Turbulent Flow Characteristics Research Articles

Numerical study of location and depth of rectangular grooves on the turbulent heat transfer performance and characteristics of CuO-water nanofluid flow

This current work expresses numerical simulation of forced turbulent flow convection in a grooved cylinder. Rectangular grooves with a spacing of A = 1, A = 1.1, and A = 1.3, and groove depth to cylinder diameter of e/D = 0.1 and 0.2 were considered. This research concentrates on the effect of groove depth, location of the grooves and CuO nanoparticles on the heat transfer for Reynolds numbers 10000, 12,500, 15,000 and 17,500 in volume fractions of 0, 1, 2, 3 and 4% of nanoparticles. Results show that grooves improve heat transfer. This behavior at a lower A ratio results in a significant Nu number increase so that the highest Nu number occurs for A ratio of 1, 1.1 and 1.3. Increasing e/D ratio, due to increasing the channel section in this area, results in loss of velocity and dissipation of flow momentum, resulting in lower convective heat transfer and lower Nu number. Changing the pitch for e/D = 0.1 results in a 1.1 to 1.6 times increase of Nu number compared with the smooth channel, and for e/D = 0.2 this value is 1.1–1.5 times the smooth channel for similar Re, φ and geometry. Changing groove pitch at e/D = 0.1 results in a 2.1–2.9 times increase in friction factor compared with the smooth channel in similar conditions. For e/D = 0.2, this increase is 1.8–2.8 times the smooth channel. In low Re, the thermal performance is higher than in higher velocities. This is because the grooved channel acts as a smooth channel at high Re, and the average Nu does not have significant growth.

Pulsating Turbulent Flows through a Square Pipe

Pulsating turbulent flows in a square pipe are studied numerically. The flow dominance regime in which the fluid flow rate remains positive in all phases of the oscillatory cycle is considered. The flows are studied at several oscillation frequencies. The results are compared with oscillating laminar flows and a steady turbulent flow in a square pipe, as well as with pulsating turbulent flows in a round pipe. The integral and fluctuating characteristics of turbulence and their dependence on the oscillation frequency are determined. In particular, it is found that at the considered Reynolds number Re = 2200 the friction coefficient in pulsating flows turns out to be lower than that in the stationary flows. The drag reduction increases with growth of the oscillation period and reaches 14.7%. A distinctive feature of turbulent flows in pipes of rectangular cross-section is the occurrence of secondary flows of Prandtl’s 2nd kind. The details of secondary flows under the pulsating flow conditions are studied at length.

Heat Transfer and Entropy Generation Analysis of a Curved Solar Air Heater With a Sinusoidal Absorber Plate

Abstract Recently, many studies have reported that a curved solar air heater (CSAH) performs better than a conventional flat SAH without using any extra material. It only requires geometrical modification. The present investigation is a two-dimensional numerical study of flow, heat transfer, and entropy generation characteristics of a CSAH having a sinusoidal profile absorber plate. Reynolds number (Re) and relative roughness pitch (λ/a) have been varied from 3800 to 18,000 and 7.143 to 17.857, respectively, while keeping the value of relative roughness height (a/Dh) at 0.042. The finite volume method (FVM) and SST k–ω model have been used to solve the governing equations. The average Nusselt number and average friction factor have been calculated to find the thermo-hydraulic performance parameter (THPP), which further helped determine the optimal arrangement of the number of sinusoidal waves in the absorber plate of the SAH. The maximum value of THPP developed with the proposed setup was found to be 5.9778. Turbulent flow features have been represented in the form of contours. Correlations have also been developed for Nuavg_r and favg_r as a function of Re and λ/a. Entropy generation per unit length due to heat transfer and fluid friction has been graphically represented.

