Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

Dynamics of vortex line in presence of stationary vortex

The motion of a thin vortex with infinitesimally small vorticity in the velocity field created by a steady straight vortex is studied. The motion is governed by non-integrable PDE generalizing the Nonlinear Schrodinger equation (NLSE). Situation is essentially different in a co-rotating case, which is analog of the defocusing NLSE and a counter-rotating case, which can be compared with the focusing NLSE. The governing equation has special solutions shaped as rotating helixes. In the counter-rotating case all helixes are unstable, while in the co-rotating case they could be both stable and unstable. Growth of instability of counter-rotating helix ends up with formation of singularity and merging of vortices. The process of merging goes in a self-similar regime. The basic equation has a rich family of solitonic solutions. Analytic calculations are supported by numerical experiment.     

一个新的射流颗粒速度差公式

从射流拉伸过程的能量关系出发 ,导出了相邻颗粒间速度差的理论公式。这个公式表明 ,速度差与射流初态及物质特性有关 ,因而也与断裂颗粒的几何形状有关。对一般颗粒形状 ,理论给出的无量纲速度与实验结果有较好的一致性。     

Velocity field and heat transfer in a vortex flow exchanger

This study deals with the flow of newtonian and non-newtonian fluids, inside a cylindrical flat cavity, provided with a tangential injection device, model of heat exchangers with spiral flow.The dynamic analysis which requires essentially a laser Doppler velocimeter focusses on the determination of the velocity field and brings out the existence of secondary flows which are important for heat transfer.In turbulent regime, the law of exchange agrees with the Chilton-Colburn analogy. On the other hand, for laminar flow, it becomes necessary to include the variations with temperature of the consistency (K); the Nusselt number (Nu) not only depends on the flow rate, but also on the density of transferred heat flux.

---

Geschwindigkeitsfeld und Wärmeübertragung in einem Wärmeüberträger mit spiralförmiger Strömung

Zusammenfassung Diese Studie betrifft die Strömung von Newton'schen oder Nicht-Newton'schen Flüssigkeiten innerhalb eines flachen zylindrischen Hohlraumes, der mit einem tangentialen Einspritzungssystem versehen ist und als Modell für Wärmeaustauscher mit spiralförmiger Strömung dient.Die dynamische Analyse, die das Laser-Dopplerverfahren (Laser-Velocimetrie) erfordert, kennzeichnet das Geschwindigkeitsfeld und beweist die Existenz von Sekundärströmungen, die für die Wärmeübertragung wichtig sind.Für den turbulenten Betrieb folgt das Gesetz des Wärmeaustausches der Chilton-Colburn Analogie. Was den laminaren Betrieb angeht, wird es erforderlich, die Variationen der BeschaffenheitK mit der Temperatur zu berücksichtigen. Die Nusseltsche Zahl hängt natürlich vom dynamischen Betrieb ebenso wie von der übertragenen Leistung ab.

---

Nomenclature Nu=[/S T]D _h/ Nusselt number - Re=V ₀ D _h/ Reynolds number - Re _g=V ₀ ^2–n D _n ^h /K generalized Reynolds number - Pr=C _p / Prandtl number - Pr _g=C _p[V ₀/D _h] ^n–1 K/ generalized Prandtl number - H height of cylinders (m) - H dimension of the entrance device (m) - S ₁ tested section - S ₂ tested section - shear stress (Pa) - K consistency (Pa s ⁿ ) - shear rate (s^–1) - n power law index - a, b constants in the consistency formulaK=a exp [–b t] - a, b constants in the rheological indexn=a exp [b T] - T, T _e,T _p temperature, inlet temp., wall temp. - p pressure (Pa) - p pressure drop (Pa) - V velocity vector (components:V ₁,V ₂,V ₃) (m/s) - V ₀ mean velocity (m/s) - X ₁,X ₂,X ₃ cylindrical coordinate system - C _f friction factor - R ₁,R ₂ radius (m) - heat flux (W) - thermal conductivity (W/(m °C)) - C _p specific heat of fluid (J/(kg C°)) - dynamic viscosity (Pa s) - Q _v volumic flow rate (m³/s) - =/S heat flux density (W/m²) - S exchange area (m²)     

Non-uniform recovery of vortex breakdown over delta wing in response to blowing along vortex core

