The present work investigates granulation or convective flow patterns in density-stratified (or anelastic) convection in spherical shells. The density-stratified thermal convection is typically present in astrophysical systems (such as solar convection); motivated by this, we performed a series of three-dimensional anelastic convection simulations in a spherical shell geometry using an in-house developed hybrid solver. We explored the effect of Rayleigh number and density scale height on the convective flow patterns. The granulation (or cell-like structures) are more prominent at higher density scale height and Rayleigh number. The granulation is further characterized by kinetic energy and helicity spectra. Our results support the argument that the convective flow patterns (or granulation) emerge due to inverse cascade owing to the presence of density stratification. Convective patterns (or granulation) are identified based on length scales, time scales, and flow velocity. The length scale of granules is further verified using a solar granulation model. Our analysis suggests the existence of inverse cascade and supergranulation on the spherical surface due to density-stratified thermal convection in spherical shells.

The present work develops, verifies, and benchmarks a hybrid discrete exterior calculus and finite difference (DEC-FD) method for density-stratified thermal convection in spherical shells. Discrete exterior calculus (DEC) is notable for its coordinate independence and structure preservation properties. The hybrid DEC-FD method for Boussinesq convection has been developed by Mantravadi et al. (2023). Motivated by astrophysics problems, we extend this method assuming anelastic convection, which retains density stratification; this has been widely used for decades to understand thermal convection in stars and giant planets. In the present work, the governing equations are splitted into surface and radial components and discrete anelastic equations are derived by replacing spherical surface operators with DEC and radial operators with FD operators. The novel feature of this work is the discretization of anelastic equations with the DEC-FD method and the assessment of a hybrid solver for density-stratified thermal convection in spherical shells. The discretized anelastic equations are verified using the method of manufactured solution (MMS). We performed a series of three-dimensional convection simulations in a spherical shell geometry and examined the effect of density ratio on convective flow structures and energy dynamics. The present observations are in agreement with the benchmark models.

The present work investigates the unsteady flow around triangular prisms with vertex angles of 30 ° , 45 ° , 60 ° , and 90 ° for shedding Reynolds number between 50 and 150. The numerical simulations of flow around triangular prisms at different vertex angles and Reynolds number has been carried out using the open-source code OpenFOAM. The wake of the prisms in different cases has been examined using instantaneous and time-averaged velocity and vorticity fields. The energy dynamics in the wake are demonstrated using enstrophy. The paper explains the shedding around a prism and reports the differences in the wake due to the different vertex angles of the prisms employed in the present work. Strouhal number and force coefficients have been obtained and compared for different prisms. The coefficient of lift and drag phase plot indicates a higher spread for prisms with larger vertex angles at higher Reynolds number. The shedding frequency has a linear variation with Reynolds numbers for the prisms. The obtained results were compared with earlier works on square cylinders and 45 ° oriented square cylinder.

Finite-difference collocated schemes are employed to solve incompressible flow in cylindrical coordinates. Pressure Poisson equation for a cylindrical coordinate is derived using predictor-corrector step similar to Simplified Marker and Cell (SMAC) method. The central theme of the present work is to solve cylindrical coordinate fluid flow problems using the SMAC scheme and the treatment of singularity at the pole. The robustness of the developed code is checked through different numerical problems. The unsteady incompressible flow simulation is performed. The cylindrical coordinate numerical schemes are assessed through the benchmark problem of the lid-driven polar cavity. Rotating annuli is the perfect problem to check the periodic condition in the theta direction. Subsequently, the singularity at the pole is checked through a rotating disk problem and flows through the pipe. It is observed that the SMAC scheme and node-based collocated grid pole-treatment solves the flow in rotating disk and pipe.

This work numerically investigates the thermal buoyancy effect on the wake-induced vibration of a heated cylinder submerged in the wake of a stationary cylinder. Simulations are performed at Richardson number Ri = [0, 1], Prandtl number Pr = 7.1 and Reynolds number Re = 100. The downstream cylinder is elastically mounted in transverse direction with reduced velocity Ur = 4 – 20. The mass ratio is set to 2 and the damping coefficient is considered zero to attain maximum oscillation. The thermal buoyancy effect on wake-induced vibration is illustrated through flow structures, heat transfer and oscillation amplitude. Thermal buoyancy influences the flow around a cylinder and suppresses the oscillation amplitude. Multiple heated cylinders in close proximity may suffer fatigue failures or structural damage. The present findings could increase the structural durability of heated cylinders.

