Unsteady state flow

Equipment in which homogeneous reactions are effected can be one of three general types the batch, the steady-state flow, and the unsteady-state flow or semibatch reactor. The last classification includes all reactors that do not fall into the first two categories. These types are shown in Fig. 4.1. 

Since fluid shear rates vary enormously across the radius of a capillary tube, this type of instrument is perhaps not well suited to the quantitative study of thixotropy. For this purpose, rotational instruments with a very small clearance between the cup and bob are usually excellent. They enable the determination of hysteresis loops on a shear-stress-shear-rate diagram, the shapes of which may be taken as quantitative measures of the degree of thixotropy (G3). Since the applicability of such loops to equipment design has not yet been shown, and since even their theoretical value is disputed by other rheologists (L4), they are not discussed here. These factors tend to indicate that the experimental study of flow of thixotropic materials in pipes might constitute the most direct approach to this problem, since theoretical work on thixotropy appears to be reasonably far from application. Preliminary estimates of the experimental approach may be taken from the one paper available on flow of thixotropic fluids in pipes (A4). In addition, a recent contribution by Schultz-Grunow (S6) has presented an empirical procedure for correlation of unsteady state flow phenomena in rotational viscometers which can perhaps be extended to this problem in pipe lines. 

A.2. Imaging Unsteady-State Flows in Fixed-Bed Reactors... 

Fig. 27. MR flow images of unsteady-state flow of water through a fixed bed with a column-to-particle diameter ratio of 2. Velocity maps measured by a standard spin-echo phase encoding velocity measurement and the GERVAIS pulse sequence are compared for values of Re of (a) 200 and (b) 300. In each case (i) is the standard spin-echo phase encoding velocity image, and (ii) and (iii) are the and flow vectors measured using GERVAIS.

UNIFAC method, 379, 457, 678-683 UNIQUAC equation, 379, 676-677 Units, 2-15, 19 conversion factors for, 570 Universal gas constant, 61-62 table of values for, 570 Unsteady-state-flow processes, 210-216... 

Introducing Darcy s equation 1.8 into the simplified continuity Equation 1.27 yields the general equation for unsteady-state flow through a water-saturated anisotropic medium under the assumed conditions listed in Section 1.2.2. 

The propeller setup was used for this purpose. From a computational standpoint, a mesh of the vessel-propeller set was created containing 8746 elements yielding 54,333 velocity equations and 8746 concentration equations. The surface mesh of the propeller (Fig. 5) comprised 964 control points. A maximum of three control points per element was used to avoid locking. Unsteady state flow simulations were performed with a 1-s time step and three coupling iterations between the Navier-Stokes equations and the solid transport equation were required per time step. Steady state was deemed obtained when the solids concentration coefficient of variation did not change. 

Fick s first law provides a method for calculation of the steady state rate of diffusion when D can be regarded as constant during the diffusion process, and the concentration is a function only of the geometric position inside the polymer. However, concentration is often a function of time as well as of position. We said Equation 14.9 describes a steady state flow, but how does the system reach this steady state The unsteady state flow, or transient state, is described by Fick s second law. For a one-dimensional diffusion process, this can be written as... 

ABSTRACT In order to analyze the law of airflow catastrophic of side branches induced by gas pressure in upward ventilation after dynamic of outburst disappearing, one dimensional unsteady-state flow momentum equation of gas flow is established. Combined with circuit airflow pressure balance equation, this equation is used in static and dynamic analysis on airflow catastrophic of side branches induced by gas pressure in upward ventilation. The research results show that gas pressure is produced in upward ventilated roadway when gas flowed by when the gas pressure is great enough, the air flow in side branches reverses. Whether the air flow in side branches reverse is affected by their own length and initial velocity. In order to prevent the air flow reversal in the side branches, it is necessary keep the fan normal operating, and avoids adding resistance in external system. The research results may be of important theoretical and practical significance for outburst accident rescue as well as effective prevention of the occurrence of secondary accidents. 

DIMENSIONAL UNSTEADY-STATE FLOW MOMENTUM EQUATION... 

This equation considers gas flow in roadways as one dimensional fluid flow, properties of gas flow are uniform in the same section of roadways. Considering flow of micro-unit along roadway branch i as object of study, the one dimensional unsteady-state flow mometum equation is as follows ... 

When outburst occurs in mine, airflow catastrophic will occur in intake airways connected with the source of outburst because of the great impact force produced by gas flow transiently released and of the gas pressure after the dynamic of outburst disappears, of which the most typical is airflow reverse of side branches. Therefore, this paper will use one dimensional unsteady-state flow momentum equation established above to analyze law of airflow reversalof side branches induced by gas pressure when upward ventilation airflow catastrophic occuring. 

Circuits airflow pressure balance equation is still tenable to dynamic network flow. Press differences between the first note and the last note can be obtained one dimensional unsteady-state flow momentum equation. For easy analysis, assuming that branch a, branch b and branch c has the same section area. 

First of all, considering the condition that airflow remain the same direction in any branch, and define that velocity of airflow is positive when airflow direction remain the same as it is before outburst, when the opposite is negative. Solve the press differences between two ends of branch a, b and c in Fig. 1 respectively, based on the one dimensional unsteady-state flow momentum equation. 

Khadilkar, M. R., Al-Dahhan, M. H., Dudukovic, M. P., Parametric study of unsteady-state flow modulation in trickle-bed reactors. Chemical Engineering Science, 1999, 54, 2585... 

The effect of residual oil saturation on polymer retention and the polymer retention during the displacement of oil from porous media has not been reported. Although some phenomena [1-11] indicated that more polymer is retained in the first segment of a porous media, the literature lacks quantitative data on the distribution of retained polymer in porous media. The mechanism of polymer retention during unsteady-state flow [11] has not been adequately described. 

It was earlier reported [11] that using the same polymer and porous media, steady-state or unsteady-state flow can be obtained depending on the flow condition. Our further laboratory studies showed that this phenomenon is commonly observed with a wide variety of water soluble polymers. However, the critical flow parameters of different polymers can vary greatly. 

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