Predicted Skin Friction Research Articles

Data-Guided Low-Reynolds-Number Corrections for Two-Equation Models

Abstract The baseline Launder–Spalding k−ε model cannot be integrated to the wall. This paper seeks to incorporate the entire law of the wall into the model while preserving the original k−ε framework structure. Our approach involves modifying the unclosed dissipation terms in the k and ε equations specifically within the wall layer according to direct numerical simulation (DNS) data. The resulting model effectively captures the mean flow characteristics in both the buffer layer and the logarithmic layer, resulting in robust predictions of skin friction for zero-pressure-gradient (ZPG) flat-plate boundary layers and plane channels. To further validate our formulation, we apply our model to boundary layers under varying pressure gradients, channels experiencing sudden deceleration, and flow over periodic hills, with highly favorable results. Although not the focus of this study, the methodology here applies equally to the k–ω formulation and yields improved predictions of the mean flow in the viscous sublayer and buffer layer.

Wall Modeling of Turbulent Flows with Varying Pressure Gradients Using Multi-Agent Reinforcement Learning

We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents receive off-wall environmental states, including pressure gradient and turbulence strain rate, ensuring adaptability to a wide range of flows characterized by pressure-gradient effects and separations. Based on these states, the agents determine an action to adjust the wall eddy viscosity and, consequently, the wall-shear stress. The model training is in situ with wall-modeled large-eddy simulation grid resolutions and does not rely on the instantaneous velocity fields from high-fidelity simulations. Throughout the training, the agents compute rewards from the relative error in the estimated wall-shear stress, which allows them to refine an optimal control policy that minimizes prediction errors. Employing this framework, wall models are trained for two distinct subgrid-scale models using low-Reynolds-number flow over periodic hills. These models are validated through simulations of flows over periodic hills at higher Reynolds numbers and flows over the Boeing Gaussian bump. The developed wall models successfully capture the acceleration and deceleration of wall-bounded turbulent flows under pressure gradients and outperform the equilibrium wall model in predicting skin friction.

Neural networks-based framework for recognizing streaming patterns in magnetized Maxwell–Oldroyd-B blood blended with tetra-hybrid nanoparticles and microbes over stenosis in an elastic artery

The proposed study delves into investigating blood flow patterns and thermal and solutal transport in an artery affected by stenosis. Specifically, it explores the behavior of blood ingrained with tetra-hybrid nanoparticles and gyrotactic microbes under magnetic effects. To capture the non-Newtonian nature of blood in such complex scenarios, the Maxwell-Oldroyd-B (MO) fluid model is employed. The pertinent nonlinear partial differential equations system accounts for similarity transformations and boundary layer assertions. Numerical results are assessed using a potent shooting approach with a fourth-order Runge–Kutta (RK4) method implemented through MATLAB’s bvp4c commands. The computational outcomes are visualized via graphical representation and tabulated data for in-depth analysis and illustration. The research yields significant insights into various model parameters. For instance, the Lorentz force is observed to exert a drag effect, hindering blood flow velocity, while the opposite trend is observed for blood temperature. Additionally, higher Peclet numbers correlate with reduced mass concentration levels, while gyrotactic microbes’ density profile exhibits an upsurge with elevated Lewis numbers. Notably, the Nusselt number for Newtonian blood is lower than MO blood, shedding light on the impact of blood properties on heat transport. Furthermore, this study proposes a technique based on artificial neural networks (ANNs) for accurately predicting skin friction coefficient, Nusselt number, Sherwood number, and microbes’ density number. The proposed algorithm achieves remarkable accuracy rates of 99.65% on the testing dataset and 99.99% during cross-validation for predicting the skin friction coefficient. The novel findings generated by this model hold promising implications for the treatment and monitoring of arterial diseases, as well as the development of cutting-edge medical devices and technologies.

