Circular cylinder turbulent flow

Before we discuss some conjectures as to the onset of turbulence, let us first of all get a qualitative feel for the different stages of behavior as the Reynolds number is increased. Consider, for example, the viscous flow around a circular cylinder ([feyn64], [bat67]). 

Probstein et al (10) Investigated the use of detached strip type turbulence promoters in the ultrafiltration of bovine serum albumin in laminar flow. His apparatus is shown in Figure 27 the detached strip type promoters tested were circular cylinders with a diameter (D) approximately one-half (0.46) of the channel height and were across the center of the channel cross-section, transverse to the flow. 

An increase in Be indicates a competition between the irreversibilities caused by heat transfer and friction. At high Reynolds numbers, the distribution of Be is relatively more uniform than at lower Re. For a circular Couette device, the Reynolds number (Re = wr2lv) at the transition from laminar to turbulent flow is strongly dependent on the ratio of the gap to the radius of the outer cylinder, 1 — n. The critical Re reaches a value 50,000 at 1 n 0.05. We may control the distribution of the irreversibility by manipulating various operational conditions such as the gap of the Couette device, the Brinkman number, and the boundary conditions. 

The characteristic length for a circular cylinder or sphere is taken to be the external diameter D. Thus, the Reynolds number is defined as Re = VD/v where V is Ihe uniform velocity of Ihe fluid as it approaches the cylinder or splicre. The critical Reynolds number for flow across a circular cylinder or sphere is about Re s 2 X 10. That is, the boundar) layer remains laminar for about Re < 2 X K) and becomes turbulent forRc 2 X l(y. ... 

FIGURE 716 Laminar boundary layer separation witli a turbulent wake flow over a circular cylinder at Re = 7.000. 

C Consider laminar flow of air across a hot circular cylinder. At what point on the cylinder will the heat liansfer be highest What would your answer be if the flow were turbulent 7-38C In flow over cylinders, why does ihe drag cocfTicient suddenly drop when the flow becomes turbulent Isn t turbulence supposed to increase the drag coefficient instead of decreasing it ... 

Similar results are given by Schlicting (12) for the heat transfer to a circular cylinder in cross-flow at varying degrees of turbulence. At the highest turbulence value. 

In the book [117], some data are given on the hydrodynamic characteristics of bodies of various shapes these data mainly pertain to the region of precrisis self-similarity. The influence of roughness of the cylinder surface and the turbulence level of the incoming flow on the drag coefficient is discussed in [522]. In [211], the relationship between hydrodynamic flow characteristics in turbulent boundary layers and the longitudinal pressure gradient is studied. Analysis of the transition to turbulence in the wake of circular cylinders is presented in [333]. 

Estimate convective mass-transfer coefficients for the following situations (a) flow paralell to a flat surface, (b) flow past a single sphere, (c) flow normal to a single cylinder, (d) turbulent flow in circular pipes, (e) flow through packed and fluidized beds, and (f) flow through the shell side of a hollow-fiber membrane module. 

In the range of Reynolds number Re = 103 to 107 (based on cyhnder diameter and free stream velocity), the flow aronnd a solid circular cylinder is periodic and transitional in character. The range of interest of the present work is located in a sub-critical flow regime (103 < Re < 105, corresponding to air velocities of - 0.1-10 m/s around a typically sized 0.1m diameter limb), in which, dne to the vortex shedding at the cylinder surface, the flow is highly unstable. The boundary layer remains fidly laminar up to the separation point and transition to turbulence... 

Couette flow is a laminar circular flow occurring between a rotating (inner) cylinder and a static one, and the extension via increased speed of rotation to centrifugally-driven instabilities leads to laminar Taylor vortex flow, tending to turbulent flow as speed increases. Poiseuille flow is axial. 

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