Subcritical Flow Regime Research Articles

Drag measurements of fluttering fabrics and their application for sportswear

Loose and baggy clothing is required by the rules of ski cross and snowboard cross. However, it is known from the literature that fluttering garments increase the aerodynamic drag. The aim of this study was to investigate the influence of flexural rigidity and fabric weight on the coefficient of drag CD. Eleven fabrics (550 mm long, 320 mm wide) with different flexural rigidity (0.016–99 µNm) and fabric weight (0.1–2.4 N/m2) were tested in a wind tunnel on a cylinder (width 325 mm, diameter 125 mm) at speeds of 25 to 120 kph (Reynolds numbers Re 60 k-280 k). The general trend showed that fluttering fabrics that are heavier and stiffer create more drag force. All but one fabric had a smaller CD than the bare cylinder in the subcritical flow regime (CD ≈ 1.1), at least within a Re window of 80 k. One fabric had a consistently higher CD (average: 1.27) than the bare cylinder. The mean CD value of the other ten fabrics ranged from 0.87 to 1.07, with minimum CD values between 0.76 and 1. The CD advantage of the ten fabrics ended at the beginning of the critical flow regime of the bare cylinder between Re 200 k and 220 k. A regression analysis showed that the magnitude of the CD is more influenced by the flexural rigidity of a fabric, normalised to its weight, than by the weight itself, at least at Re < 250 k. The results of this study suggest that ski and snowboard cross athletes’ suits should be made from light and flexible fabrics to reduce aerodynamic drag.

Turbulent flow around convex curved tandem cylinders

Turbulent flow around curved tandem cylinders has been studied for the first time, by means of direct numerical simulation. The convex configuration was used, with a nominal gap ratio of $L/D = 3$ and a Reynolds number of 3900. Along the span, the flow regimes vary from alternating overshoot/reattachment to co-shedding. Three distinct Strouhal numbers coexist in the flow that are tied directly to different tandem cylinder flow regimes. This result differs substantially from convex curved tandem cylinders at a transitional Reynolds number, where only a single dominant frequency is found. All regimes exhibit some degree of instability, so that the flow can be considered multistable. A mode switch from alternating overshoot/reattachment to symmetric reattachment is found. Complex interactions are observed between the primary instability, the shear layer instability and the flow mode alterations. As opposed to previous investigations with single and tandem straight cylinders in the subcritical flow regime, our results indicate that there may be direct feedback from the primary instability to the shear layer instability. The downdraft region in the gap exhibits slow meandering, and may travel upstream and amplify the shear layer instability, causing early transition in the gap shear layer. This downdraft is governed by the slow modulations of the vortex formation region in the lower gap, meaning that the vortex dynamics of this region may indirectly influence the shear layer instability higher up in the gap.

Experimental investigation on aerodynamic noise and flow structures of a vibrissa-shaped cylinder

The noise mitigation effect of bio-inspired geometries has attracted growing attention from both research and industry, such as the vibrissa-shaped cylinder derived from the harbor seal. Experiments were conducted to investigate the far-field noise and the near-field wake of the flow past a vibrissa cylinder, a circular cylinder, and an elliptical cylinder at Re=3.6×104, in the subcritical flow regime. The frequency characteristic of the far-field acoustic pressure and the near-field velocities are analyzed. The mean and fluctuating velocities, dominant flow modes from proper orthogonal decomposition in both vertical and horizontal planes as well as the time-frequency behavior of the dominant flow structures from wavelet transform are also presented to better understand the wake dynamics and the direct relation of these flow structures with the far-field noise. The vibrissa cylinder reduces the overall sound pressure level by 13.2 dB and 8.3 dB compared with the circular and the elliptical cylinders, respectively, with a remarkable attenuation of the tonal peak associated with vortex shedding. From the detailed velocity measurements in multiple wake planes, it is clearly observed that vortex shedding of the vibrissa cylinder is weaker in strength and significantly less coherent in the spanwise direction than the other two cylinder cases, accompanied by more transient changes. The results also reveal the distinct flow behaviors behind the nodal and saddle planes of the vibrissa cylinder, further contributing to this three-dimensional vortex shedding. Consequently, the power spectral density of the tonal peaks associated with the vortex shedding in both near-field velocities and far-field acoustic pressure are attenuated, leading to a lower noise level. Understanding the detailed flow dynamics of the vibrissa cylinder will provide useful insights into more efficient bio-inspired cylinder designs in noise mitigation and wake control.

