Wall Corrugation Research Articles

Secondary Flow in Smooth and Rough Turbulent Circular Pipes: Turbulence Kinetic Energy Budgets

Direct Numerical Simulations have been performed for turbulent flow in circular pipes with smooth and corrugated walls. The numerical method, based on second-order finite discretization together with the immersed boundary technique, was validated and applied to various types of flows. The analysis is focused on the turbulence kinetic energy and its budget. Large differences have been found in the near-wall region at low Reynolds number. The change in the near-wall turbulent structures is responsible for increase of drag and turbulence kinetic energy. To investigatselinae the effects of wall corrugations, the velocity fields have been decomposed so as to isolate coherent and incoherent motions. For corrugated walls, we find that coherent motions are strongest for walls covered with square bars aligned with the flow direction. In particular, the coherent contribution is substantial when the bars are spaced apart by a distance larger than their height. Detailed analysis of the turbulence kinetic energy budget shows for this set-up a very different behavior than for the other types of corrugations.

Interface states of dipole-like distributions in a quasi-periodic acoustic waveguide

Interface states of dipole-like distributions are experimentally observed in an acoustic waveguide with designed quasi-periodically corrugated walls. Due to the orthogonality breaking of guided transverse modes induced by the wall corrugations, a type of non-Bragg nature forbidden bands can be generated based on the interactions between different transverse modes. An interface state arises from the non-Bragg gap when we connect the two corrugated ducts to form a mirror structure. It is worth noting that the interface state in non-Bragg gaps exhibits two maximum sound pressures with totally opposite phases near the structure interface, while that in traditional Bragg gaps always has only one maximum. Our experimental measurements and numerical analysis reveal that the observed interface state with different mode characteristics is caused by the interaction of different transverse modes, which has the localization effect and high Q factor.

DEVELOPMENT OF TECHNOLOGICAL PROCESS OF FORMATION OF WIDE FLANGES ON SHEET PROCUREMENTS BY ROLLING STAMPING METHOD

The article presents the results of development and research of the technological process of forming wide outer flanges of lids of malt and distillation columns on sheet blanks by rolling stamping. For this purpose, equipment has been developed in the form of a rolling device for a lathe and an autonomous rolling unit, which allow to form the outer flanges with a conical roll. The rolling unit to the lathe provides the presence of coil springs for pressing the roll to the workpiece with the mandrel. Both settings provide the ability to change the angle of the axis of the rolling unit relative to the axis of the mandrel with the workpiece. Studies have shown that the technological capabilities of the process are limited by the corrugation of the flange wall. The power calculation of flanging of external flanges by a conical roll by the SHO method is carried out and formulas for determination of deformation forces are received. The acceptable accuracy of these formulas has been experimentally confirmed, and there is a tendency to increase the error with increasing geometric dimensions of the workpiece. To assess and expand the technological capabilities of the process, an analysis of the formation and deformed state of the workpieces. Since the main danger in the formation of external flanges by the SHO method is the loss of stability in the form of corrugations, the paper obtained an expression for determining the maximum width of the flange under the condition of a stable process. If it is necessary to obtain more developed flanges, it is proposed in the second stage to provide thinning of their wall by drawing with the use, if necessary, heating the workpiece by induction method.

Heat transfer performance of a nanofluid-filled tube with wall corrugations and center-cleared twisted-tape inserts

ABSTRACT We numerically examine the thermal performance of a round tubular heat exchanger featuring a combination of three passive techniques for heat-transfer enhancement: (i) center-cleared twisted-tape inserts, (ii) tube corrugations, and (iii) nanofluids. We consider three geometric tape parameters – the central-clearance width (C), the tape width (W), and the 180° tape pitch (H) – across a range of Reynolds numbers (500 ≤ Re ≤ 1250). For both water and a representative nanofluid (Al2O3-water), increasing W or decreasing C or H is found to increase the heat transfer coefficient at all Re. Switching from water to one of four water-based nanofluids − Al2O3-water, CuO-water, Cu-water, and TiO2-water – is found to improve the heat transfer rate sufficiently to overcome any associated rises in pressure drop, resulting in thermal efficiencies higher than those of water. The highest thermal efficiency coefficient (η = 1.157) occurs with the Cu-water nanofluid at the smallest Re (500), whereas the lowest thermal efficiency coefficient (η = 1.115) occurs with the CuO-water nanofluid at the largest Re (1250). Across the entire Re range, increasing the volume concentration of Al2O3 nanoparticles (from ϕ = 2 to 5%) is found to increase the coefficients of heat transfer and thermal efficiency. This study provides new insight into how the heat transfer capabilities of a tubular heat exchanger can be enhanced by combining center-cleared twisted-tape inserts, tube corrugations and nanofluids.

