Laminar-turbulent Transition Reynolds Number Research Articles

Determining critical Reynolds number of laminar-turbulent transition in a flat Poiseuille problem based on “discontinuous functions” method

Determining critical Reynolds number of laminar-turbulent transition in a flat Poiseuille problem based on “discontinuous functions” method

Control of Laminar-Turbulent Transition on a Swept Wing Using Surface Microreliefs

The possibility of laminarization of flow around a swept wing using surface microreliefs in the form of riblets and separate plates (winglets) set at an angle to external streamlines is theoretically investigated. This relief is shown to reduce the crossflow velocity in the boundary layer due to a change in the direction of the near-wall streamlines. On the basis of very simple models based on an analysis of the relief period-averaged boundary layer flow an increase in the Reynolds number of laminar-turbulent transition obtained using the microrelief is estimated. The reasonable surface relief parameters for experimentally investigating the effectiveness of the proposed technique of controlling laminar-turbulent transition are determined.

Tollmien-Schlichting wave generation by flow turbulence

The problem of freestream-turbulence-generated instability waves in the flat-plate boundary layer is solved on the basis of a nonlinear turbulence model admitting the deviation of the speed of propagation of vortex disturbances from the flow velocity. The solution obtained well describes the experimental dependence of the laminar-turbulent transition Reynolds number on the freestream turbulence degree.

Inherently Linear Annular-Duct-Type Laminar Flowmeter

where: C is a constant depends on a duct cross-section shape , A is the duct cross-sectional area, Dh is the hydraulic diameter of the duct, K is the incremental pressure drop number in a fully developed flow region depends both on the duct cross-section shape and on the inflow conditions , L is the distance between the flowmeter pressure taps, is fluid density, and is fluid kinematic viscosity. The first component on the right-hand side of Eq. 1 is the pressure drop in the fully developed flow. The second one describes some additional pressure drop due to momentum change and accumulated increment in wall shear between developing flow and developed flow 1 . It is seen that the relationship between produced differential pressure P and flow rate Q is not linear. As a result, in the majority of commercial laminar flowmeters, to obtain precise Q values software corrections are required. In some of the commercial “laminar flow elements” the entrance effect is ignored as a relatively low one. In order to eliminate the necessity of reading corrections and to achieve inherent linearity the second term of Eq. 1 must be removed. It can be done by locating the first pressure tap P1 at the beginning of the fully developed flow region. As the entrance length Le increases with the Reynolds number Re=DhQ / A , the distance between the duct entrance and the pressure tap P1 should not be shorter than the entrance length for the maximum flow rate, i.e., for the laminar-turbulent transition Reynolds number. The main aim of this work was to determine the design recommendation for the inherently linear laminar annular-duct flowmeter. The pressure distribution along the annular duct was measured. The entrance lengths for various inlet conditions and Reynolds numbers were investigated.

FRICTION CHARACTERISTICS OF WATER, R-134a, AND AIR IN SMALL TUBES

This manuscript provides a systematic test of friction characteristic for air, water, and liquid refrigerant R-134a in 10 tubes with inside diameters from 0.173 to 4.01 mm. The test results show that the conventional minor losses correlations for large tubes may be adequately used to estimate the related inlet, exit and acceleration components for water, refrigerant, and low-speed air flow in microtubes. For high-speed air flow, however, the flow Mach number is too high to be treated as incompressible flow. The conventional minor losses correlations may not be accurate for this condition. The laminar-turbulent transition Reynolds number varies from 1,200 to 3,800 and increases with decreasing tube diameters. The test friction factors for water and refrigerant R-134a agree very well with the conventional Blasius (f = 0.079Re d −0.25) and Poiseuille (f = 16/Re d ) equations in turbulent and laminar flow regime; however, for air flow in small tube at high Reynolds conditions, the flow is entered into the high subsonic flow regime. The Blasius equations developed for the incompressible flow will no longer be appropriate for friction factor prediction.

On the Flow of Bingham Plastic Slurries in Pipes and Between Parallel Plates

Abstract The method of Caldwell and Babbitt for determining Bingham plastic rheological constants from engineering pipe flow data has been erroneously used in many previous applications. A reanalysis of extensive pipe flow data from the literature is performed. Critical Reynolds numbers corresponding to the laminar-turbulent transition calculated from these data are found to agree with theoretically calculated values for the entire flow range studied. Similar agreement is found for the authors' own data for flow of 10 slurries between parallel plates. The Bingham plastic model is shown to be a reliable representation of the flow of non-Newtonian slurries provided it is properly applied. If the Hedstrom number He= pD ro/n greater than 10, then the linear approximation method of Caldwell and Babbitt is invalid for pipe flow data obtained in systems of ordinary engineering interest, and the complete nonlinear form of the pipe flow Bingham plastic equation must be used in determining rheological parameters. Introduction Many materials of engineering interest must be handled and transported as slurries or suspensions of insoluble particulate matter in a Newtonian liquid. These suspensions frequently exhibit non-Newtonian rheological behavior which is reasonably well described by the simple Bingham plastic rheological equation. (1) Using this particular equation to describe the laminar flow characteristics of slurries was discussed at length by Caldwell and Babbitt who considered the flow of various clay slurries and sewage sludges. The model has since been used by many others. More recently the problem of predicting the laminar turbulent transition Reynolds number for Bingham plastic fluids has been treated 8 for the case of flow in pipes. This paper points out errors which have existed in the analysis of Bingham plastic flow since the work of Caldwell and Babbitt and presents a reanalysis of the laminar turbulent transition calculation for Bingham plastic flow in pipes. In addition, new data obtained for flow of Bingham plastic slurries between parallel plates, both in laminar flow and in the laminar turbulent transition region, will be presented and compared with the theoretical analysis of laminar turbulent transition for flow between parallel plates. THEORETICAL ANALYSIS PIPE FLOW The mathematical analysis of laminar flow of a Bingham plastic fluid leads to the following equation. (2) where q less than v greater than /R is a pseudo shear rate, rw is the wall shear stress xio=To/Tw, ro is the yield stress and n is the coefficient of rigidity or plastic viscosity from Eq. 1. Caldwell and Babbitt recognized that the quartic term in Eq. 2 was small compared to the other terms whenever xio less than less than 1, and that for large values of rw a plot of Eq. 2 becomes linear. The slope of such a plot with rw as ordinate is 4n and the intercept is (4/3)ro. This approximation is illustrated schematically in Fig. 1. The shaded region between the true curve and the straight-line approximation near the origin represents the contribution of the quartic term. SPEJ P. 342ˆ