Flow measurement Reynolds number

A demonstration of this approach has been reported to evaluate the ability of a lattice-Boltzmann code to predict both spatially resolved flow fields and MR propagators characterizing flow through random packings of spheres (model fixed beds) for flows defined by Peclet (Pe) and Reynolds numbers in the range 182 < Pc <3 50 and 0.4 < Re <0.77 (85). Excellent agreement was found between the numerical predictions and experimental measurements. Current interest in this field addresses the validation and development of numerical codes predicting flows at Reynolds numbers more appropriate to real catalytic reactors. 

At velocities greater than the critical, the fluid velocity profile in the conduit is uniform across the conduit diameter except for a thin layer of fluid at the conduit wall. This boundary layer continues to move in laminar flow. In connection with flow measurement, most flowmeters have constant coefficients under turbulent flow conditions. Some flowmeters have the advantage of constant coefficients over Reynolds Number ranges encompassing both turbulent and laminar flows. See also Fluid and Fluid Flow and Reynolds Number. 

Sometimes, this expectation is not met. At high flow rates, there can be hydrodynamic instabilities that lead to secondary flows which ruin the rheological measurement. Such instabilities occur in Newtonian fluids, due, for example, to inertial effects, such as those in Poiseuille flow at Reynolds numbers exceeding 2000 (Drazin and Reid 1981). For some complex fluids, even at low Reynolds number there are instabilities that are driven by elastic effects (Larson 1992). 

High-Viscosity Systems All axial-flow impellers become radial flow as Reynolds numbers approach the viscous region. Blending in the transition and low-viscosity system is largely a measure of fluid motion throughout the tank. For close-clearance impellers, the anchor and helical impellers provide blending by having an effective action at the tank wall, which is particularly suitable for pseudoplastic fluids. 

There have been few experimental tests of the theoretical predictions of turbulent coagulation under controlled conditions. Delichaisios and Probstein (1975) measured rates of coagulation of 0.6-mm latex particles suspended in an aqueous solution in turbulent pipe flow. The Reynolds numbers ranged from 17,000 to 51,000 for flow through a 1-in. (l.D.) smooth-walled pipe. For the core of the pipe flow, the turbulence was approximately isotropic. The energy dissipation per unit mass was calculated from the relation... 

We need to develop an independent qualified flow test facility with basic measurements traceable to the National Bureau of Standards. This facility should be operated irnder the sponsorship of the gas industry. It must be capable of evaluating metering devices, both new and existing and provide documented data on performance characteristics at various temperatures, pressures, flow rates, Reynolds Number, etc. 

The equations derived for the rotating-disc electrode are limited for laminar flow. The Reynolds number was introduced as a measure for the transition to turbulent flow (Section 5.1). For the rotating disc the Reynolds number is given by the equation... 

Polymerization occurs to almost complete yield with no termination or transfer, but with two species of different activity. An example of such a reaction is the anionic polymerization of styrene, in which both the free anion and the ion pair are active species. However, these polymerizations proceed so rapidly that they can no longer be followed with the normal kinetic techniques. Kinetic measurements are therefore carried out by accelerated flow techniques (Figure 18-5). A turbulent current must prevail in this flow tube (Reynolds number over 10,000), since the chains would show growth times of differing duration with a laminar current. In a flow tube, the effective polymerization time t depends on the volume Vq of the flow tube (distance between the mixing jets) and on the volume V of the total liquid flowing through in the time t ... 

La.mina.r Flow Elements. Each of the previously discussed differential-pressure meters exhibits a square root relationship between differential pressure and flow there is one type that does not. Laminar flow meters use a series of capillary tubes, roUed metal, or sintered elements to divide the flow conduit into innumerable small passages. These passages are made small enough that the Reynolds number in each is kept below 2000 for all operating conditions. Under these conditions, the pressure drop is a measure of the viscous drag and is linear with flow rate as shown by the PoiseuiHe equation for capilary flow ... 

A turbine flowmeter consists of a straight flow tube containing a turbine which is free to rotate on a shaft supported by one or more bearings and located on the centerline of the tube. Means are provided for magnetic detection of the rotational speed, which is proportional to the volumetric flow rate. Its use is generally restric ted to clean, noncorrosive fluids. Additional information on construction, operation, range, and accuracy can be obtained from Holzbock (Instruments for Measurement and Control, 2d ed., Reinhold, New York, 1962, pp. 155-162). For performance characteristics of these meters with liquids, see Shafer,y. Basic Eng., 84,471-485 (December 1962) or May, Chem. Eng., 78(5), 105-108 (1971) and for the effect of density and Reynolds number when used in gas flowmetering, see Lee and Evans, y. Basic Eng., 82, 1043-1057 (December 1965). 

Power consuiTmtion has also been measured and correlated with impeller Reynolds number. The velocity head for a mixing impeller can be calculated, then, from flow and power data, by Eq. (18-3) or Eq. (18-5). 

Axial Dispersion and the Peclet Number Peclet numbers are measures or deviation from phig flow. They may be calculated from residence time distributions found by tracer tests. Their values in trickle beds are fA to Ve, those of flow of liquid alone at the same Reynolds numbers. A correlation by Michell and Furzer (Chem. Eng. /., 4, 53 [1972]) is... 

To achieve the goal set above, measurements for reaction rates must be made in a RR at the flow conditions, i.e., Reynolds number of the large unit and at several well-defined partial pressures and temperatures around the expected operation. Measurements at even higher flow rates than customary in a commercial reactor are also possible and should be made to check for flow effect. Each measurement is to be made at point... 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

The model experiments were carried out in a model on the scale tjf I to iO. Experience with measurements on flow from wall-mounted dif(users for displacement ventilation indicates that it is possible to ignore the level of the Reynolds number at the given dimensions, which will enable reasonable temperature differences in the model experiments. 

A reduced scale of the model requires an increased velocity level in the experiments to obtain the correct Reynolds number if Re < Re for the prob lem considered, but the experiment can be carried out at any velocity if Re > RCj.. The influence of the turbulence level is shown in Fig. 12.40. A velocity u is measured at a location in front of the opening and divided by the exhaust flow rate in order to obtain a normalized velocity. The figure show s that the normalized velocity is constant for Reynolds numbers larger than 10 000, which means that the flow around the measuring point has a fully developed turbulent structure at that velocity level. The flow may be described as a potential flow with a normalized velocity independent of the exhaust flow rate at large distances from the exhaust opening— and far away from surfaces. 

The assumption of a self-similar flow (Reynolds number-independent flow) simplifies full-scale experiments and is also a useful tool in the formulation of simple measuring procedures. This section will show two examples of self-similar flow where the Archimedes number is the only important parameter. 

The flow of water through a 50 mm pipe is measured by means of an orifice meter with a 40 mm aperture. The pressure drop recorded is 150 mm on a mercury-under-water manometer and the coefficient of discharge of the meter is 0.6. What is the Reynolds number in the pipe and what would you expect the pressure drop over a 30 m length of the pipe to be ... 

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