Axial Velocity Components Research Articles

High-frequency ultrasound imaging of left-ventricle vortex flow in a mouse model

Vector flow (VF) ultrasound is available for human cardiac imaging to quantify advanced flow parameters such as vorticity, an important component of healthy cardiac function. Similar methods have yet to translate to murine models because of the need for fine temporal and spatial resolution. We evaluate the ability of a 30-MHz high-frequency probe to quantify vorticity in the murine left ventricle (LV) using a Verasonics Vantage 256. Acoustic beam properties were characterized with an 18-um wire. A 1-cm diameter rotation phantom and a flow channel were used to validate vector estimates. Transthoracic LV image data were acquired from wild-type mice. Flow parameters were obtained with custom software that implemented a multi-angle least-squares VF method. Data were processed to obtain VF estimates and local time histories of vorticity. Velocity and vorticity estimates had more bias as the axial velocity component decreased. Aliasing was observed and a basic dealiasing approach was implemented prior to final velocity estimates. Vorticity peaked during diastole at roughly 300 rad/s, consistent with past measurements at lower frequency. Results show VF can be implemented in murine models with HF probes, but that aliasing must be addressed to obtain reliable estimates. [Work supported by NIH EB032082.]

Local Energy Velocity of the Air-Core Modes in Hollow-Core Fibers

In this paper, we consider the behavior of the local energy flow velocity of the fundamental air-core mode at the core-cladding boundary in two types of hollow-core fibers: hollow-core fibers with a negative curvature of the core boundary and single-capillary fibers with similar geometrical parameters. It is demonstrated that the behavior of both axial and radial components of the local energy velocity of the fundamental air-core mode is completely different for these two types of hollow-core fibers. The negative curvature of the core boundary leads to an alternating behavior of the radial projection of the local energy velocity and a decrease of two orders of magnitude compared to the values of this projection for a single capillary. In our opinion, this behavior of the local energy velocity of the fundamental air-core mode is caused by a periodic set of Poynting vector vortices that appear in the cladding capillary walls.

The analytical solution for the flow of a Papanastasiou fluid in ducts with variable geometry

We solve the isothermal, steady and creeping flow of the regularized Papanastasiou model in ducts, such as symmetric channels and axisymmetric pipes, with varying rigid walls. The classic lubrication approximation is invoked to simplify the governing equations and to produce an exact analytical solution for the flow field with the aid of the Lambert W function. For specific suitable values of the parameters of the Papanastasiou model, the solution reduces to the corresponding exact analytical solutions for the ideal yield-stress Bingham and Newtonian fluids. The analytical solutions derived here are used to calculate the average pressure drop required to maintain the constant volumetric flowrate through the duct. Results are provided for symmetric undulating or linearly varying channels with the emphasis put on the effects of the Bingham and regularization numbers, and the amplitude of the undulation or the wall variation, respectively. For Bn→0 the yield surface approaches the axis of symmetry, σ(z)→0, i.e., no unyielded region appears in the flow. In this case, the last term in the formula for v is well-defined at y=0 provided that the numerator is zero. This implies that p′=c/h4 where c is constant. With the aid of the total mass balance, we find that c=−16, and thus p′→−16/h4 as Bn→0. Thus, Eqs. (34) and (37) reduce to the corresponding formulas for a Newtonian fluid given in Eq. (25). Noting that f(y,z)>0, and substituting the solution for γ˙ into inequality (52) gives the trivial W(f(y,z))≥0 which holds for any value of y and z because of the properties of the Lambert function. Eq. (53) is used in conjunction with Eq. (8) to find the unknown pressure gradient, p′(z). First, we integrate by parts Eq. (8) and apply the no-slip condition at the upper wall to find ∫0h(z)y2γ˙dy=2. Then, by substituting Eq. (53) into the latter, and performing the integration with respect to y from the axis of symmetry (y=0) to the wall (y=h(z)), gives: Using properties of the Lambert function and denoting with w=w(z) the value of W function at f(y=h(z),z), i.e.: we find the integral I(z) in Eq. (54) in terms of W and w. Then, we set Φ(z)≡−p′(z)h(z)/2>0, rearrange the resulting equation and upon simplification, we derive the strongly non-linear algebraic equation for Φ: The axial velocity component, u=u(y,z), can be found by integrating Eq. (53) with respect to y between y and h(z) and applying the no-slip condition at the wall:

