Fluids turbulent flow, transition velocity

To keep the particles in suspension, the flow should be at least 0.15m/sec faster than either 1) the critical deposition velocity of the coarsest particles, or 2) the laminar/turbulent flow transition velocity. The flow rate should also be kept below approximately 3 m/sec to minimize pipe wear. The critical deposition velocity is the fluid flow rate that will just keep the coarsest particles suspended, and is dependent on the particle diameter, the effective slurry density, and the slurry viscosity. It is best determined experimentally by slurry loop testing, and for typical slurries it will lie in the range from 1 m/s to 4.5 m/sec. Many empirical models exist for estimating the value of the deposition velocity, such as the following relations, which are valid over the ranges of slurry characteristics typical for coal slurries ... 

At low velocities between the metal and the solution, the solution flow is laminar, while at high velocities it is turbulent. The transition velocity depends on the geometry, flow rate, liquid viscosity, and surface roughness. The Reynolds number accounts for these effects and predicts the transition from laminar to fluid turbulent flow. The Reynolds number is the ratio of convective to viscous forces in the fluid. For pipes experiencing flow parallel to the centerline of the pipe (4,8) ... 

For slurries exhibiting power-law fluid rheology, the transition velocity from laminar to turbulent flow is governed by the flow behaviour index n of the slurry. The equation proposed by Hanks and Ricks (1974) gives an estimate of this transition velocity in terms of the generalized Reynolds number Re. ... 

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

When a fluid flowing at a uniform velocity enters a pipe, the layers of fluid adjacent to the walls are slowed down as they are on a plane surface and a boundary layer forms at the entrance. This builds up in thickness as the fluid passes into the pipe. At some distance downstream from the entrance, the boundary layer thickness equals the pipe radius, after which conditions remain constant and fully developed flow exists. If the flow in the boundary layers is streamline where they meet, laminar flow exists in the pipe. If the transition has already taken place before they meet, turbulent flow will persist in the... 

Equation 5.2 is found to hold well for non-Newtonian shear-thinning suspensions as well, provided that the liquid flow is turbulent. However, for laminar flow of the liquid, equation 5.2 considerably overpredicts the liquid hold-up e/,. The extent of overprediction increases as the degree of shear-thinning increases and as the liquid Reynolds number becomes progressively less. A modified parameter X has therefore been defined 16 171 for a power-law fluid (Chapter 3) in such a way that it reduces to X both at the superficial velocity uL equal to the transitional velocity (m )f from streamline to turbulent flow and when the liquid exhibits Newtonian properties. The parameter X is defined by the relation... 

Measurements with different fluids, in pipes of various diameters, have shown that for Newtonian fluids the transition from laminar to turbulent flow takes place at a critical value of the quantity pudjp in which u is the volumetric average velocity of the fluid, dt is the internal diameter of the pipe, and p and p. are the fluid s density and viscosity respectively. This quantity is known as the Reynolds number Re after Osborne Reynolds who made his celebrated flow visualization experiments in 1883 ... 

The momentum, which is a certain amount of mass moving at a certain velocity (v), takes into account the fluid s density (p) and the diameter of the tube (Df). The momentum of the fluid can be increased by increasing the velocity or the diameter of the tube or both. The resistance to flow is expressed as the absolute or dynamic viscosity of the fluid (rj), which is in units of grams per centimeter-second, or centipoise (cP). The transition from laminar to turbulent-flow occurs as Re increases past a critical value between 2000 and 3000 in a straight tube having a smooth internal surface. 

Generally, the flow field is assumed as a laminar flow, due to the relatively low velocities that the air reaches inside the cell. Nevertheless, Campanari and Iora (2004) performed a fluid dynamic calculation of the flow in the air injection tube and in the annular section of the cell the results indicated a transition from laminar to turbulent flow the values of the Reynolds number found were in some cases above 1000, whereas the transition between laminar and turbulent flow is stated to be in the range between Re = 750 and Re = 2700. The regime of the flow affects the heat exchange between the gas and the solid material and the diffusion of chemical species. Li and Suzuki (2004) too performed similar calculations and found values of the Reynolds number that were consistent with a regime transition in the air injection tube, but not for the annular section (Re = 385 with a velocity lower than 7.82 m/s). Li and Chyu (2003) state that the assumption of laminar flow is to be rejected. Other researchers, such as Haynes and Wepfer (2001) previously and Stiller et al. (2005) later, assume laminar flow. 

