Skin Friction Field Research Articles

Self-similarity of obliquely impinging jet heat flux fields in a range of Mach numbers from 0.1 to 1.0

This study reveals self-similarity (Mach-number-invariance) of the normalized time-averaged surface heat flux fields measured using temperature sensitive paint (TSP) in an obliquely impinging jet in a range of the nozzle exit Mach numbers from 0.1 to 1.0. Further, this self-similarity is also found in the normalized root-mean-square (RMS) fields of the heat flux fluctuation and the normalized skin friction fields extracted from the surface temperature and heat flux fields. To elucidate the origin of this self-similarity, a semi-empirical model is proposed for the maximum surface temperature difference used for normalization, indicating that the Mach number effect on the impinging jet heat transfer is mainly represented by the recovery temperature at the impingement point.

Stochastic numerical computing for hydro-magnetic flow of Carreau-nanofluid model

This study focused on mass and heat transport in a time-dependent hydro-magnetic Carreau-nanofluid flow model (HF-CNM) over a radially stretched surface. The impacts of Brownian motion and thermophoresis on the fluid are analyzed through Buongiorno’s model. Using similarity transformation, the model’s controlling nonlinear PDEs are transformed into ODEs. These ODEs are utilized to get datasets using the Homotopy analysis methodology (HAM). By implementing Intelligent Backpropagation Networks with the Levenberg Marquardt scheme (IBPNs-LMS), the reference datasets are divided into testing, training, and validation to calculate and analyze the solution of HF-CNM. The performance analysis of the proposed IBPNs-LMS approach is validated by the MSE representation, the histogram of error, regression analysis, and transition measurements. Moreover, the effects of various variables such as magnetic parameter (M), local Weisenberg number (We), thermophoresis parameter (Nt), Brownian number (Nb), Eckert number (Ec), unsteadiness parameter (A), Schmidt number (Sc), chemical reaction parameter () and Power-law index (n) on velocity, skin friction, temperature, Nusslet number and concentration field are also investigated. Results reveal the velocity field declined as the values of We and M decreased, and the thickness of the velocity boundary layer is decreasing as well. The temperature field rises by increasing the values of Nb and Nt.

The Transportation of Maxwell Fluid in the Rotating and Stretching System: Rotor-Stator Spinning Disc Reactor Applications

We have developed a mathematical model and obtained a numerical solution for the motion of a non-Newtonian Maxwell fluid between two disks having rotation and stretching velocity with convective boundary constraints, porous medium and thermal radiation. The present Maxwell fluid flow model with specified boundary constraints is not discussed so far. The proposed model has a lot of applications in electrical power generation, nuclear energy plants, astrophysical flows, space vehicles, geothermal extractions, and spinning disc reactor. The Von Karman similarity approach is used for the solution and validation of the solution is also provided. The solution is obtained numerically with finite difference method (FDM) based ND-solve command in Mathematica software. The effects of magnetic field, porous medium, radiation parameter, Deborah number, Prandtl number, and Reynolds number on skin friction, heat transfer, flow and temperature fields are discussed in detail. Due to the significant void fraction in the medium, porosity parameter shows unique trend compared to other parameters for the radial velocity profile. It has tendency to enhance the radial velocity near both the disc but in the middle part of system, porosity parameter retards radial velocity significantly.

Heat transfer and skin friction: Beyond the Reynolds analogy

This paper describes a variational method to determine a high-resolution skin friction field from a measured surface temperature field based on the exact relation between skin friction, surface temperature and heat flux in viscous flows. The focus is the application of this method to complex three-dimensional flows to explore the intrinsic relationship between skin friction and heat transfer beyond the Reynolds analogy. Further, the underlying condition for establishing the Reynolds analogy is examined in this general theoretical framework. Essentially, this method is considered as a global variational form of the Reynolds analogy. To demonstrate the application of this method, the skin friction fields are extracted from temperature sensitive paint measurements in normally and obliquely impinging jets, revealing complex flow structures in the impingement region where the Reynolds analogy does not hold.

