Flow Velocity Vector Research Articles

On setting boundary conditions for calculations of turbomachines in 3-d computer packages

Unfortunately, in a growing number of publications of the results of the study of turbomachines in ANSYS and other packages, insufficient attention is paid to the choice of the flow model (absolute or relative) and the setting of boundary conditions in the areas adjacent to the rotating impeller: shroud seal, diaphragm (end) seals, gap over shroudless blades, steam balance holes, etc.As a rule, these areas contain such elements of geometry as a “ledge”, “projection”, “crest”, the flow around which, and, consequently, their resistance depends on the angle of incoming flow relative to the barrier. In the stages of turbomachines in sections behind fixed blade units, angle α1 between the flow velocity vector (in absolute motion) and the circumferential velocity is 10°÷25° (for steam turbine stages), 20°÷35° (for gas turbine stages) and 40°÷75° ((for axial compressor stages). It is shown (using the example of viscous flow around the “ledge + projection” system) that a change in the angle in the range of 15°÷90° changes the resistance by almost 2 times.The choice of a particular type of flow model (absolute or relative) for the domain primarily determines the value of the angle of interaction of the flow lines with an obstacle: it remains close to α1, or close to β1 = α1 + 20°÷70°, which significantly changes the qualitative picture of the viscous flow around the characteristic elements of geometry (“ledge”, “projection”, “crest”), and the values of integral parameters (flow rate, power, efficiency). The lack of recommendations on the correct choice of boundary conditions will inevitably lead not only to the inability to compare the results of various published studies, but also to their objective value. Therefore, the need to substantiate proposals for the choice of flow models in the areas of labyrinth seals, steam balance holes, gaps over shroudless blades, etc. is very relevant.

Wing-to-Wall Distance Effect On The Large-Scale Turbulent Structures Interacting With A Wall

We experimentally investigate the effect of the wing-to-wall distance, also called ground clearance, on the three-dimensional flow generated by a wing at a 4° angle of attack and a chord Reynolds number of 1400. We perform 3D velocity measurements using Particle tracking velocimetry to characterize the wake downstream of the wing, evaluate the evolution of the intensity and the size of the wingtip and secondary counter-rotating vortices, and finally compute the aerodynamic coefficients using momentum balance equations. We extended the control volume method for drag and lift calculation to the case where the transverse plane downstream of the wing does not contain the whole wake. The secondary flow's vorticity isocontours and velocity vectors show a decrease in the downwash and vortex size with the ground clearance ratio (i.e., as we approach the ground). The computation of the circulation shows that this latter decays rapidly streamwise as we get closer to the wall, indicating a dissipation of the kinetic energy contained in the trailing vortices. The aerodynamic coefficients' results based on the control volume method show that the tested wing manifests a two-force regime evolution of the drag coefficient with the ground clearance ratio, as it first decreases when moving far from the ground before increasing as we move farther from the ground. A noteworthy high lift is generated when too close to the ground. Further application of the extended control volume method on DNS data is needed to validate the method.

Relating ciliary propulsion morphology and flow to particle acquisition in marine planktonic ciliates II: the oligotrich ciliate Strombidium capitatum

Abstract The marine oligotrich ciliate Strombidium capitatum is a cruise-feeder, relying on ciliary motion and propulsion flow to individually detect and capture particles. High-speed, high-magnification digital imaging revealed that the cell swims forward by sweeping its anterior adoral membranelles (AAMs) backward, achieving a mean path-averaged speed of U = 1.7 mm s−1 (31 cell-lengths per second). Particle detection occurs through either hydrodynamic signal perception or ciliary contact perception, with a mean reaction distance of R = 20.4 μm. While executing a ciliary reversal of AAMs to handle and capture a perceived particle, the cell coordinates the ciliary motion of ventral adoral membranelles (VAMs, the “lapel”) with the ciliary reversal of AAMs (the “collar”), causing a sudden halt of cell motion, thereby functioning as a motion “brake” that is crucial for effective particle capture. The encounter rate with small prey particles is calculated using πR2U (~8.0 μL h−1, equivalent to ~ 3.5 × 106 cell volumes per day). Based on hydrodynamic modeling results, it is hypothesized that spatial structures of the flow velocity vector and acceleration fields in front of the swimming cell are essential for pushing an embedded particle forward, creating a strong enough slip velocity and hydrodynamic signal for prey perception, even for a neutrally buoyant small particle.