Often it is useful to combine variables that affect physical phenomenon into dimensionless parameters. For example, the transition from laminar to turbulent flow in a pipe depends on the Reynolds number, Re = pLv/p, where p is the fluid density, I is a characteristic dimension of the pipe, v is the velocity of flow, and // is the viscosity of the fluid. Experiments show that the transition from laminar to turbulent flow occurs at the same value of Re for different fluids, flow velocities, and pipe sizes. Analyzing dimensions is made easier if we designate mass as M, length as L, time as t, and force as F. With this notation, the dimensions of the variables in Re are ML 3 for p, (L) for L, (L/t) for v, and (FL 2t) for //. Combining these it is apparent that Re = pLu/p, is dimensionless. 

Reynolds number can be applied to either a fluid flowing around a body or a fluid flowing inside a pipe. The transition from laminar to turbulent flow occurs at different Reynolds numbers for these two cases. The Reynolds numbers at which different flow conditions prevail are tabulated in Table 4.2. Since v is the relative velocity between the medium and the body, the Reynolds number is the same whether the body is moving through a stationary fluid or the fluid is flowing around a stationary body. 

Equation 9.11 is usually referred to as Poiseuille s law and sometimes as the Hagen-Poiseuille law. It assumes that the fluid in the cylinder moves in layers, or laminae, with each layer gliding over the adjacent one (Fig. 9-14). Such laminar movement occurs only if the flow is slow enough to meet a criterion deduced by Osborne Reynolds in 1883. Specifically, the Reynolds number Re, which equals vd/v (Eq. 7.19), must be less than 2000 (the mean velocity of fluid movement v equals JV, d is the cylinder diameter, and v is the kinematic viscosity). Otherwise, a transition to turbulent flow occurs, and Equation 9.11 is no longer valid. Due to frictional interactions, the fluid in Poiseuille (laminar) flow is stationary at the wall of the cylinder (Fig. 9-14). The speed of solution flow increases in a parabolic fashion to a maximum value in the center of the tube, where it is twice the average speed, Jv. Thus the flows in Equation 9.11 are actually the mean flows averaged over the entire cross section of cylinders of radius r (Fig. 9-14). 

The transition from laminar to turbulent flow depends on the surface geometry, surface roughness, upstream velocity, surface temperature, and the type of fluid, among other things, and is best characterized by the Reynolds number. The Reynolds number at a distance x from the leading edge of a flat plate... 

FHow in a tube can be laminar or turbulent, depending on the flow conditions Ruid flow is streamlined and thus laminar at low velocities, but turns turbulent as the velocity is increased beyond a critical value. Transition from laminar lo turbulent flow does not occur suddenly rather, it occurs over some range of velocity where the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent. Most pipe flows encountered in practice are turbulent. Laminar flow is encountered when highly viscous fluids such as oils flow in small diameter tubes or narrow passages. 

In transverse flow along a flat plate the transition from laminar to turbulent flow occurs at Reynolds numbers waL/v between 3 105 and 5 10s wa is the initial flow velocity, L is the length of the plate over which the fluid is flowing. The heat and mass transfer in turbulent flows is more intensive than in laminar. In general, at the same time there is also an increase in the pressure drop. 

Reynold s number It describes the nature of hydraulic regime such as laminar flow, transitional flow or turbulent flow. It is defined as the ratio of the product of hydraulic diameter and mass flow velocity to that of fluid viscosity. Mass velocity is the product of cross-flow velocity and fluid density. Laminar flow exists for Reynold s numbers below 2000 whereas turbulent is characterized by Reynold s numbers greater than 4000. 

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