Mass flow measurement transfer

The use of downstream heat transfer for mass flow measurement does directly relate to the mass flow rate, as the heat transfer mechanism relies on the mass and velocity of each individual particle, However the technique does rely on the injection of heat uniformly to all sections of the pipe and a uniform sensing throughout the pipe cross section. The requirements for a uniform excitation and sensing field are not peculiar to this application however. 

Of course the spectrum of quantities, which need to be measured in a fluidized bed, is much wider. These include, for example, local solids volume concentrations, solids velocities and solids mass flows, the vertical and the horizontal distribution of solids inside the system or the lateral distribution of the fluidizing gas. In response to these needs a number of more sophisticated measurement techniques were proposed. For example, suction probes were developed to measure local solids and mass flow, heat transfer probes were proposed for detection of de-fluidized zones and solids flow inside fluidized-bed reactors. Other techniques include capacitance probes, optical probes, or y-ray densitometry - a detailed review was given recently by Werther [1]. Cody et al. 2 reported the use of an acoustic probe to measure particle velocity at the wall of fluidized beds. 

Mullis (M10), Bastress (B4), and Carlson and Seader (Cl) have conducted experimental studies to determine the heat-transfer characteristics of typical rocket-exhaust igniters. In these studies, the total rate of heat transfer to the propellant or simulated propellant surface was measured as a function of mass flow rate, geometry, and impingement angle between the igniter exhaust... 

Wall-to-bed heat-transfer coefficients were also measured by Viswanathan et al. (V6). The bed diameter was 2 in. and the media used were air, water, and quartz particles of 0.649- and 0.928-mm mean diameter. All experiments were carried out with constant bed height, whereas the amount of solid particles as well as the gas and liquid flow rates were varied. The results are presented in that paper as plots of heat-transfer coefficient versus the ratio between mass flow rate of gas and mass flow rate of liquid. The heat-transfer coefficient increased sharply to a maximum value, which was reached for relatively low gas-liquid ratios, and further increase of the ratio led to a reduction of the heat-transfer coefficient. It was also observed that the maximum value of the heat-transfer coefficient depends on the amount of solid particles in the column. Thus, for 0.928-mm particles, the maximum value of the heat-transfer coefficient obtained in experiments with 750-gm solids was approximately 40% higher than those obtained in experiments with 250- and 1250-gm solids. 

Consider an experiment in which an air-cooled device is being tested and it is desired to determine the rate of heat transfer Q to the cooling air (ASME 2000). This can be accomplished by measuring the mass flow rate m, and the inlet and outlet air temperatures, Tin and Tout, and computing ... 

Mass and heat transfer to the walls in turbulent flows is a complex mixture of molecular transport and transport by turbulent eddies. The generally assumed analogy between mass and heat transfer by assuming Sh = Nu, is not valid for turbulent flows [26]. Simulations and measurements have shown that there is a laminar film close to the surface where most of the mass transfer resistance for high Sc liquids is located. This fUm is located below y+ = 1 and for low Sc fluids, and for heat transfer the whole boundary layer is important [27]. 

Three different principles govern the design of bench-scale calorimetric units heat flow, heat balance, and power consumption. The RC1 [184], for example, is based on the heat-flow principle, by measuring the temperature difference between the reaction mixture and the heat transfer fluid in the reactor jacket. In order to determine the heat release rate, the heat transfer coefficient and area must be known. The Contalab [185], as originally marketed by Contraves, is based on the heat balance principle, by measuring the difference between the temperature of the heat transfer fluid at the jacket inlet and the outlet. Knowledge of the characteristics of the heat transfer fluid, such as mass flow rates and the specific heat, is required. ThermoMetric instruments, such as the CPA [188], are designed on the power compensation principle (i.e., the supply or removal of heat to or from the reactor vessel to maintain reactor contents at a prescribed temperature is measured). 

The HTE characteristics that apply for gas-phase reactions (i.e., measurement under nondiffusion-limited conditions, equal distribution of gas flows and temperature, avoidance of crosscontamination, etc.) also apply for catalytic reactions in the liquid-phase. In addition, in liquid phase reactions mass-transport phenomena of the reactants are a vital point, especially if one of the reactants is a gas. It is worth spending some time to reflect on the topic of mass transfer related to liquid-gas-phase reactions. As we discussed before, for gas-phase catalysis, a crucial point is the measurement of catalysts under conditions where mass transport is not limiting the reaction and yields true microkinetic data. As an additional factor for mass transport in liquid-gas-phase reactions, the rate of reaction gas saturation of the liquid can also determine the kinetics of the reaction [81], In order to avoid mass-transport limitations with regard to gas/liquid mass transport, the transfer rate of the gas into the liquid (saturation of the liquid with gas) must be higher than the consumption of the reactant gas by the reaction. Otherwise, it is not possible to obtain true kinetic data of the catalytic reaction, which allow a comparison of the different catalyst candidates on a microkinetic basis, as only the gas uptake of the liquid will govern the result of the experiment (see Figure 11.32a). In three-phase reactions (gas-liquid-solid), the transport of the reactants to the surface of the solid (and the transport from the resulting products from this surface) will also... 

