Pressure induced by thermal fluctuation of an elastic filament confined within a narrow channel

Consider a flexible macro-molecule that is immersed in water at or above room temperature. As a result of thermal motion within the water, the filament is driven to undergo random fluctuations in shape. These fluctuations are a consequence of uncoordinated motion of water molecules. If the range of filament motion is restricted by nearby surfaces, the phenomenon becomes more complex. In this study, it is presumed that the filament is restricted to lie within a plane so that the motion is two dimensional. Furthermore, the range of the planar motion of the filament is confined to the region between inflexible straight boundaries lying in the plane of motion. A result of thermal fluctuation of the filament is that, when in close proximity to a boundary, a normal pressure is induced between the filament and that confining boundary. In the present development, frictional interaction of the filament with either confining boundary is presumed to be negligible. The goal is to determine the dependence of the induced pressure on the separation distance between the confining boundaries in terms of prevailing thermal conditions and physical characteristics of the system.     

Streamwise vortices generated by impinging flows in a confined duct

Particle-tracer technique was employed for visualizing flow structures in a side-inlet square duct. The results obtained indicate that the streamwise vortices developed in the stagnation region of impinging flows are irregularly distributed. As the vortices convect downstream they are first stretched and merged, then squashed due to the non-zero pressure gradient effects caused by the flow separation regions existed along the side walls. The mechanism responsible for generating streamwise vortices in the stagnation region is suggested due to the hydrodynamic instability effect, similar to that previously found for three-dimensional disturbances growing in a two-dimensional stagnation flow.     

On the flow field induced by an oscillating disk submerged in a semi-infinite viscous fluid with a surfactant surface film

On the basis of the unsteady Stokes' equation the problem of the flow field induced by an oscillating disk fully immersed in a semi-infinite viscous fluid with a surfactant surface layer is solved. The effect of the insoluble surfactant on the hydrodynamics of the oscillating disk is found for varying values of the ratio of the coefficient of the surface shear viscosity to the coefficient of viscosity of the substrate fluid, and depth of the disk below the surface. A new theoretical analysis for obtaining the surface shear viscosity is suggested.     

Numerical investigation of confined wakes behind a square cylinder in a channel

The structure of confined wakes behind a square cylinder in a channel is investigated via the numerical solution of the unsteady Navier–Stokes equations. Vortex shedding behind the cylinder induces periodicity in the flow field. Details of the phenomenon are simulated through numerical flow visualization. The unsteady periodic wake can be characterized by the Strouhal number, which varies with the Reynolds number and the blockage ratio of the channel. The periodicity of the flow is, however, damped in the downstream region of a long duct. This damping may be attributed to the influence of side walls on the flow structure.     

Turbulent transport of particles in a straight square duct

Turbulent flow through a duct of square cross-section gives rise to off-axis secondary flows, which are known to transfer momentum between fluid layers thereby flattening the velocity profile. The aim of this study is to investigate the role of the secondary flows in the transport and dispersion of particles suspended in a turbulent square duct flow. We have numerically simulated a flow through a square duct having a Reynolds number of Re_τ = 300 through discretization of the Navier–Stokes equations, and followed the trajectories of a large number of passive tracers and finite-inertia particles under a one-way coupling assumption. Snapshots of particle locations and statistics of single-particle and particle pair dispersion were analyzed. It was found that lateral mixing is enhanced for passive tracers and low-inertia particles due to the lateral advective transport that is absent in straight pipe and channels flows. Higher inertia particles accumulate close to the wall, and thus tend to mix more efficiently in the streamwise direction since a large number of the particles spend more time in a region where the mean fluid velocity is small compared to the bulk. Passive tracers tend to remain within the secondary swirling flows, circulating between the core and boundary of the duct.     

Initial section in a square duct rotating about the transverse axis

Laminar flow in a duct uniformly rotating about the transverse axis has been the subject of a number of studies. These are reviewed, for example, in [1]. However, in all these studies only the case of stablized flow was subjected to theoretical investigation. In this paper the development of laminar flow in a prismatic duct uniformly rotating about an axis perpendicular to one of the walls is analyzed on the basis of the results of a numerical integration of the parabolized system of Navier-Stokes equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–46, September–October, 1985.     

On swirl development in a square cross-sectioned, S-shaped duct

The flow in a uniform square cross-sectioned, S-shaped duct was investigated experimentally, at Reynolds number (Re) = 4.73 × 10⁴ and 1.47 × 10⁵, using three S-ducts of different curvature and turning angle. The hydraulic diameter (D) for each S-duct is 150 mm. Besides studying the square cross-sectioned S-duct flow at moderately higher Re than current literature, the S-ducts’ geometry used in this study also have larger curvatures and higher turning angles than those reported in the literature. With surface pressure measurement and smoke wire flow visualization, flow separation at the inside wall of the first bend was detected. Using surface oil flow visualization on the bottom wall of the S-duct and cross-wires measurement at the duct exit, it is shown here that the swirl developed in the first bend was partly attenuated in the second bend due to the formation of swirl of opposite direction. The swirl of an opposite sign results in the formation of a clear dividing or separation line on the bottom wall (and top wall) of the duct. Additional flow features include the formation of streamwise vortices on the outer-wall of the second bend. These streamwise vortices can either be a pair of counter-rotating vortices or a single vortex. The formation mechanism of these streamwise vortices is explained using the Squire and Winter [J Aeronaut Sci 18(4):271–277, 1951] formula and it is shown that the said mechanism is applicable to both Re in the present study.     