Aerodynamic noise characteristics of tandem cylinders in a subcritical flow regime

The present experimental study investigates the noise generated from the subcritical flow past two tandem circular cylinders of different downstream-to-upstream diameter ratios ( d 2 /d 1). The configurations considered for the study are (A) d 2 /d 1 = 1, (B) d 2 /d 1 = 2.5 and (C) d 2 /d 1 = 0.4. The gap between cylinders has spacing to diameter ratios ( s/d) of 2 and 4, and the free stream Reynolds numbers vary from 8.4 × 103 to 3.6 × 104. At s/d = 2, acoustic tones from configurations A and B are associated with vortex shedding from the downstream cylinder, and configuration-C has broadband spectral variations. At s/d = 4, configuration-B has two acoustic tones corresponding to vortex shedding from both cylinders, with dominant higher-frequency tones from the smaller upstream cylinder, and Configuration-C has narrowband tones from the larger upstream cylinder. The mean wake velocities of configurations at s/d = 4 are lower, with relatively higher gradients than at s/d = 2. The corresponding turbulence levels are 8.3% and 6.5%, respectively. Peak tonal frequencies have a linear variation with free stream velocity, and the respective Strouhal numbers estimated are in the range from 0.17 to 0.20. Scaling of the spectra with sixth power of the free stream velocity shows the dipole behavior of noise sources. The tandem configurations have higher overall noise levels than the background noise by up to 26 dB at s/d = 2 and 21 dB at s/d = 4. Configuration-A at s/d = 2 has the highest noise level of 91 dB.

The effect of obstacle length and height in subcritical free-surface flow

Two-dimensional free-surface flow past a submerged rectangular disturbance in an open channel is considered. The forced Korteweg–de Vries model of Binder et al. (Theor Comput Fluid Dyn 20:125–144, 2006) is modified to examine the effect of varying obstacle length and height on the response of the free-surface. For a given obstacle height and flow rate in the subcritical flow regime an analysis of the steady solutions in the phase plane of the problem determines a countably infinite set of discrete obstacle lengths for which there are no waves downstream of the obstacle. A rich structure of nonlinear behaviour is also found as the height of the obstacle approaches critical values in the steady problem. The stability of the steady solutions is investigated numerically in the time-dependent problem with a pseudospectral method.

Experimental study of simple flumes with converging triangular walls

For water management, the accurate measurement of discharge in irrigation channels is essential. Static flow measuring devices such as weirs and flumes play a significant role in discharge measurement in open channels. Flumes are one of the most commonly used devices for flow measurement. Many researchers have focused on application of simple flumes in irrigation networks. This investigation aims to study the flow discharge through a simple flume with converging triangular walls under free-flow conditions. The flume is constructed by placing two right-angled triangular plates on either side of a rectangular open channel. The channel cross section is rectangular while height of the converging walls reaches to zero at the end of the flume opening. The proposed flume is inexpensive, its operation is simple, its installation is easy and does not require high maintenance (maintenance free). The present study is designed to determine the effect of different variables on flow discharge of this kind of flumes. For this, an experimental program was conducted under upstream subcritical flow regime and under free outflow conditions to formulate the flow discharge of the flume. Flume discharge relationship was deduced using dimensional analysis method and then calibrated using the experimental data collected in this study (318 runs). The proposed discharge equation has an average absolute relative error of 1.66 %, and for 96.5 % of the measured discharge values, the relative errors are within ±5 %. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equation with an average absolute relative error less than 3.44 % was presented to estimate the submergence threshold. This flume is suitable for the rectangular channel for accurate measurement of free flow at any location on field. This particular device has considerable advantages over the other devices, as it can be quickly installed and removed for use in irrigation channels. The findings and results of this study will be of interest for practical applications.