Dengler and Addoms 8 measured heat transfer to water boiling in a 6 m tube and found that the heat flux increased steadily up the tube as the percentage of vapour increased, as shown in Figure 14.4. Where convection was predominant, the data were correlated using the ratio of the observed two-phase heat transfer coefficient (htp) to that which would be obtained had the same total mass flow been all liquid (hi) as the ordinate. As discussed in Volume 6, Chapter 12, this ratio was plotted against the reciprocal of Xtt, the parameter for two-phase turbulent flow developed by Lockhart and Martinelli(9). The liquid coefficient hL is given by ... 

Sometimes it is possible to evaluate the range of validity of measurements and correlations of physical properties, phase equilibrium behavior, mass and heat transfer efficiencies and similar factors, as well as the fluctuations in temperature, pressure, flow, etc., associated with practical control systems. Then the effects of such data on the uncertainty of sizing equipment can be estimated. For example, the mass of a distillation column that is related directly to its cost depends on at least these factors ... 

One class of flow measurement which is becoming of increasing importance (particularly in the form of sensors for control systems) is the monitoring of mass flow. This is rapidly superseding the measurement of volumetric flow—especially where it is required to determine accurately the transfer of large quantities of gas and liquid in the oil, gas and water industries. Two principal approaches are employed to measure mass flow. One is indirect and uses a combination of volumetric flow and density and the other is direct in that it involves the measurement of properties which are sensitive to variations in the mass rate of flow itself. 

The mass of a particle (resp. antiparticle) is then proportional to the preonic mass flow into (resp. out of) our 3D-world, which carry a momentum flux q c . Particles (resp. antiparticles) are solitons of steady flow, whose rest mass M ) is the result of a transfer of energy from (resp. into) the u axis during the duration Tm of a measurement inside a 3D volume whose size corresponds to the volume of the particle. Then... 

For the ball-probe measurement of charge current in a dilute gas-solid suspension, prove that, for a given type of particle and a given mass flow ratio, the current measured is independent ofthe particle size for db 3> dp. It is assumed that the charge transfer coefficient is constant. 

Chang and Rochelle [12-15] investigated some aspects of SO2 absorption in an agitated cell filled with aqueous solution or suspension, and compared their measurements with those of other authors with simulated absorbed mass flows, based on enhancement factors from the film and surface renewal theory. The results showed that mass transfer, when corrected by an enhancement factor from the surface renewal theory, agreed clearly with the measurements. 

Suppose a number of experiments are conducted with measurements taken of heat-transfer rates of various fluids in turbulent flow inside smooth tubes under different temperature conditions. Different-diameter tubes may be used to vary the range of the Reynolds number in addition to variations in the mass-flow rate. We wish to generalize the results of these experiments by arriving at one empirical equation which represents all the data. As described above, we may anticipate that the heat-transfer data will be dependent, on the Reynolds and Prandtl numbers. An exponential function for each of these parameters is perhaps the simplest type of relation to use, so we assume... 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

Velocity meters measure the velocity v of fluid flow in a pipe of known cross section, thus yielding a signal linearly proportional to the volume flow rate Q. Mass meters provide signals directly proportional to the mass flow rate m = pQ, where p is the mass density. Coriolis meters, which are true mass meters, can be used only for liquids. Thermal-type flow meters use a heating element and determine the rate of heat transfer, which is proportional to the mass flow rate. This type of device is used mostly for gas measurements, but liquid flow designs are also available. 

The TEOM is a promising tool for investigation of the influence of coke on adsorption and diffusion in catalysts. As a consequence of high flow rates of the carrier gas through the sample bed, the technique minimizes the external mass and heat transfer limitations in transient experiments without affecting the accuracy of the measurements. The data are not influenced by buoyancy and flow patterns, which are significant when conventional methods are used. 

SOLUTION During an experiment involving an automotive radiator, the inlet and exit temperatures of water and air and the mass flow rate of water are measured. The overall heat transfer coefficient based on the inner surface area is to be determined. 

In this section the general trends of the measurements will be presented. Electrical power, refrigerant mass flow rate, in and outward fluid temperatures and wall temperatures were measured. From these data physical parameters of interest were computed as a function of tube length heat flux g (z), fluid temperature f h (z). vapour quality x(z) and heat transfer coefficient a(z). Table 3 presents uncertainties on some calculated parameters. 

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