Dynamic response of a rotating disk submerged and confined. Influence of the axial gap

In this paper, the natural frequencies and mode shapes of a rotating disk submerged and totally confined inside a rigid casing, have been obtained. These have been calculated analytically, numerically and experimentally for different axial gaps disk-casing. A simplified analytical model to analyse the dynamic response of a rotating disk submerged and confined, that has been used and validated in previous researches, is used in this case, generalised for arbitrary axial gaps disk-casing. To use this model, it is necessary to know the averaged rotating speed of the flow with respect to the disk. This parameter is obtained after an analytical discussion of the motion of the flow inside the casing where the disk rotates, and by means of CFD simulations for different axial positions of the disk. The natural frequencies of the rotating disk for the different axial confinements can be calculated following this method. A Finite Element Model has been built up to obtain the natural frequencies by means of computational simulation. The relative velocity of the flow with respect to the disk is also introduced in the simulation model in order to estimate the natural frequencies of the rotating disk. Experimental tests have been performed with a rotating disk test rig. A thin stainless steel disk (thickness of 8 mm, (h/r<5%) and mass of 7.6 kg) rotates inside a rigid casing. The position of the disk can be adjusted at several axial gaps disk-casing. A piezoelectric patch (PZT) attached on the rotating disk is used to excite the structure. Several miniature and submergible accelerometers have measured the response from the rotating frame. Excitation and measured signals are transmitted from the rotating to the stationary frame through a slip ring system. Experimental results are contrasted with the results obtained by the analytical and numerical model. Thereby, the influence of the axial gap disk-casing on the natural frequencies of a rotating disk totally confined and surrounded by a heavy fluid is determined.     

Turbulent flow measurement in a square duct with hybrid holographic PIV

 A hybrid holographic system has been developed for three-dimensional particle image velocimetry. With unique high pass filters, the system combines advantages of both in-line and off-axis holography without having their draw-backs. It improves the signal to noise ratio of the reconstructed image, allows use of 3–15 μm particles in water at high population and achieves large dynamic ranges in both velocity and space. With an automated image acquisition and processing system it has been used for measuring the velocity distributions in a square duct at Re=1.23×10⁵. The data consists of 97×97×87 vectors (with 50% overlapping of adjacent interrogation windows). The quality of the results is evaluated using the continuity equation. The deviation from the equation decreases rapidly with increasing control volume and reaches a level of less than 10%. Mean velocities, r.m.s. velocity fluctuations and turbulence spectra are estimated using the data. Received: 16 December 1996/Accepted: 6 March 1997     

Temperature statistics in a radiatively heated particle-laden turbulent square duct flow

Radiation absorption by preferentially concentrated particles in a turbulent square duct flow is studied experimentally. The particle-laden flow is exposed to near-infrared radiation, and the gas phase temperature statistics are measured along the wall bisector of the duct. It is found that the instantaneous temperature fluctuations are comparable to the overall mean temperature rise. The temperature statistics at the duct centerline and near the wall are qualitatively different. The former reflects preferential concentration in isotropic flows while the latter displays evidence of particle clustering into streamwise elongated streaks. Comparison of the experimental data to a simplified heat transfer model suggests that the Lagrangian evolution of particle clusters and voids, and turbulent mixing in the vicinity of particle clusters, are important. This work was motivated by particle solar receiver technology, but the findings are also relevant to systems where there is localized heat release or mass transfer from disperse particles or droplets. It shows that obtaining Lagrangian histories of particle trajectories is an important next step towards understanding thermal transport phenomena in particle-laden turbulent flows.     

Flow of second-order fluid in a curved duct with square cross-section

This paper investigates the inertial and creeping flow of a second-order fluid in a curved duct with a square cross-section. Numerical modeling is employed to analyze fluid flow, and the governing equations are discretized using the finite difference method on a staggered mesh. The marker-and-cell method is employed to allocate the parameters on the staggered mesh, and static pressure is calculated using the artificial compressibility approach. The effect of centrifugal force due to the curvature of the duct and the opposing effects of the first and second normal stress difference on the flow field are investigated. In addition, the order-of-magnitude technique is used to derive the force balance relations for the core region of flow. Based on these relations, the performance mechanism of centrifugal force and normal stress differences on the generation of secondary flows is considered. We also present an analytical relation for the axial velocity profile and flow resistance ratio of creeping flow. For this kind of flow, previous studies have investigated the effect of the first normal stress difference on the transition from one pair to two pairs of vortices while we show that the negative second normal stress difference has the opposite effect on this transition and can stabilize the flow.     

