In this paper, we consider the evolution of decaying homogeneous anisotropic turbulence without mean velocity gradients, where only the slow pressure rate of strain is nonzero. A higher degree nonlinear return-to-isotropy model has been developed for the slow pressure–strain correlation, considering anisotropies in Reynolds stress, dissipation rate, and length scale tensor. Assumption of single length scale across the flow is not sufficient, from which stems the introduction of length scale anisotropy tensor, which has been assumed to be a linear function of Reynolds stress and dissipation tensor. The present model with anisotropy in length scale shows better agreement with well-accepted experimental results and an improvement over the Sarkar and Speziale (SS) quadratic model.

In the presence of mean strain or rotation, the anisotropy of turbulence increases due to the rapid pressure strain term. In this paper, we consider the modeling of the rapid pressure strain correlation of turbulence. The anisotropy of turbulence in the presence of mean strain is studied and a new model is formulated by calibrating the model constants at the rapid distortion limit. This model is tested for a range of plane strain and elliptic flows and compared to direct numerical simulation (DNS) results. The present model shows agreement with DNS and improvements over the earlier models like those by Launder et al. (1975, “Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566.) and Speziale et al. (1991, “Modelling the Pressure–Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach,” J. Fluid Mech., 227(1), pp. 245–272.) that have been reported to give satisfactory performance for hyperbolic flows but not satisfactory for elliptic flows.

Most investigations of turbulent flows in academic studies and industrial applications use turbulence models. Out of the different turbulence modeling approaches Reynolds stress models have the highest potential to replicate complex turbulent flow phenomena at a reasonable computational expense. The Reynolds stress modeling framework is constituted by individual closures that approximate the effects of separate turbulence processes like dissipation, turbulent transport, pressure strain correlation, etc. Owing to its complexity and importance in flow evolution the modeling of the pressure strain correlation mechanism is considered the crucial challenge for the Reynolds stress modeling framework. In the present work, the modeling of the pressure strain correlation for homogeneous turbulent flows is reviewed. The importance of the pressure strain correlation and its effects on flow evolution via energy transfer are established. The fundamental challenges in pressure stain correlation modeling are analyzed and discussed. Starting from the governing equations we outline the theory behind models for both the slow and rapid pressure strain correlation. Established models for both these are introduced and their successes and shortcomings are illustrated using theoretical analysis, computational fluid dynamics simulations, and comparisons against experimental and numerical studies. Recent advances and developments in this field are presented and discussed. The application of machine learning algorithms such as Deep Neural Networks, Random Forests, and Gradient Boosted Regression Trees is summarized and examined. We report fundamental problems in the application of machine learning algorithms for pressure strain correlation modeling. Finally, challenges and hurdles for pressure strain correlation modeling are outlined and explained in detail to guide future investigations.

This article presents numerical studies on the drag evolution of an axisymmetric body of revolution with microgrooves using Reynolds stress model-based computational fluid dynamics simulations. Experimental data of drag evolution along the non-grooved body were used to validate the numerical model predictions. After validation of the model predictions, a series of numerical simulations were performed to study the effect of toroidal grooving of the axisymmetric body on the drag evolution by varying the depth to the surface radius of the grooves at different Reynolds numbers. A maximum drag reduction of 43% was achieved with such effort. This was possible because of the drastic reduction of turbulent shear stress in the boundary layer, which has a direct relationship with the skin friction drag evolution along the body.

In this article, the hydrodynamic characteristics of Autonomous Underwater Vehicles (AUVs) are investigated and analyzed under the influence of rotating flow fields, which were generated in a recirculating water tank via a rotating propeller. Initially, experiments were carried out to measure flow field variables and quantities of Interest across the AUV in the presence of the rotating propeller while varying the rotational speed and the extent of rotational flow strength. The flow field across the AUV was measured using an Acoustic Doppler Velocimeter (ADV). These measured turbulent flow statistics were used to validate the Reynolds Stress Model (RSM) based numerical predictions in a commercial CFD solver. After preliminary validation of the turbulent flow statistics with the numerical predictions, a series of numerical simulations were performed to investigate the effect of the rotational flow field of the propeller on the drag, skin friction, and pressure coefficients of the AUV. The operating speed and location of the propeller were also varied to check their effects on the hydrodynamic performance of the AUV. The results provided in this article will be useful for the design optimization of AUVs cruising in shallow water where the flow is highly rotational because of wave-current interactions. Additionally, the results and analysis are relevant to study the design and operation of AUVs that have to operate in a group of unmanned underwater vehicles or near submarines and ships where the flow field is highly complex and such rotational effects are present.