Boundary Layer Method Research Articles

Investigation of heat generation and radiation effects on boundary layer flow of Prandtl liquid with Cattaneo–Christov double diffusion models

In this analysis, a bidirectional stretched sheet is used to produce a 3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{D}$$\\end{document} flow of Prandtl liquid with improve mass diffusion and heat conduction models. This study advances knowledge of magnetohydrodynamics, radiation impacts, and heat production in fluid dynamics and transport processes. The Prandtl fluid model is critical for modeling non-Newtonian fluids, capturing its viscoelastic features, and allowing for precise simulation in industrial applications. It gives a mathematical foundation for analyzing complex fluid behaviors, which is necessary for optimizing operations utilizing such fluids. It uses the boundary layer method to simplify the fundamental equations and Cattaneo–Christov double diffusion models. The optimal homotopy analysis method is used to solve nonlinear ODEs caused by non-dimensional similarity variables. This investigation undertakes the calculation of drag coefficient for surfaces mass transfer rates and heat transfer rates proximate to the solid boundary. Furthermore, it conducts a comprehensive analysis of the influences exerted by various parameters on concentration and temperature profiles employing graphical representations for a rigorous examination. The Prandtl fluid model describes the viscoelastic characteristics of non-Newtonian fluids through constitutive equations, dimensional evaluation, and numerical simulations, which are frequently validated by experiments. The results show that changes in thermal and concentration relaxation parameters are accompanied by a decline in temperature. Temperature field rises as the thermal radiation parameter and heat generation increases. The work's novelty consists in its advanced modeling of Prandtl non-Newtonian fluids via Cattaneo–Christov double diffusion models, which incorporate magnetohydrodynamics and radiation effects and use optimal homotopy analysis for accurate parametric analyses of heat and mass transfer.

Power-law fluid flow in the entrance region between two parallel plates

Flow of non-Newtonian fluids between parallel plates has many uses including heat transfer applications. Many non-Newtonian fluids can be categorized as pseudoplastic fluids. A broader category, power-law fluids, covers in addition dilatant and Newtonian fluids. Models for developing power-law fluid flow between parallel plates include computational and integral boundary layer methods. Most published studies include partial results and apply to one of the three categories. The present work addresses the three cases and exclusively shows the transition from developing to fully developed flow. In the inlet region, viscous effects are restricted to the boundary layer. The present approach is based on the inlet-filled region concept, and includes an additional zone, called filled region in which viscous effects are present in the whole region, with the flow asymptotically reaching the fully developed solution. The integral boundary layer method is used in both regions to solve for the flow. The results are found to be in good agreement with published Newtonian, pseudoplastic and dilatant fluid results for boundary layer thickness, centerline velocity, local friction factor, pressure drop profiles, and entrance region size. The present model is fundamentally analytical with minor computational work required.

Adaptive immune fuzzy quasi-sliding mode control for leader–follower formation of wheeled mobile robots under uncertainties and disturbances with obstacle avoidance

PurposeThis paper aims to propose a robust kinematic controller based on sliding mode theory designed to solve the trajectory tracking problem and also the formation control using the leader–follower strategy for nonholonomic differential-drive wheeled mobile robots with a PD dynamic controller.Design/methodology/approachTo deal with classical sliding mode control shortcomings, such as the chattering and the requirement of a priori knowledge of the limits of the effects of disturbances, an immune regulation mechanism-inspired approach is proposed to adjust the control effort magnitude adaptively. A simple fuzzy boundary layer method and an adaptation law for the immune portion gain online adjustment are also considered. An obstacle avoidance reactive strategy is proposed for the leader robot, given the importance of the leader in the formation control structure.FindingsTo verify the adaptability of the controller, obstacles are distributed along the reference trajectory, and the simulation and experimental results show the effectiveness of the proposed controller, which was capable of generating control signals avoiding chattering, compensating for disturbances and avoiding the obstacles.Originality/valueThe proposed design stands out for the ability to adapt in a case involving obstacle avoidance, trajectory tracking and leader–follower formation control by nonholonomic robots under the incidence of uncertainties and disturbances and also considering that the immune-based control provided chattering mitigation by adjusting the magnitude of the control effort, with adaptability improved by a simple integral-type adaptive law derived by Lyapunov stability analysis.

