Upstream Body Research Articles

Cyclist Reynolds number effects and drag crisis distribution

The Reynolds number effects on body limbs of a cyclist model, namely leg and arm, are investigated via robotic volumetric Particle Image Velocimetry measurements in the velocity range from 5 ​m/s to 25 ​m/s. The near wakes of such body limbs feature recirculation regions whose width and length are governed not only by the taper of the body parts, but also by the presence of coherent streamwise vortical structures. Moreover, the interaction with the wakes of the upstream body parts plays a role in the local wake properties. While reductions of the wake width are observed on both lower leg and arm with increasing free-stream velocity, the wake of the upper leg follows an opposite trend increasing in size at higher velocity. Such variations of wake width with the Reynolds number are related to the behaviour of the local drag coefficient, indicating a drag crisis behaviour on both leg and arm. The distribution of the so-called critical velocity upon these body segments is discussed, as it determines the freestream speed where a minimum value for the drag can occur.

Prediction of Unsteady Developed Tip Vortex Cavitation and Its Effect on the Induced Hull Pressures

Reducing the on-board noise and fluctuating pressures on the ship hull has been challenging and represent added value research tasks in the maritime industry. Among the possible sources for the unpalatable vibrations on the hull, propeller-induced pressures have been one of the main causes due to the inherent rotational motion of propeller and its proximity to the hull. In previous work, a boundary element method, which solves for the diffraction potentials on the ship hull due to the propeller, has been used to determine the propeller induced hull pressures. The flow around the propeller was evaluated via a panel method which solves in time for the propeller loading, trailing wake, and the sheet cavities. In this article, the propeller panel method is extended so that it also solves for the shape of developed tip vortex cavities, the effects of which are also included in the evaluation of the hull pressures. The employed unsteady wake alignment scheme is first applied, in the absence of cavitation, to investigate the propeller performance in non-axisymmetric inflow, such as the inclined-shaft flow or the flow behind an upstream body. In the latter case, the propeller panel method is coupled with a Reynolds-Averaged Navier–Stokes (RANS) solver to determine the effective wake at the propeller plane. The results, including the propeller induced hull pressures, are compared with those measured in the experiments as well as with those from RANS, where the propeller is also simulated as a solid boundary. Then the methods are applied in the cases where partial cavities and developed tip vortex cavities coexist. The predicted cavity patterns, the developed tip vortex trajectories, and the propeller-induced hull pressures are compared with those measured in the experiments.

Triangular Separation Distance Effects on Wave Electrical Energy Harvester Performance

Energy scavenging has become a topic of interest toward green and environmentally friendly. Vortex generated in the wake region behind a bluff body is potential to be harvested and transform the mechanical vortices into electrical energy. Therefore, the study of the fluid flow and piezoelectric material is highly potent and a promising research area. Thus, the vortex-induced vibration (VIV) energy harvesting of two bluff bodies in a tandem arrangement is investigated using the 3D simulation. There are four sets of bluff bodies with various distance ratio, x/D from 3 to 6, were analyzed in this simulation. The coupling analysis was analyzed using ANSYS Transient Structural and computational fluid dynamic Fluent module. The triangular width, to 100 mm and the fluid average flow velocity is 1.46 ms−1, which corresponds to Reynold number (Re) of 10k. Four types of analysis have, out; velocity vector, turbulence kinetic energy, piezoelectric tip deformation, and generated output voltage. The results show the bluff shape with spacing ratio 6 has better vortex shedding formation and turbulence kinetic energy formed on both upstream and downstream triangular bluff body. The tips mesh displacement for piezoelectric is highest at space ratio 6 with 7.0 x 10−5 essential, and after 10s the beam deflection is continuing at around 1 x 10−5 m. While the voltage generated is, at spacing ratio 6 with 0.2 v produced. The obtained results are essential to VIV analysis of the dual triangular cylinder with piezoelectric film, which is vital in energy scavenging knowledge.

