Leading Stagnation Point Research Articles

Passive control of flow-induced vibration of a sphere using a trip wire

We experimentally investigated the potential of a trip wire as a passive control mechanism for controlling flow-induced vibration (FIV) of a three-dimensional bluff body. The effect of a surface trip wire was investigated for varying diameter ratio in the range 1.3×10−2⩽k/D⩽6.7×10−2, where k is the wire diameter and D is the sphere diameter, and trip-wire location in the range 20∘≤ϕ≤60∘, where the angle ϕ was measured from the leading stagnation point. The FIV response of the sphere is characterised for a wide range of reduced velocities 3⩽U∗⩽20, defined as U∗=U/fnwD, where U is the free stream velocity and fnw is the natural frequency of the system in water. It was found that for a fixed trip-wire diameter ratio, the vibration amplitude decreased progressively with increasing ϕ. Furthermore, the synchronisation regime became narrower, and the mode II and the plateau branches of the FIV response occurred for lower reduced velocities, compared to those for a smooth sphere. The control was highly effective for high reduced velocities (U∗>10) with a maximum reduction of up to 97.8% for ϕ=60∘. Interestingly, thicker trip wires (k/D>1.3×10−2) were effective in disrupting Mode I, but induced a galloping-like response for higher reduced velocities. Tripping proved to be an effective passive control strategy for spheres, with the optimal trip-wire size varying across Mode I to Mode III.

Inertia–Gravity Waves Generated within a Dipole Vortex

Abstract Vortex dipoles provide a simple representation of localized atmospheric jets. Numerical simulations of a synoptic-scale dipole in surface potential temperature are considered in a rotating, stratified fluid with approximately uniform potential vorticity. Following an initial period of adjustment, the dipole propagates along a slightly curved trajectory at a nearly steady rate and with a nearly fixed structure for more than 50 days. Downstream from the jet maximum, the flow also contains smaller-scale, upward-propagating inertia–gravity waves that are embedded within and stationary relative to the dipole. The waves form elongated bows along the leading edge of the dipole. Consistent with propagation in horizontal deformation and vertical shear, the waves’ horizontal scale shrinks and the vertical slope varies as they approach the leading stagnation point in the dipole’s flow. Because the waves persist for tens of days despite explicit dissipation in the numerical model that would otherwise damp the waves on a time scale of a few hours, they must be inherent features of the dipole itself, rather than remnants of imbalances in the initial conditions. The wave amplitude varies with the strength of the dipole, with waves becoming obvious once the maximum vertical vorticity in the dipole is roughly half the Coriolis parameter. Possible mechanisms for the wave generation are spontaneous wave emission and the instability of the underlying balanced dipole.

Turbulent wake of an inclined cylinder with water running

This paper presents the results of an experimental study of fluid dynamics around an inclined circular cylinder with and without water running over its surface, covering water rivulet formation, fluid forces on the cylinder, near wake and their interrelationships. The cylinder inclination angle (α) with respect to incident flow was between 55° and 80°. It has been found that water running over the cylinder surface may behave quite differently, depending on the Reynolds number (Re), and subsequently impact greatly upon the fluid dynamics around the cylinder. As such, five flow categories are classified. CategoryA: one water rivulet was observed, irrespective of α, at the leading stagnation point at a smallRe. CategoryB: the rivulet splits into two, symmetrically arranged about the leading stagnation line, onceReexceeds a critical value that depends on α. The two rivulets may further switch back to one, and vice versa. CategoryC: two symmetrical straight rivulets occur. CategoryD: the two rivulets shift towards the flow separation line with increasingReand oscillate circumferentially. The oscillation reaches significant amplitude when the rivulets occur at about 70° from the leading stagnation point. This increased amplitude is coupled with a rapid climb in the mean and fluctuating drag and lift, by a factor of near 5 for the fluctuating lift at α = 80°. Meanwhile, the flow structure exhibits a marked variation. For example, Strouhal number and vortex formation length decrease, along with an increase in spanwise vorticity concentration, velocity deficit, and coherence between vortex shedding and fluctuating lift. All these observations point to the occurrence of a ‘lock-in’ phenomenon, i.e. the rivulet oscillation synchronizing with flow separation. A rivulet–vortex-induced instability is proposed to be responsible for the well reported rain–wind-induced vibration associated with the stay cables of cable-stayed bridges. CategoryE: the two rivulets shift further downstream just beyond the separation line; the shear layers behind the rivulets become highly turbulent, resulting in weakened vortex shedding, flow fluctuating velocities and fluctuating fluid forces. Based on the equilibrium of water rivulet weight, aerodynamic pressure and friction force between fluid and surface, an analysis is developed to predict the rivulet position on the cylinder, which agrees well with measurements.

