Turbulent time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y ₉₀. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.     

Comparison of length scale estimates for a sudden expansion flow estimated from spatial and auto correlation LDV measurements

Two-point velocity correlation measurements were made in the anisotropic flow field of an axisymmetric sudden expansion using two single component LDV systems. The integral length scales and Taylor microscales were estimated and compared with those obtained from auto correlation measurements in conjunction with Taylor's hypothesis. The agreement of the integral scales was within 20% and the values scale well with the flow geometry, while the agreement of the microscales was within 43%.     

An LDV system for turbulence length scale measurements

An LDV system for making spatial correlation measurements of velocity fluctuations in turbulent nonreacting and reacting flows is presented. The LDV system is the dual beam type and consists of an elongated probe volume and a two-point optical fiber detector. Results are presented of the integral length scale measured in a nonreacting grid generated turbulent flow.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD, Vol. 66     

Effects of time scales on velocity bias in LDA measurements using sample and hold processing

Sample and hold processors may be used to avoid velocity bias errors in laser Doppler anemometer (LDA) measurements if the ratio of flow to measurement time scale is sufficiently high, typically greater than 5. It has been widely assumed that the flow time scale refers to the Taylor time microscale. This paper shows with experimental verification that the appropriate flow time scale is, in fact, the integral time scale of the flow. Furthermore, it shows that if velocity bias exists with a sample and hold processor, it can in many cases be predicted. It has been shown elsewhere that the integral time scale is also the relevant one for the prediction of velocity bias of a controlled processor.     

Combined CARS/LDA instrument for simultaneous temperature and velocity measurements

The performance of a combined CARS/LDA instrument capable of measuring temperature and two velocity components with a time coincidence of about 4 s is evaluated in a turbulent premixed propane-air Bunsen-burner flame. Measurements near the base of the flame exhibit negative axial correlations, indicative of normal gradient transport; those near the flame tip show strong positive axial correlations, indicative of transport counter to the temperature gradient. The radial correlations are positive both in the reaction zone and in the plume. An analysis of temperature data from measurements made (1) independent of and (2) coincidental with LDA measurements indicates that the CARS/LDA instrument provides a density-weighted velocity, temperature, and velocity temperature correlation due to the density variations in the flame.     

LDA measurements of steady streaming flows of Newtonian and viscoelastic fluids

LDA experiments have been conducted in a two-dimensional steady streaming flow field in order to determine the secondary velocity profiles. We describe here an LDA system developed to resolve small secondary-flow velocities and to detect flow reversals due to viscoelasticity. Results compare well with theoretical predictions. A detailed analysis of the errors and uncertainties involved in the measurements confirms the reliability and reproducibility of the measurements. Although the method has been applied here to a specific flow field, the technique should be applicable to a number of secondary flows, such as those which can occur in curved pipes and in oscillating pipe flows.The authors have benefited from discussions with Professor Bruce Chehroudi, from the Department of Mechanical Engineering, University of Illinois at Chicago. This work was supported by the Office of Naval Research through Contract Number N00015-85-K-0201.     

Slip velocity measurements in an upward bubbly flow by combined LDA and electrodiffusional techniques

 An experimental technique for the measurement of the local slip velocity of spherical bubbles is reported. It is based on the measurement of the local liquid velocity by an electrodiffusional method, and the bubble velocity by a specially adapted LDA (Laser Doppler anemometer) with a short measuring volume. The bubble velocity is measured taking into account the shift between the bubble centre and the centre of the LDA measuring volume. The slip velocity is obtained by subtracting the liquid velocity from the bubble velocity at the point corresponding to the bubble centre. The technique is applicable for flows with high velocity gradients. Results of the slip velocity measurements in an upward bubbly flow at laminar pipe Reynolds numbers are presented. Received: 25 July 1996/Accepted: 13 April 1998     

LDA/PDA measurements of instantaneous characteristics in high pressure fuel injection and swirl spray

 Transient dynamics of two injection flows, upstream and downstream a swirl injector, are investigated. Capillary n-heptane pipe flow is measured using laser Doppler anemometer to obtain instantaneous time series of centerline velocity and to reconstruct series of instantaneous and integrated flow rates and pressure gradient. A collimated laser sheet and a high-speed video camera visualize injected spray flow. Finally, the phase Doppler anemometer measurements are introduced to analyze instantaneous patterns of droplets velocity-size and number density into fuel spray. All measurements are employed at similar temporal resolution close to 30 μs. Results indicate that both flows are strongly time-dependent and well correlated in time-phases. Initial transitions are completed by 100 μs. Opening or closing of the injector valve affects both flows as strong delta oscillation causes spray penetration dynamics and a post injection effect. A combination of intrusive laser-based techniques allows indication of the basic injection and spraying characteristics need to optimize high-pressure fuel injectors and combustion late injection mode at a high speed. Received: 19 December 1998/Accepted: 13 August 1998     