Influence of air flow field computation on an ice accretion simulation of airfoils

Ice accretion simulation is an important research technology for aircraft icing problems. Air flow field prediction of an iced aircraft is an essential step of ice accretion simulation. However, commonly used turbulence models have difficulty predicting the large flow separation of the iced aircraft, which makes air flow field calculation insufficiently accurate and further affects the ice accretion simulation. In this paper, the influence of air flow field computation on ice accretion simulation of airfoils is numerically studied. Several different turbulence models are applied to predict air flow fields of iced airfoils. Then, the Eulerian method of water droplets, integral boundary layer method and Myers model are used to simulate ice accretion. Different airfoils with several icing conditions, including glaze ice and rime ice cases, are numerically tested and compared with experimental data. The results show that the separating shear layer fixed k−ω model is more accurate than other turbulence models in predicting the pressure distribution of the iced airfoil, especially the leading-edge suction peak. Thus, a more reasonable droplet collection efficiency distribution and convective heat transfer distribution can be obtained, yielding a more consistent ice height compared with the experimental data.

Urbanization significantly increases greenhouse gas emissions from a subtropical headwater stream in Southeast China

Streams are disproportionately significant contributors to increases in greenhouse gas (GHG) effluxes in river networks. In the context of global urbanization, a growing number of streams are affected by urbanization, which has been suggested to stimulate the water-air GHG emissions from fluvial systems. This study investigated the seasonal and longitudinal profiles of GHG (N2O, CH4, and CO2) concentrations of Jiuxianghe Stream, a headwater stream undergoing urbanization, and estimated its GHG diffusive fluxes and global warming potentials (GWPs) using the boundary layer method. The results showed that N2O, CH4, and CO2 concentrations in Jiuxianghe Stream were 0.45–7.19 μg L−1, 0.31–586.85 μg L−1, and 0.16–11.60 mg L−1, respectively. N2O, CH4, and CO2 concentrations in the stream showed 4.55-, 23.70-, and 7.68-fold increases from headwaters to downstream, respectively, corresponding to the forest-urban transition within the watershed. Multiple linear regression indicated that NO3−–N, NH4+–N, and DOC:NO3−–N accurately predicted N2O and CO2 concentrations, indicating that N nutrients were the driving factors. The Jiuxianghe Stream was a source of atmospheric GHGs with a daily GWP of 7.31 g CO2-eq m−2 d−1 on average and was significantly positively correlated with the ratio of construction land and forest in the sub-watershed. This study highlights the critical role of urbanization in amplifying GHG emissions from streams, thereby augmenting our understanding of GHG emissions from river networks. With global urbanization on the rise, streams experiencing urbanization are expected to make an unprecedentedly significant contribution to riverine GHG budgets in the future.

Establishment of Linear Stability Analysis Method of Hypersonic Boundary Layer Reflecting Porous Surface Effect

Establishment of Linear Stability Analysis Method of Hypersonic Boundary Layer Reflecting Porous Surface Effect

A Novel Method for Characterizing the Inter‐ and Intra‐Lake Variability of CH4 Emissions: Validation and Application Across a Latitudinal Transect in the Alpine Region

AbstractLakes in the Alpine region are recognized as critical methane (CH4) emitters, but a robust characterization of the magnitude and variability of CH4 fluxes is missing. We developed a mobile platform for CH4 eddy covariance (EC) flux measurements to tackle this gap. The mobile system was deployed at nine lakes across a latitudinal transect in the Alps and validated by comparing the measured fluxes with fixed on‐shore EC station and to chamber and boundary layer flux estimates. Our approach was shown to be well suited to capture different CH4 emission pathways and to integrate the within lake variability, therefore, overcoming the limitations of other methods (e.g., boundary layer method). Additionally, this mobile system offers a tool to characterize inter‐lake variability of fluxes with consistent measurements. Methane fluxes were explained by dissolved nitrogen, total phosphorus, dissolved oxygen, seston and lake size. The highest fluxes and most substantial seasonal variability were found in a shallow low‐altitude lake in the Southern Alps. We suggest that characterizing the intra‐lake emission heterogeneity and consistent measurements for a better understanding of inter‐lake emission differences is fundamental for a solid estimate of freshwater CH4 budgets.

