Wavy Bottom Research Articles

Magneto-nanofluidic thermal transport and irreversibility in semicircular systems with heated wavy bottom under constant fluid volume and cooling surface constraints

PurposeThis study aims to investigate the influence of wall curvature in a semicircular thermal annular system on magneto-nanofluidic flow, heat transfer and entropy generation. The analysis is conducted under constant cooling surface and fluid volume constraints.Design/methodology/approachThe mathematical equations describing the thermo-fluid flow in the semicircular system are solved using the finite element technique. Four different heating wall configurations are considered, varying the undulation numbers of the heated wall. Parametric variations of bottom wall undulation (f), buoyancy force characterized by the Rayleigh number (Ra), magnetic field strength represented by the Hartmann number (Ha) and inclination of the magnetic field (γ) on the overall thermal performance are studied extensively.FindingsThis study reveals that the fluid circulation strength is maximum in the case of a flat bottom wall. The analysis shows that the bottom wall contour and other control parameters significantly influence fluid flow, entropy production and heat transfer. The modified heated wall with a single undulation exhibits the highest entropy production and thermal convection, leading to a heat transfer enhancement of up to 21.85% compared to a flat bottom. The magnetic field intensity and orientation have a significant effect on heat transfer and irreversibility production.Research limitations/implicationsFurther research can explore a wider range of parameter values, alternative heating wall profiles and boundary conditions to expand the understanding of magneto-nanofluidic flow in semicircular thermal systems.Originality/valueThis study introduces a constraint-based analysis of magneto-nanofluidic thermal behavior in a complex semicircular thermal system, providing insights into the impact of wall curvature on heat transfer performance. The findings contribute to the design and optimization of thermal systems in various applications.

Selection of vortex ripple dimensions in sinusoidal oscillatory flows. Part 1. Ripple dimensions and fluid kinematics

Subaqueous vortex ripples in equilibrium are characterized by their unique geometry and dimensions. Motivated by the recent direct numerical simulation study of oscillatory turbulent flow over a wavy bottom by Önder & Yuan (J. Fluid Mech., vol. 858, 2019, pp. 264–314), the objective of this study is to further investigate the fluid dynamical controls that determine the distinctive equilibrium dimensions of vortex ripples. We use direct numerical simulations to investigate the differences in flow kinetics between sinusoidal oscillatory flow over equilibrium and out-of-equilibrium vortex ripples. In comparison with the equilibrium case, the spanwise coherent vortices, the averaged bottom shear stress on overlying flow and the shear stress distribution on the ripple surface are identified as the key fluid dynamical controls on equilibrium dimensions. Based on these controls, we propose mechanisms in the selection of vortex ripple dimensions. We observe that the flow adjusts in such a way that the interaction between overlying flow and vortex ripples tends to generate the strongest coherent vortices while the ripple surface (or overlying flow) experiences the smallest shear stress averaged over ripple wavelength during the selection process. Through a triple decomposition of the flow, the component of the ripple-induced fluctuation is found to dictate these fluid dynamical controls, which implies that this component plays an important role in the evolution of vortex ripples.

Optimization of silver/water-based porous wavy direct absorption solar collector

Direct Absorption Solar Collectors (DASCs) are a widely utilized technology in residential applications. However, having known the limitation in DASC size, the efficiency must be enhanced by applying effective modifications and optimizing design parameters. In this study, the performance of a wavy bottom-shaped collector filled with an aluminum porous medium was investigated and the most influential characteristic parameters are specified. Then a design for DASC using Polyvinylpyrrolidone-coated silver nanofluid is proposed and characteristic parameters are optimized based on the full factorial design of the experiment methodology. The model consists of four primary factors, including nanofluid volume concentration (C=0.025%,0.05%,0.1%), porosity (ε=0.8,0.88,0.95), bottom wave amplitude (A=2.5,5,7.5mm), and bottom wavenumber (λ=15,30,60m−1). The results indicated that lowering porosity and increasing nanofluid concentrations improves collector efficiency, whereas rising the wave amplitude and wavenumber causes a higher pressure drop. Additionally, by employing the full factorial design, the main and interaction effects of factors on the efficiency and pressure drop of DASC as the response variables are evaluated. Thus, an optimum value is observed for wave amplitude to reach maximum efficiency and minimize pressure drop. By integrating a porous medium and a wavy bottom with nanofluid, the efficiency of DASC is enhanced from 52 to 93.7%, paving the way for their use in residential applications.