The effect of FIV on forced convection heat transfer from two elastically mounted tandem cylinders of unequal diameters has been investigated. The present numerical simulation demonstrates the effect of the diameter ratio (d/D=0.2 - 1) on the heat transfer of an upstream cylinder with variable diameter 'd' and a downstream cylinder with constant diameter 'D'. The flow is considered incompressible, twodimensional, laminar at Re=150 and Pr=0.71. The two elastically mounted heated cylinders are allowed to oscillate in the transverse direction with reduced velocity Ur=4 and 6, mass ratio m∗=2, damping ratio ξ=0. The gap ratio between cylinders G/D=1.5 and 3.5 are considered to elucidate the effect of heat transfer in extended body regime (G/D=1.5) and reattachment regime (G/D=3.5). The impact of the diameter ratio (d/D=0.2 - 1) on flow dynamics and heat transfer characteristics is demonstrated through oscillation amplitude, flow structures and Nusselt number.

This work numerically investigates the effect of FIV on the heat transfer performance of three heated tandem cylinders at different spacing ratios and reduced velocity. The simulation is performed at Reynolds number Re=100, Prandtl number Pr=0.7. The three elastically mounted heated cylinders are allowed to oscillate in the transverse direction with reduced velocity Ur=2-20, mass ratio m*=2, and zero damping coefficient for maximum oscillation. The spacing ratio between cylinders G*=2 and 4 are considered to elucidate the effect of FIV on heat transfer in extended body regime (G*=2) and reattachment regime (G*=4). The effect of the spacing ratio on FIV and heat transfer is observed through flow structures and quantified through oscillation amplitude, shedding frequency, pressure coefficient, and Nusselt number. The flow around the cylinders and the associated heat transfer depend strongly on the spacing ratio. The present findings can be utilized to develop a strategy for reducing fouling and removing contaminants and wax in piggyback pipes used in nuclear power plants or offshore oil extraction.

A comprehensive experimental and computational investigation of flow past over a generic aircraft carrier with ski-jump is presented in this paper. The study has been performed to gain a deeper understanding of the airwake aerodynamics past such an aircraft carrier for different crosswind conditions. An experimental investigation is carried out in a wind tunnel on a prototype model of having a length of 1.1 m (1:250 scale). The prototype model was conceived from the various aircraft carriers existing in the world. A five-hole cobra probe is used to measure all the three velocity components along the 3° aircraft's landing slope for validation purposes. Reynolds-Averaged Navier-Stokes (RANS) based computational investigations are conducted to predict the overall airwake aerodynamics over the flight deck. Subsequently, a detailed parametric study has been conducted to examine the effect of relative wind conditions on the aircraft's landing slope. Detailed comparisons of velocity variations along the aircraft glide slope are discussed along with the experimental data. Results show that the top deck island structure and the oblique wind conditions are the two main contributors for adverse airwake aerodynamics over the flight deck.

This work numerically investigates flow-induced vibration (FIV) of two tandem cylinders of unequal diameters at a Reynolds number of 100 and at a range of reduced velocity 2 − 10. Particular attention is paid to assimilating the effects of the cylinder diameter ratio (0.2 − 1) and the cylinder spacing ratio 1.5, 3.5 and 5.5 on vibration responses, frequency responses, lock-in, and wake structure. The cylinder-to-fluid mass ratio is considered as one, and the damping coefficient is set to zero to attain maximum oscillation amplitude. The obtained results reveal that FIV is highly sensitive to both diameter and spacing ratios, and the wake interference involved is intricate. With a decrease in diameter ratio, the upstream cylinder oscillation is affected due to a change in its effective Reynolds number while its wake induces a significant effect on the downstream cylinder. The lowest diameter ratio of 0.2 exhibits a de-energized wake suppressing the oscillation of the downstream cylinder. At a moderate diameter ratio of 0.6, suppressed and excited oscillations of the downstream cylinder are observed at spacing ratios 1.5 and 3.5, respectively.

