Numerical Investigation of Flow and Heat Transfer from Twin Circular Cylinders Present in Double Forward-Facing Step

Effective heat transfer is of utmost importance in the design and operation of industrial components, such as heat exchanger tube bundles, as it directly dictates their efficiency and durability. These components often encounter flow-induced vibrations, which subsequently influence the heat transfer characteristics. This study focuses on investigating heat transfer and flow-induced vibrations in two circular cylinders. The Reynolds number (Re) is set at 100, and the reduced velocity (Ur) is increased from 2 to 14. The cylinders’ dimensionless spacing (L/D), arranged in tandem, is changed from 1.5 to 6, and the stagger angle (α) between the cylinders is varied from tandem (0°) to staggered (45°) and side-by-side arrangement (90°). The lift (CL) and drag (CD) coefficients, streamwise and transverse vibrational amplitudes (Ax/D and Ay/D), average Nusselt number (Nuavg), Strouhal number (St), vortex shedding patterns, and temperature distribution are analyzed. Results reveal that the lock-in occurs at Ur = 8 for all arrangements. The results demonstrate that the Nuavg for the downstream cylinder is consistently lower than the upstream cylinder in the tandem arrangement due to the upstream cylinder providing a shielding effect. Rising L/D to 6 from 1.5 increases the Nuavg by 8.6% and 9.8% for downstream and upstream cylinders, respectively. As the L/D increases, the Nuavg for both cylinders increases, implying a reduction in the effect of each cylinder on the other. However, in the staggered and side-by-side arrangement, the Nuavg for both cylinders are similar, indicating that the cylinders have little to no influence on each other. The highest Nuavg is observed at the lock-in condition for all L/D and α values. The temperature contours mirror the vorticity contours, suggesting that vortex shedding has a positive effect on heat transfer.

Flow-induced vibration (FIV) on two tandem cylinders with forced convection is numerically investigated at a constant Re = 150. Elastically mounted cylinder with four different values of corner radii (r* = r/R: r = radius of fillet; R = radius of circle) = 0 (square cylinder), 0.25, 0.75, and 1 (circular cylinder) with two spacing ratio (L/D) = 4 and 2 is studied. Transverse oscillations are generated from the cylinder having non-dimensional mass (m*) = 10. The structural damping coefficient is assigned a zero value with varying reduced velocity Ur=2−10. The two-dimensional incompressible Navier–Stokes and energy equations are solved together with Newton's second law governing the motion of the cylinders. Both cylinders' surfaces are maintained at a higher constant temperature of T*=1, and incoming flow is set to be at T*=0 with Prandtl number (Pr) = 0.7. The effect of r* and L/D is observed on the flow structure and FIV parameters. Flow characteristics at L/D=4 such as steady flow, reattachment, and unsteady flow are examined. A “shift” in vibrational amplitude is noted from r* = 1 and 0.75 to r* = 0 and 0.5, respectively. The downstream cylinder (DC) experiences a hike in vibration amplitude due to the impingement of vortex shedding from the upstream cylinder (UC). r* = 1 has 18.1% higher vibrational amplitude than r* = 0 at their respective lock-in regimes for DC. For L/D=2, vortices from upstream and downstream cylinders interact to form C(2S) and 2S types of vortex shedding. Different regimes, such as single body, reattachment, and co-shedding, have been observed while changing L/D. r* = 0.75 results in 13.3% higher oscillation amplitude as compared to r* = 0.5 for DC. The average Nusselt number (Nuavg) strongly depends on flow topology, corner radius, and vibrational amplitude A/D. At low L/D, heat transfer from the downstream cylinder is plummeted due to rolling of shear layers over the cylinder. There is a significant change in Nuavg due to higher vibration; for example, increase in 10.71% change is observed from Ur=2 to Ur=6 for r*=1 and L/D=4. Corner radii also alter the Nuavg as a decrease in 27.39% from r* = 1 to r* = 0 at Ur=10 and L/D=4 (UC).

Predictions are reported for mixed convection using various types of nanofluids over forward-facing double steps in a duct. The continuity, momentum and energy equations are discretized and the simple algorithm is applied to link the pressure and flow fields inside the domain. Different types of nanoparticles Al2O3, CuO, SiO2 and ZnO, with different volume fractions in range of 1-4% are investigated to identify their effects on the heat transfer and fluid characteristics. Numerical investigations are conducted using finite volume method. The results indicate that SiO2 -water has the highest Nusselt number followed by Al2O3-water, CuO -water and ZnO-water. The Nusselt number increases as the volume fraction increases but decreases as the nanoparticles diameter increases.

The heat transfer and wake-induced vibrations of a cylinder of circular cross section in the wake of another identical cylinder are numerically studied in this work at a Reynolds number (Re) = 100. The reduced velocities (Ur) are varied in the range of 2–14. The downstream cylinder is allowed to oscillate in two degrees of freedom, i.e., in the transverse as well as in the streamwise direction. The mass ratio (m*) is taken as 10, while the structural damping is ignored to get the maximum amplitude of vibration. The spacing ratio (L/D) between the cylinders is varied from 1.5 to 6, covering the major regimes, i.e., single body, reattachment, and co-shedding. The coefficients of lift (CL) and drag (CD), vibrational amplitudes of the cylinder, the Nusselt number (Nu), the Strouhal number (St), and vortex shedding patterns are studied. The results are discussed with the help of lift-displacement phase plots, cylinder trajectory plots, and vorticity and temperature contours. The lock-in condition at Ur = 8 is observed for all values of L/D, whereas the lock-in zone is the widest for the co-shedding regime at L/D = 6. By increasing L/D from 1.5 to 2.5 at Ur = 8, the CL of the downstream cylinder increases by 43%, whereas the CL of the upstream cylinder decreases by 61%. The downstream cylinder experiences lower drag as compared to the upstream cylinder and stationary isolated cylinder. A maximum decrease in the average drag coefficient of 107%, as compared to the stationary isolated cylinder, was observed for the downstream cylinder at L/D = 1.5 and Ur = 2, leading to the negative drag. Mostly, the 2S and C(2S) vortex shedding pattern is observed, whereas a steady flow and chaotic pattern emerged in a few cases. The results reveal that with increasing L/D, the average Nu for both the upstream and downstream cylinders increases as the effect of each cylinder on the other diminishes.