Hypersonic turbulent boundary layer over the windward side of a lifting body

In the present study, we performed direct numerical simulations for a hypersonic turbulent boundary layer over the windward side of a lifting body, the HyTRV model, at Mach number $6$ and attack angle 2 $^{\circ }$ to investigate the global and local turbulent features, and evaluate its difference from canonical turbulent boundary layers. By scrutinizing the instantaneous and averaged flow fields, we found that the transverse curvature on the windward side of the HyTRV model induces the transverse opposing pressure gradients that push the flow on both sides towards the windward symmetry plane, yielding significant effects of the azimuthal inhomogeneity and large-scale cross-stream circulations, moderate and azimuthal independent influences of adverse pressure gradient, and negligible impact of the mean flow three-dimensionality. Further inspecting the local turbulent statistics, we identified that the mean and fluctuating velocity become increasingly similar to the highly decelerated turbulent boundary layers over flat plates in that the mean velocity deficit is enhanced, and the outer layer Reynolds stresses are amplified as it approaches the windward symmetry plane, and prove to be self-similar under the scaling of Wei & Knopp (J. Fluid Mech., vol. 958, 2023, A9) for adverse-pressure-gradient turbulent boundary layers. Conditionally averaged Reynolds stresses based on strong sweeping and ejection events demonstrated that the Kelvin–Helmholtz instability of the strong embedded shear layer induced by the large-scale cross-stream circulations is responsible for the turbulence amplification in the outer layer. The strong Reynolds analogy that relates the mean velocity and temperature was refined to incorporate the non-canonical effects, showing considerable improvements in the accuracy of such a formula. On the other hand, the temperature fluctuations are still transported passively, as indicated by their resemblance to the velocity. The conclusions obtained in the present study provide potentially profitable information for turbulent modelling modification for the accurate predictions of skin friction and wall heat transfer.

Effect of the yaw angle on the riblet performance

Direct numerical simulations are performed to investigate the effect of the yaw angle (α) on the drag-reduction performance by riblets in a turbulent channel flow. The yaw angles of α=0° and 90° correspond to the riblets parallel and perpendicular to the free-stream direction, respectively. It is well known that maximum drag reduction occurs at α=0°, and the drag-reduction performance by riblets is degraded with increasing α. We obtain the critical yaw angle below which drag reduction can be achieved and investigate the corresponding mechanism. From a parametric study, drag reductions are achieved for α<20°. As α increases, the form drag increases more rapidly than the skin-friction drag decreases, resulting in the increase in the total drag. At drag reducing and increasing yaw angles, the mean velocity profiles in wall units shift upward and downward, respectively, and the latter profile suggests that the drag-increasing riblet is similar to a rough surface. With increasing α, the wall-normal and spanwise velocity fluctuations and Reynolds shear stress increase, and stronger near-wall vortices are generated. By applying a scaling analysis to the momentum equation in the riblet-perpendicular direction and the FIK (Fukagata–Iwamoto–Kasagi) identity [Fukagata et al., “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73–L76 (2002); Peet and Sagaut, “Theoretical prediction of turbulent skin friction on geometrically complex surfaces,” Phys. Fluids 21, 105105 (2009); Bannier et al., “Riblet flow model based on an extended FIK identity,” Flow Turbul. Combust. 95, 351–376 (2015)] to the riblet-parallel direction, the total drag is expressed as a linear function of sin2α.

Mathematical modelling of HMT through porous stretching sheet using artificial neural network

The influence of heat radiation on HMT, MHD on a porous stretched sheet has been explained in this study. The governing PDEs are converted to ODEs via similarity transformations. The coefficient of skin friction, rate of HMT are calculated using the MATLAB software for various parameter values. The controlling boundary layer PDEs are turned into a system of coupled nonlinear ODEs via similarity techniques, which are numerically solved using the shooting technique in conjunction with the fourth order Runge Kutta method, and then ANN is applied to them. Validation of numerical results using ANN results. We discovered that using engineering standpoints, an ANN model may produce high-efficiency estimates for heat transfer rates. The achieved R squared values of 99% for predicting Skin friction, Nusselt number and Sherwood number coefficients highlight the remarkable effectiveness of neural network models in these predictions. This efficacy not only demonstrates the accuracy of the models but also results in a significant reduction in the computational time required compared to traditional numerical methods. Furthermore, when compared to alternative numerical approaches, the current ANN model stands out for its applicability to more complex mathematical models, because its efficiency in minimizing both time and processing capacity demands in solving such problems.

