Turbulent Flow Parameters Research Articles

CFD-based investigation of turbulent flow behavior in 90-deg pipe bends

This work investigated the influence of bend curvature on the parameters of turbulent flow through a 90° pipe bend using the numerical CFD method, implemented in ANSYS Fluent. The numerical predictions were validated to be in good agreement with existing experimental measurements. The turbulence of the secondary motion was found to be generally stronger at the outer end of the pipe bend, with the most adverse effect recorded at about 45° along the bend. It was also observed that the RMS velocity is larger near the wall, especially at the outer wall region, and it is highest at 45° due to an increase in the circulation of dean vortices, indicating a turbulence generation. In addition, the RMS velocity increases downstream due to an additional mean strain resulting from the creation of secondary flow as the flow travels through the bend. Furthermore, larger static pressure and turbulent viscosity were observed at the outer wall due to the flow deceleration and swirling. Therefore, it can be established that the bend curvature affects the stability of the flow field inside a pipe bend.

Uncertainty Analysis in Airfoil–Turbulence Interaction Noise Using Polynomial Chaos Expansion

Airfoil–turbulence interaction noise is a known source of environmental disturbance and acoustic performance loss in aeroacoustics and hydroacoustics. This noise can be predicted using semi-analytical models that require input measurements of the incoming turbulent flow parameters. However, the turbulence parameters are inherently difficult to measure accurately. These parameters, which include the turbulence kinetic energy and its dissipation rate, have a stochastic nature. This study aims to investigate how small variations in the measurements of turbulence parameters affect the uncertainty of the predicted airfoil–turbulence interaction noise. This is achieved by applying polynomial chaos expansion (PCE) to the semi-analytical model of Amiet’s theory for airfoil-interaction noise. The validity of the deterministic and stochastic simulations is ensured by comparisons against available experimental data from the literature, and Monte Carlo simulations, respectively. Uncertainty quantification is then performed using a stochastic collocation technique, where the aerodynamic noise is evaluated at specific collocation points to estimate the coefficients required for PCE. Both the individual and combined effects of varying the uncertain input turbulence parameters are simulated to quantify the uncertainty of the output aerodynamic noise. The insights gained from the results suggest it is important to incorporate the stochastic behavior of the incoming turbulent flow in operational models for airfoil–turbulence interaction noise predictions.

Characterizing the Effect of Sinusoidal Wall Amplitude on Turbulent Wall Jet Flow Parameters

Abstract The influence of wavy wall amplitude on the turbulent wall jet flow parameters has been investigated experimentally. For the present study, a sinusoidal wavy wall (y=A* sin(ωx)) has been used where “A=Amp/a” is the amplitude, which is normalized by the nozzle height “a.” The amplitude of the wavy wall is varied as 0.2, 0.4, and 0.6, and the results are compared with the results of plane wall jet. The constant temperature anemometer (CTA) has been used for the measurement of flow by using a transverse mechanism. The results for the mean velocity profile, turbulent intensity, and power spectral density are plotted at the crest and trough separately for more clear discussions. From the velocity profile, it is noticed that the formation of self-similar profile is delayed as the amplitude increases from 0.2 to 0.6, which means flow takes longer time to develop. There is an increase in the local maximum streamwise velocity Umax at crests for increasing amplitude. At the first crest, the rise in Umax is maximum, i.e., Umax is increased by 26%, 37%, and 60% for the amplitudes 0.2, 0.4, and 0.6, respectively, with respect to the plane wall case. In the near flow field, the turbulent intensity also becomes larger for the higher amplitude, which shows higher intermixing of fluid within the jet. This paper also produces the benchmark results which can be used for the validation of the numerical model dealing with the turbulent wall jet flowing over a wavy surface.