Effect of Upstream Leakage Flow on Film Cooling Characteristic of a Turbine Convex Endwall

Abstract This paper investigates the effect of upstream leakage coolant flow on the film cooling performance of the convex endwall. The experiment is conducted in an annular passage with four vanes, and the endwall film cooling effectiveness distribution is measured by the pressure-sensitive paint technique. The near-wall flow field distribution predicted by computational fluid dynamics is employed to gain a deeper understanding of the influence of the passage secondary flow on the film cooling characteristic of the endwall. Furthermore, the effect of mass flow ratios (MFR = 0.75%, 1.0%, 1.25%, and 1.5%), leakage slot inclination angles (α = 30 deg, 45 deg, and 60 deg), density ratios (DR = 1.0, 1.5, and 2.0), as well as Reynolds number (Re = 2.0 × 105, 3.0 × 105, and 4.0 × 105) on the endwall film cooling is also investigated. Results indicate that the mass flow ratio has a great influence on the endwall film cooling effectiveness distribution, and a larger uncooled region can be observed when MFR is less than 1.25% due to the cooling air more easily being entrained by the secondary flow near the endwall. Reducing the inclination angle of the leakage slot enhances the axial velocity component of the coolant flow, thereby weakening the secondary flow near the endwall and improving the film cooling effectiveness distribution of the endwall. As the density ratio increases, the jet momentum of the leakage flow is reduced, particularly for higher MFR cases, which results in a significant reduction in the film cooling performance of the endwall. Besides, thinning the incoming boundary layer of the passage reduces the strength and size of the secondary flow in the passage and improves the endwall adiabatic effectiveness distribution when the Reynolds number is increased.

Improved asymptotic expansion method for laminar fluid flow and heat transfer in conical gaps with disks rotating

PurposeThe purpose of this paper was to study laminar fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4° for the case of disk rotation with a fixed cone.Design/methodology/approachIn this paper, the improved asymptotic expansion method developed by the author was applied to the self-similar Navier–Stokes equations. The characteristic Reynolds number ranged from 0.001 to 2.0, and the Prandtl numbers ranged from 0.71 to 10.FindingsCompared to previous approaches, the improved asymptotic expansion method has an accuracy like the self-similar solution in a significantly wider range of Reynolds and Prandtl numbers. Including radial thermal conductivity in the energy equation at small conicity angle leads to insignificant deviations of the Nusselt number (maximum 1.23%).Practical implicationsThis problem has applications in rheometry to experimentally determine viscosity of liquids, as well as in bioengineering and medicine, where cone-and-disk devices serve as an incubator for nurturing endothelial cells.Social implicationsThe study can help design more effective devices to nurture endothelial cells, which regulate exchanges between the bloodstream and the surrounding tissues.Originality/valueTo the best of the authors’ knowledge, for the first time, novel approximate analytical solutions were obtained for the radial, tangential and axial velocity components, flow swirl angle on the disk, tangential stresses on both surfaces, as well as static pressure, which varies not only with the Reynolds number but also across the gap. These solutions are in excellent agreement with the self-similar solution.

Thermodynamic study of hybrid nanofluid to explore synergistic effects of multiple ferromagnetic nanoparticles in co-axial disks for magnetized fluid

We Consider the physical model of two-dimensional hybrid nanofluids flow, which is time dependent, laminar, incompressible inside the two co-axial stretchable disks. The length of upper and lower disks is2s(t). The two axial and radial velocity components (u,w) depends upper the radial of disks r and normal of direction z. There exists temperature T1>T2 which is constant for upper and lower disks. The continuity, momentum and energy equations are modeled in cylindrical coordinates system. The finite element technique is used to evaluate numerical solutions. It is observed that the velocity near upper and lower disks decreases by increasing the values of magnetic parameter. Increased the values of shape factorNs of (Nanoparticles) then the thermal conductivity (HDnf) decreased. The shear stress and heat transfer rate decreased by influence α,ϕ1,ϕ2 but an opposite reaction observed when increase the values of M,Re andNs.