Flow-induced oscillations of three tandem circular cylinders in a two-dimensional flow

Flow-induced oscillations of three identical circular cylinders, arranged in tandem configuration, are studied via two-dimensional finite element computations. Cylinders are mounted on elastic supports in the streamwise and transverse directions. Each downstream cylinder is placed at a distance of 5 diameters (5D) from its immediate upstream neighbor. Nondimensional mass ( m∗) of 2, and zero damping (ξ) are considered. Simulations are performed with the objective of understanding dynamic response of cylinders, as they are subject to wake interference, at constant Reynolds number, Re=150, and for varying reduced velocity (U∗) in the range of U∗=2−14. Similar to the behavior of an isolated cylinder at low Re, oscillation response of the upstream body exhibits initial excitation and lower lock-in regimes. However, for both the downstream cylinders, depending on their amplitude and frequency responses, the synchronization regime of U∗ can be categorized into three distinct regions: initial excitation, upper and lower lock-in regions. First downstream cylinder undergoes gradual transition between initial excitation and upper region, whereas the second downstream body exhibits this transition in two phases, which are separated by a periodic oscillation response regime. Upper lock-in region is characterized by periodic oscillations, while amplitude is modulated in the lower region. Only 2S shedding mode is observed for all the U∗ considered.

Wake-induced vibration of a circular cylinder at a low Reynolds number of 100

Wake-induced vibration (WIV) of a circular cylinder in the wake of a stationary bluff body at a low Reynolds number of 100 is numerically investigated in this work. Square prism, rectangular plate, and triangular prism with the same projected width as the diameter of the circular cylinder are employed as the upstream bluff body to examine the effect of obstacle’s shape on the wake interference and WIV. The downstream circular cylinder is allowed to oscillate in both inline and crossflow directions. Three spacing ratios of 2, 4, and 6 are considered in the computations that carried out for a wide range of reduced velocities (Ur = 2–20). In terms of shear layer reattachment, vortex impingement, and wake interference, three distinct flow regimes are identified for the upstream-stationary-downstream-vibrating tandem cylinders, i.e., continuous reattachment regime, alternating reattachment regime, and coshedding regime. The wake flow pattern is sensitive to the spacing ratio and the reduced velocity. Due to the vigorous streamwise response, the gap between the tandem cylinders varies over time and hence the switching of wake regime. Both the hydrodynamic forces and vibration response are tightly associated with the wake interaction. Among the three configurations, the cylinder behind a square prism possesses the largest cross-flow amplitude, while the cylinder behind a plate and that behind a triangular prism present more oscillating characteristics in the response amplitude, due mainly to the unstable and irregular vortex evolution.

Passing the Wake: Using Multiple Fins to Shape Forces for Swimming.

Fish use coordinated motions of multiple fins and their body to swim and maneuver underwater with more agility than contemporary unmanned underwater vehicles (UUVs). The location, utilization and kinematics of fins vary for different locomotory tasks and fish species. The relative position and timing (phase) of fins affects how the downstream fins interact with the wake shed by the upstream fins and body, and change the magnitude and temporal profile of the net force vector. A multifin biorobotic experimental platform and a two-dimensional computational fluid dynamic simulation were used to understand how the propulsive forces produced by multiple fins were affected by the phase and geometric relationships between them. This investigation has revealed that forces produced by interacting fins are very different from the vector sum of forces from combinations of noninteracting fins, and that manipulating the phase and location of multiple interacting fins greatly affect the magnitude and shape of the produced propulsive forces. The changes in net forces are due, in large part, to time-varying wakes from dorsal and anal fins altering the flow experienced by the downstream body and caudal fin. These findings represent a potentially powerful means of manipulating the swimming forces produced by multifinned robotic systems.

Effects of Downstream Structures on Aero Elastic Energy Harvesters From Wake-Induced Vibration

An upstream cylindrical bluff body connected to a tip body via an aluminum cantilever beam was tested as energy harvester in a wind tunnel. The characteristics and behavior of the different tip body configurations and lengths of aluminum cantilever beam were studied to optimize design to extract wind energy. Particular attention was paid to measure vibration amplitude and frequency response as a function of reduced velocity. Dynamic response showed that the device's behavior was dependent on both tip body shape and cantilever beam length. Flow visualization tests showed that high amplitude vibration was obtainable when a vortex was fully formed on each side of the downstream tip body. This was exemplified in a symmetrical triangular prism tip body at L/D1 = 5, where its structure's vibration frequency was close to its natural frequency. At such configuration, electrical energy was captured using a polyvinylidene fluoride (PVDF) piezoelectric beam of different load resistances, where an optimized load resistance could be found for each Reynolds number. Although power output and efficiency obtained were considerably weak when compared to those of traditional wind turbine, the design merits further research to improve its performance under various circumstances.