Near-critical turbulent free-surface flow over a wavy bottom

Steady plane turbulent free-surface flow over a slightly wavy bottom is considered for very large Reynolds numbers, very small bottom slopes, and Froude numbers close to the critical value 1. As in previous works, the slope and the deviation from the critical Froude number are assumed to be coupled such that turbulence modeling is not required. The amplitudes of the periodic bottom elevations, however, are assumed to be half an order of magnitude larger than in the previous case of bumps or ramps of finite length. Asymptotic expansions give a steady-state version of an extended Korteweg–deVries (KdV) equation for the surface elevation. The extension consists of a forcing term due to the unevenness of the bottom and a damping term due to friction at the bottom. Other flow quantities, such as pressure, flow velocity components, local Froude number and bottom friction force, can be expressed in terms of the surface elevation. Exact solutions of the extended KdV equation, describing stationary cnoidal waves, are obtained for bottoms of particular periodic shapes. As a limiting case, the solitary waves over a bottom ramp are re-obtained in accord with previous results.

Nonlinear Bragg scattering of surface waves over a two-dimensional periodic structure

Bragg scattering of nonlinear surface waves over a wavy bottom is studied using two-dimensional fully nonlinear numerical wave tanks (NWTs). In particular, we consider cases of high nonlinearity which lead to complex wave generation and transformations, hence possible multiple Bragg resonances. The performance of the NWTs is well verified by benchmarking experiments. Classic Bragg resonances associated with second-order triad interactions among two surface (linear incident and reflected waves) and one bottom wave components (class I), and third-order quartet interactions among three surface (linear incident and reflected waves, and second-order reflected/transmitted waves) and one bottom wave components (class III) are observed. In addition, class I Bragg resonance occurring for the second-order (rather than linear) transmitted waves, and Bragg resonance arising from quintet interactions among three surface and two bottom wave components, are newly captured. The latter is denoted class IV Bragg resonance which magnifies bottom nonlinearity. It is also found that wave reflection and transmission at class III Bragg resonance have a quadratic rather than a linear relation with the bottom slope if the bottom size increases to a certain level. The surface wave and bottom nonlinearities are found to play opposite roles in shifting the Bragg resonance conditions. Finally, the results indicate that Bragg resonances are responsible for the phenomena of beating and parasitic beating, leading to a significantly large local free surface motion in front of the depth transition.

Generalized IBL models for gravity-driven flow over inclined surfaces

In this investigation we propose several generalized first-order integral-boundary-layer (IBL) models to simulate the two-dimensional gravity-driven flow of a thin fluid layer down an incline. Various cases are considered and include: isothermal and non-isothermal flows, flat and wavy bottoms, porous and non-porous surfaces, constant and variable fluid properties, and Newtonian and non-Newtonian fluids. A numerical solution procedure is also proposed to solve the various model equations. Presented here are some results from our numerical experiments. To validate the generalized IBL models comparisons were made with existing results and the agreement was found to be reasonable.

Waves and instabilities of viscoelastic fluid film flowing down an inclined wavy bottom.

Evolution of waves and hydrodynamic instabilities of a thin viscoelastic fluid film flowing down an inclined wavy bottom of moderate steepness have been analyzed analytically and numerically. The classical long-wave expansion method has been used to formulate a nonlinear evolution equation for the development of the free surface. A normal-mode approach has been adopted to discuss the linear stability analysis from the viewpoint of the spatial and temporal study. The method of multiple scales is used to derive a Ginzburg-Landau-type nonlinear equation for studying the weakly nonlinear stability solutions. Two significant wave families, viz., γ_{1} and γ_{2}, are found and discussed in detail along with the traveling wave solution of the evolution system. A time-dependent numerical study is performed with Scikit-FDif. The entire investigation is conducted primarily for a general periodic bottom, and the detailed results of a particular case study of sinusoidal topography are then discussed. The case study reveals that the bottom steepness ζ plays a dual role in the linear regime. Increasing ζ has a stabilizing effect in the uphill region, and the opposite occurs in the downhill region. While the viscoelastic parameter Γ has a destabilizing effect throughout the domain in both the linear and the nonlinear regime. Both supercritical and subcritical solutions are possible through a weakly nonlinear analysis. It is interesting to note that the unconditional zone decreases and the explosive zone increases in the downhill region rather than the uphill region for a fixed Γ and ζ. The same phenomena occur in a particular region if we increase Γ and keep ζ fixed. The traveling wave solution reveals the fact that to get the γ_{1} family of waves we need to increase the Reynolds number a bit more than the value at which the γ_{2} family of waves is found. The spatiotemporal evolution of the nonlinear surface equation indicates that different kinds of finite-amplitude permanent waves exist.