Thermal analysis of Non-Newtonian visco-inelastic fluid MHD flow between rotating disks

Analytical techniques are used in this article to examine the forced flow and heat transfer in a non-Newtonian Reiner-Rivlin fluid between two infinitely revolving disks in a magnetic field. The partial differential equations (PDEs) emphasizing flow and heat transfer were transformed into a nonlinear ordinary differential equations (ODEs) system using the Von Karman similarity transformation. The system of nonlinear ODEs with boundary conditions was solved using the Homotopy Perturbation Method (HPM) and Akbari-Ganji's Method (AGM). The study assessed the effects of physical factors on temperature profiles and the radial, transverse, and axial velocity components, including the visco-inelastic parameter, Reynolds number, Prandtl number, forced parameter, and magnetic field. The Python programming language was used for symbolic and numeric calculations of velocity components and temperature profiles. The accuracy of the results obtained through the analytical approach validates the applicability and efficiency of the proposed approach for studying the forced flow and heat transfer in non-Newtonian fluids between rotating disks.

Numerical Simulation and Characterization of Swirl Fluid Motion through Cylindrical Chambers

Axisymmetric solution of radial, axial and tangential components of velocity of flow through a cylindrical chamber with an inflow containing swirl and outflowis investigated numerically using Finite Volume Method. An in-house developed computer code for solving the three components of velocity and pressure is developed and validated using experimental data available from literature on the problem of axial vortex breakdown of confined flow in a cylinder due to rotation of one of the end walls. The code uses a staggered approach and fractional step projection method for decoupling the velocity and pressure. The convection and diffusion terms are approximated using a second-order accurate central difference scheme. This paper discusses the characteristics features of flow such as mixing streams, streams of fluid flowing close to the solid walls (cooling streams), swirl motion and development of flow structures.

Effects of liquid viscosity on interfacial and wall friction factors of swirling annular flows in a vertical pipe

Experiments of gas–liquid swirling annular flows in a vertical pipe of diameter D = 30 mm were carried out to obtain interfacial and wall friction factors, fi and fw, based on a three-fluid model. The liquid phase was two kinds of glycerol-water solutions with the kinematic viscosity νL of two or four times larger than that of water. Experimental data were obtained in two axial sections with short and long axial distances from the swirler, which corresponds to swirling and non-swirling annular flow regimes, respectively. Both the azimuthal and axial components of interfacial velocity decayed with increasing νL. The interfacial swirl number si, which is the ratio of the azimuthal component to the axial component of interfacial velocity, was not affected by νL for z*(=z/D) ≤ 3.8, where z is the axial coordinate in the test section. The mean interfacial swirl number si∗, which is the arithmetic mean of si in z* ≤ 3.8, was expressed in terms of dimensionless numbers based on the gas and liquid volumetric fluxes without νL. The interfacial friction factor decreased with increasing νL in swirling flows. The functional form of the Colebrook equation had a prospect of correlating fi in both swirling and non-swirling annular flows. The wall friction factor ratio of fw in the swirling annular flow regime to that in the non-swirling annular flow regime decreased as νL increased for si∗ > 0.33. The wall friction factor ratio was well correlated in terms of si∗ and νL.

Numerical modelling of stirring characteristics of gas−slag−copper matte multiphase flow in bath with top submerged lance

The hydrodynamics and stirring characteristics of the nitrogen−slag−copper matte in a bath with top submerged lance were numerically studied via the volume-of-fluid (VOF) method. The relationship between the bubble behavior and fluid velocity was elucidated. The effects of gas injecting velocity and swirling flow on the fluid vortex structure, gas penetration depth, and fluid velocity were investigated. The results demonstrate that the formation and rising of the bubble increase and reduce the fluid velocity, respectively. The V-shaped and W-shaped temperature distributions of the fluid are observed at the height of 0.43 and 0.52 m, respectively, resulting from the injection of the low-temperature gas phase. Compared to the gas injection velocity of 58 m/s, the time-averaged and maximum penetration depths of the gas phase with the injection velocity of 96 m/s increase by 78.4 % and 31.9 %, respectively. Swirling flow reduces the gas penetration depth, enhances the momentum transfer efficiency between phases, and suppresses the slag splashing, which is attributed to the reduced axial velocity component.

