Steady Axial Flow Research Articles

Numerical Simulation of Horizontal Axis Wind Turbines with Vortex Generators

In the present study, a simulation about the effects of vortex generators on horizontal axis wind turbine rotor blade was numerically conducted using a static coupled CFD–CSD method. A Navier–Stokes CFD flow solver based on unstructured meshes was used to obtain the blade aerodynamic loads. A FEM-based CSD solver employing a nonlinear coupled flap-lag-torsion beam theory was utilized to calculate the blade elastic deformation. The coupling of the CFD and CSD solvers was accomplished in a loosely coupled manner by exchanging the information between the two solvers at infrequent intervals. The static coupled CFD–CSD method was applied to the NREL 5 MW reference wind turbine rotor under steady axial flow conditions. Triangular counter-rotating vortex generators were adopted to control flow separation and radial flow in the inboard section of the NREL 5 MW reference rotor blades. They were installed on the inboard part of the blade from 0.2 to 0.4 R. As a result of the flow analysis considering the counter-rotating vortex generators, strong vortices were generated by counter-rotating vortex generators. It can be seen that the regions where flow separation and radial flow occur in the inboard sections were reduced compared to the baseline wind turbine. For this reason, the maximum power improvement due to counter-rotating vortex generators was 1.04% at the rated wind speed.

Nonlinear static response of low-aspect-ratio inverted flags subjected to a steady flow

The nonlinear static response of inverted flags, otherwise known as cantilevered plates in a reverse steady axial flow, is investigated. Recent studies have shown that the stability of low-aspect-ratio inverted flags in fluid flow is different to that of wide inverted flags. The latter undergo a supercritical divergence with increasing flow velocity, while a low-aspect-ratio inverted flag buckles abruptly within a wide bistable region. This paper aims to understand the effect of aspect ratio on the stability and bifurcation characteristics of the multiple equilibria of low-aspect-ratio inverted flags. To this end, the inverted flag is idealized as a thin Euler–Bernoulli beam coupled with the time-invariant form of the fluid forces obtained from a potential flow theory. A Hamiltonian framework is employed to derive the nonlinear integro-differential equation governing the motion expressed in terms of the mid-line rotation angle of the flag along its longitudinal axis. This allows for reliable predictions even at very large deflection amplitudes. The presence of an initial curvature along the length of the flag is also accounted for in the modelling. The Galerkin modal decomposition technique along with a Newton method is employed and the fixed-points of the governing equation are found. Bifurcation diagrams of the response with respect to the flow velocity are constructed. It is shown that the system with small aspect ratio undergoes a static divergence via a subcritical pitchfork bifurcation followed by a saddle–node bifurcation. Supercritical pitchfork bifurcations are expected for sufficiently large aspect ratios. In addition, numerical simulations are performed to investigate the effect of initial curvature amplitude on the nonlinear response of the system. The numerical predictions stemming from the proposed model compare well with existing experimental measurements available in the literature. However, it should be noted that some of the reported static responses of the inverted flag might violate the assumption of potential flow theory.

Numerical and experimental investigation on opening direction steady axial flow force compensation of converged flow cartridge proportional valve

This paper proposes a method to optimize a structure that can compensate the steady axial flow force acting on the spool in a converged flow cartridge proportional valve. The negative flow force working on the origin conical poppet, which can be as large as 13% of the control force, acts as a big disturbance to the conical spool position adjustment, resulting in poor lowering speed control performance of the proportional valve or even instability of the conical spool. Firstly, by introducing a damping tail structure to the conical poppet, the direction and the value of the flow forces can be regulated, and through changing parameters of damping tail, the optimal structure can be obtained. Computational fluid dynamics (CFD) calculations were conducted to analyze how the damping tail parameters affect the flow forces and obtain the best parameter combinations. A test rig was set up to verify the effect of above methods. Good agreement of the CFD calculations and experiment results indicates that the proposed methods can provide guidance for the flow force regulation of other valve poppets.