APPLICATION OF TRADITIONAL OIL-FLOW-VISUALIZATION TECHNIQUE IN DETERMINING SKIN-FRICTION FIELDS ON AXISYMMETRIC AFTERBODY MODEL

This study evaluated the application of the traditional oil-flow-visualization technique in determining skin-friction fields for surface flow of an axisymmetric afterbody model at lowspeed conditions. Oil liquid, which was mixed of kerosene, titanium dioxide and oleic acid, was painted on the surface of model before experimental process. The movement of the oil was recorded by camera for data processing. The algorithm for extracting skin-friction fields was developed by the author and was validated. The method applied for boattail model. The results indicated that the traditional oil-flow-visualization technique provided sufficiently good outcomes for extracting skin-friction fields. Lagrange multiplier in range from 5 to 500 and number of selected pair images between 10 and 20 have a small effect on the skin-friction topology. The flow streamlines of the proposed method were also discussed detail in this study. Although the separation position was not captured well by the method, the reattachment position showed close results to previous observations. Consequently, the technique can be applied to analyze skin-friction fields of moving vehicles.

Visualization of Pressure and Skin-Friction Fields on Rotating Blade Under Low-Pressure Conditions

Distributions of the pressure and mass transfer coefficient on rotating blades under low-pressure (low-Reynolds-number) conditions were visualized, whereas the latter is closely related to the skin-friction distribution. Two types of optical measurement techniques, lifetime-based pressure-sensitive paint (PSP) measurements and sublimation visualization, were implemented for the experiment inside a low-pressure chamber. For the lifetime-based PSP measurement, different types of PSP were compared, and the one most suitable in low-pressure applications was selected. In addition, the gate time setting for the low-pressure condition was determined. For the sublimation method, naphthalene was selected as the sublimation surface based on previous studies. The rotating blade test model was a 0.3-m-diam rotor system with two rectangular blades with an aspect ratio of two. The experiments were carried out at a rotational speed of 2400 rpm and at an ambient pressure of 10 kPa. The three-fourth-span Reynolds number was 9000. The pitch angle of the blades was set to 0–20 deg. Both methods successfully illustrated clear images of the distribution of pressure and mass transfer coefficients on the upper surface of the blade, and the measurement in the low-pressure environment was successful.

Skin friction and surface optical flow in viscous flows

The relationship between skin friction and the surface optical flow (SOF) in viscous flows is discussed based on the evolution equations of surface temperature, scalar, and enstrophy, where the SOF is defined as the convection velocity of these quantities. It is found that the SOF is proportional to skin friction, which can be determined by solving the optical flow equation re-cast from these evolution equations. This optical flow method can be applied to surface temperature and mass transfer visualizations to extract skin friction fields in experiments. To examine this method, it is first applied to complex surface enstrophy structures obtained in direct numerical simulation data of a turbulent channel flow. Furthermore, it is applied to surface temperature structures obtained in time-resolved temperature sensitive paint measurements in a flow over a National Advisory Committee for Aeronautics (NACA) 0015 airfoil model and an impinging jet.

Influence of spacing of a delta-winglet vortex generator pair on the flow behavior and heat transfer at the internal tip of gas turbine blades

The hot erosion of turbine tip and the maintenance of tip reliability and service times have always been great challenges for researchers. This work presents a novel design of a tip wall with the internal surface fitted with delta-winglet vortex generator pairs (DVGP). Various spacing of DVGP is considered to study the influence of spacing on the internal tip heat transfer and flow behavior in the turn region of a serpentine cooling channel inside a blade. A smooth internal cooling channel is regarded as the Baseline. Five spacings of the leading edge of the DVGP, i.e., 0.03Dh(hydraulic diameter), 0.07Dh, 0.13Dh, 0.2Dh, 0.27Dh, respectively, are considered. Topological analysis in the skin friction field is introduced to better illustrate the 3D fluid flow. The inlet Reynolds number is set in the range of 10,000 to 50,000. Results show that the variation of the spacing between the DVGPs has a remarkable influence on the thermal performance of the internal blade tip. The heat transfer on each side of the DVGP is weakened increaseing spacing, which is caused by the movement of the attachment line on the surface of the DVGP and the weakening of the vortex energy. The optimal thermal performance appears for the narrow spacing (0.03Dh) of the leading edge of the DVGP, and the heat transfer augmentation is approximately 7.90% compared with the two-pass channel with a smooth tip. The delta-winglet vortex generator arranged narrowly on the internal tip is aimed for enhancement of heat transfer. The analysis and results of this work are beneficial to the tip design of internal passages in gas turbine blades.

