Transient flow development

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. 

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... 

The present lecture summarizes some of tiie most recent joint research results from tiie cooperation between the Federal University of Rio de Janeiro, Brasil, and tiie University of Miami, USA, on tiie fransient analysis of both fluid flow and heat transfer within microchannels. This collaborative link is a natural extension of a long term cooperation between the two groups, in the context of fimdamental work on transient forced convection, aimed at tiie development of hybrid numerical-analytical techniques and tiie experimental validation of proposed models md methodologies [1- 9]. The motivation of this new phase of tiie cooperation was thus to extend the previously developed hybrid tools to handle both transient flow and transient convection problems in microchannels within the slip flow regime. 

In this section we present said discuss a few numerical results for the two problems considered, transient flow said hmsient convection in microchannels, which were respectively handled by the full and the partial integral hmsformation approaches. The aim is to demonshate file convergence behavior within each strategy and to illushate some physical aspects on file fiansient phenomena at the micro-scale. Although the developed solutions sae readily applicable to dififerent physical situations of eifiier hquid or gas flow, we here concentrate om illustiation of results on typical ex ples of lamina gas slip flow. 

This work discusses hybrid numerical-analytical solutions and mixed symbolic-numerical algorithms for solving transient fully developed flow and transient forced convection in micro-channels, making use of the Generalized Integral Transform Technique (GITT) and the Mathematica system. 

Development of this model is continuing in our laboratory, and among the aspects still under development are capabilities for transient flows, reactive fluids, free surfaces, and wall slip. Although incorporation of fluid elasticity is desired due to its importance in many polymer melt flows, such a development has proven elusive to a number of well qualified groups in the past several years. At present, it seems prudent to let the theoretical aspects of elastic effects be developed further before attempting their incorporation in a general process model. 

Instead of polarized noble gases, thermally polarized NMR microimaging was used to study of liquid and gas flow in monolithic catalysts. Two-dimensional spatial maps of flow velocity distributions for acetylene, propane, and butane flowing along the transport channels of shaped monolithic alumina catalysts were obtained at 7 T by NMR, with true in-plane resolution of 400 xm and reasonable detection times. The flow maps reveal the highly nonuniform spatial distribution of shear rates within the monolith channels of square cross-section, the kind of information essential for evaluation and improvement of the efficiency of mass transfer in shaped catalysts. The water flow imaging, for comparison, demonstrates the transformation of a transient flow pattern observed closer to the inflow edge of a monolith into a fully developed one further downstream. 

Gruesbeek Collin (1982) concluded that fine concentration in porous media is related with flow speed. The density remains constant in steady flow, while it will boost in scales influenced by transient flow. Accordingly, the transient drainage system will lead to fine production and migration in coal seam, and destruction in coal texture within area of primary coal developed is the main cause of coal fines. 

Three important (complicating) possibilities were not considered in the treatment of reactors presented in earlier chapters (1) the residence time of the reactant molecules need not always be fully defined in terms of plug flow or fully mixed flow (2) the equations describing certain situations can have more than one solution, leading to multiple steady states and (3) there could be periods of unsteady-state operation with detrimental effects on performance, that is, transients could develop in a reactor. 

Momentum Equation of Liquid-Liquid Flow We now consider a transient, fully developed, laminar, liquid-liquid stratified electroosmotic flow through a rectangular channel as illustrated in Fig. 2. For electroosmotic flow in an open-end channel, it is assumed that there is no pressure gradient along the microchannel. 

This chapter is devoted to the molecular rheology of transient networks made up of associating polymers in which the network junctions break and recombine. After an introduction to theoretical description of the model networks, the linear response of the network to oscillatory deformations is studied in detail. The analysis is then developed to the nonlinear regime. Stationary nonhnear viscosity, and first and second normal stresses, are calculated and compared with the experiments. The criterion for thickening and thinning of the flows is presented in terms of the molecular parameters. Transient flows such as nonhnear relaxation, start-up flow, etc., are studied within the same theoretical framework. Macroscopic properties such as strain hardening and stress overshoot are related to the tension-elongation curve of the constituent network polymers. 

Phytoplankton and zooplankton populations in the river are largely transient, flowing from one area to another. However, characteristic endemic groups of plankton generally have insufficient time to develop in the Hanford Reach (DOE-RL 1990). 

Recently, robust developments in the capabilities of computers have led to the modeling of transient turbulent flows becoming much less challenging. The experimental analysis of PCD, which requires sophisticated measurements (e.g., LDA, PDA, pressure, temperature, noise, etc.) is difficult, hostile (e.g., high noise level, around 110-130 dB) and expensive to carry out in comparison with numerical simulations (Zbicinski, 2002). Computational fluid dynamics (CFD) models for a steady or transient flow, for example, as generated by the pulse combustor, differ... 

In many books, radial flow theory is studied superficially and dismissed after cursory derivation of the log r pressure solution. Here we will consider single-phase radial flow in detail. We will examine analytical formulations that are possible in various physical limits, for different types of liquids and gases, and develop efficient models for time and cost-effective solutions. Steady-state flows of constant density liquids and compressible gases can be solved analytically, and these are considered first. In Examples 6-1 to 6-3, different formulations are presented, solved, and discussed the results are useful in formation evaluation and drilling applications. Then, we introduce finite difference methods for steady and transient flows in a natural, informal, hands-on way, and combine the resulting algorithms with analytical results to provide the foundation for a powerful write it yourself radial flow simulator. Concepts such as explicit versus implicit schemes, von Neumann stability, and truncation error are discussed in a self-contained exposition. 

Then, the algorithm and Fortran implementation developed for compressible transient flows applies without change. In the limit when U does not vanish, we write the governing PDE in the form Cldx = ( )/k 9C/9t -1- U/k dCldx, or... 

On the other hand, systems composed of two or more coupled NCLs have not been much investigated. The objectives of the present notes include development of model equations for steady-state and transient flows in coupled NCLs, including realistic BC representations. The design of such systems, an interesting optimization problem, is not addressed here. 

Using finite element techniqnes, a mathematical model was developed for the two-dimensional analysis of non-isothermal and transient flow and mixing of a generalised Newtonian fluid with an inert filler. The model could incorporate no-slip, partial-slip or perfect-slip wall conditions using a universally applicable numerical technique. The model was used to simulate the convection of carbon black with flowing rubber in the dispersive section of a tangential rotor (Banbury) mixer. The Carreau equation was used to model the rheological behaviour of the fluid in this example. 31 refs. 

Likewise, if 2-phase flow develops in a rotary liquid transfer pump, the mass flow output will be reduced or the pump may fail to prime altogether, leading to overheating and mechanical failure. Transient or continuous oscillations may also lead to mechanical damage. 

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