This study investigates skin-friction drag reduction in fully developed turbulent vertical channel flows using direct numerical simulations. Spanwise-periodic wall heating and cooling are imposed to generate buoyancy-driven large-scale vortical motions near the walls. The drag-reduction performance is evaluated for different Richardson numbers, spanwise wavelengths, and phase differences between the two walls. The out-of-phase condition yields greater drag reduction than the in-phase condition, and the drag reduction further increases with increasing wavelength. Flow visualisations show that out-of-phase forcing produces a quasi-stationary large-scale coherent structure, whereas in-phase forcing leads to an unsteady response without a persistently phase-locked pattern. A three-component decomposition and the FIK identity indicate that drag reduction results from a balance between a decrease in the turbulent contribution and an increase in the coherent contribution to the friction coefficient.
This paper focuses on the development and application of a parallel implementation of a hybrid numerical method. It combines a mesh-based approach-specifically, the Finite Element Method (FEM)-for solving the Navier-Stokes equations, with a semi-Lagrangian particle method for the advection-diffusion of a scalar function. Both methods are implemented in parallel on distributed-memory supercomputers and are coupled in a one-way fashion, where the velocity field from the mesh-based solver feeds into the semi-Lagrangian solver. Parallelisation of the solvers and their coupling is achieved using the MPI library. Special attention is paid to the efficiency of the implementation. Computational performance is enhanced through the integration of an external library that minimises the busy-waiting behaviour of MPI subroutines during data exchange, ensuring optimal utilisation of available computational resources. Finally, the method is applied to simulate the advection of a high-Schmidt-number scalar in a jet flow, demonstrating its effectiveness and performance.
In this study, the effect of constant magnetic field (MF) on the thermohydraulic performance (THP) of turbulent Fe3O4/H2O flow in teardrop-shaped dimpled tube (TDDT) is numerically investigated. Numerical analyses were performed at Reynolds numbers (10,000 <= Re <= 50,000) under a constant heat flux (q" = 20 kW/m2) and MF strengths (0.03T <= B <= 0.3 T) applied at x/D = 20 (320-420 mm from the TDDT inlet) while the Fe3O4/H2O volumetric concentration was varied in the range of 0.0%<=phi <= 2.0%. The results show that the use of teardrop-shaped dimple increases the Nusselt number (Nu) by 33.6% at Re = 50,000 with only a 4.2% increase in the friction factor (ff). Applying a B = 0.3 T enhances Nu by 12.7% at Re = 10,000 and phi = 2.0% while causing only a 2.1% increase in ff. The study demonstrated that applying MF to magnetizable ferrofluids (FFs) can be effectively utilised in engineering applications, particularly in heat exchangers, electronic cooling, and thermal systems.
Efficient reduced-order models are needed for real-time simulation and control of high-dimensional nonlinear partial differential equations (PDEs). Global Proper Orthogonal Decomposition (POD) often underperforms because it assumes a single linear subspace, which is inadequate for nonlinear manifolds. We propose a Cluster-POD approach that partitions snapshot data and computes local POD bases, with manifold distances approximated locally using Euclidean metrics. Applied to the two-dimensional (2D) Burgers' equations, Cluster-POD achieves lower reconstruction error than standard POD for the same number of modes. A linear quadratic regulator (LQR) is designed using the reduced-order model and validated in closed loop on the full-order system, demonstrating improved tracking and stability with fewer modes and comparable control cost. The Burgers' equations are used as a proxy for Navier-Stokes due to their shared quadratic nonlinearity and lower computational cost. Overall, Cluster-POD offers an effective balance between accuracy and computational efficiency for data-driven control of nonlinear flows.
