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Numerical Methods for Boundary-Layer-Type Equations
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
The prediction of turbulent boundary-layer flows is another matter. The issue of turbulence modeling adds complexity and uncertainty to the prediction. Turbulence models can be adjusted to give good predictions for a limited class of flows, but when applied to other flows containing conditions not accounted for by the model, poor agreement is often noted. Because of the usual level of uncertainty in both the experimental measurements and turbulence models, agreement to within ±3%–4% is generally considered good for turbulent flows.
On Computational Heat Transfer Procedures for Heat Exchangers in Single-Phase Flow Operation
Published in W. J. Minkowycz, E. M. Sparrow, J. P. Abraham, J. M. Gorman, Advances in Numerical Heat Transfer, 2017
The instantaneous mass conservation, momentum, and energy equations form a closed set of five unknowns: u, v, w, p, and T. However, the computing requirements—in terms of resolution in space and time for direct solution of the time-dependent equations of fully turbulent flows at high Reynolds numbers (so-called direct numerical simulation [DNS] calculations)—are enormous, and major developments in computer hardware are needed. Thus, DNS is more often viewed as a research tool for relatively simple flows at moderate Reynolds numbers, with supercomputer calculations required. Meanwhile, practicing thermal engineers need computational procedures that supply information about the turbulent processes but avoid the need for predicting the effects of every eddy in the flow. This calls for information about the time-averaged properties of the flow and temperature fields (e.g., mean velocities, mean stresses, and mean temperature). Usually, a time-averaging operation, known as Reynolds decomposition, is carried out. Every variable is then written as a sum of a time-averaged value and a superimposed fluctuating value. In the governing equations, additional unknowns appear—six for the momentum equations and three for the temperature field equation. The additional terms in the differential equations are called turbulent stresses and turbulent heat fluxes, respectively. The task of turbulence modeling is to provide procedures for predicting the additional unknowns (i.e., the turbulent stresses and turbulent heat fluxes) with sufficient generality and accuracy. Methods based on the Reynolds-averaged equations are commonly referred as Reynolds-averaged Navier–Stokes (RANS) equation methods. Large eddy simulation (LES) lies between the DNS and RANS approaches in terms of computational demand. Like DNS, three-dimensional simulations are carried out over many time steps, but only the larger eddies are resolved. An LES grid can be coarser in space and the time steps can be larger than for DNS because the small-scale fluid motions are treated by a sub-grid-scale (SGS) model.
In silico modeling for personalized stenting in aortic coarctation
Published in Engineering Applications of Computational Fluid Mechanics, 2022
Dandan Ma, Yong Wang, Mueed Azhar, Ansgar Adler, Michael Steinmetz, Martin Uecker
For in silico modeling of personalized stent intervention in CoA, a protocol for virtual geometry deformation (Neugebauer et al., 2016) and a validated numerical method to accurately predict the blood flow in the aorta are required. Regardless of the erythrocytes, leukocytes, and platelets in blood, the flow in the aorta is normally modelled as Newtonian fluid (Pedley, 1980) considering the relatively large Reynolds number Re, which is proportional to the flow velocity and aorta diameter and inversely proportional to the blood viscosity. Computational fluid dynamics (CFD) (Taha, 2005) plays an important role in biomedical engineering applications, such as drug delivery (Alishiri et al., 2021) and understanding of carotid stenosis (Kang, Mukherjee, Kim, et al., 2021; Kang, Mukherjee, & Ryu, 2021) and aortic dissection (Cheng et al., 2013, 2015). Due to the personalized and complex 3D geometry and jet flows induced by heart contraction and local narrowing, laminar flow, turbulent flow and transition between them may coexist spatiotemporally (Ku, 1997; Stein & Sabbah, 1976). Thus, to accurately resolve such aortic flow, both turbulence and complex geometry should be considered in CFD simulations. Three approaches, including Reynolds-averaged Navier–Stokes equations (RANS), large eddy simulation (LES), and direct numerical simulation (DNS), are typically used for turbulence modeling. From RANS to DNS, both the accuracy and computational demand increase due to more and more details that need to be resolved.
Is Coefficient of Variation a Realistic Index for Characterizing Mixing Efficiency in Ozone Applications?
Published in Ozone: Science & Engineering, 2020
Srikanth. S. Pathapati, Daniel W. Smith, Justin P. Bennett, Angelo L. Mazzei
Multiphase flows are modeled with a Eulerian-Eulerian approach or a Eulerian-Lagrangian approach (van Wachem and Almstedt 2003). The latter is commonly accepted to be suited to modeling dilute flows, defined as flows with a second phase volume fraction (PVF) less than 10% (Brennen 2005). Since the gas volume fractions in this study exceed 10% (particularly at the nozzle discharge point surrounding close vicinity), an Eulerian-Eulerian approach was utilized. At volume fractions less than 10% for gas-liquid flow,the phase interaction can be assumed to be unidirectional (Ranade 2001) and as such, a simplified version of the Eulerian-Eulerian approach, the mixture model, was utilized in this study. The mixture model (Manninen, Taivassalo, and Kallio 1996) is used to model bubbly flows where phases move at different velocities. In the mixture model, phases are assumed to be interpenetrating. The mixture model solves the continuity equation for the mixture, the momentum equation for the mixture, the energy equation for the mixture, and the volume fraction equation for the secondary phases, as well as algebraic expressions for the relative velocities (if the phases are moving at different velocities). The two-equation, realizable k-Epsilon model (Versteeg and Malalasekera 2007) was utilized for turbulence modeling.
Numerical and experimental analysis of shallow turbulent flow over complex roughness beds
Published in International Journal of Computational Fluid Dynamics, 2019
Yong Zhang, Matteo Rubinato, Ehsan Kazemi, Jaan H. Pu, Yuefei Huang, Pengzhi Lin
The nature of turbulence is fundamentally three-dimensional (3D). Historically, 3D approaches on the turbulence modelling mainly included the Direct Numerical Simulation (DNS), Large-Eddy Simulation (LES), and Reynolds-Averaged Navier-Stokes (RANS) modelling (Rodi and Mansour 1993; Pope 2000; Bhaganagar, Kim, and Coleman 2004; Hinterberger, Fröhlich, and Rodi 2008). Along the rivers and coastal regions, the flow domain is quite complex and spacious, and hence to characterise the flow structures it would be excessively time-consuming to apply any of these three approaches, which would require a large number of grid nodes in order to provide the accurate results (Erpicum et al. 2009). The two-dimensional (2D) Shallow Water Equations (SWE) coupled with the benchmark turbulence closure model is much faster and enables the interpretation of turbulent characteristics using a smaller vertical length scale (z) as compared with the two horizontal ones (x and y) in those regions (Younus and Chaudhry 1994; Pu, Shao, and Huang 2014; Cao et al. 2015; Campomaggiore et al. 2016). Furthermore, to obtain more accurate and repeatable results, it is also critical to select the appropriate coefficients in these turbulence closure equations.