Integral Turbulence Research Articles

An Integrated Turbulence Scheme for Boundary Layers with Shallow Cumulus Applied to Pollutant Transport

Abstract A scheme is described that provides an integrated description of turbulent transport in free convective boundary layers with shallow cumulus. The scheme uses a mass-flux formulation, as is commonly found in cumulus schemes, and a 1.5-order closure, involving turbulent kinetic energy and eddy diffusivity. Both components are active in both the subcloud and cloud layers. The scheme is called “mass flux–diffusion.” In the subcloud layer, the mass-flux component provides nonlocal transport. The scheme combines elements from schemes that are conceptually similar but differ in detail. An entraining plume model is used to find the mass flux. The mass flux is continuous through the cloud base. The lateral fractional entrainment rate is constant with height, while the detrainment-rate profile reduces the mass flux smoothly to zero at the cloud top. The eddy diffusivity comes from a turbulent kinetic energy–length scale formulation. The scheme has been implemented in a simple one-dimensional (single column) model. Results of simulations of a standard case that has been used for other model intercomparisons [Atmospheric Radiation Measurement (ARM), 21 June 1997] are shown and indicate that the scheme provides good results. The model also simulates the profile of a conserved scalar; this capability is applied to a case from the 1999 Southern Oxidants Study Nashville (Tennessee) experiment, where it produces good simulations of vertical profiles of carbon monoxide in a cloud-topped boundary layer.

Turbulence flux measurement above the overstory of a subtropical Pinus plantation over the hilly region in southeastern China

Continuous turbulence flux measurement using the eddy covariance (EC) technique was made from January 1 to December 31 in 2003 at two and three canopy heights of a subtropical Pinus plantation on the red earth hilly region in southeastern China. To be able to make sure that the measured turbulence flux will equal the net ecosystem/atmosphere exchange, the quality of the data has to be assessed. Three criteria were investigated here, including the power spectra and cospectra analyses, flux variance similarity (integral turbulence test) and energy balance closure. The spectral analyses suggested that above-canopy power spectral slopes for all velocity components and scalars such as CO2, H2O and air temperature followed the expected -2/3 power law in the inertial subrange, and their cospectral slopes were close to -4/3 power law in the inertial subrange. The important contribution of large-scale motions to energy and mass transfer above the canopy at higher measurement level was also confirmed by the spectral analyses. The eddy covariance systems have the ability to resolve fluctuations associated with small-scale eddies and did not induce an obvious underestimation of the measured turbulence flux. The Monin-Obukhov similarity functions for the normalized standard deviation of vertical wind speed and air temperature were well-defined functions of atmospheric stability at two heights above the forest canopy, which indicated that turbulence flux measurements made at two heights were within the surface layer. Nocturnal flux underestimation and departures of this normalized standard deviation of vertical wind speed similarity function from that expected from Monin-Obukhov theory were a function of friction velocity. Thus, an optimal criterion of friction velocity was determined to be greater than 0.2-0.3 m s-1 for nocturnal fluxes so that the eddy covariance flux measurement was under high turbulent mixing conditions. Energy balance closure reached about 72%-81% at the studied site, which was comparable to the 10%-30% of energy imbalance reported in the literature. However, the energy balance closure could be only used as a useful reference criterion.

Quantifying nighttime ecosystem respiration of a meadow using eddy covariance, chambers and modelling

Aim of the present paper is to quantify the ecosystem respiration of a mountain meadow in the Austrian Alps during the vegetation period 2002 by constraining nighttime eddy covariance measurements with ecosystem respiration derived from (i) daytime eddy covariance, (ii) ecosystem chamber and (iii) scaled up leaf and soil chamber measurements. The study showed that the discrimination of valid nighttime eddy covariance measurements based on friction velocity ( u *), the so-called u *-correction, is very sensitive to the imposed quality control criteria. Excluding half-hourly nighttime data, which deviate more than 30% from the stationarity and integral turbulence tests caused the magnitude of the u *-correction to be significantly reduced. Based solely on nighttime eddy covariance data, we are currently unable to decide whether the observed high CO 2 fluxes during intermittent turbulence represent artefacts and should be screened out, or whether these reflect a genuine transport of CO 2 not accounted for by the storage term and must be retained. Evidence against the inclusion of these data is derived from soil respiration rates measured in situ and calculated inversely from the other approaches, which were significantly lower as compared to soil respiration calculated from inversion of the half-hourly nighttime data inclusive of the observations which failed to meet the specified quality control criteria. Seasonal (8 March–8 November 2002) nighttime carbon balances simulated based on the parameters derived from the remaining approaches agreed with each other to within 35%, which is of the order of the uncertainty of each individual approach.

