Zero-pressure Gradient Research Articles

Direct numerical simulation of the drag-reducing turbulent boundary layer of viscoelastic fluid

Direct numerical simulation of a zero-pressure gradient drag-reducing turbulent boundary layer of homogeneous viscoelastic fluids was performed using constitutive equation models such as the Oldroyd-B and Giesekus models. Mean velocity profiles and turbulence statistics at the different streamwise locations were discussed using both inner and outer scaling. The maximum drag reduction ratio for the Oldroyd-B model, which has the higher elongational viscosity, is larger than for the Giesekus model. The distinct difference in turbulence statistics near the wall between the Oldroyd-B model and Newtonian fluid is observed, as reported in the drag-reducing turbulent channel flow, while in the outer region, distributions of turbulence statistics for the Oldroyd-B model with a drag reduction ratio of about 40% are similar to those for Newtonian fluid. The production term for the turbulent boundary layer does not correspond to the amount of drag reduction, which is consistent with the fact that the streamwise turbulence intensity profile is not a direct indication of the drag reduction. The contribution of the advection term to the budget of streamwise Reynolds normal stress, which does not appear for the turbulent channel flow, is not negligible near the wall for the Oldroyd-B model. For the Oldroyd-B model with a maximum drag reduction ratio of 42%, we can see that quasi-streamwise vortices are weakened and become larger in the streamwise direction, compared to Newtonian fluid. On the other hand, quasi-streamwise vortices for the Giesekus model with a maximum drag reduction ratio of 16% are slightly larger than those for Newtonian fluid. These modifications of near-wall coherent structures are explained by the profile of the trace of mean viscoelastic stress and the elastic energy theory presented by Min et al. [J. Fluid Mech. 486, 213 (2003)] for the drag-reducing turbulent channel flow.

A three-velocity-component laser-Doppler velocimeter for measurements inside the linear compressor cascade

A 24′′ (610 mm) access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements in a low speed linear cascade wind tunnel with moving wall simulation. The probe has a 610 mm access length and achieves a measurement spatial resolution of 100 μm by using off-axis optical heads. With the relatively large access length, the LDV probe allows for measurements from the side of a wind tunnel instead of through the tunnel floor, while the high spatial resolution allows for quality near-wall measurements. The probe has been tested in a zero-pressure gradient 2D turbulent boundary layer and the test results agree well with the experimental data measured with different LDV systems and hot-wire anemometery for the boundary layer flows. The energy spectral density was estimated using a slot correlation, and Von Karman’s model for the energy-spectrum function was used to analyze the measured spectral data to estimate the turbulent kinetic energy dissipation rate, which compares favorably with the measured production values in the log-layer region of the turbulent boundary layer. Measurements are presented for the moving endwall boundary layer at the inlet of the linear compressor cascade facility to validate the capability of this LDV for tip leakage flow measurements. These results indicate that the moving endwall reduces velocity gradients in the near-wall region and results in less production of Reynolds stresses and turbulent kinetic energy compared to the stationary endwall case.

Particle image velocimetry study of turbulent flow over transverse square ribs in an asymmetric diffuser

The objective of this paper is to study the combined effects of rib roughness and adverse pressure gradient produced in an asymmetric diffuser on turbulent flows. The two-dimensional asymmetric diffuser was comprised of a straight flat floor and a curved roof. The diffuser section was preceded and followed by straight parallel walls. The complete test conditions were comprised of a reference smooth floor and repeated arrays of transverse square ribs glued onto the floor to produce three pitch-to-height ratios, p∕k=3, 6, and 8. The curved roof was kept smooth in all the experiments. For each of the four test conditions, a particle image velocimetry was used to conduct detailed velocity measurements within the diverging section and also at locations upstream and downstream of the diverging section. From these measurements, the mean streamlines, mean velocities, turbulent intensities, Reynolds shear stress, and production terms in the transport equations for the turbulent kinetic energy and Reynolds stresses were obtained. The results obtained in the diverging section showed that the boundary layers that developed on the ribs thickened considerably at the expense of those adjacent to the roof opposite to the ribs. The streamlines and mean velocity profiles over the ribs showed that adverse pressure gradient increased the roughness sublayer substantially. Adverse pressure gradient and rib roughness also increased the drag and levels of the turbulent intensities, Reynolds shear stress and production terms compared to smooth-wall zero pressure gradient turbulent boundary layer. It appears, however, that adverse pressure gradient enhanced turbulence more effectively than it increased drag.

Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers

A new set of experiments have been performed in order to study the effects of surface roughness and Reynolds number on a zero pressure gradient turbulent boundary layer. In order to properly capture the x dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed which enabled the use of the full boundary layer equations to calculate the skin friction. This quantity was obtained within 3% and 5% accuracy for smooth and rough surfaces, respectively. For the sand grain type roughnesses used, only the Zagarola and Smits scaling, U∞δ*∕δ, was able to remove the effects of roughness and Reynolds number from the velocity profiles in outer variables. However, each scaling used for the velocity deficit profiles resulted in self-similar solutions for fixed experimental conditions. When examining the Reynolds stresses in the inner region [i.e., 0<(y+ϵ)+<0.1δ+], the ⟨u2⟩ component showed the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables showed self-similarity for fixed experimental conditions. However, as the roughness parameter, k+ increases, all Reynolds stress profiles became similar in shape indicating increased isotropy near the wall. Furthermore, the boundary layer parameters also showed a considerable increase due to roughness.

Characteristics of Loose Rough Boundary Streams at Near-Threshold

Laboratory experimental results on the turbulent flow characteristics, measured by an acoustic Doppler velocimeter, over loose rough boundaries at the near-threshold of motion are reported. The primary endeavor was to investigate the response of the turbulent flow field, having zero-pressure gradient, to the uniform gravel beds at the near-threshold of motion with reasonably wide range of relative roughness ε∕h (0.02<ε∕h<0.15; where ε=Nikuradse’s equivalent roughness and h=flow depth). Five uniform gravel sizes, ranging from 4.1to14.25mm, were used in the experiments. The vertical distributions of time-averaged velocity, turbulence intensities and the Reynolds stress were measured and analyzed. The variation of the mixing-length is considerably linear with the depth within the inner layer, whose thickness is 0.23 times the boundary layer thickness δ, and the von Kármán constant is obtained as 0.35. The boundary shear stresses were determined by three independent methods, such as using the logarithmic law (the Clauser method), Reynolds stress profiles and bed slope. It is observed that in the inner layer, the logarithmic law of wall for the time-averaged streamwise velocity holds with the von Kármán constant 0.35 and a constant of integration 7.8; whereas in the outer layer, the law of the wake defines the velocity profiles with average value of the Coles’ wake parameter 0.11. Alternatively, velocity profiles based on 1∕nth power law are also put forward, where n is expressed as a function of ε∕δ. The equation of the friction factor f is obtained from the depth averaging of the velocity profile; and the collapse of the estimated f and the measured data (experimental and field) is reasonable. The turbulence intensities being non-isotropic can be defined by an exponential law; whereas the Reynolds stress varies almost linearly with the depth. The values of the Shields parameter for the threshold of gravel motion obtained experimentally correspond closely with the curve obtained from the modified model of Dey considering the present logarithmic law of velocity. For all the aforementioned parameters, thorough statistical and error analyses of the experimental data are done to ascertain the adequacy of the proposed equations.

The spatial relationships between dissipation and production rates and vortical structures in turbulent boundary and mixing layers

