Sinusoidal Tube Research Articles

Convective Heat Transfer Characteristics of Laminar Flow in Sinusoidal Corrugated Tube

A new type of corrugated tube based on sine function is proposed by introducing a parameter of sine camber. The heat transfer and flow around sinusoidal corrugated tubes with different sine camber e are investigated in this paper. Computational Fluid Dynamics (CFD) was used to analysis flow state and sine camber of tube influence on the heat transfer and flow, a correlation equations of Nu (Nusselt) =f(Re) is given. At last, the theoretical comparative analysis with field synergy principle is carried out for the heat transfer and flow resistance in smooth tube and sinusoidal corrugated tube. The results show that the experiment basically tallies with the value of numerical calculation of laminar flow. In the range of 500 < Re < 1000, flow resistance coefficient has great decrease extent, while low resistance coefficient has small decrease extent of 1500 < Re < 2300. The effect of field synergy is poor in the smooth tube, which is opposite to that in sinusoidal corrugated tube, and it can improve the efficiency of around 2.7 times.

Numerical heat transfer analysis of laminar film condensation on a vertical fluted tube

The purpose of this study is to find a convenient and practical procedure for calculating heat transfer of laminar film condensation on a vertical fluted tube. The condensate film on the tube surface along the axial direction was divided into two portions: the initial portion and the developing portion. The developing portion was analyzed in details. The film thickness equation of condensate film over the crest and the momentum equation of condensate film in the trough were established respectively after some simplifications and coupled with two-dimensional thermal conduction equation. The relationship between the heat transfer rate and the length of the flute was obtained through solving the equations numerically. The present procedure was tested on a sinusoidal fluted tube. The amount of heat transfer rates Qt of the tube were calculated at different temperature differences by using this procedure. The calculation was compared with the experimental data quoted. The results were in good agreement with a maximum deviation of 18%. So the present procedure is reliable and can be used in the parameter design of sinusoidal fluted tubes.

Convective heat transfer augmentation through vortex shedding in sinusoidal constricted tube

PurposeThe purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature.Design/methodology/approachThe problem is written with classical homogeneous boundary conditions. We use a shift operator to impose non‐homogeneous boundary conditions. Consequently, this method introduces source terms in the Galerkin formulation. The momentum equations and the energy equation which govern this problem are numerically solved in space by a spectral Galerkin method especially oriented to this situation. A Crank‐Nicolson scheme permits the resolution in time.FindingsFrom the temperature field, the heat transfer phenomenon is presented, discussed and compared to those obtained in straight cylindrical pipes. This study showed the existence of zones of dead fluid that locally have a negative influence on heat transfer. Substantial modifications of the thermal convective heat transfer are highlighted at the entry and the minimum duct sections.Practical implicationsPulsated flows in axisymmetric geometries can be applied to medical industries, mechanical engineering and technological processes.Originality/valueOne of the original features of this study is the choice of Chebyshev polynomials basis in both axial and radial directions for spectral methods, combined with the use of a shift operator to satisfy non‐homogeneous boundary conditions.

A study on particle deposition morphology within a constricted tube in the presence and absence of the detachment mechanism

With/without considering the detachment mechanism, the deposition morphology of Brownian and non-Brownian particles within a constricted tube is investigated by applying the Brownian dynamics simulation method in the present paper. Two different geometric structures, the parabolic constricted tube (PCT) and the sinusoidal constricted tube (SCT), are adopted. The effects of various types of the total interaction energy curves of the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory and increasing flow velocity on the particle deposition morphology are also examined. For PCT without considering the detachment mechanism, under the same interaction energy curve, it is found that the number of non-Brownian particles deposited is higher than that of the Brownian particles. Since the deposition location moves closer to the constriction part of the tube, the number of Brownian and non-Brownian particles increases with a decrease in flow velocity. The SCT behaves differently, it is found that the number of non-Brownian particles deposited is only slightly higher than that of Brownian particles. When the detachment mechanism is considered, same results are obtained for those non-Brownian and Brownian particles within a PCT/SCT with the increase of the flow velocity. When comparing with the deposition morphology between PCT and SCT, it is found that a more uniform dendrite of four or five layers can be formed on the tube walls of PCT than that of SCT. Joining of individual dendrites at the blockage stage is not observed for both PCT and SCT in the present simulation.