Vanishing Shear Viscosity Limit for the Navier–Stokes Equations with Cylindrical Symmetry: Boundary Layer and Optimal Convergence Rate

We consider the initial boundary-value problem for the nonisentropic compressible Navier–Stokes equations with cylindrical symmetry and degenerate heat conductivity coefficient. The vanishing shear viscosity limit with strong boundary layer effect for arbitrarily large data is investigated. Compared with the existing result in [X. Qin et al. Arch. Rational Mech. Anal., 216 (2015) 1049–1086], where the optimal convergence rate in terms of shear viscosity is obtained for the angular and axial velocity components, we derive the optimal convergence rate. The main challenges include that the presence of the strong boundary layer effect will prevent the convergence over the whole spatial domain, and that the quantities of a nonisentropic flow interact strongly with each other not only through the pressure term but also through the strongly nonlinear term in the temperature equation which would possibly slow down the convergence rate. Our main strategy is to find some new functions via asymptotic matching methods such that both the strong boundary layer effect and those quantities decaying at a lower speed can be canceled.

ВЗАИМОДЕЙСТВИЕ И ДИНАМИКА ТОПОЛОГИЧЕСКИХ ДЕФЕКТОВ В ДОМЕННОЙ СТРУКТУРЕ ЗАКРУЧЕННОГО НЕМАТИКА

The dynamics and interaction of topological defects in the domain structure of π/2 twisted nematic liquid crystal are studied. A feature of Williams domains in twisted nematics is that hydrodynamic flows in them, along with the tangential velocity component, also have an axial component, the direction of which is opposite in neighboring domains. The axial velocity component arises as a result of the strong coupling between the initial twisted director orientation n and the hydrodynamic flow velocity. In domain structures of π/2 twisted nematics, as well as in planar oriented ones, edge dislocations with topological charges S =±1 arise. With increasing applied voltage density of dislocations grows. Dislocations move both along the Williams domains ( climb ) and perpendicular to them ( glide ). At a certain rate of the increasing applied voltage U > U c, distortions of the domain structure begin to propagate on both sides of the defect core. This leads to the formation of a special topological defects - dislocations with a “diffused” core, or linear defects, which are oriented perpendicular to the Williams domains and move mainly along them. The arising linear defect has the same topological charge as the initial dislocation. It is shown that their interaction is qualitatively well described by the perturbed sine-Gordon equation.

Smokestack gas velocity measurements using 3D pitot tubes in a coal-fired power plant

On the path to carbon neutrality to reduce greenhouse gas (GHG) emissions, the Korean government has mandated legislation for controlling and monitoring GHG emissions emitted from smokestacks. A continuous emission measurement (CEM) method is considered to be the most reliable for determining CO2 emissions from stationary sources. In Korea, an S-type Pitot tube is the most popular technique to measure the gas velocity in a smokestack, but it will result in a certain error when the non-axial velocity components exist. To vanquish this limitation, Korea Research Institute of Standards and Science (KRISS) developed a nulling smokestack flow measurement (NSFM) instrument equipped with 3D Pitot tubes for taking on-site stack gas velocity measurements. 3D Pitot tubes used in this research, such as prism Pitot tube and sphere Pitot tube, are calibrated in the KRISS airspeed system. The instrument using 3D Pitot tubes with the nulling technique is expected to diminish the restriction on S-type Pitot tubes, and to enhance the quality of the GHG emission measurements in the smokestack. The 3D Pitot tubes can measure both axial and non-axial velocity components of a flow, whereas the S-type Pitot tubes can measure only the axial velocity component. The averaged axial velocity of the stack gas as measured by this instrument has expanded uncertainty of 3.3% (P = 95%, k = 2) for both prism and sphere Pitot tubes.

