The jet edge-tone feedback cycle; linear theory for the operating stages

The unsteady Kutta condition is discussed in the light of some recent experimental measurements made near the trailing edge of a long flat plate and a 10C4 airfoil. The hierachy of disagreement from the theoretically predicted zero trailing edge loading caused by viscous instabilities is found to be acoustically correlated vortex shedding, natural vortex shedding, Tollmien-Schlichting waves, and, by implication, turbulent boundary-layer eddies. The region of significant chordwise disagreement scales with the wake perturbation wavelength of the corresponding instability. Coordinating the vorticity of the turbulent boundary layer shed from the profile airfoil with a transverse acoustic resonance produced a distinct disagreement of the Kutta condition at high reduced frequency parameters ( = wc/U). In this case and for vortex shedding, the extrapolated loading coefficient at the trailing edge increased with the nondimensional acoustic amplitude. I. Introduction T^HE Kutta condition as applied in unsteady JL potential airfoil analyses is essentially an extension of steady theory. Kutta ! postulated that a value of circulation should be chosen in his steady potential model to avoid a velocity singularity at the sharp trailing edge of an airfoil. This condition can be established if the trailing edge is also the rear stagnation point. The resulting modeled flow pattern agrees with that observed in steady flow and also predicts the lift and its chordwise distribution well at low angles of attack. The theoretical consequences of this hypothesis are that the lift loading or chordwise vorticity jump approaches zero at the trailing edge. An alternative statement is that the surface velocities on either side of the airfoil approach a common value at the rear stagnation point. For rounded trailing edges, the position of the rear stagnation point is indeterminate , as there is no velocity singularity to be avoided and so fix its location. In this case and for the situation of real flows with viscosity, Taylor2 proposed the condition of zero net vorticity discharge to establish the steady lift value. Preston3 explained the deviation of the lift of an airfoil at low angles of incidence from the potential theory value as due to the profile alteration from the boundary-layer growth. His calculations incorporated Taylor's vorticity discharge condition. Various approximate steady lift calculation methods for the rounded trailing edge geometry have been proposed by Gostello 4 and others. These extend the upper and lower lift distributions, at a selected chordwise position, to the trailing edge to give zero loading and thereby remove the stagnation point indeterminacy. In the unsteady case there are all the previous theoretical difficulties and, in addition, the unsteady effects on the viscous boundary layer and the shed vorticity. The latter complicates the airfoil response, making it a function of the airfoil's vorticity history. However, same theoretical assumption for the Kutta condition, of no unsteady loading at the

An experimental investigation has been made for a turbulent boundary layer near the trailing edge on a long flat plate. The flow was controlled by an additional splitter plate fitted to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from a half, to five times the trailing edge thickness, h. Measurements of base pressure behind the trailing edge and of mean velocity and pressure distribution in the turbulent boundary layer on the flat plate were made under the freestream zero-pressure gradient. The absolute value of base pressure coefficient of the long flat plate was considerably smaller than that of the short flat plate (bluff body) without splitter plate (l/h=0). A significant increase in the normalized base pressure coefficient (about 50% as same as short one) was achieved with the splitter plate (l/h≥1) fitted to the long flat plate. Within an inner layer in the turbulent boundary layer near the trailing edge, mean velocity increased than that in the upstream position, especially in the case without splitter plate. With splitter plate, however, the base pressure rise made mean velocity distribution come closer to that of fully developed turbulent boundary layer. In the case of l/h≥1, the affected range of acceleration decreased from 10 h upstream of the trailing edge without splitter plate to 5 h upstream.

The source of audible tones occurring with a coaxial nozzle is explored experimentally as well as computationally. The hardware is comprised of an inner and an outer nozzle, without a center-body, that are held together by a set of four struts. With increasing jet Mach number ( Mj), first a tone occurred at about 2550 Hz around Mj = 0.06. At higher Mj, a tone at 5200 Hz dominated the noise spectra. The corresponding non-dimensional frequency, based on the effective thickness of the inner nozzle lip and jet exit velocity, turned out to be about 0.2, a value characteristic of Karman vortex shedding. Thus, vortex shedding from the inner nozzle lip could be linked to the tones. From a comparison of acoustic wavelengths and nozzle dimensions, as well as locations of the pressure nodes and anti-nodes from the computational results, it was inferred that the vortex shedding excited one-quarter-wave resonances within the divergent sections of the nozzle. Such resonances in the inner and the outer nozzles produced the higher and the lower frequency tones, respectively.

An experimental investigation has been made on a turbulent boundary layer near the trailing edge on a long flat plate. The flow was controlled by an additional splitter plate fitted to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from a half, to five times the trailing edge thickness, h. Measurements of base pressure behind the trailing edge and of mean velocity and pressure distribution in the turbulent boundary layer on the flat plate were made under the freestream zero-pressure gradient. The absolute value of the base pressure coefficient of the long flat plate was considerably smaller than that of the short flat plate without the splitter plate. A significant increase in the base pressure coefficient was achieved with the splitter plate (l / h ≧ 1), fitted to the long flat plate. Within an inner layer in the turbulent boundary layer near the trailing edge, the mean velocity increased more than that in the upstream position in the case without the splitter plate. With the splitter plate, however, the base pressure rise made the mean velocity distribution more closely approach that of a fully-developed turbulent boundary layer.