Generalization of the Thwaites integral method for laminar boundary-layers due to moving continuous surfaces

In this study, attention has been given towards the development of an approximate method for the boundary-layer flows involving no pressure gradient (the flows due to moving continuous surfaces in a still fluid). The integral method devised in this study is an extension of the existing Thwaites integral method; applicable to boundary-layer flows over the stationary surfaces of finite length (which, in general, involve the pressure gradient because of the presence of external potential flow, except for the case of uniform external flow). The existing Thwaites integral method does not give an acceptable approximation for the flows over moving continuous surfaces in a quiescent fluid, involving no pressure gradient. Therefore, the extension of the existing Thwaites integral method, proposed in this study, will make it applicable to the flows due to moving continuous surfaces in a stationary fluid (involving no pressure gradient), also. With the combination of the two, the existing, and the extended Thwaites integral method, the generalized Thwaites integral method is proposed, applicable to the boundary-layer flows whether involving a pressure gradient or not.

UTLIZATION OF GENERALIZED HEAT FLUX MODEL ON THERMAL TRANSPORT OF POWELL-EYRING MODEL VIA OHAM WITH HEAT GENEARTION ASPECTS

The focus of this work is on the flow of a spinning Powell-Eyring nanofluid in the boundary layer in three dimensions using magnetohydrodynamics (MHD). The research simulates mass transfer processes and heat transfer processes using non-Fick's mass flux theory and non-Fourier heat flux theory, respectively. Heat transport phenomena are analyzed by the integration of non-linear heat generation/absorption and thermal radiation properties. The boundary layer method is employed to solve a system of nonlinear partial differential equations (PDE) in the mathematical formulation. These equations are converted into nonlinear ordinary differential equations (ODES), and then the optimal OHAM with convergence control parameters is used to solve them. The impact of various physical movement circumstances on concentration and temperature profiles is visually represented through the generation of diagrams. This study provides important new understandings for both applied and scholarly research on complex heat transfer and fluid dynamics mechanisms in the context of three-dimensional MHD boundary layer flows of rotating Powell-Eyring nanofluids.

Utilization of variable thermal conductivity and diffusion coefficient on non-Newtonian Prandtl model with modified heat and mass fluxes

PurposeThis study aims to analyze the Prandtl fluid flow in the presence of better mass diffusion and heat conduction models. By taking into account a linearly bidirectional stretchable sheet, flow is produced. Heat generation effect, thermal radiation, variable thermal conductivity, variable diffusion coefficient and Cattaneo–Christov double diffusion models are used to evaluate thermal and concentration diffusions.Design/methodology/approachThe governing partial differential equations (PDEs) have been made simpler using a boundary layer method. Strong nonlinear ordinary differential equations (ODEs) relate to appropriate non-dimensional similarity variables. The optimal homotopy analysis technique is used to develop solution.FindingsGraphs analyze the impact of many relevant factors on temperature and concentration. The physical parameters, such as mass and heat transfer rates at the wall and surface drag coefficients, are also displayed and explained.Originality/valueThe reported work discusses the contribution of generalized flux models to note their impact on heat and mass transport.

A new wall function method for hypersonic laminar boundary layers

A new wall function method for hypersonic laminar boundary layers (HLBLs) is proposed to reduce the near-wall grid dependence of skin friction $c_f$ and wall heat flux $q_w$ in numerical simulations, aiming for fast and accurate predictions. First, an analytic laminar velocity law of the wall is derived, which achieves a universal scaling of the near-wall velocity of HLBLs. Then an accurate temperature–velocity relation is deduced by introducing the general recovery factor to address the invalidation of the Walz relation under the cold wall effect. Based on the laminar laws of the wall, a new wall function method for HLBLs is proposed. To avoid introducing the boundary layer edge quantities, the laminar laws of the wall are reformed by modifying the outer boundary conditions of the differential equation in deriving the temperature–velocity relation. Unlike the wall function method in turbulence, the new wall function obtains directly the accurate $c_f$ and $q_w$ by post-processing without being involved in the simulation iteration. The numerical experiments of a Mach 8 HLBL over the flat plate show that effectively, the new wall function can enlarge the distance of the first grid point off the wall $\Delta y_1$ from $10^{-6}$ m to $10^{-3}$ m, which brings a 50 times enhancement of the simulation efficiency. Meanwhile, the simulation errors of $c_f$ and $q_w$ of the mesh with $\Delta y_1=10^{-3}$ m are reduced significantly from 24.2 % and 18.5 % to 0.5 % and 0.1 %, respectively. Due to the new wall function removing the boundary layer edge quantities, success is also achieved under the curved walls.