PREDICTING GEOTECHNICAL AXIAL CAPACITY OF REINFORCED CONCRETE DRIVEN PILE USING MACHINE LEARNING TECHNIQUE

Modified Meyerhof method is a popular method to calculate pile geotechnical axial capacity in Malaysia currently. From past experience, pile design based on empirical and analytical method produce variability of predicted capacity, in which, there is a wide scatter of predicted capacities and tendency for the predictions to be conservative, i.e. to underestimate the load capacity. This study provides options of machine learning and statistical approach for prediction of pile capacity based on soil investigation and dynamic pile load test result. It serves as an additional checking for engineer during design of pile based on conventional empirical method. It also helps to provide deeper insights of non-linear variables related to pile capacity through machine learning and statistical approach. This study helps engineer to design pile foundation optimally, economically and safely. The prediction of pile geotechnical axial capacity with machine learning technique and statistical approach for local marine clay soil in Penang, Malaysia is proposed in this study. The information from soil investigation report and dynamic pile load test report are gathered from six projects at Batu Kawan and Nibong Tebal located in Penang state that contributed 439 numbers of data. The skin friction factor, end bearing factor and pile geotechnical axial capacity are computed and predicted using empirical method, machine learning model and statistical model. Support Vector Machine illustrate best fit model for predicting skin friction factor with R2 of 0.517 while Random Forest seems to be the best fit model for predicting end bearing factor with R2 of 0.264. Random Forest is found to be the best model in predicting the geotechnical pile axial capacity compare to other models as it explains 96.2% of the variability of pile capacity.

Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness – a data-driven approach

Despite decades of research, a universal method for prediction of roughness-induced skin friction in a turbulent flow over an arbitrary rough surface is still elusive. The purpose of the present work is to examine two possibilities; first, predicting equivalent sand-grain roughness size $k_s$ based on the roughness height probability density function and power spectrum (PS) leveraging machine learning as a regression tool; and second, extracting information about relevance of different roughness scales to skin-friction drag by interpreting the output of the trained data-driven model. The model is an ensemble neural network (ENN) consisting of 50 deep neural networks. The data for the training of the model are obtained from direct numerical simulations (DNS) of turbulent flow in plane channels over 85 irregular multi-scale roughness samples at friction Reynolds number $Re_\tau =800$ . The 85 roughness samples are selected from a repository of 4200 samples, covering a wide parameter space, through an active learning (AL) framework. The selection is made in several iterations, based on the informativeness of samples in the repository, quantified by the variance of ENN predictions. This AL framework aims to maximize the generalizability of the predictions with a certain amount of data. This is examined using three different testing data sets with different types of roughness, including 21 surfaces from the literature. The model yields overall mean error 5 %–10 % on different testing data sets. Subsequently, a data interpretation technique, known as layer-wise relevance propagation, is applied to measure the contributions of different roughness wavelengths to the predicted $k_s$ . High-pass filtering is then applied to the roughness PS to exclude the wavenumbers identified as drag-irrelevant. The filtered rough surfaces are investigated using DNS, and it is demonstrated that despite significant impact of filtering on the roughness topographical appearance and statistics, the skin-friction coefficient of the original roughness is preserved successfully.

Analyze the Flow Behavior for MHD Power-Law Fluids

Objective: This study investigates the Numerical solution of laminar boundary layer flow of Magnetohydrodynamics (MHD) model for power-law fluid over a continuous moving surface in the presence of a transverse magnetic. Methods: The governing partial differential equation for the flow was transformed into non-linear ordinary differential equation using the Group theoretic method. Firstly, we convert this non-linear ordinary differential equation (ODE) into linear by using quasilinearization process. This linear ODE was solved numerically by applying the Spline collocation method suggested by Bickley. Findings: The solution for displacement profile and velocity profile were obtained as functions of the magnetic parameters. The effect of the magnetic parameters was discussed graphically. We used MATLAB software for finding the outcomes. Novelty: The main goal of this article is to analyze boundary layer flow of Magneto hydrodynamics (MHD) model for power-law fluid over a continuous moving surface in the presence of a transverse magnetic. The conservation equations of mass, momentum and energy are converted into ordinary differential equations along with boundary conditions by appropriate similarity transformations and solved by applying Spline Collocation Method. The convergence of solutions is important for providing the developing linear functions of solutions, which is a benefit of the Spline Collocation Method. These research findings are applicable, for example, in predicting skin friction and heat transfer rate over a stretching sheet, which has implications in technological and manufacturing industries such as polymer extrusion. Comparisons with previously published works are made, and the results show a high level of agreement. This type of research is applicable to work in fire dynamics in insulation, solar collection systems, recovery of petroleum products, etc. Keywords: Power-Law Fluids; Magnetic Field; Nonlinear Differential Equation; Quasilinearization; Bickley’s Method; Linear Equations

