A film-based wall shear stress sensor for wall-bounded turbulent flows

In wall-bounded turbulent flows, determination of wall shear stress is an important task. The main objective of the present work is to develop a sensor which is capable of measuring surface shear stress over an extended region applicable to wall-bounded turbulent flows. This sensor, as a direct method for measuring wall shear stress, consists of mounting a thin flexible film on the solid surface. The sensor is made of a homogeneous, isotropic, and incompressible material. The geometry and mechanical properties of the film are measured, and particles with the nominal size of 11 μm in diameter are embedded on the film’s surface to act as markers. An optical technique is used to measure the film deformation caused by the flow. The film has typically deflection of less than 2% of the material thickness under maximum loading. The sensor sensitivity can be adjusted by changing the thickness of the layer or the shear modulus of the film’s material. The paper reports the sensor fabrication, static and dynamic calibration procedure, and its application to a fully developed turbulent channel flow at Reynolds numbers in the range of 90,000–130,000 based on the bulk velocity and channel full height. The results are compared to alternative wall shear stress measurement methods.     

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger , two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.     

Passive Scalar in a Turbulent Channel Flow with Wall Velocity Disturbances

Direct Numerical Simulations (DNS) of a passive scalar in a turbulent channel flow with a normal velocity disturbance on the lower wall are presented for high and low Reynolds numbers. The aim is to reproduce the complex physics of turbulent rough flows without dealing with the geometric complexity. In addition, isothermal walls that cannot be easily assigned in an experiment, are considered. The paper explains the increase of heat transfer through the changes of the velocity and thermal structures. As in real rough flows, the transpiration produces an isotropization of the turbulence near the wall.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

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).     

An Attempt to Combine Large Eddy Simulation with the k-ε Model in a Channel-Flow Calculation

Large eddy simulation (LES) is combined with the Reynolds-averaged Navier–Stokes (RANS) equation in a turbulent channel-flow calculation. A one-equation subgrid-scale model is solved in a three-dimensional grid in the near-wall region whereas the standard k–ε model is solved in a one-dimensional grid in the outer region away from the wall. The two grid systems are overlapped to connect the two models smoothly. A turbulent channel flow is calculated at Reynolds numbers higher than typical LES and several statistical quantities are examined. The mean velocity profile is in good agreement with the logarithmic law. The profile of the turbulent kinetic energy in the near-wall region is smoothly connected with that of the turbulent energy for the k–ε model in the outer region. Turbulence statistics show that the solution in the near-wall region is as accurate as a usual LES. The present approach is different from wall modeling in LES that uses a RANS model near the wall. The former is not as efficient as the latter for calculating high-Reynolds-number flows. Nevertheless, the present method of combining the two models is expected to pave the way for constructing a unified turbulence model that is useful for many purposes including wall modeling. Received 11 June 1999 and accepted 15 December 2000     

Turbulence Characteristics in Flows Over Solid and Porous Square Ribs Mounted on Porous Walls

PIV measurements have been performed for turbulent flows in a rib-mounted channel whose bottom wall is made of a porous layer. The ratio of the rib and channel heights is fixed at 0.5. The effects of the wall and rib permeability are investigated focusing on the separating and reattaching flows at the bulk Reynolds number of 10³???10⁴. Three kinds of foamed ceramics are employed as the porous media. They have the same porosity of 0.8 but each permeability is different from the others. Its normalized values by the rib height are 0.89 × 10^???4, 1.47 × 10^???4 and 3.87 × 10^???4. Two kinds of square cylinder ribs: an impermeable smooth solid rib or a permeable porous rib which is made of the same porous medium as that for the bottom wall are used. The obtained turbulent velocity fields of the solid rib flows indicate that the turbulent intensity behind the rib becomes weak and the recirculation bubble in the clear channel tends to vanish as the the wall permeability increases. In the porous rib flow, the recirculation and the reattachment point shift downstream and turbulence becomes weaker due to the bleeding flow through the rib. In the higher permeability cases, the recirculation bubble hardly exists due to the flows through not only the bottom wall but also the porous rib. From the measurements, it is suggested that in the solid rib flows, a reverse flow region exists inside the porous wall whereas in porous rib flows, such reverse flow does not exist at higher permeability.     

Developed turbulent flow in a plane channel with simultaneous injection through one porous wall and suction through the other

Results of a numerical-theoretical study of a developed turbulent flow of an incompressible fluid in a plane channel with simultaneous injection of mass through one porous wall and suction of the same mass through the other are presented. The system of equations of averaged motion is closed using a turbulent-stress model. The calculated data of the mean and fluctuational characteristics are in reasonable agreement with experimental results for two values of the Reynolds number of the main flow (Re=10,400 and34,000). Al-Farabi Kazakh National State University, Almaty 480121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 61–68, January–February, 1998.     

Predictive Capabilities of an Improved Cubic k–ε Model for Inert Steady Flows

Through an improved ε transport equation, a major quality enhancement of the cubic k–ε model, earlier developed in[13], is obtained. The ε-equation of [13],yielding good results for wall-bounded and rotating flows, is combined with the one derived by Shih et al. [20], which produces good results for free shear flows (e.g. the plane jet–round jet anomaly is resolved).Results are presented for the following flows: fully developed stationary and rotating channel and pipe, backward-facing step, sudden pipe expansion, smooth channel expansion and contraction, plane and round jet. Heat transfer predictions in turbulent impinging jets are also discussed. Accurate results are obtained for the mean flow quantities for all test cases, without case dependent model tuning. This revised version was published online in July 2006 with corrections to the Cover Date.     

Parametric study of unsteady laminar flows

Results of a parametric study of unsteady laminar flows are analyzed. Three-dimensional unsteady equations of hydromechanics for a compressible medium are solved. The range of the characteristic Reynolds number Re = 400–900 is considered. It is demonstrated that the laminar flow in a plane channel ceases to be steady at Re = 415. As the Reynolds number increases, the unsteady processes become more intense, disturbances penetrate inward the channel, and separation zones lose their stability. In the vicinity of the channel exit, however, the flow tends to stabilize, though it remains unsteady. No transition to a turbulent flow occurs in the examined range of Reynolds numbers.     

Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method

A turbulent channel flow and the flow around a cubic obstacle are calculated by the moving particle semi‐implicit method with the subparticle‐scale turbulent model and a wall model, which is based on the zero equation RANS (Reynolds Averaged Navier‐Stokes). The wall model is useful in practical problems that often involve high Reynolds numbers and wall turbulence, because it is difficult to keep high resolution in the near‐wall region in particle simulation. A turbulent channel flow is calculated by the present method to validate our wall model. The mean velocity distribution agrees with the log‐law velocity profile near the wall. Statistical values are also the same order and tendency as experimental results with emulating viscous layer by the wall model. We also investigated the influence of numerical oscillations on turbulence analysis in using the moving particle semi‐implicit method. Finally, the turbulent flow around a cubic obstacle is calculated by the present method to demonstrate capability of calculating practical turbulent flows. Three characteristic eddies appear in front of, over, and in the back of the cube both in our calculation and the experimental result that was obtained by Martinuzzi and Tropea. Mean velocity and turbulent intensity profiles are predicted in the same order and have similar tendency as the experimental result. Copyright © 2012 John Wiley & Sons, Ltd.     

A vorticity stretching diagnostic for turbulent and transitional flows

Vorticity stretching in wall-bounded turbulent and transitional flows has been investigated by means of a new diagnostic measure, denoted by Γ, designed to pick up regions with large amounts of vorticity stretching. It is based on the maximum vorticity stretching component in every spatial point, thus yielding a three-dimensional scalar field. The measure was applied in four different flows with increasing complexity: (a) the near-wall cycle in an asymptotic suction boundary layer (ASBL), (b) K-type transition in a plane channel flow, (c) fully turbulent channel flow at Re _τ = 180 and (d) a complex turbulent three-dimensional separated flow. Instantaneous data show that the coherent structures associated with intense vorticity stretching in all four cases have the shape of flat ‘pancake’ structures in the vicinity of high-speed streaks, here denoted ‘h-type’ events. The other event found is of ‘l-type’, present on top of an unstable low-speed streak. These events (l-type) are further thought to be associated with the exponential growth of streamwise vorticity in the turbulent near-wall cycle. It was found that the largest occurrence of vorticity stretching in the fully turbulent wall-bounded flows is present at a wall-normal distance of y ⁺?=?6.5, i.e. in the transition between the viscous sublayer and buffer layer. The associated structures have a streamwise length of ~200–300 wall units. In K-type transition, the Γ-measure accurately locates the regions of interest, in particular the formation of high-speed streaks near the wall (h-type) and the appearance of the hairpin vortex (l-type). In the turbulent separated flow, the structures containing large amounts of vorticity stretching increase in size and magnitude in the shear layer upstream of the separation bubble but vanish in the backflow region itself. Overall, the measure proved to be useful in showing growing instabilities before they develop into structures, highlighting the mechanisms creating high shear region on a wall and showing turbulence creation associated with instantaneous separations.     

Experiments on the linear instability of flow in a wavy channel

The effects of wall corrugation on the stability of wall-bounded shear flows have been examined experimentally in plane channel flows. One of the channel walls has been modified by introduction of the wavy wall model with the amplitude of 4% of the channel half height and the wave number of 1.02. The experiment is focused on the two-dimensional travelling wave instability and the results are compared with the theory [J.M. Floryan, Two-dimensional instability of flow in a rough channel, Phys. Fluids 17 (2005) 044101 (also: Rept. ESFD-1/2003, Dept. of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, 2003)]. It is shown that the flow is destabilized by the wall corrugation at subcritical Reynolds numbers below 5772, as predicted by the theory. For the present corrugation geometry, the critical Reynolds number is decreased down to about 4000. The spatial growth rates, the disturbance wave numbers and the distribution of disturbance amplitude measured over such wavy wall also agree well with the theoretical results.     

Turbulent Channel Flow with an Artificial Two-Dimensional Wall Layer

Turbulent flow of an incompressible fluid in a plane channel with parallel walls is considered. The three-dimensional time-dependent Navier-Stokes equations are solved numerically using the spectral finite-difference method. An artificial force which completely suppresses lateral oscillations of the velocity is introduced in the near-wall zone (10 % of the channel half-width in the neighborhood of each wall). Thus, the three-dimensional flow zone, in which turbulent oscillations can develop, is separated from the wall by a fluid layer. It is found that the elimination of three-dimensionality in the neighborhood of the walls leads to a significant reduction in the drag. However, complete laminarization does not occur. The flow in the stream core remains turbulent and can be interpreted as a turbulent flow in a channel with walls located on the boundary of the two-dimensional layer and traveling at the local mean-flow velocity. The oscillations developing inside the two-dimensional layer, which have significant amplitude, distort the flow only in the adjacent zone. Beyond this zone the distributions of the mean characteristics and the structure of instantaneous fields completely correspond to ordinary turbulent flow in a channel with rigid walls. The results obtained confirm the hypothesis of the unimportance of the no-slip boundary conditions for the fluctuating velocity component in the mechanism of onset and self-maintenance of turbulence in wall flows.     

Hydrodynamics study in a plane ultrafiltration module using an electrochemical method and particle image velocimetry visualization

 The wall shear stress is determined at the surface of a plane sheet of Plexiglas, taking the place of a membrane, using an electrochemical method. Several microelectrodes are mounted flush to this plane plate, and maps of shear stress are determined for two inlet and outlet configurations and three channel heights. The heterogeneity of the wall shear stress is observed for both configurations. Furthermore, the study of the turbulence features of the flow shows a decreasing fluctuating rate of velocity gradient when the channel height is decreased. The wall velocity gradients and turbulent intensity rates analysis are confirmed by a flow visualization using the particle image velocimetry method. Received: 25 September 2000 / Accepted: 23 April 2001     

A New Low-Reynolds-Number One-Equation Model of Turbulence

In this study, we propose a new Low-Reynolds-Number (LRN)one-equation model, which is derived from an LRN two-equation(k-ε) model. The derivation of the transport equation, in principle, is based on the assumption that the turbulent structure parameter remains constant. However, the relation for the turbulent structure parameter a ₁(=|− |/k) is modified to account for near-wall turbulence. As a result, the present one-equation model contains a term which takes the near-wall limiting behavior explicitly into account. Thus, the present model provides the correct wall-limiting behavior of turbulence in the vicinity of the wall and can be applied to the analysis of heat transfer. The validity of the present model is tested in channel flows, boundary layer flows with and without pressure gradient, plane wall jet, and flow with separation and reattachment. The calculated results showed good agreement with the direct numerical simulation (DNS) and experimental data. This revised version was published online in July 2006 with corrections to the Cover Date.     

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。     

Method of calculation of interaction of wall flows

A flow of viscous compressible fluid in the neighborhood of the line of interaction of wall flows is considered. A method of calculating the line of interaction and the direction of the self-induced secondary flow is developed. Papers [1–3] are devoted to the simulation of a separation flow with singularities in the neighborhood of singular lines and points, where boundary-layer equations are invalid. However, the theories of local separation used at present have mainly been developed only for two-dimensional problems, while the models of viscous-inviscid interaction have restrictions in application for turbulent flows with developed separation. The interaction of three-dimensional wall turbulent flows is considered below. It is assumed that the thickness of the boundary layers and the scales of the interaction zones are small in comparison with the characteristic dimension of the system, while the line of discontinuity of the solutions of the three-dimensional boundary layer equations is the same as the line of interaction of the wall flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–59, March–April, 1987.The author is grateful to G. Yu. Stepanov and V. N. Ershov for their interest in my work and their valuable remarks.     

Influence of blowing on the anisotropy of the Reynolds stress tensor in a turbulent channel flow

The effects of localized wall blowing through a porous strip are investigated using hot-wire anemometry in a turbulent channel flow. Three blowing magnitudes are studied: σ=0.22, 0.36 and 0.58, where σ is the momentum flux gain ratio and that of the incoming channel flow at three different positions from the spanwise porous strip. The main emphasis of this work was the departure from isotropy of the turbulent flow with localized blowing. The anisotropic invariant map (AIM) for the Reynolds stress tensor revealed that blowing decreased the anisotropy of the turbulent structure in the near-wall region, and a decrease in the longitudinal integral length scale was observed when the blowing rate increased.     

Transient growth and bypass transition in stenotic flow with a physiological waveform

A direct analysis method is applied to compute optimal transient growth initial conditions for physiologically relevant pulsatile flows in a smooth axisymmetric stenosis with 75% occlusion. The flow waveform employed represents phase-average measurements obtained in the human common carotid artery. Floquet analysis shows that the periodic flow is stable to infinitesimal eigenmodal-type perturbations that would grow from one cycle to the next at the Reynolds numbers considered. However, the same flows display explosive transient growth of optimal disturbances, with our analysis predicting disturbance energy growths of order 10²⁵ within half a pulse period at a mean bulk flow Reynolds number Re = 300, which is significantly lower than the physiological value of Re = 450 at this location. Direct numerical simulation at Re = 300 shows that when the base flow is perturbed a small amount with the optimal growth initial condition, the disturbance grows rapidly in time in agreement with the linear analysis, and saturates to provide a locally turbulent state within half a pulse period. This transition resulting from non-normal growth mechanisms shows the flow exhibits bypass transition to turbulence. Our analysis suggests that this route to localized turbulent states could be relatively common in human arterial flows.