A comparison study of the behaviors of single-phase turbulent flow at low to moderate Reynolds numbers through a vertical pipe: 3D counters analysis

The study presented three-dimensional (3D) analysis of water's upward flowing through the vertical pipe under turbulent characteristic considerations. Both numerical constructed and improved the model of 3D for cylindrical coordinates of governing equations for incompressible turbulent flow with the Reynolds Average Navier-Stokes (RANS) model using the improved constants of the (k–ε) type. The present model is then compared with a previous study to give the feasibility of the present single-phase turbulent flow parameters. The pipe length is tested to measure how much it affected the turbulent parameters though one of the expected factors is the turbulent time scale. On the other hand, the model is numerically examined to determine the velocity profile, shear rate, and surface deformation of the water domain. While the pressure distribution, turbulent kinetic energy, and turbulent dissipation rate, these parameters are classified as the mechanic's system factors. The simulation is done with wide software used to simulate industrial is COMSOL 5.4 Multiphysics software. The results obtained increased the velocity of three inlet water velocities used ranging from (0.087, 0.105, and 0.123 m/sec) of upward flow. High fluctuation in the water flow moves along the entire pipe length and it can notice the sensitivity to any change in water properties or mechanical properties. The liquid upward flow in turbulent conditions is suffered from many characteristics such them related to liquid properties and others related to the mechanics of the application through the systems. The interaction between the fluid film (fluid boarded the pipe inner diameter) has been observed by the shear rate and liquid surface deformation

Settling behavior of polydisperse droplets in homogeneous isotropic turbulence

The settling behavior of polydisperse droplets in homogeneous and isotropic turbulence was measured by an ultra-high-resolution two-dimensional Particle Image Velocimetry. The aim of the present study is to provide new insight on the dependence of multi-scale particle settling behavior on characteristic parameters of two-phase turbulent flow via a sophisticate conditional analysis. The relative settling strength (defined as the ratio of mean droplet settling velocity to root mean square velocity of turbulence), whose effect on droplet settling behavior is of the primary interest, ranges as SvL=0.5–2.0. The turbulence Taylor Reynolds number is Reλ=200–300, and the droplet Stokes number is Stp=0.1–10. Voronoï analysis is performed to obtain the concentration field of discrete droplets from particle images. Particle structures including clusters or voids are detected, and the droplet settling velocities corresponding to various probing conditions, such as Stp, local particle concentration, and size of particle structures, were then analyzed. For the present configuration (droplet net sedimentation), there is a non-monotonic dependency of the settling velocity on local particle concentration. The negative correlation between them occurs in the moderate-concentration sub-regime and is insensitive to the variation of SvL, in which individual droplets interact with turbulent flow independently. It can be well explained by the commonly invoked preferential sweeping mechanisms. On the other hand, the dense-concentration regime, in which droplets prefer to accumulate into clusters, presents a positive correlation; namely, the conditional-averaged settling velocity decreases with the increase in local particle concentration. In this sub-regime, it is not the scale of single particles but the scale of particle clusters and the relative strength of turbulence (measured by SvL) that jointly determines the droplet settling behavior. Such a process, to our knowledge, is consistent with the so-called multi-scale preferential sweeping effect.

To the development of hydraulic regulations of turbulent flows in pipelines

The results of the theoretical analysis of the turbulent movement of water in pipelines are given. It is proposed to evaluate the parameters of turbulent flows based on the indicators of molecular and turbulent viscosity with the introduction of the conditional relative thickness of the boundary layer into the calculations. The dependencies of the logarithmic law of the distribution of averaged velocities in the cross-sections of pipelines have been clarified. Unlike similar formulas of the semi-empirical theory of turbulent motion, they correspond to the boundary conditions on the pipeline wall. New theoretical dependencies between the main parameters of turbulent flows in pipelines were obtained. It is proved that the magnitude of the coefficients of hydraulic friction is determined by two parameters: the conditional relative thickness of the boundary layer and the proportionality factor, which takes into account the change in tangential stresses in the turbulent flow. The adequacy of the obtained dependencies is confirmed by their correspondence to the experimental data of the hydraulic dependencies of turbulent flows, on the basis of which the current standards for hydraulic calculations of water pipes were developed. For hydraulically smooth pipes, an explicit dependence was obtained for hydraulic friction coefficients in a wide range of Reynolds numbers (from 7 10³ to 10⁷). It almost completely corresponds to the well-known Prandtl-Colebrook’s formula, which has an implicit form. Numerical values and analytical dependencies between parameters of turbulent flow in hydraulically smooth pipelines are determined. It was established that with an increase in the Reynolds number, the values of both the conditional and absolute thicknesses of the boundary layer decrease, and with the increasing of the pipe diameters, they grow. It is shown that the thickness of the boundary layer depends on the type and magnitude of the roughness of the inner surface of the pipes and it is decisive when other parameters of turbulent flows in pipelines are evaluating.

