Transient flow

Ghoreishy, M. H. R. and Nassehi, V., 1997. Modelling the transient flow of rubber compounds in the dispersive section of an internal mixer with slip-stick boundary conditions. Adv. Poly. Tech. 16, 45-68. 

Many transient flows of liquids may be analyzed by using the full time-dependent equations of motion for incompressible flow. However, there are some phenomena that are controlled by the small compressibility of liquids. These phenomena are generally called hydraulic transients. 

For positive displacement pumps, a bypass-type control valve should be furnished to set the primary lube system pressure. The valve should be able to maintain system pressure during pump startup and pump transfers, which includes relieving the capacity of one pump, while both are running. The valve should provide stable, constant pressure during these transients. Flow turndown of 8 to 1 is not unusual. Multiple valves in parallel should be used if a single valve is not suitable. The valve should be sized to operate between 10 and 90% of the flow coefficient (Cv). Additional pressure control valves should be furnished as required to pro ide any of the intermediate pressure levels. 

An unsteady flow is one in which the conditions at any point van with time such a flow is also called a transient flow. 

Quite specific effects in the flow of dispersions of long fibers are connected with particles orientation in the flow. Indeed, the state of fibers during the flow changes greatly as compared the initial state, so that the material in a steady-state flow is an anisotropic medium. Therefore the viscosity of such a suspension may become independent of a fiber s length [30], The most strong effects caused by a deformation of anisotropic particles should be expected in transient flows, in particular if the particles themselves are flexible and deformed in the flow. 

The treatment of experimental data constitutes an essential step in any chemical kinetics study. Although a large part of the present section is based on the investigations in transient flow degradation, the procedure should be general enough to be applicable to other experimental flow arrangements. 

The exponent x is an empirical parameter to be determined from experiments. For a fully extended chain in stagnant elongational flow, x is equal to 2 whereas a value of 1 was found under transient flow conditions (Sect. 5.4). 

In order to observe any temperature dependence in transient flow degradation, it would be necessary to prolong considerably the effective residence time of the polymer coil. This can be accomplished either by recirculating the solution or by using an oscillatory flow equipment as described in Sect. 4.1 (Figs. 23 and 24). 

In a few studies, solvent viscosity was varied as a result of change in temperature [109, 165]. In transient flow, the direct effect of temperature on the scission rate was shown to be minimal (Sect. 5.7). Even so, it is desirable to look for a system where the solvent viscosity can be studied independently of the other kinetics parameters [166], Ideally, the solvents used should satisfy the following criteria ... 

In most of the gas lubrication problems in nano-gaps, gas flow usually locates in the slip flow or the transient flow regime, depending on working conditions and local geometry. Therefore, both of the macroscopic and microscopic models are introduced to analyze the gas lubrication problems. 

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 analysis of transient flows is necessary for safety analysis of nuclear reactors. Such efforts usually result in the development of large computer codes (e.g., RELAP-5, RETRAN, COBRA, TRAC). Rather than going into the details of such codes, this section gives the principles and basic models involved in the analysis. 

In terms of transient behaviors, the most important parameters are the fluid compressibility and the viscous losses. In most field problems the inertia term is small compared with other terms in Eq. (128), and it is sometimes omitted in the analysis of natural gas transient flows (G4). Equations (123) and (128) constitute a pair of partial differential equations with p and W as dependent variables and t and x as independent variables. The equations are hyperbolic as shown, but become parabolic if the inertia term is omitted from Eq. (128). As we shall see later, the hyperbolic form must be retained if the method of characteristics (Section V,B,1) is to be used in the solution. 

In contrast to the method of characteristics, which gives faithful simulation of transient flows but which is very restrictive in time step sizes, the stability of the implicit methods permit large time steps and drastic reduc-... 

In simulating transient flows in pipeline networks, the importance of accuracy cannot be over-emphasized. Because the transient behaviors are less well-understood, they are often rich in surprises. Physical intuition affords less guidance in these situations than in steady-state phenomena. Rachford and Dupont (R2) provided two instructive and deceptively simple examples to illustrate the interaction between regulators and compressors and the oscillatory response which can produce pressures higher than the supply pressure through reinforcement. 

C. U. Ikoku, Transient Flow of Non-newtonian, Power Law Fluids, Ph.D. Thesis, Petroleum Engineering Department, Stanford University, (1978). 

The emphasis in this chapter is on the fruitful application of Large Eddy Simulations for reproducing the local and transient flow conditions in which these processes are carried out and on which their performance depends. In addition, examples are given of using Direct Numerical Simulations of flow and transport phenomena in small periodic boxes with the view to find out about relevant details of the local processes. Finally, substantial attention is paid throughout this chapter to the attractiveness and success of exploiting lattice-Boltzmann techniques for the more advanced CFD approaches. 

First of all, the increased computer power makes it possible to switch to transient simulations and to increase spatial resolution. One no longer has to be content with steady flow simulations on relatively coarse grids comprising 104-105 nodes. Full-scale Large Eddy Simulations (LES) on fine grids of 106—107 nodes currently belong to the possibilities and deliver realistic reproductions of transient flow and transport phenomena. Comparisons with quantitative experimental data have increased the confidence in LES. The present review stresses that this does not only apply to the hydrodynamics but relates to the physical operations and chemical processes carried out in stirred vessels as well. Examples of LES-based simulations of such operations and processes are due to Flollander et al. (2001a,b, 2003), Venneker et al. (2002), Van Vliet et al. (2005, 2006), and Flartmann et al. (2006). 

Once the explosion occurs it creates a blast wave that has a very steep pressure rise at the wave front and a blast wind that is a transient flow behind the blast wave. The impact of the blast wave on structures near the explosion is known as blast loading. The two important aspects of the blast loading concern is the prediction of the magnitude of the blast and of the pressure loading onto the local structures. Pressure loading predications as a result of a blast, resemble a pulse of trapezoidal or triangular shape. They normally have a duration of between approximately 40 msec and 400 msec. The time to maximum pressure is typically 20 msec. 

Under the conditions encountered, the pressure difference across the bursting disc is large enough to ensure that choking occurs. As a result, on failure of the disc, gas flows at the local sonic speed towards the second device. The transient flow will occupy the whole cross section, a vena contracta forming later. When the sonic gas flow meets the second device there will be a pressure rise just as if the flow had been steady and an obstruction were placed across the flow. 

The first numerical study on the transient flow of a single liquid droplet impinging onto a flat surface, into a shallow or deep pool was performed by Harlow and Shannon)397 In their work, the full Navier-Stokes equations were solved numerically in cylindrical... 

Kool, J. B. and Parker, J. C., 1988, Analysis of the Inverse Problem for Unsaturated Transient Flow Water Resources Research, Vol. 24, pp. 814—830. 

For regions in which the flow is not quasisteady, a transient-flow solution may be possible. For example, Lakin and Lakin and Fox developed a two-dimensional transient-flow solution for an idealized symmetric bifurcation during the period at the end of inspiration and before expiration. Their finding that vortidty decreases at the carina or bifurcation apex suggests that particle- and gas-deposition rates may be increased at these sites in the respiratory tract. It also suggests that reactive-gas deposition rates during normal oscUlatory breathing differ... 

Richards equation (Richards 1931), based on a mass conservation balance, together with Eq. 9.1, can be used to describe the transient flow of water through a partially saturated porous medium. In one dimension (vertically), Richards equation is given as... 

---