Non-dimensional Wavelength Research Articles

Heat transfer augmentation of solar air heater using discrete transverse sinewave corrugations

The influence of discretely placed sinewave corrugations on the effective thermal performance of the solar air heater system is presented using numerical methodology. The effect of forward and backward arrangement, normalised wavelength and amplitude on heat transfer enhancement is evaluated for different Reynolds number ranging between 6000 and 24,000. The non-dimensional wavelength and amplitude is varied as 0.0125–0.05 and 0.05–0.2 respectively while the non-dimensional pitch is taken as 1.875. The results show that the forward arrangement pattern of sinewave corrugation provides better thermo-hydraulic performance than the backward arrangement. For any given non-dimensional wavelength, lower non-dimensional amplitude exhibits greater thermal enhancement factor while for a fixed non-dimensional amplitude, the wavelength ratio of 0.025 provides greater thermal enhancement factor. The corrugation having amplitude ratio of 0.1 and wavelength ratio of 0.025 exhibits the highest thermal enhancement factor of 1.69 at Reynolds Number of 6000. It is also observed that, for Reynolds Number lesser than 9000, the configuration of amplitude ratio of 0.1 is found to exhibit higher thermal enhancement factor for any given non-dimensional wavelength. However, for Reynolds Number greater than 9000, the configuration of amplitude ratio of 0.05 is found to exhibit higher thermal enhancement factor for any given non-dimensional wavelength.

Spanwise phase transition between pure modes A and B in a circular cylinder’s wake. Part II: spatiotemporal evolution of vorticity

Through direct numerical simulation, the transition from pure mode A to mode B in the near wake of a circular cylinder is studied without consideration of vortex dislocations. The Reynolds number is calculated from 100 to 330 with a computational spanwise length of 4 diameters. In the present section, the spatiotemporal evolution of the vorticity and its sign are analyzed. The results show that mode B, as a kind of weak disturbed vorticity with opposite signs, actually appears partially on the rear surface of the cylinder and in the shear layers once Re exceeds 193. With increasing , the vortex-shedding patterns in the near wake undergo the initial generation stage of mode B coupling with the fully developed pure mode A (), the mode swapping or coexistence stage between modes A and B (), the self-adjustment stage of the nondimensional spanwise wavelength from 0.8 to 1 in dominant mode B (), and the full development stage of mode B (). In particular, the spanwise phase transition initially occurs at a certain spanwise position in the initial generation stage where a part of mode A and a part of mode B with specific vorticity signs appear, e.g. the vortex in mode A and the vortex in mode B, in which and vortices are vortices with three vorticity components satisfying the vorticity sign law and shed from the upper and lower shear layers, respectively.

Experimental investigation of three-dimensional modes in the wake of a rotationally oscillating cylinder

Three-dimensionalities in the wake of flow past a circular cylinder executing sinusoidal rotary oscillations about its axis is studied experimentally. The results of water tunnel experiments on a rotationally oscillating cylinder for Reynolds number of 250 with varying amplitude and forcing frequency are discussed. Qualitative studies using hydrogen bubble and laser-induced fluorescence flow visualisation techniques are performed. Observation made for oscillating amplitude, $\theta _{0} = {\rm \pi}/4$ and $\theta _{0}=3{\rm \pi} /4$ , and a low normalised forcing frequency, $FR$ , of 0.75 and 0.5, respectively, confirmed a mode having a spanwise non-dimensional wavelength of $\sim$ 1.8 which is also observed for a rotating cylinder. On increasing forcing frequency this mode disappears and a new mode with a bean-shaped structure and a much smaller spanwise normalised wavelength of $\sim$ 0.8 appears at an $FR$ of 1 and an oscillation amplitude of ${\rm \pi} /2$ . This mode remains almost stable until a forcing frequency of $FR=1.4$ . At higher forcing frequency, $FR=2.75$ , and oscillation amplitude of $3{\rm \pi} /4$ , a mode with cellular structure and a normalised spanwise wavelength of $\sim$ 1.6 is identified. The cells in this mode flatten up with increasing downstream distance and are shed alternately with respect to the adjacent cell. Certain combinations of forcing parameters resulted in a forced two-dimensionality of the wake. Quantitative studies using hot-wire measurements and particle image velocimetry confirm the presence of these modes and wake characteristics. Wake mode map in the forcing frequency and amplitude plane is presented showing regions of newly discovered modes and wake lock-on boundaries.