The deposition morphology of Brownian/non-Brownian particles within a constricted tube

The deposition morphology of Brownian/non-Brownian particles within a constricted tube is investigated by applying the Brownian dynamics simulation method in the present paper. Two different geometric structures, the parabolic constricted tube (PCT) and the sinusoidal constricted tube (SCT), are adopted. The effect of various types of the total interaction energy curves of the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, and of the shadow area cast by those deposited particles, on the particles’ collection efficiencies are also examined. For the PCT structure, under the same interaction energy curve, it is found that the non-Brownian particles always own a higher collection efficiency than that of the Brownian particles. Since the deposition location moves closer to the constriction part of the tube, the collection efficiencies of the Brownian/non-Brownian particles increase with the decrease of flow velocity. The SCT behaves differently, it is found that the collection efficiencies of non-Brownian particles are only slightly higher than those of Brownian particles when SCT is adopted. The steep slope of the tube wall near the constriction part of SCT dominates the whole deposition process of Brownian/non-Brownian particles. In comparison with the available experimental data, it is found that the present method can give a good simulation result.

Fluid flow and mass transfer in a sinusoidal wavy‐walled tube at moderate Reynolds numbers

AbstractFluid flow and mass transfer characteristics in an axisymmetric sinusoidal wavy‐walled tube are experimentally investigated in the Reynolds number range of 50 to 1000. Attention is paid to the transitional flow, which is observed in the Reynolds number range of 160 to 200. In the laminar flow regime, wall shear stress and mass transfer rate increase with the slopes of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slopes of 3/2 and 3/5, respectively. In the transitional flow regime they increase dramatically, with a sharp slope. It is found that in this flow regime, laminar‐like motion and turbulent‐like motion alternatively take place at different time intervals. This is quite different from the flow instability for the wavy‐walled channel, where Tollmien‐Schlichting waves are observed. The flow instability in the wavy‐walled tube in the transitional flow regime is considered to be responsible for a significant increase in the wall shear stress and mass transfer rate. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 650–661, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10121

Fluid flow and mass transfer characteristics in a sinusoidal wavy-walled tube at moderate Reynolds numbers for steady flow

Flow and mass transfer characteristics in an axisymmetric sinusoidal wavy-walled tube are investigated experimentally in the Reynolds number range from 50 to 1000. The flow patterns are visualized by the aluminum dust method. The measurements of the wall shear stress and the mass transfer rate for high Schmidt number are performed by the electrochemical method. The attention is focused on their characteristics, including the transitional flow. It was observed that steady flow changes into unsteady flow when the Reynolds number exceeds about 160. The wall shear stress in the minimum circular cross section of the tube and the mass transfer rate for one wavelength are shown to depend upon the Reynolds number. In the laminar flow regime they increase with the slope of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slope of 3/2 and 3/5, respectively. In the transitional flow regime both of them increase significantly with further larger slope. It is found that the laminar-like motion and turbulent-like motion occur alternatively, with different time intervals, indicating intermittent flow behavior. This is quite different from the flow instability of the wavy-walled channel in which Tollmien-Schlichting waves keeping a time-periodic flow appear.

Fluid Flow and Mass Transfer in a Sinusoidal Wavy-Walled Tube at Moderate Reynolds Numbers.

Fluid flow and mass transfer characteristics in an axisymmetric sinusoidal wavy-walled tube are investigated experimentally in the Reynolds number range from 50 to 1 000. The attention is paid to the transitional flow, which is observed in the Reynolds number range of 160 to 200. In the laminar flow regime wall shear stress and mass transfer rate increase with the slope of 1 and 1/3, respectively, whereas in the turbulent flow regime they increase with the slope of 3/2 and 3/5, respectively. In the transitional flow regime they increase dramatically with a sharp slope. It is found that lamiar-like motion and turbulent-like motion alternatively take place with different time intervals in this flow regime. This is quite different from the flow instability for the wavy-walled channel, in which the Tollmien-Schlichting waves are observed. The flow instability in the wavy-walled tube is considered to be responsible for a significant increment of the wall shear stress and mass transfer rate in the transitional flow regime.