Application of Optical Measurement for Skin Friction Field around Tires of a Simplified Vehicle Model

The objective of this study is to apply the Global Luminescent Oil-Film Skin-Friction (GLOF) meter, which optically observes the skin friction vectors on the object surface, to reveal the fluid structure around the wheelhouse. The image analysis results show characteristic longitudinal vortices on the side surface of the front wheel and the wheelhouse. In contrast, the separation line at the rear end of the side near the rear wheelhouse is curved significantly upstream, and the separation area expands in the lower half of the rear end, probably due to the suction flow generated between the wheel and the wheelhouse.

Features of surface physical quantities and temporal-spatial evolution of wall-normal enstrophy flux in wall-bounded flows

This paper presents a concise derivation of the temporal-spatial evolution equation of the wall-normal enstrophy flux on a no-slip flat wall. Each contribution to the evolution is explicitly expressed using the two fundamental surface quantities: skin friction (or equivalently surface vorticity) and surface pressure which are coupled through the boundary enstrophy flux (BEF). The newly derived relation is then used to explore, in a preliminary manner, the physical features of surface quantities and their dynamical roles in wall-bounded laminar and turbulent flows. It is confirmed that the BEF usually changes its sign near the separation and attachment lines in the skin friction field. For the simulated incompressible turbulent channel flow at Reτ=180, violent variations of different terms in the derived formulation are observed in the regions below the strong wall-normal velocity events (SWNVEs) when compared to other common regions. Near the SWNVEs, the evolution of the wall-normal enstrophy flux is found to be dominated by the wall-normal diffusion of the vortex stretching term which is relatively weak or negligible for laminar flows. Combined with our previous research results, it is conjectured that the strong interaction between the quasi-streamwise vortex and the channel wall intensifies the temporal-spatial evolution of the wall-normal enstrophy flux on the wall, which accounts for the highly intermittent feature of the viscous sublayer.

Experimental Study of the Skin-Friction Topology Around the Ahmed Body in Cross-Wind Conditions

Abstract In this study, skin friction around a ½-scale Ahmed body was measured experimentally at a Reynolds number of Re = 2 × 105. The slant angle of the Ahmed body was 25 deg, and the yaw angles ranged from 0 deg to 8 deg. This study focused on the flow structure on the slant surface under different cross-wind conditions. A force balance system was applied to measure the aerodynamic drag of the model. The global skin-friction topology was measured by applying a luminescent oil layer with a subgrid data processing algorithm. The method used to measure the skin friction was conducted for the first time on the Ahmed body. The results indicated that the technique is highly capable of extracting the skin-friction topology. For a yaw angle below 3 deg, the flow on the slant surface was not significantly affected by the cross-wind condition, and the drag of the model was nearly constant. However, at yaw angles above 3 deg, the flow on the slant surface was highly affected by the roof longitudinal vortexes on the windward side, leading to a dramatic increase in the drag of the model. High consistency in the drag and skin-friction fields was observed. The detailed skin-friction structure at different yaw angles will be discussed in this study.

Temperature and skin-friction maps on a lifting hydrofoil in a propeller wake

There are at least two direct links between the friction acting on the surface of a (slightly warmer or colder) body under the influence of an incompressible flow and the temperature distribution on the surface of the body itself. The first relies on the energy equation, which connects the evolution of the temperature distribution at the wall to the action of the skin-friction field. On the other hand, the equation of passive transport of temperature perturbations at the wall unveils a direct relationship between the celerity of propagation of thermal blobs and the friction velocity. Grounding on these relationships, this paper reports about the application of different methodologies, developed to determine skin-friction fields from surface temperature maps, to the analysis of the complex flow evolution on a lifting NACA 0015 hydrofoil immersed in a non-uniform, unsteady wake induced by a marine propeller. The adopted temperature-sensitive paint technique allows obtaining the global temperature data with the appropriate, high resolution in space and time. The approach based on the energy equation leads to an unconventional, single-snapshots optical-flow-like methodology, which allows obtaining time-resolved, relative skin-friction fields. The two approaches based on the displacement of the wall temperature perturbations enable the determination of time- and phase-averaged, quantitative skin-friction fields. One approach grounds on a classical tracking of the thermal disturbances via optical flow, the other one relies on minimizing the discrepancy between the celerity of propagation of thermal fluctuations and the behavior expected according to the Taylor hypothesis. The analysis of the skin-friction fields obtained via the three uncorrelated, complementary approaches discloses the evolution and the mutual interaction of different flow structures (manifolds) over the hydrofoil surface at lifting and zero-lift conditions: the hub and tip vortices, the blade wake, the laminar separation bubble, and the separation at trailing edge.