Turbulent flow interacting with flexible trawl net structure including simulation catch in flume tank

The interaction between fluid and the midwater trawl with stocked catches is extremely complex, but essential to improve the understanding of the drag force acting on the trawl, the behavior of the fishing structure during a trawling process, and to predict its selectivity process. The present study assesses the turbulent characteristics inside and around the midwater trawls with catch and without catch linked to its fluttering motion. The analysis is based on three-dimensional electromagnetic current velocity meter measurements performed in the multiple points inside and outside different parts of a 1/35 scaled midwater trawl model with the aim of access the main turbulent flow structure inside and around the gear. Time-averaged normalized flow velocity fields and turbulent flow parameters were analyzed from the measured flow data. Furthermore, Fourier analysis was conducted by watching the time–frequency Power spectrum content of instantaneous flow velocities fields, the fluttering trawl motions, turbulent kinetic energy, and momentum flux. Based on successive analyzes of mean flow characteristics and turbulent flow parameters, it has been demonstrated that the presence of catch inside the trawl net impacts the evolution of unsteady turbulent flow by creating large trawl fluttering motions that strongly affect the flow passage. The results showed that the time-averaged normalized streamwise and transverse flow velocities inside and around the trawl net with catch were 12.41% lower compared with that obtained inside and around the trawl without catch. The turbulent length scale and turbulent Reynolds number obtained in the different part of the trawl net with catch were about 33.05% greater than those obtained on the trawl net without catch, confirming that the unsteady turbulent flow developing inside and around the midwater trawl is influence by the catch and liner. It is observed that the motions of both the trawl without catch and the trawl with catch are mainly of a low-frequency activity and another component related to unsteady turbulent flow street. A complex fluid–structure interaction is then demonstrated where the fluttering motions of the trawl net affect the fluid flow inside and around trawl net, the fluid force, turbulent pattern, and simultaneously, the periodic unsteady turbulent flow influence the trawl motions.

Numerical Simulation of Turbulent Flow Control at Pipe Inlet to Advance Flow Relaminarization

Various methods of flow relaminarization in a pipe are considered by means of controlling the average and turbulent flow parameters. For numerical simulation of flows with turbulence growth and suppression it is proposed to use a three-parameter RANS turbulence model, which has shown good results in modeling existing experiments on relaminarization. Calculations for three variants of inlet devices with different velocity profiles and the same small-scale turbulence at the inlet show the possibility of achieving flow relaminarization in pipes at Reynolds numbers Re > 10 000. Among three variants of inlet devices considered, the most effective one is the variant with organization of a two-zone flow with slow flow in the central region of the pipe and accelerated flow in the near-wall region. In this version, relaminarization occurs up to the Reynolds number Re* = 16 000. It is shown that decrease in the turbulence intensity and scale leads to an even larger value of the relaminarization Reynolds number Re*.

Numerical Simulation of Turbulent Flow Control

Various methods of flow relaminarization in a pipe are considered by means of controlling the average and turbulent flow parameters. For numerical simulation of flows with turbulence growth and suppression it is proposed to use a three-parameter RANS turbulence model, which has shown good results in modeling existing experiments on relaminarization. Calculations for three variants of inlet devices with different velocity profiles and the same small-scale turbulence at the inlet show the possibility of achieving flow relaminarization in pipes at Reynolds numbers Re 10000. Among three variants of inlet devices considered, the most effective one is the variant with organization of a twozone flow with slow flow in the central region of the pipe and accelerated flow in the near-wall region. In this version, relaminarization occurs up to the Reynolds number Re* = 16000. It is shown that decrease in the turbulence intensity and scale leads to an even larger value of the relaminarization Reynolds number Re*.

A Fast-Tracking-Particle-Inspired Flow-Aided Control Approach for Air Vehicles in Turbulent Flow.