On the effect of flow regime and slope of the channel bed on the hydraulic performance of the sharp-crested rectangular side weir: a numerical simulation

The aim of this study is to numerically investigate the effect of bed slope on the hydraulic performance of side weirs in supercritical and subcritical flow regimes. Increasing the bed slope decreases the weir efficiency and discharge coefficient in the subcritical flow regime up to 14.54% and in the supercritical flow regime up to 9.26%. By examining the longitudinal velocity distribution, it was observed that in the subcritical flow regime, the maximum longitudinal velocity occurs at the beginning of the upstream of the side weir, and by moving towards the downstream of the weir, the flow velocity decreases and increases again after leaving the length of the weir. In the supercritical flow regime, it has an increasing trend when the flow enters from the upstream of the side weir. The increase in discharge coefficient with the increase of the weir height varied between 4.6% and 7.8%. With increase of the slope of the channel bed, the velocity along the length of the weir increases by 10.88% and 6.17%, respectively, in the subcritical and supercritical regimes, and the transverse velocity along the transverse direction for the subcritical and supercritical flow regimes decreased by 22.23% and 4.80%, respectively.

Analysis of discharge characteristics of a symmetrical stepped labyrinth side weir based on global sensitivity

Abstract In this paper, the discharge coefficient prediction model for this structure in a subcritical flow regime is first established by extreme learning machine (ELM) and Bayesian network, and the model's performance is analyzed and verified in detail. In addition, the global sensitivity analysis method is introduced to the optimal prediction model to analyze the sensitivity for the dimensionless parameters affecting the discharge coefficient. The results show that the Bayesian extreme learning machine (BELM) can effectively predict the discharge coefficients of the symmetric stepped labyrinth side weir. The range of 95% confidence interval [−0.055,0.040] is also significantly smaller than that of the ELM ([−0.089,0.076]) and the Kernel extreme learning machine (KELM) ([−0.091,0.081]) at the testing stage. The dimensionless parameter ratio of upstream water depth of stepped labyrinth side weir p/y1 has the greatest effect on the discharge coefficient Cd, accounting for 55.57 and 54.17% under single action and other parameter interactions, respectively. Dimensionless step number bs/L has little effect on Cd, which can be ignored. Meanwhile, when the number of steps is less (N = 4) and the internal head angle is smaller (θ = 45°), a larger discharge coefficient value can be obtained.

Modulation of wake evolution, separation, and radiated noise by a cylinder with porous media cladding

In this paper, the effects of porous media parameters on circular cylinder wake flow and radiation noise are investigated using large eddy simulations and Ffowcs Williams–Hawkings acoustic analogy. We performed three-dimensional numerical simulations for flow around the cylinder coated with a porous layer of different pores per inch in a subcritical flow regime (ReD=4.7×104) to explore the control mechanism of porous media on wake and radiation noise. The results show that the application of porous media significantly alters the separation pattern behind the cylinder and stabilizes the shear layer detached from the cylinder. The existence of porous layers leads to the transformation of chaotic and irregular vortex structures into more orderly vortices. Moreover, this study also reveals that the cylinder coated with high pore density can provide the desired noise reduction. The analysis of vortex sound theory indicates that porous media reduces the interaction area and magnitude of the positive and negative Lamb vector divergences, which is beneficial for drag reduction and noise attenuation. In addition, the comparison of sound pressure contours shows that the application of porous media does not change the radiation mode of noise, but the porous media with high pore density helps to decrease the generation of noise and intensity of the sound source.

Direct numerical simulations of flows around an array of rough cylinders partially coated with porous media at Re = 3900

In recent years, interest has been growing in the stability control of cylindrical structures in a flow field using full/partial coatings of porous media. However, the partial application of porous coatings to arrays of cylinders with rough surfaces has rarely been studied. This paper numerically investigates the passive flow control of an array of rough cylinders partially coated with porous media on their leeward side in the subcritical flow regime (Re = 3900). This is achieved through two-dimensional direct numerical simulations and the Cartesian cut-cell method, which facilitate flow simulations around complex porous media and rough surfaces in an accurate and flexible manner. In contrast to macroscopic models, this study employs a quasi-microscopic model to simplify the porous structure for each cylinder, providing an accurate and intuitive means of describing the inflow details of porous media near the central cylinder. The porosities and pores per inch of the porous media are defined in terms of the alignment angles and radii. Similarly, the surface roughness of a cylinder is simulated by the attachment of small circular appendages. The accuracy and capacity of the presented numerical approach are demonstrated via a numerical case study with a single smooth cylinder. The influence of the porous media on the flows around a single rough cylinder and an array of rough cylinders is thoroughly investigated and discussed.

