Velocity In Turbulent Flow Research Articles

Statistics of Lagrangian velocities in turbulent flows.

We present a generalized Fokker-Planck equation for the joint position-velocity probability distribution of a single fluid particle in a turbulent flow. Based on a simple estimate, the diffusion term is related to the two-point two-time Eulerian acceleration-acceleration correlation. Dimensional analysis yields a velocity increment probability distribution with normal scaling v approximately t(1/2). However, the statistics need not be Gaussian.

Development of emulsions from biomass pyrolysis liquid and diesel and their use in engines—Part 2: tests in diesel engines

The use of biomass derived pyrolysis oils, bio crude oil (BCO), in diesel engine requires deep modifications to the engine, such as the adoption of dual fuel systems and pilot injection: BCO/diesel emulsions are expected to significantly reduce the need for these adaptations. This paper describe the effects of various BCO/diesel emulsions on the injection systems of different diesel engines. Materials used for injectors’ nozzles and needles are investigated and compared. The issue of the erosion and/or corrosion of the injector nozzle is examined, and dedicated tests have been carried out. The experimental results suggested that corrosion accelerated by the high velocity turbulent flow in the spray channels is the dominant factor. A stainless steel nozzle has been built and successfully tested. Long term validation is however still needed.

Electrochemical machining: The role of steel microstructure in high-rate anodic dissolution

Electrochemical machining (ECM) of metals, particularly steels, plays an important role in many industrial microsystem technologies. This paper presents an overview of investigations into the anodic metal dissolution at high current densities of the technically important carbon steel 100Cr6 in aqueous NaCl- and NaNO3-electrolytes. The practice of ECM was simulated in flow channel experiments, where high current densities (up to 70 A/cm2) and turbulent electrolyte flow velocities (7 m/s) were applied. Insoluble carbide particles, enriching at the substrate surface, cause an apparent current efficiency > 100% in NaCl and > 67% in NaNO3 at high current densities. The role of the steel microstructure as controlled by its prior heat treatment is discussed with reference to a qualitative erosion-corrosion model proposed for the anodic dissolution process.

Effect of temporal pulsations of a turbulent flow on the flame velocity

Recently, a hypothesis has been proposed that temporal pulsations of a turbulent flow may explain the reduction and even saturation of the flame velocity at large turbulent intensities. However, the study was limited to very anisotropic flows. In this paper, we investigate the effect under more general conditions, which use the dependence of the velocity in the mean direction of propagation. Analytical formulae for the flame velocity in a time-dependent turbulent flow are obtained at low turbulent intensity and generalized to high intensity by using the renormalization method. These results are compared to numerical simulations. We show that the temporal pulsations do not lead to saturation of the flame velocity at high turbulent intensity, even if some effects appear at lower root-mean-square velocity.

Finite element method simulation of turbulent wavy core–annular flows using a k– ω turbulence model method

A numerical simulation of wavy core flow was carried out previously. They calculated the interfacial wave shape for laminar flow. In our present simulation, the shear stress transport turbulence model is used to solve the turbulent kinetic energy and dissipation rate equations and a splitting method is used to solve Navier–Stokes equations for the wave shape, pressure gradient and the profiles of velocity and pressure in turbulent wavy core flows. The wavelength decreases with Reynolds number R and with the volume ratio η. The pressure gradient increases with Reynolds number R and with the volume ratio η. High pressures are generated at a stagnation point leading to wave steepening, while low pressures are generated at a reattachment point. The computed wave shapes and frictional losses are in satisfactory agreement with experiments and greatly improve on previous results.

Stochastic Lagrangian models of velocity in homogeneous turbulent shear flow

Stochastic Lagrangian models for the velocity following a fluid particle are used both in studies of turbulent dispersion and in probability density function (PDF) modeling of turbulent flows. A general linear model is examined for the important case of homogeneous turbulent shear flow, for which there are recent direct numerical simulation (DNS) data on Lagrangian statistics. The model is defined by a drift coefficient tensor and a diffusion tensor, and it is shown that these are uniquely determined by the normalized Reynolds-stress and timescale tensors determined from DNS. With the coefficients thus determined, the model yields autocorrelation functions in good agreement with the DNS data. It is found that the diffusion tensor is significantly anisotropic—contrary to the Kolmogorov hypotheses and conventional modeling—which may be a low-Reynolds-number effect. The performance of two PDF models is also compared to the DNS data. These are the simplified Lagrangian model and the Lagrangian isotropization of production model. There are significant differences between the autocorrelation functions generated by these models and the DNS data.