Transient Fluid Flow in a Continuous Casting Tundish during Ladle Change and Steady-state Casting

Transient effects occur during both steady-state casting as well as transient casting, e.g. a ladle change. These effects are caused by transient boundary conditions at the inlet of the tundish. A time-dependent inlet temperature causes a free convection flow during steady-state casting. During transient casting, such as during a ladle change, the mass flow at the inlet is time-dependent and thus a transient flow develops. In general, transient flow is unwanted because transient flow means a change of conditions for the separation of non-metallic particles. The analysis of the flow in the tundish is carried out by numerical as well as physical simulations. In this case experimental investigations are carried out on a water model. The results of laser optical investigations using Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (DPIV) serve as a validation of the numerical results. The numerical results are then used for the investigation of the thermal melt flow. The effects caused by a changing bath level during transient casting (ladle change) are investigated using the Volume-of-Fluid (VoF) model. Beyond this, the interaction between the melt and slag is taken into account, by using the three phase system melt-slag-air. In addition to the classical methods a new zonal approach is introduced in this paper. The integral balance localises high turbulence mixing regions as well as the development and intensity of back flows. The levelling of the momentum flux between the inlet and the outlet can also be described.

남극 세종기지에서의 지표 플럭스 관측: I. 난류 특성과 현열 플럭스

The Antarctic Peninsula is important in terms of global warming research due to pronounced increase of air temperature over the last century. The first eddy covariance system was established at King Sejong Station located in the northern region of the Antarctic Peninsula in December of 2002 and has been operated over one year. Here, we analyze turbulent characteristics to determine quality control criteria for turbulent sensible heat flux data as well as to diagnose the possibility of long term eddy covariance measurement under extreme weather conditions of the Antarctic Peninsula. We also report the preliminary result on sensible heat flux. Based on the analyses on turbulent characteristics such as integral turbulence characteristics of vertical velocity (w) and heat (T), stationarity test and investigation of correlation coefficient, they fallow the Monin-Obukhov similarity and eddy covariance flux data were reliable. of total retrieved sensible heat flux data could be used for further analysis. Daytime averaged sensible heat flux showed a pronounced seasonal variation, with a maximum of up to in summer. In conclusion, continuous and long-term eddy covariance measurement may be possible at the study site and the land surface may influence the atmosphere significantly through heat transport in summer.

Dual particle image velocimetry for transient flow field measurements

This paper describes an experimental approach to obtain transient flow structure and flow turbulence characteristics with the mean of a dual particle image velocimetry (PIV) system. Temporal evolution of the tumble motion is visualised on two sequences of consecutive velocity fields with a short delay time in the range of 70 µs. Original experimental set-up and synchronisation are proposed for this purpose and a detailed description of the set-up along with the solutions adopted for the implementation and synchronisation of a dual PIV are given. As traditional PIV analysis consists of instantaneous measurement of a 2D velocity field, the new approach allows a comparison to be made over time between results obtained with two instant consecutive velocity fields with dual PIV and over space because of the technique itself. Consequently, the analysis of the reciprocating engine turbulence, particularly the characterisation of the time and space autocorrelation coefficients, and the time and length macro scales on the analogy of the integral time scale turbulence for stationary flows are proposed. Results give spatio-temporal evolution of the autocorrelation coefficients. The calculation of the integral scales for different crank angles shows a changing pattern during the admission and compression processes. Characteristic mean velocities are proposed according to the integral length and time scales.

On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when ‘streaky structures’ of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity.The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976).The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Stanford Center for Integrated Turbulence Simulations

Using massively parallel computing, the Center for Integrated Turbulence Simulations is advancing the physics based numerical simulation of aircraft engine flow and combustion. It is also helping to develop the advanced computer platforms necessary to perform these simulations. The article outlines the CITS' challenges, program, and progress.