Semi-analytical unsteady aerodynamic model of a flexible thin airfoil

This paper presents a geometrically exact semi-analytical approach to model the unsteady aerodynamics of a flexible thin airfoil in incompressible potential flow. The velocity field is described by a complex potential, which is developed by mapping the airfoil boundary onto a circle. This methodology, well established for small disturbances, is here generalized to evaluate the aerodynamic load on an airfoil subject to prescribed arbitrary rigid-body motion and deformation. The model also includes the effects of free wake, modeled by a large number of discrete vortices. A general semi-analytical solution for the aerodynamic pressure distribution is obtained, specialized to the case of curvature of constant sign along the airfoil chord, and validated with reference linearized results. Next, the model validity for large curvatures is discussed by comparing velocity fields around increasingly deformed airfoils with numerical solutions from suitable panel methods. Finally, results for a cantilevered flexible airfoil subject to prescribed deformation in a steady axial flow are presented to point out different unsteady mechanisms influencing the aerodynamic pressure distribution and responsible for its changes in time. This insight is peculiar of the semi-analytical nature of the present formulation and cannot be easily obtained through numerical handling of the problem. The paper ends by outlining future developments of the present work toward the ultimate goal of studying coupled fluid–structure interaction problems in presence of very large deformations.

Visualization Calculation and Experimental Verification of Steady Axial Flow Force on the Converged Flow Sliding Valve

Visualization Calculation and Experimental Verification of Steady Axial Flow Force on the Converged Flow Sliding Valve

Predicting wind turbine blade loads and aeroelastic response using a coupled CFD–CSD method

The aeroelastic response and the airloads of horizontal-axis wind turbine rotor blades were numerically investigated using a coupled CFD–CSD method. The blade aerodynamic loads were obtained from a Navier–Stokes CFD flow solver based on unstructured meshes. The blade elastic deformation was calculated using a FEM-based CSD solver which employs a nonlinear coupled flap-lag-torsion beam theory. The coupling of the CFD and CSD solvers was accomplished in a loosely coupled manner by exchanging the information between the two solvers at infrequent intervals. At first, the present coupled CFD–CSD method was applied to the NREL 5MW reference wind turbine rotor under steady axial flow conditions, and the mean rotor loads and the static blade deformation were compared with other predicted results. Then, the unsteady blade aerodynamic loads and the dynamic blade response due to rotor shaft tilt and tower interference were investigated, along with the influence of the gravitational force. It was found that due to the aeroelastic blade deformation, the blade aerodynamic loads are significantly reduced, and the unsteady dynamic load behaviors are also changed, particularly by the torsional deformation. From the observation of the tower interference, it was also found that the aerodynamic loads are abruptly reduced as the blades pass by the tower, resulting in oscillatory blade deformation and vibratory loads, particularly in the flapwise direction.

Mixing strategies in the top seeded solution growth-slow cooling of doped KGd(PO[formula omitted])[formula omitted] crystals

A 3D numerical simulation is presented here to analyze the growth of doped KGd(PO3)4 single crystals. A quasi-steady approximation of the whole growth based on three independent sets of simulations considering three different crystal sizes has been made. Under this approximation, the steady axial flow rate shows a double linear dependence on the crystal size and on the rotation rate externally applied. In addition, the present calculations indicate that the sixteen vanes rotating platinum stirrer used in real growth experiments does not improve the axial flow toward the crystal/s, only increases the tangential velocity of the liquid system.. Finally, according to the axial flow criterion, it can be concluded that the best situations are obtained using one or two eccentric rotating crystals without stirrer.

Experimental Measurements of the Interface Thermal Conductance of a Lithium Metatitanate Pebble Bed

The thermal properties of the lithium ceramics pebble beds have a significant impact on the temperature profile of the Helium Cooled Pebble Bed blanket and the extraction of heat from the pebble beds to the coolant. The literature review showed a lack of experimental data on the interface thermal conductance (h) of lithium metatitanate pebble beds, therefore the objective of this study is to present experimental values of h. The measuring technique is based on the principles of steady state and axial heat flow methods. The lithium metatitanate pebble bed is single size (˜O1.7-2.0mm pebbles) with a packing fraction of 61%. The values of h were measured at the interface of the pebbles with their container’s wall (made of stainless steel 316). The results showed that h increased from 1800 to 5300W/m2.K with the increase of the wall temperature from 24 to 570°C. The theoretical values of h, calculated by three models, were compared with the experimental values. The theoretical and experimental values of h showed similar behavior with the increase of temperature. The present values of h will help to create a reliable database of the thermal properties of the lithium ceramics pebble beds.