A method for reconstruction of residual stress fields from measurements made in an incompatible region

A method is introduced by which the complete state of residual stress in an elastic body may be inferred from a limited set of experimental measurements. Two techniques for carrying out this reconstruction using finite element analysis are compared and it is shown that for exact reconstruction of the stress field via this method, the stress field must be measured over all eigenstrain-containing regions of the object. The effects of error and incompleteness in the measured part of the stress field on the subsequent analysis are investigated in a series of numerical experiments using synthetic measurement data based on the NeT TG1 round-robin weld specimen. It is hence shown that accurate residual stress field reconstruction is possible using measurement data of a quality achievable using current experimental techniques.     

Simultaneous temperature and 2D velocity measurements in a turbulent heated jet using combined laser-induced fluorescence and LDA

 This paper presents an efficient technique for the characterization of thermal transport properties in turbulent flows. The method is based on the temperature dependence of fluorescence, induced by laser radiation, of an organic dye. The laser-induced fluorescence technique is combined with 2D laser Doppler anemometry, in order to measure in the same sample volume simultaneously and instantaneously the temperature and velocity. The technique is demonstrated on a turbulent heated round jet: the mean and fluctuating dynamic and thermal fields are investigated, and the temperature-velocity cross-correlations are determined in order to characterize the turbulent diffusivity and the turbulent Prandtl number. Received: 30 October 1997/Accepted: 14 July 1998     

Error estimates for Rayleigh scattering density and temperature measurements in premixed flames

Rayleigh scattering has become an accepted technique for the determination of total number density during the combustion process. The interpretation of the ratio of total Rayleigh scattering signal as a ratio of densities or temperatures is hampered by the changing composition through a flame, since the average Rayleigh scattering cross-section depends on the gas composition. Typical correction factors as a function of degree of reaction, fuel and equivalence ratio were calculated. The fuels considered were H₂, CH₄, C₂H₄, C₂H₆ and C₃H₈. Factors as low as 0.7 and 0.56 were found for the heaviest hydrocarbon fuel at large equivalence ratio for interpreting the Rayleigh scattering intensity as gas density and inverse temperature, respectively. This is primarily due to the presence of CO and H₂ as intermediates. As CO and H₂ are subsequently oxidized to CO₂ and H₂O, these factors approach 1.0. Conversely, the worst case, when using H₂ as a fuel, occurs in the post flame zone. However, the correction factors for H₂ are near 1.0 and the errors involved will, in general, remain within the expected experimental accuracy of a typical Rayleigh scattering system. Linear correlations of correction factors with equivalene ratio and with the product of equivalence ratio and fuel molecular weight were found and presented. The interpretation of Rayleigh scattering as temperature was found to have larger errors than the interpretation as density. Corrections for changes in gas composition were applied to Rayleigh scattering temperature measurements in the post flame region of CH₄ and C₃H₈ flames with equivalence ratios of 0.75 and 1.0. The corrected temperatures were in excellent agreement with thermocouple measurements.List of symbols A ₁, A ₂ correlation coefficients - B ₁, B ₂ correlation coefficients - C ₁, C ₂ correlation coefficients - D ₁, D ₂ correlation coefficients - C calibration constant for Rayleigh scattering optics - H total enthalpy - Î I _R /I _RO - I _i incident laser intensity - I _R Rayleigh scattering intensity - I _R0 Rayleigh scattering intensity at reference condition - N total number density of gas - N ₀ total number density of gas at reference condition - n _i index of refraction of species i - – T/T _O - T temperature - T _a adiabatic flame temperature - T ₀ reference temperature - t time - W/W ₀ - W mean molecular weight - W ₀ mean molecular weight at reference condition - W _ij rate of production of species i by reaction j - X _i mole fraction of species i - degree of reaction (T – T ₀)/(T _a – T ₀) - laser wavelength - ₀ Loschmidt number - /₀ - density - ₀ density at reference condition - dimensionless mean Rayleigh scattering cross-section - _Ri Rayleigh scattering cross-section of species i - scattering angle measured from the electromagnetic field vector - equivalence ratio     

