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Flow in Closed Conduits
Published in William S. Janna, Introduction to Fluid Mechanics, Sixth Edition, 2020
For turbulent flow, the entrance length varies with the one-sixth power of the Reynolds number. Conceptually, there is no upper limit for the Reynolds number in turbulent flow, but in many engineering applications, 104 < Re < 106. Over this range, we calculate, with Equation 5.3: 20<LeD<44
Fundamentals of Fluid Mechanics
Published in Ethirajan Rathakrishnan, Instrumentation, Measurements, and Experiments in Fluids, 2016
The zone upstream of the boundary layer merging point is called the entrance or flow development length and the zone downstream of the merging point is termed fully developed region. In the fully developed region, the velocity profile remains unchanged. Dimensional analysis shows that Reynolds number is the only parameter influencing the entrance length. In the functional form, the entrance length can be expressed as Le=f(ρ,V,d,μ)Led=f1(ρVdμ)=f1(Re)
Fluid Flow and Its Modeling Using Computational Fluid Dynamics
Published in Shyam S. Sablani, M. Shafiur Rahman, Ashim K. Datta, Arun S. Mujumdar, Handbook of Food and Bioprocess Modeling Techniques, 2006
This is a simple flow problem where an analytical solution is available. The length of the pipe between the start and the point where the fully developed flow begins is called the entrance length, Le. This length has been correlated with the Reynolds Number of the flow. For laminar flow, this distance is approximately Entrance Length≈0.06×Re×diameter.
Development and Optimisation of a DNS Solver Using Open-source Library for High-performance Computing
Published in International Journal of Computational Fluid Dynamics, 2021
Hamid Hassan Khan, Syed Fahad Anwer, Nadeem Hasan, Sanjeev Sanghi
Han (1960) depicted the linear solution of the Navier–Stokes equation of the square duct and reported the velocity profile. Entrance length is defined as the distance from the inlet to the point at which the centreline velocity approaches to 99 of the fully developed velocity. Figure 10(a) displays the mesh of the square duct. The velocity and contours at different cross-sectional plane of hydrodynamic developing square duct is shown in Figure 10(b). The centreline axial velocity distribution as a function of x/Re is plotted in Figure 10(c). In entrance length, the Han (1960) centreline velocity from analytical solution is slightly higher than the experimental (Goldstein and Kreid 1967), numerical (Curr, Sharma, and Tatchell 1972) and present DNS simulation centreline velocity. In contrast, Han's prediction for developing flow was over predicted as compared to the Goldstein and Kreid (1967) experimental results. However, the present DNS results are in close agreement with the Goldstein and Kreid (1967) experimental results. The experiment data of a laminar flow data in a square duct presented by Goldstein and Kreid (1967) were in close agreement with Han's prediction for fully developed flow. In fully developed region, the analytical (Han 1960), experimental (Goldstein and Kreid 1967), numerical (Curr, Sharma, and Tatchell 1972) and present results are in good agreement.
Heat transfer and pressure drop correlations for laminar flow in an in-line and staggered array of circular cylinders
Published in Numerical Heat Transfer, Part A: Applications, 2019
Hannes Fugmann, Lena Schnabel, Bettina Frohnapfel
For several applications, it is helpful to know the thermal entrance length of a flow through a structure beyond which the flow is thermally developed. This knowledge allows an estimation whether the entrance region has to be considered in performance evaluation or could be neglected. Following the definition in Eq. (12), the thermal entrance length is nondimensionalized as
Validation of CFD model of multiphase flow through pipeline and annular geometries
Published in Particulate Science and Technology, 2019
Rasel A. Sultan, M. Aziz Rahman, Sayeed Rushd, Sohrab Zendehboudi, Vassilios C. Kelessidis
The minimum length from the entrance to a fully developed flow section, i.e., the entrance length, is around 50Dh, where Dh is the hydraulic diameter (Wasp, Kenny, and Gandhi 1977). The length of the pipelines/annulus was maintained to be long enough (>50Dh) to achieve length-independent results of pressure losses at the fully developed flow section. An example of length independence analyses is shown in Figure 4.