Influence of splitter plate on the reverse flow in a channel

This study is to measure the impact pressure of high-speed water jet injected in water at the stand-off distance from the nozzle exit. The high-speed water jets are generated by the impact of a projectile, which known as impact acceleration method, launched by Horizontal Single Stage Power Gun. The maximum averaged jet velocity of about 374.24 m/s in water was generated in this experiment. The impact pressure of high-speed water jet in water at the stand-off distance 15, 20, 30 and 40 mm from the nozzle exit was measured by the PVDF pressure sensor. Moreover, the impact phenomena of the jet were visualized by a high-speed video camera with shadowgraph optical arrangement. From the pressure sensor, two peak over-pressures are always observed in this experiment. From visualization, it was found that the two peak over-pressures of 24 GPa and 35 GPa at x = 15 mm were generated by the jet and the bubble impact, respectively. The peak over-pressure decreases exponentially as the stand-off distance between the PVDF pressure sensor to the nozzle exit increases. Moreover, the jet and the bubble impact on the PVDF pressure sensor, shock waves, and bubble deformation were obviously observed in this study.

An experimental study was performed on a flat plate turbulent boundary layer disturbed by a square rod attached with a splitter plate. Spectrum analysis of the fluctuating velocity revealed that the periodical shedding of the Karman-like vortex from the square rod could be controlled by attaching the splitter plate to the square rod and suppressed with an increase of the plate length, L. It was found that noticeable heat transfer enhancement was achieved with the insertion of the square rod, but this enhancement became less noticeable with an increase of L. Skin friction acting on the flat plate was reduced but its magnitude was not significantly altered by changing the value of L. Therefore, the strength of the generated dissimilarity first increased and then decreased with an increase of L. Selective intensification of the interactive fluid motions near the wall was again concluded to be the generation mechanism of the dissimilarity. Furthermore, wavelet analysis applied to the fluctuating velocity signals indicated that this intensification of the interactive fluid motions was related to the near-wall fluid motion occurring in a synchronized fashion with the Karman-like vortex intermittently.

The current work is an analysis of the laminar, two‐dimensional, and transient flow over a circular cylinder with a two‐branched splitter plate. For complex nonlinear governing equations, the finite element method is used as a computational approach. The objective of the current study is to determine the best conditions using geometrical characteristics along with the impact of Reynolds number Re.The geometric parameters, α which is the angle of separation between the pair of splitter plates of length L and G/D which is the gap from diameter ratio of the splitter plate to cylinder diameter, are the controlling tools for the present study. Due to its little impact on flow characteristics, it was discovered that using a two‐branched splitter plate in Reynolds numbers under 100 is not desirable. A complete vortex shedding has been achieved with α = 0° and G/D = 2 at Re = 100 and also the periodic behavior of velocity has been controlled. The least drag force is observed at an angle of 30° between the two plates compared to another angle of 0°. It is not advised to use two splitter plates at angles more than 30° because this will not further contribute in the drag reduction. Since the gap to diameter ratio between the splitter plates and the cylinder increased up to a significant value, the overall control on hydrodynamic effects is achieved. It is concluded that the maximum drag reduction of 48% over the cylinder has taken place when the Re is 200, α is 30°, and G/D is 2.

Numerical simulation of flow over a circular cylinder with a splitter plate near a moving wall

Vortex-induced vibration and structure instability for a circular cylinder with flexible splitter plates

In this study, two-dimensional unsteady laminar flow over a semi-circular cylinder (SCC) near a splitter plate was investigated numerically. Adding a splitter plate along the wake centreline downstream of the bluff bodies is an efficient passive means of controlling fully developed vortex shedding. Numerical simulations were done for different Reynolds numbers ranging from 100 to 500 in three different gaps ( g: g = 0.0 D to 4.5 D) and two different splitter lengths ( LSP = 1 and 2 D). Results indicate that by increasing the gap ratio, vortex shedding formed in the wake is suppressed and the oscillating amplitude of the lift coefficient decreases. On the other hand, drag, lift, and pressure coefficients representing the flow characteristics also vary as a function of the gap ratio at different Reynolds numbers. Extensive results on streamline patterns, wake characteristics (recirculation length), drag, lift, and pressure coefficients are presented to elucidate the interplay between the gap ratio and the Reynolds number and their influence on drag. Using the splitter plate at the downstream of the SCC causes the stretching of the vortex core and moves the centre of the vortex cores towards the leading edge of the plate. This phenomenon is caused by the reduction of the lift and drag coefficients.

Experimental and computational examinations of the effect of splitter plate length on the aerodynamic performance and vortex shedding behavior of a blunt trailing-edge airfoil are presented along with an evaluation of spanwise shedding coherence. The FB-3500-1750 airfoil, which has a maximum thickness of 35% chord and trailing-edge thickness of 17.5% chord, was tested in the University of California, Davis, Aeronautical Wind Tunnel at a chord Reynolds number of 666,000. The flow behavior was also examined computationally using OVERFLOW, a Reynolds-averaged Navier–Stokes solver. Splitter plates with lengths ranging from 50 to 150% of the trailing-edge thickness were applied to the airfoil model. Drag reductions of at least 27% from the baseline were observed with the inclusion of a splitter plate with length 50% of the trailing-edge thickness, accompanied by a 5% loss in maximum lift. An increasing splitter plate length was shown to decrease the base drag, maximum lift, and stall angle. The Strouhal number also increased with an increasing splitter plate length over the range examined. The spanwise correlation length of the vortex shedding was determined to be four to five times the trailing-edge thickness for both fixed and free transition at two different angles of attack.

Flow-induced vibration of a circular cylinder with rigid splitter plate

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

Simulation of interference effects in particle streams following impact with a flat surface: Part II. Parametric study and implications for erosion testing and blast cleaning