Numerical analysis of a pressure distribution field and fluid flow velocity vectors near cumulative perforation holes

Relevance. The need to determine a reliable pressure distribution field and fluid filtration velocity vectors inside the perforation hole and the reservoir rock surrounding it. Aim. On the basis of numerical finite element modeling of the fluid flow inside the perforation holes and its filtration in the surrounding reservoir rock, to reveal the patterns of pressure distribution and fluid filtration vectors in the perforation hole, on its walls and in the near-wellbore zone. Objects. Near-wellbore zone of a limestone reservoir of one of the oil fields in the south of the Perm Region, including perforations. Methods. Numerical finite element method for calculating the flow and filtration of liquid in the near-wellbore zone, taking into account the geometry of perforation holes. Results. The paper considers the main relationships used in numerical simulation of fluid flow and filtration in the ANSYS finite element modeling software package. The authors have developed the finite element scheme of the near-wellbore zone, including cumulative perforation holes and taking into account their geometric parameters, as well as the fact that inside the holes the fluid flow is modeled in open space using the Navier–Stokes equations, and in the surrounding reservoir rock based on the filtration equations and Darcy's law. Numerical calculations were carried out, on the basis of which the distribution of pressure, flow velocities and fluid filtration inside the holes and in the near-wellbore zone as a whole was obtained. Calculations were made with varying pressure in the well (or pressure drawdown), as well as for different values of reservoir permeability. The calculation results showed that for the actual drawdown values of 10 MPa and the reservoir permeability of 50 mD, the value of pressure change inside the perforation holes will not exceed 0.01 MPa, i.e. it can be assumed that it practically does not change inside the hole. It is noted that the maximum value of the filtration rate corresponds to the top of the perforation holes and then its value decreases as it approaches the borehole wall. It is concluded that in further modeling of the stress-strain state of the near-wellbore zone, taking into account the holes of cumulative perforation on the surface of the holes, it is permissible to set a constant pressure value equal to the pressure in the well, and not logarithmic or any other distribution of it.

Исследование колебаний призмы в воздушном потоке с использованием акселерометра и контроллера Arduino

The rotational oscillations of a square prism mounted on a spring suspension in the test section of a low-speed wind tunnel are studied. The ratio of the length of the prism to the transverse size is 2.6. The prism can oscillate around the axis passing through the center of the prism and perpendicular to the velocity vector of the incoming flow and the longitudinal axis of the prism. The longitudinal axis of the prism in an equilibrium position is directed along the velocity vector of the incoming flow, or forms a small angle with it. An accelerometer GY-521 based on the MPU 6050 chip is used to register oscillations, it is connected to the Piranha UNO patronymic controller, which is an analog of the widespread Arduino UNO controller. In the absence of a flow, the rotational oscillations of the prism are damped. If the flow velocity is greater than a certain value, oscillations with a constant amplitude occur. The amplitude rises with an increase in the velocity of the incoming flow. The mathematical model proposed earlier to describe the rotational vibrations of the cylinder works satisfactorily to describe the oscillations of the prism.

Forward Modeling of 3‐D Ion Properties in Jupiter’s Magnetosphere Using Juno/JADE‐I Data

AbstractThe Jovian Auroral Distributions Experiment Ion sensor (JADE‐I) on NASA’s Juno mission provides in‐situ measurements of ions from 0.1 to 46.2 keV/q inside Jupiter’s magnetosphere. JADE‐I is used to study the plasma with two types of datasets from the same measurement: Time‐of‐flight (TOF) and SPECIES. The TOF dataset provides mass‐per‐charge measurements with a range of 1–64 amu/q but oversamples particles over 6π steradian viewing per spacecraft spin and has little directional information. On the other hand, the SPECIES dataset can provide a good measurement of the flow direction but does not provide mass‐per‐charge information due to the telemetry limit. In this study, we developed a 2‐step forward modeling method that combines the advantages and avoids the disadvantages of TOF and SPECIES data to derive the 3‐D properties of heavy ions. Assuming that the ion velocity distribution can be described with the kappa distribution, we first perform the forward model fit of the TOF data to calculate the relative abundance of heavy ion species. Then we fix the relative abundance and perform the second forward model fit on the SPECIES data. Using this method, we obtain the densities of different heavy ions, the shared temperature and kappa value, and the 3‐D flow velocity vector. Some data examples of the equatorial plasma disk before Perijove 24 are included to demonstrate the method. Plasma properties can then be mapped to explore spatial and temporal variabilities in Jupiter’s magnetosphere.

