Abstract
Visual research of characteristic features and measurement of velocity and pressure fields of a vortex flow inside and nearby of a pair of the oval dimples on hydraulically smooth flat plate are conducted. It is established that depending on the flow regime inside the oval dimples, potential and vortex flows with ejection of vortex structures outside of dimples in the boundary layer are formed. In the conditions of a laminar flow, a vortex motion inside dimples is not observed. With an increase of flow velocity in dimples, boundary layer separation, shear layer, and potential and circulating flows are formed inside the oval dimples. In the conditions of the turbulent flow, the potential motion disappears, and intensive vortex motion is formed. The profiles of longitudinal velocity and the dynamic and wall-pressure fluctuations are studied inside and on the streamlined surface of the pair of oval dimples. The maximum wall-pressure fluctuation levels are pointed out on the aft walls of the dimples. The tonal components corresponding to oscillation frequencies of vortical flow inside the dimples and ejection frequencies of the large-scale vortical structures outside the dimples are observed in velocity and pressure fluctuation spectra.
Keywords
- dimple generator
- oval dimple
- visualization
- vortex structure
- velocity profile
- wall-pressure fluctuations
1. Introduction
Various inhomogeneities of the streamlined surface in the form of cavities or dimples are present in many hydraulic structures and constructions. Under appropriate conditions of the flow, large-scale coherent vortex systems and small-scale vortices are formed inside dimples that generate intense fluctuations of velocity, pressure, temperature, vorticity, and other turbulence parameters [1, 2, 3]. Boundary layer control uses these artificial vortex structures for drag reduction, increase of mixing, and noise minimization. Vortex structures of various scales, directions, rotational frequencies, and oscillations are generated in space and in time depending on the flow regime, the geometric parameters, and the shape of the cavities. Experimental and numerical results of aerodynamic and thermophysical studies showed a rather high efficiency of dimple reliefs, which allowed to increase heat and mass transfer for a slight increase in the level of hydrodynamic losses [4, 5, 6].
The boundary layer separation from the frontal edge of the cavity and the instability of the shear layer flow generate vortex structures inside the cavity. With the increase of flow velocity, one of the edges of vortex structures, circulating in the cavity, is separated from the streamlined surface of the cavity and is extracted following the flow. These inclined structures have a longitudinal dimension that substantially exceeds their lateral scale. They intensively initiate the interaction of medium of the cavity and the surrounding area [2, 3, 7, 8].
The experience achieved by scientists and engineers when using dimple surfaces indicates that the creation of time and space stable vortex systems generated inside the cavities has a perspective value for boundary layer control. The creation of large-scale coherent vortex structures, with predefined qualities, allows you to change the structure of the boundary layer or the separation flow. It improves the heat and mass transfer, reduces the drag of streamlined structures, or changes the spectral composition of aerohydrodynamic noise, in order to reduce it [3, 9, 10].
In Refs. [11, 12], it was noted that spherical cavities for heat and hydraulic efficiency are not the best for turbulent regime of heat carrier flow and for laminar regime; their use is practically not justified. The presence of a switching mechanism of generation and ejection of vortex structures inside spherical cavities on a streamlined surface [13, 14, 15] does not allow to form longitudinal vortex structures that are stable in space and time, which are necessary for boundary layer control. This defect is absent in oval dimples, which are at an angle to the current direction. Asymmetry of the dimple shape due to its lateral deformation allows transforming the vortex structure and intensifying the transverse flow of liquid within its boundaries. Adding a shallow dimple of an asymmetric shape leads to a reorganization of its flow. A two-dimensional vortical structure in the dimple, generated in a symmetrical dimple during its laminar flow, is changed to an inclined monovortex. The high stability of the inclined structure should be noted, which ensures the stability of vortex intensification of heat transfer [16, 17, 18].
In this connection, the purpose of this experimental work is to study the characteristic features of the flow of a system of oval dimples on a flat plate and to study the fields of dynamic and wall-pressure fluctuations inside and on the streamlined surface of the inclined oval dimples and in their vicinity.
