Vortex quadrupoles and two-dimensional oscillating grid turbulence

The planar motions induced by a localized forcing of the type of a point force-dipole is reproduced using a vertical rod oscillating horizontally in a thin layer of fluid. This forcing gives rise to the formation of a vortex quadrupole. To model a chaotic vortical flow, a system of quadrupoles is generated using a linear grid of oscillating rods. As a result of quadrupole interactions, a turbulent layer with two sharp boundaries forms and propagates from the grid.     

A novel tethered-sphere add-on to enhance grid turbulence

The new turbulence generator consists of a standard uniform grid with tethered spheres attached to its nodes and is capable of producing approximately twice the turbulence energy per unit pressure drop coefficient C _p than the same bare grid without the spheres. At the same time, the Reynolds number Re_λ based on the Taylor microscale is also amplified by a factor of roughly 2, and the turbulence anisotropy is reduced to a constant level of 10% at all downstream distances without further flow conditioning after the grid. The new grid’s simple design makes it suitable for a variety of fluid-flow facilities, in particular smaller water tunnels. Its performance in comparison with the plain grid is documented by measurements of the streamwise decay of turbulence energy and velocity spectra in the Re_λ range of 50–100.     

High-order strand grid methods for shock turbulence interaction

ABSTRACT

In this work, we examine the flux correction method for three-dimensional transonic turbulent flows on strand grids. Building upon previous work, we treat flux derivatives along strands with high-order summation-by-parts operators and penalty-based boundary conditions. A finite-volume like limiting strategy is implemented in the flux correction algorithm in order to sharply capture shocks. To achieve turbulence closure in the Reynolds-Averaged Navier–Stokes equations, a robust version of the Spalart–Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. Validation studies are considered which demonstrate the flux correction method achieves a high degree of accuracy for turbulent shock interaction flows.     

Statistical behavior of post-shock overpressure past grid turbulence

When a shock wave ejected from the exit of a 5.4-mm inner diameter, stainless steel tube propagated through grid turbulence across a distance of 215 mm, which is 5–15 times larger than its integral length scale \(L_{u}\) , and was normally incident onto a flat surface; the peak value of post-shock overpressure, \(\Delta P_{\mathrm{peak}}\) , at a shock Mach number of 1.0009 on the flat surface experienced a standard deviation of up to about 9 % of its ensemble average. This value was more than 40 times larger than the dynamic pressure fluctuation corresponding to the maximum value of the root-mean-square velocity fluctuation, \(u^{\prime }= 1.2~\hbox {m}/\hbox {s}\) . By varying \(u^{\prime }\) and \(L_{u}\) , the statistical behavior of \(\Delta P_{\mathrm{peak}}\) was obtained after at least 500 runs were performed for each condition. The standard deviation of \(\Delta P_{\mathrm{peak}}\) due to the turbulence was almost proportional to \(u^{{\prime }}\) . Although the overpressure modulations at two points 200 mm apart were independent of each other, we observed a weak positive correlation between the peak overpressure difference and the relative arrival time difference.     

Transverse velocity and temperature derivative measurements in grid turbulence

The same probe, comprising two parallel wires, is used to measure either velocity or temperature derivatives in shearless grid turbulence at a Taylor microscale Reynolds number of about 40. The aerodynamic interference of the probe affects the mean velocity when the transverse separation jy between the wires is smaller than about 3m, where m (ۂ.4 mm for the present experiments) is the Kolmogorov length scale, but not the mean temperature. Spectra and corresponding moments of transverse velocity and temperature derivatives are significantly but similarly affected when jyh3m, thus suggesting that this effect is more likely to be caused by electronic noise than aerodynamic interference. Indeed, after noise corrections are applied, the resulting derivative variances are brought into alignment with values inferred from two-point correlations with respect to y. Transverse derivative variances and their corresponding spectra satisfy isotropy closely but second-order structure functions satisfy it only when the separation is less than about 10m, i.e. the dissipative range scales.     

Effect of a small axisymmetric contraction on grid turbulence

Measurements downstream of a grid followed by a contraction with an area ratio of 1.36 have been made with a one-component vorticity probe. The velocity data indicate that there is indeed an improvement in isotropy of the large scales when such a contraction is used. In particular, the spectrum of u loses a significant amount of low frequency energy and its peak is shifted towards that of v. Although the v spectrum is less affected than the u spectrum, the relative magnitudes of the u and v spectra satisfy isotropy more closely with than without the contraction. In particular, isotropy is most closely approximated when the contraction is used in combination with a grid designed to minimise vortex shedding. The lateral vorticity spectrum is essentially unaffected, irrespective of the grid that is used or the magnitude of the wavenumber.     