Natural phenomena such as insect migration and the thermal soaring of birds in turbulent environments demonstrate animals' abilities to exploit complex flow structures without knowledge of global velocity profiles. Similar energy-harvesting features can be observed in other natural phenomena such as particle transport in turbulent fluids. This paper presents a new feedback control approach inspired by experimental studies on particle transport that have recently illuminated particles' ability to traverse homogeneous turbulence through the so-called fast-tracking effect. While in nature fast tracking is observed only in particles with inertial characteristics that match the flow parameters, the new fast-tracking feedback control approach presented in this paper employs available propulsion and actuation to allow the vehicle to respond to the surrounding flow in the same manner as ideal fast-tracking particles would. The resulting fast-tracking closed-loop controlled vehicle is then able to leverage homogeneous turbulent flow structures, such as sweeping eddies, to reduce travel time and energy consumption. The fast-tracking approach is shown to significantly outperform existing optimal control solutions, such as linear quadratic regulator and bang-bang control, and to be robust to changes in the vehicle characteristics and/or turbulent flow parameters.

Conditional analysis of temperature and strain rate effects on dissipation structure in turbulent non-premixed jet flames

This work presents results from simultaneous high-resolution temperature and velocity measurements in a series of turbulent non-premixed jet flames. The filtered Rayleigh scattering (FRS)-based temperature measurements demonstrate sufficient signal-to-noise (SNR) and spatial resolution to estimate the smallest scalar length scales and accurately determine dissipation rate fields. A comprehensive set of conditional statistics are used to characterize the small-scale structure, including the dependence of dissipation layer widths on Reynolds number, temperature, and dissipation magnitude. In general, the dissipation layer thickness decrease with increasing Reynolds number and increase with increasing temperature. However, dissipation layer widths show two distinct behaviors with respect to dissipation magnitude. For small dissipation values, increases in magnitude results in broadening of the dissipation layer, while for larger magnitude values of dissipation, the layer widths are thinned, highlighting the complexity of small-scale turbulent mixing. Additionally, measured ratios of the dissipation layer width to the Batchelor length scale are consistent across all Reynolds numbers and agree with previous studies in non-reacting flows. The unique aspect about the current set of measurements is the ability to examine the interaction of dissipation structure with turbulent flow parameters for the first time in turbulent non-premixed flames. Particularly, the strain rate/dissipation relationship is examined and compared to previous studies in non-reacting flows. It is found that the dissipation layers tend to align normal to the principal compressive strain axis and this tendency increases with increasing Reynolds number. For the lowest Reynolds number case, no dependence of the dissipation layer width nor dissipation rate magnitude on strain rate is found. However, for higher Reynolds numbers, a strong dependence of the dissipation layer width and dissipation rate magnitude on the principal compressive strain rate is observed. These results indicate the direct role of the compressive strain rate field on small-scale mixing structure in reacting flows.

Interaction of Irregular Distribution of Submerged Rigid Vegetation and Flow within a Straight Pool

The interaction of bedform and vegetation cover significantly affects the turbulent flow parameters. To investigate this interaction, experiments were carried out in both a gravel-bed river and a laboratory flume. The purpose of field investigations was to find the slopes for both the entrance section and exit section of pools, the grain size of the bed material, and the flow condition. Based on field data, without considering any scaling analysis, a straight pool was constructed in a laboratory flume that was 0.9 m wide, 0.6 m deep, and 14 m long. The entry and exit slopes of the straight pool were 7.4° and 4°, respectively. The straight pool had vertical side walls and a gravel bed with a median grain size of d50 = 23.3 mm. Plastic cylinders planted in an irregular pattern in the channel beds were used to model rigid submerged vegetation. The velocity components were recorded by using an ADV at 200 Hz. In this study, the distributions of velocity, Reynolds stress, and TKE were investigated for flows in the presence of submerged rigid vegetation in channel beds with various area densities of vegetation. Results show that the shape of Reynolds stress distribution depends on the entrance and exit slopes of the pool, as well as the irregular distribution pattern of vegetated elements. Inside the pool with the presence of submerged vegetation in the channel bed, the maximum TKE appears above the bed surface with a larger distance depending on the area density of vegetation in the channel bed. However, the momentum exchange and turbulent energy are likely influenced by the secondary circulation of the flows associated with the irregular distribution of vegetated elements in the channel bed. Results of the quadrant analysis show that the momentum between the flow, bedform, and vegetated elements is mostly transferred by sweep and ejection events. The outward event tends to grow toward the water surface, reaching the highest amount near the water surface. At the pool entrance section where the flow is decelerating, the ejection event is dominant near the bed while the sweep event is strong near the water surface. With the decrease in the vegetation density in the pool bed, both the ejection and outward events become dominant.

