Modeling fluid flows is a general procedure to handle engineering problems. Here we present a systematic study of the flow and heat transfer around a circular cylinder by introducing a new representative appropriate drag coefficient concept. We demonstrate that the new modified drag coefficient may be a preferable dimensionless parameter to describe more appropriately the fluid flow physical behavior. A break in symmetry in the global structure of the entire flow field increases the difficulty of predicting heat and mass transfer behavior. A general simple drag model with high accuracy is further developed over the entire range of Reynolds numbers met in practice. In addition, we observe that there may exist an inherent relation between the drag and heat and mass transfer. A simple analogy model is established to predict heat transfer behavior from the cylinder drag data. This finding provides great insight into the underlying physical mechanism.

https://www.mdpi.com/2073-8994/12/4/658/pdf

Similarities of Flow and Heat Transfer around a Circular Cylinder

We present a local stability analysis to investigate the effects of differential diffusion between momentum and density (quantified by the Schmidt number ) on the three-dimensional, short-wavelength instabilities in planar vortices with a uniform stable stratification along the vorticity axis. Assuming small diffusion in both momentum and density, but arbitrary values for , we present a detailed analytical/numerical analysis for three different classes of base flows: (i) an axisymmetric vortex, (ii) an elliptical vortex and (iii) the flow in the neighbourhood of a hyperbolic stagnation point. While a centrifugally stable axisymmetric vortex remains stable for any , it is shown that can have significant effects in a centrifugally unstable axisymmetric vortex: the range of unstable perturbations increases when is taken away from unity, with the extent of increase being larger for than for . Additionally, for , we report the possibility of oscillatory instability. In an elliptical vortex with a stable stratification, is shown to non-trivially influence the three different inviscid instabilities (subharmonic, fundamental and superharmonic) that have been previously reported, and also introduce a new branch of oscillatory instability that is not present at . The unstable parameter space for the subharmonic (instability IA) and fundamental (instability IB) inviscid instabilities are shown to be significantly increased for and , respectively. Importantly, for sufficiently small and large , respectively, the maximum growth rate for instabilities IA and IB occurs away from the inviscid limit. The new oscillatory instability (instability III) is shown to occur only for sufficiently small , the signature of which is nevertheless present with zero growth rate in the inviscid limit. The Schmidt number is then shown to play no role in the evolution of transverse perturbations on the flow around a hyperbolic stagnation point with a stable stratification. We conclude by discussing the physical length scales associated with the instabilities, and their potential relevance in various realistic settings.

Effects of Schmidt number on the short-wavelength instabilities in stratified vortices

The structure of streamwise vortices that arise due to secondary instabilities in the wake of a two-dimensional blunt body with a chord-to-thickness ratio of 12.5 was investigated using high-speed stereoscopic particle image velocimetry. Reynolds numbers spanning an order of magnitude from to 25 800 were considered, where is the height of the blunt trailing edge. A modified two-dimensional -criterion ( ) was applied to identify the streamwise vortices. The wavelength of the streamwise vortices, defined as the spanwise distance between adjacent streamwise vortex pairs in the wake, was investigated by applying an autocorrelation algorithm to snapshots of . The most probable wavelength was found to range from to with increasing , and the mean wavelengths increased from to . These wavelength values appeared to increase asymptotically. Visual inspection and cross-correlation analyses based on showed that the streamwise vortices maintain their directions of rotation during primary shedding cycles. The latter analysis was carried out at low because of a large amount of wake distortion and the absence of time-resolved data at high . The characteristics of the streamwise vortex structure found here match those of mode B, which, at similar , dominates the wakes of circular and square cylinders and has also recently been shown to exist in the wake of an elongated blunt body with a larger chord-to-thickness ratio of 46.5 (Gibeau et al., J. Fluid Mech., vol. 846, 2018, pp. 578–604).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/96902F0B5708A2903A2A37DFCCC0A89B/S0022112019009315a.pdf/div-class-title-the-mode-b-structure-of-streamwise-vortices-in-the-wake-of-a-two-dimensional-blunt-trailing-edge-div.pdf

The mode B structure of streamwise vortices in the wake of a two-dimensional blunt trailing edge

We present a numerical investigation of three-dimensional, short-wavelength linear instabilities in Kelvin-Helmholtz (KH) vortices in homogeneous and stratified environments. The base flow, generated using two-dimensional numerical simulations, is characterized by the Reynolds number and the Richardson number defined based on the initial one-dimensional velocity and buoyancy profiles. The local stability equations are then solved on closed streamlines in the vortical base flow, which is assumed quasi-steady. For the unstratified case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case, the early time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability strongly influenced by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of instability (convective branch) that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability branches appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with results from global instability studies for both homogeneous and stratified cases. Compartmentalized analyses are then used to elucidate the role of shear and stratification on the identified instabilities. The role of buoyancy is shown to be critical after the primary KH instability saturates, with the dominant convective instability shown to occur in regions with the strongest statically unstable layering. We conclude by highlighting the potentially insightful role that the local approach may offer in understanding the secondary instabilities in other flows.