Numerical study on conjugate heat transfer in a liquid-metal-cooled pipe based on a four-equation turbulent heat transfer model

Conjugate heat transfer between liquid metal and solid is a common phenomenon in a liquid-metal-cooled fast reactor's fuel assembly and heat exchanger, dramatically affecting the reactor’s safety and economy. Therefore, comprehensively studying the sophisticated conjugate heat transfer in a liquid-metal-cooled fast reactor is profound. However, it has been evidenced that the traditional Simple Gradient Diffusion Hypothesis (SGDH), assuming a constant turbulent Prandtl number (Prt, usually 0.85 - 1.0), is inappropriate in the Computational Fluid Dynamics (CFD) simulations of liquid metal. In recent decades, numerous studies have been performed on the four-equation model, which is expected to improve the precision of liquid metal’s CFD simulations but has not been introduced into the conjugate heat transfer calculation between liquid metal and solid. Consequently, a four-equation model, consisting of the Abe k−ε turbulence model and the Manservisi kθ−εθ heat transfer model, is applied to study the conjugate heat transfer concerning liquid metal in the present work. To verify the numerical validity of the four-equation model used in the conjugate heat transfer simulations, we reproduce Johnson’s experiments of the liquid lead-bismuth-cooled turbulent pipe flow using the four-equation model and the traditional SGDH model. The simulation results obtained with different models are compared with the available experimental data, revealing that the relative errors of the local Nusselt number and mean heat transfer coefficient obtained with the four-equation model are considerably reduced compared with the SGDH model. Then, the thermal-hydraulic characteristics of liquid metal turbulent pipe flow obtained with the four-equation model are analyzed. Moreover, the impact of the turbulence model used in the four-equation model on overall simulation performance is investigated. At last, the effectiveness of the four-equation model in the CFD simulations of liquid sodium conjugate heat transfer is assessed. This paper mainly proves that it is feasible to use the four-equation model in the study of liquid metal conjugate heat transfer and provides a reference for the research of conjugate heat transfer in a liquid-metal-cooled fast reactor.

Numerical simulation and experimental research of fiber motion in vortex spinning

The application of high speed air flow in the textile field represents the frontier development direction in this field. However, the coupling mechanism between air flow and fiber is extremely complicated which greatly limits the development and application of new textile technologies. For this reason, this research study is intended to focus on the common cutting-edge basic scientific problem of the air-flow-fiber coupling mechanism, the vortex spinning technology is taken as a breakthrough point for research. Three-dimensional numerical models of air flow in vortex spinning nozzle and a free-end fiber were established. The hybrid grids including the structured hexahedral grids and the unstructured tetrahedral grids were used to divide the air-flow computational region, the realizable κ- ε model was used to solve the turbulent characteristics of air flow, and the wall function method was used to solve the air flow in the near wall region. The displacement and deformation of a single free-end fiber under the action of the air-flow force was solved by the second-order nonlinear double asymptotic method and interpolation method. The dynamic twist process of a free-end fiber was simulated in three-dimensional space by taking into account the fiber characteristics, such as straightening, bending, and torsion. In addition, a high magnification microscope was used to observe the free-end fiber motion during the spinning process. The results show that the numerical simulation is consistent with the experimental observation, proving that dynamic numerical simulation can solve difficult problems in the unobserved dynamic twisting process, and this deepens the understanding of the spinning mechanism in vortex spinning.

Numerical investigation on the swirling vortical characteristics of a Stairmand cyclone separator with slotted vortex finder

The slotted vortex finder (SVF) represents a novelly modified cyclone vortex finder, which is validated to be valuable and prospective for industrial applications. The main purpose of present study is to illustrate the effect of slotted vortex finder on the swirling turbulent flow characteristics of cyclone separator in comparison with conventional vortex finder (CVF). Based on three cyclone models (CVF, SVF_D1, SVF_D2), the differences of swirling vortical characteristics between SVF and CVF models are comprehensively tested and the influence of SVF insertion length on the cyclone performance was discussed. The overall detailed features and variations of flow pattern, such as velocity profile distribution, unsteady particle tracking, swirl number comparison and special flow phenomena of vortex eccentricity in the whole cyclone separator body, are analyzed in detail. Specifically, The SVF_D2 model could improve the cyclone separation efficiency (about 20% reduction of pressure drop and 4.2% reduction of cut off size) and also reduce 40% of central vortex rotation frequency compared with CVF model at vin = 16.1 m/s. The current study is beneficial to further clarify the influence of SVF on the mechanism of the particle separation motion in cyclone separator and identify the characterization differences between traditional cyclone separator and cyclone with installation of SVF.

Self-similar temporal turbulent boundary layer flow

Direct numerical simulations of temporally evolving boundary layer flows are considered with solutions restricted to self-similar profiles. A new set of modified Navier–Stokes equations is solved with periodic boundary conditions in the streamwise direction, and solutions reach statistically steady states, independent of the initial conditions. The results are presented for different cases, with and without a pressure gradient, and found to be in agreement with existing results of spatial turbulent boundary layer flows. Thus, self-similar temporal solutions are able to reproduce the general features of turbulent boundary layer flows. Finally, the model is applied to simulate a turbulent spot in equilibrium, which is difficult to obtain otherwise.