Experimental and Computational Study on Effect of Vanes on Heat Transfer and Flow Structure of Swirling Impinging Jet

The study focuses on heat transfer performance and flow structure associated with swirling jet on a flat target surface. The analysis is carried out with helicoid inserts of swirl number S = 1.3 by varying the number of vanes with Reynolds number between 11200 and 35600. The comparison of swirling jet with circular jet is carried out on its heat transfer performance. The heat transfer and flow structure are visualized using thermo-chromic liquid crystal sheet and oil film technique respectively. The numerical simulation is also performed at Re = 24700 for H/D distance between 1 and 4 using computational fluid dynamics. The heat transfer results reveal that the presence of axial recirculation zone at Re = 29800 and 35600 for the triple helicoid affects the uniformity of heat transfer distribution at 0 < X/D < 1.5 at H/D = 3. The axial component of velocity with respect to swirling jet is less than zero in the stagnation area and it increases at 0.57 < r/D < 0.97 for single vane and 0.63 < r/D < 0.97 for double and triple vanes. While the steep increase in tangential velocity of the triple vane jet is apparent at 0 < r/D < 0.5 at H/D = 2 and 3, the maximum value of point radially shifts inward towards the jet. The location of maximum turbulent kinetic energy approaching the surface at about r/D = 0.9 - 1.2 which characterizes the swirling jet at H/D = 2.

On the Unsteady Rotationally Symmetric Flow Between a Stationary and a Finite Rotating Disk With a Given Change in the Axial Velocity

Abstract We consider the scenario of an unsteady viscous flow between two coaxial finite disks, one stationary and the other rotating with an axial velocity changing impulsively from zero to a constant value. The three-dimensional (3D) incompressible Navier–Stokes equations are analytically solved by postulating the polynomial profiles for the axial and circumferential velocity components and by employing the open-end condition of zero pressure difference and an integral approach. It is shown that the time-dependent squeezing of the fluid between the disks and the edge effects of the finite open-ended disks in the flow domain are determined by the compressing Reynolds number and the rotating Reynolds number for the case of laminar flow at low Reynolds numbers and small aspect ratios. The general explicit formulae are derived for the velocity and pressure distributions as a function of the compressing and rotating Reynolds numbers in this unsteady flow process (and the steady-state solutions are then obtainable as the compressing Reynolds number vanishes). A simple theoretical relationship between the radial and axial pressure gradients is deduced to hinge the radial and circumferential velocity components together. The values of the compression and rotation Reynolds numbers suitable to this theory are also suggested for the problem of rotating disk flows at low Reynolds numbers. The validity of the theoretical predictions for the circumferential, radial, and axial velocity components is partially verified through comparison with previous steady experimental and numerical results. These analytical results have the immediate engineering applications of fluid flows with varying gap widths, including wet brakes, wet clutches, hydrostatic bearings, face seals, and rotating heat exchangers.

Экспериментальное исследование запорного устройства вихревого типа

Modern technologies for obtaining materials include chemical reactions occurring at excess pressure and high temperatures accompanied by phase transitions. Such processes take place in devices for sulfuric acid production, heterogeneous catalysis and chemical synthesis, in devices for drying, burning and melting bulk materials and other furnaces. The technological processes under consideration are accompanied by the loading of bulk material into the internal cavity of the apparatus – the reactor. In this case, the material loading window is sealed by a mechanical locking device which opens at the stage of the technological process, accompanied by loading of raw materials into the reactor. In this case, the air-tightness of the reactor is broken and gases can be released into the environment, which poses a threat to the health of the working staff and the environment as a whole. The article focuses on an experimental study of the gas-dynamic characteristics of the air flow at the exit of the annular nozzle of a vortex-type pneumatic shut-off device. The paper analyzes the methods for studying hydro-gas-dynamic parameters of vortex flows with justification for the choice of the study method. It also describes the laboratory setup and instrumentation for the study. The results of the research include the distribution of total pressure from the axial component of velocity and its structure. We also constructed the diagrams of the distribution of the axial component of the active air velocity and obtained a refined velocity distribution along the nozzle radius. The results of the study indicate the operability of the device and can be used in the physical and mathematical description of the working process of a vortex pneumatic shut-off device, as well as in the development of methods for optimal profiling of the device.

