The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible vi...The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.展开更多
This paper investigate some important works done on numerical analysis and modeling of laminar flow in pipes. This review is focused on some methods of approach and the analytical tools used in analyzing of the import...This paper investigate some important works done on numerical analysis and modeling of laminar flow in pipes. This review is focused on some methods of approach and the analytical tools used in analyzing of the important parameters to be considered in laminar flow;such as frictional losses, heat transfer etc. in laminar flow in pipes of different shapes, and the importance of laminar flow in its areas of applications. Prominent researchers have approached this from different perspectives. Some carried out analysis on the pressure drop as a function of permeability, some worked on friction factor analysis, some discussed heat transfer effects of laminar flow in the entrance region, while some discussed its applications in various industries. Some of these works were done considering a given form of pipe configuration or shape which is circular pipes. Only a few, of the literature reviewed have related their considerations to different forms of pipes. Most consider pipes to be majorly circular in shape, but in industries today some circular pipes have become elliptical in shape due to long time usage of the pipes, which would have contributed to increase in some different forms of losses in the industries. In engineering, efficiency and effectiveness improvement is the major goal, if a research work has been done, considering the important parameters in laminar flow showing their effects on different forms of pipe configuration as a result of pipe deformation due to usage, huge amount of money will be saved. This will show clearly how the efficiency of a given circular pipe has seriously been affected due to deformation, and the level of loss this has resulted to.展开更多
Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the ...Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.展开更多
文摘The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.
文摘This paper investigate some important works done on numerical analysis and modeling of laminar flow in pipes. This review is focused on some methods of approach and the analytical tools used in analyzing of the important parameters to be considered in laminar flow;such as frictional losses, heat transfer etc. in laminar flow in pipes of different shapes, and the importance of laminar flow in its areas of applications. Prominent researchers have approached this from different perspectives. Some carried out analysis on the pressure drop as a function of permeability, some worked on friction factor analysis, some discussed heat transfer effects of laminar flow in the entrance region, while some discussed its applications in various industries. Some of these works were done considering a given form of pipe configuration or shape which is circular pipes. Only a few, of the literature reviewed have related their considerations to different forms of pipes. Most consider pipes to be majorly circular in shape, but in industries today some circular pipes have become elliptical in shape due to long time usage of the pipes, which would have contributed to increase in some different forms of losses in the industries. In engineering, efficiency and effectiveness improvement is the major goal, if a research work has been done, considering the important parameters in laminar flow showing their effects on different forms of pipe configuration as a result of pipe deformation due to usage, huge amount of money will be saved. This will show clearly how the efficiency of a given circular pipe has seriously been affected due to deformation, and the level of loss this has resulted to.
文摘Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence c (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where c = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+= 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of c against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, c - 25, and for plate flow, c - 151.5. These findings suggest that a certain combination of c and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence.