Measurements of turbulent developing flow in a moderately curved square duct

Laser-Doppler measurements in the turbulent flow in a right-angled bend of square cross-section, radius/duct-width ratio 7.0, are presented and show the development of secondary circulation in cross-stream planes. Distribution of the streamwise and radial components of the mean velocity and turbulence intensity, and the corresponding Reynolds shear stress, are presented as contour plots and are intended for use in the further development of numerical flow prediction methods.     

A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

The structure of water-air bubble grid turbulence in a square duct

Local measurements of void fraction and continuous phase velocity field in water-air bubble, grid turbulence were conducted in a channel of vertical, square test section. The measured statistics indicate that, due mainly to the interaction of mean shear with the dispersed phase, the turbulence structure of the flow is modified. The observed change is characterized by a strong spatial dependence of void fraction and liquid flow properties, and the emergence of two spatial regions controlled by different physical processes. Intensity measurements indicate significant departure from isotropy in the flow. Two distinct regimes corresponding to low and high values of void fraction have been also identified. The autocorrelation and spectra measurements indicate that for low void fraction the scales of turbulence decrease while for higher values of void fraction increase again and inverse cascade is observed.     

Waves induced by a submerged moving dipole in a two-layer fluid of finite depth

The waves induced by a moving dipole in a twofluid system are analytically and experimentally investigated.The velocity potential of a dipole moving horizontally in the lower layer of a two-layer fluid with finite depth is derived by superposing Green‘s functions of sources (or sinks). The far-field waves are studied by using the method of stationary phase. The effects of two resulting modes, i.e. the surfaceand internal-wave modes, on both the surface divergence field and the interfacial elevation are analyzed. A laboratory study on the internal waves generated by a moving sphere in a two-layer fluid is conducted in a towing tank under the same conditions as in the theoretical approach. The qualitative consistency between the present theory and the laboratory study is examined and confirmed.     

Vortex shedding induced by a solitary wave propagating over a submerged vertical plate

Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet.     

Natural convection induced in a fluid by the hot inner walls of a “submerged” channel

The jet flows induced around a submerged channel due to the hot inner channel walls and the flow inside the channel are calculated. The formation of high-and low-density regions at the inlet and outlet of the channel is detected. The dependence of the flow rate on the channel orientation relative to the gravity force is analyzed. The onset of coherent flow structures results in the development of unsteady oscillating flows. Natural convection in the fluid is studied using the JoinCAD/FEM program package. The regularized Oberbeck-Boussinesq equations are solved using a finite-element method with the same order of the approximating functions.     

Laminar flow and heat transfer in confined channel flow past square bars arranged side by side

A numerical investigation was conducted to analyze the unsteady laminar flow field and heat transfer characteristics in a plane channel with two square bars mounted side by side to the approaching flow. A finite volume technique is applied with a fine grid and time resolution. The transverse separation distance between the bars (G/d) is varied from 0 to 5, whereas the bar height to channel height is d/H=1/8, and the channel length is L=5H. Different flow regimes develop in the channel due the interaction between the two mounted square bars, steady flow, flow with vortex shedding synchronization either in phase or in anti-phase, or biased flow with low frequency modulation of vortex shedding are found. Results show that the pressure drop increase and heat transfer enhancement are strongly dependent of the transverse separation distance of the bars and the channel Reynolds number.     

Flow of a viscous incompressible fluid in a thin layer confined by a rigid free surface

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 117–125, January–February, 1989.     

The near-corner mass transfer associated with turbulent flow in a square duct

Mass transfer to a nearly fully developed turbulent flow in a square duct is studied. Measurements are taken either on one or two adjacent walls in the region of a developing mass transfer boundary layer. Effects of the secondary flow on mass transfer are observed near the corners. The effects are initially small, but grow to a significant degree further downstream. The location of the maximum and its lateral spread is affected by the Reynolds number, as well as the adjacent wall mass transfer.

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Stoffübertragung in der Nähe einer Ecke bei turbulenter Strömung in einem quadratischen Rohr

Zusammenfassung Es wird über den Massentransport in einer nahezu vollentwickelten turbulenten Strömung in einem Kanal mit quadratischem Querschnitt berichtet. Messungen werden an einer oder an zwei benachbarten Wänden im Bereich der sich entwickelnden Massenübergangsgrenzschicht durchgeführt. Im Bereich der Kanalecken werden Effekte der Sekundärströmung beobachtet. Diese Effekte sind anfänglich gering, wachsen jedoch weiter stromabwärts beträchtlich an. Die Lage des Maximums und seine laterale Ausbreitung werden sowohl durch die Reynoldszahl als auch durch den benachbarten Massenübergang zur Wand beeinflußt.

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Nomenclature D Duct's span - Dh Hydraulic diameter - Re Reynolds number (U _bulk Dh/v) - Sh Sherwood number - U Axial velocity - U _bulk Bulk velocity - x, y, z Coordinate system, Fig. 1 - x Axial distance from the duct's inlet - Kinematic viscosity Dedicated to Prof. Dr.-Ing. U. Grigull's 80th birthday