Effects of Surface Waviness on Fan Blade Boundary Layer Transition and Profile Loss—Part II: Experimental Assessments and Applications

AbstractPart II describes the experimental assessment and the application of the ideas in Part I concerning the mechanisms that determine the role of blade surface waviness on laminar-turbulent transition and their consequent effect on civil aircraft fan performance. A natural transition wind tunnel was designed and constructed to characterize the impact of surface waviness on transition, using both hotwire anemometry and infrared thermography. The experimental results support the new hypothesis presented in Part I, concerning the way in which blade surface waviness affects fan performance through motion of the transition onset location due to interaction between surface waviness and Tollmien–Schlichting (TS) boundary layer instability. In particular, the theoretical amplification of the TS waves, and the corresponding transition onset location movement due to surface waviness, was borne out over a range of variations in Reynolds number, nondimensional surface wavelength, nondimensional surface wave height, and location of surface wave initiation, relevant to composite fan blade parameters. Further, the increase of receptivity coefficient, and thus, the initial amplitude of disturbances due to geometric resonance between surface wavelength and TS wavelength was also confirmed by the experiments. Surface waviness was estimated, in some cases, to result in a nearly 1% decrease in fan efficiency compared to a nonwavy blade. Suggestions are given for mitigation of the effects of waviness, including the idea of blade curvature rescheduling as a method to delay transition and thus decrease loss.

Controlling Flow Separation on a Thick Airfoil Using Backward Traveling Waves

Large-eddy simulations (LESs) of low-Reynolds-number flow () over a NACA0018 airfoil are performed to investigate flow control at the stall angle of attack (15 deg) by low-amplitude surface waves (actuations) of different types (backward/forward traveling and standing waves) on the airfoil’s suction side. It is found that the backward (toward downstream) traveling waves, inspired from aquatic swimmers, are more effective than forward traveling and standing wave actuations. The results of simulations show that a backward traveling wave with a reduced frequency (, where is frequency; , chord length; and , free flow velocity), a nondimensional wavelength (, where is dimensional wavelength), and a nondimensional amplitude (, where is dimensional amplitude) can suppress stall. In contrast, the flow over the airfoil with either standing or forward traveling wave actuations separates from the leading edge similar to the baseline. Consequently, the backward traveling wave creates the highest lift-to-drag ratio. For traveling waves at a higher amplitude (), however, the shear layer becomes unstable from the actuation point and creates periodic coherent structures. Therefore, the lift coefficient decreases compared with the low-amplitude case.

Self-propulsion of fishes-like undulating hydrofoil: A unified kinematics based unsteady hydrodynamics study

Unsteady flow characteristics and propulsive performance during self-propulsion of various types of fishes-like undulating 2D NACA0012 hydrofoil are studied using a unified kinematic model. The model considers a range of non-dimensional wavelength of undulation λ∗ (0.8−∞), with the smaller value corresponding to body undulation of anguilliform fishes and the larger value corresponding to the caudal-fin pitching motion of carangiform fishes. The study is conducted at various frequency based Reynolds number Ref500−1750 at a constant maximum amplitude of undulation of 0.1. A level-set function based immersed interface method is used for the numerical simulations. Comparative analysis of dynamic-transient flow and propulsion characteristics of different types of fishes-like self-propulsion is presented. Time-wise varying dynamic-transient results are presented for flow patterns, propulsion velocity, net thrust force, and power input. After the onset of pitching or undulation, the vorticity patterns shows a dipole formation along with a jet formation based momentum excess behind the foil that leads to a net thrust force coefficient CTmnet. The dipole and the momentum excess disappears at the dynamic-steady state leading to zero CTmnet. It was found that the pitching as compared to the undulating foil accelerates faster and reaches a larger propulsion velocity. Further, the pitching based propulsion results in a fluctuating velocity and larger lateral force coefficient leading to instability. Furthermore, for the pitching motion, a smaller lateral force in the initial time period leading to maximum stability and a slightly larger propulsive efficiency is found during the initial as compared to later time periods. This work presents a detailed analysis of the dynamic-transient state leading to the dynamic-steady state for different types of fishes-like self-propulsion − which can be used for designing aquatic propulsion systems.