Third-Order Transport and Nonlocal Turbulence Closures for Convective Boundary Layers*

The turbulence closure problem for convective boundary layers is considered with the chief aim to advance the understanding and modeling of nonlocal transport due to large-scale semiorganized structures. The key role here is played by third-order moments (fluxes of fluxes). The problem is treated by the example of the vertical turbulent flux of potential temperature. An overview is given of various schemes ranging from comparatively simple countergradient-transport formulations to sophisticated turbulence closures based on budget equations for the second-order moments. As an alternative to conventional “turbulent diffusion parameterization” for the flux of flux of potential temperature, a “turbulent advection plus diffusion parameterization” is developed and diagnostically tested against data from a large eddy simulation. Employing this parameterization, the budget equation for the potential temperature flux provides a nonlocal turbulence closure formulation for the flux in question. The solution to this equation in terms of the Green function is nothing but an integral turbulence closure. In particular cases it reduces to closure schemes proposed earlier, for example, the Deardorff countergradient correction closure, the Wyngaard and Weil transport-asymmetry closure employing the second derivative of transported scalar, and the Berkowicz and Prahm integral closure for passive scalars. Moreover, the proposed Green-function solution provides a mathematically rigorous procedure for the Wyngaard decomposition of turbulence statistics into the bottom-up and top-down components. The Green-function decomposition exhibits nonlinear vertical profiles of the bottom-up and top-down components of the potential temperature flux in sharp contrast to universally adopted linear profiles. For modeling applications, the proposed closure should be equipped with recommendations as to how to specify the temperature and vertical velocity variances and the vertical velocity skewness.

Aeroacoustic response of a six-bladed axial fan to installation effects

First, the effects of the duct on the aeroacoustic response of an axial fan have been studied experimentally and theoretically. The loading effect was modeled by a 1D model in the plane-wave frequency domain. This model was validated experimentally by changing duct lengths and fan positions. Second, an experimental characterization of the inflow turbulence has been done. Single degree-of-freedom statistical parameters have been measured as autocorrelation and temporal autospectrum for the axial turbulence components in order to estimate the integral scale and turbulence intensity. In parallel (the fan being located between an anechoic room and a reverberant room), sound pressure and sound-power measurements have been carried out. Different grids and supercritical screens have been designed to change the inflow conditions. The next task is to determine the spectral pattern in both the temporal frequency and tangential wave number domains and correlate it to acoustic response. Only the tonal part of the spectrum is considered. [Work supported by EEC.]

Renormalization group in the problem of fully developed turbulence of a compressible fluid

A model of fully developed turbulence of a compressible liquid (gas), based on the stochastic Navier-Stokes equation, is considered by means of the renormalization group. It is proved that the model is multiplicatively renormalized in terms of the “velocity-logarithm of density” variables. The scaling dimensions of the fields and parameters are calculated in the one-loop approximation. Dependence of the effective sound velocity and the Mach number on the integral turbulence scale L is studied.

On turbulent flux of trace constituents measurements in the surface layer: Part I: Tests on vertical velocity stationarity

During some non stationary events, mainly under very unstable conditions, spectral and cospectral functions point out the contribution of low frequencies (< 10 −2 Hertz) to the calculation of turbulent fluxes. The purpose of this work is to present an example of criteria for assessing the quality of vertical velocity measurements. Tests are based on the ratio between the standard deviation for vertical velocity and the mean horizontal wind component (turbulence rate), in accordance with Taylor's hypothesis, and on the comparison of filtered and non filtered integral length scale for vertical velocity, with a view to detecting non stationary samples. Thus, the limits of automatic routine flux determination (black box) by the eddy correlation method are shown. After selection of the samples, the relationship between integral turbulence characteristics and stability parameter is established. The laws obtained, describing the evolution of these characteristics for a surface layer over a forest are then presented.