A novel approach for studying the spatial relationship between the production and dissipation rates of turbulent kinetic energy and vortical structures is presented. Two turbulent flows were investigated: the zero pressure gradient boundary layer and the two-stream mixing layer. In both flows, a multisensor hot-wire probe was used to measure the velocity components in all three coordinate directions, as well as six components of the velocity gradient tensor. The remaining three velocity gradients were determined using Taylor’s hypothesis. With these data, the “instantaneous” production and dissipation rates, defined by P=−(∂U¯i∕∂xj)uiuj and D=−ν[(∂ui∕∂xj)2+(∂ui∕∂xj)(∂uj∕∂xi)], respectively, were determined. Cross-correlating the fluctuations of these two signals reveals that they are not randomly distributed in time with respect to each other; rather they display significant levels of correlation. Plotting the cross-correlation coefficients versus a dimensionless length scale, defined as L′=sgn(τ)∣τ∣∕νU¯, reveals an asymmetric pattern that persists at several cross-stream locations for both flows. Furthermore, correlating both the dissipation and production rates with a vortex identifier, ωxy=[(ωx)2+(ωy)2]1∕2, also reveals consistent cross-stream patterns. The magnitude of these correlations and their persistent shapes across the flows suggest that the spatial separation between regions of concentrated dissipation and production rates is associated with the presence of quasistreamwise vortices in both of these flows. More specifically, they imply that regions of concentrated rates of dissipation are primarily in the cores of the vortices, whereas regions of rates of production are more concentrated on their periphery.

Incompressible Turbulent Flow Simulation Using theκ-ɛModel and Upwind Schemes

In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynoldsκ-ɛmodel and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of theFreeflowsimulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

Effect of surface roughness on the coefficients of a power law for the mean velocity in a turbulent boundary layer

Mean velocity profiles in a two-dimensional zero pressure gradient turbulent boundary layer were obtained for a hydraulically smooth surface and 10 different rough surfaces created from sand paper, steel perforated sheet, and steel woven wire mesh. The physical size and geometry of the roughness elements were chosen to achieve transitionally rough and fully rough flow regimes. The measurements were made in a subsonic wind tunnel, and the Reynolds number based on the momentum thickness ranged from 3730 to 13 550. The power law formulation of George and Castillo (1997, Applied Mechanics Review, 50, 689) was used to estimate the skin friction coefficients for transitionally rough and fully rough flows, as well as hydraulically smooth flow. The values of the friction velocity obtained for the rough surfaces using the defect law and the power law profile fitting techniques were within ±3%. Values of the power law coefficient C i and exponent γ were determined by fitting the power law formulation to the experimental data. The surface roughness was found to significantly affect the behaviour of the coefficient C i and exponent γ in the power law relations. Based on the experimental results, correlations are proposed for the coefficient C i and exponent γ as a function of the roughness shift Δ U + for transitionally rough flows.

Direct Numerical Simulation of Drag-Reducing Turbulent Boundary Layer of Viscoelastic Fluid (2nd Report, Energy Transfer and Coherent Structures)

Energy transfer and turbulence structures in a zero-pressure gradient turbulent boundary layer of a drag-reducing viscoelastic solution were investigated using the direct numerical simulation (DNS) data with the Oldroyd-B and Giesekus models. This work is an extension of the first report, in which mean velocity profiles and turbulence statistics have been investigated. It is found that the contribution to turbulent kinetic energy transfer due to the polymer stress work term is not negligible for the Oldroyd-B model, whereas it is negligible for the Giesekus model. The polymer diffusion term for both the Oldroyd-B and Giesekus models is negligible. For the Oldroyd-B model, we can see that quasi-streamwise vortices are weakened and become larger in the streamwise direction, compared to Newtonian fluids. On the other hand, quasi-streamwise vortices for the Giesekus model are similar to those for Newtonian fluid.

108 粘弾性流体の抵抗低減壁乱流に関する直接数値シミュレーション(2)(OS1-2 流れの抵抗低減,OS1 流れの抵抗抵減,オーガナイズドセッション)

Direct numerical simulation of a zero-pressure gradient drag-reducing turbulent boundary layer of viscoelastic fluids was performed at the momentum-thickness Reynolds number Re_θ_0=500 and Weissenberg number We=25 using constitutive equation models such as the Oldroyd-B, Giesekus (the mobility factor α=0.01, 0.001, 0.0001) and FENE-P models (the extensibility parameter L^2=100, 1000, 10000). It was found that the maximum drag reduction ratio DR(= 45%) for the Giesekus model with α=0.0001 was the largest. In the case of the same elongational viscosity, the drag reduction ratio for the Giesekus model is larger than that for the FENE-P model.

