Conditional Sampling Procedure Research Articles

Transient large-scale two-phase flow structures in a 3D bubble column reactor

This paper analyses the local and time-dependent behavior of large-scale structures responsible for liquid circulation in gas-water flow of a 3-D cylindrical bubble column of high aspect ratio with a multiple orifice for uniform aeration. The large-scale flow structures play an important role in the mixing and the mass transfer while coherent structures dominate hydrodynamic characteristics of the turbulent flow field. A three-dimensional Euler-Euler large eddy simulation (LES) model was used to calculate large-scale structures and their interaction with bubbles at inlet superficial gas velocities of UG= 6 and 8.4 cm/s where vortical-spiral and turbulent flow regimes occur. The two-phase model gives good agreements with experimental measurements. We use a conditional sampling procedure of liquid velocity and gas hold-up time series to identify and educe the development of coherent flow structures which consists in a pair of counter-rotating vortices convected in a staggered pattern along the column in both the vortical-spiral and central plume regions. On average, the detected instantaneous events for each template account for about 12–15% of the data recorded and may appear simultaneously. These events produce important fluctuations in the axial liquid velocity and gas void fraction. The sampling procedure yielded the averaged topology of the three-dimensional large-scale structures which was visualized using isosurfaces of the vorticity for different gas flow rates. The structures have spiral tube-shaped topology rotating along the column near the walls with a pair of counter-rotating cells sustained through the flow. This work provides deep insights into turbulent flow field in gas-liquid bubble column by LES and pattern recognition.

RANS simulations of neutral atmospheric boundary layer flow over complex terrain with comparisons to field measurements

AbstractMicro‐scale Reynolds‐averaged Navier‐Stokes (RANS) simulations of the neutral atmospheric boundary layer (ABL) over complex terrain and a comparison of the results with conditionally averaged met‐tower data are presented. A robust conditional sampling procedure for the meteorological tower (met‐tower) data to identify near‐neutral conditions based on a criterion for the turbulence intensity is developed. The conditionally averaged wind data on 14 met‐towers are used for the model validation. The ABL flow simulations are conducted over complex terrain which includes a prominent hill using the OpenFOAM‐based simulator for on/offshore wind farm applications (SOWFA) with the k−ϵ and the SST k−ω turbulence models. The discretization of the production term in the transport equation for the turbulent kinetic energy (TKE) is modified to greatly reduce the commonly observed nonphysical near surface TKE peak. The driving inflow is generated through an iterative approach using a precursor method to reproduce the measured wind statistics at the reference tower. Both of the RANS models are able to capture the flow behavior windward of the hill. The SST k−ω model predicts more intense flow separation than the k−ϵ model downstream of the steepest sections of the hill. The wind statistics predicted at the location of the met‐towers by both of the RANS models are fairly consistent. Overall, the comparisons of the direction, mean, and standard deviation of the wind between the simulations and the tower data show reasonable agreement except for the differences of the mean wind speeds at four met‐towers located closer to the main ridge of the hill in a region of strong terrain variations.

Observing the Whole-Canopy Short-Term Dynamic Response to Natural Step Changes in Incident Light: Characteristics of Tropical and Temperate Forests