Determinations of both length scale and surface elastic parameters for fcc metals

In the present research, a systematical study of trans-scale mechanics theory is performed. The surface/interface energy density varying with material deformation is considered, and the general surface/interface elastic constitutive equations are derived. New methods to determine the material length scale parameter and the surface elastic parameters based on a simple quasi-continuum method, i.e. the Cauchy–Born rule, are developed and applied to typical fcc metals. In the present research, the material length parameters will be determined through an equivalent condition of the strain energy density calculated by adopting the strain gradient theory and by adopting the Cauchy–Born rule, respectively. Based on the surface constitutive equations obtained in the present research, the surface elastic parameters are calculated by using the Gibbs definition of surface energy density and the Cauchy–Born rule method.     

Equivalent particle diameter and length scale for pressure drop in porous metals

The internal architecture of metal foam is significantly different from that of traditional porous media. This provides a set of challenges for understanding the fluid flow in this relatively new class of materials. This paper proposes that despite the geometrical differences between metal foam and traditional porous media, the Ergun correlation is a good fit for the linear pressure drop as a function of the Darcian velocity, provided that an appropriate equivalent particle diameter is used. The paper investigates an appropriate particle diameter considering the physics of energy dissipation, i.e. the viscous shear and the form drag. The above approach is supported by wind tunnel steady-state unidirectional pressure drop measurements for airflow through several isotropic open-cell aluminum foam samples having different porosities and pore densities. For each foam sample, the equivalent particle diameter correlated well with the surface area per unit volume of the foam. This was also very well valid for previous porous metal pressure drop data in the open literature.     

Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments

The enhanced gradient plasticity theories formulate a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical plasticity and the classical continuum plasticity. They are successful in explaining the size effects encountered in many micro- and nano-advanced technologies due to the incorporation of an intrinsic material length parameter into the constitutive modeling. However, the full utility of the gradient-type theories hinges on one's ability to determine the intrinsic material length that scales with strain gradients, and this study aims at addressing and remedying this situation. Based on the Taylor's hardening law, a micromechanical model that assesses a nonlinear coupling between the statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) is used here in order to derive an analytical form for the deformation-gradient-related intrinsic length-scale parameter in terms of measurable microstructural physical parameters. This work also presents a method for identifying the length-scale parameter from micro- and nano-indentation experiments using both spherical and pyramidal indenters. The deviation of the Nix and Gao [Mech. Phys. Solids 46 (1998) 411] and Swadener et al. [J. Mech. Phys. Solids 50 (2002) 681; Scr. Mater. 47 (2002) 343] indentation size effect (ISE) models’ predictions from hardness results at small depths for the case of conical indenters and at small diameters for the case of spherical indenters, respectively, is largely corrected by incorporating an interaction coefficient that compensates for the proper coupling between the SSDs and GNDs during indentation. Experimental results are also presented which show that the ISE for pyramidal and spherical indenters can be correlated successfully by using the proposed model.     

Separating viscoelasticity and poroelasticity of gels with diferent length and time scales简

Viscoelasticity and poroelasticity commonly coexist as time-dependent behaviors in polymer gels. Engineering applications often require knowledge of both behaviors separated; however, few methods exist to decouple viscoelastic and poroelastic properties of gels. We propose a method capable of separating viscoelasticity and poroelasticity of gels in various mechanical tests. The viscoelastic char- acteristic time and the poroelastic diffusivity of a gel define an intrinsic material length scale of the gel. The experimen- tal setup gives a sample length scale, over which the solvent migrates in the gel. By setting the sample length to be much larger or smaller than the material length, the viscoelasticity and poroelasticity of the gel will dominate at different time scales in a test. Therefore, the viscoelastic and poroelastic properties of the gel can be probed separately at different time scales of the test. We further validate the method by finite-element models and stress-relaxation experiments.     

Separating viscoelasticity and poroelasticity of gels with diferent length and time scales

Viscoelasticity and poroelasticity commonly coexist as time-dependent behaviors in polymer gels.Engineering applications often require knowledge of both behaviors separated;however,few methods exist to decouple viscoelastic and poroelastic properties of gels.We propose a method capable of separating viscoelasticity and poroelasticity of gels in various mechanical tests.The viscoelastic characteristic time and the poroelastic difusivity of a gel define an intrinsic material length scale of the gel.The experimental setup gives a sample length scale,over which the solvent migrates in the gel.By setting the sample length to be much larger or smaller than the material length,the viscoelasticity and poroelasticity of the gel will dominate at diferent time scales in a test.Therefore,the viscoelastic and poroelastic properties of the gel can be probed separately at diferent time scales of the test.We further validate the method by finite-element models and stress-relaxation experiments.     