Modeling Aircraft Fuel Jettison Using Smoothed Particle Hydrodynamics on Finite-Volume Meshes

Weakly compressible smoothed particle hydrodynamics is used to investigate aircraft fuel jettison using a single-phase model. Fuel simulations are coupled to the aircraft computational fluid dynamics flowfield using cell containment checks on the finite-volume mesh to locate any smoothed particle hydrodynamics (SPH) particle within the mesh, after which the local flow velocity vector is retrieved and then used to apply an approximate aerodynamic force to the SPH particle based on a continuum correction to discrete droplet calculations. Further downstream, the SPH simulation may be continued, or a switch may be made to implicit particle tracking (IPT) in order to accelerate the simulation. Comparison to IPT results shows that a fluid model of the initial continuum breakup of the jet is required, but following this transition to IPT is reasonable to reduce computation time. Models are validated against volume of fluid (VOF) simulations, with the runtime of the proposed model being approximately 100 times less than the VOF, and good qualitative agreement is also found compared to recorded flight results.

Investigating the Turbulent Flow around Semi-Circular Cylinder

The Spalart-Allmaras turbulence model is used to study the flow patterns around a semi-circular cylinder surrounded by water in two dimensions with various angles of strike owing to rotating the cylinder by an angle. The rotation angle ranges from zero to 360° and the ANSYS Fluent software is employed to implement the required simulation. The Spalart-Allmaras turbulence model is used to determine the flow velocity vector, velocity contours, and pressure contours. Moreover, this turbulent model is used to calculate three different non-dimensional parameters, the drag coefficient, lift coefficient, and skin friction factors. Two different Reynolds numbers (Re) are adopted in the calculation of the three non-dimensional parameters with various values for the angle of the cylinder rotation. Here, the semi-circular cylinder is considered stationary but it is placed in a water domain in various positions. Due to the scarcity in information about using the Spalart-Allmaras turbulence model as compared with other models, which are widely used to investigate the flow around the cylinder, three turbulent models are employed to verify the results obtained by the Spalart-Allmaras model, these models are (standard), (RNG), and (Realizable). Results show an excellent agreement between the four turbulent models compared, where there is no significant variation in the obtained results, all results are very similar.

Damping oscillations of a cylinder with a coaxial disc and a stabilizer

The damped rotational oscillations of the cylinder, which is equipped with a coaxial disk in the head part, and has a stabilizer in the tail part, are studied. The elongation of the cylinder (the ratio of length to diameter) is nine. The cylinder is mounted in the test section of the low velocities wind tunnel with a wire suspension containing steel springs. In the equilibrium position, the axis of the cylinder is horizontal and parallel to the velocity vector of the incoming flow. Under the action of the air flow, the attenuation of rotational oscillations of the cylinder changes. A semiconductor strain gauge is attached to one of the suspension springs, which measures the dependence of spring tension on time during oscillations. The voltage at the output of the strain gauge is transmitted to the PC oscilloscope. The digital signal of the oscilloscope is transmitted to the computer. After calibration of the device, the frequency and amplitude of damped rotational oscillations around a horizontal axis passing through the center of the cylinder and perpendicular to the velocity vector of the incoming flow are determined. The effect of the air flow is described by analogues of rotational derivatives, which in the case of bluff bodies depend on the amplitude of the oscillations of the angle of inclination of the body and on the amplitude of the angular velocity. A simple model of the stabilizer’s effect on rotational derivatives is proposed.

Study of fluidized bed freeboard for effect of Geldart A particles shape using particle image velocimetry (PIV)

A study was carried out using Particle Image Velocimetry (PIV) to reveal velocity vector flow fields in the freeboard region of a Geldart A fluidized bed. For the first time the effect of particle shape, was studied for three powder types, namely China clay (platelet-like), Diatomite (spherical) and Quartz (irregular). A bench-scale fluidized bed set-up of perspex glass was used for direct PIV imagining over a substantial inlet gas velocity range. Interestingly the freeboard was not found to be highly turbulent as has been reported in the case of Geldart B particles. Rather a transition regime was observed which was dominated by laminar streamlines and punctuated by short-lived eddies with life span even less than 400 μs. Bed expansion was significantly affected by particle shape. This was explained by an ‘effective cluster size’ hypothesis for the three powder types. The ‘uniformity’ of the velocity field was also quantified for each powder.