Aerodynamic Noise Simulation and Quadrupole Noise Problem of 600km/h High-Speed Train

The quadrupole aerodynamic noise is a difficult problem in numerical simulation of the aerodynamic noise. The Kirchhoff-Ffowcs Williams and Hawkings (K-FWH) equation method and the three-dimensional compressible Large Eddy Simulation (LES) method are adopted in this manuscript for aerodynamic noise accuracy simulation of 600km/h high-speed train. The influence of different distributions of penetrable integral surfaces on the results of far-field aerodynamic noise is discussed. The optimum combination form of penetrable integral surfaces is obtained. The aerodynamic noise of high-speed train considering quadrupole can be calculated efficiently and accurately by using the upstream body surface and wake area penetrable integral surface as sound source surface. The wake area penetrable integral surface should contain the main vorticity structure of the wake as far as possible and the surface vorticity amplitude should be insignificant. The contribution rate of the dipole and quadrupole to the total aerodynamic noise energy of high-speed train is different. The aerodynamic noise energy of the upstream measurement points is mainly dipole aerodynamic noise energy, while that of the downstream measurement points is mainly dipole and quadrupole noise energy. The method proposed in this manuscript is of great significance in the aerodynamic noise numerical simulation of 600km/h high-speed train.

Energy Concentration by Bluff Bodies—A Particle Image Velocimetry Investigation

Particle image velocimetry (PIV) of four cylinders with different cross sections were performed in a recirculating water channel at Reynolds numbers of 5000 and 10,000. The cylinders were split into two distinct categories; semicircular and convex-edged triangular (c-triangular) prisms which have a smooth diverging fore-face and a flat, backward facing step aft-face, and a trapezoid which has a flat fore face and a backward-facing step aft-face. The resulting streamwise and transverse velocity vectors (u and v, respectively) were analyzed to provide a qualitative comparison of the bluff body wakes to the circular cylinder, which is the standard upstream stationary body in wake-induced vibration (WIV) energy technology. The Reynolds stresses, turbulent kinetic energy (TKE), mean spanwise vorticity, and the energy in the fluctuating component of the wake were compared. The main findings are: (i) a convex fore-face and a backward-facing step aft face are more effective at converting the flow energy to temporal wake energy (+20%) compared to a circular cylinder, (ii) a trapezoid type shape is less effective at converting flow energy to temporal wake energy (−40%) compared to a circular cylinder, (iii) increasing Reynolds number reduces the efficiency of conversion of upstream flow energy to downstream transverse temporal energy. Utilizing stationary upstream bodies such as the semicircle and the c-triangle can result in concentrating more energy in the fluctuating components for the downstream transversely vibrating bluff body in a WIV system, and hence can realize in more efficient WIV technology.

Reduksi Gaya Drag Silinder Sirkular dengan Penambahan Square Disturbance Body Melalui Simulasi Numerik 2D Unsteady-RANS pada Reynolds Number 34800

Circular cylinder has a strong adverse pressure gradient. When a fluid flows around the circular cylinder, it will produce aerodynamics force. One of them is the drag force which strong enough. Hence, control of flow need to reduce the drag force with placed a disturbance body on the upstream side. The purpose of this study is to compare and complement the experimental research of drag reduction that has been done before. The aerodynamics characteristics of the disturbance body and cylinder are modelled in two dimensions Unsteady-RANS by using fluent with turbulent flow. It is found that the mean drag and the lift fluctuation of the cylinder can be reduced by the upstream disturbance body with the s/D = 0.107 (here s and D are side length of the disturbance body and the diameter of cylinder, respectively). The position of the disturbance body is varied at (α) 20o, 30o, 40o, 50o and 60o with a gap distance (δ = 0.4mm). Reynolds number based on cylinder diameter ReD = 3.48x10 4 . Fluid interaction between circular cylinder with two disturbance body can increase boundary layer transition from laminer to turbulent to produce small drag. It is found that the characteristics of the flow significantly depend on the position of disturbance body. The optimum condition for the drag force reduction is at the angle α = 30o about 53 %.