Darcy–Brinkman Flow in a Corrugated Curved Channel

A theoretical analysis of a viscous flow in a corrugated curved channel enclosing a porous medium is carried out. The alignment of the corrugations of the outer and the inner curved walls is taken arbitrarily, and the corrugations are considered to be sinusoidal in nature with periodicity. The flow problem is described by Darcy–Brinkman model, derived in the curvilinear coordinates. The effects of the channel curvature, the wall corrugations and the medium permeability are studied through the boundary perturbation technique, for small corrugation amplitude. A substantial effect of the porous medium on the flow is observed when compared to that of the flow in a corrugated curved channel with clear conduit, especially for low permeability medium. Flow enhancement is found to take place for small corrugation wavenumbers, and maximum augmentation is realized for the completely out-of-phase alignment of the two corrugated curved walls. However, the flow reduces for large enough wavenumbers, and the alignment of corrugated curved walls eventually becomes irrelevant, with no influence on the flow. For low permeability medium, the results also show no effect of the wall alignment on the flow. In general, the effect of the channel curvature on the corrugated curved channel flow is discussed relative to a corrugated straight channel flow to demonstrate the implications of the wall geometry enclosing the porous medium.

Resonant Reflection From Cylindrical Grating-Waveguide Under Holistic Excitation

The phenomenon of resonant reflection from a grating-coupled waveguide mode is conceptually, technologically, and experimentally transposed from a planar corrugated waveguide structure under plane wave excitation to a circularly symmetrical waveguide at the inner wall of a tube under cylindrical wave excitation. The mode coupling element is an azimuthally periodic wall corrugation having an integer number of lines parallel to the tube axis. The grating is defined by diffractive coordinate transform of a radial grating phase-mask transverse to the tube axis under axial beam exposure onto a photoresist-coated TiO2 sol-gel wall-waveguide. The holistic excitation of a waveguide mode is achieved by transforming a broad spectrum, centered axial incident beam into a cylindrical wave by a centered, 90° apex reflective cone. The expected resonantly reflected cylindrical wave at the mode-coupling wavelength is in turn transformed back into an axial beam by the cone. TE resonant reflection is demonstrated experimentally.

Magnetohydrodynamics forced convection of nanofluid in multi-layered U-shaped vented cavity with a porous region considering wall corrugation effects

Abstract Magnetohydrodynamics forced convection of CNT-water nanofluid in a layered U-shaped vented cavity involving a porous region is investigated under the impact of wall corrugation. The numerical study is performed by using the finite volume method. Impacts of Reynolds number (between 100 and 1000), Hartmann number (between 0 and 50), Darcy number (between 10−4 and 5 × 10−2), porous layer height (between 0.1H and 0.5H), height (between 0 and 0.5H) and number of triangular waves (between 1 and 16) and curvature (between 0.01H and 0.2H) at the U-turn of the vented cavity on the convective heat transfer features are examined. The flow field and heat transfer are affected by variations in the Reynolds number, magnetic field strength and permeability of the porous medium. The average Nusselt number increases significantly with higher magnetic field strength and at Hartmann number of 50, the amount of enhancement is 112% while the impact is reverse for highest value of Darcy number of the porous compound. The corrugation of the bottom wall which is a triangular wave was found to be used as an effective tool for fluid flow and heat transfer features. The average heat transfer rate reduces with higher number of corrugation waves (68.2% reduction) while it first increases then reduces with higher height of the corrugation. The curvature of the neck in the U-shaped cavity reduced the heat transfer rate which is 15.5% at the highest value.

Influence of Backfill Compaction on Mechanical Characteristics of High-Density Polyethylene Double-Wall Corrugated Pipelines

For flexible pipelines, the influence of backfill compaction on the deformation of the pipe has always been the focus of researchers. Through the finite element software, a three-dimensional soil model matching the exterior wall corrugation of the high-density polyethylene pipe was skillfully established, and the “real” finite element model of pipe-soil interaction verified the accuracy through field test. Based on the model, the strain distribution at any position of the buried HDPE pipe can be obtained. Changing the location and extent of the loose backfill, the strain and radial displacement distributions of the interior and exterior walls of the HDPE pipe under different backfill conditions when external load applied to the foundation were analyzed, and the dangerous parts of the pipe where local buckling and fracture may occur were identified. It is pointed out that when the backfill is loose, near the interface between the backfill loose region and the well-compacted region, the maximum circumferential strain occurs frequently, the exterior wall strain is more likely to increase greatly on the region near crown or invert, the interior wall strains increase in amplitude at springline, and the location of the loose region has a greater influence on the strain of the pipe than the size of the loose area.