Mass Transfer Enhancement in a Sinusoidal Wavy-Walled Tube for Pulsatile Flow.

This study describes experimentally mass transfer enhancement in a wavy-walled tube for pulsatile flow. Three flow parameters are considered, i. e. net flow Reynolds number, oscillatory fraction and oscillatory frequency. The attention is paid especially to the effect of oscillatory frequency on mass transfer enhancement under conditions of no reverse flow. We show that the mass transfer enhancement factor varies with the net flow Reynolds number and oscillatory fraction. When the net flow is located just before the transitional flow regime for steady flow, the effective mass transfer enhancement is available. Furthermore we found that the resonant transport enhancement observed in a grooved channel, does not exist in the wavy-walled tube. A peak transport enhancement takes place in an optimum Strouhal number, which depends on the oscillatory fraction. The pulsatile flow state tends to be stable in the acceleration phase and unstable in the deceleration phase. The unstable flow state is found to lead to a strong fluid exchange between the mainstream and the recirculation vortex, and thus contributes to the mass transfer enhancement.

Analysis of surface dose variation in CT procedures.

An experimental and theoretical study has been made of the variations in air kerma-length product (AKLP) at the surface of a phantom exposed in a CT scanner, using clinical parameters. For the theoretical part, a computer simulation was developed, based on a simple analytical model, requiring information generic to the scanner model. The effects of patient size, position within the gantry plane and beam-shaping filter type were studied using three different elliptical phantoms. A dose reduction technique based on a sinusoidal tube current modulation system was also investigated. The surface AKLP was shown to be independent of phantom size (within experimental error) but decreases as the surface moves vertically away from the isocentre. The major contributor to this variation is the beam-shaping filter. A maximum difference of 19% between the values of surface AKLP was calculated for the two beam-shaping filters available. When the tube current modulation system was used, the maximum surface dose reduction was 18%. A maximum difference of 2% was found between measurements and computer simulations. It is therefore possible to predict the behaviour of AKLP using the analytical model. As the dose measured on the surface of a patient is simply related to AKLP, the model can be applied to data obtained from patient surface dose surveys and can be helpful in interpreting the sources of variation in the latter.

STUDYING THE CONTACT POINT AND INTERFACE MOVING IN A SINUSOIDAL TUBE WITH LATTICE BOLTZMANN METHOD

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are non-wetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

Understanding utero-placental blood flow in normal and hypertensive pregnancy through a mathematical model.

Normal development of utero-placental circulation is crucial not only for the survival and growth of the fetus in utero, but also for maternal well-being. Any disturbance or abnormality may reflect underlying pathology. Geometric conversion of a pre-pregnant spiral vessel into a divergent low-resistance vessel is believed to be responsible for the increased utero-placental blood flow in normal pregnancy. Known biomedical investigative techniques have failed to explain many such underlying haemodynamic changes taking place in the utero-placental system. Therefore, proper understanding of the system using a mathematical model has been found to be useful. The physiological fluid dynamic study is the first in this branch of physiology. Abnormal pressure gradient, axial velocity, volume flow and shear rate are obtained for various slowly changing geometries such as, tapering, divergence, local constrictions and sinusoidal tube for low Womersley parameters. The model can explain many enhanced patho-physiological changes, such as persistence or the appearance of local constriction in the utero-placental vessels. Such pathological changes are considered to be responsible for very high utero-placental resistance, leading to blood flow insufficiency in pre-eclampsia or intra-uterine growth retardations. It is believed that these changes may be caused by low shear rate on the pre-existing deranged or abnormal endothelium. Furthermore, this derangement is caused by an abnormal proliferation of either spiral vessels or the invading non-villous trophoblasts. Doppler flow study can explain and validate some of the theoretically derived flow velocity results. The study opens up a new area of research into utero-placental physiological fluid dynamics.

