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Fluid Flow and Its Modeling Using Computational Fluid Dynamics
Published in Shyam S. Sablani, M. Shafiur Rahman, Ashim K. Datta, Arun S. Mujumdar, Handbook of Food and Bioprocess Modeling Techniques, 2006
There are three major laws of conservation. The first, conservation of mass, says that the mass is neither created nor destroyed in the fluid parcel. The second, conservation of momentum, says that the rate of momentum’s change is the sum of the forces acting on the fluid. Third, the conservation of energy, says that the change in total energy is net heat transfer minus net work done by the fluid. These equations can become highly nonlinear, and only a few simple problems have exact solutions. The numerical techniques are used to obtain approximate solutions to these problems, and this field is termed as the computational fluid dynamics (CFD) that is explained in more detail in a later section of this chapter. Although fluid dynamics implies the study of the dynamics of fluids, many applications not only deal with just the motion of fluids, but they also involve heat transfer, mass transfer, and chemical reactions. They often involve solid parts as well. However, this chapter will focus on the study of fluids. The heat and mass transfer are explained in their respective chapters in this handbook.
Geophysical Fluid Dynamics
Published in Osamu Morita, Classical Mechanics in Geophysical Fluid Dynamics, 2019
Gases and liquids are called fluids collectively. A fluid consists of many molecules, which move about randomly and collide with each other. In fluid dynamics, we ignore molecular behavior of a fluid and treat it as a continuous medium, or continuum. A small fluid element with an infinitesimal volume but containing a large number of molecules is referred to as a fluid parcel, which is the analogous concept of a particle or a point mass in Newtonian mechanics. Physical quantities (velocity, pressure, density and temperature) are defined for a fluid parcel.
On the ambiguity of premixed flame thickness definition of highly pre-heated mixtures and its implication on turbulent combustion regimes
Published in Combustion Theory and Modelling, 2020
Andreas H. Rauch, Harsha K. Chelliah
To find the volumetric heat release of a reaction, , the heat release rate of a fluid parcel of fixed volume as it passes through the flame is integrated in time, which can be written as where v is the velocity. The total volumetric heat release (Q) is then the sum of over all reactions. Similarly, the heat release of a reaction across part of the flame, e.g. from to , can be written as where τ is the time at which the fluid parcel is at the spatial location . The summation of Equation (3) over all reactions can be used to estimate the fraction of heat release in the main or tail regions. The starting point of the ‘tail’ region is here defined as the intersection of the tangent to with the axis . According to this definition the heat release profile is separated into a ‘main’ region and a ‘tail’ region as seen in Figures 1–3.
Development and testing of a soot particle concentration estimator using Lagrangian post-processing
Published in Engineering Applications of Computational Fluid Mechanics, 2018
Raymond Alexander, Sepehr Bozorgzadeh, Ali Khosousi, Seth B. Dworkin
Step five of the estimator development uses a Lagrangian parcel-tracking CFD data processor (Veshkini et al., 2014). Theoretically, the formation or destruction of a soot particle is determined by its entire history from inception to oxidation. Therefore, in the present work, it is proposed to integrate variable histories of a fluid parcel in order to generate soot volume fraction correlations. For example, integrated temperature history can be a gauge for relative heat transfer into the particles, which is a suitable indicator of soot processes. The aggregated history of each variable can be expressed by the integral of each local variable with respect to time along a pathline traversed by a fluid parcel that may contain soot. The mathematical definition used herein of integrated temperature, molecular species, and mixture fraction histories are expressed in the following equations:
Numerical Analysis of the Effect of Fire Source Configuration on Fire-Wind Enhancement
Published in Heat Transfer Engineering, 2021
Esmaeel Eftekharian, Maryam Ghodrat, Yaping He, Robert H. Ong, Kenny C. S. Kwok, Ming Zhao
Based on the momentum equation, the force imposed on the infinitesimal fluid parcel is equal to the fluid parcel mass multiplied by the acceleration: where ∀ is volume, is flow acceleration and f is the force per unit volume. Symbols denote accelerations due to pressure force, gravitaionl force and viscuss force respectively.