Stream-tube method

The stream-tube method is more closely related to the Protean coordinate approach. It refers to the flow analysis introduced some yeans ago by Clermont [40,53], which may be applied to the study of two- or three-dimensional duct or free surface flows [54-56] and pure circulatory or vortex flows [57]. In this analysis, the unknowns of the problem are, in addition to the pressure p, a one-to-one transformation between the physical flow domain D (or a subdomain D of D)... 

The main features of the stream-tube method in 2D and 3D flows, discussed more extensively elsewhere [40,53,55], are now summarized for two-dimensional situations. Flows with open streamlines are considered. The main flow region D of the physical domain D (D 2 D ) is mapped into a domain D such that the transformed streamlines are straight and parallel to an assumed main direction Oz of the flow. An example corresponding to 2D flows is illustrated in Fig 11. 

Viscoelastic constitutive equations in the stream-tube method... 

The stress equations are considered together with the dynamic equations, leading to a set of equations involving the primary variables /, g and the pressure p or a mixed formulation with the stress components Tij. Both cases were considered in nTunerical applications of the stream-tube method. 

Despite the fact that the stream-tube method was limited to the computation of main flows (the flow may involve secondary flows, but the recirciilations are not simulated), the present analysis is still considered to be attractive for the following reasons ... 

Application of the stream-tube method to duct and free-surface flows... 

Under assumption of the existence of a main direction Oz of the flow, the stream-tube method may be applied to computation of flows in ducts, even those where recirculations are encoimtered and flows involving free surfaces, as those corresponding to the die-swell flow problem. We present here the procedures related to those flow situations. 

Flow experiments were carried out at LRMP for axisymmetric contractions and at CEMEF for plane geometries. Numerical simulations were performed at Laboratoire de Rheologie, with Wagner memory-integral constitutive equations, with the stream-tube method (sub-section 5.1) and at CEMEF, where the finite-... 

Quartz Tube Method the sample is burned in a quartz tube and a stream of purified air carries the combustion gases into a hydrogen peroxide solution. 

The complex flow pattern on the shell-side, and the great number of variables involved, make it difficult to predict the shell-side coefficient and pressure drop with complete assurance. In methods used for the design of exchangers prior to about 1960 no attempt was made to account for the leakage and bypass streams. Correlations were based on the total stream flow, and empirical methods were used to account for the performance of real exchangers compared with that for cross flow over ideal tube banks. Typical of these bulk-flow methods are those of Kern (1950) and Donohue (1955). Reliable predictions can only be achieved by comprehensive analysis of the contribution to heat transfer and pressure drop made by the individual streams shown in Figure 12.26. Tinker (1951, 1958) published the first detailed stream-analysis method for predicting shell-side heat-transfer coefficients and pressure drop, and the methods subsequently developed... 

Regarding niunerical aspects, analysis of a single stream tube allows us to consider relative differences between the problem variables which are less important than those that could be observed in a computational method involving the total flow domain. This limits convergence problems ... 

Wang, H.G. Wu, F.L. 2011. Method of calculation of a methane concentration field in gob areas with a knovra velodty field based on the model of stream tubes. Mining Science and Technology (China) 21(201 l)i277 280. 

A capillary-tube method to analyze binary liquid diffusivity was reported in Mickley et al. (1957) a straight, narrow bore capillary tube of known internal length has one end sealed and is filled with a binary solution of known composition. The capillary is maintained in a vertical position with the open end pointed upward. A slow stream of pure solvent is allowed to continuously sweep past the open mouth of the capillary tube. We shall designate species A as solute and species B as solvent. After an elapsed time, t, the capillary is removed and the solution it contains is well mixed and then analyzed for composition, to find how much solute A was extracted. Generally, several such experiments are conducted at different values of r. 

Hydrobromic acid. Method 1 (from bromine and sulphur dioxide). A mixture of 600 g. (or 188-6 ml.) of bromine, 250 ml. of water and 760 g. of crushed ice is placed in a 1 6 litre round-bottomed flask and a rapid stream of sulphur dioxide (from a siphon of the liquefied gas) is passed into the flask, care being taken that the outlet of the gas-delivery tube is below the surface of the bromine layer. The rate of flow of the gas is adjusted so that it is completely absorbed. It is advisable to cool the flask in ice and also to shake the contents from time to time. The reduction is complete when the mixture assumes a uniform yellowish-brown or yellow colour, which is unaffected by further introduction of sulphur dioxide excess of the latter gas should be avoided as it will be... 

Translate the heat-transfer area deterrnined above into corresponding tube bundle dimensions. If different from those assumed in step (2), repeat steps (2) through (8) until satisfactory agreement is reached. The method caimot be appHed to cases in which U varies along the tube length or the stream... 

An alternate means of reboiler control is to remove the control valve from the steam line and provide a condensate level controller for the chest cascaded from the tray temperature. The alternate method uses A tube surface for control, with the condensate covering more or less tube surface to vary the area exposed to condensing stream. Condensing area is many times more effective for heat transfer than area covered by relatively stagnant condensate. The reboiler must have extra surface to allow part of its surface to be derated for control purposes. 

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