Experimental investigation on a turbulence generation system with high-blockage plates

An experimental study was conducted to develop and characterize systematically a new turbulence generator system to yield large turbulent Reynolds numbers in a compact configuration. The effect of the geometric parameters of two families of high-blockage plates on the resulting turbulent flow field was systematically studied: one series of plates was characterized by the number and distribution of circular openings; a second series had non-circular opening(s) with different shapes, distribution and position of the opening(s). The plates were placed upstream of a contoured contraction and the near field at the centerline of the resulting turbulent free jet was characterized by hot-wire anemometry in terms of mean axial velocity, turbulence intensity, turbulence length scales and corresponding Reynolds numbers. The plate with a central, non-circular opening produced the best compromise of highest turbulence levels along with excellent uniformity in average velocity and turbulence intensity, as evidenced by scan in the transverse direction. It appears to be the most promising one. By comparison with more traditional approaches to turbulence generation, we increased the turbulent Reynolds numbers based on the integral length scale to values on the order of 1000, which was one of the design objectives. Other plate geometries also yielded intense turbulence, but, in some cases, exhibited spurious frequency peaks in their power spectrum. The turbulent generation approach is to be adapted to combustion studies to reproduce conditions typical of practical system in relatively small experimental set-ups that are well-suited for bench-top experiments.     

Tollmien-Schlichting wave generation by flow turbulence

The problem of freestream-turbulence-generated instability waves in the flat-plate boundary layer is solved on the basis of a nonlinear turbulence model admitting the deviation of the speed of propagation of vortex disturbances from the flow velocity. The solution obtained well describes the experimental dependence of the laminar-turbulent transition Reynolds number on the freestream turbulence degree.     

On the generation of large-scale homogeneous turbulence

An active turbulence generating grid, based on the rotating-vane design of Makita (1991), was developed for a large wind tunnel. At 2.14 m square, the grid is the largest of this type ever developed. To improve the isotropy of the turbulence generated, the grid was placed in the wind tunnel contraction. Measurements show that the grid produces a closely uniform mean flow and homogeneous isotropic turbulence to within two integral scales from the wall. By systematically varying the flow speed and parameters controlling the random motion of the vanes, grid turbulence with a wide variety of characteristics was produced and the dependence of those characteristics on the operating parameters of the grid revealed. Taylor Reynolds numbers of the grid turbulence varied from 100 to 1,360 and integral scales from 5 to almost 70 cm. The extreme cases represent some of the highest Reynolds number and largest scale homogeneous turbulent flows ever generated in a wind tunnel.     

Large-scale vortex generation driven by nonequilibrium turbulence

The development of large-scale perturbations in a heated layer of rotating fluid is studied within the framework of the nonequilibrium turbulence model with asymmetric Reynolds stress tensor. It is shown that, as in spiral turbulence, when there is no equilibrium on one of the boundaries of the layer large-scale structures develop. Conditions under which both perfect intrinsic matching of turbulence and convection and internal resonance development exist are determined. It is shown that the manifestation in a turbulent medium of properties of the convective vector field such as spirality may be caused by constraints imposed by the angular momentum conservation law.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 47–55, January–February, 1996.     

Behavior of homogeneous turbulence in channels with variable cross-sectional area

On the basis of the equation describing the behavior of the spectral tensor of the energy of the pulsation velocity for one-dimensional flow in a channel with variable cross-sectional area, we obtained a system of equations for the meansquare components of the pulsation velocity vector and integral scales of the turbulence length in various directions, enabling us to use these parameters in the initial section of the channel for determining their behavior along the channel. We made use of some ideas of A. N. Kolmogorov and J. Rotta concerning the possibility of describing viscous and nonlinear terms in the equations for the components of the tensor of Reynolds stresses in terms of the energy of pulsation motion and the integral scale of the turbulence length. The resulting system, in the special cases of very low intensity of turbulence, leads to the results of the linear theory; for constant cross-sectional area (or for a very high intensity of turbulence, when the damping affects the turbulence much more strongly than does the deformation effect) it describes the known empirical laws of the degeneration of turbulence beyond grids. We made a comparison with the data available in the literature on the behavior of the characteristics of turbulence in channels with variable cross-sectional area.     

