Three-segment electrodiffusion probes for measuring velocity fields close to a wall

Three-segment electrodiffusion probes embedded in a wall allow to determine simultaneously the three kinematic parameters of flow close to the probe surface: the flow direction, the wall shear rateq, and the normal velocity coefficientA,v _z = –A z ². A well-controlled three-dimensional flow, generated by a rotating disk, was used to demonstrate the capabilities of this new kind of electrodiffusion probes by comparing experimental results with the prediction based on the well-known hydrodynamical theory.List of symbols A normal flow coefficient, Eq. (1) - A axis of the adjustment rod, Fig. 2 - c ₀ concentration of depolarizer (mol/m³) - D diffusivity of depolarizer (m²/s) - E correction of total current on normal flow effect - e _x reference direction of the probe, Figs. 1 and 3 - F Faraday constant (F = 96,464 C/mol) - F _s normalized directional characteristic fors-th segment - f _sm ,g _sm Fourier coefficients of directional characteristics, Eq. (4) and Table 3 - h _m corrections of Fourier coefficients on normal flow effect, Eqs. (4) and (7) - i _s limiting diffusion current throughs-th segment (A) - i _tot (r) total current through the probe in dependence on its eccentricity (A) - K transport coefficient, Eqs. (3) and (5) - n number of electrons involved in redox reaction - O axis of the rotating disk, Fig. 2 - P centre of the probe, Fig. 2 - q magnitude of vectorial wall shear rate (s^-1) - q _x ,q _y components of vectorial wall shear rate - Q ratio of the currents in an eccentric and the central position of the probe, Eq. (15) - r radial coordinate, eccentricity of the probe - r _A eccentricity of the adjustment rod (r _A = , Fig. 2) - r, , z polar coordinates on the rotating disk - R effective radius of the probe (R = 0.337 mm) - S macroscopic area of the probe (S = 0.357 mm²) - x, y, z Cartesian coordinates moving with the probe - adjustment angle, Figs. 2 and 3 - angle included between local radius-vector ¯P of the probe and local direction of flow, Fig. 3 - angle included between reference directione _x of the probe and local direction of flow, Fig. 3 - ₀ theoretical prediction of, Eq. (11) - x ₀ theoretical prediction ofx, Eq. (14) - x _exp x calculated from experimental data using Eq. (4) - v kinematic viscosity (m²/s) - angle implied between gradient ofq and direction of flow, Eq. (8) - angular speed of the rotating disk (rad/s)     

Sensitivity computations of eddy viscosity models with an application in drag computation

This paper presents a numerical study of the sensitivity of an eddy viscosity model with respect to the variation of the eddy viscosity parameter for the two‐dimensional driven cavity problem and flow around a cylinder. The main objective is to provide a comparison between computing the sensitivity using sensitivity equation and computing the sensitivity using finite difference methods and also numerically illustrate the application of the sensitivity computations in improving drag flow functional. Copyright © 2006 John Wiley & Sons, Ltd.     

Mathematical model of the effect of electrodiffusion on biomineralization

Biofilm-induced mineral precipitation is a fundamentally important phenomenon with many potential applications including carbon sequestration and bioremediation. Based on a mixture model consisting of three phases (calcite, biofilm, and solvent) and also accounting for chemistry, mechanics, thermodynamics, fluid, and electrodiffusive transport effects, we describe the self-induced generation of an electric field due to different diffusivities of different ion species and study the effects of this field on ionic transport and calcite precipitation. Numerical simulations suggest that one of these effects is enhanced precipitation.     

Experimental investigation of horizontal two-phase flow by an electrodiffusion method

The results of an experimental investigation of the local mean and fluctuating friction at the wall of a horizontal tube are presented for the case where a gas-liquid stream flows in the tube with a wide range of regime parameters. The electrodiffusion method is used for measuring the friction. Curves of the tangential stresses along the perimeter of the tube as well as along its length are constructed, permitting an objective determination of certain flow regimes. The experimental results are compared with those of the existing computational methods.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 101–108, March–April, 1973.     

