scholarly journals A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equation

2021 ◽  
Author(s):  
Taofiq Omoniyi Amoloye
Keyword(s):  
Fluid Dynamics ◽  
Reynolds Number ◽  
Analytical Solution ◽  
Numerical Simulations ◽  
Closed Form ◽  
Continuity Equation ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Consistent Solution ◽  
Closed Form Analytical Solution

Abstract The three main approaches to exploring fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity equation and Navier-Stokes equations (NSE) that govern experimental observations of fluid dynamics. Theoretical solutions can offer huge advantages over numerical solutions and experiments in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, theoretical solutions have been limited by the prized NSE problem that seeks a physically consistent solution than what classical potential theory (CPT) offers. Therefore, the current author embarked on a doctoral research on the refinement of CPT. He introduced the Refined Potential Theory (RPT) that provides the Kwasu function as a physically consistent solution to the NSE problem. The Kwasu function is a viscous scalar potential function that captures known and observable unsteady features of experimentally observed wall bounded flows including flow separation, wake formation, vortex shedding, compressibility effects, turbulence and Reynolds-number-dependence. It is appropriately defined to combine the properties of a three-dimensional potential function to satisfy the inertia terms of the NSE and the features of a stream function to satisfy the continuity equation, the viscous vorticity equation and the viscous terms of the NSE. RPT has been verified and validated against experimental and numerical results of incompressible unsteady sub-critical Reynolds number flows on stationary finite circular cylinder, sphere and spheroid. It is concluded that the Kwasu function is a physically consistent and closed-form analytical solution to the NSE problem.

scholarly journals A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equations

2021 ◽  
Author(s):  
Taofiq Amoloye
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Potential Theory ◽  
Stream Function ◽  
Continuity Equation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Consistent Solution

Abstract The three main approaches in fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity equation and Navier-Stokes equations (NSE) that govern experimental observations of fluid dynamics.Theoretical solutions can offer huge advantages over numerical solutions and experiments in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, theoretical solutions have been limited by the prized NSE problem that seeks a physically consistent solution than what classical potential theory (CPT) offers. Therefore, the current author refined CPT. He introduced refined potential theory (RPT) that provides a viscous potential/stream function as a physically consistent solution to the NSE problem. This function captures observable unsteady flow features including separation, wake, vortex shedding, compressibility, turbulence, and Reynolds-number-dependence. It appropriately combines the properties of a three-dimensional potential function that satisfy the inertia terms of NSE and the features of a stream function that satisfy the continuity equation, the viscous vorticity equation, and the viscous terms of NSE. RPT has been verified and validated against experimental and numerical results of incompressible unsteady sub-critical Reynolds number flows on stationary finite circular cylinder, sphere, and spheroid.

scholarly journals A computational fluid dynamics investigation of the flow behavior near a wellbore using three-dimensional Navier–Stokes equations

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987325
Author(s):  
Mohammad Jalal Ahammad ◽  
Mohammad Azizur Rahman ◽  
Jahrul Alam ◽  
Stephen Butt
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Hydrocarbon Reservoir ◽  
Wellbore Pressure

The analysis of fluid flow near the wellbore region of a hydrocarbon reservoir is a complex phenomenon. The pressure drop and flow rates change in the near wellbore with time, and the understanding of this system is important. Besides existing theoretical and experimental approaches, computational fluid dynamics studies can help understanding the nature of fluid flow from a reservoir into the wellbore. In this research, a near wellbore model using three-dimensional Navier–Stokes equations is presented for analyzing the flow around the wellbore. Pressure and velocity are coupled into a single system which is solved by an algebraic multigrid method for the optimal computational cost. The computational fluid dynamics model is verified against the analytical solution of the Darcy model for reservoir flow, as well as against the analytical solution of pressure diffusivity equation. The streamlines indicate that the flow is radially symmetric with respect to the vertical plane as expected. The present computational fluid dynamics investigation observes that the motion of reservoir fluid becomes nonlinear at the region of near wellbore. Moreover, this nonlinear behavior has an influence on the hydrocarbon recovery. The flow performance through wellbore is analyzed using the inflow performance relations curve for the steady-state and time-dependent solution. Finally, the investigation suggests that the Navier–Stokes equations along with a near-optimal solver provide an efficient computational fluid dynamics framework for analyzing fluid flow in a wellbore and its surrounding region.

scholarly journals Computational Analysis to Factor Wind into the Design of an Architectural Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Hassam Nasarullah Chaudhry ◽  
John Kaiser Calautit ◽  
Ben Richard Hughes
Keyword(s):  
Fluid Dynamics ◽  
Power Generation ◽  
Computational Fluid Dynamics ◽  
Three Dimensional ◽  
Numerical Data ◽  
Navier Stokes ◽  
Windward Side ◽  
Average Value ◽  
Continuity Equations ◽  
Prevailing Wind Direction

The effect of wind distribution on the architectural domain of the Bahrain Trade Centre was numerically analysed using computational fluid dynamics (CFD). Using the numerical data, the power generation potential of the building-integrated wind turbines was determined in response to the prevailing wind direction. The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations along with the momentum and continuity equations were solved for obtaining the velocity and pressure field. Simulating a reference wind speed of 6 m/s, the findings from the study quantified an estimate power generation of 6.4 kW indicating a capacity factor of 2.9% for the benchmark model. At the windward side of the building, it was observed that the layers of turbulence intensified in inverse proportion to the height of the building with an average value of 0.45 J/kg. The air velocity was found to gradually increase in direct proportion to the elevation with the turbine located at higher altitude receiving maximum exposure to incoming wind. This work highlighted the potential of using advanced computational fluid dynamics in order to factor wind into the design of any architectural environment.