The transient characteristics of vortical structure over delta wing are studied experimentally when subject to single along-core blowing perturbation. Two half delta wing models with different sweep angle = 60° and = 75° are investigated in this study. For = 75°, the transient location of the onset of vortex breakdown moves upstream monotonously toward the unperturbed location. However, for =60°, there exists a chordwise region where the upstream propagation of the onset location of vortex breakdown is temporarily delayed. This delay causes the recovery process (upstream propagation) of the onset location of vortex breakdown to be non-uniform. In fact, this non-uniform recovery may take on different appearance such as a plateau or overshoots and will last for several times of the convective time scaleC/U . Furthermore, the location of chordwise region corresponding to this delay depends strongly upon the angle of attack (AOA). In additions, the non-uniform recovering characteristic of the onset of vortex breakdown may not be observed at high AOA if the blowing rate is too low. The mechanism governing the non-uniform recovering characteristic is clearly verified through the LDA measurement and the phase-locked flow visualization. Evidently the mutual interaction between the primary vortex structure and the secondary vortex is the key mechanism that leads to non-uniform recovering character over delta wing with sweep angle of 60°The authors are grateful for the support of the this investigation from National Science Foundation of the Republic of China under the grant no. NSC-83-0424-E-005-006.     

Fast numerical evaluation of flow fields with vortex cells

A vortex cell (in this paper) is an aerodynamically shaped cavity in the surface of a body, for example a wing, designed specially to trap the separated vortex within it, thus preventing large-scale unsteady vortex shedding from the wing. Vortex stabilisation can be achieved either by the special geometry, as has already been done experimentally, or by a system of active control. In realistic conditions the boundary and mixing layers in the vortex cell are always turbulent. In the present study a model for calculating the flow in a vortex cell was obtained by replacing the laminar viscosity with the turbulent viscosity in the known high-Reynolds-number asymptotic theory of steady laminar flows in vortex cells. The model was implemented numerically and was shown to be faster than solving the Reynolds-averaged Navier–Stokes equations. An experimental facility with a vortex cell was built and experiments performed. Comparisons of the experimental results with the predictions of the model are reasonably satisfactory. The results also indicate that at least for flows in near-circular vortex cells it is sufficient to have accurate turbulence models only in thin viscous layers, while outside the viscosity should only be small enough to make the flow effectively inviscid.     

Diffusion of a line vortex in a second-order fluid

In this paper, the diffusion of a line vortex in a second-order fluid is considered. The Hankel transform is used to solve this problem and an exact solution for the velocity distribution is found in terms of a definite integral. The integrand is an oscillatory function and the integration is performed by a numerical technique. It is found that there are pronounced effects of viscoelastic properties on the velocity distribution with respect to that of the Newtonian fluid.     

Velocity field generated by wing vibrations propagating along the surface

The velocity field generated by wing vibrations propagating along an elastic wing surface with finite velocity is studied.The gasdynamic problem is reduced to a mixed boundary-value problem with a moving boundary for the three-dimensional wave equation. The solution is obtained in closed form when the wing travels at supersonic velocity following an arbitrary law, the vibration propagation front is an arbitrary curve displacing along the wing surface, and the wing edges are supersonic.     

Interaction of a line vortex with a round parachute canopy

The interaction of a rectilinear vortex with an inflated round parachute canopy model was studied experimentally in a water tunnel where the vortex core was aligned with the axis of the canopy. Three different canopy diameters were used, and the canopy model was attached to a streamlined forebody. Dye flow visualization indicated that vortex breakdown was present when the core trajectory was within the canopy opening. Vortex breakdown occurred about one to two canopy diameters upstream of the canopy opening. The vortex core completely disintegrated when it interacted with the forebody near the canopy centerline. The vortex breakdown and disintegration caused unsteady, asymmetric deformations on the canopy surface. A reduction in the time-averaged drag and an increase in the fluctuating drag was observed when the vortex core was within the canopy opening. The disintegration of the vortex core near the canopy centerline lessened the drag reduction brought on by the presence of the core.     

Velocity fields around spheres and bubbles investigated by laser-doppler anemometry

An experimental investigation is presented in which the velocity fields around sheres and bubbles moving in a cylinder have been measured by laser-Doppler anemometry (LDA). Instabilities in the flow field at rather low Deborah numbers have been discovered and these instabilities are damped by inertia forces. It is shown that the wall correction factor K is a rapidly decreasing function of the Deborah number. The experimental measurements have been compared with numerical simulations, and on the basis of this comparison it has been possible to identify a time constant and a zero-shear-rate viscosity for the test liquid.     