An experimentally based approach for the space-averaged laminar burning velocity used for modeling premixed turbulent combustion

Turbulent flame front propagation of methane/, ethane/, and propane/ air mixtures has been investigatedover a wide range of equivalence ratios inside a closed cylindrical vessel. Pressure/time relationships were recorded by a piezoelectric pressure transducer, in order to evaluate turbulent burning velocities using a thermodynamic model. To generate different scales of turbulence, two fans with variable speed of rotation were positioned within the explosion vessel. Turbulent flow velocities were measured under isothermal conditions by a forward scattering laser Doppler anemometry system, while integral length scale data were obtained calculating the cross-correlation function of the signals of two hot-wire probes positioned at variable distances from each other. Turbulent explosion experiments exhibit a strong influence of preferential diffusion/stretch interactionson the turbulent burning velocity. These effects cause a stronger increase in the turbulent burning velocity for lean methane/air mixtures than for rich ones and, in the opposite sense, for ethane/ and propane/air mixtures. Based on the flamelet assumption, an equation was derived to allow for flame straining reduction in the space-averaged laminar burning velocity S L,T . Starting from a theoretical model which is based on the superposition of characteristic timescales, a new combustion model was developed which takes into account preferential diffusion/stretch effects on the turbulent burning velocity. With the assumption that the space-averaged laminar burning velocity is approximately independent of turbulence parameters, comparison of experimentally determined turbulent burning velocities with those determined from the model shows satisfactory agreement. With mixtures characterized by high positive Markstein numbers, quenching phenomena could be observed at high turbulence intensities. In this regime, the reaction model used is no longer valid. A criterion based on the Karlovitz number was derived which was proven to be in close agreement with quenching limits from previous research.

Distribution of Gas Flow Parameters in Mass Transfer Columns with Regularly Spaced Shelves

Laminar and turbulent flows in channels with regularly spaced shelves symmetrically separated with an axial grid are numerically modeled using stream function–vortex strength Navier–Stokes equations. Flow velocity distribution in the initial and steady state regions is derived for laminar flow. Basic dynamic parameters of turbulent flow (velocity profiles, stream-function isolines, vortex strength, turbulent kinetic energy, turbulence scale, and effective viscosity) are calculated using the K–e model and the Kolmogorov–Prandtl closure. Stagnant and circulation zones form in both zigzag channels and channels with horizontal shelves, suggesting that the relevant computational algorithms and programs can be unified.

Characteristics of turbulent spray combustion in a piloted jet flame burner

A laboratory burner has been developed for turbulent combustion of a spray jet, with special emphasis on case of modeling. The flow field is fluid mechanically well understood, so that the focus can be on evaporation and other aspects of turbulence/droplet interaction. Droplet size, volume flux, and two-component velocities are measured at several axial locations downstream of the burner exit with the phase-Doppler anemometry technique. The gas flow velocity profiles of the spray flames investigated here are similar to those of conventional premixed jet flames. This is attributed mainly to the use of air as the spray carrier. There is clear evidence that droplets greater than 30 μ m do not follow the turbulent flow velocity fluctuations. Between a high- and a low-speed spray flame, self-similarity on the domain of the flight time is observed in droplet mean diameters and the droplet number density. The effect of turbulence on local droplet evaporation is found to be negligible.

Electrochemical machining of the steel 100Cr6 in aqueous NaCl and NaNO 3 solutions: microstructure of surface films formed by carbides

Application of electrochemical machining in microsystem technologies has to take into account the role of microscopic heterogeneities of steel, e.g. of carbides. Therefore, the anodic metal dissolution of the alloyed carbon steel 100Cr6 was investigated in NaCl and NaNO 3 electrolytes. In flow channel experiments, high current densities up to 70 A/cm 2 and turbulent electrolyte flow velocities were applied. Insoluble carbide particles cause an apparent current efficiency >100% in NaCl and >67% in NaNO 3. These particles are enriched at the surface in NaCl solution and detected by ex situ scanning electron microscopy and energy dispersive X-ray experiments. Auger electron spectroscopy, in combination with sputter depth profiling, was used to determine the film composition resulting from the NaNO 3 process. This proves the enrichment of carbide particles not yet separated from the surrounding steel. Qualitative metal dissolution models on the basis of the experimental results were proposed for the metal dissolution processes in the NaCl and NaNO 3 electrolytes.