Numerical investigation of turbulent mixed convection flow and heat transfer characteristics of 2 × 2 subchannels with spacer grids

AbstractIn turbulent mixed convection conditions, flow and heat transfer can deteriorate under specific conditions, thus affecting the performance of the safety of the system, which could imperil the safety of the nuclear reactor. In this paper, by analyzing the velocity, temperature distributions, and other thermal‐hydraulic parameters, the steady‐state computational fluid dynamics approach with the SST k–ω turbulence model used in this study was verified. Then, flow and heat transfer characteristics in turbulent mixed convection inside 2 × 2 subchannels with and without spacer grids were investigated. The results showed that the velocity profiles were distorted and the heat transfer capacity was impaired due to the influence of buoyancy. The Nusselt number ratio (Nu/Nuf) between turbulent mixed convection and forced convection increased with the increase of Reynolds number (Re) until unity but decreased with the increases of Grashof number (Gr) and Buoyancy parameter (Bo*).

Characteristics of Shallow Flows in a Vegetated Pool—An Experimental Study

Pools are often observed in gravel-bed rivers, together with the presence of vegetation patches. In the present study, a conceptual model of a gradual varied flow with both convective deceleration and acceleration flow sections has been constructed in a flume to study turbulent flow structures. Vegetation patches with extended canopies were planted in the pool sections in order to increase the thickness of the boundary layer inside the inner zone. The effects of different flows (namely decelerating, uniform and accelerating flows) along an artificial pool on flow velocity, shear stress and bursting events have been investigated. In addition, due to the occurrence of secondary currents in shallow streams, the characteristics of turbulent shallow flow have been investigated along two axes that are parallel to the sidewall of the flume. The results showed that the application of the log law should be used with care to estimate shear velocity along a pool with a vegetated bed. The presence of a vegetation patch causes an increase in Reynolds shear stress, especially along the entrance section of the pool where the flow decelerates. The results of the quadrant analysis reveal that the sweep and ejection events have the most dominant influence over the vegetation patch in the pool; however, the contributions of outward and inward events increase near the bed, especially in the entrance section of the pool where the flow is decelerating. The distribution of stream-wise RMS of turbulence intensity along the pool generally presents a convex shape.

FEATURES OF THE BOUNDARY LAYER ORGANIZATION IN TESLA DISC TURBINES

To ensure maximum efficiency of bladeless Tesla turbines, it is important to maintain a laminar flow regime within the boundary layer that forms on the disc surfaces. Depending on the flow regime, the state of the disc surfaces, and the geometry of the interdisk gaps, the nature of the boundary layer varies. It is crucial for the flow regime to remain laminar, and the distance between the discs should not exceed twice the thickness of the boundary layer. Experimental investigations of the characteristics of the boundary layer during the flow around turbine blades were proposed to determine the parameters necessary for achieving maximum efficiency. These experiments were conducted in an aerodynamic test rig that provided a uniform velocity field with minimal turbulence (0.7 %) within a speed range up to 0.33 Mach. The primary focus of these studies was to determine the location of the transition zone within the boundary layer, which allows for the examination of conditions for stable maintenance and characteristics of laminar flow. The transition zone was determined based on changes in the tangential friction stress in the experiments. The obtained results facilitated the establishment of the necessary dimensions for the inter-disk gaps and the optimum values of the similarity criterion Re from the perspective of flow regime. For a smooth surface, laminar flow within the boundary layer is maintained up to a relative coordinate of 0.17 x= from the start of the surface, across a wide range of Reynolds numbers. For a rough surface, the extent of the zone with a laminar boundary layer is approximately the same as that for a smooth surface at Re=3.6∙105. However, at Re=7.4∙105 the laminar flow terminates slightly earlier, at 0.13 x= , with a very short transitional zone between laminar and turbulent flow characteristics. The thickness of the laminar boundary layer on a smooth surface is 0.5…0.7 mm, while for a rough surface, it is slightly greater at 0.7…0.8 mm. Therefore, to ensure high efficiency of Tesla disc turbines, the distance between the discs should be maintained at 1…1.5 mm, considering the requirements for laminar flow.