Renormalization-group study of correlation functions and composite operators in the stochastic magnetohydrodynamic model

By means of the renormalization-group approach, the scaling behavior of the correlation functions in stochastic magnetohydrodynamics is studied for the case of developed turbulence. To complete the results obtained previously, we investigate the infrared asymptotics of the Green's functions with an arbitrary number of external fields in both the “kinetic” and “magnetic” regimes. Special consideration is given to the problem of dynamic scaling behavior in the magnetic regime. The critical dimensions of the composite operators of the energy functional are calculated. Using the short-distance expansion, we find the relation between the correlation functions within the inertial range and the integral turbulence scale.

Structure of the probability density of turbulent concentration pulsations with very large amplitudes

The structure of the probability density of very large values of the concentration of a passive admixture is considered. The solution of this problem is of importance for modeling the emission of carbon monoxide and unburnt hydrocarbons. A theoretical model is constructed on the basis of the following ideas: (1) the dimension of the zones in which the concentration pulsations with vary large amplitudes are observed is of the order of the integral turbulence scale; (2) the probability of these zones being generated is very low. It is shown that there is a certain limiting large value of the concentration in the neighborhood of which the probability density can be described by a power function. On the basis of the theory of locally uniform turbulence it is shown that, generally speaking, if certain relationships between the unknown quantities entering into the theory are not satisfied, the probability density of very large values of the concentration depends on the Reynolds number.

The Eddy Structure Model of Turbulent Flamelet Propagation, the Expanding Spherical and Steady Planar Cases

Abstract A structural model of turbulence, composed of vortex tubes which are based on direct simulations of turbulence, is used to model the flame area enhancement found in direct simulations of passive flame propagation. The resulting model produces a turbulent premixed flame speed ST within a chamber which has the experimentally observed integral length scale and turbulence intensity behavior. The excess flame area is proportional to where R, is the flame radius,. is the Taylor length scale and the diameter of the vortex tube, u’ is the turbulence intensity and SL is the burning velocity. This first model yields a linear dependence between and and additionally, gives as the steady-state planar propagation, where A is the integral scale. This planar relation can also be expressed as s/t/ReJ\5SL, and this relation has been shown to correlate experimental turbulent flame speed results and direct turbulence simulations of passive flamelet propagation. A second propagation model uses a function that exhibits a maximum value of to replace the in the above excess area estimate. This eddy structure model yields departure from the linear u’/SL behavior of the first model, and this departure agrees with the experimental results. The maximum in is caused by vortical structures which are not space filling, and depends upon the ratio of. The two constants in this eddy structure model are determined from experimental results, however, their values are close to those estimated from the spatial structure of vorticity. A model of flame propagation for internal combustion applications is proposed and the effect of the chamber geometry upon the turbulent flame speed is discussed.

Use of tensor polynomials for constructing an equation for turbulence scale in semiempirical models

Thek-kl-model of turbulence based on the equation of second two-point moments (pointsA andB) of the fluctuating velocity field is presented. The second and third moments entering into this equation are expressed using polynomials whose terms are products of the tensor components characterizing a given turbulent motion and scalar functions of the distanceAB. ForAB=0 the equation obtained gives thek-turbulence energy balance equation and, on being integrated overAB from 0 to ∞, the transport equation for thekl-quantity (l is the integral turbulence scale). The model is used for calculating mixing layers, plane and circular jets, the wake behind a cylinder, tube and channel flows, and the boundary layer on a plate. The results of all the calculations agree well with the experimental data for a single set of empirical coefficients.

Turbulent flows. Models and numerical investigations. A review

Russian papers on differential models of turbulence and numerical simulation of nonequilibrium turbulent flows of liquids, gases, and conducting media, published for the most part in this journal over the last 10–15 years, are reviewed. The turbulence models considered in this review are based on Kolmogorov's ideas, which generated a new approach to the mathematical modeling of turbulent flows consisting in the use of transport equations for the turbulence properties. The subsequent development of these models was due to the emergence of computers which made it possible to change over from a qualitative analysis in particular regions to obtaining quantitative results with the influence of viscosity, and also such effects as diffusion and convection, taken directly into account in the mathematical simulation of turbulent flows. In this review the models are selected in accordance with the following criteria. 1. Only differential models are considered, that is models in which transport equations are used for the main turbulence properties: the turbulence energy, shear stress or the turbulent viscosity and a parameter involving the integral turbulence scale. According to the number of the transport equations the models are classified as one-, two-, or three-parameter. The application of the models is restricted to flows for which the boundary layer approximation holds true. 2. The models must have been put to practical use in the analysis of particular flows, and their most efficient areas of application specified. The models must have been tested by comparison with the most reliable experimental data. The models must be highly universal, thus making it possible, without adjusting the constants entering into the model, to take into account the inlet and boundary conditions, the variations of the physical properties of the medium, and external influences. The review aims to demonstrate the potential of the turbulence models considered in relation to a wide variety of flows in boundary layers and channels, and also to draw them to the attention of users and researchers developing scientific and applied computational programs for the description and control of devices with complicated working processes in aviation and space technology, and other areas.