DNS of Turbulent Heat Transfer in Channel Flow With Heat Conduction in the Solid Wall

The Direct Numerical Simulation (DNS) of the fully developed velocity and temperature fields in the two-dimensional turbulent channel flow coupled with the unsteady conduction in the heated walls was carried out. Simulations were performed at constant friction Reynolds number 150 and Prandtl numbers between 0.71 and 7 considering the fluid temperature as a passive scalar. The obtained statistical quantities like root-mean-square temperature fluctuations and turbulent heat fluxes were verified with existing DNS studies obtained with ideal thermal boundary conditions. Results of the present study were compared to the findings of Polyakov (1974), who made a similar study with linearization of the fluid equations in the viscous sublayer that allowed analytical approach and results of Kasagi et al. (1989), who performed similar calculation with deterministic near-wall turbulence model and numerical approach. The present DNS results pointed to the main weakness of the previous studies, which underestimated the values of the wall temperature fluctuations for the limiting cases of the ideal-isoflux boundary conditions. With the results of the present DNS it can be decided, which behavior has to be expected in a real fluid-solid system and which one of the limiting boundary conditions is valid for calculation, or whether more expensive conjugate heat transfer calculation is required.

On the pseudomomentum and generalized Stokes drift in a spectrum of rotational waves

Two Lagrangian-mean measures crucial to the accurate estimation of mean particle velocities in wavy or turbulent shear flows are considered. The measures are the pseudomomentum and generalized Stokes drift and of particular interest is their expression in terms of quantities directly measurable by fixed instruments. To proceed, the measures are first calculated for broad spectra of progressive symmetric rotational wave pairs of small amplitude. Both discrete and continuous spectra are considered and the waves may grow or decay. The expressions are then cast into a form composed of quantities that are measurable in a fixed reference frame, such as the surface slope spectrum of surface gravity waves or space–time velocity correlations in the interior of wavy shear flows. Finally, an example is given in which the measures are calculated for a plane channel flow subject to a broad spectrum of discrete progressive waves, specifically a numerical simulation of turbulent channel flow. It is seen that while the streamwise component of pseudomomentum is everywhere negative in the flow, the generalized Stokes drift changes sign, giving rise to an enhanced mass transport close to the boundary and a reduction in transport some distance from it. The sign change occurs 12.5 viscous units from the wall, near the centre of a 15 viscous units thick highly sheared layer of Stokes drift.

Simultaneous measurement of velocity and temperature in high-temperature turbulent flows: a combination of LDV and a three-wire temperature probe

This paper deals with a simple and reliable technique for simultaneous measurement of velocity and temperature in high-temperature turbulent flows, including combustion. The technique is based on the combination of laser Doppler velocimetry and a digitally compensated fine-wire thermocouple. For temperature measurement, a two-thermocouple probe with a fine cold wire [Tagawa et al. (1998) Rev Sci Instrum 69: 3370–3378] is used, which enables in situ measurement of thermocouple time constants and accurate compensation of the thermocouple response. When tested in a turbulent wake behind a heated cylinder, the technique proves to be highly reliable and effective for investigating heat transport processes in various non-isothermal turbulent flows.

Discrete wavelets auto-correlation of axial turbulence velocity in spiral single phase flow

Time–frequency distributions of axial turbulence velocities of spiral pipe flow and typical turbulent flow have been clearly decomposed in a range from low frequency level (low wavenumber) to high frequency level (high wavenumber) by means of discrete wavelets transform and its auto-correlation. As a result, fluctuation levels of spiral flow are extremely low as compared with those of typical turbulent flow. Moreover, spiral flow has a time periodicity on wavelets Level 3 at a central point and on Levels 1 and 2 near wall of a pipeline. However, typical turbulent flow does not have the tendency. Spiral flow has an orderly radial velocity, which contributes to the lower fluctuation level and the time periodicity at the central point. The mean velocity of the air flow in the vertical pipe was 1.50 m/s, and Reynolds number was about 4200. The originality of this paper lies in applying discrete wavelets transform and its auto-correlation to analyzing the stable spiral flow motion in time–frequency dimension.

