptibly increases when the gust hits the structure. A maximum deformation of about 10% of its height is observed during the highly dynamic gust event. Given (1) the availability of synchronously recorded data for both the fluid flow and the structure deformation, (2) the simplicity of the structure's geometry, and (3) the moderate Reynolds number of about 4×104, this case also serves as a well-suited benchmark test case for evaluating simulation methodologies for strongly coupled, highly dynamic FSI problems.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141700793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chao Lv, Zhaoxiang Ji, Haiwei Zhang, Tao Yang, Hongliang Zhao
The volume of fluid-continuum surface force model is used to systematically study the influence of characteristic parameters, internal pressure on the dynamic characteristics, finite deformation mode, and fracture mode of compound droplets in air. The simulation results indicate that the morphology evolution of compound droplets can be divided into two stages: expansion deformation stage and irregular deformation stage. And for the first time, it is proposed that the crushing methods of compound droplets can be divided into two types: overall oscillation and local oscillation. Increasing the internal pressure of the compound droplet will cause severe deformation of the compound droplet, and the time required for the expansion and deformation stage will be reduced. However, the influence of fluid interfacial tension and viscosity on the bottom dynamics of compound droplets is often complex, leading to significant changes in the deformation mode of compound droplets. In addition, the influence of feature parameters We and Ca is further discussed. The research results can provide theoretical guidance for precise control of their arrangement in core–shell driven microfluidic technology.
利用流体-真空表面力体积模型，系统研究了特征参数、内压对空气中复合液滴动态特性、有限变形模式和断裂模式的影响。模拟结果表明，复合液滴的形态演变可分为两个阶段：膨胀变形阶段和不规则变形阶段。并首次提出复合液滴的破碎方式可分为整体振荡和局部振荡两种。增加复合液滴的内部压力会引起复合液滴的剧烈变形，并缩短膨胀变形阶段所需的时间。然而，流体界面张力和粘度对复合液滴底部动力学的影响往往比较复杂，导致复合液滴的变形模式发生显著变化。此外，还进一步讨论了特征参数 We 和 Ca 的影响。研究成果可为在核壳驱动微流控技术中精确控制它们的排列提供理论指导。
{"title":"A numerical investigation on the morphology evolution of compound droplets","authors":"Chao Lv, Zhaoxiang Ji, Haiwei Zhang, Tao Yang, Hongliang Zhao","doi":"10.1063/5.0218423","DOIUrl":"https://doi.org/10.1063/5.0218423","url":null,"abstract":"The volume of fluid-continuum surface force model is used to systematically study the influence of characteristic parameters, internal pressure on the dynamic characteristics, finite deformation mode, and fracture mode of compound droplets in air. The simulation results indicate that the morphology evolution of compound droplets can be divided into two stages: expansion deformation stage and irregular deformation stage. And for the first time, it is proposed that the crushing methods of compound droplets can be divided into two types: overall oscillation and local oscillation. Increasing the internal pressure of the compound droplet will cause severe deformation of the compound droplet, and the time required for the expansion and deformation stage will be reduced. However, the influence of fluid interfacial tension and viscosity on the bottom dynamics of compound droplets is often complex, leading to significant changes in the deformation mode of compound droplets. In addition, the influence of feature parameters We and Ca is further discussed. The research results can provide theoretical guidance for precise control of their arrangement in core–shell driven microfluidic technology.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141710164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this study was to characterize the impact of the diversion angle on the bed morphology, flow structure, and sediment fluxes at mobile-bed, open channel bifurcations, both uncontrolled and controlled with a submerged vane-field. The study also addressed the effects of the skew angle of the vanes and of the mobility of the diversion channel bed. For these purposes, 24 experiments were carried out with the diversion angles θ = {30°, 45°, 60°, 75°, 90°, 120°}. The recirculation zones in the diversion channel were classified according to their aspect ratios and two governing secondary circulations were identified inside these zones. In the presence of a vane-field, a strong vortex developed in the main channel all along the vane-field until past the diversion entrance. This vortex incorporated the main channel leg of the unique two-leg vortex that is otherwise identified in the absence of vanes at the downstream diversion corner. An independent diversion channel vortex replaced the diversion channel leg of the two-leg vortex. The best desilting efficiency was achieved for the diversion angle θ = 30°, regardless of the presence or the absence of vanes and the mobility of the diversion channel bed. In fully mobile-bed bifurcations, complete desilting was achieved for θ = 30° and α = 45°. This was also achieved for any of the tested skew angles, α = {15°, 45°}, when the diversion channel bed was rigid.
