The scaling law for the horizontal length scale ℓ relative to the domain height L, originating from the linear theory of quasi-static magnetoconvection, ℓ/L∼Q^-1/6, has been verified through two-dimensional (2-D) direct numerical simulation (DNS), particularly at high values of the Chandrasekhar number (Q). This relationship remains valid within a specific flow regime characterized by columnar structures aligned with the magnetic field. Expanding upon the Q-dependence of the horizontal length scale, we have derived scaling laws for the Nusselt number (Nu) and the Reynolds number (Re) as functions of the driving forces (Rayleigh number (Ra) and Q) in quasi-static magnetoconvection influenced by a strong magnetic field. These scaling relations, Nu∼Ra/Q and Re∼RaQ^-5/6, have been successfully validated using 2-D DNS data spanning a wide range of five decades in Q, ranging from 10⁵ to 10⁹. The successful validation of the relations at large Q values, combined with our theoretical analysis of dissipation rates and the incorporation of the horizontal length scale's influence on scaling behaviour, presents a valid approach for deriving scaling laws under various conditions.

Driven by the need for simulating compressible flows, Germano identity-based [Z. Yin and P. A. Durbin, “An adaptive DES model that allows wall-resolved eddy simulation,” Int. J. Heat Fluid Flow 62, 499–509 (2016)] and Vreman operator-based [Bader et al., “A hybrid model for turbulence and transition, with a locally varying coefficient,” Flow, Turbul. Combust. 108, 935–954 (2022)] dynamic ℓ²-ω delayed detached eddy simulation (DDES) formulations are constructed on the k x shear stress transport (SST) model. The Bachalo–Johnson transonic axisymmetric bump is simulated to assess the models’ capability in handling the compressible boundary layers under pressure gradient and transonic shock–boundary layer interaction. The new dynamic ℓ²-ω DDES formulation based on k-ω SST overcomes the issues of freestream sensitivity and inaccurate compressible boundary layer profile observed in the original k-ω (88) based model. The new SST-based dynamic model using the Vreman operator to compute the model coefficient (Vreman-dynamic model) has superior performance against Germano identity-based model due to its capability of suppressing the subgrid viscosity during the initial devel- opment of a separating shear layer. The Vreman-dynamic model predicts a reattachment location similar to the zonal improved-DDES/direct numerical simulation approach by Spalart et al. [“Large-eddy and direct numerical simulations of the bachalo-johnson flow with shock- induced separation,” Flow, Turbul. Combust. 99, 865–885 (2017)] on a much coarser mesh demonstrating its potential for application in industrial flows.

In this paper, the experiment of flat plate transition under freestream turbulence with heat transfer conducted by Blair (1983) is reproduced using subgrid dynamic scalar-flux models (Bader and Durbin, 2020; Moin et al., 1991). The advantage of adopting tensorial subgrid diffusivity is quantified. A set of Reynolds Averaged scalar-flux models is also evaluated using the LES data. Based upon the observations, an improved Higher Order Generalized Gradient Diffusion Hypothesis (HOGGDH) model is proposed with a modified, spatially varying model coefficient. The model coefficient is made a function of the turbulent Reynolds number , which enables it to detect the near wall region, thereby increasing the accuracy down to the wall. The mean temperature predictions and the scalar fluxes in the wall-normal as well as the streamwise directions by the improved version of the HOGGDH model are shown to be accurate compared to the HOGGDH model with a constant coefficient and other considered models.

This is a review article on modeling for turbulent heat transport. Models for Reynolds averaged and hybrid simulation of turbulent flow and heat transfer are reviewed. Concepts that underly the models are summarized and literature is cited. Representing turbulent heat flux by an effective Prandtl number is discussed at length. In addition to its prescription for Reynolds averaged modeling, methods to compute it dynamically during a simulation are reviewed. Asymmetry of the heat diffusivity is described. Methods to specify the diffusion tensor by algebraic flux approximation and generalized gradient diffusion are surveyed.

In this paper, a simple method to locally compute the model coefficient C DES in Reddy et al. (Int J Heat Fluid Flow 50:103-113, 2014. https:// doi. org/ 10. 1016/j. ijhea tflui dflow. 2014. 06. 002) is presented. The formula for the coefficient is derived from the structural function B of Vreman (Phys Fluids 16(10):3670-3681, 2004. https:// doi. org/ 10. 1063/1. 17851 31). It, therefore, does not involve explicit filtering or averaging procedures. By virtue of the variable coefficient being based on B , the model is expected to retain the property of relatively small dissipation in transitional and near-wall regions. This property enables the present formulation to be a reasonable candidate to predict transitional flows. The formulation is validated in the canonical, fully developed turbulent channel and backward facing step flows, followed by simulations of orderly, bypass and separation induced laminar-to-turbulent transition in a spatially developing boundary layer over a flat plate.

A dynamic subgrid-scale (SGS) scalar-flux model, based on the exact rate of production of turbulent scalar fluxes, is proposed. The model is derived from an assumption that the pressure-scalar correlation in the equation for turbulent scalar flux is a vector that is approximately aligned with the scalar flux itself. The formulation then yields a tensor diffusivity which allows nonalignment of the SGS scalar fluxes with respect to the resolved scalar gradient. In contrast to eddy diffusivity models and to general gradient diffusion hypothesis models, for which the diffusivity tensor is symmetric, the present formulation produces an asymmetric diffusion tensor; for theoretical and experimental reasons, that tensor is known to be very asymmetric. The model contains a single coefficient, which is determined dynamically. The model is validated in fully developed turbulent channel flow and in separated and reattaching flow over a backstep.

Wind turbine farms suffer from wake losses, where the downstream turbines generate less power, and/or the leading turbines are throttled to reduce the downstream power losses. In this paper, we focus on possible external modifications that can enhance the wind turbines' performance when they are operating in a farm environment. In particular, this study is interested in enhancing the performance of the downstream turbines in wind farms. The idea is to move each turbine's wake down and away from subsequent turbines. This goal is achieved by using stationary external airfoils that are placed in proximity to the rotating blades. A number of different designs are tested and the design concepts are tested using Reynolds-Averaged Navier-Stokes simulations of an aligned array of 2 wind turbines. The turbines are modeled as actuator disks with axial induction and are placed in a velocity field that is modeled as a turbulent atmospheric boundary layer. It is found that fixed external airfoils can enable partial or full power recovery at turbine separations of as small as 3 rotor diameters downstream. We will also demonstrate that some devices can also improve the performance of the upstream turbine. The physical reasons for these power recovery phenomena are discussed.