Short-wavelength secondary instabilities in homogeneous and stably stratified shear flows

In practical applications of inkjet printing the nozzles in a printhead have intermittent idle periods, during which ink can evaporate from the nozzle exit. Inks are usually multicomponent where each component has its own characteristic evaporation rate resulting in concentration gradients within the ink. These gradients may directly and indirectly (via Marangoni flows) alter the jetting process and thereby its reproducibility and the resulting print quality. In the present work, we study selective evaporation from an inkjet nozzle for water-glycerol mixtures. Through experiments, analytical modeling, and numerical simulations, we investigate changes in mixture composition with drying time. By monitoring the acoustics within the printhead, and subsequently modeling the system as a mass-spring-damper system, the composition of the mixture can be obtained as a function of drying time. The results from the analytical model are validated using numerical simulations of the full fluid mechanical equations governing the printhead flows and pressure fields. Furthermore, the numerical simulations reveal that the time independent concentration gradient we observe in the experiments is due to the steady state of water flux through the printhead. Finally, we measure the number of drop formation events required in this system before the mixture concentration within the nozzle attains the initial (pre-drying) value, and find a stronger than exponential trend in the number of drop formations required. These results shed light on the complex physiochemical hydrodynamics associated with the drying of ink at a printhead nozzle, and help in increasing the stability and reproducibility of inkjet printing.

/pdf/selective-evaporation-at-the-nozzle-exit-in-piezoacoustic-s2h289wk.pdf

Selective Evaporation at the Nozzle Exit in Piezoacoustic Inkjet Printing

We perform a three-dimensional, short-wavelength stability analysis on the numerically simulated two-dimensional flow past a circular cylinder for Reynolds numbers in the range $50\le Re\le300$; here, $Re = U_{\infty}D/\nu$ with $U_\infty$, $D$ and $\nu$ being the free-stream velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. For a given $Re$, inviscid local stability equations from the geometric optics approach are solved on three distinct closed fluid particle trajectories (denoted as orbits 1, 2 & 3) for purely transverse perturbations. The inviscid instability on orbits 1 & 2, which are symmetric counterparts of one another, is shown to undergo bifurcations at $Re\approx50$ and $Re\approx250$. Upon incorporating finite-wavenumber, finite-Reynolds number effects to compute corrected local instability growth rates, the inviscid instability on orbits 1 & 2 is shown to be suppressed for $Re\lesssim262$. Orbits 1 & 2 are thus shown to exhibit a synchronous instability for $Re\gtrsim262$, which is remarkably close to the critical Reynolds number for the mode-B secondary instability. Further evidence for the connection between the local instability on orbits 1 & 2, and the mode-B secondary instability, is provided via a comparison of the growth rate variation with span-wise wavenumber between the local and global stability approaches. In summary, our results strongly suggest that the three-dimensional short-wavelength instability on orbits 1 & 2 is a possible mechanism for the emergence of the mode B secondary instability.

Secondary instabilities in the flow past a cylinder: insights from a local stability analysis

Local origin of mode-B secondary instability in the flow past a circular cylinder

Microbubbles entrained in a piezo-driven drop-on-demand printhead disturb the acoustics of the microfluidic ink channel and, thereby, the jetting behavior. Here, the resonance behavior of an ink channel as a function of the microbubble size and number of bubbles is studied through theoretical modeling and experiments. The system is modeled as a set of two coupled harmonic oscillators: one corresponds to the compliant ink channel and the other corresponds to the microbubble. The predicted and measured eigenfrequencies are in excellent agreement. It was found that the resonance frequency is independent of the bubble size as long as the compliance of the bubble dominates over that of the piezo actuator. An accurate description of the eigenfrequency of the coupled system requires the inclusion of the increased inertance of the entrained microbubble due to confinement. It is shown that the inertance of a confined bubble can be accurately obtained by using a simple potential flow approach. The model is further validated by the excellent agreement between the modeled and measured microbubble resonance curves. The present work, therefore, provides physical insight into the coupled dynamics of a compliant ink channel with an entrained microbubble.

/pdf/resonance-behavior-of-a-compliant-piezo-driven-inkjet-3ogj5bga.pdf

Resonance behavior of a compliant piezo-driven inkjet channel with an entrained microbubble.

We perform a three-dimensional, short-wavelength stability analysis on the numerically simulated two-dimensional flow past a circular cylinder for Reynolds numbers in the range $50\le Re\le300$; here, $Re = U_{\infty}D/\nu$ with $U_\infty$, $D$ and $\nu$ being the free-stream velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. For a given $Re$, inviscid local stability equations from the geometric optics approach are solved on three distinct closed fluid particle trajectories (denoted as orbits 1, 2 & 3) for purely transverse perturbations. The instability on orbits 1 & 2, which are symmetric counterparts of one another, is shown to undergo a bifurcation at $Re\approx50$, and two more bifurcations at $Re\approx250$, which is around the same value at which mode B secondary instability becomes dominant. This instability on orbits 1 & 2 is shown to be stable for all $Re\leq262$ after incorporating finite-wavenumber, finite-Reynolds number corrections on the computed local stability growth rates. The transition Reynolds number for the corrected growth rate $Re\approx 262$, above which the instability on orbits 1 & 2 is synchronous, is remarkably close to the mode B critical Reynolds number ($Re=259$) estimated from global stability analysis in an earlier study. Furthermore, for $Re= 280$, the corrected growth rate variation with the span-wise wavelength is shown to display great qualitative and quantitative agreement with the mode B instability growth rates from the global analysis. These results strongly suggest that the short-wavelength instability on orbit 1 & 2 is a possible mechanism for the birth of the mode B secondary instability.

Yogesh Jethani

Papers

Secondary instabilities in the flow past a cylinder: insights from a local stability analysis

Local origin of mode-B secondary instability in the flow past a circular cylinder

Resonance behavior of a compliant piezo-driven inkjet channel with an entrained microbubble.

Bifurcations of short-wavelength instabilities in the vortex shedding flow behind a two-dimensional cylinder