Effect of obstacle positions for turbulent forced convection heat transfer and fluid flow over a double forward facing step

Hydrothermal performance and entropy generation analysis for mixed convective flows over a backward facing step channel with baffle

This article presents heat transfer characteristics of circular and elliptic cylinders in cross flow for various Reynolds numbers. Numerical investigations as well as wind tunnel experiments are carried out to study the convective heat transfer of in-line cylinder banks. In particular, the heat transfer characteristics of upstream and downstream cylinders are compared in terms of local and average Nusselt numbers. The effects of turbulence induced by upstream cylinders on the heat transfer of downstream cylinders are discussed with the help of detailed numerical results.

Effect of Non-Newtonian Fluid Behavior on Forced Convection from a Cluster of Four Circular Cylinders in a Duct, Part II: Bingham Plastic Fluids

A three-dimensional numerical investigation of fluid flow and heat transfer in corrugated sinusoidal wavy channels with uniform wall temperature is performed for air (Pr=0.696) in the low Reynolds numbers regime (Re=40~1000). Constant properties, periodically fully developed laminar flow and heat transfer are considered. The effects of channel plate spacing (ε), plate corrugation severity (γ) and air mass flow rate (Re) on flow and heat transfer are discussed. Moreover, the analysis of influence degree of the shape factors on relevant parameters indicates that the effect of shape factor γ is more pronounced than that of ε on the friction factor (f) and heat transfer coefficient Nusselt number (Nu). The f and Nu factors increase with the increases of the wave severity (γ) and plate spacing (ff<;0.375). Performance evaluation is carried out by comparison the flow area goodness factor. An optimum goodness is attained on the geometries having the smallest ε or the smallest γ. The general relations for f versus Re and shape factors are derived. The local distributions of the vorticity and the Nu are presented.

• Two tandem-cylinder configurations are experimentally studied, showing distinct vibration mechanisms in oscillation cylinders. • Stationary cylinder diameter and spacing affect vibration amplitude and the transition between lock-in and galloping regimes. • Optimal power generation conditions differ between cases, governed by geometric parameters and flow velocity. • A nonlinear wake oscillator model effectively supports the isolated-cylinder vibration behavior. This study experimentally investigates flow-induced vibrations and energy harvesting in tandem circular cylinders under two configurations: an upstream vibrating cylinder with a stationary downstream cylinder, and a downstream vibrating cylinder placed in the wake of a stationary upstream cylinder. Displacement amplitudes were measured using high-speed imaging, while electrical output was obtained through a piezoelectric transducer. In Case 1, where the upstream cylinder vibrates, the presence of a downstream stationary cylinder substantially increases vibration levels, especially for larger stationary-cylinder diameters. At S = 4 c m , the maximum displacement amplitudes occur for D 2 = 5 c m , with increases of 84% and 25% when increasing the stationary-cylinder diameter from 3 to 4 cm and 4 to 5 cm, respectively. Compared to the isolated cylinder (peak amplitude at U = 6.5 m / s ), the vibrating upstream cylinder exhibits increases of 56% and 96% for D = 4 and D = 5 c m , respectively. Optimal power generation in Case 1 is achieved at S = 4 c m , D 2 = 4 c m , and flow velocities of 6 − 8 m / s . In Case 2, where the downstream cylinder vibrates in the wake of an upstream stationary cylinder, galloping and wake-induced vibration dominate the response. The strongest amplification occurs for D 1 = 3 cm at S = 8 c m , where displacement amplitudes rise sharply with increasing flow velocity, exhibiting an 88% increase relative to the isolated cylinder at low velocities and up to 114% at higher velocities. Voltage and power outputs similarly peak at S = 8 c m , particularly for the smallest upstream-cylinder diameter.

A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

Numerical investigation on flow-induced vibrations of two tandem cylinders localized selective roughness with different natural frequencies

Investigation of convective heat transfer and flow hydrodynamics in rectangular grooved channels

Flow-induced vibrations of two circular cylinders in tandem arrangement. Part 1: Characteristics of vibration

A numerical investigation of laminar mixed convection heat transfer in a lid-driven cavity filled with nanofluid under the influence of a magnetic field is executed. The left and right vertical walls of the cavity are insulated while the top and bottom horizontal walls are kept constant but different temperatures. The top wall is moving on its own plane at a constant speed while other walls are fixed. A uniform magnetic field is applied in the vertical direction normal to the moving wall. The governing differential equations are discretised by the control volume approach and the coupling between velocity and pressure is solved using the SIMPLE algorithm. The heat and mass transfer mechanisms and the flow characteristics inside the cavity depended strongly on the strength of the magnetic field. A comparison is also presented between the results obtained from the Maxwell and modified Maxwell models. The results show that the heat transfer is generally higher based on the modified Maxwell model.