Large eddy simulations of a turbulent channel flow with a deforming wall undergoing high steepness traveling waves

Backward traveling waves over a wall of a fully developed turbulent channel are known to reduce the drag coefficient, flow separation, and turbulence intensity. Based on previous studies of traveling waves with a small steepness (s = a/λ < 0.0625, a: nondimensional amplitude, λ: nondimensional wavelength), it is thought that the nondimensional wave-speed (C = C*/U*, C*: dimensional wave-speed, U*: mean channel velocity) is required to be more than one to have a zero net drag and a high reduction in the turbulent kinetic energy (TKE). This idea is tested here for waves with higher wave steepness (0.05 < s < 0.15) at various wave-speeds using large eddy simulations of a fully developed turbulent channel in which one wall is undergoing a traveling wave. It is found that the increase in wave steepness decreases the wave-speed at which a net zero drag is obtained, e.g., for waves with steepness of s = 0.05, 0.075, and 0.15, the wave-speed is, approximately, C = 1.6 ± 0.1, 0.9 ± 0.1, and 0.7 ± 0.1, respectively. Similarly, the increase in wave steepness decreases the wave-speed at which TKE of the flow in the vicinity of the wave is highly reduced, e.g., qualitatively minimized. In fact, the wave-speeds at which the high reduction in TKE is observed in this study are C = 1.2, 1.2, and 0.6 for waves with wave steepness of 0.05, 0.075, and 0.15, respectively.

Theoretical investigation of nonhydrostatic effects on convectively forced flows: Propagating and evanescent gravity-wave modes

Nonhydrostatic effects on convectively forced mesoscale flows are theoretically investigated using a linearized, two-dimensional, steady-state, nonrotating, Boussinesq airflow system with prescribed convective forcing. The nondimensionalized airflow system contains the nonhydrostaticity factor β = U/Na, where U is the basic-state wind speed, N is the basic-state buoyancy frequency, and a is the half-width of the convective forcing. In an inviscid-limit system, the solution for vertical velocity is classified into the propagating mode (k ≤ β−1, where k is the nondimensional horizontal wavenumber) and the evanescent mode (k > β−1). As β increases, an alternating wavy pattern of updrafts and downdrafts appears downstream of the convective forcing with a nondimensional horizontal wavelength of 2πβ corresponding to the nondimensional critical horizontal wavenumber kc = β−1. The momentum flux analysis shows that the alternating updrafts and downdrafts are almost horizontally propagating gravity waves of the propagating mode whose k is slightly smaller than kc and that these gravity waves strengthen the momentum flux above the convective forcing. In a viscous system, the solution for vertical velocity has propagating and decaying components simultaneously that cannot be explicitly separated. Here, the propagating mode and two evanescent modes are defined by comparing the magnitudes of the nondimensional vertical wavenumber and decay rate. For large viscous coefficients, the k-range of the propagating mode becomes narrow and the alternating updrafts and downdrafts are dissipated. As β increases, the propagating mode, which strengthens the momentum flux above the convective forcing, is effectively dissipated even with a small viscous coefficient.

UNSTEADY CHARACTERISTICS OF THE SHOCK PROPAGATION IN A CONVERGENT SHOCK TUBE WITH SMALL ANGLE

The whole evolution of the incident shock propagation in a convergent shock tube with small angle is studied in detail by using the direct numerical simulation. Specifically, the shape of the curved shock and the unsteady flow patterns which differs from the K-H instability, have been evaluated. The results show that as a disturbance of the inclined wall on the shock, the bending position of the incident shock represents periodically changed and its non-dimensional wavelength is larger when the convergent angle becomes greater, indicating a faster response to the curvature variation. At the same time, two different flow instable patterns for the shock propagation in the area reduction channel are discovered, one of which is the asymmetric shock bifurcations when the reflected shock from the collision of the right wall interacts with the boundary layer. This instability is closely related to the unsteady vortex shedding behind the bifurcated feet, resulting in the dramatic pressure fluctuation. Another pattern occurs when the reflected shocks generated by the curved incident shock impinge on the upper and lower walls. The collision position moves at a modest speed, which causes the formation of small vortices near the reflection regions. Article DOI: https://dx.doi.org/10.20319/mijst.2018.42.4662 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Numerical investigation on heat transfer enhancement of solar air heater using sinusoidal corrugations on absorber plate

