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Turbulent Flow Heat Transfer
Published in Je-Chin Han, Lesley M. Wright, Analytical Heat Transfer, 2022
Most common models are based on a two-equation turbulence model, namely, the k−ε model, low Reynolds number k−ε model, and low Reynolds number k−ω model. Advanced Reynolds stress models and the second-moment closure model are also employed [7,8]. The advanced second-order Reynolds stress (second-moment) turbulence models are capable of providing detailed three-dimensional velocity, pressure, temperature, Reynolds stresses, and turbulent heat fluxes that were not available in most of the experimental studies. Various turbulence models and CFD simulations have been applied for numerous engineering designs. For example, to improve gas turbine heat transfer and cooling systems, some of the above-mentioned turbulence models and CFD predictions are reviewed and documented in Chapter 7 of reference [9].
Turbulence
Published in Wioletta Podgórska, Multiphase Particulate Systems in Turbulent Flows, 2019
In stress transport models the turbulent viscosity hypothesis is not needed as the transport equations are solved for the individual Reynolds stresses (Equation (4.270)). This group of models is referred to as second-order closure or second-moment closure models. In such models we do not need to assume that the normal stresses are equal even when the mean strain vanishes. The transport equations contain convection, production, and optionally also body force terms, which respond automatically to different effects including system rotation. Finally, the dissipation and turbulent terms indicate the presence of time scales unrelated to mean flow time scales and, therefore, the effects of flow history should be better represented than in models based on the Boussinesq approximation (Wilcox, 2006).
Modelling of Turbulent Combustion
Published in Achintya Mukhopadhyay, Swarnendu Sen, Fundamentals of Combustion Engineering, 2019
Achintya Mukhopadhyay, Swarnendu Sen
The main idea in conditional moment closure (CMC) modelling is to focus on particular states in combustion. Only conditional moments are considered in this modelling approach. The main advantage of this approach is that it can be applied to all combustion regimes and is relatively easy to implement. However, it is much more computationally expensive than flamelet based methods.
A double-averaged Navier-Stokes k – ω turbulence model for wall flows over rough surfaces with heat transfer
Published in Journal of Turbulence, 2021
The momentum equation in the DANS formulation makes appear three terms requiring models. The first one is related to the mean form drag of the roughness elements and concentrated a lot of efforts in the past because of its major role on wall friction. For many years, the model proposed by Taylor et al. [16] was used without questioning but recent studies by Kuwata and Kawagushi [26] or Chedevergne and Forooghi [27] proved the necessity to use more advanced models. From these drag models, the last two terms can then be examined. There are composed of the volume-averaged Reynolds stresses and the so-called dispersive stresses . Kuwata et al. [25] used a second moment closure to compute the Reynolds stresses, based on the two-component limit pressure-strain model [28] and choose to drop the dispersive stresses. They argued that a previous study by Kuwata and Kawagushi [26,29] confirmed the validity of omitting the dispersive stresses by analysing the budget terms in the turbulent kinetic energy transport equation from DNS over randomly distributed rough surfaces. They successfully applied their model to several semi-complex rough surfaces composed of randomly distributed hemispheres, including potential overlappings, and to real marine paint rough surfaces. This model can be considered as the most advanced implementation of the DANS equations for roughness configurations. Although very promising, the recourse to second moment closure makes it hard to implement in some industrial workflow. In addition, heat transfer are not accounted for in this model. There is a need for a DANS model based on a first-order closure for the Reynolds stresses and capable of predicting heat transfer. Therefore, this paper focuses on a first-order DANS model associated with the drag model derived by Chedevergne and Forooghi [27] and a specific closure for the energy equation to include heat transfer in the presence of roughness. The proposed model is based on the SST model [30] and can be seen as an extension of the latter to rough surfaces without boundary conditions modifications, contrary to equivalent sand grain corrections.