Hydrodynamics and instabilities of falling liquid film over a non-uniformly heated inclined wavy bottom

Hydrodynamics and instabilities of a thin viscous liquid film flowing down an undulated inclined plate with linear temperature variation have been investigated. Using the long-wave expansion method, a non-linear evolution equation for the development of the free surface is derived under the assumption that the bottom undulations are of moderate steepness. A normal mode approach has been considered to take into account the linear stability of the film to investigate both the spatial and temporal instabilities, while the method of multiple scales is used to obtain the Ginzburg–Landau-type worldly equation for studying the weakly non-linear stability solutions. The numerical study has been carried out in python with a newly developed library Scikit–FDif. The entire investigation is done for a general bottom profile followed by a case study with a sinusoidal topography. The case study reveals that the Marangoni effect destabilizes the film flow throughout the domain, whereas the bottom steepness ζ gives a dual effect for the linear stability. In the “uphill” portion, an increase in ζ stabilizes the flow, and in the “downhill” portion, an increase in ζ gives a destabilizing effect. Furthermore, a weakly non-linear study shows that both supercritical and subcritical solutions are possible for the system. It is noted that the unconditional stable region decreases and all the other region increases in the “downhill” portion in comparison with the “uphill” portion for a fixed set of parameters. The stability analysis of a truncated bimodal system is investigated. The spatial uniform solution of the complex Ginzburg–Landau equation for sideband disturbances has also been discussed. Numerical simulation indicates that a different kind of finite-amplitude permanent wave exists. The amplitudes and the phase speeds of the wave are dependent on thermocapillary as well as the bottom steepness.

Near‐critical turbulent open‐channel flow over wavy bottom

AbstractSteady two‐dimensional turbulent free‐surface flow in a channel with mild baseline slope is considered. The shape of the channel bottom is assumed to be undular with a very small amplitude. Asymptotic expansions for large Reynolds numbers and Froude numbers slightly above the critical value 1, respectively, give for the surface elevation a differential equation of KdV‐type, with the additional terms representing turbulent dissipation and forcing due to the wavy bottom, respectively. No turbulence modelling is required. This asymptotic approach was used in [1] to describe stationary solitary waves in a channel with plain bottom and small variations in the bottom friction coefficient. It was shown recently [2,3] that there exist stationary single‐wave solutions of a different kind that are characterized by smaller wave amplitudes. In [4], both kinds of single stationary waves above single obstacles (bumps, ramps) are investigated theoretically and experimentally. In this paper, stationary space‐periodic surface waves for channel bottoms with undular shape are studied. First, a one‐parametric family of exact solutions for particular bottom shapes is derived. Remarkably, these particular solutions exist only in a narrow parameter range. The solutions are reproduced with a numerical solver to verify that the solver gives correct results. Secondly, a different type of asymptotic expansion is performed in order to describe solutions characterized by smaller wave amplitudes. The resulting linear differential equation is solved numerically. Both solutions are briefly discussed.

Alt Duvarı Dalgalı Kapalı Kare Geometride Yüzey Işınımı ile Doğal Taşınımın Sayısal İncelenmesi

Alt Duvarı Dalgalı Kapalı Kare Geometride Yüzey Işınımı ile Doğal Taşınımın Sayısal İncelenmesi

Large‐Scale Forces Under Surface Gravity Waves at a Wavy Bottom: A Mechanism for the Generation of Primary Microseisms

AbstractPrimary microseisms are background seismic oscillations recorded everywhere on Earth with typical frequencies 0.05 < f < 0.1 Hz. They appear to be generated by ocean waves of the same frequency f, propagating over shallow bottom topography. Previous quantitative models for the generation of primary microseisms considered wave propagation over topographic features with either large scales, equivalent to a vertical point force, or small scales matching ocean wave wavelengths, equivalent to a horizontal force. While the first requires unrealistic bottom slopes to explain measured Rayleigh wave amplitudes, the second produced Love waves and not enough Rayleigh waves. Here we show how the small scales actually produce comparable horizontal and vertical forces. For example, a realistic rough bottom over an area of 100 km2 with depths around 15 m is enough to explain the vertical ground motion observed at a seismic station located 150 km away. Ocean waves propagating over small‐scale topography is thus a plausible explanation for the observed microseisms at frequencies around 0.07 Hz.

