The paper “ Pressure, Velocity, Reynolds Number and Mach Numbers of Two Fluids Flowing through the Pipes” is a fascinating version of a lab report on physics. The paper is about a simulation of two fluid with different viscosity and density. Through an S bend having a diameter of 20 mm. The two conditions are air as a fluid with an initial Reynolds number of 500 and the second fluids with initial Reynolds number of 50000. The geometry of the pipe applicable in the two cases is similar. For both the experiments the fluid had different densities and viscosities.
This was meant to be able to study the relationship of Reynolds number as well as the inlet match numbers (Versteeg, p. 60). Reynolds numberIt is essential in determining the flow patterns of different flow situations. Some of its applications involve the flow of liquids in a pipe as well as establishing the flow of air through pipes and aircraft wings. It also helps in defining the transition point between the laminar and turbulent flows. This is the ratio of the forces of inertia to friction in flowing fluid through a pipe.
The internal movement is caused by the presence of varying velocities at various points of the fluid. The number can be used to determine the dynamic similitude that flows for two fluids having different velocities. For laminar flows, the corresponding Reynolds number is low because of the forces involved in the movement of the fluid. In turbulent flows, the number is usually high due to the higher levels of inertial forces. The Reynolds number can be derived as follows by the following equation (Larsson, p.
293). Whereρ = fluid density (SI units: kg/m3)u = fluid velocity in relation to the object (m/s)L = characteristic linear dimension (m)μ =fluid dynamic viscosity (Pa· s or N· s/m2 or kg/m· s)ν = fluid kinematic viscosity (m2/s). Density and the viscosity of fluid are essential in the definition of a Reynolds number of a given fluid. When studying the flow in a pipe, the Reynolds number can be defined as follows. Where DH = pipe hydraulic diameter of the pipe (the inside diameter of the pipe is circular) (m). Q = volumetric flow rate (m3/s). A = pipe's cross-sectional area (m2). υ =mean velocity of the fluid (m/s). μ = dynamic viscosity of the fluid (Pa· s = N· s/m2 = kg/(m· s)). ν (nu) = kinematic viscosity (ν = μ /ρ ) (m2/s). ρ = fluid density (kg/m3). After the fluid has flowed for some time, it loses its laminar characteristic resulting in the formation of a turbulent flow.
As long as the Reynolds number is less than 1000, then the flow is a laminar flow. However, when the number exceeds one thousand, the flow converts to turbulent. The transition value for the Reynolds number is known as the critical Reynolds number.
Whenever a fluid flows through the pipes, there is friction that occurs at the contact surfaces of the fluid and the pipe. The diagram below shows the transition between laminar and turbulent flow (Larsson, p. 293). Inlet Mach numbersThis refers to the ratio of the speed of flow of fluid to the sound produced by the same fluid. For incompressible fluids, the Match number is mostly less than the value of 0.3. This is attributed to the fact that density changes caused by differences in velocity are less than five percent.
For compressible fluids, the figure is relatively high because the differences in densities caused by the velocity changes are greater than five percent. The figure below is a demonstration of the spectrum of the Mach number (Larsson, p. 293).
Versteeg, Henk Kaarle, and Weeratunge Malalasekera. An introduction to computational fluid dynamics: the finite volume method. Pearson Education, (2007):56-98.
Moin, Parviz, et al. "A dynamic subgrid‐scale model for compressible turbulence and scalar transport." Physics of Fluids A: Fluid Dynamics 3.11 (1991): 2746-2757.
Brown, David L., Ricardo Cortez, and Michael L. Minion. "Accurate projection methods for the incompressible Navier–Stokes equations." Journal of computational physics 168.2 (2001): 464-499.
Larsson, Johan, Ivan Bermejo-Moreno, and Sanjiva K. Lele. "Reynolds-and Mach-number effects in canonical shock-turbulence interaction." Journal of Fluid Mechanics 717 (2013): 293.