{"title":"Effect of diversion angle and vanes' skew angle on the hydro-morpho-dynamics of mobile-bed open-channel bifurcations controlled by submerged vane-fields","authors":"Firat Gumgum, António Heleno Cardoso","doi":"10.1063/5.0211623","DOIUrl":"https://doi.org/10.1063/5.0211623","url":null,"abstract":"The aim of this study was to characterize the impact of the diversion angle on the bed morphology, flow structure, and sediment fluxes at mobile-bed, open channel bifurcations, both uncontrolled and controlled with a submerged vane-field. The study also addressed the effects of the skew angle of the vanes and of the mobility of the diversion channel bed. For these purposes, 24 experiments were carried out with the diversion angles θ = {30°, 45°, 60°, 75°, 90°, 120°}. The recirculation zones in the diversion channel were classified according to their aspect ratios and two governing secondary circulations were identified inside these zones. In the presence of a vane-field, a strong vortex developed in the main channel all along the vane-field until past the diversion entrance. This vortex incorporated the main channel leg of the unique two-leg vortex that is otherwise identified in the absence of vanes at the downstream diversion corner. An independent diversion channel vortex replaced the diversion channel leg of the two-leg vortex. The best desilting efficiency was achieved for the diversion angle θ = 30°, regardless of the presence or the absence of vanes and the mobility of the diversion channel bed. In fully mobile-bed bifurcations, complete desilting was achieved for θ = 30° and α = 45°. This was also achieved for any of the tested skew angles, α = {15°, 45°}, when the diversion channel bed was rigid.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141690247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In harsh flow environments, traditional particle-based velocimetry methods face challenges. This study explores the use of seedless schlieren images for velocimetry through a novel algorithm, namely, wavelet-based optical flow velocimetry (wOFV). Various data term constraints for wOFV were examined. It is found that the data term derived from the integrated continuity equation (ICE) outperformed the conventional displaced frame difference constraint and the schlieren-tailored constraints (SE and SSE). Evaluation based on the root mean square error (RMSE) and turbulence energy spectrum (TES) reveals that the choice of wavelet becomes insignificant for the optimal estimated velocity field when the wavelet support length is sufficiently long. In addition, the implementation of a proper truncation in wOFV shows little dependence of the RMSE on the weighting coefficient, therefore alleviating the uncertainty associated with selecting an appropriate weighting coefficient. It is found that the retrieved flow field from schlieren images approximates a down-sampled result based on available structural scales in images. Considering the prevalence of under-resolved velocity field in practical applications, schlieren-based wOFV offers a reasonable alternative to particle-based velocimetry, particularly in harsh flow environments.
{"title":"Evaluation of seedless wavelet-based optical flow velocimetry for schlieren images","authors":"Mingjia Chen, Zhixin Zhao, Yuchen Hou, Jiajian Zhu, Mingbo Sun, Bo Zhou","doi":"10.1063/5.0208692","DOIUrl":"https://doi.org/10.1063/5.0208692","url":null,"abstract":"In harsh flow environments, traditional particle-based velocimetry methods face challenges. This study explores the use of seedless schlieren images for velocimetry through a novel algorithm, namely, wavelet-based optical flow velocimetry (wOFV). Various data term constraints for wOFV were examined. It is found that the data term derived from the integrated continuity equation (ICE) outperformed the conventional displaced frame difference constraint and the schlieren-tailored constraints (SE and SSE). Evaluation based on the root mean square error (RMSE) and turbulence energy spectrum (TES) reveals that the choice of wavelet becomes insignificant for the optimal estimated velocity field when the wavelet support length is sufficiently long. In addition, the implementation of a proper truncation in wOFV shows little dependence of the RMSE on the weighting coefficient, therefore alleviating the uncertainty associated with selecting an appropriate weighting coefficient. It is found that the retrieved flow field from schlieren images approximates a down-sampled result based on available structural scales in images. Considering the prevalence of under-resolved velocity field in practical applications, schlieren-based wOFV offers a reasonable alternative to particle-based velocimetry, particularly in harsh flow environments.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The hydraulic properties of a fractured rock mass are largely controlled by connected fracture networks. A thorough understanding of the physical flow processes in fracture networks is essential for assessing the transport capacity of the rock mass. However, the fracture surface roughness morphology, fracture distribution characteristics, and fluid flow regimes strongly influence the flow capacity of a fracture network. To this end, the rough topographic characteristics of fracture surfaces were quantified using fractal theory, and then the effective permeability model and nonlinear seepage effect assessment model of the rough fracture network for different flow regimes were developed based on the possible occurrence of laminar and turbulent flows in a single fracture. Finally, the influences of the geometric parameters of the fracture network on the effective permeability and nonlinear flow characteristics were analyzed. The results show that the prediction results of the proposed models are in good agreement with the field test data and can effectively reveal the seepage influence mechanisms under different flow regimes. Additionally, the results show that the effective permeability is closely related to the fractal dimension, relative roughness, aperture scale, distribution characteristics, and hydraulic gradient of the fractures. The nonlinear behavior of fluid flow significantly reduces the effective permeability of the rock mass. The proposed models can provide a reference for evaluating the transport capacity of rock masses under different fracture distributions and flow regimes.