The structure of inhomogeneous turbulence in variable density nonpremixed flames

Some observations concerning the structure of turbulence associated with an exothermic nonpremixed reacting flow are presented. Direct numerical simulations (DNS) with a resolution of 128³ grid points and an initial Reynolds number R =33 provide data for the analysis. In these simulations the density varies with temperature and the resulting flow field is inhomogeneous. Conditional probabilities of the vorticity and rate-of-strain, three-dimensional visualization, and topological characteristics are presented and compared with those of a constant density flow. Initially, thermal expansion causes significant changes in the small-scale statistics. As the development continues, the statistics reflect the competing mechanisms of vortex stretching, dilatation, and baroclinic torque. Preferential alignment of the vorticity with the eigenvector associated with either the intermediate or most extensional principal strain is observed depending on the value of the local mixture fraction. Intermittent vortex structures tend to exist as sheets or ribbons rather than tubes due to the diminishing levels of vorticity and a change in the distribution and preferential orientation of the principal strains. Topological characteristics not present in constant density flows are observed. However, as the flow develops and the divergence decreases, the topology becomes similar to those of incompressible turbulence.This research was supported in part by an award from the Universitywide Energy Research Group (UERG). A portion of the allocation at SDSC was provided by the University of California, Irvine. The first author also received support through a President's Dissertation Year Fellowship from the University of California.     

On the Lighthill relationship and sound generation from isotropic turbulence

In 1952 Lighthill (1952) developed a theory for determining the sound generated by a turbulent motion of a fluid. With some statistical assumptions, Proudman (1952) applied this theory to estimate the acoustic power of isotropic turbulence. Recently, Lighthill established a simple relationship that relates the fourth-order retarded-time and space covariance of his stress tensor to the corresponding second-order covariance and the turbulent flatness factor, without making statistical assumptions for a homogeneous turbulence. Lilley (1994) revisited Proudman's work and applied the Lighthill relationship to evaluate the radiated acoustic power directly from isotropic turbulence. After choosing the time separation dependence in the two-point velocity time and space covariance based on the insights gained from direct numerical simulations, Lilley concluded that the Proudman constant is determined by the turbulent flatness factor and the second-order spatial velocity covariance. In order to estimate the Proudman constant at high Reynolds numbers, we analyzed a unique data set of measurements in a large wind tunnel and atmospheric surface layer that covers a range of the Taylor microscale-based Reynolds number 2.0×10³R 12.7×10³. Our measurements demonstrate that the Lighthill relationship is a good approximation, providing additional support to Lilley's approach. The flatness factor is found between 2.7 and 3.3 and the second-order spatial velocity covariance is obtained. Based on these experimental data, the Proudman constant is estimated to be 0.68–3.68.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the first author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Development and evaluation of a new turbulence generator for atomization research

Planar Mie scattering visualizations in compressible mixing layers are used to compute the probability density function of a passive scalar. Mixing layer flows with relative Mach numbers of 0.63 and 1.49 are studied. Ethanol condensation is used to generate both scalar transport seeding and product formation seeding. All PDFs exhibit a marching behavior. The condensation process in the product formation seeding is modeled to provide an estimate of the error embedded in the scalar transport PDFs. The mixing efficiency is found to be 0.56 in the product formation experiments, and the overprediction of mixing efficiency by the scalar PDFs is estimated to be 11% based on results from the ethanol condensation model.List of Symbols _291-01 Damköhler number based on - J droplet nucleation rate - k Boltzmann constant - m _c molecular mass of ethanol - M _r relative Mach number, M _r = 2U/(a₁ + a₂) - N ^* number of nucleated droplets - p(,) probability density function - P _d internal droplet pressure - P _m total mixed fluid probability - P _sat ethanol saturation partial pressure - P _v ethanol vapor partial pressure - r freestream velocity ratio, r=U ₂/U₁; droplet radius - r ^* critical nucleation radius - R gas constant for air - _291-2 Reynolds number based on - s freestream density ratio, s = ₂/₁ - T local static temperature - U ₁ high speed freestream velocity - U ₂ low speed freestream velocity - U _c large structure convection velocity, - U freestream velocity difference, U=U ₁–U₂ - x streamwise coordinate - y transverse coordinate - mixing layer thickness - _i incompressible mixing layer thickness - mixture fraction - similarity variable, = (y–y ₀)/ - _c condensed phase ethanol density - droplet surface tension     

The generation of nearly isotropic turbulence by means of grids

Grids have been used as a means of generating nearly isotropic turbulence for about fifty years. Even so, there does not appear to be a single document which gives adequate and simple rules for the design of such devices in an airflow installation. This paper attempts to fill this gap by means of a synthesis of experimental data with simple analyses, such that useful design guidelines are derived. Pressure losses, turbulence intensities, spectra, correlation functions and length scales are all examined. The present results are found to agree well with other data published in the literature.     