We examine the physical and biological responses of forest canopies to step changes in light caused by passing low cumulus clouds that intermittently block the direct solar beam. Using data obtained at a tropical rainforest and at a midlatitude deciduous forest, we estimate the course of sensible heat flux, net ecosystem exchange, evapotranspiration, and water-use efficiency in response to the rapid changes in the incident radiative flux. To describe these fluxes during the interval over which the effects of stomatal time delays can be most influential, eddy fluxes are estimated over minute or shorter intervals by invoking a conditional-sampling procedure based on forming a Reynolds-average ensemble. The most important differences between the two forests’ physical responses are in the thermal balances and heat-flux time response constants. During the initial period after the light transition the only mean variables that show appreciable changes are the blackbody and air temperatures, the other scalars being little affected. We find that a distinct transient thermal internal boundary layer appears ≈ 20 m thick above the temperate deciduous forest and ≈ 45 m thick above the tropical rainforest. At each forest, the effective thickness of the inferred thermal outer-canopy ‘big leaf’ is about 1 mm. Twenty minutes after the abrupt change in incident light, ensemble eddy-flux estimates approach those found using conventional time averaging, confirming the validity of the ensemble approach. Previously unrecognized transient maxima in net ecosystem exchange and evapotranspiration are evident 5–10 min following the shadow-to-light transition, longer than the average light interval between shadows observed on partly-cloudy days in each case. Short-term variations in sensible heat flux, net ecosystem exchange, and evapotranspiration approximate an exponential adjustment, implying that first-order time-dependent single-leaf models are adequate to describe whole-canopy processes in these cases, providing an experimental method for determining whole-canopy bulk stomatal time constants. During the sunlit interval (direct and diffuse radiative fluxes combined) net ecosystem exchange is enhanced, while under cloud shadow (only diffuse radiative flux) water-use efficiency increases. This light and shadow alternation provides a mechanism describing the observed enhanced net ecosystem exchange and water-use efficiency under certain types of partly-cloudy sky. We apply empirical flux-response curves to an idealized case of radiative flux varying in a regular on–off light and shadow pattern. For this case, an analytical solution for mean net ecosystem exchange flux as a function of diffuse-radiation fraction yields results that strongly resemble previous findings based on conventional time-averaged fluxes. Our analysis and modelling indicates that a well-known correlation between diffuse radiative flux and enhanced net ecosystem exchange and water-use efficiency on cloudy days is in many cases not causal, but rather to be a consequence of time averaging over light-and-shadow intervals. By linking processes associated with photosynthesis in fluctuating light at the leaf scale to the canopy scale, our efforts facilitate the scaling-up of leaf responses to the ecosystem scale.

Acceleration and wall pressure fluctuations generated by an incompressible jet in installed configuration

In this work, the cross-statistics of acceleration and wall pressure fluctuations generated by an incompressible jet interacting with a tangential flat-plate are presented. The results are derived from an experimental test campaign on a laboratory-scale model involving simultaneous velocity and wall pressure measurements. The pressure footprint of the jet on the surface was measured through a cavity-mounted microphone array, whereas pointwise velocity measurements were carried out by a hot wire anemometer. The time derivative of the velocity signal has been taken as an estimation of the local acceleration of the jet. The multivariate statistics between acceleration and wall pressure are achieved through cross-correlations and cross-spectra, highlighting that the causality relation is more significant in the potential core where the Kelvin–Helmholtz instability is dominant. The application of a conditional sampling procedure based on wavelet transform allowed us to educe the acceleration flow structures related to the energetic wall-pressure events. The analysis revealed that, unlike the velocity, the acceleration signatures were detected only for positions where the jet had not yet impinged on the plate, their shape being related to a convected wavepacket structure.

Fourier and wavelet analyses of intermittent and resonant pressure components in a slot burner

In laboratory-scale burner it has been observed that the acoustic excitations change the flame topology inducing asymmetry and oscillations. Hence, an acoustic and aeroacoustic study in non reactive condition is of primary importance during the design stage of a new burner in order to avoid the development of standing waves which can force the flame. So wall pressure fluctuations inside and outside of a novel slot burner have been studied experimentally and numerically for a broad range of geometrical parameters and mass flow rates. Wall pressure fluctuations have been measured through cavity-mounted microphones, providing uni- and multi-variate pressure statistics in both the time and frequency domains. Furthermore, since the onset of combustion-driven oscillations is always presaged by intermittent bursts of high amplitude, a wavelet-based conditional sampling procedure was applied to the database in order to detect coherent signatures embedded in the pressure time signals. Since for a particular case the coherent structures identified have a multi-scale signature, a wavelet-based decomposition technique was proposed as well to separate the contribution of the large- and small-scale flow structures to the pressure fluctuation field. As a main outcome of the activity no coupling between standing waves and velocity fluctuations was observed, but only well localized pressure signatures with shape strongly affected by the neighbouring flow physics.

Designing of Variables Modified Chain Sampling Plan Based on the Process Capability Index with Unknown Mean and Variance

SYNOPTIC ABSTRACTThis article proposes a variables-modified chain sampling plan based on the process capability index Cpk for the inspection of normally distributed quality characteristics with unknown mean and variance. The modified chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be very useful, particularly in compliance testing. Tables are also constructed to select the optimal parameters of the variables modified chain sampling plan for specified two points on the operating characteristic curve by minimizing the average sample number. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. The optimization problem is formulated as a nonlinear programming problem where the objective function to be minimized is the average sample number, and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

Multivariate and conditioned statistics of velocity and wall pressure fluctuations induced by a jet interacting with a flat plate