Scalar mixing in the field of a gaseous laminar line vortex

An experimental study of scalar mixing in a laminar vortex is presented for vortices generated between two gas streams flowing parallel to each other in a rectangular flow channel. An isolated line vortex is initiated on demand by momentarily increasing one stream velocity in relation to the other using an electromagnetically actuated piston. The temporal piston motion profile is tailored to generate vortices of different strengths corresponding to vortex Reynolds numbers, Re≡Γ/2πν=130–210. Evolution of mixing is monitored by laser-induced fluorescence of acetone vapor premixed into one of the gas streams as the vortex structure evolves with increasing downstream distance from its point of origin. Vortex is generated by pulsing either of the gas streams (seeded or unseeded stream). Vortex initiation process affects the abundance of the gas in the vortex core from the pulsed stream. Spatial mixing statistics are obtained by determining scalar concentration probability density functions (pdf) and the mean mixed fluid concentrations obtained from these pdfs. It is found that the interfacial area generation as a result of vortex kinematics and molecular diffusion along this interface are principally responsible for mixing. The mean mixed fluid concentration in the vortex interaction region scales with the product of vortex circulation and the elapsed time of interaction. These results are similar to those found in liquid mixing experiments, but the rate of mixing is significantly higher due to higher diffusivity of gases.     

Velocity fields and streamline patterns of miscible displacements in cylindrical tubes

Displacements of a viscous fluid by a miscible fluid of a lesser viscosity and density in cylindrical tubes were investigated experimentally. Details of velocity and Stokes streamline fields in vertical tubes were measured using a DPIV (digital particle image velocimetry) technique. In a reference frame moving with the fingertip, the streamline patterns around the fingertip obtained from the present measurements confirm the hypothesis of Taylor (1961) for the external patterns, and that of Petitjeans and Maxworthy (1996) for the internal patterns. As discussed in these papers, the dependent variable, m, a measure of the volume of viscous fluid left on the tube wall after the passage of the displacing finger, is a parameter that determines the flow pattern. When m>0.5 there is one stagnation point at the tip of the finger; when m<0.5 there are two stagnation points on the centerline, one at the tip and the other inside the fingertip, and a stagnation ring on the finger surface with a toroidal recirculation in the fingertip between the two stagnation points. The finger profile is obtained from the zero streamline of the streamline pattern.An erratum to this article can be found at     

Velocity and concentration fields in settling tank of non-interacting solid particles

Summary In this paper there is a synthetic presentation of the theoretical principles of the phase difference method for the simultaneous measurements of size, velocity and concentration of particles dispersed in fluid, its application to spherical glass particles free falling in water at rest, and the measured velocity and concentration fields of the particles in a settling tank model. Particles with diameter between 75÷150 m were used. The method used seems reliable in obtaining the necessary information to analyze the performance of settling tanks in relation to the influencing factors the particles settling.

---

Sommario In questo articolo sono presentati in forma sintetica i principi teorici del metodo della differenza di fase per la misura simultanea di velocità, dimensione e concentrazione di particelle disperse in un fluido, ed un'applicazione di tale metodo al caso di particelle di vetro, di dimensioni fra i 75–150 m, disperse in acqua. Le misure effettuate sono relative alla sedimentazione di particelle in acqua in quiete ed ai campi di velocità e concentrazione delle particelle che si realizzano in un modello fisico di vasca di sedimentazione rettangolare. I risultati ottenuti sembrano confermare l'adeguatezza del metodo impiegato per analizzare l'efficienza delle vasche di sedimentazione in relazione ai fattori che influenzano la sedimentazione di particelle.

---

---

This work was supported by the Italian Ministry of Education.     

An immersed lifting and dragging line model for the vortex particle-mesh method

Theoretical and Computational Fluid Dynamics - The numerical study of the wake of full-scale slender devices such as aircraft wings and wind turbine blades requires high-fidelity large eddy...     

Displacement measurement along a line by the diffractographic method

The diffractographic method, a recently developed experimental technique, has been extended to solve the problem of determining the displacement information along the length of a beam. The method, which uses the diffraction of monochromatic light through a variable aperture whose size is a function of the beam displacement, demonstrates that this displacement along a line technique offers a new and accurate method occupying the unique position between point detectors and whole-field procedures.     

Elastic fields of line defects in a cracked body

Elastic fields are presented for line forces and dislocations in the vicinity of a crack tip and of a contained, double-ended planar crack. The fields of line force couples are also derived. The corresponding stress intensity factors are listed. The use of these results as two-dimensional Green functions for more general cases is discussed.     

Velocity distributions in Taylor vortex flow with imposed laminar axial flow and isothermal surface heat transfer

Fully-developed flow in a concentric annulus formed by a stationary outer cylinder, which may be heated isothermally, and a rotatable inner cylinder has been studied experimentally by means of hot-wire anemometry techniques. Velocity profiles for the axial, tangential, and radial directions of flow have been obtained for adiabatic conditions and for wide and narrow annular gaps.It has been shown that the onset of Taylor vortex flow has a pronounced effect on the velocity profiles for all three directions. However, while the profiles for the axial and tangential directions are explicable, those for the radial direction are not so, at present. Also, it was found that heat transfer through the outer annular surface had a greater effect on the radial velocity profile than on the axial or tangential, but in the narrow gap case only.