Skin Friction Field Research Articles

Chaotic mixing in crystalline granular media

We study the Lagrangian kinematics of steady three-dimensional Stokes flow over simple cubic (SC) and body-centred cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing in these crystalline structures. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media, such as open pore networks, with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices posses the same symmetry point group, these differences are explained in terms of their space groups. This insight is used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation. These results point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

Conditionally averaged flow topology about a critical point pair in the skin friction field of pipe flows using direct numerical simulations

It has recently been shown that critical points in the skin friction field of wall turbulence exist and negative streamwise skin friction events occur. Further analysis of the critical points at the wall using direct numerical simulation data of turbulent pipe flow is presented here. After identifying and characterizing features of the no-slip critical points in a turbulent pipe flow, conditional averages of the flow are presented to reveal the magnitude and extent of the fluctuations in the flow around these extreme events. It is found that the velocity and skin friction fields near critical points resemble the three-dimensional U separation proposed by Perry and Chong [J. Fluid Mech. 173, 207 (1986)JFLSA70022-112010.1017/S0022112086001143].

Effect of boattail angles on the flow pattern on an axisymmetric afterbody surface at low speed

The surface flow pattern over a conical boattail on an axisymmetric body was investigated experimentally under low-speed and turbulent-boundary-layer conditions. Seven conical boattails with the same length but different angles from 10° to 22° were tested at a Reynolds number around 4.3 × 104, based on the model diameter. The study used the global luminescent oil-film (GLOF) skin friction measurement technique. The skin friction fields were measured and the corresponding flow topologies were extracted from the GLOF measurements. The effect of oil-film thickness on the separation position was also evaluated. Experimental results showed three different flow types on the boattail surface: (1) flow without separation, (2) flow with a separation bubble, and (3) fully separated flow. The critical angles for the transitions are discussed and compared with classic results for similar boattail models. The separation bubble generated at moderate boattail angles was observed for what we believe to be the first time under low-speed conditions, and the flow topology was clearly shown by the GLOF results. The azimuthally-averaged skin friction projected on the centerline showed different trends inside and behind the reattachment position when the boattail angle increased.

Linear least-squares method for global luminescent oil film skin friction field analysis.

A data analysis method based on the linear least-squares (LLS) method was developed for the extraction of high-resolution skin friction fields from global luminescent oil film (GLOF) visualization images of a surface in an aerodynamic flow. In this method, the oil film thickness distribution and its spatiotemporal development are measured by detecting the luminescence intensity of the thin oil film. From the resulting set of GLOF images, the thin oil film equation is solved to obtain an ensemble-averaged (steady) skin friction field as an inverse problem. In this paper, the formulation of a discrete linear system of equations for the LLS method is described, and an error analysis is given to identify the main error sources and the relevant parameters. Simulations were conducted to evaluate the accuracy of the LLS method and the effects of the image patterns, image noise, and sample numbers on the results in comparison with the previous snapshot-solution-averaging (SSA) method. An experimental case is shown to enable the comparison of the results obtained using conventional oil flow visualization and those obtained using both the LLS and SSA methods. The overall results show that the LLS method is more reliable than the SSA method and the LLS method can yield a more detailed skin friction topology in an objective way.

Effect of Jet Oscillation on the Maximum Impingement Plate Skin Friction

The maximum impingement plate skin friction and flow field is measured for an acoustically forced planar impinging gas jet using oil film interferometry (OFI) and particle image velocimetry (PIV), respectively. The study is performed at a jet Reynolds number of Rejet = 11,000 and an impingement distance H, which is set to eight times the nozzle width W. The planar impinging gas jet is forced at the jet nozzle exit using Strouhal numbers StH = 0.39, 0.76, and 1.1, which are similar to those associated with the jet-plate tones measured in air-knife wiping experiments. The flow-field measurements indicate that the jet column oscillates at the applied forcing frequency, and depending on the forcing frequency, organized vortex structures can be identified in the shear layers that impinge on the plate surface. Both of these jet oscillation features result in a reduction in the time-averaged maximum impingement plate skin friction. This skin friction reduction is attributed to momentum loss at the jet centerline caused by increased levels of fluid entrainment and mixing of the surrounding quiescent fluid.

