This paper aims to present a new well-balanced,accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation laws.It is a scheme that combines both finite volume approach and characteri...This paper aims to present a new well-balanced,accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation laws.It is a scheme that combines both finite volume approach and characteristic method.In this study,we consider a shallow water system with Coriolis effect and bottom friction stresses where this new Finite Volume Characteristics(FVC)scheme has been applied.The physical and mathematical properties of the system,including the C-property,have been well preserved.First,we developed this approach by preserving the advantages of the finite volume discretization such as conservation property and the method of characteristics,in order to avoid Riemann solvers and to enhance the accuracy without any complexity of the MUSCL reconstruction.Afterward,a discretization was applied to the bottom source term that leads to a well-balanced scheme satisfying the steady-state condition of still water.A semi-implicit treatment will also be presented in this study to avoid stability problems due to source terms.Finally,the proposed finite volume method is verified on several benchmark tests and shows good agreement with analytical solutions and experimental results;moreover,it gives a noteworthy accuracy and rapidity improvement compared to the original approaches.展开更多
Desupersaturation is a complex cooling operation that involves hydrodynamic,thermal and mechanical phenomena.This process requires continuous agitation to avoid fouling problems and sludge deposition.The current work ...Desupersaturation is a complex cooling operation that involves hydrodynamic,thermal and mechanical phenomena.This process requires continuous agitation to avoid fouling problems and sludge deposition.The current work aims to investigate the well mixedness in the desupersaturation tank for optimal performance.For this purpose,a multi-fluid CFD study was conducted based on the Euler–Euler modeling approach,considering a multiphase flow involving a liquid phase(phosphoric acid)and a poly-dispersed solid phase,i.e.a sludge with three different sizes where each size is considered as a separate phase.First,the hydrodynamic behavior of the flow within the agitated desupersaturator is analyzed through the investigation of the velocity fields as well as the power and pumping numbers,to determine both the agitator capacity to pump the flow and its power consumption during the operation.Then,in order to assess the mixture homogeneity,we evaluated the solid suspension in the desupersaturation reactor following conventional methods and two new proposed methodologies:the first approach is to evaluate the suspension quality in the mixing system by compartment and the second consists on the assessment of the uniform convergence of the solid concentration.Furthermore,we calculated the time required to achieve a full suspension at different solid concentrations.On other hand,we conducted a detailed analysis of the solid distribution dependency on the impeller rotational speed at different solid volume fraction,which allows a good understanding of the parameters controlling the homogenization in the desupersaturator.展开更多
基金supported by the HPC Project Alkhwarizmi department,MSDA-UM6P.
文摘This paper aims to present a new well-balanced,accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation laws.It is a scheme that combines both finite volume approach and characteristic method.In this study,we consider a shallow water system with Coriolis effect and bottom friction stresses where this new Finite Volume Characteristics(FVC)scheme has been applied.The physical and mathematical properties of the system,including the C-property,have been well preserved.First,we developed this approach by preserving the advantages of the finite volume discretization such as conservation property and the method of characteristics,in order to avoid Riemann solvers and to enhance the accuracy without any complexity of the MUSCL reconstruction.Afterward,a discretization was applied to the bottom source term that leads to a well-balanced scheme satisfying the steady-state condition of still water.A semi-implicit treatment will also be presented in this study to avoid stability problems due to source terms.Finally,the proposed finite volume method is verified on several benchmark tests and shows good agreement with analytical solutions and experimental results;moreover,it gives a noteworthy accuracy and rapidity improvement compared to the original approaches.
文摘Desupersaturation is a complex cooling operation that involves hydrodynamic,thermal and mechanical phenomena.This process requires continuous agitation to avoid fouling problems and sludge deposition.The current work aims to investigate the well mixedness in the desupersaturation tank for optimal performance.For this purpose,a multi-fluid CFD study was conducted based on the Euler–Euler modeling approach,considering a multiphase flow involving a liquid phase(phosphoric acid)and a poly-dispersed solid phase,i.e.a sludge with three different sizes where each size is considered as a separate phase.First,the hydrodynamic behavior of the flow within the agitated desupersaturator is analyzed through the investigation of the velocity fields as well as the power and pumping numbers,to determine both the agitator capacity to pump the flow and its power consumption during the operation.Then,in order to assess the mixture homogeneity,we evaluated the solid suspension in the desupersaturation reactor following conventional methods and two new proposed methodologies:the first approach is to evaluate the suspension quality in the mixing system by compartment and the second consists on the assessment of the uniform convergence of the solid concentration.Furthermore,we calculated the time required to achieve a full suspension at different solid concentrations.On other hand,we conducted a detailed analysis of the solid distribution dependency on the impeller rotational speed at different solid volume fraction,which allows a good understanding of the parameters controlling the homogenization in the desupersaturator.