Experimental characterization of starting jet dynamics

The dynamics of a laminar starting jet are explored in a series of laboratory experiments and numerical simulations. We identify new, objective methods for characterizing the leading vortex ring, enabling robust comparisons with results from a numerical model. Observations of circulation in the initial vortex ring and for the total jet are reported along with strain rate at the leading stagnation point. Growth and pairing of shear instabilities trailing the leading vortex ring is observed. Development of these secondary vortices and their subsequent interactions with the leading vortex has significant effects on the characteristics of the primary vortex ring. Strong fluctuations in strain rate at the leading edge are associated with the pairing of the initial vortex ring with a trailing secondary ring.

Method of Variational Imbedding for the Inverse Problem of Boundary-Layer Thickness Identification

The inverse problem of identification of boundary-layer thickness is replaced by the higher-order boundary value problem for the Euler–Lagrange equations for minimization of the quadratic functional of the original system (Method of Variational Imbedding – MVI). The imbedding problem is correct in the sense of Hadamard and consists of an explicit differential equation for the boundary-layer thickness. The existence and uniqueness of solution of the linearized imbedding problem is demonstrated and a difference scheme of splitting type is proposed for its numerical solution. The performance of the technique is demonstrated for three different boundary-layer problems: the Blasius problem, flow in the vicinity of plane stagnation point and the flow in the leading stagnation point on a circular cylinder. Comparisons with the self-similar solutions where available are quantitatively very good.

Feedback control of von Kármán vortex shedding behind a circular cylinder at low Reynolds numbers

A computational study of the feedback control of von Kármán vortex shedding behind a circular cylinder at low Reynolds numbers is reported. The two-dimensional Navier–Stokes equations with feedback are solved numerically. The control actuators are a pair of blowing/suction slots located at ±110° from the leading stagnation point. A single feedback sensor is used and the actuators are 180° out of phase with each other. Complete suppression of vortex shedding is achieved for the simulation at Reynolds number Re=60. The suppression window in the feedback sensor location xs is narrow. With the feedback sensor location fixed at the optimum location, vortex shedding becomes suppressed with increasing feedback gain α. However, further increase of the feedback gain destabilizes the flow again. At Reynolds number Re=80, and above, the feedback control stabilizes the primary vortex shedding mode, but a secondary mode which may be lower or higher in frequency than the primary depending upon the phase of the feedback (feedback sensor location xs) and the feedback gain α arises.

A thermally non-equilibrium viscous shock layer past slender blunted cones

Physical-chemical processes in a shock layer past a slender spherically blunted body at high supersonic velocities are investigated. Using a gas-dynamic model, defined by the complete viscous shock-layer equations [1], the steady laminar axisymmetric flow of viscous, heat-conducting, partially dissociated and ionized air under chemical and thermal non-equilibrium is considered throughout the region between the body and the required thin shock wave. Attention is concentrated on the non-equilibrium chemical, ionization, and relaxation kinetics at large distances from the leading stagnation point. Multicomponent diffusion and the reverse influence of dissociation-recombination on the relaxation of vibrational quantum states, i.e. coupling vibration-dissociation-vibration (CVDV), are taken into account. A new model is used to describe dissociation-relaxation process [2]. The model includes the effect of non-equilibrium excitation of vibrations and the equilibrium excitation of rotational molecular modes on the dissociation rate constants. Comparisons with experimentally verified calculations and calculations within the scope of the chemically equilibrium full viscous shock-layer model indicate that the model is physically adequate. The calculations highlighted physical effects in the non-equilibrium viscous shock layer past a slender spherically blunted cone at various distances from the stagnation point.

The distribution of the pressure of the dispersed phase along a surface of a bubble with an irregular leading stagnation point

The plane problem of a deformed bubble rising in a fluidized bed is considered. The bubble is represented by a reflection of a circular segment in a vertical axis.

The effect of conjugated and radiant heat exchange on the process of non-stationary combustion of the products of intense gasification of a solid in a stream of gas

This paper develops further the results obtained in /1–4/ and uses the approximate mathematical model /2/ of the combustion of the products of intense gasification of the neighbourhood of the leading stagnation point of the body to analyse the effect of the conjugation parameters on the heat exchange, radiation and other factors on the conditions of uniqueness and stability of the stationary combustion modes. When the gasification is carried out at a constant mass flow rate, an analogy is established, depending on the relations between the parameters of the problem, between the model in question and the models of a homogeneous chemical continuous action reactor with a fluidized catalyst layer, and a reactor with a temperature regulator /5/. Simple necessary conditions for the instability of the stationary modes and the appearance of selfexcited oscillations are obtained. A strong stabilizing influence of the conjugated heat exchange and intense injection on the combustion process is established, and a destablishing influence of radiant heat exchange is found.

Qualitative analysis of unsteady heat and mass transfer modes in a boundary layer with chemical reactions and intensive detections: PMM vol. 42, no. 6, 1978, pp. 1056–1067

The effect of chemical reactions in the gas phase on unsteady heat and mass transfer in the neighborhood of the leading stagnation point of a streamlined body is investigated using the qualitative theory of dynamic systems. The necessary and sufficient conditions of uniqueness and stability of steady heat and mass transfer modes are formulated.