Cross-helix corrugation: The optimal geometry for effective food thermal processing

In the present paper, an innovative and effective heat transfer enhancement technique for food processing, cross-helix profile wall corrugation, is proposed and tested. In the food industry, the two most promising corrugation profiles are the transversal and single-helix ones because they both satisfy hygienic design principles. Among the available wall corrugation techniques, transversal corrugation allows for the highest heat transfer performance, and the spirally corrugated tubes guarantee the easiest manufacturing. For this reason, single-helix corrugated tubes are the most commonly employed in heat exchangers for food processing. The cross-helix profile presented in this work represents an intermediate solution between transversal and single-helix corrugation aimed at combining their positive aspects.One of the main goals of the current research is to identify an optimal geometry that maximises the heat transfer performance by limiting the pressure drop augmentation for this specific engineering application (i.e., food thermal processing). For this purpose, the effect of the geometrical parameters of the corrugation profile is investigated by varying two of the most influent quantities in terms of heat transfer performance and pressure drop: corrugation depth and corrugation pitch. Six pipes characterised by different cross-helix corrugations are tested. Their performance is evaluated by studying the forced convective heat transfer in the Reynolds and Prandtl numbers ranges (50–14,000 and 5–150, respectively), using ethylene glycol, water and a mixture of the two as the working fluids.The outcomes show that corrugation depth plays a crucial role in enhancing the heat transfer performance of the tested pipes. An optimal geometry is established, and correlations to describe its thermal and fluid flow behaviours are proposed. This optimal geometry shows superior performance to that of the most widely adopted types of corrugation. For the low/intermediate Reynolds number range (i.e., 200–2000), the efficiency of the proposed cross-helix profile is up to three times greater than that of the single helix and is also greater than that of transversally corrugated tubes. These outcomes make cross-helix a recommended option to be used in the design of optimised heat exchangers.Because the studied geometry is expressly developed for food industry application, a set of measurements is also performed in which apricot juice is adopted as the working fluid. The findings confirm the efficiency of the proposed correlations with non-Newtonian fluid foods and enable them to be extended to a wide range of real food industrial applications.

Selectivity Properties of Cylindrical Waveguides with Longitudinal Wall Corrugations for Second-Harmonic Gyrotrons

Spatial harmonic method is applied to investigate selectivity properties of longitudinally corrugated waveguides for potential application in second-harmonic gyrotrons. The effect of corrugations on frequencies, ohmic losses, and mode conversion of guiding TE modes is studied in details. Numerical results are presented for operating second-harmonic and competing first-harmonic modes of a 0.4-THz gyrotron with corrugated RF structure. It is shown that longitudinal wall corrugations of proper dimensions can ensure increase in ohmic losses and decrease in beam-wave coupling strength for the first-harmonic modes, while their effect on the operating mode is only slight. This demonstrates improved selectivity properties of corrugated waveguides for second-harmonic gyrotrons.

Analysis of the mass transport in corrugated membraneless flow batteries

A novel strategy to improve the mass transport performance in membraneless redox flow batteries (MRFB) is proposed, based on a symmetrical sinusoidal wall corrugation of the solid electrodes. The continuity, Navier–Stokes, and mass transport equations are solved with a hybrid analytical-numerical method known as the Generalized Integral Transform Technique (GITT). The effects of the Reynolds number and the amplitude of the corrugation are analyzed. The corrugated MRFBs are shown to be more suitable for higher Reynolds number applications, still within the laminar flow regime, when crossover is a less limiting factor. For smaller Reynolds numbers, the crossover is shown to offset the gains in reactant conversion with the introduction of the corrugation. In addition, the benefits in terms of limiting current density with corrugated RFBs are mainly associated with the increase in reactive area with its use.