Salt Rejection in a Sinusoidal Capillary Tube

Electrokinetic models for electrolyte transport in narrow sinusoidal capillary tubes were used to study salt rejection. Two approaches were adopted. The first formulation made use of Gouy-Chapman model of the double layer coupled with the creeping flow and Nernst-Planck equations. The elliptic nature of the formulation was retained. The second formulation was an adaptation of Dresner's model where Boltzmann distribution was assumed to hold in the radial direction. The salt rejection as evaluated by the two formulations was fairly close. However, the details of the electrokinetic field variables obtained from the two formulations were not in close agreement. The dimensionless inverse Debye length, κa, based on the average tube radius, a, was found to play a major role in the salt rejection. When the electrical double layers overlap, i.e., κa is small, the salt rejection is governed by the surface potential, flow Peclet number, and the amplitude of the tube surface. In addition, for high Peclet numbers, the tube surface potential becomes the sole parameter controlling the salt rejection. When the electrical double layers do not overlap, i.e., κa is large, the salt rejection becomes a strong function of the tube geometry as well as the surface potential and Peclet number.

Parametric Study of Particle Deposition in Sinusoidal Pores of Arbitrary Orientation

A parametric study of particle deposition during flow of suspensions through single constricted pores is presented in order to identify the effects of the various forces acting on the particles on the simulated deposition rate and to assess the sensitivity of the filtration efficiency predictions on the uncertainty involved when evaluating the relevant parameters. The calculations of the impacted particle fraction are based on the calculation of 3-D particle trajectories in sinusoidal tubes under the action of hydrodynamic forces and torques, gravity, the double ionic layer force, and the London force. It is found that the five dimensionless parameter groups that enter the calculation of the surface forces affect the deposition rate in a similar manner. Two distinct regions can be identified for each group; in each region the impacted fraction remains almost insensitive to changes in the group value. However, transition from one region to the other causes a spectacular, abrupt change of the impacted fraction by more than five orders of magnitude. Among the main conclusions of this parametric analysis is that the determination of the filtration efficiency rests mainly on the easily measured gravitational group and is insensitive to the precise value of the five surface force parameter groups, as long as it is known that each of them is larger or smaller than a corresponding critical value given here. Finally, the impacted fraction up to various depths into a unit cell and the impacted fraction per unit length are calculated for vertical and horizontal cells and for variable particle size.

網内系学説と現在の肝類洞壁細胞像

The wall of hepatic sinusoids is a morphological and functional unit made up of four different cell populations, i.e., endothelial cells, Kupffer cells, perisinusoidal stellate cells (fat-storing cells), and lymphocytes including pit cells (liver-associated LGLs).The core element of this unit is the endothelial lining which provides a bed for other sinusoidal cells. Endothelial cells are highly fenestrated and sieve the fluids exchanged between the sinusoidal lumen and the space of Disse. Presence of numerous receptors on endothelial cells supports the receptor-mediated endocytosis of various substances. Adhesion molecules are expressed on the surface of these cells. Kupffer cells are resident macrophages, and clear endotoxin from the blood stream. When activated, Kupffer cells secrete metabolites of arachidonic acid, TNF, IL-1, IFN, and reactive oxygen products. Stellate cells are located perisinusoidally surrounding the sinusoidal tubes and, on the other hand, send thorn-like microprojections to parenchymal cells. Stellate cells store vitamin A and produce Type I, III and IV collagens and other extracellular matrix. Pit cells are characterized by the presence of dense granules and rod-cored vesicles. After administration of BRMs, number of pit cells increases adhering to the endothelial lining and liver-associated NK activity is augmented. Paracrine and autocrine secretions of mediators and cytokines from sinusoidal cells modulate functions of the sinusoidal wall and parenchymal cells.Currently the RES is restricted only to the system of macrophages. From the modern concept of sinusoidal cells in the liver, however, phagocytosis is only the trigger for starting the cascade of broad RES functions beyond the single cell line. The liver RES is not only Kupffer cells but the sinusoidal wall itself which provides a microenvironment between the blood stream and parenchymal cells. The RES is specifically organized tissue in the body, as suggested by early investigators.

Kinetics of liquid penetration into periodically constricted capillaries

An equation is derived for the rate of penetration of a liquid into a periodically constricted tube (PCT) of capillary dimensions. Its solution yields an apparent diameter for the PCT. A comparison of predicted and experimentally derived values of Dapp for sinusoidal tubes shows good agreement. Examination of the rate equation indicates that under certain conditions, the meniscus is arrested. This is verified by free-energy calculations. The implications of this phenomenon for the modelling of liquid penetration into porous structures are discussed briefly.