2. Experimental setup
Experimental research was carried out in a hydrodynamic flume with an open surface of water 16 m long, 1 m wide, and 0.4 m deep. The scheme of the experimental stand and the location of the measuring plate with dimples are given in works [19, 20]. At a distance of about 8 m from the input part of the flume, there were a measuring section equipped with control equipment and means of visual recording of the flow characteristics, coordinate devices, lighting equipment, and other auxiliary tools necessary for conducting experimental research. The design and equipment of the hydrodynamic flume allowed the flow velocity and water depth control in wide limits.
Transparent walls of a hydrodynamic flume, which were made of thick shock-proof glass, ensured high-quality visual research.
Hydraulically flat plate made of polished organic glass of 0.01 m thick, 0.5 m in width, and 2 m in length was sharpened from one (front) and from the other (aft) side. End washers are fixed to the lateral sides of the plate. At a distance of
According to the developed program and experimental research methodology, visual studies were initially carried out. Then, in the characteristic points of the vortex generation and the places of interaction of vortices with a streamlined surface, measurements of the fields of velocity and pressure were carried out. Visualization was carried out by drawing of contrasting coatings on the streamlined surface and coloring agents that were introduced into the stream. Paints and labeled particles through a small diameter tube were introduced into the boundary layer before the dimple and/or inside the dimple.
The study of the pressure fluctuation fields on the streamlined surface of the oval dimples and the plate, as well as the velocity fields of the vortex flow over the investigated surfaces, was carried out using miniature piezoceramic and piezoresistive sensors of pressure fluctuations and differential electronic manometers (Figure 2a). Specially designed and manufactured pressure sensors were installed in a level with a streamlined surface and measured the absolute pressure and the wall-pressure fluctuations [9, 21, 22]. Inside of the system of oval dimples and in their near wake, 12 sensors of pressure fluctuations were used (Figure 2b). The field of velocity fluctuations inside a pair of oval dimples and over a streamlined plate surface was measured by sensors of the dynamic pressure fluctuations or dynamic velocity pressure based on piezoceramic sensing elements.
The degree of the flow turbulence in the hydrodynamic flume did not exceed 10% for the velocity range from 0.03 to 0.5 m/s. The levels of acoustic radiation in the area of the dimples were no more than 90 dB relative to 2 × 10−5 Pa in the frequency range from 20 Hz to 20 kHz, and the vibration levels of the test plate with a pair of dimples and sensor holder did not exceed −55 dB relative to
3. Research results
The vortical motion in the middle of the dimples is not what was observed (Figure 3a) for a laminar flow regime over a pair of oval dimples (
When the flow velocity was increased to (0.08…0.12) m/s, then a separation zone of the boundary layer appeared inside the front parts of the oval dimples. A shear layer began to form over the dimple opening, generating a circulating flow and a slow vortex motion inside the dimples (Figure 3b). This fluid motion had a kind of longitudinal spirals and was slow and almost symmetrical in each of the dimples. The liquid of the dimples fluctuated in three mutually perpendicular planes. The oscillation frequencies in each of the dimples were practically equal, but the destruction of the vortex sheet did not occur simultaneously. Contrast material went inside the dimples along their front semispherical and cylindrical parts. The separation and circulation areas behind the front edge of the dimple occupied almost half the volume of the dimple. There was a very slow rotation of the fluid inside the dimples, and its direction was coincided with the direction of the flow as well as its fluctuations along the longitudinal and transverse axes of the dimples. The disturbance package was transferred in the direction of the flow at a transfer velocity of approximately (0.4…0.5)
The vortex motion became more intense when the flow velocity over the dimple system was increased up to (0.2…0.3) m/s (
The contrast dye inside the dimple was concentrated inside the front spherical parts of the dimple (Figure 4b) for developed turbulent flow and flow velocity (0.4…0.5) m/s (
The intensity of the fluctuations of the longitudinal velocity over the streamlined surface of the oval dimple (
The change of the rms values of the wall-pressure fluctuations measured on the streamlined surface of the oval dimple and in its vicinity is presented in Figure 5b depending on the Reynolds number. The normalization of the root mean square values of the wall-pressure fluctuations was carried out by the dynamic pressure (
Thus, the wall-pressure fluctuations on a flat surface before the dimples are subjected to a quadratic dependence on the flow velocity. It should be noted that the wall-pressure fluctuations normalized by the dynamic pressure in the undisturbed boundary layer before the oval dimples are approximately 0.01, practically, in the entire range of studied Reynolds numbers.