On Simulation of the Inflammation Period in Spark Ignition Engines

ABSTRACT A simulation model has been evolved which performs the duration of the inflammation period tEP. The principal parameters of this model are environmental condition, air supply, mixture composition with including residual gas. and engine speed. Due to the intention of the model to be a design tool rather than a precise but complicated model for fundamental research the algorithms used are fast and according to physical properties. These algorithms have been fitted to experimental results obtained by a spark ignition engine. The prediction of tEP at reference conditions has been formulated based on combination of mixture density at a particular crankangle and the ratio of integral length scale and turbulence intensity at ignition time. Deviation flame speed relations. The influence of engine speed has been assumed to result in changed turbulence intensity which influences tEP. The in mixture composition from reference conditions has been performed by laminar performance of the model is good, on most...

The principle of maximum randomness in the theory of fully developed turbulence. II. Isotropic decaying turbulence

A statistical model for describing the decay of developed isotropic turbulence of an incompressible fluid is proposed. The model uses the distribution function of the velocity pulsations introduced earlier by the authors on the basis of the principle of maximum randomness of the velocity field for a given spectral energy flux. The renormalization-group technique and e′ expansion are used to calculate the correlation functions of the velocity that occur in the equation of spectral energy balance. This leads to a closed equation for the dependence of the energy spectrum on the integral turbulence scalerc(t). In the inertial interval, this equation gives the Kolmogorov asymptotic spectrum, while for the time dependence ofrc(t) and the pulsation energye(t) it predicts the power lawsrc(t)∼t2/5 andr(t)∼t−6/5.

On the response of the ocean upper layer to synoptic variability of the atmosphere

The response of the ocean upper layer to synoptic atmosphere variability is examined using a nonlocal integral model of the subtropical gyre. Our main goal is the analysis of the nonlinear, nonlocal oceanic response to two typical atmospheric disturbances, which were postulated to be of the same intensity but of opposite sign. Thus, we study the nonlinear effects in the response of a horizontally inhomogeneous ocean to synoptic disturbances in the subtropical gyre. It was shown that synoptic atmospheric variability generates an oceanic response which may have climatic consequences. Synoptic upper mixed layer (UML) thermal anomalies reach about 1–2°C over an area of more than 1000 km × 1000 km, and influence directly the large-scale atmosphere-ocean interaction. This influence is comparatively short term. On the other hand, a series of storms may influence the thermal regime of the whole baroclinic layer. This leads to long-term consequences. Therefore, the simulation of such fluctuations in large-scale models of atmosphere-ocean interaction is necessary. Oceanic horizontal inhomogeneity is most important in the integral heat, momentum and kinetic energy turbulence (KET) balances of the UML after the passage of storms. The effect of oceanic inhomogeneity is at a maximum in the storm-induced frontal zone and is shown particularly in the advective h variations ( h is the UML thickness), which are of the same order as the local h variations, as well as in generation of the gradient currents/gradient advection, which are of the same order as the drift currents/drift advection (but slightly less). Obviously, drift advection is the main effect of the UML horizontal inhomogeneity. During the action of strong winds, the heat, momentum and KET balances of the mid-ocean UML are approximately one-dimensional for most of the storm track. During this period, the synoptic vertical motions at the base of the UML must also be considered. Vertical thermal storm-induced advection in the main thermocline exceeds the vertical diffusion by one and a half orders, and may strongly influence the thermal regime of the main thermocline if there are several storms of the same sign and trajectory.