Flow measurement momentum mass

General Principles There are two main types of mass flowmeters (1) the so-called true mass flowmeter, which responds directly to mass flow rate, and (2) the inferential mass flowmeter, which commonly measures volume flow rate aud flmd density separately. A variety of types of true mass flowmeters have been developed, including the following (a) the Maguus-effect mass flowmeter, (b) the axial-flow, transverse-momentum mass flowmeter, (c) the radial-flow, transverse-momentum mass flowmeter, (d) the gyroscopic transverse-momentum mass flowmeter, aud (e) the thermal mass flowmeter. Type b is the basis for several commercial mass flowmeters, one version of which is briefly described here. 

Axial-Flow Transverse Momentum Mass Flowmeter. Figure 8.15 shows a schematic of an axial flow transverse momentum flowmeter. Substantially all of the fluid flows through both the impeller and the turbine. The impeller and the turbine are geometrically similar cylinders mounted in a cylindrical flow conduit on an axis coinciding with the conduit centerline. Each element is mounted on a separate shaft. Both the impeller and turbine are composed of several straight vanes located at the periphery of the elements and parallel to the centerline of the conduit. A means is provided for measuring the torque on the turbine shaft. If the impeller were locked (not rotating), the torque on the turbine shaft would be zero. 

The servo voltage is a function of mass-flow rate. Axial-flow angular-momentum meters are sometimes used in measuring jet engine fuel flow as the fuel energy content correlates much mote closely with mass than volume. 

Axial-Flow Transverse-Momentimi Mass Flowmeter This type is also referred to as an angular-momentum mass flowmeter. One embodiment of its principle involves the use of axial flow through a driven impeller and a turbine in series. The impeller imparts angular momentum to the fluid, which in turn causes a torque to be imparted to the turbine, which is restrained from rotating by a spring. The torque, which can be measured, is proportional to the rotational speed of the impeller and the mass flow rate. 

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... 

The measurement of mass flow can be obtained by multiplying the volumetric flow with density or by the direct measurement of Coriolis, thermal, impact, and angular momentum effects. 

The present focus is on the gas-liquid flow riser. The model used is a complex nonlinear infinite-dimensional system accounting for momentum, mass and energy balances [3], and the measurements available include temperature and pressure at different locations along the riser. Since the problem being tackled is of distributed parameter nature, location where such measurements are taken, along with its type, is crucial for estimator performance. Moving horizon estimation (MHE) is well suited as it facilitates the sensor structure selection (both in a dynamic and static sense). MHE is proven to outperform... 

The iirteraction of a fluid flow with the surface of a solid body is a subject of great interest. Matty technical measurements are aimed to determine the shear forces, pressure forces, or heating loads apphed by the flow to the body. A possible means of estimating the rates of momentum, mass, and heat transfer is to visualize the flow pattern very close to the body surface. For this purpose, the body surface can be coated with a thin layer of a substance that, upon the interaction with the fluid flow, develops a certain visible pattern. This pattern can be interpreted qualitatively, and in some cases, it is possible to measure certain properties of the flow close to the surface. Three different interaction processes can be used for generating different kinds of information. 

The momentum meters are a rather new entry into cryogenic flow measurement. The main advantage is a direct reading of mass flow. Precision (3cr) is good and may even be improved relative to volumetric meters when the density measurement uncertainty is added to the volumetric flow to give inferred mass flow. 

In streamline flow, E is very small and approaches zero, so that xj p determines the shear stress. In turbulent flow, E is negligible at the wall and increases very rapidly with distance from the wall. LAUFER(7), using very small hot-wire anemometers, measured the velocity fluctuations and gave a valuable account of the structure of turbulent flow. In the operations of mass, heat, and momentum transfer, the transfer has to be effected through the laminar layer near the wall, and it is here that the greatest resistance to transfer lies. 