Compliant riblets: Problem formulation and effective macrostructural properties

Small-scale, deformable riblets, embedded within the viscous sublayer of a turbulent boundary layer and capable to adapt to the overlying motion, are studied. The wall micro-grooves are made of a linearly elastic material and can undergo small deformations; their collective behavior is assumed to occur over a large, elastic wavelength. The presence of two length scales allows for the use of a multiscale homogenization approach yielding microscopic problems for convolution kernels and parameters, which must then be employed in macroscopic boundary conditions to be enforced at a virtual wall through the riblets. The results found suggest that, in analogy to the case of rigid riblets, compliant, blade-like wall corrugations are more effective than triangular riblets in reducing skin friction drag, provided the spanwise periodicity of the indentations is sufficiently small for the creeping flow approximation to be tenable.

Heat transfer intensification in an actuated heat exchanger submitted to an imposed pressure drop

This paper is dedicated to the analysis of the improvement of heat transfer and the reduction of the pressure losses induced by the use of an active exchanger of millimeter size in a cooling loop. For pressure conditions imposed at the terminals of such a mini-channel whose upper wall is deformed by a progressive sinusoidal wave and for low Reynolds numbers (Re < 1000), we study the influence of the deformation parameters on the thermo-hydraulic performance of the exchanger (flow, heat transfer). The mechanical power applied to the deformed wall is connected to these parameters as well as to the pressure difference imposed by the external pump. The overall performance increases slightly with the value of the mechanical power up to a critical value for a given wall corrugation. Nevertheless, overall performance is up to 2 orders of magnitude higher than conventional static corrugated channels.

Impact of the slip condition on the resonance of a film flow over an inclined slippery topography plate

This study addresses the linear and nonlinear resonance of the film flow on an inclined slippery topography plate in the frame of long-wave theory. The influence of the surface tension is taken into account. The fluid flow is assumed to be steady, and confined to the limit of a small amplitude of the wall corrugation. The influence of the slip condition is the main factor in the study. The effects of various parameters on the flow properties, and the instability criteria through some numerical applications were investigated.

Effect of wall corrugations on scalar transfer to a wavy falling liquid film

Direct numerical simulation is employed to study the effect of small-scale wall corrugations on scalar transfer through the wavy surface of a vertically falling liquid film in interaction with a strongly confined counter-current gas flow. Three wall geometries are considered: (i) a flat wall for reference; (ii) a sinusoidal corrugation typically found on structured packings in chemical engineering devices; and (iii) a heuristic design consisting of isolated semicircular bumps distanced by the wavelength of the surface waves. We consider the limiting case of a Dirichlet condition for the transported scalar (temperature or mass fraction) at the liquid–gas interface and focus on liquid-side transport. We consider convection-dominated regimes at moderate and large Péclet numbers, representative of heat and mass transfer respectively, and confront forced and noise-driven wave regimes. Our results show that sinusoidal wall corrugations increase transfer by up to 30 per cent in terms of the exchange length required to transfer a fixed amount of the transported quantity. A slightly greater intensification is achieved through the bump-shaped corrugations, which intermittently disrupt the moving-frame vortex forming within the large-amplitude solitary waves, allowing these to replenish with unsaturated liquid. However, when the velocity of the strongly confined gas flow is increased above a certain threshold, the bumps can trigger the flooding of the channel.

Flow dynamics in longitudinally grooved duct

Flow in a finite-width rectangular duct with a corrugated top-bottom wall has been studied. The primary goal is to establish geometries that allow early flow destabilization at a possibly low drag increase. The flow is assumed periodic in the streamwise direction and bounded by the duct sidewalls in the spanwise direction; the top and bottom wall corrugations have a form of sinusoidal waves oriented transversely to the flow and form longitudinal grooves; i.e., the lines of constant elevation (or phase) are parallel to the direction of the flow. The analysis is performed up to the Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is focused on the properties of the two-dimensional base flow. Mainly, the dependence of hydraulic losses and drag reducing properties on duct’s geometry is characterized. The second part of the analysis discusses the onset of the three-dimensional travelling wave instability over a wide spectrum of geometric configurations. Linear stability is investigated by means of the direct numerical simulation of the Navier-Stokes equations. Critical conditions for the onset of instabilities at a range of geometric parameters are determined. Finally, the nonlinear saturation of unstable modes and the resulting secondary flows are examined. We have shown that in the state resulting from the nonlinear saturation of the disturbance, the flow becomes more complex while the drag reducing properties of the base flow can be maintained.