Decay of passive-scalar fluctuations in slightly stretched grid turbulence

Isotropic turbulence is closely approximated by stretching a grid flow through a short (1.36:1) secondary contraction. The flow is operated at small values of the Taylor microscale Reynolds number (about 25–55) and is slightly heated just downstream of the grid, so that the temperature serves as a passive scalar and the initial velocity/thermal length-scale ratio is about 1. For the same grid, the contraction reduces the skewness and kurtosis of the thermal fluctuations and their derivative. The thermal fluctuations and their mean dissipation rates follow a power-law rate of decay that depends on the geometry of the grid. Comparison with velocity measurements shows that, for three different grids, the ratio between the temperature and velocity power-law exponents closely matches the velocity/thermal timescale ratio. For the present measurements, the timescale ratio is slightly larger than 1 but does not exceed 1.2, in accordance with the proposal by Corrsin (J Aeronaut Sci 18(6):417–423, 1951b).     

On the power law of decay of grid turbulence

Fluid Dynamics - The power-law dependence used to approximate the experimental data in the initial section of decay of turbulence in a flow behind grids is analyzed using results published in the...     

Experimental study on oscillating grid turbulence and free surface fluctuation

This paper analyses the interaction between the turbulence and free surface. The phenomenon takes place in many natural flows and industrial processes. In the present experiments, turbulence is generated by a vertically oscillating grid moving beneath the free surface. Fluid velocity has been measured through a hot-film anemometer, and the free surface elevation has been measured by an ultrasonic sensor. Integral length scales and several turbulence estimators have been computed. In order to detect the generation of turbulence near the free surface, the correlation between free surface elevation and the underneath flow velocity has been studied, as well as the time lag between turbulence and free surface. The free surface dynamics has been characterized by a velocity scale and a length scale. The kinetic energy associated with the free surface fluctuations increases with the Reynolds number at a rate depending on the frequency of the grid movement. For Reynolds number larger than ≈1000, however, the relationships collapse to a single curve characterized by a lower rate. The present experiments do not achieve the inertial sub-range in the vertical velocity fluctuations, and the estimated spectrum decays with an exponent smaller than ?3, which is the typical value for the two-dimensional turbulence in the inertial sub-range. The macro length scale, estimated by using the Taylor’s frozen turbulence hypothesis, experiences a decay away from the grid, which follows reasonably well the profile of Thompson and Turner (J Fluid Mechanics 67: 349–368, 1975). The micro length scale reduces immediately beneath the free surface, which can be interpreted by the increase of dissipation rate in the subsurface layer. The classification diagram by Brocchini and Peregrine (J Fluid Mech 449: 225–254, 2001) indicates that most tests fall in the weak turbulence domain, but some tests fall in the wavy domain. The vertical velocity fluctuations and the free surface level show a significant correlation with a negative phase lag, that is, the free surface fluctuations are ahead of the vertical velocity fluctuations.     

Calibration of a temperature dissipation probe in decaying grid turbulence

A four cold-wire probe, which allows all three components of the temperature dissipation rate ? _θ to be measured, is “calibrated” in decaying grid turbulence, where <? _θ >, the mean value of ? _θ , can be determined accurately from the decay of the temperature variance <θ ²>. The probe yields values of the three components of <? _θ > which are in reasonable agreement with local isotropy, in the range x ₁/M?50. The pdfs and spectra of the three temperature derivatives also satisfy local isotropy reasonably well.     

Decay of turbulence behind a double grid of cylinders with opposite motion of the grids

The results are given of an experimental investigation into the decay of turbulence in a flow behind a double grid of cylinders with the grids moving in opposite directions. It is shown that the distribution of the turbulence parameters behind such a grid is more uniform than for other known methods of generating turbulence.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 17–25, May–June, 1979.     

The structure of water-air bubble grid turbulence in a square duct

Local measurements of void fraction and continuous phase velocity field in water-air bubble, grid turbulence were conducted in a channel of vertical, square test section. The measured statistics indicate that, due mainly to the interaction of mean shear with the dispersed phase, the turbulence structure of the flow is modified. The observed change is characterized by a strong spatial dependence of void fraction and liquid flow properties, and the emergence of two spatial regions controlled by different physical processes. Intensity measurements indicate significant departure from isotropy in the flow. Two distinct regimes corresponding to low and high values of void fraction have been also identified. The autocorrelation and spectra measurements indicate that for low void fraction the scales of turbulence decrease while for higher values of void fraction increase again and inverse cascade is observed.     