РАСПРОСТРАНЕНИЕ ПУЛЬСАЦИЙ ПО ПОТОКУ ЖИДКОГО МЕТАЛЛА

This work develops a method for measuring the speed of an isothermal flow of liquid metal in a cylindrical channel. The method does not require calibration, is non-contact and is based on a correlation technique. The generation of pulses is carried out using rotating magnetic field inductors. Pulses of the axial velocity component are recorded by recording the electromagnetic response of local velocity meters. It is shown that with a small number of pulses, the value of the correlation function is small, which does not allow the velocity to be reliably measured, even with increasing pulse intensity. Conversely, a high degree of correlation for this technique is achieved with a significant increase in the number of pulses, which entails an increase in the duration of measurements.

Magnetized Tri-hybrid Nanofluids flow with binary Chemical Reaction and activation Energy through the porous Surfaces

Hybrid nanofluids are important to researchers because of their industrial applications due to their high heat transfer rates. Tri hybrid different types of nanoparticles are discussed here with Newtonian fluids under the effect of MHD. The most important chemical reaction associated with mass transfer and activation energy parameters hasbeen discussed in detail. The current research focuses on two-dimensional fluids with heat transfer enhancement flowing over a porous surface. The mathematical modeling of the problem, as well as empirical relations for nanoparticle materials, is expressed as PDEs, which are then translated into ODEs using appropriate variables. The Runge–Kutta and shooting methods are combined to solve the problems of the created coupled differential system. Variations in nanoparticle volume fraction at the lower and upper walls of porous plates, as well as heat transfer rate measurements, are computed using controlling physical factors. The impact of flow-related variables on the axial, radial, and temperature components of velocity and temperature distribution is also assessed.

Evaluation of different window heights and facade porosities in naturally cross-ventilated buildings: CFD validation

The natural ventilation (NV) evaluation of an isolated building with axial windows is presented. The windows are located at bottom, middle or top heights on the windward and leeward facades. Three facade porosities P (0.05, 0.10 and 0.20) are tested. The study is performed using Computational Fluid Dynamics simulations validated with experiments from the literature. A validation methodology that includes the normalized axial-velocity component and surface pressure coefficients is proposed. This methodology complements the best existing practice guidelines. The normalized average velocity magnitude U∗ and the velocity homogeneity index H, both calculated in the living zone, are used as the NV evaluation parameters. The normalized volumetric flow Q∗ is also reported. The simulation results show that the increase in the window height produces a decrease of U∗ and an increase in H and Q∗. The increase of P produces an increase in U∗ and Q∗, but it does not imply a systematic increase or decrease of H. The Bottom and Middle window configurations with P=0.20 have relative high values of U∗ and H. Therefore these two are the window configurations with the best NV performance.

Similarity solution for isothermal flow behind the magnetogasdynamic cylindrical shock wave in a rotating non-ideal gas with the effect of the gravitational field

In this paper, we investigate a system of quasilinear hyperbolic partial differential equations, which describes the propagation of cylindrical shock waves in a rotating non-ideal gas with the effects of the gravitational field and the axial magnetic field. It is assumed that the flow is isothermal. The Lie group of transformations is used to generate the self-similar solutions of the considered problem in the medium of uniform density. The axial and azimuthal components of fluid velocity and magnetic field are supposed to be varying. We find the generators of the Lie group of transformations by employing the invariant surface criteria. We discovered four alternative solutions by selecting the arbitrary constants indicated in the generators' phrase. Only in three out of these four cases, the self-similar solutions exist. Two types of shock paths appear while solving the above cases. The power-law shock path appears in the first and third cases, while the exponential-law shock path appears in the second case. To find self-similar solutions, these cases have been solved numerically. We graphically show the distributions of flow variables behind the shock wave so that we can observe the effect on flow variables of the various values of the non-ideal parameter, Alfvén Mach number, adiabatic exponent, gravitational parameter, and ambient azimuthal velocity exponent. For the computational task, we used “MATLAB” software.