Multi-body interaction effect on the energy harvesting performance of a flapping hydrofoil

Abstract The effect of an upstream bluff body on energy harvesting performance of a heaving and pitching hydrofoil is investigated numerically using a two-dimensional immersed boundary method at R e = 1000 . The presence of the upstream body changes flow structure around the hydrofoil and enhances efficiency significantly by two mechanisms. Mutual interaction of the vortex shed from the upstream body and the leading-edge vortex of the hydrofoil precipitates the separation of the leading-edge vortex from the hydrofoil and its streamwise transport. The incoming flow deflected by the upstream body changes the effective angle of attack for the hydrofoil. These phenomena significantly increase heaving force and pitching moment during stroke reversal, and major contribution to efficiency enhancement is from the change in pitching moment. 30% increase in efficiency, relative to a hydrofoil without an upstream body, can be achieved for same kinematics. However, the upstream body may be disadvantageous in some configurations. If the hydrofoil is placed closely to the body in transverse direction, the leading-edge vortex formation is suppressed after stroke reversal. When flapping frequency does not match with vortex shedding frequency of the upstream body, non-periodic flow structure formed around the hydrofoil can cause efficiency drop and irregular power generation.

Vortex-induced vibrations of three staggered circular cylinders at low Reynolds numbers

Vortex-induced vibrations of three staggered circular cylinders are investigated via two-dimensional finite element computations. All the cylinders are of equal diameter (D) and are mounted on elastic supports in both streamwise (x−) and transverse (y−) directions. The two downstream cylinders are placed symmetrically on either side of the upstream body at a streamwise gap of 5D, with the vertical distance between them being 3D. Flow simulations are carried out for Reynolds numbers (Re) in the range of Re = 60-160. Reduced mass (m*) of 10 is considered and the damping is set to zero value. The present investigations show that the upstream cylinder exhibits initial and lower synchronization response modes like an isolated cylinder does at low Re. Whereas for both the downstream cylinders, the upper lock-in branch also appears. The initial and the upper modes are characterized by periodic oscillations, while the lower lock-in branch is associated with nonperiodic vibrations. The 2S mode of vortex shedding is observed in the near wake of all the cylinders for all Re, except for the upper branch corresponding to the downstream bodies. In the upper branch, both the downstream cylinders shed the primary vortices of the P+S mode. For the upstream cylinder, the phase between lift and the transverse displacement exhibits a 180° jump at certain Re in the lower branch. On the other hand, the downstream bodies undergo transverse oscillations in phase with lift in all lock-in modes, while the phase jumps by 180° as the oscillation response reaches the desynchronization regime.

Dynamics of a flag behind a bluff body

Flow-induced vibration of an elastic structure such as a flag has drawn attention recently because of its complicated coupling mechanisms and potential application to energy harvesting. For both air and water flows, we experimentally investigate the effect of an upstream bluff body on the dynamics of two types of a downstream flag, a conventional flag and an inverted flag, on and off a midline. In contrast to the conventional flag, the trailing edge of the inverted flag is clamped, and its leading edge is free to move. By using smoke visualization and particle image velocimetry, the interaction of the flag with the vortices shedding from the bluff body was also identified. With the deployment of a bluff body, the conventional flag displays two distinct periodic flapping modes. While synchronization with the vortices shedding from the bluff body and a resultant fundamental mode appear in a low free-stream velocity range for the conventional flag lying on the midline behind the bluff body, the conventional flag off the midline shows a second harmonic mode by flutter instability in a higher free-stream velocity range. Meanwhile, the inverted flag reveals both small-amplitude flapping mode by a lock-in process and large-amplitude flapping mode by divergence stability at a given location on the midline and farther from the bluff body. However, only large-amplitude flapping mode is observed for the inverted flag off the midline. Even though the critical free-stream velocity when the inverted flag starts large-amplitude flapping depends on its relative streamwise and crosswise positions, the flag in flapping mode exhibits similar maximum amplitude and frequency pattern regardless of its relative locations.