The Maximum Skin Friction and Flow Field of a Planar Impinging Gas Jet

The maximum skin friction and flow field are experimentally measured on a planar impinging gas jet using oil film interferometry (OFI) and particle image velocimetry (PIV), respectively. A jet nozzle width of W = 15 mm, impingement ratios H/W = 4, 6, 8, 10, and a range of jet Reynolds numbers Rejet = 11,000–40,000 are tested to provide a parametric map of the maximum skin friction. The maximum skin friction predictions of Phares et al. (2000, “The Wall Shear Stress Produced by the Normal Impingement of a Jet on a Flat Surface,” J. Fluid Mech., 418, pp. 351–375) for plane jets agree within 5% of the current OFI results for H/W = 6, but deviates upward of 28% for other impingement ratios. The maximum skin friction is found to be less sensitive to changes in the impingement ratio when the jet standoff distance is roughly within the potential core length of the jet. PIV measurements show turbulence transition locations moving toward the nozzle exit with increasing Reynolds number, saturation in the downstream evolution of the maximum axial turbulence intensity before reaching a maximum peak upon impingement, followed by sudden damping at the plate surface. As the flow is redirected, there is an orthogonal redistribution of the fluctuating velocity components, and local peaks in both the axial and transverse turbulence intensity distributions at the plate locations of the maximum skin friction.

Global and local skin friction diagnostics from TSP surface patterns on an underwater cylinder in crossflow

A systematical method is formulated for extracting skin-friction fields from Temperature Sensitive Paint (TSP) images in the sense of time-averaging and phase-averaging. The method is applied to an underwater cylinder in crossflow at two subcritical regimes (Re = 72 000 and 144 000). TSP maps are decomposed in a time-averaged, a phase-averaged, and a random component. The asymptotic form of the energy equation at the wall provides an Euler-Lagrange equation set that is solved numerically to gain the relative skin friction time- and phase-averaged fields from the TSP surface temperature maps. The comparison of the time averaged relative skin-friction profiles with the literature data shows an excellent agreement on the whole laminar boundary layer up to the laminar separation line. Downstream of separation, time averaged results identify the secondary reattachment/separation events, which are lost in the available literature data. The periodic behavior of the skin-friction is taken, describing how the laminar separation bubble evolves by providing the time history of the laminar separation line and of the secondary reattachment/separation over the entire vortex shedding period. Instantaneous skin friction maps reveal the existence of coherent structures by capturing their footprint on the cylinder’s surface. An array of Π-shaped traces marks the existence of counter-rotating, streamwise-oriented vortices just before the laminar separation line. Their interaction with the laminar boundary layer and with the separation line is briefly described. An example of the intermittent excerpt of their influence through the laminar separation line is reported.

Feasibility of skin-friction diagnostics based on surface pressure gradient field

An intrinsic relation is given between the skin-friction vector and the surface pressure gradient through the boundary enstrophy flux (BEF), and it is used to study the possibility to extract some skin-friction structures from a surface pressure field. This attempt contains two related parts. In the first part, when the BEF field is given, a projected skin-friction field in the image plane can be sought from a surface pressure image based on a variational solution of an optical-flow-like equation. This approach is validated in several classical flows. The second part deals with a practical problem in which the BEF field is not known a priori. In this case, a so-called auxiliary skin-friction field is determined from a surface pressure image alone by using the same variational approach. The auxiliary skin-friction field has the magnitude proportional to the skin-friction magnitude and the direction of the negative surface pressure gradient. The physical meaning of the auxiliary skin-friction field and its applicability to global skin-friction diagnostics are discussed.

Phenomenology of a flow around a circular cylinder at sub-critical and critical Reynolds numbers

In this work, the flow around a circular cylinder is investigated at Reynolds numbers ranging from 79 000 up to 238 000 by means of a combined acquisition system based on Temperature Sensitive Paint (TSP) and particle velocimetry. The proposed setup allows simultaneous and time-resolved measurement of absolute temperature and relative skin friction fields onto the cylinder surface and near-wake velocity field. Combination of time-resolved surface measurements and planar near-field velocity data allows the investigation of the profound modifications undergone by the wall shear stress topology and its connections to the near-field structure as the flow regime travels from the sub-critical to the critical regime. Laminar boundary-layer separation, transition, and re-attachment are analyzed in the light of temperature, relative skin friction maps, and Reynolds stress fields bringing about a new perspective on the relationship between boundary layer development and shear layer evolution. The fast-responding TSP employed allows high acquisition frequency and calculation of power spectral density from surface data. Correlation maps of surface and near-wake data provide insight into the relationship between boundary-layer evolution and vortex shedding. We find that as the Reynolds number approaches the critical state, the separation line oscillations feature an increasingly weaker spectrum peak compared to the near-wake velocity spectrum. In the critical regime, separation line oscillations are strongly reduced and the correlation to the local vorticity undergoes an overall decrease giving evidence of modifications in the vortex shedding mechanism.