The capability of large eddy simulation to predict relaminarization

The boundary layer which represents the narrow zone between a solid body and the free stream can have a laminar or a turbulent state. This state influences on the one hand the properties of the near-wall flow like skin friction or heat transfer and on the other hand also the free-stream flow itself, e.g. the downstream flow angle of a turbomachinery blade. Thus it is important for designers of fluid machinery to understand and predict the state of the boundary layer as well as the transition processes between the two states.In this work the so-called relaminarization is investigated which represents a reverse transition from a turbulent to a laminar boundary layer. At the Institute for Thermal Turbomachinery and Machine Dynamics at Graz University of Technology a test bench has been designed in order to produce a highly accelerated flow, thus triggering relaminarization. In the present work, the flow in this test bench is numerically investigated with Reynolds-averaged Navier-Stokes (RANS) flow simulation as well as with a large eddy simulation (LES).An outcome of this paper is, that the LES shows a very good agreement to the measurement results and is capable of predicting relaminarization.     

Theory of electrodiffusion measurements of friction in microdispersed liquids. Diffusion layer approximation

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 123–126, July–August, 1991.     

Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.     

Sensitivity of Stokes flow to geometry

An experimental investigation of low Reynolds number flow in a rotating tank indicates that in some cases closed eddies in Stokes flow are very sensitive to geometry, especially if the eddies are slender. It is not known if such flows are merely extremely sensitive to the bounding geometry, or if they are actually geometrically unstable.     

Application of ultrasonic velocity profile meter to vortex shedding and empirical eigenfunctional analysis

 The vortex shedding behind a cylinder in a fully developed pipe flow is investigated by applying new measurement and data-analysis techniques. An ultrasound anemometry technique, providing the multipoint information of the flow, is employed. The measured instantaneous velocity fluctuations are decomposed by the empirical eigenfunctional analysis known as the proper orthogonal decomposition. The predominant modes of fluid motions are well identified by this technique, and their time–frequency features are discussed. Received: 11 April 2000/Accepted: 20 March 2001     

Coupling of vortex shedding with a cavity

A pulsating flow within a tube with one end sealed and the other end open, facing a low-velocity wind tunnel flow, may be generated by using a wedge trip placed upstream of the open end of the tube. However, a reasonable explanation about the generating mechanism of the pulsating flow within the resonator coupled with a tripping device has not been given yet.

In order to get a better understanding of the coupling of the flow around the wedge trip and the flow oscillation within the resonator, the interaction between the wedge wake and the pulsating flow has been experimentally investigated by means of the hydraulic analogy. The results of flow visualization with shadow-graph technique have provided a good understanding of the coupling phenomena of vortex shedding on the wedge with the flow at the resonator mouth.     

壁湍流相干结构的教学实验(六)--湍流测量中X形热膜探针的标定

为了进行湍流度二分量的实验测量，介绍了标定Ｘ形热膜探针的全速度－偏航角方法的细节。     

Sensitivity of the shear gage to normal strains

This paper documents an experimental study that was conducted to demonstrate the sensitivity of the shear gage to the presence of normal strains. The shear gage is a specially designed strain gage rosette that measures the average shear strain in the test section of notched specimens such as the losipescu, Arcan and compact shear specimens. These specimens can have complicated stress states with high shear and normal strain gradients. To evaluate the sensitivity of the shear gage to normal strains, shear gages were tested on an Arcan specimen. The Arcan specimen is a notched specimen that can be loaded in pure shear (90 deg), pure tension (0 deg) and at intermediate 15- deg increments. The shear modulus for an aluminum specimen was determined at each of these loading angles. It was found that the gages display nearly zero sensitivity to normal strains ( _x, _y). Moiré interferometry was used to document the shear and normal strain distributions in the test section and to provide an independent method for determining the average shear strain. These results reinforce the robust nature of testing with the shear gage.     