Origin of the proximal coronary artery stems and a review of ventricular vascularization in the chick embryo

The objective of this study was to determine how the coronary artery stems develop in the chick embryo. The hearts of 51 ink-injected and cleared chick embryos, aged embryonic days 6, 6.5, 7, 7.5, 9, and 10, were dissected, examined, and selectively photographed. Two representative hearts from each group were paraffin embedded, serially sectioned at 10 microns, and examined for aortic endothelial budding. We found that the proximal coronary artery did not appear to grow outward from the aorta as commonly described in the literature. It appeared to originate from a capillary ring which encircled the aortic and pulmonary outflow tracts. On embryonic day 7.5, one to three channels arising from this ring penetrated each aortic sinus, in an area of darker textured endothelium. Histologically and grossly, multiple channels were still apparent on day 9, particularly in the left coronary artery. One of these channels always became dominant to form the stem. Each stem, which varied in length from embryo to embryo, always ended in a plexus of sinusoidal endothelial tubes. By day 10, the coronary artery stems were longer, with many major branches. Histologically, evidence of multiple channels still was visible. It is significant that channels from the bulbar vascular ring penetrated the aorta at very specific points in the aortic sinuses and did not penetrate the pulmonary trunk or other aortic sites. We believe this fact indicates that the penetration of the aortic sinuses by channels from the bulbar vascular ring represents a controlled invasion of the aorta.

Film condensation on a vertical sinusoidal fluted tube

An analysis of laminar film condensation on a vertical fluted tube has been made considering gravitational and surface tension effects over the entire fluted surface, and using surface-oriented coordinates. For the first time surface tension effects are determined, as they should be, from the shape of the condensate-vapor interface rather than from the shape of the flute. Two-dimensional conduction within the condensate film as well as in the fluted tube wall is considered. A finite difference solution of the highly nonlinear partial differential equation for the film thickness is coupled with a finite element solution of the conduction problem. The procedure has been tested on a sinusoidal flute with amplitude-to-pitch ratio ≈0.2. A linear extrapolation on a log-log basis of the results shows good agreement with experiment data.

A hydrodynamic model developed for the condensate flowing over a sinusoidal fluted tube

Fluted tubes which were designed by Gregorig considering the use of surface tension forces are commonly used in evaporators and condensers for desalination purposes. In this study the surface profile of a fluted tube, which cannot be described by any conventional coordinate system is obtained numerically by using an intrinsic-coordinate system. Navier-Stokes equations are solved after some simplifications for the condensate flowing over the sinusoidal fluted profile to find the volumetric flow rate. The results are found to be in good agreement with the experimental findings.

Network models for two-phase flow in porous media Part 2. Motion of oil ganglia

The behaviour of non-wetting ganglia undergoing immiscible displacement in a porous medium is studied with the help of a theoretical simulator. The porous medium is represented by a network of randomly sized unit cells of the constricted-tube type. The fluid of a non-wetting ganglion is in contact with the wetting fluid at menisci which are assumed to be spherical cups. The flow in every constricted unit cell occupied by a single fluid is modelled as flow in a sinusoidal tube. The flow in every unit cell that contains a meniscus and portions of both fluids is treated with a combination of a Washburn-type analysis and a lubrication-theory approximation. The flow problem is thus reduced to a system of linear equations the solution of which gives the instantaneous pressures on the nodes, the flowrates through the unit cells, and the velocities of the menisci. The motion of a ganglion is determined by assuming quasi-static flow, taking a small time increment, updating the positions of the menisci, and iterating. The behaviour of solitary ganglia is studied under conditions of quasi-static displacement (Ca slightly larger than critical), as well as dynamic displacement (Ca substantially larger than critical). Shape evolution, rate of flow, mode of break-up, and stranding are examined. The stranding and break-up coefficients are determined as functions of the capillary number and the ganglion size for a 100 × 200 sandpack. The dependence of the average ganglion velocity on ganglion size, capillary number, viscosity ratio and dynamic contact angle is examined for the simple case of motion between straight rows of spheres. It is found, among other things, that when μo < μw the velocity of ganglia can be substantially larger than that of the displacing fluid.