CFD Study for Wave Run-up Characteristics Around a Truncated Cylinder with Damper

In this study, numerical simulations for a single fixed truncated circular cylinder in regular waves were conducted to investigate the nonlinear wave run-up under various dampers and wave period conditions. The present study used the volume of fluid (VOF) technique to capture the air-water interface. The unsteady Reynolds-averaged Navier–Stokes (URANS) equation with the k– ϵ turbulence model was solved using the commercial computational fluid dynamics (CFD) software STAR-CCM+. First, a systematic spatial convergence study was conducted to assess the performance and precision of the present numerical wave tank. The numerical scheme was validated by comparing the numerical results of wave run-up on a bare truncated cylinder with the experimental results, and a good agreement was achieved. Then, a series of parametric studies were carried out to examine the wave run-up time series around the truncated cylinder with single and dual dampers in terms of the first- and second-order harmonic and mean set-up components. Additionally, the local wave field and the flow velocity vectors adjacent to the cylinder were evaluated. It was confirmed that under short wave conditions, the high position of the damper led to a noticeable increase in the wave run-ups with significant changes in the first- and second-order harmonic components.

High-resolution light-field particle imaging velocimetry with color-and-depth encoded illumination

Three-dimensional and three-components (3D-3C) measurement of flow velocity vector is important for the investigation of mechanism underlying flow structure. Light-field particle imaging velocimetry (LF-PIV) is a newly emerged technique for flow velocity measurement. However, LF-PIV suffers low axial resolution, prohibiting it for high fidelity imaging. To overcome this limitation, we proposed to employ color-depth-encoded illumination in light-field PIV (Code LF-PIV) to refine the particle's axial location with the color-depth information of the illumination beam. Code LF-PIV is the first system that integrates the snapshot acquisition of light-field acquisition and the high resolution capability of color coded illumination. Compared to conventional light-field PIV, Code LF-PIV can achieve much higher axial resolution due to the new illumination strategy. Compared to traditional coded illumination PIV, such as Rainbow PIV, Code LF-PIV has higher flexibility for variant imaging applications because of the elimination of customized diffractive optical element. We demonstrated the superiority of our system by imaging fixed particle, randomly distributed cavities inside crystal cube, and the square lid-driven cavity flow, where our Code LF system has increased the axial resolution by a factor of 23 when compared to the conventional LF system, and has achieved a comparable axial resolution as the depth super-resolved Rainbow PIV. Comprehensive evaluation of the imaging results demonstrated that Code LF-PIV combines the advantages of the high resolution of color-depth coded method with the convenient volumetric imaging of light-field camera, making Code LF-PIV a useful technique for high-resolution and large-scale flow measurement.

Моделирование процесса прокатки слоистого композита АМг3/Д16/АМг3

Introduction. Over the past decades, laminated composites based on aluminum alloys have been increasingly used in the aerospace and automotive industries. Laminated composites are usually produced by accumulative roll bonding, which results in the metallurgical bonding of initially prepared sheets. Hence, the main task of accumulative roll bonding is to obtain a reliable bond between materials. However, at present, the process of joining similar or dissimilar materials by plastic deformation is still a poorly understood phenomenon. In this regard, in recent years, methods of finite element modeling of the processes of joining materials have begun to develop intensively. The purpose of the work is to establish a relationship between stress-strain state parameters and the formation of a stable bond between aluminum alloys of different compositions. To achieve this goal, the following tasks are formulated: 1. Simulation of the laminated composite “AMg3/D16/AMg3” rolling process using data corresponding to physical experiments carried out at the Institute of Engineering Science of the Ural Branch of the Russian Academy of Sciences; 2. Selection and analysis of the most important stress-strain state parameters of the laminated composite “AMg3/D16/AMg3” rolling process. Research methods. Process simulation system Deform-3D was chosen as the main research tool. Results and Discussion. An analysis of the coordinate grid distortion and velocity vectors of material flow of layers revealed that the deformation is distributed inhomogeneously in the cross section after rolling: the outer layers flow more intensively compared to the middle layer. The maximum scatter of strain intensity ei in the cross section, observed at a maximum reduction ratio of 75%, is 12%. This allows one to accept for analytical calculations in the first approximation the assumption of deformation uniformity. A relationship is established between the beginning of the formation of a bond between composite layers and the threshold expansion of the contact surface and normal pressure at the interlayer boundary. In the final part of the study, future directions for improving the approaches of simulation the laminated composites rolling processes are proposed.