Heat transfer analysis in magnetohydrodynamic nanofluid flow induced by a rotating rough disk with non-Fourier heat flux: aspects of modified Maxwell-Bruggeman and Krieger-Dougherty models.

Non-Newtonian fluids have unique heat transfer properties compared to Newtonian fluids. The present study examines the flow of a Maxwell nanofluid across a rotating rough disk under the effect of a magnetic field. Furthermore, the Cattaneo-Christov heat flux model is adopted to explore heat transport features. In addition, a comparison of fluid flow without and with aggregation is performed. Using similarity variables, the governing partial differential equations are transformed into a system of ordinary differential equations, and this system is then solved by employing the Runge-Kutta Fehlberg fourth-fifth order method to obtain the numerical solution. Graphical depictions are used to examine the notable effects of various parameters on velocity and thermal profiles. The results reveal that an increase in the value of Deborah number decreases the velocity profile. An increase in the thermal relaxation time parameter decreases the thermal profile. An artificial neural network is employed to calculate the rate of heat transfer and surface drag force. The R values for skin friction and Nusselt number were computed. The results demonstrate that artificial neural networks accurately predicted skin friction and Nusselt number values.

Analysis of a higher-order vorticity confinement scheme in flux correction form

This article presents a detailed comparison of the classical source-term formulation of higher-order Vorticity Confinement with a flux-correction version, through an application to a series of well-documented cases. Both formulations and their numerical implementation are presented first. Then the methods are applied to the simple case of the long-time advection of an inviscid and isentropic vortex. A shock-vortex interaction case is also computed to demonstrate the compatibility of the method with the shock-capturing properties of the baseline scheme. Both methods are finally applied to a ZDES mode 3 (Wall-Modelled LES) simulation of a zero-pressure-gradient flat-plate turbulent boundary layer, showing a better preservation of smaller-scale vortical structures with respect to standard higher-order numerical schemes. Furthermore, the flux-correction form of Vorticity Confinement significantly improves the prediction of skin friction with respect to both the baseline scheme and the classical source-term formulation, thus showing that the flux-correction form of confinement is essential for a reliable prediction of this quantity.

Determination of Skin Friction Factor in Gravel Bed Rivers: Considering the Effect of Large-Scale Topographic Forms in Non-Uniform Flows

Determination of skin friction factor has been a controversial topic, particularly in gravel-bed rivers where total flow resistance is influenced by the existence of small-scale skin roughness and large-scale topographic forms. The accuracy of existing models predicting skin friction factors in conditions where small-scale skin roughness and large-scale topographic forms exist is very low. The objective of this study is to develop a modified model that improves the accuracy of the determination of skin friction factors in gravel-bed rivers. To this end, 100 velocity profile data obtained from eight gravel-bed rivers were utilized to develop an analytical method that considers the momentum thickness of the boundary layer and its deviation in large-scale topographic bedforms in a 1D force-balance model. The results show that the accuracy of the skin friction factors is enhanced when (1) the model is in the form of an exponential function of energy slope, and (2) the deviation of momentum thickness is considered in the model. The proposed model results in high accuracy of the predicted skin friction factors for energy slopes between 0.001 and 0.1, which exist in most gravel-bed rivers with different morphologies. Additionally, this study model was used to modify the classic Einstein–Strickler equation. The modified equation resulted in improved accuracy of the predicted skin friction factors in non-uniform flow conditions even when velocity profiles and energy slope were not available.