Direct Numerical Simulation of Oscillatory Flow Over a Wavy, Rough, and Permeable Bottom

AbstractThe results of a direct numerical simulation of oscillatory flow over a wavy bottom composed of different layers of spherical particles are described. The amplitude of wavy bottom is much smaller in scale than typical bed forms such as sand ripples. The spherical particles are packed in such a way to reproduce a bottom profile observed during an experiment conducted in a laboratory flow tunnel with well‐sorted coarse sand. The amplitude and period of the external forcing flow as well as the size of the particles are set equal to the experimental values and the computed velocity field is compared with the measured velocity profiles. The direct numerical simulation allows for the evaluation of quantities, which are difficult to measure in a laboratory experiment (e.g., vorticity, seepage flow velocity, and hydrodynamic force acting on sediment particles). In particular, attention is focused on the coherent vortex structures generated by the vorticity shed by both the spherical particles and the bottom waviness. Results show that the wavy bottom triggers transition to turbulence. Moreover, the forces acting on the spherical particles are computed to investigate the mechanisms through which they are possibly mobilized by the oscillatory flow. It was found that forces capable of mobilizing surface particles are strongly correlated with the particle position above the mean bed elevation and the passage of coherent vortices above them.

Experimental Study on Upstream-Advancing Waves Induced by Currents

ABSTRACT Fan, J.; Zheng, J.; Tao, A.; Yu, H, and Wang, Y, 2016. Experimental study on upstream-advancing waves induced by currents. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 846–850. Coconut Creek (Florida), ISSN 0749-0208. Due to the widespread existence of large-scale continuous submarine sandbars the coasts and estuaries, the interaction between the ambient current and this kind of topography is important and complicated. It has been known that regular free surface waves can be generated and propagate in the upstream direction, when a steady current with specific depth and velocity flows past the fixed periodic wavy bottoms with large steepness. This particular free surface response, called the upstream-advancing wave, has drawn attention in the past few decades but still lacks detailed quantitative study identifying the critical conditio...

Prior sheet buckling leading to wrinkling formation in a gas forming a V-trough with wavy bottom

When the amount of stretching strain exceeds material's intrinsic capability in gas forming a complex shape metallic sheet, gas pressurization operation can fail due to sheet material's perforation. A hot-bent assisted gas forming method for shaping a long V-trough with deep bottom of longitudinal wavy shape is proposed for obtaining the product with harmless wrinkle and relatively uniform thickness. This method consists of three sequential actions—an instant hot V-shape bending together with die closing followed by controlled pressurized gas blowing for a period of time. For this method, the depth of hot bending is varied as a parameter to generate pre-forms bearing various contours which consequently determine wrinkling situation in the subsequent gas forming product. Two groups of specimens differing in sheet size are adopted. Regular AA5052 (coarsely grained) and superplastic grade AA5083 (fine grained) alloys are used for experimental works.

A note on the onset of recirculation in a 2D Couette flow over a wavy bottom

Laminar Couette flow over a fixed wavy surface was studied with direct numerical simulation in a 2D periodic numerical domain. The mesh was generated by a conformal transformation that sets horizontal flow at the top of the domain, where a constant velocity boundary condition is given. The bottom of the domain is a wavy sinusoidal surface of wave slope 2πa/λ. The combined effect of bottom shape, inertia, and viscosity was explored using different Reynolds numbers (Re) and two dimensionless parameters in terms of channel width h, wavelength λ, and the amplitude of the wavy bottom a. Even if the Reynolds number was large, the simulations were not perturbed so the regime was always laminar. However, a recirculation appeared at the vicinity of the trough. The horizontal location of the eddy center was reported as a function of 2πa/λ and Reλ/h. The conditions for the onset of this recirculation were studied and compared with results from the literature. Two regimes can be clearly identified from the numerical results; a viscous regime with a weak dependence between 2πa/λ and Reλ/h for small Reynolds numbers and an inertial regime with an exponential dependence between 2πa/λ and Reλ/h for large Reynolds numbers, which presents an approximate slope of −1/3. Almost all results collapse in one single curve that characterizes the phenomenon (with the exception of some points where the flow is confined due to a large λ/h ratio).