Studies of Stable Stratification Effect on Dynamic and Thermal Roughness Lengths of Urban-Type Canopy Using Large-Eddy Simulation

Abstract Large-eddy simulations (LES) of neutrally and stably stratified turbulent flows over urban-type surfaces with relatively low plan area ratios are presented. Numerical experiments were performed for different shapes of streamlined objects and at different static stability. A new method for setting up a numerical experiment aimed at studying the heat and momentum transfer within the roughness layer and investigating the thermal and dynamic interaction between the turbulent flow and the surface as a whole has been proposed. This method enables us to obtain an equilibrium state for values of parameters determining the characteristics of the external turbulent flow chosen beforehand. A strong dependence of the thermal roughness length on stratification was found. We also discuss the physical mechanisms that lead to the maintenance of turbulence above the canopy when the ground surface is strongly cooled. Significance Statement Using LES, we identify a mechanism that contributes to the maintenance of turbulence in the atmospheric boundary layer under the condition of strong surface cooling. Although these results are obtained for an urban canopy, we believe that the qualitative conclusions should be general for a wide type of surfaces with large-scale roughness elements. We hope that the new results will be useful for improving surface flux schemes in NWP and climate atmospheric models that suffer from attenuated mixing in a very stable boundary layer and the effect of “surface decoupling.” The found effect gives a physically justified alternative way to parameterize the air–surface exchange under strong stability compared to the often ad hoc modification of the MOST universal functions.

Experimental and numerical studies of the effects of the contraction ratios on the swirling flow characteristics of the model combustor outlet in lean gas turbines

Large Eddy Simulation (LES) is utilized in this work to study isothermal turbulent swirling flow characteristics for a lean partially premixed gas turbine model combustor. The goal is to investigate the influence of contraction ratio (CR) variation on the vortex breakdown phenomena features and the turbulence structure in these combustors. Particle image velocimetry (2D-PIV) measurements were carried out on a single-case model combustor using (air-air) phase to perform the mean flow behavior and the validation process under atmospheric conditions with CR equal to 0 (largest diameter, Dinlet = Doutlet), the equivalence ratio (φ) of 0.3, swirl number of (Sn) = 0.66 and Reynolds number of (Re) = 42,000. While five test cases with various CRs were applied in LES under the same conditions using (air-CH4) phase to predict the vortical structure and the precession vortex core (PVC). The CRs ranged as follows: 0, 50 %, 60 %, 70 % and 80 % (smallest diameter). Experimental and LES results show that there was a reasonable agreement between the PIV and LES results with maximum deviations of 2.8 % and 4.65 % for the normalized mean axial and radial velocities, respectively. As the CR was increased, the pressure drop and the mean axial velocity increased linearly at the contraction part. In addition, the downstream stagnation point and the size of the central toroidal recirculation zone (CTRZ) stabilized when CR = 60 %, 70 %, and 80 %. The swirl level was further enhanced by 40 % when CR = 60 % and 80 %. The presence of CR successfully suppressed the pressure and axial velocity fluctuations generated in the shear layer zones by 35 %. LES data was analyzed by Fast Fourier Transformation (FFT) and Proper Orthogonal Decomposition (POD) to investigate the PVC dynamics. The FFT showed four dominant frequencies as a result of the appearance of the PVC and vortex breakdown oscillation. The frequency of PVC (fpvc) decreased linearly with an increase in the CR where the fpvc was 20.8 Hz when CR = 0 and became 12.5 Hz at CR = 80 %. In contrast, the other frequencies were still constant even with increased CR at 187 Hz, 562 Hz, and 979 Hz. The POD analysis showed the first mode was more energetic and had 40 % of the total pressure fluctuations.

Особенности турбулентности в электромагнитном перемешивателе жидкого металла

In the research work, conduction velocity sensors were successfully used to study the characteristics of turbulent flows arising in a liquid metal under the action of a rotating magnetic field in a vertical cylinder. At a certain magnitude of electromagnetic influence, on the graphs showing spectral energy of velocity pulsations there is observed a slope of ‘-5/3’, indicating developed homogeneous isotropic turbulence and spreading in a frequency range of up to two decades. The level of velocity pulsations varies from 4 to 10 % of the azimuthal rotation velocity. It is shown that the identified peaks in the velocity pulsation spectra correspond to the frequency of the liquid metal rotation around the cylinder axis. A nonlinear graph of the dependence of the liquid metal rotation frequency on the current frequency in the coils with a maximum near 50-75 Hz was obtained.