Production of temperature fluctuations in grid turbulence: Wiskind's experiment revisited

Measurements have been made in nearly-isotropic grid turbulence on which is superimposed a linearly-varying transverse temperature distribution. The mean-square temperature fluctuations, , increase indefinitely with streamwise distance, in accordance with theoretical predictions, and consistent with an excess of production over dissipation some 50% greater than values recorded in previous experiments. This high level of production has the effect of reducing the ratio,r, of the time scales of the fluctuating velocity and temperature fields. The results have been used to estimate the coefficient,C, in Monin's return-to-isotropy model for the slow part of the pressure terms in the temperature-flux equations. An empirical expression by Shih and Lumley is consistent with the results of earlier experiments in whichr 1.5, C 3.0, but not with the present data where r 0.5, C 1.6. Monin's model is improved when it incorporates both time scales.List of symbols C coefficient in Monin model, Eq. (5) - M grid mesh length - m exponent in power law for temperature variance, x ^m - n turbulence-energy decay exponent,q ² x ^-n - p production rate of - p pressure - q ² - R microscale Reynolds number - r time-scale ratiot/t - T mean temperature - U mean velocity - mean-square velocity fluctuations (turbulent energy components) - turbulent temperature flux - x, y, z spatial coordinates - temperature gradient dT/dy - thermal diffusivity - dissipation rate ofq ²/2 - dissipation rate of - Taylor microscale (₂=5q₂/) - temperature microscale - _v temperature-flux correlation coefficient, /v - dimensionless distance from the grid,x/M     

Effect of initial conditions on decaying grid turbulence at low R λ

The transport equations for the second-order velocity structure functions 〈(δu)²〉 and 〈(δq)²〉 are used as a scale-by-scale budget to quantify the effect of initial conditions at low Reynolds numbers, typical of grid turbulence. The validity of these equations is first investigated via hot-wire measurements of velocity and transverse vorticity fluctuations. The transport equation for 〈(δq)²〉 is shown to be balanced at all scales, while anisotropy of the large scales leads to a significant imbalance in the equation for 〈(δu)²〉. The effect of using similarity to evaluate the transport equation is rigorously tested. This approach has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous term of the transport equation. The similarity form of the 〈(δq)²〉 equation produces nearly identical results as those obtained without the similarity assumption. In the case of the 〈(δu)²〉 equation, the similarity method forces a balance at large separation, although the imbalance due to large scale anisotropy remains. The initial conditions of the turbulence at constant R _M ≃ 10,400 (28≤ R _λ≤ 55) are changed by using three grids of different geometries. Initial conditions affect the shape and magnitude of the second- and third-order structure functions, as well as the anisotropy of the large scales. The effect of initial conditions on the scale-by-scale budget is restricted to the inhomogeneous term of the transport equations, while the dissipation term remains unaffected despite the low R _λ. Scales as small as λ are affected by the changes in initial conditions.     

Transport equations for the mean energy and temperature dissipation rates in grid turbulence

 Simultaneous measurements of velocity and temperature fluctuations were made in the turbulent flow downstream of a grid-heated screen combination. The magnitudes of n and m, the power-law exponents for the decay of turbulent energy and temperature variances, are nearly equal. This approximate equality is in conformity with the locations of the peaks in the three-dimensional turbulent energy and temperature spectra. The values of n and m are consistent with the isotropic forms of the transport equations for the mean turbulent energy and temperature variance. They are also consistent, allowing for the measurement accuracy, with the isotropic forms of the equations for the mean turbulent energy and temperature dissipation rates. Received: 20 October 1998 / Accepted: 26 March 1999     

Polymer-induced turbulence modifications in an impinging jet

This effort explores the impact of dilute polymer solutions on the turbulence characteristics in a submerged liquid impinging-jet configuration. Turbulent impinging jets are commonly used in technological applications such as drying, scouring, cooling, or heating due to an enhancement in transport characteristics in the impingement region under certain nozzle-to-wall configurations. Previous efforts have identified significant turbulence modifications in the presence of dilute concentrations of polymer in both bounded and unbounded flows, though the former has received considerably more attention. To this end, particle-image velocimetry measurements were taken for an axisymmetric turbulent impinging jet with a nozzle-to-wall distance H/D = 6.8 and nominal Reynolds number of 26,000. Measurements were performed for both plain water and dilute polymer solutions of polyethylene oxide at concentrations of 50 and 100 ppm. The mean and turbulence characteristics of these three flows are contrasted and it is observed that the two polymer solutions modify both the mean and turbulent characteristics of the jet in all three regions of interest (the free-jet, impingement, and wall-jet regions). Of interest, the 50 ppm case yielded a slight suppression of the turbulence in the free-jet region accompanied by a longer axial length of the potential core compared to the case of plain water. In contrast, the 100 ppm case exhibits clear enhancement of the turbulence in the free-jet region and a shortening of the potential core length. The effect of polymer was opposite in the impingement and wall-jet regions wherein the turbulence was slightly suppressed in the 100 ppm case in a manner consistent with the onset of the Toms effect in this wall-bounded region of the flow.