The increasing size of aircraft engines is leading to reconsideration of their conventional integration in the under-wing configuration due to the strong interaction between the jet and the airframe components. As a consequence, more insight is needed into the complex mechanisms underlying the interaction phenomenon between the jet flow and a surface. The objective of this paper is to carry out a series of experimental tests on a simplified laboratory-scale model to approach/deepen the problem. This analysis is the continuation of a previous study (Di Marco et al., J. Fluid Mech., vol. 770, 2015, pp. 247–272) on a rigid flat plate installed tangentially to the axis of an incompressible jet. In the present work, the velocity and wall pressure fields were simultaneously measured for different radial distances of the plate from the nozzle axis. Pointwise hot-wire anemometer measurements were carried out to characterize the effect of the plate on the velocity field statistics up to the fourth-order moment. The analysis revealed that the presence of the plate brings about a deflection of the mean aerodynamic field over the surface and a reduction of the turbulence intensity. Wall pressure fluctuations induced by the jet flow over the plate were measured by a linear array of cavity-mounted microphones placed along the streamwise direction. The velocity/pressure cross-statistics are achieved in the time and frequency domains using cross-correlations and Fourier analysis. A wavelet-based conditional sampling procedure is applied as well to characterize the flow signatures related to the velocity and wall pressure fluctuations, revealing that the surface induces the breakdown of the large-scale turbulent structures. The dependence of the multivariate and conditioned statistics on the plate distance from the jet as well as on the streamwise and crosswise probe positions is extensively discussed. Different organized flow motions over the surface are found based on the wall pressure events detected. A scaling criterion for velocity signatures is also presented addressing the governing parameters of the jet–plate interaction phenomenon.

Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

We investigate the optimal designing of chain sampling plan for the application of normally distributed quality characteristics. The chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be useful when testing is costly and destructive. The advantages of this proposed variables plan over variables single sampling plan and variables double sampling plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables chain sampling plan for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level, along with the producer’s and consumer’s risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

Stochastic Generalized Method of Moments

The generalized method of moments (GMM) is a very popular estimation and inference procedure based on moment conditions. When likelihood-based methods are difficult to implement, one can often derive various moment conditions and construct the GMM objective function. However, minimization of the objective function in the GMM may be challenging, especially over a large parameter space. Due to the special structure of the GMM, we propose a new sampling-based algorithm, the stochastic GMM sampler, which replaces the multivariate minimization problem by a series of conditional sampling procedures. We develop the theoretical properties of the proposed iterative Monte Carlo method, and demonstrate its superior performance over other GMM estimation procedures in simulation studies. As an illustration, we apply the stochastic GMM sampler to a Medfly life longevity study. Supplemental materials for the article are available online.

A conditional sampling-based method for noise and resolution corrections for scalar dissipation rate measurements

A conditional sampling-based method for correcting noise and resolution effects for scalar dissipation rate measurements is developed. Noise and resolution effects on the measured dissipation rate have opposite trends, making their separation and accurate corrections difficult. A major task in dissipation rate correction, therefore, is to isolate each effect. The conditional-sampling method presented in this work uses instantaneous local scalar mean and variance as conditioning variables, and is based in part on Kolmogorov’s refined similarity hypotheses. It ensures selection of instantaneous fully resolved local scalar fields, which are analyzed to determine the measurement noise. Noise correction is applied to potentially under-resolved local scalar fields, also selected using the conditional-sampling procedure, effectively separating the effects of noise from those of resolution. The error function is used as a model for the potentially under-resolved local scalar fields to evaluate their dissipation length scales and to make corrections for the dissipation rate. The present method uses local instead of spectral analyses; therefore, can be applied to the mean scalar dissipation rate conditional on the scalar values. An application of the method to temperature dissipation rate in a slightly heated turbulent jet shows excellent results, validating the method. The method can also be applied to other challenge situations, such as turbulent flames.

Scale of Vortex Structure and Turbulence Property in Impinging Jet

The flow field in a turbulent jet impinging on a flat plate is studied. When the two dimensional free jet impinges on the wedge object, so called the edge tone is generated. This accompanies a loud noise and coherent motions. Although most attention has been paid to reveal its mechanisms and control the coherent motions in order to reduce the sound noise, we are interested in the effect of coherent motions on the typical length scale. Adopting the three-component analysis, it was found that coherent motion has a great influence on the integral scale and Taylor micro scale, but has little on the Kolmogorov length scale. Also we focus on the area where the coherent motions survive after impinging on the edge of flat plate. By way of conditional sampling procedure, both the periodic component caused by coherent motions and the non-periodic component are analyzed. The periodic component remains close to wall even far from the top of the plate, but the non-periodic component indicates the large values only around the edge.