Visualization of Turbulent Flow Fields Around a Circular Cylinder at Reynolds Number 1.4×105 Using PIV

This study investigates the experimental parameters of particle image velocimetry (PIV) to enhance the measurement technique for turbulent flow fields around a circular cylinder at a Reynolds number (Re) of 1.4×10&lt;sup&gt;5&lt;/sup&gt;. At the Korea Research Institute of Ships &amp; Ocean Engineering (KRISO), we utilized the cavitation tunnel and PIV system to capture the instantaneous flow fields and statistically obtained the mean flow fields. An aspect ratio and blockage ratio of 16.7% and 6.0%, respectively, were considered to minimize the tunnel wall effect on the cylinder wakes. The optimal values of the pulse time and the number of flow fields were determined by comparing the contours of mean streamlines, velocities, Reynolds shear stresses, and turbulent kinetic energy under their different values to ensure accurate and converged results. Based on the findings, we recommend a pulse time of 45 μs corresponding to a particle moving time of 3–4 pixels, and at least 3,000 instantaneous flow fields to accurately obtain the mean flow fields. The results of the present study agree well with those of previous studies that examined the end of the subcritical flow regime.

Plunging Flow and Coherent Turbulent Structures in a Straight Pool‐Riffle

AbstractPool‐riffle units are naturally occurring topographical elements of rivers. Various hypotheses have been proposed to describe how the hydrodynamics in pool‐riffle units may lead to scour and sediment transport. However, most hypotheses have focused on time averaged properties, and a physical mechanism for observations of high near‐bed velocities has not been proposed. In this study, we apply Large Eddy Simulations to examine the dynamics of flow over straight riffles. We show that a high velocity core of fluid can alternately skim or plunge toward the bed as a function of the Froude number (Fr) at the crest of the riffle, even within a subcritical flow regime. Coherent turbulent structures are generated in the pool and induce high magnitude fluctuations of shear stress and bed pressure. Four different turbulent structures are described and the concept of vortex resistance is used to discuss how turbulence can induce the observed bifurcation in pool hydrodynamics. Despite the simple geometry, the hydraulic scaling means that the results provide a novel physical explanation of near‐bed high velocity flow observations in natural pool‐riffles. The results are also significant because turbulent shear stresses in the head of a pool exceed what occurs elsewhere in the channel, including the riffles. Further research should examine the conditions under which plunging flow may occur and turbulence may lead to sediment entrainment in other riffle pool geometries.

Discharge Coefficient of Symmetrical Stepped and Triangular Labyrinth Side Weirs in a Subcritical Flow Regime

The labyrinth side weir structure is an optimal solution to regulate and divert excess flows across rivers, and irrigation and drainage channels when the opening length of the side weir is limited. Changing the geometry of the side weir is considered one way to improve its efficiency. The present study investigates the hydraulic effects of stepped labyrinth side weirs to increase their discharge capacity. To estimate the outflow over symmetrical stepped labyrinth side weir, the discharge coefficient needs to be determined. Normal triangular labyrinth side weir in one cycle mode has been modified by increasing the crest path using different steps. A total of 417 experiments were conducted on normal and stepped side weirs for various weir opening lengths, weir heights, internal head angles, and hydraulic conditions. The results were analyzed and compared. It was found that efficiency improved, and the discharge coefficient increased as the number of the steps decreased. Furthermore, the water surface profile becomes more uniform with decreasing number of steps. A lower number of steps, smaller head angle, and high weir length produce a higher discharge coefficient by approximately 15%–35% compared to a normal triangular labyrinth side weir; in addition, the Knope length decreases by approximately 40%–70% for the same effective length. Additionally, a reliable equation to estimate the discharge coefficient of the stepped labyrinth side weir was presented. The results of this study can be used to design side weirs with high hydraulic performance when the weir-included angle selected is small or there is a lack of space.