An orthogonal-plane PIV technique for the investigations of three-dimensional vortical structures in a turbulent boundary layer flow

An experimental investigation was carried out regarding a three-dimensional topology of a zero-pressure gradient turbulent boundary layer. In this study, the polarization separation technique has been applied to the PIV measurements. Two mutually perpendicular measurement planes have been employed in x–y and x–z planes, respectively. Synchronization between a stereoscopic PIV with another plane PIV system was made toward the detection of such salient features of the coherent structure as the legs and the head of the hairpin vortices. Polarization rotation via a half-waveplate and subsequent particle image separation using polarizer minimized the spurious particle images. The PIV results clearly demonstrate the presence of hairpin-like coherent vortical structures and coincidence between the near-wall quasi-streamwise vortex pair and the legs of the hairpin vortex.

The Effects of Splitter Plates on Turbulent Boundary Layer Developing on a Flat Plate near the Trailing Edge

An experimental investigation has been made for a turbulent boundary layer near the trailing edge on a long flat plate. The flow was controlled by an additional splitter plate fitted to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from a half, to five times the trailing edge thickness, h. Measurements of base pressure behind the trailing edge and of mean velocity and pressure distribution in the turbulent boundary layer on the flat plate were made under the freestream zero-pressure gradient. The absolute value of base pressure coefficient of the long flat plate was considerably smaller than that of the short flat plate (bluff body) without splitter plate (l/h=0). A significant increase in the normalized base pressure coefficient (about 50% as same as short one) was achieved with the splitter plate (l/h≥1) fitted to the long flat plate. Within an inner layer in the turbulent boundary layer near the trailing edge, mean velocity increased than that in the upstream position, especially in the case without splitter plate. With splitter plate, however, the base pressure rise made mean velocity distribution come closer to that of fully developed turbulent boundary layer. In the case of l/h≥1, the affected range of acceleration decreased from 10 h upstream of the trailing edge without splitter plate to 5 h upstream.

An experimental and numerical investigation of drag reduction in a turbulent boundary layer using a rigid rodlike polymer

The drag reduction in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) using a rigid rodlike polymer was experimentally and numerically investigated. Using injection of the rigid polysaccharide scleroglucan, drag reductions of approximately 10–15 % were observed, with three distinct drag reduction regimes: a non-Newtonian flow region near the injector, followed by a region of nearly constant drag reduction, and finally a region of negligible drag reduction. Decreasing the effective rotary Peclét number reduced the drag reduction effectiveness. Increasing the concentration did not improve the drag reduction, but instead shifted the spatial development of the drag reduction further downstream. A complementary direct numerical simulation of the ZPG TBL using the rigid rod constitutive equation was performed at a matching inlet Reynolds number. The simulation assumed a homogeneous concentration distribution and used estimated effective parameters for the rodlike additive. Spatial evolution of the fiber stresses is rapid and develops asynchronously with the flow structure. The simulated turbulence statistics and experimental measurements at a position 23 boundary layer thicknesses downstream compare favorably, with the primary differences due to the concentration distribution assumed in the simulation.

Self-similar profile of probability density functions in zero-pressure gradient turbulent boundary layers

The probability density function (pdf) of a streamwise velocity component is studied in zero-pressure gradient boundary layers. From analyzing the data up to R θ ≃ 13 , 000 , it is found that pdfs have self-similar profiles ranging from y + ≃ 180 to 0.049 Δ + , where Δ is Rotta–Clauser boundary layer thickness. Pdf profiles asymptote to the universal shape very close to the Gaussian, but are positively skewed at the core region, indicating smaller values in the tail parts. Based on this experimental fact, the mean velocity profile is reconsidered from the standpoint of pdf equation. The log-law profile is expected as the mean velocity distribution. The Kármán constant is evaluated to be 0.38, and the log-region starts at y s + = 180 and ends at y r + = 0.021 Δ + + 96.5 for R θ > 4000 . The end point locates in 0.15 δ + ⩽ y r + ⩽ 0.2 δ + . The relation to the new scaling law derived from Lie-group theory is also discussed.