A mixing layer in a homogeneous fluid

A mathematical model for the evolution of a mixing layer in shear flows is constructed. The problem of a mixing layer with pressure gradient is solved: in particular, the distributions of the velocity and basic characteristics of turbulent flow in the mixing layer are obtained.

Statistical modelling of mass transfer in turbulent two-phase dispersed flows — 1. Model development

A closed equation for probability density function (PDF) of particles coordinates and velocities in a nonhomogeneous turbulent flow is obtained. On the base of the equation for PDF, a closed system of balance equations for concentration, momentum and energy of a chaotic motion of dispersed phase in Eulerian variables is derived. For the system of balance equations boundary conditions, describing particles interaction with a surface in a two-phase flow are found.

A statistical model of particle transport and heat transfer in turbulent shear flows

The objective of the paper is to present a statistical model for predicting particle transport and heat transfer in two-phase quasi-homogeneous turbulent shear flows. This statistical model is based on a kinetic equation for the probability density function of the particle velocity and temperature distributions in nonuniform turbulent flows. The model developed is applied to predict the fluctuating particle motion in both homogeneous and near-wall turbulent shear flows.

Simultaneous Measurement of Velocity and Temperature in High-Temperature Turbulent Flows.

This paper deals with a simple and reliable technique for simultaneous measurement of velocity and temperature in high-temperature turbulent flows, including combustion. The technique is based on the combination of laser Doppler velocimetry (LDV) and a digitally compensated fine-wire thermocouple. A central issue of this study is to find the applicability and reliability of the technique proposed. For this purpose, a two-thermocouple probe with a fine cold wire (Tagawa, Shimoji and Ohta, 1998), which enables in situ measurement of thermocouple time constants and accurate compensation of the thermocouple response, is combined with LDV. The technique is tested in a turbulent wake behind a heated cylinder, whose thermal field is of ordinary temperature and fluctuates with relatively small amplitude. This enables critical assessment of the measurement accuracy. The results show that the technique is highly reliable and effective for investigating heat transport processes in various non-isothermal turbulent flows.

تأثير الجهد المنبعث من قطع تركيب الأنابيب على توزيع قطرات مزيج من الماء و البترول في حالة تدفق مضطرب

Drop size distribution data for kerosene-water dispersion were obtained in 1."I.D. pipe at a range of velocities in turbulent flow for a straight horizontal pipe. U shaped pipe and an offset pipe fitting oriented horizontally and vertically (upward and downward) to the main flow. A Lightnin in line static mixer was used as a premixer and the drop size distribution was measured by a Malvern 2600 analyzer. By changing the number of internal elements from 4 to 18 the mixer produced a primary dispersion with the mean drop sizes in the range of 50-700 um for the flow rates of 20 to 84 l/minute. The Sauter mean diameter, d32, was found to decrease as the number of elements was increased until an equilibrium drop size was reached. This equilibrium drop size varied with the fluid velocity through the mixer. For a dispersion of ~0.5% kerosene in water, the correlation of drop site with energy dissipation rate, e, was found to give a reasonable agreement with Kolmogoroff’s theory with an exponent in the range of -0.47 to -0.56 for a horizontal pipe and -0.60 to -0.72 for U-shaped and offset pipe fittings. The Sauter mean diameter was also correlated against Weber number with an exponent in the range of -0.71 to -0.83 for all the linings used.

Intrinsic kinetics of biofilms formed under turbulent flow and low substrate concentrations

Reactor operating conditions strongly affect the behaviour of biofilm systems, namely their stability and the substrate removal. In this paper, the penetration of substrate and the activity of biofilms formed by Pseudomonas fluorescens under turbulent flow and low substrate concentrations, are studied. A first order diffusion-reaction model was applied to results of biofilm accumulation in steady and non-steady-state. The substrate consumption rate of the biofilm was calculated based on the on-line determination of the biofilm accumulated on the surface. This approach is important when the residence time or the substrate concentration on the reactor is very low. Also, the mass transfer of substrate inside the biofilm was measured for every case under study and introduced in the model. The fraction of biofilm penetrated by the substrate depends on the velocity of the fluid that contacts the biological matrix: contrary to biofilms formed at higher velocities, lower velocities give raise to non completely penetrated biofilms. This fact seems to be associated to the biofilm internal structure in terms of biomass density and compactness of the matrix. They remove more substrate per reactor volume, but are less resistant from an hydrodynamic point of view. In conclusion, biofilms formed at higher velocities in turbulent flow allow a more stable reactor operation.