Experimental Establishing of Moving Hydraulic Jump in a Trapezoidal Channel

This research was prepared as a preliminary laboratory study to achieve a moving hydraulic jump with controlled discharges. It is an initial part of the study that is being prepared to treat the salt tide occurring in the Shatt al-Arab due to the lack of water imports that were coming from the Karun and Karkheh rivers from Iranian territory, as this scarcity caused a salt tide that affected significantly the environmental reality of the city of Basra and the agricultural lands surrounding the Shatt al-Arab, such as the Shatt al-Arab district and the Siba orchards. As part of the proposed solutions, a moving hydraulic jump is created that pushes the salt tongue into the Persian Gulf; the results were promising. A moving hydraulic leap is a good example of unstable super- and sub-critical flow regimes and is regarded as a specific case of unsteady flow in a channel. There aren't many published experiments on this particular flow type, and the quantitative simulation of such a flow state has some inherent complexity. An experimental setup was created for this work in order to assess the hydraulic performance of a moving hydraulic jump in a trapezoidal flume. A sluice gate was installed at the flume's upstream edge to provide an unstable supercritical flow regime, movable hydraulic jumps along the channel, and temporal water stages at the gate's upstream side for the various downstream end boundary situations. Several flow factors, including energy head, pressure head, and flow depth, were estimated from the recorded data. The study found connections between discharge and shifting hydraulic jump variables. By employing relatively stable momentum and energy formulas, simple and time-independent formulas were developed that accurately predicted the pressure head in the subcritical region of an unstable mixed flow. As a result, the moving hydraulic jump factor can be correctly predicted using time-independent correlations by using the discharge variation as a boundary scenario. Doi: 10.28991/CEJ-2023-09-04-08 Full Text: PDF

On the cylinder noise and drag reductions in different Reynolds number ranges using surface pattern fabrics

This study experimentally investigates the potential of using surface pattern fabrics for the cylinder noise and drag control in different Reynolds number ranges. The aerodynamic and aeroacoustic effects were evaluated through the noise and force measurements in an anechoic wind tunnel. It was observed that the noise and drag reductions take place simultaneously but in different Reynolds number ranges, corresponding to the cylinder flow in different flow regimes, e.g., sub-critical, critical, and supercritical flow regimes. Microphone arc array measurements reveal that the suppression of the Aeolian tone in the critical regime is the major cause of noise reductions, and the noise directivity gradually loses dipole features in the critical and supercritical flow regimes, which is probably related to the reduced lift fluctuation coefficient and the spanwise segment of the sound sources. Further hotwire wake survey revealed significant changes in flow dynamics, which explain the variations of noise and drag in different flow regimes. We have shown for the first time that fabric with different surface patterns can effectively reduce cylinder drag and noise in different Reynolds number ranges. Since the Reynolds number is a key factor that determines the flow state in practical engineering applications, e.g., cycling aerodynamics, this study suggests that optimal drag and noise reductions can be realized by employing the combinations of different surface pattern fabrics to account for the Reynolds number effects.

CFD simulation of vortex-induced vibration of an elastic cylinder in subcritical flow regime using a two-way coupled model validated by experiment

The vortex-induced vibration (VIV) responses of an elastic cylinder have been numerically investigated using the two-way fluid-structure interaction model. The crossflow displacement (y) responses obtained from experiments agree well with that the results obtained from the numerical simulation. Further, the parametric study has been carried out on an elastic cylinder for various reduced velocities (Vr) ranging from 6.25 to 15.00 with an aspect ratio (L/D) of 100 using two way coupled model. The higher-order frequency components were observed in the force coefficients except for Vr of 13.13. In contrast, only a single frequency component was observed in both crossflow and inline displacements, except for Vr of 15.00 in inline response. The infinite lock-in was observed for the crossflow amplitude responses in the Vr range of 6.25–15.00. The finite lock-in was observed in the inline amplitude responses in the Vr range of 6.25–15.00 and reached the maximum amplitude in the Vr range of 9.88–11.49, where the drag force first frequency component is synchronized with the structure's second natural frequency and then decreases up to Vr of 15.00. The drag force frequency component follows harmonics in the limited range of Vr 6.25 to 9.59.

Experimental study of simple flumes with trapezoidal contraction

There are different devices available for measuring the flow discharge. Static measuring devices such as weirs and flumes (without any moving parts) play a significant role in discharge measurement in open channels. Many researchers have focused on application of flumes in irrigation networks. This investigation set out to study the flow discharge through a trapezoidal cut-throated flume (TCTF). The flume is simply constructed by placing two triangular plates on either side of a rectangular open channel to form a trapezoidal throat. The channel cross section is rectangular while throat cross section of the flume is trapezoidal. The proposed flume is simple, low-cost, easy to install and does not require high maintenance. The present study was designed to determine the effect of different variables on the flume discharge. For this, an experimental study was carried out under free outflow conditions and under upstream subcritical flow regime to formulate the flume discharge. Three models are defined for flume discharge relation based on the Buckingham's theorem of dimensional analysis, and then calibrated using the experimental data collected during this study. The first discharge model has an average error of 1.81%, while the second and third improved models have average errors of 0.96% and 1.44% respectively. To reliably estimate the flume discharge, free-flow and submerged-flow conditions should be distinguished. For this, suitable equations with an average error less than 2.23% were presented to estimate the submergence threshold. The results of this study indicate that while the downstream wall slope influences the submergence threshold, the flume discharge is not influenced by this variable. The proposed models are simple and accurate and present appropriate estimation of discharge for flows through the TCTFs. The findings of this study will be of interest for practical hydraulic engineers.