Auto-correlation measurements and integral time scales in three-dimensional turbulent boundary layers

Auto-correlation, time and length scales of the three components of turbulence and power spectra in a three-dimensional turbulent boundary layer developing on a yawed flat plate have been obtained. The measurements indicate that close to the wall, in the region of turbulence production, there is a marked disparity among the time scales but as the outer edge of the boundary layer is approached, the scales become comparable to one another. Also, the behaviour of the length scales and the power spectra across the boundary layer is presented.Nomenclature Boundary layer thickness where Q/Q _e=0.995 - E _u(f) one dimensional frequency spectra - f frequency in Hz - k ₁ wave number defined as k ₁=2f/Q - L length scale defined as: time scale times local mean velocity - Q local mean velocity - Q _e free stream velocity - R _u, R _v, R _w Auto-correlation coefficients of u, v and w respectively as defined in equation (1) - T _u, T _v, T _w the time scales of u, v and w fluctuations as defined in equation (2) - delay time - u fluctuating velocity component in x-direction - v fluctuation velocity component in y-direction - w fluctuation velocity component in z-direction - x coordinate axis in the streamwise direction - y coordinate axis normal to the surface - z coordinate axis normal to the x-direction and parallel to the wall     

Assessment of the SST-IDDES with a shear-layer-adapted subgrid length scale for attached and separated flows

A shear-layer-adapted subgrid length scale is applied to the improved delayed detached eddy simulation using the shear stress transport background model (SST-IDDES). The aim is to assess the combination of the wall-modeled LES (WMLES) branch of the SST-IDDES with the new length scale in computing attached flows, as well as to assess the effect of the new length scale when it is applied to the SST-IDDES for mitigating the “grey area” issue through initiating a dramatic drop of eddy viscosity in the initial region of a free shear layer. The assessment is conducted through simulations of a turbulent boundary layer, a fully developed channel flow, a near-sonic turbulent jet and a backward-facing step flow. The results provide strong evidence for the conclusion that the SST-IDDES combined with the new length scale performs the same as the original SST-IDDES when its WMLES branch is applied to compute the resolved parts of an attached flow, and the combination helps mitigate the “grey area” issue of the SST-IDDES and accurately represent the K-H instability in the initial region of a free shear layer. In addition, the superiority is particularly remarkable for the simulations with coarse grids.     

Investigation of fine scale structure of turbulent and molecular diffusion in coaxial jets of He/CO2 in air by LDA and Rayleigh scattering

This paper revisits the important issue of differential diffusion and provides new experimental results and subsequent analysis that attempts to quantify the relationship between molecular diffusion, turbulent diffusion and their mutual interference in non-reacting axisymmetric coaxial jets of variable Reynolds number. The reported investigation has been focused on the analysis of molecular diffusion of a He/CO₂ mixture in air by combining line imaging of Rayleigh scattering and laser Doppler anemometry (LDA) to determine length scales associated with differential diffusion and turbulent transport. Line imaging Rayleigh scattering was performed applying the index-matching method with a mixture of two gaseous species having scattering cross-sections respectively lower and higher of that of air and the cross-section of the mixture identical to that of the co-flowing air. Any measured variation in scattering intensity is therefore due to differential diffusion between the two species. Instantaneous and ensemble averaged line profiles of Rayleigh scattering intensity are presented and a characteristic length scale associated with differential diffusion is deduced. Autocorrelation analysis is applied to obtain the characteristic scale of differential diffusion fluctuations and the integral length scales of velocity fluctuations, as measured by LDA. Theoretical information from the literature is used in relating these scales to the molecular and turbulent diffusion coefficients, assuming homogeneous and isotropic turbulence, and the ratio of molecular to turbulent diffusivity is estimated as a function of the Reynolds number. The results confirm that the average contribution of molecular diffusion to the effective diffusivity into the air stream progressively reduces when the turbulence level increases. They also suggest that, at higher Re, the differential diffusion remains significant down to the scalar dissipation length scale, and could influence mixing at the molecular level and thus chemical reactions.