Inference of statistical bounds for multistage stochastic programming problems

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fixing a feasible first-stage solution and then solving the sampling approximation of the corresponding (T−1)-stage problem, does not give a valid statistical upper bound for the optimal value of the true problem.

A Conditional Sampling and a Stochastic Model of Bursting Process in a Rotating Turbulent Boundary Layer.

Coherent structures or large scale motions in a turbulent boundary layer on a rotating cylinder in a quiescent fluid are considered by various conditional sampling procedures. As it is clear from previous investigations that the coherent structures are depending on the conditional technique of sampling, here we discuss some dynamical aspects of them. Several conditional sampling procedures are adopted here, and also the variable interval time average (VITA) technique is modified with a reasonable assumption. Turbulent velocity signal and a random process generated by a Langevin equation are analyzed by these techniques. With comparing these results, we found that statistial properties of the coherent structure are well modeled by the Langevin equation as far as the conditional sampling is assigned.

Choice of the threshold level in a velocity-based conditional sampling procedure

Analysis of velocity traces obtained in the intermittent region of a wake by means of a rake of hot-wire probes has clearly shown that many of the weak fluctuations observed in the outer, very low-intermittency-factor region of the flow are associated with the turbulent bulges and are not potential flow fluctuations, as might be concluded from single probe measurements. Since most velocity-based conditional sampling techniques rely, to some extent, on a visual comparison of the intermittent signal and its indicator function, the choice of the threshold level associated with these techniques is rather subjective and, consequently, identification of these weak turbulent-zone fluctuations is often not made. A relatively objective and robust method of obtaining the threshold level for a velocity-based turbulent detector function is presented and discussed.

Laser measurement techniques applied to turbulent combustion in piston engines

The application of experimental laser diagnostic techniques to the study of turbulent flame propagation in homogeneous-charge internal combustion engines is demonstrated. A variety of laser refraction and scattering techniques are employed: the qualitative shape and detailed internal turbulence structure of the flame surface is investigated using laser schlieren photography; the flame location and local flame speed are measured using multibeam laser refraction; the instantaneous flame thickness is measured using Rayleigh scattering; gas temperatures are measured using Rayleigh and Raman scattering; gas velocity, turbulence intensities, and time scales of turbulence are measured using laser Doppler velocimetry. The problem of cyclic variation bias in turbulence measurements is addressed using conditional sampling procedures that involve the simultaneous implementation of multiple diagnostics. This paper focuses on the thermodynamic and fluid mechanic properties of interest to turbulence combustion studies, illustrating how laser diagnostics can be used to research the critical areas of interest.

An Investigation of the Wake Structures of a Circular Cylinder Using a Computer Aided Flow Visualization : 1st Report, Generation and Dissipation of the Vorticities

Wake structures behind a circular cylinder at Reynolds number of 3.7 × 104 are investigated using a computer aided flow visualization technique, which includes our newly developed conditional sampling procedure. Phase-averaged velocity distributions in the boundary layer on a cylinder are measured and the process of generation and shedding of vorticity are presented. Total circulation discharged from the cylinder surface in a shedding cycle is directly evaluated. Phase-averaged stream-lines and vorticity fields in the wake are obtained, and using these results the coherent structures of the wake flow, i.e., geometrical arrangement, convection speed, a total circulation of a shedding vortex and inner structures of vortices are described. Less than 40% of the discharged vorticity appears in a shedding vortex, and a vorticity distribution in the vortex in the near wake is quite similar to that in an isolated theoretical viscous vortex. But the spacing ratio, convection speed and the drag coefficient obtained do not agree with those calculated from a classical theory.

Intermittency of the noise emission in subsonic cold jets

Intermittency of the noise emission has been investigated by means of measurements of instantaneous cross-correlation between the far field acoustic pressure and the velocity component in the jet towards the microphone (pressure signal allowing for the acoustic propagation time). The noise is found to be associated with active periods of the second time derivative of the velocity signal. A conditional sampling procedure with a criterion based on the amplitude of this derivative, has made it possible to show that 50% of the noise is produced during only 10 to 20% of the time. The sections of the jet considered are located between 4 and 10 diameters from the nozzle, a region in which most of the averaged jet noise originates. An attempt to establish a relationship with the large scale structures of the jet has also been made. Examination of various time traces seems to indicate that the noise emission would take place at the upstream side of the large structures where most of the non-turbulent fluid is being caught up and rapidly entrained.