Laminar flow computational fluid dynamics

Patera A (1984) The spectral element method for fluid dynamics laminar flow in a channel expansion. J Comput Phys 54 468-488... 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

Computational fluid dynamics were used to describe the flow which undergoes a fast transition from laminar (at the fluid outlets) to turbulent (in the large mixing chamber) [41]. Using the commercial tool FLUENT, the following different turbulence models were applied a ke model, an RNC-ki model and a Reynolds-stress model. For the last model, each stream is solved by a separate equation for the two first models, two-equation models are applied. To have the simulations at... 

It is important to know how mixing can influence the selectivity of chemical reactions, and computational fluid dynamics (CFD) simulations are quite helpful in providing a deeper insight into this issue. The calculations are based on a laminar flow model where mixing takes place only by molecular diffusion (Figure 6.9). Let us focus on the competitive... 

One natural approach to describing mixing is to solve the equations of motion of the fluid. In fluid systems, the type of fluid flow is obviously important, and we should consider both laminar and turbulent flow, and various mechanisms of diffusion (molecular diffusion, eddy diffusion). Using fluid mechanics to describe all cases of interest is a difficult problem, both from the modeling and computational perspectives. Rapid developments in computational fluid dynamics (CFD), however, make this approach increasingly attractive 1]. 

This partial differential equation is deterministic by nature. In practice, however, many hydrodynamic phenomena (e.g., transition from laminar to turbulent flow) have chaotic features (deterministic chaos [Stewart 1993]). The reason for this is that the Navier-Stokes equation assumes a homogeneous ideal fluid, whereas a real fluid consists of atoms and molecules. Today highly developed numerical flow simulators (computational fluid dynamics, CFD) are available for solving the Navier-Stokes equation under certain boundary conditions (e.g.. Fluent Deutschland GmbH). These even allow complex flow conditions, including particle, droplet, bubble, plug, and free surface flow, as well as multiphase flow such as that foundin fluidized-bed reactors and bubble columns, to be treated numerically [Fluent 1998]. 

Solving the full Navier-Stokes equations in the channels requires a rigorous computational fluid dynamics (CFD) simulation. During transient operation, such as start-up and shut-down, the flow fields can have a significant effect on the concentration and temperature profiles in the system. Under normal operation, it may be desirable to assume fuUy developed laminar flow to reduce the computational time and quickly estimate flow parameters based on fluid dynamics correlations. 

The effect of drag reducers on the turbulence is modelled with computational fluid dynamics (CFD) by using a two-layer turbulence model. In the laminar buffer layer, the one-equation model of Hassid and Poreh (1975) is used to describe the enhanced dissipation of turbulence caused by drag reducers. The standard k-e model is applied in the fully turbulent regions. The flow conditions necessary to elongate the polymer, the drag reduction efficiency of polymers of different apparent molar masses and their degradation kinetics have been measured. This data has been used in the model development. 

Due to the complex weave pattern for LAD screens, it is difficult to derive an exact solution for the flow through a LAD screen. An empirical solution from Armour and Cannon (1968) has been proposed, as well as basic computational fluid dynamics simulations from Zhang et al. (2009) for the flow through a LAD screen. Using the logic from Armour and Cannon (1968), the approximate solution is formulated as the sum of the pressure drop due to viscous (laminar) and inertial (turbulent) resistance. 

Consequently, numerical solution of the equations of change has been an important research topic for many decades, both in solid mechanics and in fluid mechanics. Solid mechanics is significantly simpler than fluid mechanics because of the absence of the nonlinear convection term, and the finite element method has become the standard method. In fluid mechanics, however, the finite element method is primarily used for laminar flows, and other methods, such as the finite difference and finite volume methods, are used for both laminar and turbulent flows. The recently developed lattice-Boltzmann method is also being used, primarily in academic circles. All of these methods involve the approximation of the field equations defined over a continuous domain by discrete eqnalions associated with a finite set of discrete points within the domain and specified by the user, directly or through an antomated algorithm. Regardless of the method, the numerical solution of the conservation equations for fluid flow is known as computational fluid dynamics (CFD). 

At 700°C and 1 atm this leads to a diffusion constant of 0.81 cm /s The flow field around a superheater tube is very complex involving both laminar and turbulent boundary layers and the estimation of the local boundary layer thicknesses (velocity, diffusion and thermal boundary layers) around the tube requires computer simulations with computational fluid dynamic (CFD) software packages. However, for this rough analysis an average value of the thermal boundary layer thickness around the tube is enough and can be estimated if the average Nusselt number around the tube is known... 

Equation (3) provides details of gas flow movements. The full treatment requires a rigorous computational fluid dynamics (CFD) tool. Startup and transient processes as well as variations in certain operating parameters may have a sizeable effect on flow and concentration profiles, but the effect on overall electrochemical performance of the cell is not necessarily of the same order. Sometimes it is desirable to make a simplification such as assuming laminar flow to reduce the computation cost and allow quick estimates of certain flow properties. For example, the pressure drop of a laminar flow through a channel can be estimated as... 

Assuming that the first-stage reaction is faster than the second-stage reaction, simulations using computational fluid dynamics (CFD) were carried out (Fig. 7.9). The flow reactor contains laminar flows of A and B. Mixing is assumed to be... 

Analytically Reduced Mechanisms Some problems can be described by models that involve a full reaction mechanism in combination with simplied fluid dynamics. Other applications may involve laminar or turbulent multidimensional reactive flows. For problems that require a complex mathematical flow description (possibly CFD), the computational cost of using a full mechanism may be prohibitive. An alternative is to describe... 

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