Experimental measurements of the effective thermal conductivity of a lithium titanate (Li 2TiO 3) pebbles-packed bed

Tritium breeding materials, which have the ability to react with neutrons and produce tritium, are required to fuel fusion reactions. Tritium is produced inside the fusion blanket by neutron irradiation of lithium ceramics (tritium breeders). Using the lithium ceramics in form of pebbles-packed bed is a promising concept for fusion blankets, and worldwide efforts have been dedicated to its R&D. Thermal properties of lithium ceramic pebble beds have a significant impact upon the thermal performance of the fusion blanket. Specifically, the effective thermal conductivity of lithium ceramic pebble beds is important for the design and analysis of fusion blankets. The experimental apparatus of this study was designed and built based on the principles of the steady state and axial heat flow methods in order to conduct the required measurements. The objective of this study is to measure the effective thermal conductivity of a Li 2TiO 3 pebble bed as a function of the average bed temperature. The pebble bed has pebbles of 1.7–2.0 mm diameter and a packing fraction of 61%. Helium at atmospheric pressure was used as a filling gas. The experimental results showed that the effective thermal conductivity decreased from 1.40 to 0.94 W/m K with the increase of the average bed temperature from 50 to 500 °C. The results presented in this work will help to create a database of the effective thermal conductivity of Li 2TiO 3 pebble beds which can be used for the design and analysis of fusion blankets.

Classification of aeroacoustically relevant surface modes in cylindrical lined ducts

Wave modes in a straight cylindrical duct with a locally reacting boundary and a steady subsonic axial flow are investigated. The duct modes are separated into ordinary duct modes and surface modes confined to a neighbourhood of the boundary. Previous asymptotic results of Rienstra for the surface modes assume that the dimensionless frequency ω is large, and that the azimuthal order m ≪ ω. In this paper, these results are generalized to arbitrary values of m, as applicable to rotor-alone noise in aeroengines where m is a multiple of the number of blades and is typically O ( ω). A dimensionless number λ is found to govern the surface modes’ behaviour, and qualitatively different behaviour is seen for λ in four distinct regions, separated by critical values depending only on the steady flow Mach number. For aeroacoustically relevant parameters, our generalized asymptotics are shown to provide a distinctly better approximation to the full equations than previous approximations.

Presentation of a test system in terms of generated pulsatile flow characteristics

A complete test system associative with the measurement and data acquisition components was designed and constructed for an experimental investigation on pulsatile pipe flows. The basics of the test system and conducted experiments directed towards the determination of pulsatile flow characteristics at the measurement site in passage from laminar to turbulent regime are presented in this paper. Pulsatile flow was produced by superimposing a purely sinusoidal oscillation on steady axial flow in a rigid circular cross-sectional pipe. The flow nature at the measurement site was determined via cross-sectional velocity and wall pressure gradient measurements in the range of time-averaged Reynolds number; Re ta 1800≤ Re ta≤60,000. The covered ranges for the dominant oscillation parameters; dimensionless frequency parameter ω′ and the oscillation velocity amplitude ratio; A 1 were 5≤ ω′ ≤28 and 0.0035≤ A 1≤0.7113 respectively. The so-called flow reversal observed for the cases with ω′ =7 and ω′ =12.5 was represented in terms of correlations between Re ta, oscillating Reynolds number; Re os and A 1 to describe the flow behaviour in the critical stage prior to the flow reversal.

Transient fluid motions in a simplified model for oilfield plug cementing

Transient motions are considered in closed inclined slot filled with two miscible Bingham fluids of differing densities. This situation forms a simple model for buoyant flows found in the oilfield process of plug cementing. A minimisation method is used to compute the volume flux in each phase, to satisfy the constraint of zero net-flow. Interface propagation is then studied via numerical solution of a hyperbolic conservation law, for which a third-order compact finite difference method is used. Shocks are found to form for all nontrivial solutions. There are typically two shocks, moving both up and down the inclined slot, stretching the interface between them. The parametric variation of shock propagation speed with the fluid yield stresses and plastic viscosities is studied. Finally, the fully transient problem is analysed qualitatively. It is shown that for sufficiently large yield stresses, for which the steady axial flow has only trivial solutions, the velocity of the fully transient problem decays to zero in a finite time. The decay timescale is controlled by the magnitudes of the yield stresses and plastic viscosities.

