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Governing Equations of Fluid Mechanics and Heat Transfer
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
Modeling for stress transport equations has followed the pioneering work of Rotta (1951). A commonly used example of the stress-equation approach is the Reynolds stress model proposed by Launder et al. (1975), although numerous variations have since been suggested. Because of their computational complexity, the Reynolds stress models have not been widely used for engineering applications. Because they are not restricted by the Boussinesq approximation and because the closure contains the greatest number of model PDEs and constants of all the models considered, it would seem that the Reynolds stress models would have the best chance of emerging as “ultimate” turbulence models. Such ultimate turbulence models may eventually appear, but after more than 20 years of serious numerical research with these models, the results have been somewhat disappointing, considering the computational effort needed to implement the models.
Prediction of maneuvering coefficients of Delft catamaran 372 hull form
Published in Petar Georgiev, C. Guedes Soares, Sustainable Development and Innovations in Marine Technologies, 2019
Ship maneuver is actually the problem of resistance in which the hull is moving. Therefore, it is necessary to concentrate on the prediction of resistance components. In typical straight-ahead towing tests, the frictional resistance of the hull is calculated by the ITTC-57 friction line. In the viscous solutions, there is a need for high processing power computers to be able to compute the flow properties such as velocity and pressure in the vicinity of the wall where turbulence is effective. To manage that, the Reynolds stress term is modeled by various turbulence models which are designed according to experimental studies. One of the commonly used method for solving the fluid flow in the boundary layer in RANS simulations is to define a wall function that works when the non-dimensional wall distance (y+) is between 30 and 300. In this study, Realizable k-ε turbulence model has been used to calculate the Reynolds stress terms in both static and dynamic simulations.
Preliminary Concepts
Published in Hillel Rubin, Joseph Atkinson, Environmental Fluid Mechanics, 2001
The last term on the right-hand side of Eq. (5.5.10), when multiplied by ρ0, represents the Reynolds stresses. This term produces an effect similar to that of viscous stresses, though it should be kept in mind that the physical basis for viscous stress is fluid viscosity, while turbulent shear stress (Reynolds stresses) results from the fluctuating nature of the velocity field. In other words, the turbulent eddies transport various fluid properties by their random three-dimensional motions, superimposed on top of the mean flow (advective) transport. This process is illustrated in Fig. 5.14.
Analysis of cavitation and shear in bellows pump: transient CFD modelling and high-speed visualization
Published in Engineering Applications of Computational Fluid Mechanics, 2023
Tianyi Ge, Liang Hu, Rui Su, Xiaodong Ruan
On the basis of Reynolds decomposition, the governing equations of the homogeneous mixture (Equations (1) and (2)) become: Compared with Equations (1) and (2), additional terms appear in the momentum equation (12). The term , which represents the effect of turbulence, is called Reynolds stresses. In order to close Equations (11) and (12), the Reynolds stresses must be modelled. The Boussinesq hypothesis relates the Reynolds stresses linearly to the averaged strain rate: where is the turbulent viscosity (also called the eddy viscosity), is the turbulent kinetic energy, and is the Kronecker delta. Depending on the methods used to compute the turbulent viscosity , the linear eddy viscosity model can be divided into several categories.
Wind induced pressures on a large low-sloped gable roof building with parapet
Published in Architectural Science Review, 2023
Aly Mousaad Aly, Matthew Thomas
Concurrently, simultaneous collection of the wind velocity and pressures is necessary to ascertain that they are within target ranges. This measure is crucial for accuracy in the data acquisition stage as the velocity, at reference height, directly affects the time history of pressures. Therefore, high-resolution flow measuring devices such as Cobra probes, with the ability to capture subtle changes in the free stream velocity, are used in this study. Two Cobra probes are positioned upstream at mean roof height. The probes measure mean and time-varying speed, pitch and yaw angles, and local static pressure, and the data collection software calculates all six components of Reynolds stress. The measurements' accuracy depends on the turbulence levels but is generally within ±0.5 m/s (∼1.64 ft/s), ± 1°, and 30% for wind speed, pitch and yaw angles, and turbulence intensity, respectively.
Turbulent characteristics of sinuous river bend
Published in ISH Journal of Hydraulic Engineering, 2021
Jyotismita Taye, Jyotirmoy Barman, Mahesh Patel, Bimlesh Kumar
The velocity fluctuations , and in turbulent flow influences the development of time-mean velocity components (,,) which increases the resistance to deformation. This ultimately leads to apparent stresses, called Reynolds stresses. Reynolds stresses provide important details regarding the flow behaviour. Two components of Reynolds stresses are the Reynolds shear stress (RSS) and Reynolds normal stress (RNS). The components of Reynolds stresses are of symmetric second-order tensor. Pope (2000) defined two components of stresses: the diagonal component (RNS) and the off-diagonal component (RSS).