Skin Friction Extracted from Surface Pressure in Incident Shock-Wave/Boundary-Layer Interaction

High-resolution skin-friction fields are extracted from pressure-sensitive paint (PSP) data obtained in shock-wave/boundary-layer interaction (SWBLI). The method of extracting skin friction from surface pressure is described, including the fundamental relation between skin friction and surface pressure, the variational method, error analysis, and an approximate iterative method. The proposed method is based on a coupling relation between skin friction and surface pressure, where the boundary enstrophy flux is suitably modeled or approximated. This method is applied to unsteady PSP data obtained in incident SWBLIs at Mach 2.5 for different Reynolds numbers, revealing the skin-friction structures of the flows: particularly, the separation bubble induced by the incident shock wave. The extracted results are in good agreement with the data obtained by the surface-stress-sensitive film.

Application of the temperature-sensitive paint method for quantitative measurements in water

In this paper the characteristics of a Europium-based temperature-sensitive paint (TSP) in polyurethane (PUR) clear coat submerged in water are investigated. It is shown that the temperature sensitivity is not affected by water. However, the optical transmission of the PUR is reduced, which reduces the measurable emission of the TSP. Furthermore, a TSP measurement in the laminar water channel at the Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, was set up. In this experiment the skin friction field for two types of roughness elements, i.e. a truncated cylinder and an array of cuboids, in a Blasius-like boundary layer is investigated. Additionally, the temperature field was recorded with sub-millimeter resolution while an artificial heat flux was applied. A modification of the Colburn analogy is used to derive the skin friction from the temperature measurement. Skin friction results derived from velocity measurements are in good agreement with the TSP results. The experimental setup provides a resolution of the temperature and skin friction measurement of K and N m−2 ( skin friction of the undisturbed flow), respectively. Additionally the uncertainty of the temperature and skin friction measurement is analyzed.

Feasibility of skin-friction field measurements in a transonic wind tunnel using a global luminescent oil film

The feasibility of skin-friction field measurements using the global luminescent oil-film skin-friction field estimation method was evaluated for a challenging case of a supercritical airfoil model under transonic wind-tunnel conditions (freestream Mach number of 0.72) at a high Reynolds number (10 million, based on the model chord length). The oil-film thickness and skin-friction coefficient distributions were estimated over the airfoil model upper surface for a range of angles of attack (from -0.4^{circ } to 2.0^{circ }), thus enabling the study of different boundary-layer stability situations with laminar–turbulent transition, including cases with shock-wave/boundary-layer interaction. Conventional pressure measurements on the surface and in the wake of the model as well as Schlieren flow visualizations were conducted to support the oil-film based investigations. In the laminar-flow regions, the oil-film thickness could be generally kept below the critical limit of roughness that would induce premature boundary-layer transition. The skin friction in this region could be estimated with a moderate confidence level, as confirmed for portions of the chord by the reasonable agreement with numerical data obtained via laminar boundary-layer computations. Moreover, the location of transition onset was evaluated from the skin-friction estimations with relatively low uncertainty, thus enabling the examination of the transition location evolution with varying angle of attack. The estimated locations of transition onset were shown to be in general agreement with reference transition locations measured via temperature-sensitive paint. On the other hand, the oil-film thickness in the turbulent-flow regions was larger than the height of the viscous sublayer, which led to an hydraulically rough surface with increased skin friction, as compared to the clean configuration. For this reason, quantitative skin-friction estimations were not feasible in the turbulent-flow regions. The global effects of the oil-film setup on the flow around the airfoil were evaluated from the estimations of the aerodynamic coefficients. In particular, it was shown that the presence of the specific base coat used for the application of the oil film already induced a significant increase in airfoil drag, as compared to the clean configuration, whereas a thin oil film led to negligible or small additional increases in drag. Based on the present observations, considerations for the further improvement of the global luminescent oil-film skin-friction field estimation method in transonic flow experiments at high Reynolds numbers are elucidated.Graphic abstract

Evaluating the applicability of a phase-averaged processing of skin-friction field measurement using an optical flow method

The phase-averaged skin-friction analysis based on global luminescent oil film (GLOF) was conducted for periodically fluctuating unsteady phenomena at the frequency of approximately 150 Hz which is estimated based on Karman vortex shedding. An unsteady pressure transducer and a camera were synchronized, and the time-averaged and phase-averaged skin-friction fields were investigated. The time-series image pair data obtained by the camera were decomposed into eight intervals of a phase angle of $$\pi /4$$ with synchronizing the signal of the unsteady pressure. The phase-averaged result shows the periodical pattern corresponding to the vortices structure generated from the edge of the test model which was not resolved by the time-averaged result. The phase-averaged processing was successfully applied to the GLOF measurement, and the results showed the detail information of skin friction at each phase.