Stability of viscoelastic shear flows subjected to steady or oscillatory transverse flow

Experiments and theory show that hydrodynamic instabilities can arise during flow of viscoelastic liquids in curved geometries. A recent study has found that a relatively weak steady transverse flow can delay the onset of instability in the circular Couette geometry until the azimuthal Weissenberg number Weθ is significantly higher than without axial flow. In this work we investigate the effect of superposition of a time-periodic axial Couette flow on the viscoelastic circular Couette and Dean flow instabilities. The analysis, carried out for the upper-convected Maxwell and Oldroyd-B fluids, generally shows increased stability compared to when there is no axial flow. However, we also find that the system shows instability – synchronous resonance – for some values of the axial Weissenberg number, Wez and forcing frequency ω. In particular, instability can be induced not only when ω is of the order of the inverse relaxation time of the fluid but also when it is much smaller. Scaling arguments and numerical results indicate that the high-ω, low-Wez regime is essentially equivalent to Wez=0 in the steady case, implying no stabilization. At high values of ω and Wez, scaling analysis shows that the flow will always be stable. Numerical results are in agreement with these conclusions. Consistent with previous results on parametrically forced systems, we find that the zero-frequency limit is singular. In this limit, the disturbances display quiescent intervals punctuated by periods of large transient growth and subsequent decay.This study also presents linear and nonlinear stability results for the addition of steady axial Couette and Poiseuille flows to viscoelastic instabilities in azimuthal Dean flows. It is shown that, for high Wez, the qualitative effect of adding a steady axial flow is similar to that in the circular Couette geometry, with a linear relationship between the critical Weθ and Wez. For low Wez, we find that the flow is stabilized, unlike in the circular Couette flow where the critical value of Weθ decreases at low Wez. Further, weakly nonlinear analysis shows that the criticality of the bifurcation depends on the value of Wez and the solvent viscosity, S. Finally, we also show the presence of a codimension-2 Takens–Bogdanov bifurcation point in the linear stability curve of Dean flow. This point represents a transition from one mechanism of instability to another.

Flow in a porous medium induced by torsional oscillation of a disk near its surface

Torsional oscillation of an infinite disk in a viscous liquid bounded by a porous medium fully saturated with the liquid has been discussed. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equation and that in the porous medium by Brinkman equation. Flows in the two regions are matched at the interface by assuming that the velocity and stress components are continuous at it. It is found that the depth of penetration of the flow in the porous medium is proportional to the square root of the permeability of the medium. The oscillation of the disk induces a steady radial-axial flow in both the regions in such a way that there is a steady axial flow of the fluid from the porous medium to the free flow region i.e. the fluid is expelled out from the porous medium. The steady flow in the porous medium increases with the increase of the permeability of the medium and with the decrease of the distance between the oscillating disk and porous surface.

Numerical study on the effect of steady axial flow development in the human aorta on local shear stresses in abdominal aortic branches

The three-dimensional flow through a rigid model of the human abdominal aorta complete with iliac and renal arteries was predicted numerically using the steady-state Navier–Stokes equations for an incompressible, Newtonian fluid. The model adapted for our purposes was determined from data obtained from cine-CT images taken of a glass chamber that was constructed based on anatomical averages. The iliac arteries had a bifurcation angle of approximately 35° and a branch-to-trunk area ratio of 1.27, whereas the renal arteries had left and right branch angles of 40° and an area ratio of 0.73. The numerical tool FLOW3D (AEA Industrial Technology, Oxfordshire, UK) utilized body-fitted coordinates and a finite volume discretization procedure. Purely axial velocity profiles were introduced at the entrance of the model for a range of cardiac outputs. The four-branch numerical model developed for this investigation produced flow and shear conditions comparable to those found in other reported works. The total wall shear stress distribution in the iliac and renal arteries followed standard trends, with maximum shear stresses occurring in the apex region and lower shear stresses occurring along the lateral walls. Shear stresses and flow rate ratios in the downstream arteries were more effected by inlet Re than the upstream arteries. These results will be used to compare further simulations which take into effect the rotational component of flow which is present in the aortic arch.

