Merging of two or more plumes arranged around a circle

A model is presented of merging turbulent plumes from sources evenly spaced around a horizontal circle in a quiescent, unstratified background. This follows the previously developed method of (i) identifying the boundaries of interacting plumes with velocity-potential contours of line sinks and (ii) closing the generalised plume equations with an entrainment assumption based on the integrated flux across the plume boundaries. It includes the simplest case of two merging plumes, as well as being applicable to plume flows in restricted corner configurations. The model is shown to display the expected limiting behaviour for the source plumes and the merged plume. Consideration of the plume fluxes in the merging region leads to a revision of the entrainment assumption. The resulting revised model compares satisfactorily with previous estimates of volume flux in two merging plumes.

Processing of calibration measurements on EZB-3

Processing of calibration measurements on EZB-3The calibration of horizontal circles results in a set of discrete correction values. These corrections are obtained in specific circle positions chosen by the size of the calibration step. For further use it is necessary to know the correction values for any location on a horizontal circle; therefore, it is necessary to know the function of the continuous corrections of a horizontal circle. This could be achieved from the measured values by several methods. In the article two methods are presented for determining this function through the approximation of polynomial and trigonometric series.

Circular flight kite tests: converting to standard results

Kite testing by flying in a horizontal circle, was developed in order to address the inevitable accuracy problems inherent in pre-existing kite measurement techniques. However the raw results from this circular flight method are not directly comparable with traditional kite performance measurements. To enable direct comparisons to be made, modifying equations have been developed to convert the raw circular flight results into the traditional measurements of lift to drag ratio, and lift coefficient. This paper derives the modifying equations, and presents experimental results comparing traditional measurements with both the raw and modified circular flight results. The modifying equations are applied to an example set of results to assess the sensitivity of the test environment parameters. It is concluded that for many cases, the discrepancy between the raw circular flight test results and traditional measurement techniques is small enough to ignore. Alternatively, the modifying equations given in the paper may readily be encoded so that traditional results may be quickly obtained from this novel test method.

Near-surface turbulence in a grid-stirred tank

In order to elucidate the turbulent structure below a shear-free gas-liquid interface, turbulence measurements were made in a 50 cm square by 40 cm deep tank stirred by a vertically oscillating grid well below the surface, using a split-film anemometer probe rotating in a horizontal circle. This instrument is able to measure both vertical and horizontal velocity fluctuations to within 0.4 mm of the surface, from which spatial spectra and profiles of r.m.s. velocity fluctuations and integral lengthscales can be calculated. The turbulent structure is affected by the presence of the surface within a ‘surface-influenced layer’ roughly one integral scale, or ten per cent of the distance from the surface to the centre of the grid stroke, in thickness. The shapes of the spectra and profiles within the surface-influenced layer are predicted to a good first approximation by the source theory of Hunt & Graham (1978), which treats the turbulent structure as the superposition of homogeneous turbulence with an irrotational velocity field driven by a source distribution at the surface which cancels the vertical velocity fluctuations there. The magnitudes (as opposed to the shapes) of the profiles scale according to the values that would otherwise occur in the vicinity of the surface-influenced layer were the surface not present. These magnitudes are adequately predicted by the bulk relations determined by Hopfinger & Toly (1976) and Thompson & Turner (1975), with no apparent dependence on turbulent Reynolds number. There are some minor discrepancies between the measured profiles and those of Hunt & Graham. A thin layer of reduced velocity fluctuations below what would be expected from the theory was observed near the surface. Also, anisotropy in the velocity spectra at depths within the surface-influenced layer extended well into the inertial subrange, whereas the Hunt & Graham theory predicts no anisotropy at high wavenumbers.

Motion in a Horizontal Circle

(f) Let the tangent at the vertex of the parabola meet XL and XM at Q and R respectively. Then the points X, Q, S and R are concyclic. By inversion QR cuts the pair of orthogonal circles of the previous section (e) at points Q1 and R1 respectively such that the points X1, Q1, R1 and S1 are concyclic.