This paper presents the effect of sinusoidal profiled absorber plate on augmented heat transfer and corresponding thermo-hydraulic performance of solar air heater using three dimensional Computational Fluid Dynamics (CFD) simulation for the flow Reynolds number ranging between 4,000 and 24,000. The effect of variation of design parameters of corrugated absorber plate such as the non-dimensional wavelength and aspect ratio on the thermo-hydraulic performance is brought out. The aspect ratio is varied between 1.5 and 4.0 while the normalized wavelength is varied between 1.0 and 6.0. The study reveals that the presence of sinusoidal corrugations provides increased flow disturbances leading to considerable enhancement in heat transfer. It is found that the use of lower values of non-dimensional wavelength and aspect ratio leads to higher thermal efficiency. The average increase in thermal efficiency is about 12.5% as compared to the base model for the configuration having an aspect ratio of 1.5 and non-dimensional wavelength of 1.0. In terms of effective efficiency, the sinusoidal corrugations are found to be highly effective at lower flow rate conditions and generally have a relatively narrow useful operating range of flow Reynolds number. The aspect ratio and non-dimensional wavelength have significant influence on the effective efficiency. The pumping power requirement is generally found to be relatively higher as compared to the base model owing to increased flow obstruction by the corrugations.

Periodically Fully Developed Heat and Fluid Flow Characteristics in a Furrowed Wavy Channel

abstractPeriodically fully developed two-dimensional (2D) flow in a furrowed wavy channel is investigated numerically at various Reynolds numbers (100–2123). For the laminar and transitional flow regime, the study is done for six geometrically different channels; corresponding to various nondimensional amplitude (0.05, 0.075, and 0.1) and wavelength (0.5 and 1). Critical Reynolds number—for the onset of periodic flow—decreases with increasing amplitude and wavelength. A flow regime map—demarcating steady and unsteady flow regime—is proposed. It is shown that the size of the vortex in streamlines and waviness in isotherms increase with increasing Reynolds number, amplitude and wavelength. The performance of wavy as compared to straight channel is studied with the help of ratio of Nusselt number, friction factor and area-goodness factor, and thermal-performance factor. With increasing Reynolds number, all these parameters remain almost constant in the steady regime and increase almost linearly in the unsteady regime. For the largest Reynolds number (close to 2000) studied here, the increase in the Nusselt number ratio—within the periodic flow regime—is 11.21% and 133% for the amplitude equal to 0.075 and 0.1, respectively, at a wavelength of 0.5; at a wavelength of 1.0, the increase is 101%, 134%, and 181% for the amplitude of 0.05, 0.075, and 0.1, respectively.

Numerical and experimental studies on the propulsion performance of a Wave Glide propulsor

This paper introduces a newly developed Unmanned Wave Glide Vehicle (UWGV), which is driven only by extracting energy from gravity waves, and presents a comprehensive study on the propulsion performance of the UWGV’s propulsor―Wave Glide Propulsor (WGP) in a regular wave. By simplifying the WGP as six 2D tandem asynchronous flapping foils (TAFFs), a CFD method based on Navier–Stokes equations was first used to analyze the hydrodynamic performance of TAFFs with different parameters of non-dimensional wave length m and non-dimensional wave height n. Then, a series of hydrodynamic experiments were performed. The computational results agree well with the experimental results when n≤0.07 and both of them show the thrust force and input power of the WGP are larger at smaller m or larger n. By analyzing the flow field of TAFFs, we can see that a larger m is beneficial to the forming, merging and shredding of the TAFFs’ vortices; as TAFFs are arranged in tandem and have the same motions, the leading edge vortex and wake vortex of the TAFFs are meaningful for improving the thrust force of their adjacent ones.