Ultrasonic Velocity Profiler for the Measurement of a Bubbly Flow Velocity Vector in Small Channels

The multi-dimensional velocity distribution of coolant in bubbly flow within the fuel rod bundles of the reactor core in boiling water reactors (BWRs) is elucidated by experimental investigationin this study. Since a measurement technique is required for such an investigation, this paper proposes the development of an ultrasonic velocity profiler (UVP). The combination of special ultrasonic transducers and modified signal processing on the UVP is proposed to obtain a multi-dimensional velocity vector of the bubbles and liquid in bubbly flow. The ability of the proposed technique is demonstrated by performing an experiment in swirling bubbly flowand itsapplicability confirmed by comparing the resultswith another technique. The sound pressure distribution in the narrow channel of the rod bundle isthenmeasuredprior to the verification ofthe ultrasonic wave emitted through a small channel. The echo signal reflected from reflectors dispersed in the liquid,bubble, and tracer particles in the small channel of the rod bundle indicates that the proposed UVP can be applied inthis application with a low level of multi-reflection. Finally, the UVP system is demonstrated to measure the velocity vector of bubbly flow in the narrow flow channel on the rod bundle, andthe velocity vector of the bubble and liquid obtained simultaneously.

Full-scale numerical simulation of hemodynamics based on left ventricular assist device.

Ventricular assist devices have been widely used and accepted to treat patients with end-stage heart failure. The role of VAD is to improve circulatory dysfunction or temporarily maintain the circulatory status of patients. In order to be closer to the medical practice, a multi-Domain model of the left ventricular coupled axial flow artificial heart was considered to study the effect of its hemodynamics on the aorta. Because whether LVAD itself was connected between the left ventricular apex and the ascending aorta by catheter in the loop was not very important for the analysis of simulation results, on the premise of ensuring the multi-Domain simulation, the simulation data of the import and export ends of LVAD were imported to simplify the model. In this paper, the hemodynamic parameters in the ascending aorta, such as blood flow velocity vector, wall shear stress distribution, vorticity current intensity, vorticity flow generation, etc., have been calculated. The numerical conclusion of this study showed the vorticity intensity under LVAD was significantly higher than that under patients' conditions and the overall condition is similar to that of a healthy ventricular spin, which can improve heart failure patients' condition while minimizing other pitfalls. In addition, high velocity blood flow during left ventricular assist surgery is mainly concentrated near the lining of the ascending aorta lumen. What's more, the paper proposes to use Q criterion to determine the generation of vorticity flow. The Q criterion of LVAD is much higher than that of patients with heart failure, and the closer the LVAD is to the wall of the ascending aorta, the greater the Q criterion is. All these are beneficial to the effectiveness of LVAD in the treatment of heart failure patients and provide clinical suggestions for the LVAD implantation in clinical practice.

Hydrodynamic behaviour of composite bucket foundation with random waves

In real sea conditions, the effect of nonlinear phenomena, such as wave run-up and wave pressure, on the foundations of offshore wind structures may threaten the safety of the platforms. This study investigated the hydrodynamic behaviour of a composite bucket foundation (CBF) under random waves. A hydrodynamic simulation model of the interaction between random waves and the CBF was developed using the renormalisation group (RNG) k-ε model, which was verified through experiments. The relationship between wave run-up and wave parameters was studied, and the distributions of wave pressure around the CBF was described. The flow field and velocity vector distribution characteristics around the CBF were analysed. The results show that two types of wave fields appear around the CBF. The maximum run-up value of the CBF is 100%–150% higher than the minimum value, and the run-up value at the back side is 50%–70% higher than the minimum value. A larger wave steepness parameter leads to a smaller wave run-up value at the location of the smallest wave run-up value. The results can provide a reference for the practical application of a CBF.