A turbulence model with variable coefficients for calculating mixing layers and jets

Currently available turbulence models for calculating mixing layers and jets are considered. The reasons for inadequate modeling of initial jet regions are analyzed. The problem of the sensitivity of certain turbulence models to the freestream value of ω is studied. The necessity of introducing variable turbulent-transport coefficients and a correction for axial symmetry is shown. A differential model with variable coefficients for the Reynolds stresses is proposed which makes it possible to obtain adequate solutions in the self-similar regions of mixing layers and jets.     

The generation of turbulence from displaced cross-members in uniform flow

This paper presents details of an experimental investigation into the nature of turbulence generated in the wake of a single grid node. The latter has been considered as two members placed perpendicular to each other in the geometry of a cross, with square and circular sections representing bars and rods respectively. The effect of member spacing has been examined in an attempt to identify the complex flow phenomena associated with such a configuration, and in this respect a critical gap width has been found.List of symbols C _p pressure coefficient, (p — p ₀)/1/2 U ₀ ² - C _pb pressure coefficient measured on the base centre-line - C _ps pressure coefficient measured at stagnation point - D diameter/section depth of model - L distance between central axis of two cylinders or bars - n vortex shedding frequency - p local pressure on model's surface - p ₀ static pressure - R () autocorrelation coefficient - R _e Reynolds number, DU ₀/v - St Strouhal number, n D/U ₀ - U ₀ mean freestream velocity in X-direction - ovu local mean velocity in X-direction - u velocity fluctuation in X-direction - ovv local mean velocity in Y-direction - ovw local mean velocity in Z-direction - X cartesian co-ordinate in longitudinal direction - Y cartesian co-ordinate perpendicular to wind tunnel floor - Z cartesian co-ordinate in lateral direction - dynamic viscosity of fluid - v kinematic viscosity of fluid, / - _n spectral energy, 4 ₀ R () cos 2 n d - density of fluid - _x longitudinal component of vorticity, /y – /z This paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986     

Development of lattice turbulence in a stream with a constant velocity gradient

On the basis of the equations for the Reynolds stresses and the equation for the scale of the turbulence, an analysis is made of the development of lattice turbulence in a stream with a constant velocity gradient. The constants in the equations are determined under the assumption that, far from the lattice and with large Reynolds numbers, the structure of the turbulence tends toward a limiting state with constant values of the correlation coefficient, the degree of anisotropy, and the dimensionless velocity gradient. The constants in terms containing the viscosity are determined from a consideration of the flow beyond the lattice without a velocity gradient in the final stage of decay of the turbulence. The equations obtained were solved in an electronic computer. The calculation is in satisfactory agreement with the existing experimental data. For calculating flows with a variable velocity gradient, instead of the equation of the scale, it is proposed to use an equation for the frequency of the turbulent pulsations obtained in the present work. The computer calculations were made by S. I. Bekritskaya.     

The generation of nearly isotropic turbulence downstream of streamwise tube bundles

Tube bundles were used to generate a field of nearly isotropic turbulence. A wide range of geometric and aerodynamic parameters were systematically studied, with measurements being made of pressure losses, turbulence intensities, spectra. auto-correlations and length scales. Simple analyses were utilized to correlate effectively these results and to aid in their understanding. The results agree well with other (limited) results published in the literature.     