Influences of the wall thickness on the granular dispersion in a dense gas–solid coaxial jet

The granular dispersion for different wall thicknesses of the inner channel in a dense gas–solid coaxial jet is investigated by morphology. In the wave dispersion, the Kelvin–Helmholtz instability has a strong influence on the granular stream. However, increasing the wall thickness damps the K–H instability, namely weakens the wave dispersion. Consequently, the non-dimensional wavelength increases and the non-dimensional amplitude decreases as the wall thickness increases for the same annular gas velocity. The instability analysis combining with the modification of the vorticity thickness of the annular gas stream indicates that the non-dimensional wavelength increases linearly with the non-dimensional modified vorticity thickness. The relation between the amplitude of the granular dispersion and the non-dimensional modified vorticity thickness is reliable for the wave dispersion as well. In addition, the granular dispersion angle is proportional to the annular gas velocity, which slightly depends on the wall thickness.

Transmission coefficients of a floating rectangular breakwater with porous side plates

The interaction between incident waves and a floating rectangular breakwater with the vertical porous side plates has been investigated in the context of the two-dimensional linear potential theory. The matched eigenfunction expansion method(MEEM) for multiple domains is applied to obtain the analytic solutions. The dependence of the transmitted coefficients and motion responses on the design parameters, such as porosity and protruding depth of side plates, is systematically analyzed. It is found that the non-dimensional wavelength where the sudden drop of transmission coefficients occurs, corresponds to the heave resonant frequency obtained from Ruol et al. (2013) for π-type floating breakwater. It is concluded that both properly selected porosity and deeper protruding depth of side plates are helpful in reducing the transmission coefficients and also extending the wider applicable extent of incident wavelength for performance enhancement.

From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

AbstractWe study numerically a succession of transitions in pipe Poiseuille flow that lead from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade are twofold azimuthally periodic, shift–reflect symmetric, and have a non-dimensional axial wavelength of $1. 927$ diameters. As the Reynolds number is increased, successive transitions result in a wide range of time-dependent solutions that include spiralling, modulated travelling, modulated spiralling, doubly modulated spiralling and mildly chaotic waves. Numerical evidence suggests that the latter spring from heteroclinic tangles of the stable and unstable invariant manifolds of two shift–reflect symmetric, modulated travelling waves. The chaotic set thus produced is confined to a limited range of Reynolds numbers, bounded by the occurrence of manifold tangencies. The subspace of discrete symmetry to which the states studied here belong makes many of the bifurcation and path-following investigations presented readily accessible. However, we expect that most of the phenomenology carries over to the full state space, thus suggesting a mechanism for the formation and break-up of invariant states that can give rise to chaotic dynamics.

서해연안 상세해상을 통한 천해조석 및 조석비대칭 재현

Finite element grid system using h-refinement on the Yellow Sea was constructed based on previous study (Suh, 1999b) from 14 K to 210 K and special attention was concentrated on refining the coastal zone. In grid generation, depth change between adjacent points and non-dimensional tidal wave length ratio were considered. As a result approximately a quarter of the total nodes are located nearby 5 m of shallow area. Accurate bathymetry data using 30`s and ETOPO1 with open boundary conditions of 8 major tidal constituents extracted automatically from FES2004 have been applied. In tidal simulation a 3-dimensional nonlinear harmonic model was setup and tidal amplification due to changes in vertical turbulent and bottom friction were simulated. In this study not only 8 major tidal constituents but also nonlinear shallow tides , and long period , were reproduced. It is found that implication of spatial variation of friction coefficient plays a very important role in reproduction of astronomical and shallow tides which are computed by iterative computation of nonlinear terms. Also it should be considered differently with respect to tidal periods. To understand the distribution of tidal asymmetry, amplitude ratio of and phase differences were calculated. Tidal distortion ratio marks up to 0.2 on the west coast showing shallow coastal characteristics and somewhat wide range of ebb-dominances in front of Mokpo area are reproduced.