Numerical Study on the Distribution of Rodlike Particles in Laminar Flows of Power Law Fluids Past a Cylinder.

The contraction/expansion laminar flow containing rodlike particles in power-law fluid is studied numerically when the particles are in a dilute phase. The fluid velocity vector and streamline of flow are given at the finite Reynolds number (Re) region. The effects of Re, power index n and particle aspect ratio β on the spatial and orientation distributions of particles are analyzed. The results showed that for the shear-thickening fluid, particles are dispersed in the whole area in the contraction flow, while more particles are gathered near the two walls in the expansion flow. The spatial distribution of particles with small β is more regular. Β has a significant, n has a moderate, but Re has a small impact on the spatial distribution of particles in the contraction and expansion flow. In the case of large Re, most particles are oriented in the flow direction. The particles near the wall show obvious orientation along the flow direction. In shear-thickening fluid, when the flow changes from contraction to expansion, the orientation distribution of particles becomes more dispersed; while in shear-thinning fluid, the opposite is true. More particles orient to the flow direction in expansion flow than that in contraction flow. The particles with a large β tend to align with the flow direction more obviously. Re, n and β have great influence on the orientation distribution of particles in the contraction and expansion flow. Whether the particles initially located at the inlet can bypass the cylinder depends on the transverse position and initial orientation of the particles at the inlet. The number of particles with θ0 = 90° bypassing the cylinder is the largest, followed by θ0 = 45° and θ0 = 0°. The conclusions obtained in this paper have reference value for practical engineering applications.

Flow Structure and Transition to Local Turbulence Downstream of an Asymmetric Narrowing that Imitates Arterial Stenosis

The results of experimental studies and numerical simulation of the flow structure in the separation region downstream of an asymmetric narrowing of smooth canal that simulates 70% one-sided stenosis of the artery are presented. The Reynolds number was equal to 1800. The instantaneous flow velocity vector fields were measured using the SIV technique. The numerical solution was obtained by the large eddy simulation (LES) method. Setting the disturbances in numerical simulation close to the experimental conditions made it possible to obtain a satisfactory agreement between the calculated and experimental velocity fields and the components of the Reynolds stress tensor. The data on formation of the local flow turbulence region behind the constriction and subsequent downstream flow relaminarization are obtained. It is shown that a pair of secondary eddies localized within the region of flow separation is formed near the throat of the constriction.

Soft-Sensor Modeling of Temperature Variation in a Room under Cooling Conditions

Non-uniform temperature distributions in air-conditioned areas can reduce the energy efficiency of air conditioners and cause uncomfortable thermal sensations for occupants. Furthermore, it is impractical to use physical sensors to measure the local temperature at every position. This study developed a soft-sensing model that integrates the fundamentals of thermodynamics and transport phenomena to predict the temperature at the target position in space. Water experiments were conducted to simulate indoor conditions in an air-conditioning cooling mode. The transient temperatures of various positions were measured for model training and validation. The velocity vectors of water flow were acquired using the particle image velocimetry method. Correlation analysis of various positions was conducted to select the input variable. The soft-sensing model was developed using the multiple linear regression method. The model for the top layer was modified by the correction of dead time. The experimental results showed the temperature inhomogeneity between different layers. The temperature at each target position under two initial temperatures and two flow rates was accurately predicted with a mean absolute error within 0.69 K. Moreover, the temperature under different flow rates can be predicted with one model. Therefore, this soft-sensing model has the potential to be integrated into air-conditioning systems.

Flow Structure and Transition to Local Turbulence Downstream of an Asymmetric Narrowing that Imitates Arterial Stenosis

The results of experimental studies and numerical simulation of the flow structure in the separation region downstream of an asymmetric narrowing of smooth canal that simulates 70% onesided stenosis of the artery are presented. The Reynolds number was equal to 1800. The instantaneous flow velocity vector fields were measured using the SIV technique. The numerical solution was obtained by the large eddy simulation (LES) method. Setting the disturbances in numerical simulation close to the experimental conditions made it possible to obtain a satisfactory agreement between the calculated and experimental velocity fields and the components of the Reynolds stress tensor. The data on formation of the local flow turbulence region behind the constriction and subsequent downstream flow relaminarization are obtained. It is shown that a pair of secondary eddies localized within the region of flow separation is formed near the throat of the constriction.