Numerical Simulation on Turbulent Flow Characteristics Analyzation of Lead-Bismuth Alloy in Narrow Rectangular Channel

Numerical Simulation on Turbulent Flow Characteristics Analyzation of Lead-Bismuth Alloy in Narrow Rectangular Channel

Performance of mitigation measures on emitted droplets in dental atomization procedure

Cross-infection risk induced by dental-related droplets and aerosol particles has challenged service providers and patients alike. The dental clinic has been widely treated as one of the most vulnerable healthcare organizations with a high exposure risk to infection. The present study aims to investigate the effect of high-volume evacuation (HVE) on the emitted droplets and aerosol particles during dental atomization procedures. Ultrasonic scaling, one type of atomization procedure, is performed in the dental clinic. The laser light scattering method is employed to visualize the immediate moment with and without the cooperation of HVE on ultrasonic scaling. The Proper Orthogonal Decomposition analysis is employed to investigate the turbulent flow characteristics. The previous hypothesis about the moderate performance of HVE on tiny high-velocity droplets has been proven in the present study. The HVE can be characterized as significantly low-threshold measures to reduce the contaminated region. Besides, a pair of vortexes presented near the facial region of dental professionals will be eliminated when cooperating with HVE. The HVE can significantly reduce the emitted droplets (about 60%) and the airborne lifetime of suspended particles. HVE acting as additional mitigation measures could augment traditional/primary decontamination strategies such as ventilation and personal protective equipment.

Experimental and Numerical Study of Open Channel Flow with T-Section Artificial Bed Roughness

Experimental and numerical studies have been conducted on the effects of bed roughness elements such as cubic and T-section elements that are regularly half-channel arrayed on one side of the river on turbulent flow characteristics and bed erosion downstream of the roughness elements. The experimental study has been done for two types of bed roughness elements (cubic and T-section shape) to study the effect of these elements on the velocity profile downstream the elements with respect to different water flow discharges and water depths. A comparison between the cubic and T-section artificial bed roughness showed that the velocity profile downstream the T-section increased in smooth side from the river and decrease in the rough side from it compared with the case when a cubic artificial bed roughness is used. By comparing the results for the element shapes, it can be notices that the T-section bed roughness element more effective compared to cubic shape for both sides of the channel. The numerical method has been done using Computational Fluid Dynamic (CFD) method. A validation for the CFD model with the experimental study have been carried out for a specific flow discharge and water depth. The results indicated that the velocity distribution profiles downstream the bed roughness elements in both sides shown very good agreement for manning coefficients between the numerical and experimental studies. The range of errors between the experimental and numerical study have been calculated using Root Mean Square Error (RMSE) approach, which is found that the RMSE is approximately equal to 1 in case of cubic bed roughness and the RMSE is about 1.5 in case of T-section bed roughness for both smooth and rough sides. Furthermore, the influence of the velocity profile and the bed erosion downstream of the T-section element under the effect of tides have been investigated using the CFD method, which is commonly happened in Shat al-Arab south of Iraq. The results show that the tide of the flow has a reverse effect on the velocity profiles for both sides. Since the velocity profile downstream of bed roughness region increase in the rough side and decrease in the smooth side compared with the normal flow of the river.

Effect of fluid distribution on the cooling performance of hybrid microchannel and slot-jet impingement system

Hybrid microchannel heat sink and slot-jet impingement system (MCSJ) is favored by researchers for its advantages in the cooling of high-heat-flux electronic device. In this study, the effect of fluid distribution on the hydraulic and thermal performance of MCSJ is numerically investigated with a realizable k-ε turbulence model. Firstly, the influence of the cooling water entrance position on the turbulent flow and heat transfer characteristics of MCSJ was studied. It is found that the MCSJ-2 exhibits the best cooling performance. Compared with the conventional design (MCSJ-5), when the inlet water velocity was set as v = 6 m/s, 8 m/s, and 12 m/s respectively, the total thermal resistance of MCSJ-2 decreased by 2.43 %, 2.07 % and 0.71 %, correspondingly; and the temperature difference of the bottom surface in MCSJ-2 decreased by 11.08 % (v = 6 m/s), 6.86 % (v = 8 m/s), and 4.99 % (v = 12 m/s), respectively. Measures to improve the uniformity of fluid distribution among the microchannels in MCSJ-2 were then analyzed. The results show that inserting fin-ribs in the distribution chamber of MCSJ-2 can effectively decrease the pressure drop and improve the thermal uniformity performance of the hybrid system. The fin-ribs’ height and length have different effects on the hydraulic and thermal performance of MCSJ-2.