Effect of axial flow on viscoelastic Taylor–Couette instability

Viscoelastic flow instabilities can arise from gradients in elastic stresses in flows with curved streamlines. Circular Couette flow displays the prototypical instability of this type, when the azimuthal Weissenberg number Weθ is O(ε−1/2), where ε measures the streamline curvature. We consider here the effect of superimposed steady axial Couette or Poiseuille flow on this instability. For inertialess flow of an upper-convected Maxwell or Oldroyd-B fluid in the narrow gap limit (ε[Lt ]1), the analysis predicts that the addition of a relatively weak steady axial Couette flow (axial Weissenberg number Wez=O(1)) can delay the onset of instability until Weθ is significantly higher than without axial flow. Weakly nonlinear analysis shows that these bifurcations are subcritical. The numerical results are consistent with a scaling analysis for Wez[Gt ]1, which shows that the critical azimuthal Weissenberg number for instability increases linearly with Wez. Non-axisymmetric disturbances are very strongly suppressed, becoming unstable only when ε1/2Weθ= O(We2z). A similar, but smaller, stabilizing effect occurs if steady axial Poiseuille flow is added. In this case, however, the bifurcations are converted from subcritical to supercritical as Wez increases. The observed stabilization is due to the axial stresses introduced by the axial flow, which overshadow the destabilizing hoop stress. If only a weak (Wez[les ]1) steady axial flow is added, the flow is actually slightly destabilized. The analysis also elucidates new aspects of the stability problems for plane shear flows, including the exact structure of the modes in the continuous spectrum, and illustrates the connection between these problems and the viscoelastic circular Couette flow.

定常流体軸力におよぼすスプール弁スリーブ流入出部形状の影響

In recent years, oil hydraulic spool valves have been widely used in electricmechanical control systems. However, the steady axial flow forces in the oil hydraulic spool valves are produced by the internal oil flow, and control of oil hydraulic spool valves becomes difficult owing to the effect of the steady axial flow forces.In this paper, whole domain of fluid inside a spool valve is simulated by the boundary element method.Shapes of sleeves are modified, and steady axial flow forces, flow patterns and boundary pressure distribution are calculated and compared. It is found that when a sleeve takes a shape shown in Fig.6, the steady axial flow forces applied on the spool are greatly decreased, and the angle θn of injection fluid at jet orifice also increases due to coanda effect of the flow.

221 傾斜した軸流段付き円柱周りの流れ

The characteristics of a steady axial flow around a stepped cylinder with small attack angle was investigated by means of the flow visualization technique of the smoke method at the Reynolds numbers less than 2×105. The experiments were carried out with the protrusion step length of the cylinder between -1.5mm and 16mm. The attack angle of cylinder model has an maximum value of 5 degrees. The pressure distributions on the cylinder surface were measured with respect to the two cases at the velocity of 15m/s and 30m/s.

逆問題手法を用いたスプール弁最適形状の設計

In the present study, the optimal shape of a spool valve was determined to reduce axial flow forces by solving the inverse problem. The basic assumptions in the present calculation are that the axisymmetric flow is incompressible, steady and inviscid. The basic equations were led by taking the stream function and the velocity potential as independent variables, and the equations were solved by the relaxation method. Next, the steady axial flow forces on spools of a conventional valve and the valve calculated by the present method were measured with a load cell. Furthermore, the unsteady axial flow forces for sudden valve opening were also measured and the effect of the spool valve obtained by the present method on reducing the axial flow force was investigated.

Heat transfer for MHD flow through a rectangular pipe with discontinuity in wall temperatures

The temperature distribution for steady MHD axial flow through a rectangular pipe has been calculated numerically. Owing to the discontinuity in the wall temperatures, the resulting differential equation which is a 3-dim. elliptic partial differential equation with variable coefficients, becomes impossible to handle analytically. The traditional finite difference methods become unsuitable due to the very large number of unknowns involved. The ADI method is found to be most suitable for the problem as it saves time as well as computer storage. Graphs are given to depict the temperature distribution near and away from the discontinuity for various Hartmann numbers.