Wall-Modeled Large Eddy Simulation of High Speed Flows

The use of wall-modeled large-eddy simulation (WMLES) is explored in the context of compressible flows with a focus on cold-wall boundary layers and flows with shock-induced separation. It is observed that for cold-wall flows, a “mixed” scaling for the length scale appearing in the eddy viscosity formulation outperforms the classical semilocal scaling for obtaining predictions of heat flux and skin friction. A few shock/boundary-layer interaction (SBLI) cases are examined in some detail, and model modifications are proposed to overcome identified deficiencies. It is shown that using WMLES the low-frequency characteristics of SBLI at high Reynolds number can be quantitatively captured. A dynamically switched version of the equilibrium model is proposed; this shows promise for relatively inexpensive simulations at these conditions.

The importance of turbulent equilibrium for Reynolds-stress modeling

Turbulence equilibrium state is analyzed for the modeled Reynolds-stress transport equation, assuming the most general formulation of pressure–strain correlation. In a two-dimensional mean flow at a high-Reynolds number, an algebraic equation system is obtained, providing Reynolds-stress anisotropies as functions of pressure–strain model coefficients. Conversely, the equations provide calibration conditions for the model coefficients to predict specified equilibrium anisotropies. The predicted von-Kármán constant depends on the predicted equilibrium anisotropies and, hence, the pressure–strain model coefficients. Identical equilibrium anisotropies can be obtained with different sets of model coefficients. Identical equilibrium values of invariants of the Reynolds-stress anisotropy tensor can be achieved, despite the differing anisotropy components. Numerical simulations with the Speziale–Sarkar–Gatski (SSG) model, using different sets of model coefficients, confirm the results of the theoretical analysis. They show that the predicted equilibrium value of the Reynolds-shear stress anisotropy determines the predicted skin friction of a boundary layer as well as the predicted spreading rate of a plane mixing layer. However, different values and, hence, different sets of model coefficients are required for achieving good agreement with experimental data for both flows. Therefore, for general improvement of turbulence models, the set of model coefficients probably needs to be adapted to the local type of flow. The required classification is supposed to be suitable for machine learning methods.

Evaluation of the SU2 Open-Source Code for a Hypersonic Flow at Mach Number 5

This paper presents the evaluation of the Stanford University Unstructured (SU2) open-source computational software package for a high Mach number 5 flow. The test case selected is an impinging shock wave turbulent boundary layer interaction (SWTBLI) on a flat plate where the experimental data of Sch¨ulein et al. [27] is used for validation purposes. Two turbulence models, the Spalart–Allmaras (SA) and the k-ω Shear Stress Transport (SST) within the SU2 code are evaluated in this study. Flow parameters, such as skin friction, wall pressure distribution and boundary layer profiles are compared with experimental values. The results demonstrate the performance of the SU2 code at a high Mach number flow and highlight its limitations in predicting fluid flow physics. At higher shock generator angles, the discrepancy between experimental and CFD data is more significant. Within the interaction and flow separation zones, a smaller separation bubble and delayed separation are predicted by the SA model while the k-ω SST model predicts early separation. Both models are able to predict wall pressure distribution correctly within the experimental values. However, discrepancies were observed in the prediction of skin friction due to the inability of the models to capture the boundary layer recovery after shock impingement.

Data-driven model for improving wall-modeled large-eddy simulation of supersonic turbulent flows with separation

A machine learning algorithm is presented, serving as a data-driven modeling tool for wall-modeled large eddy simulations (WMLESs). The proposed model is formulated to address the problems of log layer mismatch and inaccurate prediction of skin friction, particularly for supersonic separated and reattached flows. This machine learning algorithm uses random forest regression to map the local mean flow fields to the discrepancies in the skin friction (heat flux) while complying with Galilean invariance as the flow features input is provided using relative velocities. The model is tested on two different supersonic flows, namely, flow over a flat plate and flow around an expansion-compression corner. The performance is evaluated by comparing the skin friction (heat flux) and flow properties with exact values. The ultimate goal is to build a robust and generalizable machine learning model to improve the prediction of WMLES of supersonic flows. To this end, the model is trained by a set of flows containing some essential flow physics to devise a generalizable model. Although the general machine learning model shows some advantages over the baseline WMLES model, it is concluded the data set is far from being representative of the rich flow physics model; therefore, the machine learning model should be trained and tested by a broader set of flows.

Some Aspects of Shear Behavior of Soft Soil-Concrete Interfaces and Its Consequences in Pile Shaft Friction Modeling.