{"title":"Combined effects of the roughness, aperture, and fractal features on the equivalent permeability and nonlinear flow behavior of rock fracture networks","authors":"Mingkai Zhao, Desen Kong, Sen Teng, Jian Shi","doi":"10.1063/5.0208425","DOIUrl":"https://doi.org/10.1063/5.0208425","url":null,"abstract":"The hydraulic properties of a fractured rock mass are largely controlled by connected fracture networks. A thorough understanding of the physical flow processes in fracture networks is essential for assessing the transport capacity of the rock mass. However, the fracture surface roughness morphology, fracture distribution characteristics, and fluid flow regimes strongly influence the flow capacity of a fracture network. To this end, the rough topographic characteristics of fracture surfaces were quantified using fractal theory, and then the effective permeability model and nonlinear seepage effect assessment model of the rough fracture network for different flow regimes were developed based on the possible occurrence of laminar and turbulent flows in a single fracture. Finally, the influences of the geometric parameters of the fracture network on the effective permeability and nonlinear flow characteristics were analyzed. The results show that the prediction results of the proposed models are in good agreement with the field test data and can effectively reveal the seepage influence mechanisms under different flow regimes. Additionally, the results show that the effective permeability is closely related to the fractal dimension, relative roughness, aperture scale, distribution characteristics, and hydraulic gradient of the fractures. The nonlinear behavior of fluid flow significantly reduces the effective permeability of the rock mass. The proposed models can provide a reference for evaluating the transport capacity of rock masses under different fracture distributions and flow regimes.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141696396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reducing the reliance on intrusive flow probes is a critical task in active flow control based on deep reinforcement learning (DRL). Although a scarcity of flow data captured by probes adversely impacts the control proficiency of the DRL agent, leading to suboptimal flow modulation, minimizing the use of redundant probes significantly reduces the overall implementation costs, making the control strategy more economically viable. In this paper, we propose an active flow control method based on physics-informed DRL. This method integrates a physics-informed neural network into the DRL framework, harnessing the inherent physical characteristics of the flow field using strategically placed probes. We analyze the impact of probe placement, probe quantity, and DRL agent sampling strategies on the fidelity of flow predictions and the efficacy of flow control. Using the wake control of a two-dimensional cylinder flow with a Reynolds number of 100 as a case study, we position a specific number of flow probes within the flow field to gather pertinent information. When benchmarked against traditional DRL techniques, the results are unequivocal: in terms of training efficiency, physics-informed DRL reduces the training cycle by up to 30 rounds. Furthermore, by decreasing the number of flow probes in the flow field from 164 to just 4, the physics-based DRL achieves superior drag reduction through more precise control. Notably, compared to traditional DRL control, the drag reduction effect is enhanced by a significant 6%.