Characteristics of Heat Transfer and Turbulent Flow in a Baffled Pipe with Different Arrangements

In the heat transfer, fluid flow and energy fields, baffles are an advanced enhancer to improve heat transfer and fluid mixing by working as an obstacle to the flow particles and then increasing the turbulence. The present paper numerically investigates the thermal performance of a circular pipe with a centralized baffle in two arrangements, with a Reynolds number (Re) (ranging from 10,000-50,000) under constant wall heat flux boundary conditions. Ansys Fluent software is used to solve the flow field considering six conical baffles with different Pitch ratios (PR) (from 1 to 5). Results show that baffles shape, arrangement, and PR have a significant impact on the properties of flow and heat transfer. The obtained results show an effective role for the baffles to promote thermal performance when it is used in heated pipes. Heat transfer rate is increased for the baffled pipe by 1-2 compared with the smooth pipe. Moreover, the best value of friction factor, thermal performance, and Nusselt number is recorded at PR= 5 at Re=30000 in the baffled pipe for the second arrangement.

Three-dimensional density measurements of a heated jet using laser-speckle tomographic background-oriented schlieren

Tomographic background-oriented schlieren (TBOS) is a promising optical technique for 3D density field measurement in turbulent flows. Path-integrated information on refractive index gradients is captured by cameras looking through the flow at textured background patterns in the form of apparent displacements of the patterns. A tomographic reconstruction of the three-dimensional refractive index gradients is performed, from which the instantaneous three-dimensional density field is obtained. Most TBOS measurements to date have been limited by large temporal blurring and/or large defocus blurring. Our 15-camera experimental set-up uses a pulsed laser for both illumination and creation of a laser-speckle background pattern. The high-power laser ensures adequate exposures in nanoseconds, so temporal integration is minimised in each measurement. The beam is spread to illuminate a surface that is observed by fifteen cameras that are evenly spaced circumferentially around the flow. Laser speckle patterns are observed by the cameras due to the diffuse reflection and interference of coherent light from roughness on the surface. We develop a methodology for selecting the optimal focal length, focus distance, and lens aperture by considering the compromise between displacement sensitivity, defocus blurring and speckle size. Low temporal- and spatial-blurring 3D temperature field measurements with excellent resolution of turbulent flow features are obtained and good agreement with thermocouple. Classical behaviours of the potential core instability such as vortex rollup and radial ejections are identified. The behaviour of the potential core is examined further, which reveals that the potential core undergoes considerable deformation and fragmentation during the transition to turbulence.

Serpentine and furrowed wavy channels-based enhancement in heat transfer for a rocket engine chamber

The thermal protection of the rocket engine combustion chamber is one of the fundamental challenges in supersonic flight. This paper investigates serpentine and furrowed wavy cooling channels with a rectangular cross-section to enhance heat transfer performance and hydrogen turbulent fluid flow characteristics. Ansys fluent was used to investigate the effects of configuration, wavy amplitude, and channel wavelength on the heat wall temperature, Nusselt number, coolant velocity, pressure drop, turbulent kinetic energy, and thermal stratification phenomena. Four different wave amplitudes and three wavelengths are compared to determine the optimal structure required to achieve the best heat transfer enhancement with acceptable pressure drop. Compared to the straight channel, the maximum temperature of the furrowed channel (Case 6) was decreased by 15.38% at an amplitude of 0.2 mm. Furthermore, the thermal performance factor is evaluated for eight furrowed wavy structures. The result is shown that the structure with an amplitude of 0.2 mm and a wavelength of 1 mm (Case 6) can demonstrate better thermal performance, which is increased by 31.55% compared to the straight channel. The wavy surfaces cause separation in diverging zones and secondary flows in converging zones, which disturbs the boundary layer, enhances particle mixing and improves convective heat transfer.