Effect of Outer Fin Axial Gap on the Sealing Effectiveness and Fluid Dynamics of Radial Rim Seal

2017 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Liming Song ◽  
Qing Gao ◽  
Xin Yan ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Flow Rate ◽  
Gas Turbines ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Coolant Flow ◽  
Coolant Flow Rate ◽  
Navier Stokes ◽  
Hot Gas

The modern gas turbine is widely applied in the aviation propulsion and power generation. The rim seal is usually designed at the periphery of the wheel-space and prevented the hot gas ingestion in modern gas turbines. The high sealing effectiveness of rim seal can improve the aerodynamic performance of gas turbines and avoid of the disc overheating. Effect of outer fin axial gap of radial rim seal on the sealing effectiveness and fluid dynamics was numerically investigated in this work. The sealing effectiveness and fluid dynamics of radial rim seal with three different outer fin axial gaps was conducted at different coolant flow rates using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) and SST turbulent model solutions. The accuracy of the presented numerical approach for the prediction of the sealing performance of the turbine rim seal was demonstrated. The obtained results show that the sealing effectiveness of radial rim seal increases with increase of coolant flow rate at the fixed axial outer fin gap. The sealing effectiveness increases with decrease of the axial outer fin gap at the fixed coolant flow rate. Furthermore, at the fixed coolant flow rate, the hot gas ingestion increases with the increase of the axial outer fin gap. This flow behavior intensifies the interaction between the hot gas and coolant flow at the clearance of radial rim seal. The preswirl coefficient in the wheel-space cavity is also illustrated to analyze the flow dynamics of radial rim seal at different axial outer fin gaps.

scholarly journals Three-Dimensional Aerodynamic Analysis of a Darrieus Wind Turbine Blade Using Computational Fluid Dynamics and Lifting Line Theory

2017 ◽  
Author(s):  
Francesco Balduzzi ◽  
Alessandro Bianchini ◽  
Giovanni Ferrara ◽  
David Marten ◽  
George Pechlivanoglou ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
High Performance ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Cost Effective ◽  
Navier Stokes ◽  
Line Theory ◽  
Wake Model ◽  
Lifting Line

Due to the rapid progress in high-performance computing and the availability of increasingly large computational resources, Navier-Stokes computational fluid dynamics (CFD) now offers a cost-effective, versatile and accurate means to improve the understanding of the unsteady aerodynamics of Darrieus wind turbines and deliver more efficient designs. In particular, the possibility of determining a fully resolved flow field past the blades by means of CFD offers the opportunity to both further understand the physics underlying the turbine fluid dynamics and to use this knowledge to validate lower-order models, which can have a wider diffusion in the wind energy sector, particularly for industrial use, in the light of their lower computational burden. In this context, highly spatially and temporally refined time-dependent three-dimensional Navier-Stokes simulations were carried out using more than 16,000 processor cores per simulation on an IBM BG/Q cluster in order to investigate thoroughly the three-dimensional unsteady aerodynamics of a single blade in Darrieus-like motion. Particular attention was payed to tip losses, dynamic stall, and blade/wake interaction. CFD results are compared with those obtained with an open-source code based on the Lifting Line Free Vortex Wake Model (LLFVW). At present, this approach is the most refined method among the “lower-fidelity” models and, as the wake is explicitly resolved in contrast to BEM-based methods, LLFVW analyses provide three-dimensional flow solutions. Extended comparisons between the two approaches are presented and a critical analysis is carried out to identify the benefits and drawbacks of the two approaches.

scholarly journals Three-Dimensional Aerodynamic Analysis of a Darrieus Wind Turbine Blade Using Computational Fluid Dynamics and Lifting Line Theory

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Francesco Balduzzi ◽  
David Marten ◽  
Alessandro Bianchini ◽  
Jernej Drofelnik ◽  
Lorenzo Ferrari ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
High Performance ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Cost Effective ◽  
Navier Stokes ◽  
Line Theory ◽  
Wake Model ◽  
Lifting Line

Due to the rapid progress in high-performance computing and the availability of increasingly large computational resources, Navier–Stokes (NS) computational fluid dynamics (CFD) now offers a cost-effective, versatile, and accurate means to improve the understanding of the unsteady aerodynamics of Darrieus wind turbines and deliver more efficient designs. In particular, the possibility of determining a fully resolved flow field past the blades by means of CFD offers the opportunity to both further understand the physics underlying the turbine fluid dynamics and to use this knowledge to validate lower-order models, which can have a wider diffusion in the wind energy sector, particularly for industrial use, in the light of their lower computational burden. In this context, highly spatially and temporally refined time-dependent three-dimensional (3D) NS simulations were carried out using more than 16,000 processor cores per simulation on an IBM BG/Q cluster in order to investigate thoroughly the 3D unsteady aerodynamics of a single blade in Darrieus-like motion. Particular attention was paid to tip losses, dynamic stall, and blade/wake interaction. CFD results are compared with those obtained with an open-source code based on the lifting line free vortex wake model (LLFVW). At present, this approach is the most refined method among the “lower-fidelity” models, and as the wake is explicitly resolved in contrast to blade element momentum (BEM)-based methods, LLFVW analyses provide 3D flow solutions. Extended comparisons between the two approaches are presented and a critical analysis is carried out to identify the benefits and drawbacks of the two approaches.

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