CFD study on heat transfer augmentation of rectangular shaped pinfin heatsink through the insertion of perforation and bulges

Due to the rapid minimization of electronic gadgets, a significant amount of heat is generated in the electric parts and it becomes a serious concern. Hence, it is necessary to minimize heat to get better performance of the equipment. A numerical investigation is conducted to observe the effect of convective heat transfer enhancement for rectangular shaped pin fin heatsinks. Different shapes of holes in fins and different heights of bulges are added to create more surface area to reduce the excess heat for better performance. The addition of bulge is the novelty of the present work. Hence, a passive cooling technique and staggered arrangement of pin fin have been proposed for a better flow characteristic and heat transfer performance. To predict the turbulent flow parameters, working fluid is modeled using Navier-Stokes’s equations and RANS-based k-? turbulent model. The research is carried out utilizing CFD software (COMSOL Multiphysics 5.4) based on the FEM for turbulent flow region. The numerical results show that rectangular-shaped elliptical perforated with a bulge height of 4.5 mm pin fin heatsink, ensuring the highest hydro-thermal performance factor of 1.262 to 1.297 which shows the improvement of around 26% to 29% when compared to previous findings.

Digital Image Correlation for stereoscopic measurement of water surface dynamics in a partially filled pipe

This paper presents a novel method for measuring three-dimensional (3D) water surface dynamics in a partially filled pipe. The study on investigation of the 3D free surface dynamics in partially filled pipes is very limited. The method involves tinting the water white with titanium dioxide so that the water surface appears like a solid surface to image-based measuring systems. This method uses a high-resolution projector to project a stochastic pattern of light onto the water surface and uses two high-resolution cameras to capture the pattern on the deformed water surface. The 3D instantaneous water surface fluctuation can be computed from the images captured by the two cameras using a standard Digital Image Correlation algorithm. It is demonstrated that the surface dynamics parameters of turbulent flow in partially filled pipes, including surface fluctuations and surface velocity, can be measured using the projector, high-resolution cameras and DIC algorithm.

Investigations of Turbulence in the IIAEM Wind Tunnel Using Computational Fluid Dynamics

Turbulence is important to be assessed in the design of wind tunnels. Undesired turbulence levels undermine the quality of fluid flow and accordingly the quality of scientific data. At the test section, the level of turbulence is critical. The amount of turbulence present in the test section of a subsonic wind tunnel has not been investigated in earlier researches. In the present research, a subsonic open-section wind tunnel installed at the authors’ facility is used as a testbed for turbulence investigation. Computational Fluid Dynamics that solves Reynolds Averaged Navier Stokes equations (RANS) is used as the scientific method for calculating the turbulent flow parameters. RANS instead of Large Eddy Simulation or Direct Numerical Simulation is adopted as a first step to identify large-scale eddies. The characterization of turbulence is performed though decomposition of fluctuating velocity components (u and v) in two-dimension.

Numerical study and optimization of important parameters of non-Newtonian nanofluid turbulent flow in a channel with triangular vortex generators using artificial neural network

The current research investigated the turbulent flow field as well as heat transfer rate (HTR) of the non-Newtonian H2O-Al2O3-carboxymethyl (CMC) in some channel having vortex generators (VGs). The partial differential equations were solved using the finite volume approach and the SIMPLE algorithm. The results also revealed that the VG depth change, which was in a few millimeters range, had no considerable impacts on the Nu as well as pressure decrease. In addition, the rise of Re (higher turbulent flow) remarkably increased HTR. Furthermore, due to the formation of vortex movements, local Nu variations revealed a significant rise near the considered VG. With the increase of the VG attack angle, there was a sudden the fluid flow change in the VG zone, resulting a larger DP, especially for the angle of attack of 60°For the 60° attack angle, a number of vortexes were formed behind the VGs, resulting a sudden variation of velocity on the contact surface of the VG. The greatest Nusselt number was 51.321, and the maximum pressure drop was 94993, according to the artificial neural network findings. As a consequence of the Pareto findings, there is a greater pressure decrease when there are more Nusselt.