Role of critical points of the skin friction field in formation of plumes in thermal convection.

The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio Γ=1 and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of linelike thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian coherent structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincaré-Hopf index theorem for two-dimensional vector fields.

Effects of pitch, yaw, and roll on delta wing skin friction topology

High-resolution skin friction fields in separated flows over a 65° delta wing and a 76/40° double-delta wing with different junction fillets are obtained by using quantitative global skin friction diagnostics based on luminescent oil visualizations. The topological features such as separation and attachment lines on these delta wings are identified, and the effects of the pitch, yaw, and roll angles on the skin friction topology are studied systematically. The topological consistency of the measured skin friction fields on the delta wings is examined by using the Poincare–Bendixson index formula.

Skin Friction Fields and Surface Dye Patterns on Delta Wings in Water Flows

This paper discusses the relationship between skin friction fields and surface dye patterns in surface luminescent dye visualizations in water flows, providing a theoretical foundation for extraction of high-resolution skin friction fields. The limiting form of the mass diffusion equation at a wall is recast as an optical flow equation connecting skin friction with the luminescent dye intensity. Snapshot solutions are obtained from a time sequence of luminescent intensity images by solving the optical flow equation via the variational method, and then a normalized skin friction field is reconstructed by averaging the snapshot solutions. An error analysis is given to identify the major error sources and the limitations of the technique. To evaluate the feasibility of this technique, surface luminescent dye visualizations on a 65 deg delta wing and a 76/40 deg double-delta wing are conducted in a water tunnel. The extracted skin friction topology on the delta wings and the velocity fields obtained by using particle image velocimetry (PIV) are discussed.

Global Skin-Friction Diagnostics Based on Surface Mass-Transfer Visualizations

The theoretical foundations are formulated for extraction of skin-friction fields from surface mass-transfer visualizations with pressure-sensitive paint and sublimating coatings. The asymptotic form of the mass transport equation at a wall is expressed as the optical flow equation in the image plane. Then, a relative skin-friction field is obtained by solving the optical flow equation as an inverse problem via the variational method. For steady-state visualizations with pressure-sensitive paint and sublimating coatings, a relative skin-friction field can be obtained from a single normalized intensity image. Further, a superposition procedure of a snapshot solution and a variation solution associated with the unsteady effect is proposed to reconstruct an unsteady skin-friction field from a time sequence of pressure-sensitive paint visualization images. The capability of the proposed method is examined by applying it to pressure-sensitive paint visualizations in impinging nitrogen jets. This method is also used to extract skin-friction fields from sublimation visualization images on a delta wing in a low-speed flow and on a flat surface in fin shock/boundary-layer interaction at Mach 6. The skin-friction topology in these cases is revealed by using this method. In addition, the limitations of this method are discussed.

Skin-friction critical points in wall-bounded flows

Critical points in the skin friction field of wall-bounded ows were investigated using data from direct numerical simulations of channels at Reτ = 934 and Reτ = 1834. A method for their detection and characterisation is outlined, and a statistical description of their properties is reported. Their lifetime, average distance, velocity and area density were computed. Conditionally averaged fields were calculated in order to examine the average ow in the vicinity of a critical point. It was found that the critical points are connected to surprisingly large features in the channel. A mechanism for the generation of the critical points is postulated, based on the conditional averages and analysis of time sequences in the ow above them.

Extraction of skin-friction fields from surface flow visualizations as an inverse problem

Extraction of high-resolution skin-friction fields from surface flow visualization images as an inverse problem is discussed from a unified perspective. The surface flow visualizations used in this study are luminescent oil-film visualization and heat-transfer and mass-transfer visualizations with temperature- and pressure-sensitive paints (TSPs and PSPs). The theoretical foundations of these global methods are the thin-oil-film equation and the limiting forms of the energy- and mass-transport equations at a wall, which are projected onto the image plane to provide the relationships between a skin-friction field and the relevant quantities measured by using an imaging system. Since these equations can be re-cast in the same mathematical form as the optical flow equation, they can be solved by using the variational method in the image plane to extract relative or normalized skin-friction fields from images. Furthermore, in terms of instrumentation, essentially the same imaging system for measurements of luminescence can be used in these surface flow visualizations. Examples are given to demonstrate the applications of these methods in global skin-friction diagnostics of complex flows.