Extension of the local domain-free discretization method to large eddy simulation of turbulent flows

In this work, an immersed boundary method, called the local domain-free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near-wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES-DFD method. The predicted results agree well with the published experimental or numerical data.     

The eddy viscosity of turbulent equilibrium layers

Summary Similarity laws for the mean flow and scaling laws for the turbulent motion are used in an attempt to obtain a general expression for the eddy viscosity of equilibrium layers. It is found that =0.09 w ² /w*, in which w ² is a Reynolds stress representative for the region of overlap between the law of the wall and the velocity-defect law, while w* is the logarithmic slope of the mean velocity profile in that region. The distinction between w and w* is related to the strong inhomogeneity of the mean rate of strain in the inner layer. The results of the theory agree with experimental evidence obtained from transpired equilibrium layers.     

Boundary-Layer Approach to Shape Design Sensitivity Analysis

ABSTRACT

In a domain approach to shape design sensitivity analysis, shape design sensitivity is calculated by summing contributions from the entire domain. For mechanical systems with general geometries, defining design velocity field over the entire domain can be very complicated. A design boundary-layer is introduced to minimize difficulties associated with the domain approach. The design boundary-layer is a pre-selected part of the domain, near the varying boundary. A nonzero design velocity field is defined over only the design boundary-layer. The boundary-layer approach is shown to be easier to apply and more efficient to use than conventional full domain methods.     

Large eddy simulation of compressible channel flow

Astract The present study is a contribution to the analysis of wall-bounded compressible flows, including a special focus on wall modeling for compressible turbulent boundary layer in a plane channel. large eddy simulation (LES) of fully developed isothermal channel flows at Re = 3,000 and Re = 4,880 with a sufficient mesh refinement at the wall are carried out in the Mach number range 0.3 ≤ M ≤ 3 for two different source term formulations: first the classical extension of the incompressible configuration by Coleman et al. (J. Fluid Mech. 305:159–183, 1995), second a formulation presently derived to model both streamwise pressure drop and streamwise internal energy loss in a spatially developed compressible channel flow. It is shown that the second formulation is consistent with the spatial problem and yields a much stronger cooling effect at the wall than the classical formulation. Based on the present LES data bank, compressibility and low Reynolds number effects are analysed in terms of coherent structure and statistics. A study of the universality of the structure of the turbulence in non-hypersonic compressible boundary layers (M≤5) is performed in reference to Bradshaw (Annu. Rev. Fluid. Mech. 9:33–54, 1977). An improvement of the van Driest transformation is proposed; it accounts for both density and viscosity changes in the wall layer. Consistently, a new integral wall scaling (y ^c+) which accounts for strong temperature gradients at the wall is developed for the present non-adiabatic compressible flow. The modification of the strong Reynolds analogy proposed by Huang et al. (J. Fluid Mech. 305:185–218, 1995) to model the correlation between velocity and temperature for non-adiabatic wall layers is assessed on the basis of a Crocco–Busemann relation specific to channel flow. The key role of the mixing turbulent Prandtl number Pr _m is pointed out. Results show very good agreement for both source formulations although each of them involve a very different amount of energy transfer at the wall. The present work was performed within the framework of the French–German research initiative “large eddy simulation of complex flows’ (UR 507). The computing resources were provided by IDRIS-France. The authors gratefully acknowledge the financial support from the Centre National de la Recherche Scientifique (CNRS), the Centre d’été Mathématique de Recherche Avancée en Calcul Scientifique (CEMRACS) and the Direction Générale de l’Armement (DGA/D4S).     

Ultrasonic probes and data processing to study interfacial solitary waves

 In this paper we report the results of a small scale experiment (a 3 m long flume) to measure long waves of small to large amplitude at the interface of two non-miscible fluids (water and petrol). Ultrasonic (2 MHz) probes are used to measure the interface displacement. We discuss a fitting method to remove noise while preserving the highly nonlinear features of our data. We find very good agreements between inviscid theories and our experimental data. Received: 18 June 1996 / Accepted: 12 November 1996