Unsteady skin-friction field estimation based on global luminescent oil-film image analysis

A global luminescent oil-film (GLOF) image analysis method to estimate unsteady skin-friction fields in an unsteady flow field is proposed and demonstrated. A governing equation describing the dynamics of the oil film (the thin-oil-film equation) is employed for the unsteady oil-film images. The frequency response of the oil-film movement is analyzed, and a cutoff frequency is defined as a function of the oil-film thickness and the kinematic oil viscosity. The estimating skin-friction vector is defined along with a spatiotemporal weighted window and obtained by solving the overdetermined system of the thin-oil-film equation. The system can be solved by using the weighted linear least-squares method, and the time-resolved skin-friction field can be estimated. The time-resolved GLOF image analysis method is demonstrated on an experiment of a junction flow on a flat surface with a square cylinder. The GLOF images in the Karman vortex shedding bounding the flat surface were acquired, and the time-resolved skin-friction fields were obtained. The results showed that fluctuation in the skin-friction vectors corresponds to the shedding frequency, and the vortices bounding the surface were extracted. The averaged skin-friction field is compared with the result of the previous study based on the time-independent model. The normalized skin friction from both methods showed good agreement, which indicates that the quantitative value will be obtained when a calibration process is involved in a future study.

Prediction and Analysis of the Aerodynamic Characteristics of a Spinning Projectile Based on Computational Fluid Dynamics

Numerical simulations of a spinning projectile with a diameter of 120 mm were conducted to predict the aerodynamic coefficients, and the CFD results were compared with the semiempirical method, PRODAS. Six coefficients or coefficient derivatives, including zero and the quadratic drag coefficient, lift force coefficient derivative, Magnus force coefficient derivative, overturning moment coefficient, and spinning damping moment coefficient, which are important parameters for solving the equations of motion of the spinning projectile, were investigated. Additionally, the nonlinear behavior of these coefficients and coefficient derivatives were analyzed through the predicted flow fields. The considered Mach number ranges from 0.14 to 1.2, and the nondimensional spinning rate (PD/2V) is set to 0.186. To calculate the coefficient derivative of the corresponding force or moment, additional simulations were conducted at the angle of attack of 2.5 degrees. The simulation results were able to predict nonlinear behavior, the especially abrupt change of the predicted coefficients and derivatives at the transonic Mach number, 0.95. The simulation results, including the skin friction, pressure, and velocity field, allow the characterization of the nonlinear behavior of the aerodynamic coefficients, thus, enabling better predictions of projectile trajectories.

Validation and uncertainty analysis of global luminescent oil-film skin-friction field measurement

Results from a skin-friction-field measurement method using global luminescent oil-film images, in which the oil film covers a large portion of the surface, were examined by comparing them with those obtained from conventional hot-wire measurements. The measurement processes including calibrations, oil-film image acquisition, and image processing are explained, and error sources are analyzed. The experimental results show that the skin frictions measured by both methods in a turbulent boundary layer on a flat surface agree when the oil-film thickness is less than the height of the viscous sublayer (corresponding to an oil-film thickness of less than five wall units). The uncertainty of the measurements is presented. When the measurement conditions were optimum (illumination, exposure time, frame rate, oil height, etc), the uncertainty was approximately 3%–4%.

Self-similarity of surface heat transfer fields on a pre-heated rectangular plate in an obliquely impinging sonic jet

This paper presents an experimental study of the time-dependent surface temperature, heat flux and Nusselt number fields on a pre-heated, rectangular aluminum plate due to an obliquely impinging sonic jet at different total pressures. Surface temperatures are measured by detecting the luminescent emission from temperature sensitive paint. An analytical inverse solution of the one-dimensional time-dependent heat conduction equation is used to determine the heat flux from the temperature measurements. When normalized, the ensemble-averaged heat transfer fields (surface temperature, heat flux and Nusselt number) exhibit self-similarity (time-invariance) for different test conditions and therefore are found to exhibit a somewhat universal nature. A theoretical description of the self-similar behavior is presented for scaling experimental heat transfer data. Furthermore, the skin friction fields extracted from surface temperature and heat flux fields reveal generic topological structures of the flows.