Numerical Solutions of 2-D Incompressible Driven Cavity Flow with Wavy Bottom Surface

In the present numerical study is devoted to investigate the lid-driven cavity flow with wavy bottom surface. The cavity upper wall is moving with a uniform velocity by unity and the other walls are no-slip. The physical problem is represented mathematically by a set of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. The wide ranges of governing parameters, i. e., the Reynolds number (Re), and the number of undulations (λ) on the flow structures are investigated in detail. The behavior of the force coefficient Cf also has been examined. Streamline plots provide the details of fluid flow. The fluid contained inside a squared cavity is set into motion by the top wall which is sliding at constant velocity from left to right and the undulation which was induced at the bottom surface. It is found that these parameters have significant effect on the flow fields in the cavity. Furthermore, the trends of skin friction for different values of the aforementioned parameters are presented in this investigation.

Hydro-Magnetic Mixed Convection Flow in a Lid-Driven Cavity with Wavy Bottom Surface

Mixed convection flow in the presence of magnetic field is examined in a lid-driven cavity with wavy bottom surface. The magnetic field is applied in perpendicular direction to the cavity. Moreover, the cavity is heated from top while the bottom surface is taken as a wavy pattern. The vertical walls of the cavity are adiabatic. The governing equations have been solved by using Galerkin weighted residual method of finite element formulation. To uncover the flow patterns and heat transfer mechanisms within the cavity, the results are presented in terms of streamlines and isotherms for different Reynolds number, Grashof number, Hartmann number and number of undulations offered by the wavy bottom surface. Also the effects of these parameters are shown on the Local Nusselt number. It is observed that the wavy lid-driven cavity can be considered as an effective heat transfer mechanism in presence of magnetic field at larger wavy surface amplitudes and low Richardson numbers.

Effect of Accelerating on Sediment Incipient Motion over Dunes under Shallow Water Condition

Due to the complexity of bed form morphology and dune movement, this paper selected a series of 2-D asymmetric dunes in order to address the development of a flow region associated with velocity profile characteristics and sediment incipient motion under shallow water condition. Experiments were conducted over four asymmetric dunes of one crest length (4 m), two crest height (0.3m,0.4m) and two uniform sediments with mean grain sizes D=0.5 and 0.7 mm at the TianJin Research Institute For Water Transport Engineering, China. By using Acoustic Doppler Velocimeter (ADV), the instantaneous velocities were measured at four cross sections giving a total of 16 measured profiles. The variations of velocity profile along the flow affected by the wavy bottom have been studied. The results show that the effect of flow acceleration plays an important role in governing incipient motion over dunes.

EXPERIMENTAL STUDY ON CRITICAL RESONANT STATE OF UPSTREAM-ADVANCED WAVES

It is known that the upstream-advancing waves can be excited when a steady current travelling over a wavy bottom. While the generation mechanisms are still inconclusive and the related dynamic and kinematic characteristics of the excited water waves are not clear. Focusing on the dynamics of this kind of upstream-advancing waves, especially the critical generation conditions, a series of experiments were carried out in a wave-current-wind flume (80m*1.0m*1.5m) with fixed sinusoidal bottom corrugations. By varying the current velocity and relative water depth, altogether 137 cases were realized. It is found that there exist a region of the current velocity for the exciting of upstream-advancing waves, based on the whole processes recorded, from the pure current to the present of clear upstream-advancing waves to the disappear of the evident waves again. The most unstable conditions correspond to the largest wave amplitudes were investigated in details. The dynamics of the excited waves were analyzed primarily for understanding of the generation mechanisms.

Rossby Solitary Waves Generated by Wavy Bottom in Stratified Fluids

Rossby solitary waves generated by a wavy bottom are studied in stratified fluids. From the quasigeostrophic vorticity equation including a wavy bottom and dissipation, by employing perturbation expansions and stretching transforms of time and space, a forced KdV-ILW-Burgers equation is derived through a new scale analysis, modelling the evolution of Rossby solitary waves. By analysis and calculation, based on the conservation relations of the KdV-ILW-Burgers equation, the conservation laws of Rossby solitary waves are obtained. Finally, the numerical solutions of the forced KdV-ILW-Burgers equation are given by using the pseudospectral method, and the evolutional feature of solitary waves generated by a wavy bottom is discussed. The results show that, besides the solitary waves, an additional harmonic wave appears in the wavy bottom forcing region, and they propagate independently and do not interfere with each other. Furthermore, the wavy bottom forcing can prevent wave breaking to some extent. Meanwhile, the effect of dissipation and detuning parameter on Rossby solitary waves is also studied. Research on the wavy bottom effect on the Rossby solitary waves dynamics is of interest in analytical geophysicalfluid dynamics.