Turbulent nature

In this context, it is important to note that a model test simulating the operation of an air pollution control scheme can also be modeled in water. For some air pollution problems, an air model might become quite large in order to ensure modeling the turbulent nature of the prototype flow rate. For some applications, a water model can be used which will give a reasonable scale size. 

Additionally, as a result of the turbulent nature of the flow of FW as it passes through the system, both new and old debris also may continue to pass through and eventually lodge in the boiler. As a consequence, the transport of corrosion products and debris from various parts of the overall boiler plant system through the pre-boiler section (where additional debris may originate) and on to the boiler continues to be a... 

The term numerical diffusion describes the effect of artificial diffusive fluxes which are induced by discretization errors. This effect becomes visible when the transport of quantities with small diffusivities [with the exact meaning of small yet to be specified in Eq. (42)] is considered. In macroscopic systems such small diffusivities are rarely found, at least when being looked at from a phenomenological point of view. The reason for the reduced importance of numerical diffusion in many macroscopic systems lies in the turbulent nature of most macro flows. The turbulent velocity fluctuations induce an effective diffusivity of comparatively large magnitude which includes transport effects due to turbulent eddies [1]. The effective diffusivity often dominates the numerical diffusivity. In contrast, micro flows are often laminar, and especially for liquid flows numerical diffusion can become the major effect limiting the accuracy of the model predictions. 

Let us just consider the piloted ignition case. Then, at Tpy a sufficient fuel mass flux is released at the surface. Under typical fire conditions, the fuel vapor will diffuse by turbulent natural convection to meet incoming air within the boundary layer. This will take some increment of time to reach the pilot, whereby the surface temperature has continued to rise. 

Now let us consider the mixing time, t. This will be estimated by an order of magnitude estimate for diffusion to occur across the boundary layer thickness, <5Bl- If we have turbulent natural conditions, it is common to represent the heat transfer in terms of the Nusselt number for a vertical plate of height, , as... 

Convections to objects in a fire environment usually occur under natural convection conditions. Turbulent natural convection is independent of scale and might be estimated from... 

Nooren, P. A., H. A. Wouters, T. W. J. Peeters, D. Roekaerts, U. Maas, and D. Schmidt (1997). Monte Carlo PDF modelling of a turbulent natural-gas diffusion flame. 

Induction furnaces offer certain advantages over electric arc or cupola furnaces. An induction furnace emits 75 percent less dust and fumes, due to the less turbulent nature of the heating employed inside the furnace. When coupled with the use of relatively clean scrap material, the need for emission control equipment may be avoided. For more information on induction furnaces, refer to USEPA (1985), and Danielson (1973). 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

Equation (8.166) cannot be directly applied to natural convective boundary layer flows because in such flows the velocity is zero at the outer edge of the boundary layer. However, Eq. (8.166) should give a good description of the velocity distribution near the wall. It is therefore assumed that in a turbulent natural convective boundary layer ... 

To proceed further, relationships for the wall shear stress, tw> and the wall heat transfer rate, qw, must be assumed. It is consistent with the assumption that the flow near the wall in a turbulent natural convective boundary layer is similar to that in a turbulent forced convective boundary layer to assume that the expressions for tw and qw that have been found to apply in forced convection should apply in natural convection. It will therefore be assumed here that the following apply in a natural convective boundary layer ... 

Turbulent natural convective flows can also be analyzed by numerically solving the governing equations together with some form of turbulence model. This is... 

Comparison of measured and predicted Nusselt number variations for turbulent natural convective flow over a vertical plate. 

Solution. The following integrals arise in the approximate solution for turbulent natural convective boundary layer flow over a flat plate discussed above ... 

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

Cheesewright, R.. "Turbulent Natural Convection from a vertical Plane Surface , J. Heat Transfer, Vol. 90. p. 1, 1968. 

Warner, C.Y. and Arpaci, V.S.. An Experimental Investigation of Turbulent Natural Convection in Air at Low Pressure along a Vertical Heated Plate , Int. J. Heat Mass Transfer, Vol. 11, pp. 397-406, 1968. 

Numerically predicted variation of Nusselt number variation with Reynolds number in turbulent assisting mixed convective flow over a vertical plate. (Based on results obtained by Patel K., Armaly B.F., and Chen T.S., Transition from Turbulent Natural to Turbulent Forced Convection Adjacent to an Isothermal Vertical Plate , ASME HTD, Vol. 324, pp. 51-56, 1996. With permission.)... 

The book provides a comprehensive coverage of the subject giving a full discussion of forced, natural, and mixed convection including some discussion of turbulent natural and mixed convection. A comprehensive discussion of convective heat transfer in porous media flows and of condensation heat transfer is also provided. The book contains a large number of worked examples that illustrate the use of the derived results. All chapters in the book also contain an extensive set of problems. 

Vliet, G. C., and D. C. Ross Turbulent Natural Convection on Upward and Downward Facing Inclined Constant Heat Flux Surfaces, ASME Pap. 74-WA/HT-32. 

The break in the curve can be associated with a fundamental change in the process mechanism (such as, for example a change from laminar to turbulent flow, a change from moderate natural convection to turbulent natural convection, etc.)... 

The simulations were performed assuming that the flow is laminar. Additionally, the contact angle is assumed to be known. The initial velocity is assumed to be zero everywhere in the domain. The initial fluid temperature profile is taken to be linear in the natural convection thermal boundary layer and the thermal boundary layer thickness, 5j, is evaluated using the correlation for the turbulent natural convection on a horizontal plate as, Jj. =1. 4(vfiCil ... 

Those who investigate the order that lies behind seemingly turbulent natural systems (clouds, water flows, air turbulence, epidemics, etc.) have come to contrast what they call fractal systems with linear systems. The key difference of relevance to us is the flexibility and sturdiness of fractal processes, which can survive perturbations and function over a wide range of frequencies—a quality com-... 

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