The importance of controlling the upstream body wake in tandem cylinders system for noise reduction

This work numerically investigates the importance of controlling the wake of upstream body in the tandem cylinders aiming at aerodynamics noise reduction. The two-dimensional unsteady Reynolds-averaged Navier–Stokes approach with the k–ω turbulence model and Ffowcs Williams–Hawkings method are employed to simulate the flow field and the aerodynamics noise, respectively. The flow in the porous media is calculated by a volume-averaged model. Analogy to the mass-spring-damper system, one preliminary model is proposed to reveal the key role of stabilizing the upstream body wake. The simulations of different porous materials coating designs are implemented to corroborate the model and provide more details of flow modification by porous materials coating. Results indicate that the porous materials coating designed on the upstream cylinder can decrease the wake impingement on the downstream cylinder via suppressing the vortex shedding. Subsequently, not only the tonal noise but also the broadband noise level of tandem system can be reduced. It is also clarified that the effects of downstream cylinder absorption and downstream cylinder wake control by porous materials coating is not comparable with the upstream cylinder wake control. The present study gives a new idea to flow control and noise reduction of the multibody systems considering efficiency and economy.

Experimental investigations on flow induced vibration of an externally excited flexible plate

Flow-induced vibration of a harmonically actuated flexible plate in the wake of an upstream bluff body is experimentally investigated. The experiments are performed in an open-ended wind tunnel. A flexible plate trailing a bluff body is under fluid induced excitation due to the flowing fluid. The additional external excitation to the trailing plate is applied using an electro-magnetic exciter. The frequency and amplitude of the external harmonic excitation are selected as variable parameters in the experiments and their effect on the plate vibration and is investigated. To know the nature of acoustic pressure wave generated from the vibrating system, near-field acoustic pressure is also measured. A laser vibrometer, a pressure microphone and a high-speed camera are employed to measure the plate vibration, pressure signal, and instantaneous images of the plate motion respectively. The results obtained indicate that the dynamics of the plate is influenced by both the flow-induced excitation and external harmonic excitation. When frequency of the two excitations is close enough, a large vibration level and a high tonal sound pressure are observed. At higher amplitude of external excitation, the frequency component corresponding to the flow-induced excitation is found to reduce significantly in the frequency spectrum of the vibration signal. It is observed that, for certain range of excitation frequency, the plate vibration first reduces, reaches a minimum value and then increases with increase in the level of external excitation. A fair qualitative agreement of the experimental results with numerical simulation result of the past study has been noted. In addition to the experiments, the role of phase difference between the flow-induced excitation generated from the front obstacle and externally applied harmonic excitation is investigated through numerical simulations. The result obtained reveals that the final steady state vibration of the coupled system is independent of the initial phase difference between the two excitations.

Genome-wide screen of genes imprinted in sorghum endosperm, and the roles of allelic differential cytosine methylation.

Imprinting is an epigenetic phenomenon referring to allele-biased expression of certain genes depending on their parent of origin. Accumulated evidence suggests that, while imprinting is a conserved mechanism across kingdoms, the identities of the imprinted genes are largely species-specific. Using deep RNA sequencing of endosperm 14days after pollination in sorghum, 5683 genes (29.27% of the total 19418 expressed genes) were found to harbor diagnostic single nucleotide polymorphisms between two parental lines. The analysis of parent-of-origin expression patterns in the endosperm of a pair of reciprocal F1 hybrids between the two sorghum lines led to identification of 101 genes with ≥ fivefold allelic expression difference in both hybrids, including 85 maternal expressed genes (MEGs) and 16 paternal expressed genes (PEGs). Thirty of these genes were previously identified as imprinted in endosperm of maize (Zea mays), rice (Oryza sativa) or Arabidopsis, while the remaining 71 genes are sorghum-specific imprinted genes relative to these three plant species. Allele-biased expression of virtually all of the 14 tested imprinted genes (nine MEGs and five PEGs) was validated by pyrosequencing using independent sources of RNA from various developmental stages and dissected parts of endosperm. Forty-six imprinted genes (30 MEGs and 16 PEGs) were assayed by quantitative RT-PCR, and the majority of them showed endosperm-specific or preferential expression relative to embryo and other tissues. DNA methylation analysis of the 5' upstream region and gene body for seven imprinted genes indicated that, while three of the four PEGs were associated with hypomethylation of maternal alleles, no MEG was associated with allele-differential methylation.