Strouhal number for boundary shear flow past a circular cylinder in the subcritical flow regime

Strouhal number (St) is an essential dimensionless quantity for characterizing the vortex-shedding frequency of the flow past a cylinder. In this study, the Strouhal number for a near-wall circular cylinder fully immersed in a boundary shear flow in the subcritical flow regime was experimentally investigated in a water flume. The velocity fluctuations and flow fields of the lee-wake were systematically measured with an Acoustic Doppler Velocimeter (ADV) and an upward-illumination Particle Image Velocimetry (PIV) system, respectively. Based on dimensional analyses, a non-dimensional shear parameter (K) is introduced to characterize the shear flow. An explicit expression between K and e/D is obtained on the basis of the boundary theory and verified with the flume measurements. Spectral analysis of wake velocities indicates that the multi-peaks can be identified as the cylinder gets closer to the wall. The PIV measurements indicate that the multi-peaks spectra are predominantly induced by the intense interactions between the lower shear layer and wall boundary layer. By fitting the experimental results, empirical relationships for the variations of St with K or e/D are finally established for the subcritical flow regime.

Identification of distinct flow behaviours around twin rough cylinders at low wind incidence

Wind tunnel experiments are performed on twin rough cylinders with a centre-to-centre spacing ratio L/D=1.2. The unsteady flow field is measured at two different Reynolds numbers, Re = 45 k and 275 k, corresponding to the sub- and post-critical flow regimes, respectively. The wind incidence α is varied from 0°to 10°. The detailed analysis of the lift coefficients as a function of the wind incidence reveals the existence of three flow behaviours in both flow regimes. Bi-stabilities are observed and occur within different ranges of wind incidence depending on the flow regime. A methodology is proposed to decouple the modes which intermittently occur in case of bi-stability, allowing to identify the flow behaviour of each mode. In the sub-critical flow regime, the flow behaviour at very low wind incidences (α=0°–2°) corresponds to an alternate re-attachment on both sides of the rear cylinder. In the post-critical flow regime, the flow behaviour is bi-stable because of the intermittent re-attachment of the shear layers. For larger wind incidences (α= 4°–6°), the lower shear layer intermittently re-attaches steadily or alternately onto the rear cylinder in the sub-critical flow regime, evidencing a bi-stability. On the other hand, it always re-attaches steadily onto the rear cylinder in the post-critical flow regime. A gap flow is observed for the largest wind incidences (α=8°–10°). It is found to be stronger in the sub- than in the post-critical flow regime.

Numerical studies on wake and turbulence characteristics of aquaculture nets

This paper aims to understand the drag coefficient discrepancy between the equivalent-twine and twisted-twine nets based on their wake and turbulence characteristics. To that end, we conduct unsteady Reynolds-averaged Navier-Stokes (URANS) and the second-moment (Reynolds stress, RSM) simulations at a Reynolds number,Re=4.5×103, based on the effective diameter of the net twine, which corresponds to the subcritical flow regime. Then, the vortex structures and the turbulence statistics are assessed at AOA=90°. The results highlight that the wake interactions for the twisted-twine net are relatively strong compared to the equivalent-twine net, due to the disturbance of the helixes on the twisted twines. In comparison to the classical Karman vortex, the overall vortex shedding of these two nets is well organized. Symmetric vortices form behind the equivalent-twine net, while single vortices form behind the twisted-twine net. Moreover, the Reynolds normal and shear stresses show symmetric and anti-symmetric profiles. The addition of helixes to smooth circular cylinders changes the flow development, leading to a decrease of turbulence kinetic energy. With this understanding, engineers need to be carefully select the net type for preliminary design of marine aquaculture cages to avoid over- or underestimation of the drag forces.