The effect of diameter differences of three tandem cylinders on flow-induced vibrations (FIVs) and convection heat transfer characteristics is investigated. The diameter reduction ratios are 0, 0.2, and 0.4, and the cylinder gap ratios are 2 and 4. The simulation is performed at Reynolds number 100, Prandtl number 0.7, reduced velocity 2 - 20, and mass ratio 2. The effect of the diameter reduction ratio on FIVs and heat transfer characteristics is observed through flow structures, oscillation amplitude, shedding frequency, correlation between lift coefficient and cylinder displacement, and Nusselt number. The flow around the downstream cylinder and the associated heat transfer depend strongly on the diameter reduction ratio. The FIV of the downstream cylinder is reduced with the increase in diameter reduction ratio. Indeed, for diameter reduction ratio 0.4 and gap ratio 2, the maximum oscillation amplitude is reduced by 48%. This is because the unequal diameter results in a weaker correlation between lift force and oscillation, modulated oscillation of cylinder, and distribution of primary shedding frequency energy to secondary frequency. At the initial and upper branches of vibration, the heat transfer from the downstream cylinder is enhanced with an increase in diameter reduction ratio due to more exposure to flow and the impingement of the gap vortices. The present flow configuration unveils reduced FIV and enhanced heat transfer, which is a desirable characteristic of multiple heated tubes for structural durability and better performance.

Laminar to turbulent flow transition in a finite length square duct has been carried out by imposing novel spatiotemporal finite amplitude inlet disturbance on the laminar flow. The present direct numerical simulation study demonstrates the effect of inlet disturbance on laminar to turbulent transition. A laminar flow in a finite length square duct is considered at bulk Reynolds number Re = 2260 and Re = 1540, to which a novel spatiotemporal disturbance is introduced through a narrow banded region at the inlet of the square duct. The puff (transition) and slug (turbulent) flow dynamics indicate the laminar to turbulent transition in a square duct. Disturbance introduced at Re = 2260 laminar flow propagates downstream, giving puff and slug flow phenomena similar to pipe flows. However, at Re = 1540, inlet disturbance shows only a puff-like structure. The four vortex mean secondary flow is observed in a puff region, while the conventional eight vortex is observed in the slug region. The coherent structures of the transition (puff) flow show the presence of dual-type hairpin structures. The turbulent kinetic energy spectrum indicates conventional −5/3 spectra for slug flow and −2 energy spectra for puff flow. Thus, in this paper, it is shown that the puff and slug characteristics of laminar to turbulent transition in a square duct are similar to that of a circular duct. It is also shown that the novel inlet disturbance through a narrow banded region captures the dynamics of laminar to turbulent transition in a square duct.

We develope an optimised Direct Numerical Simulation (DNS) solver for laminar, transition, and turbulent flow. It utilises the Crank Nicholson scheme for time advancement, and it is spatially accurate up to fourth-order on uniform grids. The solver's salient features are multi-dimensional parallelisation and modular-based code, which is written in object-oriented C++ language. The DNS solver is developed in the MPI parallel platform using a cubic decomposition technique. The open-source library used for optimisation is MPI, blitz++, YAML, and HDF5 library. The parallel performance analysis of the optimised DNS solver on the multiprocessor computing system (supercomputer) shows 80 (Formula presented.) efficiency. The solver is verified and benchmarked for wall-bounded flows by simulation of laminar, transition, and turbulent flow in a square duct.

The self-sustaining turbulent flow in a straight square duct is simulated using direct numerical simulation (DNS). The underlying flow dynamics in a square duct is numerically investigated by using the three-dimensional proper orthogonal decomposition (POD) technique. The method of snapshot POD is an efficient tool to educe coherent structures from the fluctuating component of the DNS database at frictional Reynolds number of 300 (based on duct width and frictional velocity). The coherent structures are manifested through the spatial analysis of POD modes. The spatial POD modes depict the first two most energetic modes as streamwise-independent rolls (or non-propagating modes). The third and fourth most energetic mode are observed as streamwise-dependent structure (or propagating modes). The higher POD modes demonstrate the loop-like structure near the wall region and detached structures in the wake region of the square duct.

Flow around a cube is numerically studied in the laminar vortex shedding regime. The objective is to examine the three-dimensional vortex shedding mechanism and understand the temporal behavior of the wake. Vortices were identified using λ2 criterion for Re = 250-770. The wake of the cube sheds paired hairpin vortices, which moves in the streamwise direction and attains a constant shape with time. The analysis of separation distance and angular orientation of hairpin vortices for flow around a cube are presented here for the first time in the literature. The separation (d) between the paired hairpin vortices scales as t-1/2. The orientation of hairpin vortices changes with time and attains a near-normal orientation with respect to the axial direction. At Re ≥ 339, the hairpin twists with respect to axial direction losing the axisymmetry in one plane noted for 276 ≤ Re ≤ 300. The hairpin vortices disintegrate into smaller vortices at higher Re = 570 and 770. A quasi-periodic nature of the flow has been revealed by the phase plots. The drag and side forces generated due to the flow are studied with pressure force mostly contributing to the drag. One of the side force coefficients dominates owing to the asymmetry of the wake in one plane and symmetry in the other orthogonal streamwise plane. These results clearly bring out the asymmetric nature of flow in the shedding regime.