DNS of Turbulent Flows in Ducts with Complex Shape

We carry out Direct Numerical Simulation (DNS) of flows in closed straight ducts with complex peripheral shape. To perform the simulations the Navier-Stokes equations in cylindrical coordinates are discretized by a second-order finite difference scheme, and the immersed-boundary technique is used to resolve the flow close to walls of complex shape. The basic geometry is a circular pipe of radius R, with imposed sinusoidal perturbations of the type $\eta R \sin (N_{w}\theta )$ . Simulations by varying N w at fixed η were performed to investigate the effect of the perturbation wavenumber. Additional simulations by fixing N w and varying η also allow to investigate the influence of the amplitude of the wall corrugations. The modifications of the near-wall structures due to change in the shape of the walls are well depicted through contour plots of the radial component of the vorticity. The presence of geometrical disturbances anchors the structures at the locations where curvature changes, and the shape of the structures is strongly linked to the amplitude of the wall corrugation. Our interest is also in understanding the influence of the shape of the surface on wall friction. We were expecting some changes in the profile of the total stress with respect to that of the circular pipe, which instead were not found. This is a first indication that changes in the near-wall region do not affect the outer region, and that Townsend’s similarity hypothesis holds.

Radiation of charged particle bunches in corrugated waveguides with small period

Bunch radiation in periodical waveguides was mainly analyzed for situations when wavelengths are comparable to the structure period (Smith-Purcell emission). However, it is also interesting to study long wave radiation with wavelengths which are much greater than the structure period. In this paper, the electromagnetic field is analyzed using the method of equivalent boundary conditions. According to this approach, the exact boundary conditions on the complex periodic surface are replaced with certain equivalent conditions which must be fulfilled on the smooth surface. We consider a vacuum circular waveguide with a corrugated conductive wall (corrugation has rectangular form). The charge moves along the waveguide axis. The period and the depth of corrugation are much less than the waveguide radius and wavelengths under consideration. Expressions for the full field components and the wave field components are obtained. It is established that radiation consists of the only one TM waveguide mode which is excited if the charge velocity is more than certain limit value. Dependencies of the frequency and amplitude of the mode on the charge velocity and parameters of corrugation are analyzed. It is demonstrated that typical amplitude of waveguide mode from the ultra relativistic bunch has the same order as one in the ordinary regular waveguides with dielectric filling. In order to verify the method applied in this work we have simulated the electromagnetic field using the CST Particle Studio. For this purpose, we have considered the charged particle bunch with negligible thickness and Gaussian longitudinal distribution. It has been shown that the coincidence between theoretical and simulated results is good. This fact confirms that the theory based on the equivalent boundary conditions adequately describe the radiation process in the situation under consideration. The obtained results can be useful for development of methods of the electromagnetic radiation generation and technique of the wakefield acceleration of charged particles.

Instability in a channel with grooves parallel to the flow

Flow in a channel with corrugated walls has been studied, with the primary goal of establishing channel geometries that enhance achievable mixing at possibly low drag increase. The wall corrugation has the form of a sinusoidal wave oriented transversely, i.e., the lines of constant elevation (or phase) are parallel to the direction of the flow. The analysis is performed up to the Reynolds numbers resulting in the formation of secondary states. The first part of the analysis is focused on the properties of the two-dimensional, base flow. Mainly, the dependence of the drag on the channel’s geometry is characterized. The second part of the analysis discusses the onset of the three-dimensional traveling wave instability. Linear stability is investigated by the Direct Numerical Simulation of the Navier-Stokes equations. Critical conditions for the onset of instabilities at a range of geometric parameters are determined. Finally, nonlinear saturation of the unstable modes and the resulting secondary flows is examined. It is shown that the drag reduction property of the base flow can be maintained in the state resulting from non-linear saturation of the disturbance.

Low-Frequency Instabilities of Electron Beams in Weakly Irregular Transportation Channels

Evolution of low-frequency instabilities degrades electron beams in beam transportation channels and, not less importantly, deteriorates the coherence of the output radiation produced by microwave generators based on the use of such beams. These instabilities also determine the beam dynamics, including that associated with transitions of the beams from one stationary state to another. In this work, we use the method of coupled waves to study the stability of stationary states of the beams with high electron densities in weakly irregular vacuum beam transportation channels, specifically, in channels with shallow periodic wall corrugations. It is shown that in this case, the Bursian instability of the absolute type can evolve, which leads to a jump-wise transition of the beam to a state with a lower electron density.