This paper examines the stiffness degradation and interface failure load on soft soil–concrete interface. The friction behavior and its variability is investigated. The direct shear tests under constant normal load were used to establish parameters to hyperbolic interface model which provided a good approximation of the data from instrumented piles. Four instrumented piles were used to obtain reference soil–concrete interface behavior. It was found that the variability of the friction characteristics is the highest for organic clays and the lowest for organic silts. The intact samples exhibit lower shear strength than reconstituted ones. The adhesion varies significantly depending on interface and soil type, which can result in high scatter of the skin friction prediction. The analysis of parameters variability can be used to determine the upper and lower bound of friction behavior on the interface at constant normal load condition. The backward shearing results in decrease in shear strength up to 40% of the precedent forward phase but higher initial stiffness by a factor of between 2 and 3. Presented research provides basic shear and stiffness parameters for four soft soils (organic clay, organic silt, peat, and silty loam) and gives information about variability of interface characteristics.

Determination of Young Elasticity Modulus in Bored Piles Through the Global Strain Extensometer Sensors and Real-Time Monitoring Data

For friction piles depending on the friction resistance, accurate prediction of unit skin friction around the pile shaft is the dominant resistance to measure the final bearing capacity of a bored-pile. The present study measures the stress–strain transferring in two instrumented bored-piles (BP #1 & BP# 2) embedded within the soil layer in Kuala Lumpur by real-time monitoring global strain extensometer (GSE) sensors. Two bored-piles (i.e., having 1.80 m and 1.0 m diameters, as well as 36 m and 32 m lengths) have been loaded with two times to their design working loads. Extensive data are analyzed to measure the changes in stress–strain in the bored-pile. The effect of loading and unloading stages on the pile’s head and base settlement has been monitored, indicating that Young modulus of elasticity in concrete bored-pile ( E c ), average strain, and unit skin friction changed along the bored-pile based on the ground site conditions and stress registered. One example of two case studies with great real-time monitoring data has been provided to further design.

RANS prediction of open jet aerofoil interaction and design metrics

ABSTRACTRANS models remain an attractive turbulence simulation method which could provide some open jet aerofoil interaction analysis at a fraction of the cost of a high-fidelity LES approach. The present work explores the potential and limitations of RANS in this context by simulating an open jet aerofoil noise experiment using the aerospace oriented Menter SST RANS model. This model’s tendency to transition at a critical Reynolds number lower than the experimental value was found to impact the boundary layer development. However, the introduction of a low-Re correction improved the prediction of surface pressure and skin friction, enabling the suction surface separation bubble to be captured. The free shear layer’s virtual origin characteristics exhibited sensitivity to the interaction with the aerofoil, which can be developed into a metric of the interaction. The main challenge for RANS was accounting for the rise in background disturbance level in the working section, which is caused by the high-turbulence intensity in the free shear layers.

A systematic review and meta-analysis of artificial neural network application in geotechnical engineering: theory and applications

Artificial neural network (ANN) aimed to simulate the behavior of the nervous system as well as the human brain. Neural network models are mathematical computing systems inspired by the biological neural network in which try to constitute animal brains. ANNs recently extended, presented, and applied by many research scholars in the area of geotechnical engineering. After a comprehensive review of the published studies, there is a shortage of classification of study and research regarding systematic literature review about these approaches. A review of the literature reveals that artificial neural networks is well established in modeling retaining walls deflection, excavation, soil behavior, earth retaining structures, site characterization, pile bearing capacity (both skin friction and end-bearing) prediction, settlement of structures, liquefaction assessment, slope stability, landslide susceptibility mapping, and classification of soils. Therefore, the present study aimed to provide a systematic review of methodologies and applications with recent ANN developments in the subject of geotechnical engineering. Regarding this, a major database of the web of science has been selected. Furthermore, meta-analysis and systematic method which called PRISMA has been used. In this regard, the selected papers were classified according to the technique and method used, the year of publication, the authors, journals and conference names, research objectives, results and findings, and lastly solution and modeling. The outcome of the presented review will contribute to the knowledge of civil and/or geotechnical designers/practitioners in managing information in order to solve most types of geotechnical engineering problems. The methods discussed here help the geotechnical practitioner to be familiar with the limitations and strengths of ANN compared with alternative conventional mathematical modeling methods.