{"title":"Efficient deep reinforcement learning strategies for active flow control based on physics-informed neural networks","authors":"Wulong Hu, Zhangze Jiang, Mingyang Xu, Hanyu Hu","doi":"10.1063/5.0213256","DOIUrl":"https://doi.org/10.1063/5.0213256","url":null,"abstract":"Reducing the reliance on intrusive flow probes is a critical task in active flow control based on deep reinforcement learning (DRL). Although a scarcity of flow data captured by probes adversely impacts the control proficiency of the DRL agent, leading to suboptimal flow modulation, minimizing the use of redundant probes significantly reduces the overall implementation costs, making the control strategy more economically viable. In this paper, we propose an active flow control method based on physics-informed DRL. This method integrates a physics-informed neural network into the DRL framework, harnessing the inherent physical characteristics of the flow field using strategically placed probes. We analyze the impact of probe placement, probe quantity, and DRL agent sampling strategies on the fidelity of flow predictions and the efficacy of flow control. Using the wake control of a two-dimensional cylinder flow with a Reynolds number of 100 as a case study, we position a specific number of flow probes within the flow field to gather pertinent information. When benchmarked against traditional DRL techniques, the results are unequivocal: in terms of training efficiency, physics-informed DRL reduces the training cycle by up to 30 rounds. Furthermore, by decreasing the number of flow probes in the flow field from 164 to just 4, the physics-based DRL achieves superior drag reduction through more precise control. Notably, compared to traditional DRL control, the drag reduction effect is enhanced by a significant 6%.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141698695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Over the course of several decades, numerous model equations of the macroscopic fluid flow through porous media have been proposed. The application of such equations is, however, often complicated due to the requirement of variant specifications of parameters and empirical factors for different flow regimes. It is, therefore, necessary and desirable to have a unified fundamental equation that is capable of predicting porous media flows for the entire spectrum of flow regimes that are practically encountered. This work aims to fulfill that requirement. With the aid of a hypothesis-based analysis, finite-element simulations, and published experimental data, a new macroscopic transport equation has been proposed to predict statistically stationary single-phase incompressible flows through a non-deformable stationary porous medium. The new model may be written as a drag law associated with a dimensionless resistance parameter that is a function of the porous medium geometry and the flow forces. Though complex, this resistance parameter may be modeled as a power function in terms of three predictable parameters. Overall, the proposed transport equation has been found to be a more extensive form of other key models in existence. Using approximately 6000 analytical, numerical, and experimental data points, the equation has been validated as an excellent model for creeping, inertial, transitional, and turbulent porous media flows. The results show that the proposed equation is applicable to simple and complex porous media of 30%–90% porosity. Moreover, a dimensionless group in terms of the equation's resistance parameter has been established as useful for scaling.
{"title":"A unified macroscopic equation for creeping, inertial, transitional, and turbulent fluid flows through porous media","authors":"J. K. Arthur","doi":"10.1063/5.0215565","DOIUrl":"https://doi.org/10.1063/5.0215565","url":null,"abstract":"Over the course of several decades, numerous model equations of the macroscopic fluid flow through porous media have been proposed. The application of such equations is, however, often complicated due to the requirement of variant specifications of parameters and empirical factors for different flow regimes. It is, therefore, necessary and desirable to have a unified fundamental equation that is capable of predicting porous media flows for the entire spectrum of flow regimes that are practically encountered. This work aims to fulfill that requirement. With the aid of a hypothesis-based analysis, finite-element simulations, and published experimental data, a new macroscopic transport equation has been proposed to predict statistically stationary single-phase incompressible flows through a non-deformable stationary porous medium. The new model may be written as a drag law associated with a dimensionless resistance parameter that is a function of the porous medium geometry and the flow forces. Though complex, this resistance parameter may be modeled as a power function in terms of three predictable parameters. Overall, the proposed transport equation has been found to be a more extensive form of other key models in existence. Using approximately 6000 analytical, numerical, and experimental data points, the equation has been validated as an excellent model for creeping, inertial, transitional, and turbulent porous media flows. The results show that the proposed equation is applicable to simple and complex porous media of 30%–90% porosity. Moreover, a dimensionless group in terms of the equation's resistance parameter has been established as useful for scaling.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The permeable-surface Ffowcs Williams and Hawkings (FW–H) integration for computing the far-field sound has the advantage of encapsulating the sources and nonlinear propagation inside the integral surface. However, it suffers from spurious sound when the volume integral for quadrupole term outside the permeable surface is conventionally ignored. The spurious sound is often suppressed by using two distinct approaches, which modifies the FW–H integration and acoustic variables/sources, respectively. This work clarifies the connection between the two approaches by analyzing the integral of the quadrupole sources. We show that the modification of the acoustic sources can be reformulated as a modification of the FW–H integration, which means that the two distinct approaches are interconvertible. A new quadrupole correction model for the FW–H integration is proposed by delicately modifying the acoustic sources. The modified acoustic sources consist of the filtered Lighthill stress tensor, where a convection operator is used to filter out the acoustically inefficient components. The proposed quadrupole correction model is consistent with the previous work on the modification of the FW–H integration under special conditions with the uniform convection velocity. The proposed model is validated by computing the sound pressure generated by laminar and turbulent flows over bluff bodies. It is found that the sensitivity of the acoustic pressure to the FW–H surface's position is suppressed and the accuracy of the predicted sound is improved. The results suggest that the modification of acoustic variables/sources can be a powerful method to construct new quadrupole correction models for the permeable FW–H integration.
