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Introduction to the Continuum Fluid
Published in Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou, ViscousFluid Flow, 2021
Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou
Flows of highly viscous liquids are characterized by a vanishingly small Reynolds number and are called Stokes or creeping flows. Most flows of polymers are creeping flows [6]. The Reynolds number also serves to distinguish between laminar and turbulent flow. Laminar flows are characterized by the parallel sliding motion of adjacent fluid layers without intermixing, and persist for Reynolds numbers below a critical value that depends on the flow. For example, for flow in a pipe, this critical value is 2,100. Beyond that value, eddies start to develop within the fluid layers that cause intermixing and chaotic, oscillatory fluid motion, which characterizes turbulent flow. Laminar flows at Reynolds numbers sufficiently high that viscous effects are negligible are called potential or Euler flows. The Stokes number is zero in strictly horizontal flows and high in vertical flows of heavy liquids. The capillary number appears in flows with free surfaces and interfaces [7]. The surface tension, and thus the capillary number, can be altered by the addition of surfactants to the flowing liquids.
Pipe flow
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
In laminar flow, the fluid particles in one layer stay in the same layer and the layers slide without any crossing of particles from one layer to the adjacent layer. Thus, the flow is smooth and regular. On the other hand, in turbulent flow, the fluid particles jump from one layer to the adjacent layer and mix randomly. Eddies and swirls play significant roles in turbulent flow. Osborne Reynolds was the first to observe the difference between laminar and turbulent flows through his experimental studies. Turbulent flow is necessarily three-dimensional and unsteady. The transition from laminar to turbulent takes place when the Reynolds number exceeds about 2,300, but in most practical problems, it is taken as 2,000. The velocity profile for laminar flow is parabolic with the mean velocity equal to half the maximum velocity, and it can be determined theoretically as well as experimentally. Velocity profiles in turbulent flows can only be determined by experiments, and there are several empirical equations to describe the turbulent velocity profile.
Co-Visualization of Flame Structures and Species
Published in Maria da Graça Carvalho, Woodrow A. Fiveland, F. C. Lockwood, Christos Papadopoulos, Combustion Technologies for a Clean Environment, 2021
D. Proctor, I.G. Pearson, M. McLeod
The effectiveness of many combustion systems depends on the ability to maintain a stable flame at reasonably high combustion efficiency. Both aspects are closely related to the flow characteristics inside the combustor and the degree of mixing obtained between the injected fuel and the air. The mixing involves two important processes. The large-scale structures bring into the mixing layer large amounts of reacting components from the two separated streams. The fine-scale eddies enhance the mixing, at the molecular level between the reactants, which is a necessary condition to initiate the chemical reaction. The understanding of this complex gas-dynamic process requires analysis of the interactions between fluid dynamics, chemical reaction, acoustic waves and heat release of the reactive system (Broadwell and Dimotakis, 1986; Ballal, 1986).
Potent turbulence model for the computation of temperature distribution and eddy viscosity ratio in a horizontal direct-chill casting
Published in Numerical Heat Transfer, Part A: Applications, 2020
Mufutau Adekojo Waheed, Gaius Chukwuka Nzebuka, Christopher Chintua Enweremadu
Hot liquid metal has a lower density compared to the density of solid metal and is prone to instability in the flow behavior which often creates turbulence conditions. The turbulence eddies tend to promote strong mixing of hot and cold liquid melt, consequently enhancing heat transfer. It should be noted that the transition from turbulent to laminar flow of liquid hot metal completely alters the heat flow and directly affect the solidification interfaces [11]. Hence, there is a need to incorporate turbulence model to handle the effect of velocity and temperature fluctuations and turbulence eddies. In recent work, Nzebuka et al. [11] and Nzebuka and Waheed [12] have used velocity variance–elliptic relaxation () turbulence model to study flow and thermal evolution in a VDC casting. They made a comparison between the performance of the and the low Reynolds number version of the kinetic energy dissipation rate (low-Re k-ε) turbulence model in predicting the eddy viscosity ratio. The eddy viscosity ratio is the eddy viscosity divided by the molecular viscosity of the liquid metal. They discovered in their work that the turbulence model predicts a more reasonable turbulence eddy viscosity ratio within the slurry zone than the low-Re k-ε turbulence model in the VDC system.
Effect of hemispherical turbulators in a double-pipe heat exchanger for heat transfer augmentation
Published in Journal of Turbulence, 2020
Shiva Kumar, P. Dinesha, Akshith Narayanan, Rahul Nanda
When the turbulators are added in the annulus, average surface Nu is found to be higher. However, due to the addition of special hemispherical structures, the fluctuating nature of turbulent flow results in the formation of eddies, which acts as an additional mechanism for heat transfer. Unlike the laminar flow wherein energy transfer takes place mainly by molecular diffusion, in the turbulent flow conditions, the eddies will be formed, which rapidly transfer mass, momentum, energy and hence higher level of heat transfer. The turbulent flow leads to higher flow velocities as well as higher heat energy transfer. The turbulent flow also helps in preventing the development of an insulating blanket at the channel wall, thereby further diminishing the thermal boundary layer and hence augmenting the heat transfer. The two parameters that were altered were the diameter ratio (D) and the pitch ratio (P). The diameter ratios that were considered for this study were 0.29, 0.44 and 0.58. The turbulators obstruct the flow causing the fluid to move around it, resulting in higher turbulence, swirl generation and formation of vortices in the region near the turbulator. Increasing the diameter ratio, increased the surface area of this obstruction to the fluid, thereby increasing turbulence and enhancing the heat transfer rate. As the diameter ratio is increased, higher temperatures are observed along the length. This led to a higher heat transfer rate and Nu. Similarly, when the pitch ratio increases, the instances of the swirl generator reduces. This collectively reduces the total turbulence and restricts energy transfer. Hence, Nu reduces as the pitch ratio increases. It is found that the highest Nu can be observed for a combination of lower most pitch ratio and highest diameter ratio.
Characterization of Turbulence in an Optically Accessible Fan-Stirred Spherical Combustion Chamber
Published in Combustion Science and Technology, 2021
Ossama A. Mannaa, Morkous S. Mansour, Suk Ho Chung, William L. Roberts
The largest length scales of turbulence are mainly determined by geometrical boundaries encompassing turbulent flow. Large-scale eddies are determined using two-point velocity correlations. The integral length scale captures the largest eddies containing most of the turbulent kinetic energy. It is defined as: