Mean Skin Friction Research Articles

Statistical estimates for channel flows driven by a pressure gradient

We present rigorous estimates for some physical quantities related to turbulent and non-turbulent channel flows driven by a uniform pressure gradient. Such results are based on the concept of stationary statistical solutions, which is related to the notion of ensemble averages for flows in statistical equilibrium. We provide a lower bound estimate for the mean skin friction coefficient and improve on a previous upper bound estimate for the same quantity; both estimates are derived in terms of the Reynolds number. We also present lower and upper bound estimates for the mean rate of energy dissipation, the mean longitudinal bulk velocity (in the direction of the pressure gradient), and the mean kinetic energy in terms of various physical parameters. In particular, we obtain an upper bound related to the energy dissipation law, namely that the mean rate of energy dissipation is essentially bounded by a non-dimensional universal constant times the cube of the mean longitudinal bulk velocity over a characteristic macro-scale length. Finally, we investigate the scale-by-scale energy injection due to the pressure gradient, proving an upper bound estimate for the decrease of this energy injection as the scale length decreases.

A numerical study of developing slurry flow in the entrance region of a horizontal pipe

In this paper, a simplified 3-D algebraic slip mixture (ASM) model was introduced to obtain the numerical solution in sand–water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG k– ε turbulent model was used with the algebraic slip mixture model. An unstructured (block-structured), non-uniform grid was chosen to discretize the entire computation domain, and a control volume finite difference method (CVFDM) was applied to solve the governing equations. The mean pressure gradients from the numerical solution in the fully developed turbulent flow were compared with the authors’ experimental data and that in the open literature to validate the simulation results. The solutions were found to be in good agreement with the experimental data. The numerical investigations have focused mainly on illustrating and comparing the developing processes of volume fraction and density distributions, mean velocity profiles, and mean skin friction coefficient distributions in the entrance region. It was found that the difference of friction factors between single- and double-species slurries increases along flow direction in most part of the entrance region.

Rough-wall boundary layers: mean flow universality

Mean flow profiles, skin friction, and integral parameters for boundary layers developing naturally over a wide variety of fully aerodynamically rough surfaces are presented and discussed. The momentum thickness Reynolds numberReθextends to values in excess of 47000 and, unlike previous work, a very wide range of the ratio of roughness element height to boundary-layer depth is covered (0.03 <h/δ > 0.5). Comparisons are made with some classical formulations based on the assumption of a universal two-parameter form for the mean velocity profile, and also with other recent measurements. It is shown that appropriately re-written versions of the former can be used to collapse all the data, irrespective of the nature of the roughness, unless the surface is very rough, meaning that the typical roughness element height exceeds some 50% of the boundary-layer momentum thickness, corresponding to about$h/\delta\,{\widetilde{>}}\,0.2$.

Interaction of synthetic jets with a fully developed turbulent channel flow

The effects of the interaction of a spanwise array of inclined circular synthetic jets with a turbulent channel flow have been experimentally studied. The array is arranged in a convergent couple configuration, where each single jet is oriented at ± 45° in the plane perpendicular to the mean channel flow. The actuator system is derived from a commercial engine for airplane models where the oscillating piston gives rise to the periodic blowing and suction phases needed for the generation of a synthetic jet. The interaction produces couples of counter-rotating large-scale longitudinal vortical structures organized periodically in the spanwise direction. These vortices persist along the channel up to long distances from the injection section and produce an attenuation of the wall turbulence. Reductions in the mean skin friction of up to 15% and in the turbulence fluctuations (wall shear stress and streamwise velocity) of up to 12% are obtained. The efficiency of the interaction depends on the piston oscillation frequency. The near-wall activity is influenced to a great extent by the action of the large-scale vortices. The variable interval time averaging (VITA) events are reduced and the integral time macroscales are increased while the probability density function (PDF) analysis shows higher levels of intermittency. The interpretation of these effects is given in terms of regeneration mechanisms of the near-wall structures. A comparison between the present control scheme and the forcing obtained using continuous jets has also been made. In the case of synthetic jets, the forcing effects appear weaker with respect to those obtained using continuous jets, at least for the tested conditions. Drag reduction and turbulence attenuation are in fact lower when synthetic jets are used as a forcing technique.

A MEMS skin-friction sensor for time resolved measurements in separated flows

A MEMS surface fence sensor for skin-friction measurements in separated flows has been developed and tested successfully in low-speed flows. The new sensor is able to distinguish between forward and reverse flow and features a temporal resolution of up to 1 kHz. Calibrations of the sensor have been obtained in the range of –0.7 N m-2≤τw≤0.7 N m-2 with a resolution of 0.02 N m-2. Comparative measurements with the wall-pulsed wire technique in a reverse-flow region show excellent agreement with respect to the mean skin-friction coefficient cf but also reveal some discrepancies for the fluctuating part cf′.

Unsteady wall-shear measurements in turbulent boundary layers using MEMS

Fluctuating skin friction is measured in two- and three-dimensional turbulent boundary layers using a MEMS sensor and a wall-wire as reference. Skewness, flatness and spectra of the turbulent skin friction are presented to demonstrate the potential and limitations of the MEMS sensor. The measured turbulence intensities of the order of 0.4 are in general agreement with a number of experimental and DNS studies. However, the fluctuating quantities measured with this MEMS sensor, operated at an over-heat ratio of 1.3, are shown to depend on the Reynolds number or mean skin friction. Therefore, such a high over-heat ratio, which was proven to dramatically increase the accuracy of mean skin friction measurements in a previous study by the authors, may not be appropriate for the measurement of fluctuating wall-shear with MEMS sensors, particularly at low mean shear values.

Evaluation of three techniques for wall-shear measurements in three-dimensional flows

Recent improvements in three techniques for measuring skin friction in two- and three-dimensional turbulent wall-bounded shear flows are presented. The techniques are: oil-film interferometry, hot wires mounted near the wall, and surface hot-film sensors based on MEMS technology. First, we demonstrate that the oil-film interferometry technique can be used to measure the skin-friction magnitude and its direction in two- and three-dimensional wall-bounded shear flows. Second, a simple method is outlined to measure the skin friction with a wall wire located outside of the viscous sublayer. Finally, a systematic study of the parameters influencing wall-friction measurements with MEMS sensors is presented. The results demonstrate that accurate measurements of the mean skin friction with MEMS sensors are possible in two- and three-dimensional wall flows. Measurements by the three techniques are compared to each other and to past measurements in the same facility.

Laser Doppler Anemometry Study of a Turbulent Jet in Crossflow

Introduction A JET in cross ow is an importantpracticalproblemencountered in turbine cooling, fuel injection, thrust vectoring (vertical/ short takeoff and landingaircraft),andmissile control.Experiments by Fric and Roshko1 and Kelso et al.2 show that there exists a complex vortical  ow in the near Ž eld. The main vortical structures include the horseshoe vortex, the counter-rotating bound vortex pair (CVP), the jet shear-layer vortices, and the upright wake vortices. The majority of experimentaldata existing in the literaturewere obtainedwith conventionalhot-wire anemometry,which is insensitive to  ow direction and can give large errors in regions of high turbulence. The present Note investigates the effect of velocity ratio on both mean  ow topology and skin friction for a round jet exhausting normal to a  at plate raised from the side wall of a wind tunnel. Two-component laser Doppler anemometry (LDA) was employed to measure mean velocity in threemutually perpendicularplanes of the  owŽ eld near the jet exit. The choice of test conditionshas been guided by a wish to supplement existing numerical and experimental studies, notably those of Yuan et al.3 and Kim et al.4; hence, a jet-to-crossow velocity ratio of 3.3was chosen.The lower velocity ratio of 1.3 was included in the study to show parametric effects for a turbulent incoming jet. Thanks to an artiŽ cially thickened turbulent boundary layer developingon the  at plate, skin friction could be determined from velocitymeasurements close to the wall on the planeof symmetry.Results to be presentedare based on a database,5 which includes distributionsof three components of mean velocity, vorticity, turbulent kinetic energy, and all Reynolds stresses.

The inner–outer layer interface in large-eddy simulations with wall-layer models

The interaction between the inner and outer layer in large-eddy simulations (LES) that use approximate near-wall treatments is studied. In hybrid Reynolds-averaged Navier–Stokes (RANS)/LES models a transition layer exists between the RANS and LES regions, which has resulted in incorrect prediction of the velocity profiles, and errors of up to 15% in the prediction of the skin friction. Several factors affect this transition layer, but changes we made to the formulation had surprisingly little effect on the mean velocity. In general, it is found that the correct prediction of length- and time-scales of the turbulent eddies in the RANS region is important, but is not the only factor affecting the results. The inclusion of a backscatter model appears to be effective in improving the prediction of the mean velocity profile and skin-friction coefficient.

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF THE INFLUENCE OF FREE-STREAM TURBULENCE ON TURBULENT BOUNDARY LAYER DRAG REDUCTION OVER PLATES WITH STREAM-WISE MICRO-GROOVES

Experimental and numerical studies are performed to investigate the effect of free-stream turbulence on turbulent boundary layer drag reduction over plates with stream-wise micro-grooves. The data includes mean velocity, turbulence intensities, momentum thickness, and skin friction. Riblet or grooved plates of various riblet aspect ratios (h/s) have been machined with symmetrical, sharp, stream-wise triangular-shaped grooves having a peak-to-valley height (h) and peak-to-peak width (s). Three test plates, one smooth and two with triangular profile grooves (riblets) of h/s = 0.7, and 1.3 aspect ratio with fixed riblet spacing (s = 0.6 mm), have been used in this comparative study. Three screens of different sizes inserted upstream the test plates (with and without grooves) were used to study the effect of the free-stream turbulence. The turbulence intensities level varied from 1.3% to 3.2% by the screens. The Reynolds number based on the free-stream velocity and the stream-wise length, ranged from 1.4 x 106 to 4.3 x 106 covering a range of riblet spacing inwall units (s+), = st.1,/v, of 13.7 to 36.4. The measurements were made in a suction type, low-speed open-return wind tunnel using a Dantec 56C01 constant temperature anemometer (CTA) with a Dantec 55PO4 hot single-wire probe. The numerical investigation has been formulated using a finite difference method and k-r, turbulence model. The results show that the drag increases with increasing the free-stream turbulence. The data show that the drag reduction occurred whenever riblet spacing in wall units in range of 0 < s+ < 25. For grooved plates without screens, a maximum drag reduction of 9% occurred at s+ = 13.7. The maximum drag reduction reached 6.3% in the case of grooved plate with h/s = 1.3 with turbulence promoter compared with the smooth surface without turbulence promoters. Also, the results suggest increased the effectiveness of the riblets with turbulence promoters compared with the smooth surface with turbulence promoters.

Numerical investigations of liquid–solid slurry flows in a fully developed turbulent flow region

In this paper, a simplified 3D algebraic slip mixture (ASM) model is introduced to obtain the numerical solution in sand–water slurry flow. In order for the study to obtain the precise numerical solution in fully developed turbulent flow, the RNG K– ε turbulent model was used with the ASM model. An unstructured (block-structured) non-uniform grid was chosen to discretize the entire computational domain, and a control volume finite difference method was used to solve the governing equations. The mean pressure gradients from the numerical solutions were compared with the authors’ experimental data and that in the open literature. The solutions were found to be in good agreement when the slurry mean velocity is higher than the corresponding critical deposition velocity. Moreover, the numerical investigations have displayed some important slurry flow characteristics, such as volume fraction distributions, slurry density, slip velocity magnitude, slurry mean velocity distributions, and slurry mean skin friction coefficient distributions in a fully developed section, that have never been displayed in the experiments.

209 流れ方向突起により変形を受ける乱流境界層 : 平均量と壁面せん断応力

209 流れ方向突起により変形を受ける乱流境界層 : 平均量と壁面せん断応力

Multiple hot-film sensor array calibration and skin friction measurement

A method for the calibration of closely spaced multiple hot-film sensor (MHFS) arrays of nickel-on-polyimide-substrate type was presented in this paper. The hot-film sensors were calibrated individually and in situ against the values of the wall-shear stresses determined from boundary-layer velocity profiles (developed on the front portion of a circular cylinder) through a specially designed wall-mounted hot-wire probe. The accuracy and feasibility of the present method was examined through the subsequent measurements of the skin-friction distributions on a circular cylinder (including the removal and bonding of the calibrated MHFS from a 10-cm diameter calibration cylinder and onto the surface of a 8-cm diameter test cylinder) and comparison of their consistency with the published results. The present MHFS calibration method is important in the non-intrusive multipoint measurements of the mean skin friction along the surfaces of two-dimensional aerodynamic objects of interest.

The reduction and elimination of a closed separation region by free-stream turbulence

This paper is an extension of an experimental investigation by Alving &amp; Fernholz (1996). In the present experiments the effects of free-stream turbulence were investigated on a boundary layer with an adverse pressure gradient and a closed reverse-flow region. By adding free-stream turbulence the mean reverse-flow region was shortened or completely eliminated and this was used to control the size of the separation bubble. The turbulence intensity was varied between 0.2% and 6% using upstream grids while the turbulence length scale was on the order of the boundary layer thickness. Mean and fluctuating velocities as well as spectra were measured by means of hot-wire and laser-Doppler anemometry and wall shear stress by wall pulsed-wire and wall hot-wire probes.Free-stream turbulence had a small effect on the boundary layer in the mild adverse-pressure-gradient region but in the vicinity of separation and along the reverse-flow region mean velocity profiles, skin friction and turbulence structure were strongly affected. Downstream of the mean or instantaneous reverse-flow regions highly disturbed boundary layers developed in a nominally zero pressure gradient and converged to a similar turbulence structure in all three cases at the end of the test section. This state was, however, still very different from that in a canonical boundary layer.