Effect of a submerged vertical barrier on flexural gravity waves

An explicit solution is provided for the scattering of flexural gravity waves by a rigid vertical barrier submerged in an infinite depth of water. By applying recently developed mode-coupling relation for eigenfunctions, the mixed boundary value problem has been converted to solve dual integral equations with kernel consisting of trigonometric functions. And then complete analytical solutions are derived with an aid of singular integral equations whose solutions are bounded at the end points. The important hydrodynamical scattering quantities such as reflection and transmission coefficients associated with the flexural gravity wave scattering have been obtained analytically in terms of modified Bessel functions and Struve functions. It is observed that these quantities are sensitive to both combined as well as individual effect of plate thickness and barrier depth of submergence. Numerical results are computed and explained graphically for different parameters such as time period and non-dimensional wave length. Further, the effect of compressive force and plate thickness on the flexural gravity waves against a submerged vertical barrier is studied.

ゲルトラー渦間に生成する二次不安定流れの可視化(続報)

The forced wavelengths of Gortler vortices are easily given by the leading edge plates with varying the period of a saw-tooth edge, and the variation of the forced wavelengths makes transformation of secondary instability flows. The experiments with concave channel of 1 m radius of the curvature for main airflow velocity of 2.5m/s were performed using the leading edge plates. Variation in secondary instability flows was tested by smoke visualization and hot-wire measurement, and was examined from viewpoints of maximum disturbance amplitude Kmax. It was confirmed that meandering flows whose (Kmax)max varies linearly with the non-dimensional forced wavelength parameter Λ prevail at 100<Λ<200. On the other hand, horseshoe-type vortices with (Kmax)max= {-.7em} aisebox{1.1ex}{.} {.1em} aisebox{-0.2ex}{.} 0.35 are formed at Λ of 250 or greater.

Free convection in a shallow wavy enclosure

This paper presents the simulation of free convection heat transfer and fluid flow in a horizontal and shallow wavy enclosure. Its bottom wall is varied with a sinusoidal function while the top wall is flat. The wavy wall has constant hot temperature and ceiling is cold as verticals are insulated. The simulations are performed using CFDRC software. Results are presented in terms of streamlines, isotherms and Nusselt number for different aspect ratios, non-dimensional wave length and Rayleigh number. The obtained results showed that heat transfer is increased with the decreasing non-dimensional wave length and it is increased with the increasing of aspect ratio and Rayleigh number.

A viscoelastic strain energy principle expressed in fold–thrust belts and other compressional regimes

A mathematical folding theory for stratified viscoelastic media in layer parallel compression is presented. The second order fluid, in slow flow, is used to model rock rheological behavior because it is the simplest nonlinear constitutive equation exhibiting viscoelastic effects. Scaling and non-dimensionalization of the model system reveals the presence of Weissenberg number ( Wi), defined as a ratio of time scales τ */( H */ V *). V */ H * is the strain rate (s −1) imposed by an assumed far field velocity V * acting on a layer of thickness H *, while τ * (s) is related to the relaxation of normal stresses. Our most significant finding is a transitional behavior as Wi→½, which is independent of the viscosity contrast. A change of variables shows that lengths associated with this transition are scaled by a parameter α=[(1−2 Wi)/(1+2 Wi)] 1/2, which is inversely proportional to local strain energy. On this basis a scaling law representing a distribution of non-dimensional wavelengths (wavelength/layer thickness) is derived. Geologically this is consistent with a transition from folding to faulting, as observed in fold–thrust belts. Folding, a distributed deformation scaling as Wi −1, is found to be energetically favored at non-dimensional wavelengths ranging from about three to seven. Furthermore, the transition from folding to faulting, a localized deformation scaling as ( αWi) −1, is predicted at a non-dimensional wavelength of about seven. These findings are consistent with measurements of thrust sheets in the Sawtooth Mountains of western Montana, USA and other fold–thrust belts. A review of the literature reveals a similar distribution of non-dimensional wavelengths spanning a wide range of observational scales in compressional deformation. Specific examples include lithospheric scale folding in the central Indian Basin and microscopic scale failure of ice columns between splay microcracks in laboratory studies.