Numerical Studies on Turbulent Flow Field in a 90 deg Pipe Bend

Abstract This paper deals with the modeling of turbulent flow through a 90 deg pipe bend using an unsteady Reynolds-averaged Navier–Stokes (U-RANS) approach where k–ε model is used for turbulence closure. While limitations in solving complex flows of the k–ε model have been reported in the literature, this study demonstrates that for pipe flows with curvature, the k–ε model performs reasonably well. Investigations have been carried out to find out the influence of Reynolds number (Re) and bend curvature ratio (Rc/D) on turbulent flow parameters, namely, instantaneous axial velocity, turbulent kinetic energy, turbulent intensity, and wall shear stress. Bend curvature is found to strongly influence the turbulent flow characteristics, while no such high Reynolds number dependency is observed in this study range. In general, this paper presents a computationally cost-effective numerical study on the time averaged turbulent flow field in a 90 deg pipe bend, which may be used for the design and development of 90 deg pipe bends at a high Reynolds number regime.

ИССЛЕДОВАНИЕ ЭФФЕКТИВНОСТИ КАНАЛЬНЫХ СТРАТЕГИЙ УПРАВЛЕНИЯ В ЗАДАЧЕ СТАБИЛИЗАЦИИ ТУРБУЛЕНТНОГО ГИДРОДИНАМИЧЕСКОГО ПОТОКА

The article considers the problem of stabilizing the value of the turbulent flow parameters described by the stochastic chaos model. As a basic control option, versions of channel strategies based on overrunning of current observations of the stabilized parameter from the range of acceptable values (channel) are considered. On the basis of numerical experiments, the potential possibilities of channel control strategies are investigated. It is shown that the main problem for achieving flow stability is the extremely high level of the variability of the system component of observation series, which is the realization of stochastic chaos. Versions of improved channel control strategies are given, the main directions for increasing the efficiency of functioning of channel stabilization technologies for turbulent flows are indicated

Unsteady turbulent flow developing inside and around different parts of fluttering trawl net in flume tank

Fluttering motions of a trawl are affected by its geometrical shape, natural underwater flows, and unsteady turbulent flow inside and around it. Thus, knowledge of the interaction between fluttering motions and the turbulent flow developing inside and around the different parts of the trawl is essential for understanding the hydrodynamic performance and selectivity of fishing gear. This paper assesses the coupled dynamics of the fluttering motions of different parts of a trawl and their hydrodynamics behavior. The analysis is based on three-dimensional electromagnetic current velocity meter measurements carried out inside and around different parts of a 1/18 scaled bottom trawl model. Instantaneous flow velocity fields and turbulent flow parameters were analyzed from obtained flow data. Moreover, fast Fourier transform and wavelet transform analysis were conducted to analyze the time–frequency contents of instantaneous flow velocity fields and fluctuating parts. The motions of different parts of the trawl net were oscillatory quasi-periodic and related to low frequency activity. The mean velocity ratios inside and around trawl wing, square, trawl body, and codend were 0.92, 0.89, 0.86, and 0.84, respectively. These results demonstrate the existence of unsteady turbulent flow inside and around different parts of the trawl. This unsteady turbulent flow corresponds to turbulent boundary layer flow, turbulent flow because of trawl wake, and vortex shedding. The dominant frequencies of these unsteady turbulent flows showed low frequency activities and wavelet energy was transferred from small-scale to large-scale motions under unsteady shear turbulence. In addition, knowledge of unsteady turbulent flow is greatly important for better understanding the hydrodynamic forces acting on a trawl and its geometrical shape as well as for implementing various selective devices and mesh shapes to reduce juvenile by-catch.

Flow and heat transfer characteristics in a pre-swirl rotor-stator cavity

The present study investigates flow and heat transfer characteristics in a rotor-stator pre-swirl system. Considered are rotational Reynolds numbers ReФ ranging from 3.4 × 105 to 6.8 × 105, with jet Reynolds numbers Rew of approximately 8.8 × 104 to 3.81 × 105, and associated turbulent flow parameter λT = Cw/ReФ0.8 varying from 0 to 0.4. Experimentally-measured and numerically-predicted results illustrate the combined and separate influences of jet impingement and rotor entrainment, as they affect and govern flow and heat transfer characteristics within the cavity. These results show that the relative strength of the two effects varies with ReФ and Rew, with similar performance for flow conditions with similar magnitudes of the turbulent flow parameter λT. When 0<λT < 0.27, jet impingement and rotor entrainment both have important influences on flow and heat transfer characteristics. However, when λT > 0.27, the effects of rotor entrainment are less pronounced.