Oscillating plate temperature effects on a flow past an infinite vertical porous plate with constant suction and embedded in a porous medium

An approximate solution to the problem of flow of a viscous incompressible dissipative fluid past an infinite vertical porous plate embedded in a porous medium is presented here. The plate temperature is assumed to be oscillating about a constant mean temperature. Mean velocity and mean temperature, the transient velocity and temperature profiles are shown graphically. The mean skin-friction and the mean rate of heat transfer are also shown graphically. The expressions for the amplitude and the phase of the skin-friction and the rate of heat transfer are derived and their numerical values are listed in Tables. The effects of different parameters governing the unsteady flow are discussed.

Study of flow in a planar asymmetric diffuser using large-eddy simulation

Large-eddy simulation (LES) has been used to study the flow in a planar asymmetric diffuser. The wide range of spatial and temporal scales, the presence of an adverse pressure gradient, and the formation of an unsteady separation bubble in the rear part of the diffuser make this flow a challenging test case for assessing the predictive capability of LES. Simulation results for mean flow, pressure recovery and skin friction are in excellent agreement with data from two recent experiments. The inflow consists of a fully developed turbulent channel flow at a Reynolds number based on shear velocity, Reτ=500. It is found that accurate representation of the in flow velocity field is critical for accurate prediction of the flow in the diffuser. Although the simulation in the diffuser is well resolved, the subgrid-scale model plays a significant role for both mean momentum and turbulent kinetic energy balances. Subgrid-scale stresses contribute a maximum of 8% to the local value of the total shear stress with the maximum values found in the inlet duct and along the flat wall where the flow remains attached. The subgrid-scale model adapts to the enhanced turbulence levels in the rear part of the diffuser by providing more than 80% of the dissipation rate for turbulent kinetic energy. The unsteady separation excites large scales of motion which extend over the major part of the duct cross-section and penetrate deeply into the core of the flow. Instantaneous flow reversal is observed along both walls immediately behind the diffuser throat which is far upstream of the location of main separation. While the mean flow profile changes gradually as the flow enters the expansion, turbulent stresses undergo rapid changes over a short streamwise distance along the deflected wall. An explanation is offered which considers the strain field as well as the influence of geometry changes. The effect of grid resolution and spanwise domain size on the flow field prediction has been documented and this allows an assessment of the computational requirements for carrying out such simulations.

The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 2. The boundary layer with relaminarization

This is an experimental investigation of two turbulent boundary layers (cases 2 and 4) where the streamwise negative pressure gradient changes mean properties of the flow, e.g. mean velocity profiles and skin friction, so that they display laminar-like behaviour. The maximum acceleration parameter K[les ]4×10−6 and the starting value of the Reynolds number is 862 or 2564. Relaminarization occurs in both boundary layers as a gradual change of the turbulence properties and is not catastrophic. Retransition, however, is a fast process due to the remaining turbulence structure and may be compared with bypass transition. Together with an extensive investigation of the turbulence structure as in the companion paper, Part 1, which describes two cases (1 and 3) of boundary layers which remain turbulent, spectra and integral length scales for all four boundary layers are discussed.

MEAN FLOW CHARACTERISTICS OF RADIAL TURBULENT FLOW BETWEEN PARALLEL PLATES

ABSTRACT A schematic diagram of radial flow between parallel plates is shown in Fig. 1. Fluid is supplied from a pipe of diameter d at the centre of one of the two parallel plates of diameter D, which are kept separated by a small distance h. The fluid then spreads radially outward. For a fixed value of D/d equal to 9.625 the mean flow characteristics, viz. pressure, velocity and skin friction for this flow configuration have previously been obtained by Asawa (1). The present experimental investigation studied the influence of D/d on these mean flow characteristics.

Some effects of oscillation waveform and amplitude on unsteady turbulent shear flows

Some physical features of several unsteady separating turbulent boundary layers are presented for practical Reynolds numbers and reduced frequencies such as for helicopter and turbomachinery flows. The effects of unsteadiness amplitude and waveform are examined for flows along the floor of a converging and diverging wind tunnel test section. At the end of the converging portion, the mean skin friction coefficient normalized on the mean dynamic pressure is independent of the waveform and amplitude within low experimental uncertainties. In the detaching and detached portions of the flow, wall values of the fraction of time that the flow moves downstream of gamma sub pu, which is a separated flow state variable, shows that oscillation waveform and amplitude strongly influence the detached flow behavior. Distributions of gamma sub pu during a cycle indicate hysteresis within the detached flow and the effects of the higher harmonics of pressure gradient and velocity.

Unsteady free-convective flow and mass transfer in a rotating porous medium with Hall current, I

The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK* on the flow field are discussed with the help of graphs and tables.