{"title":"Frequency-domain quadrupole correction for the permeable-surface Ffowcs Williams and Hawkings integration","authors":"Zhiteng Zhou, Yi Liu, Shizhao Wang","doi":"10.1063/5.0213379","DOIUrl":"https://doi.org/10.1063/5.0213379","url":null,"abstract":"The permeable-surface Ffowcs Williams and Hawkings (FW–H) integration for computing the far-field sound has the advantage of encapsulating the sources and nonlinear propagation inside the integral surface. However, it suffers from spurious sound when the volume integral for quadrupole term outside the permeable surface is conventionally ignored. The spurious sound is often suppressed by using two distinct approaches, which modifies the FW–H integration and acoustic variables/sources, respectively. This work clarifies the connection between the two approaches by analyzing the integral of the quadrupole sources. We show that the modification of the acoustic sources can be reformulated as a modification of the FW–H integration, which means that the two distinct approaches are interconvertible. A new quadrupole correction model for the FW–H integration is proposed by delicately modifying the acoustic sources. The modified acoustic sources consist of the filtered Lighthill stress tensor, where a convection operator is used to filter out the acoustically inefficient components. The proposed quadrupole correction model is consistent with the previous work on the modification of the FW–H integration under special conditions with the uniform convection velocity. The proposed model is validated by computing the sound pressure generated by laminar and turbulent flows over bluff bodies. It is found that the sensitivity of the acoustic pressure to the FW–H surface's position is suppressed and the accuracy of the predicted sound is improved. The results suggest that the modification of acoustic variables/sources can be a powerful method to construct new quadrupole correction models for the permeable FW–H integration.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High-load counter-rotating compressor plays a crucial role in reducing the axial length and weight of the compressor and increasing the thrust-to-weight ratio of the aero-engine. However, the boundary layer flow separation induced by shock waves in the channel of high adverse pressure gradient also brings more aerodynamic losses. This paper proposed a supersonic compressor cascade modeling method based on the unique inlet angle theory and the superimposing thickness on the suction surface method. It carried out aerodynamic optimization design of cascade with inlet Mach number of 1.85 combined with numerical optimization technology, vorticity dynamics diagnosis, and planar cascade experiment. The results show that multiple shock wave combination pressurization can be realized in the supersonic cascade channel. At the design point, the static pressure ratio is 3.285, and the total pressure recovery coefficient reaches 86.82%, and the experimental results of planar cascade also verify the correctness of the simulation method. In addition, the correlation laws between the distribution of the vorticity dynamic parameter, shock wave structure, and aerodynamic performance of cascade were analyzed by the vorticity dynamic flow field diagnosis method, which provides a beneficial reference for the subsequent compressor design.
{"title":"Aerodynamic design of supersonic compressor cascade and vorticity dynamic diagnosis of flow field structure","authors":"Tingsong Yan, Peigang Yan, Zhuoming Liang, Huanlong Chen","doi":"10.1063/5.0218472","DOIUrl":"https://doi.org/10.1063/5.0218472","url":null,"abstract":"High-load counter-rotating compressor plays a crucial role in reducing the axial length and weight of the compressor and increasing the thrust-to-weight ratio of the aero-engine. However, the boundary layer flow separation induced by shock waves in the channel of high adverse pressure gradient also brings more aerodynamic losses. This paper proposed a supersonic compressor cascade modeling method based on the unique inlet angle theory and the superimposing thickness on the suction surface method. It carried out aerodynamic optimization design of cascade with inlet Mach number of 1.85 combined with numerical optimization technology, vorticity dynamics diagnosis, and planar cascade experiment. The results show that multiple shock wave combination pressurization can be realized in the supersonic cascade channel. At the design point, the static pressure ratio is 3.285, and the total pressure recovery coefficient reaches 86.82%, and the experimental results of planar cascade also verify the correctness of the simulation method. In addition, the correlation laws between the distribution of the vorticity dynamic parameter, shock wave structure, and aerodynamic performance of cascade were analyzed by the vorticity dynamic flow field diagnosis method, which provides a beneficial reference for the subsequent compressor design.","PeriodicalId":509470,"journal":{"name":"Physics of Fluids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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