The topology of skin friction and surface vorticity fields in wall-bounded flows

In previous studies, the three invariants (P, Q and R) of the velocity gradient tensor have been widely used to investigate turbulent flow structures. For incompressible flows, the first invariant P is zero and the topology of turbulent flow structures can be investigated in terms of the second and third invariants, Q and R, respectively. However, all these three invariants are zero at a no-slip wall and can no longer be used to identify and study structures at the surface in any wall-bounded flow. An alternative scheme is presented here for the classification of critical points at a no-slip wall; the skin friction vector field at the wall is given by the wall normal gradients of the streamwise and spanwise velocity components; at a critical point, these gradients are simultaneously zero. The flow close to critical points in the surface skin friction field can be described by a no-slip Taylor series expansion and the topology of the critical point in the skin friction field is defined by the three invariants (, and ) of the ‘no-slip tensor’. Like the invariants of the velocity gradient tensor, the no-slip tensor invariants can be easily computed and these invariants provide a methodology for studying the structure of turbulence at the surface of a no-slip wall in any wall-bounded flow.

Feasibility of global skin friction diagnostics using temperature sensitive paint

This paper develops the principle of global skin friction diagnostics based on temperature sensitive paint (TSP) measurements in flows. The asymptotic form of the energy equation at a wall is derived, and its inverse solution is sought by using the variational method to extract a relative or normalized skin friction field from TSP-measured surface temperature fields. The selection of the relevant parameters (the Lagrange multiplier and the standard deviation of a Gaussian filter) and the intrinsic limitations of this method are discussed in the light of uncertainty analysis. Experimental implementation of this method is described, and the feasibility of TSP-based global skin friction diagnostics is examined in impinging jet experiments. The normalized skin friction distributions extracted by using this method are in fairly good agreement with hot-film skin friction measurements and the theoretical solutions in the normal and oblique impinging jets.

Skin friction topology in a region enclosed by penetrable boundary

High-resolution skin friction fields in separated flows on a low-aspect-ratio rectangular wing are obtained by using quantitative global skin friction diagnostics based on surface luminescent oil visualizations. The topological features like the isolated singular points and the boundary switch points in regions enclosed by penetrable boundaries are identified. The conservation law given by the Poincare–Bendixson index formula for the numbers of the isolated singular points and the boundary switch points is used as a general approach to analyze the topological structure of a skin friction field in a singly connected region enclosed by a penetrable boundary in the separated flows.

Effects of Thermal Diffusion and Chemical Reaction on MHD Flow of Dusty Visco-Elastic (Walter’s Liquid Model-B) Fluid

The present note consists, the effects of thermal diffusion and chemical reaction on MHD flow of dusty viscous incom-pressible, electrically conducting fluid between two vertical heated, porous, parallel plates with heat source/sink. The plate temperature is raised linearly with time and concentration level near the plate to Cw. The variable temperature and uniform mass diffusion taking into account the chemical reaction of first order. The series solution method is used to solve the mathematical equations. Effects of various parameters like chemical reaction (K), thermal diffusion (ST) and magnetic field (M) etc. on velocity profile, skin friction, concentration profile and temperature field are displayed graphically and discussed numerically for different physical parameters. The analysis developed here for thermal diffusion, bears good agreement with real life problems.

Deposition of micron liquid droplets on wall in impinging turbulent air jet

The fluid mechanics of the deposition of micron liquid (olive oil) droplets on a glass wall in an impinging turbulent air jet is studied experimentally. The spatial patterns of droplets deposited on a wall are measured by using luminescent oil visualization technique, and the statistical data of deposited droplets are obtained through microscopic imagery. Two distinct rings of droplets deposited on a wall are found, and the mechanisms of the formation of the inner and outer rings are investigated based on global diagnostics of velocity and skin friction fields. In particular, the intriguing effects of turbulence, including large-scale coherent vortices and small-scale random turbulence, on micron droplet deposition on a wall and coalescence in the air are explored.