Actively flapping tandem flexible flags in a viscous flow

The active flapping motions of fish and cetaceans generate both propulsive and manoeuvring forces. The tail fin motions of the majority of fish can essentially be viewed as a combined pitch-and-heave motion. Downstream bodies are strongly influenced by the vortices shed from an upstream body. To investigate the interactions between flexible bodies and vortices, the present study examined tandem flexible flags in a viscous flow by using an improved version of the immersed boundary method. The upstream flag underwent passive flapping in a uniform flow while the downstream flag flapped according to a prescribed pitching and heaving motion of the leading edge. The influences of the active flapping motion on the system dynamics were examined in detail, including the frequency, the phase angle, the bending coefficient and the amplitudes of the pitching and heaving motion. The variation of the drag coefficient of the downstream flag was explored together with the instantaneous vorticity contours and the body shapes. Both the slalom mode and the interception mode were identified according to the vortex–flexible body interactions, corresponding to the low- and high-drag situations, respectively. The underlying mechanism was discussed and compared with previous studies.

Influence of drift angle on the computation of hull–propeller–rudder interaction

The operation of the propeller dominates the flow interaction effects on the upstream hull and a downstream rudder. An investigation is carried out into the sensitivity with which these effects can be resolved when an angle of drift is applied as well as the length of an upstream body is varied. The computed results are compared to a detailed wind tunnel investigation which measured changes in propeller thrust, torque and rudder forces. Variation of the upstream body length and drift angle effectively varies the magnitude of the crossflow and wake at the propeller plane. The time resolved flow was computed around the hull–propeller–rudder configuration using the Reynolds-averaged Navier–Stokes (RANS) equations and an Arbitrary Mesh Interface (AMI) model to account for the motion of the propeller. A mesh sensitivity study quantifies the necessary number of mesh cells to adequately resolve the flow field. Overall, good agreement is found between the experimental and computational results when predicting the change in propulsive efficiency, flow straightening and rudder manoeuvring performance. However, it can be seen that there is a significant computational expense associated with a time resolved propeller interaction and that alternative body force based methods are likely to still be required with the computation of self-propelled ship manoeuvres.

Numerical study of flapping filaments in a uniform fluid flow

The coupled dynamics of multiple flexible filaments (also called monodimensional flags) flapping in a uniform fluid flow is studied numerically for the cases of a side-by-side arrangement, and an in-line configuration. The modal behaviour and hydrodynamical properties of the sets of filaments are studied using a Lattice Boltzmann–Immersed Boundary method. The fluid momentum equations are solved on a Cartesian uniform lattice while the beating filaments are tracked through a series of markers, whose dynamics are functions of the forces exerted by the fluid, the filaments flexural rigidity and the tension. The instantaneous wall conditions on the filaments are imposed via a system of singular body forces, consistently discretised on the lattice of the Boltzmann equation. The results exhibit several flapping modes for two and three filaments placed side-by-side and are compared with experimental and theoretical studies. The hydrodynamical drafting, observed so far only experimentally on configurations of in-line flexible bodies, is also revisited numerically in this work, and the associated physical mechanism is identified. In certain geometrical and structural configuration, it is found that the upstream body experiences a reduced drag compared to the downstream body, which is the contrary of what is encountered on rigid bodies (cars, bicycles).

Study on hydrodynamic slug flow mitigation with wavy pipe using a 3D–1D coupling approach

Objective: A wavy pipe, constructed by connecting standard piping bends in series in one plane, was proposed to mitigate hydrodynamic slug flows in horizontal pipelines.Methods: A newly developed 3D–1D co-simulation method, i.e. STAR–OLGA coupling, was applied to model the wavy-pipe systems experiencing hydrodynamic slug flows. The flow characteristics of slug flow in the wavy-pipe systems were investigated, through which the effectiveness of the wavy pipe on slug mitigation and how the geometrical parameters of the wavy pipe affecting its performance were examined.Results: It has been found that the upstream liquid slug degenerates into a ‘liquid dense zone’ of a greater length downstream of the wavy pipe due to the gas penetration into the slug body. A reduction of the effective density of the ‘liquid dense zone’ from that of the upstream slug body is resultant showing the effectiveness of the wavy pipe on mitigating the adverse impacts of slug flow. The amount of gas penetration increases then decreases with the increasing wavy-pipe amplitude indicating that excessively higher amplitude is even less effective on introducing the gas phase into the slug body. Differently a wavy pipe with the same amplitude but a greater length, i.e. more bends, is more effective.Conclusions: It is concluded that the wavy pipe works by reducing the effective density of the liquid slug through introducing the gas phase into the slug body in the push-out process in each bend of the wavy pipe and the geometrical parameters need to be designed properly in specific applications.