Velocity measurement in turbulent boundary layer of drag-reducing surfactant solution

The influence of a drag-reducing surfactant on a zero-pressure gradient turbulent boundary layer was investigated using a two-component laser-Doppler velocimetry system. It was discovered that the streamwise turbulence intensity has a maximum near the center of the boundary layer in addition to the near-wall maximum which appears in canonical wall-bounded turbulent flow. At the location of the additional maximum, the Reynolds shear stress has a slight maximum, the skewness factor of streamwise turbulent fluctuation is zero, and the flatness factor has a minimum.

Calculation of Turbulent Boundary Layers Using Equilibrium Thermal Wakes

The combined thermal law of the wall and wake is used as the approximating sequence for the boundary layer temperature profile to solve an integral thermal energy equation for the local Stanton number distribution. The velocity profile in the turbulent boundary layer was taken to be the combined law of the wall and wake of Coles. This allows the solution of an integral form of the x-momentum equation to give the skin friction coefficient distribution. This, along with the velocity profile, is used to solve the thermal energy equation using inner coordinates. The strength of the thermal wake was found by analysis of earlier research results, in the literature, for equilibrium, constant property, turbulent boundary layers. Solutions for the Stanton number distribution with position are found for some adverse pressure gradient boundary layers as well as for those having zero pressure gradient. The zero pressure gradient results cover both fully heated plates and those with unheated starting lengths, including both isothermal surfaces and constant flux surfaces. Comparison of predictions of the present work is made with experimental data in the literature.

Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows

This paper investigates the idea that each Reynolds stress has its own velocity scale – the mean shear stress cannot provide a velocity scale for the near-wall turbulence near reattachment, for example, and cannot by definition provide a velocity scale for ‘inactive’ motion. Beneath a separation bubble, the tangential velocity fluctuations scale on the r.m.s. of the respective wall shear stress fluctuation and on v / y , which is the viscous velocity scale in the usual way, independent of the other flow. This paper also shows that the wall-normal direct stress and the shear stress have respective, independent velocity scales. Moreover, and quite remarkably, the scaling functions for these latter stresses appear to be universal in that they are unchanged for the boundary layer upstream of separation or downstream of reattachment, and are as in the canonical zero-pressure gradient boundary layer. The streamwise direct stress does not exhibit this universality, raising questions about the near wall structures: it is inferred that the change in form is associated with the disappearance and reappearance of the streak-like structures.

Investigation into clustering of synthetic jet actuators for flow separation control applications

AbstractAn investigation into the behaviour of clustered synthetic jet Actuators for flow-control applications is described. Experiments have been undertaken with two small-scale synthetic jet actuators in a zero-pressure gradient boundary-layer, in order to investigate the effect of configuration yaw angle and relative input signal phase. Oil-flow visualisation and hotwire anemometry techniques were used, demonstrating that changes in the downstream flow structure could be observed. Compared to a streamwise configuration, in which a symmetrical counter-rotating vortex pair was produced by the synthetic jet-boundary-layer interaction, a broader asymmetric interaction was produced in a 15° yaw configuration. Streamwise velocity contour plots, illustrating the development of the interaction downstream, over four phase angles, were presented. Significant differences in the PSD analyses of downstream streamwise velocity time histories were found, suggesting that input signal phase could influence the stability and hence effectiveness of flow structures used in flow-control applications.

Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.

A miniature laser-Doppler velocimeter for simultaneous three-velocity-component measurements

A miniature laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements. The probe has been tested in a zero-pressure gradient two-dimensional turbulent boundary layer and the results agree well with earlier data and several DNS data sets. The overall size of the probe is 23.3 mm × 8.7 mm × 90.6 mm and measurement spatial resolution is 50 µm. The probe volume can be traversed 32 mm vertically. The lightweight and compact design of the LDV probe head allows the probe head to be embedded inside models and machinery for three-dimensional turbulent flow measurements where larger probes are unusable.