We study the self-sustaining turbulent flow at minimal frictional Reynolds number in a straight square duct using direct numerical simulation. The flow in the square duct is maintained through a constant pressure gradient in the stream-wise direction. The computational investigation of the flow phenomenon for minimal, marginal and fully turbulent flow is studied using organized motion and dynamics of coherent structures. The central theme of the present work is to demonstrate the organized motion of the flow regimes below the frictional Reynolds number of the fully turbulent flow. The controlled direct numerical simulation study and vortex-detection technique unveil hairpin vortices in fully and minimal turbulent flow in the square duct for the first time. Bursting of streaks is detected with variable interval time average, and the evolution of hairpin vortices is also addressed. Turbulent intensities and energy spectra are reported and compared between the minimal, marginal and fully turbulent flow. The minimal turbulence in a square duct indicates transitional turbulent flow characteristics like lesser occurrence of ejection and sweep, intermittent bursting events, and a steeper variation of energy spectrum as compared to fully turbulent energy spectrum distribution.

The underlying flow dynamics in a turbulent flow in a periodic square duct is investigated by using the snapshot Proper Orthogonal Decomposition (POD) technique. In this study, the friction Reynolds number based on the duct width is fixed at 300. The coherent structures are identified through the spatial and temporal analysis of POD modes. Analysis of two sets of POD data is performed. In obtaining the first set, POD is performed on the combined fluctuating velocity vector, while for the second set, only the fluctuating velocity along the y- or z-direction is used. It was found that the first two most energetic spatial POD modes are the streamwise-independent or non-propagating roll modes. The third and fourth most energetic modes are observed to be streamwise-dependent, propagating modes. The spatio-temporal analysis of POD modes confirms the presence of traveling waves in the square duct, and its average speed is also calculated. The POD of the second dataset showed only propagating modes, and no non-propagating modes were found. These propagating modes are also rotationally symmetric. It has been shown that there is an energy exchange between non-propagating modes and propagating modes. The flow dynamics of the first four reconstructed POD modes portray the self-sustaining turbulence mechanism in a square duct. The structures obtained from the first POD dataset reconstruction of 10% energy show well organized hairpin vortices. Furthermore, it is found that the energy content of 35% gives detailed information on the coherent structures aligned along the wavy streamwise direction.

Three dimensional CFD study is done here—using a commercial software- to propose an efficient PCHE (Printed Circuit Heat Exchanger) model; used as a recuperator in International Thermonuclear Experimental Reactor (ITER). The present work is aimed to study a wavy channel based PCHE model, with certain modifications in design to demonstrate better thermal and hydraulic performance. The waviness for the hot as compared to cold channel is in anti-phase. The study is done for various angle of bend (0° (straight), 5°, 10° and 15°) and Reynolds number (350, 700, 1400 and 2100). The inlet temperature of the hot and cold channel is taken as 1173 and 813 K, respectively; and the operating pressure of the PCHE is taken as 3 MPa. Thermal hydraulic performance parameters are presented for the various periodic sections of the wavy-channel. Power density as well as pressure drop increases with increasing Reynolds number and angle of bend. Wavy as compared to plane channel based PCHE is demonstrated here to give better thermal-hydraulic performance.

CFD study is done here to propose an efficient PCHE (Printed Circuit Heat Exchanger) model; used as a recuperator in International Thermonuclear Experimental Reactor (ITER). 3D steady state conjugate heat-transfer numerical simulations are done; considering the variation of thermo-physical properties as a function of temperature. Helium is used as a working fluid and alloy 617 as solid substrate. The study is done for various angle of bend (θ = 0°(straight), 5°, 10°and 15°) and Reynolds number (Re = 350, 700, 1400 and 2100). Various types of flow patterns, within one wavy-section, are presented to analyze thermal-hydraulic characteristics. Thermal hydraulic performance parameters are presented for the various wavy-sections as well as within a section; and for the complete PCHE model. Heat transfer enhancement as compared to pressure penalty is higher for the wavy channel; and increases with increasing Re and θ. Wavy as compared to plane channel based PCHE is demonstrated here to give better thermal-hydraulic performance. A detailed characteristics as well as performance-parameters for thermal hydraulics in a 3D wavy channel based PCHE model - not found in the literature - is presented here.