A new method for the generation of representative time-domain turbulence excitations

In this paper we address the issue of generating, from the spectral and spatial parameters of turbulent flow excitations, time-domain random excitations suitable for performing representative nonlinear numerical simulations of the dynamical responses of flow-excited tubes with multiple clearance supports. The new method proposed in this work, which is anchored in a sound physical basis, can effectively deal with non-uniform turbulent flows, which display significant changes in their spatial excitation properties. Contrary to the classic technique developed by Shinozuka and coworkers, which generates a large set of correlated physical forces, the proposed method directly generates a set of correlated modal forces. Our approach is particularly effective leading to a much smaller number of generated time-histories than would be needed using physical forces to simulate the turbulence random field. In the case of strongly non-uniform flows, our approach allows for a suitable decomposition of the flow velocity profile, so that the spectral properties of the turbulence excitation are modeled in a consistent manner. The proposed method for simulating turbulence excitations is faster than Shinozuka׳s technique by two orders of magnitude. Also, in the framework of our modal computational approach, nonlinear computations are faster, because no modal projection of physical turbulent forces is needed. After presenting the theoretical background and the details of the proposed simulation method, we illustrate it with representative linear and nonlinear computations performed on a multi-supported tube.     

Identification,characterization and evolution of non-local quasi-Lagrangian structures in turbulence

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed. The quasi-Lagrangian structures, e.g., vortex surfaces in vis-cous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition, they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution. The improving understanding of the quasi-Lagrangian struc-tures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.     

Dynamic buckling of a single-degree-of-freedom system with variable mass

In this paper dynamic buckling of the single-degree-of-freedom system with variable mass is analyzed. In the system the mass variation is slow and is a function of slow variable time. Due to mass variation the impact force acts. The motion of the system is described with a nonlinear ordinary differential equation with time variable parameters. A new approximate analytic criterion of dynamic buckling for the non-autonomous systems which have the conservation law of energy type is developed. The conservation law is formed applying the Noetherian approach. The suggested method allows the determination of dynamic buckling load without solving the corresponding nonlinear differential equation of motion. For this value of dynamic load the motion of the system becomes unbounded. The obtained analytic value is compared with the numeric one. It shows a good agreement.     

A study of properties of vortex stretching and enstrophy generation in numerical and laboratory turbulence

Dynamically relevant alignments are used in order to show that regions with weak vorticity are not structureless, non-Gaussian and dynamically not passive. for example, the structure of vorticity in quasi-homogeneous/isotropic turbulent flows is associated with strong alignment between vorticity ω and the eigenvectors of the rate of strain tensor λ_i (especially — but not only — between ω and λ₂) rather than with intense vorticity only. Consequently, much larger regions of turbulent flow than just those with intense vorticity are spatially structured. The whole flow field — even with the weakest measurable enstrophy — is strongly non-Gaussian, which among other things is manifested in strong alignment between vorticity and the vortex stretching vector W_i ≡ ω_jS_ij. It is shown that the quasi-two-dimensional regions corresponding to large cos(ω, λ₂) are qualitatively different from purely two-dimensional ones, e.g. in that they possess essentially nonvanishing enstrophy generation, which is larger than its mean for the whole field.     

Characterization of a system generating a homogeneous isotropic turbulence field by free synthetic jets

A facility inspired by Hwang and Eaton (2004a, b) for generating a homogeneous isotropic turbulence was built, the objective being to study evaporating droplets in the presence of turbulence. Turbulence was produced by the mixing of six synthetic jets, in ambient atmosphere. Combined PIV and LDA techniques were used to measure the statistical turbulence properties. The turbulence produced was found to be homogeneous isotropic with a small mean flow within a domain having an average size of 50 mm × 50 mm × 50 mm. The rms fluctuations were of the order of 0.9 m/s, corresponding to a Taylor Reynolds number of 240 and an integral length scale of about 40 mm. This apparatus proved to be well suited to the study of the evaporation of droplets in a controlled turbulence field.     

The mass-centre motion of a continuously variable system of particles

Summary The vector differential equation of the mass-centre motion of a variable system of particles is found, provided that the mass variation is extended continuously on the whole (or on a part of the) surface bounding the system. Also an application is given.

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Die Bewegung des Massenmittelpunktes eines stetig veränderlichen Systems von MassenpunktenTeil 2

Übersicht Die vektorielle Differentialgleichung für die Bewegung des Massenmittelpunktes eines variablen Systems von Partikeln wird hergeleitet unter der Voraussetzung, daß der Massenstrom kontinuierlich verteilt ist über die Oberfläche des Systems (oder einen Teil von ihr). Ein Anwendungsbeispiel wird vorgestellt.

     

Reduction of a model of a mechanical system with variable reduced parameters

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 8, pp. 81–87, August, 1995.