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Viscometric flow theories describe how to extract material properties from macroscopic measurements, which are integrated quantities such as the torque or volume flow rate. For example, in pipe flow, the standard measurements are the volume flow rate and the pressure drop. The fundamental difference with spatially resolved measurements is that the local characteristics of the flows are exploited. Here we focus on one such example, steady, pressure driven flow through a tube of circular cross section. The standard assumptions are made, namely, that the flow is uni-directional and axisymmetric, with the axial component of velocity depending on the radius only. The conservation of mass is satisfied exactly and the z component of the conservation of linear momentum reduces to... 

Interfacial area measurement. Knowledge of the interfacial area is indispensable in modeling two-phase flow (Dejesus and Kawaji, 1990), which determines the interphase transfer of mass, momentum, and energy in steady and transient flow. Ultrasonic techniques are used for such measurements. Since there is no direct relationship between the measurement of ultrasonic transmission and the volumetric interfacial area in bubbly flow, some estimate of the average bubble size is necessary to permit access to the volumetric interfacial area (Delhaye, 1986). In bubbly flows with bubbles several millimeters in diameter and with high void fractions, Stravs and von Stocker (1985) were apparently the first, in 1981, to propose the use of pulsed, 1- to 10-MHz ultrasound for measuring interfacial area. Independently, Amblard et al. (1983) used the same technique but at frequencies lower than 1 MHz. The volumetric interfacial area, T, is defined by (Delhaye, 1986)... 

The trend observed in Fig. 17.5 illustrates the importance of swirl. The image sequence corresponds to data points using front swirl angles of 31°, 41°, and 68° with all other parameters fixed 4> = 0.68, RMS = 0.1, L = 12 in. (30.48 cm), total mass flow rate of 0.03 kg/s, and rear swirl angle of 85°). The chamber averaged swirl is defined as the sum of the front and rear drive angular momentum divided by the chamber radius and total mass flow. This provides a measure of the swirl experienced by the combustion chamber confined flow and allows comparison between different test conditions. The flame speed ratio... 

In process operations, simultaneous transfer of momentum, heat, and mass occur within the walls of the equipment vessels and exchangers. Transfer processes usually take place with turbulent flow, under forced convection, with or without radiation heat transfer. One of the purposes of engineering science is to provide measurements, interpretations and theories which are useful in the design of equipment and processes, in terms of the residence time required in a given process apparatus. This is why we are concerned here with the coefficients of the governing rate laws that permit such design calculations. 

In Table IV, we see that established techniques for velocity measurement allow us to determine the average momentum flux, average velocity, turbulent intensities, and shear stress. Next on the list, to complete the flow field description, is the fluctuation mass flux, and first on the combustion field list is the temperature and major species densities of the flame gases. 

The dimensionless parameters, such as the Nusselt and Reynolds numbers, can be thought of as measures of the relative importance of of certain aspects of the flow. For example, if the flow through an area dA is considered, as shown in Fig. 1.19, the rate momentum passes through this area is equal to the mass flow rate times the velocity, i.e., equal to mV dA, i.e., equal to pVVdA, i.e., equal to pV2dA. If, therefore, U is a measure of the velocity, the quantity pU1 is a measure of the magnitude of the momentum flux in the flow. This quantity is often termed the inertia force . Further, since the Newtonian viscosity law indicates that the viscous shear stresses... 

It is not difficult to observe that in all of these expressions we have a multiplication between the property gradient and a constant that characterizes the medium in which the transport occurs. As a consequence, with the introduction of a transformation coefficient we can simulate, for example, the momentum flow, the heat flow or species flow by measuring only the electric current flow. So, when we have the solution of one precise transport property, we can extend it to all the cases that present an analogous physical and mathematical description. Analogous computers [1.27] have been developed on this principle. The analogous computers, able to simulate mechanical, hydraulic and electric micro-laboratory plants, have been experimented with and used successfully to simulate heat [1.28] and mass [1.29] transport. 

In addition to these impediments to rheological measurements, some complex fluids exhibit wall slip, yield, or a material instability, so that the actual fluid deformation fails to comply with the intended one. A material instability is distinguished from a hydrodynamic instability in that the former can in principle be predicted from the constitutive relationship for the material alone, while prediction of a flow instability requires a mathematical analysis that involves not only the constitutive equation, but also the equations of motion (i.e., momentum and mass conservation). 

---