Consequently, the smallest levels of the wall-pressure fluctuations are observed at the bottom of the oval dimples, in their front parts, especially for low flow velocities and Reynolds numbers (curve 2, Figure 5b). Inside the oval dimples, the levels of the wall-pressure fluctuations are greatest in the aft spherical parts of the dimples and in the near wake immediately after the dimples (see curves 4, 7, and 9 in Figure 5b).
A spectral analysis of the wall-pressure fluctuations on the streamlined surfaces of the oval dimples and plate was performed. To do this, we used the fast Fourier transform algorithm and the Hanning weighting function, as recommended in [23, 24, 25]. Power spectral densities of the wall-pressure fluctuations on a streamlined surface of oval dimples and on a flat plate near the system of these dimples have clearly visible discrete peaks which correspond to the nature of the vortex and jet motion over the investigated surfaces.
Figure 6a shows the power spectral densities of the wall-pressure fluctuations, which were measured inside one of the oval dimples for a flow velocity of 0.25 m/s (
Oscillations of the vortex flow inside the oval dimple are observed at frequencies (0.035…0.037) Hz or
The results of the measurements of the power spectral densities of the wall-pressure fluctuations along the middle section of the oval dimple system, as well as inside the dimples, are shown in Figure 6b. It should be noted that under the boundary layer on a flat surface of a hydraulically smooth plate, the spectral levels of the wall-pressure fluctuations (curve 1) are minimal and do not have the tonal or discrete peaks observed inside and near the dimples. Behind the oval dimples, these discrete peaks are clearly visible on the spectra, but the tone frequencies near the system of oval dimples and at a distance of 2
Experiments have shown that all sensors located at a distance of 2
In the conditions of developed turbulent flow (
The features of the vortex motion, as well as wall-pressure fluctuation field, which it generates, in the near wake of the oval dimple system, in its middle section and at a distance of 2
4. Conclusions
The visual images of the vortex flow formed inside the oval dimple system are obtained, and the characteristic features of vortex formation for different flow regimes are determined. It has been experimentally established that the separation flow was not observed inside the dimples for laminar regime. For transient flow regime and small flow velocities within the oval dimples, the formation of very intense longitudinal spirals is observed, which are rotated and slowly fluctuated along the longitudinal and transverse axes of the dimples. For a turbulent flow regime inside the oval dimples, the spindle-shaped vortices are formed, which, with increasing velocity, are pressed against the front spherical parts of the dimples. These spindle-shaped vortices, reaching the scales of the dimples, are ejected from the oval dimples, disturbing the structure of the boundary layer. Inside the oval dimples, there is a low-frequency oscillatory motion in mutually perpendicular planes relative to the axes of the dimples, whose frequency is increased with increasing flow velocity.
It is shown that the intensity of the field of the velocity fluctuations has maximum values near the streamlined surface and also on the boundary of the shear layer in the opening of the oval dimple. The intensity of the wall-pressure fluctuation field is greatest in the interaction region between vortex structures of the shear layer and large-scale vortex systems ejected from the dimples with the aft wall of the oval dimple. The smallest intensity of the wall-pressure fluctuations occurred at the bottom of the oval dimple in its forward spherical part.
It has been established that depending on the flow regimes in the spectral characteristics of the field of the wall-pressure fluctuations measured on the streamlined surface, characteristic features appear in the form of discrete peaks corresponding to the frequencies of low-frequency oscillations of the vortex flow inside the oval dimples and the ejection frequencies of large-scale vortex systems from the dimples. In the middle section of the system of oval dimples (in their near wake), there is no interaction of vortex structures that are ejected from the dimples. With a distance of more than two diameters of the dimple, intensive tone peaks are observed in the spectral dependences. They correspond to the ejection frequencies of large-scale vortices and the frequency of oscillations of the vortex motion inside the dimples, both in the middle section of the system of the dimples and behind their aft spherical parts. With the distance from the system of oval dimples, the intensity of the tonal oscillations, which are characteristic for the vortical motion inside the dimples, is decreased, and the boundary layer is restored.
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