An extension of Thwaites’ method for turbulent boundary layers

Thwaites (Aeronaut. Q., vol. 1, 1949, pp. 245–280) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations (Alber, 9th Aerospace Sciences Meeting, 1971). The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

Calculation and Selection of Airfoil for Flapping-Wing Aircraft Based on Integral Boundary Layer Equations

The flight of a migratory bird-like flapping-wing aircraft is characterized by a low Reynolds number and unsteadiness. The selection of airfoil profiles is critical to designing an efficient flapping-wing aircraft. To choose the suitable airfoil for various wing sections, it is necessary to calculate the aerodynamic forces of the unsteady two-dimensional airfoil with a Reynolds number in the range of 105. While accurate, calculating this by solving the Navier–Stokes equations is impractical for early design stages due to its high consumption of computing resources and time. The computational demands for extending it to 3D aerodynamic calculations are even more prohibitive. In this paper, a relatively simple method is proposed. The two-dimensional unsteady panel method is utilized to derive the inviscid flow field, the unsteady integral boundary layer method is utilized to solve the boundary layer viscous flow, and the eN transition model is adopted to predict the position of the transition. These models are coupled with the semi-inverse interaction method to solve the aerodynamics of the unsteady low-Reynolds-number two-dimensional airfoil. The unsteady aerodynamics of the symmetric and cambered airfoils at different wing sections are calculated respectively by the proposed method. Mechanism analysis of the calculation results is conducted, and a symmetrical airfoil or a slightly cambered airfoil is recommended for the wing tip, a moderately cambered airfoil is suggested for the outer-wing section, and a highly cambered airfoil is suggested for the inner-wing section.

Roughness implementation and convective heat transfer coefficient computation toward ice accretion simulation

In the simulation of icing, the calculation of the convective heat transfer coefficient for rough surfaces has significant importance. Our study investigates the extension of the γ-Reθt transition model for rough icing surfaces and aims to provide an alternative to the integral boundary layer method for facilitating the calculation of the heat transfer coefficient in three-dimensional icing simulations. Initially, the performance of the γ-Reθt transition model in predicting the transition characteristics and heat transfer for smooth surfaces is examined. Subsequently, to compensate for the deficiency of the γ-Reθt transition model in predicting the premature transition caused by roughness, an additional model equation Ar is introduced to simulate the influence of the surface roughness. Three test cases, including a clean cylinder, an iced cylinder, and a swept wing, are used to validate the applicability of the γ-Reθt-Ar transition model for heat transfer computations on rough surfaces. The results demonstrate that the γ-Reθt-Ar model is superior to other turbulence models in computing convective heat transfer for two-dimensional and three-dimensional icing rough surfaces and shows its potential for ice accretion simulation.

Computational Assessment of ZrO2-Al2O3/EG and ZrO2-Al2O3-Cu/EG Nanomaterial on Blasius-Rayleigh-Stokes Flow Influenced by an Aligned Magnetic Field

In this work, the flow of a modified nanofluid is analysed as it passes over a moving surface to investigate the influence of nonlinear radiative heat transfer and the effects of magnetic fields that are aligned. In addition, ethylene glycol is used as the solvent while zirconium oxide and alumina are combined to generate a hybrid nanomaterial. Ternary nanomaterials consist of zirconium oxide, alumina, and copper dissolved in the ethylene glycol. For this mathematical model, Navier–Stokes equations were used to represent the assumed flow. The Navier–Stokes equations were approximated using the boundary layer method under the flow assumptions, yielding the PDE’s. Similarity transformations are used to translate this system into ODE’s. The bvp4c method is used to explain a dimensionless system. The impacts of the relevant physical parameters are elucidated quantitatively and visually. A greater temperature ratio parameter is observed to increase the temperature profile. In addition to this, when the magnetic field parameter is increased, the momentum layer becomes thicker.

Extended integral boundary layer method for reactive species mass transfer in rotating films

AbstractThe present work extends the Integral Boundary Layer (IBL) Method to centrifugal force driven thin film flow with mass transfer. The proposed hybrid approach combines the IBL based solution of the flow field with a Finite Difference based solution of the mass transport equation, avoiding any concentration profile assumptions and restrictions on surface chemistry. In comparison against results from highly resolved Computational Fluid Dynamics (CFD) simulations, the proposed concept is proven as a computationally efficient and accurate method well applicable to infinitely fast surface reactions as well as finite rate kinetics.

Multidisciplinary Design Optimization of Transonic Wings with Boundary-Layer Suction

A quasi-three-dimensional aerodynamic solver is developed for the aerodynamic analysis of wings in a transonic regime that is able to capture the effect of BLS in hybrid laminar flow control (HLFC) application or transition to turbulent flow for natural laminar flow (NLF). The tool provides accurate results, but without the high computational cost of high-fidelity tools. The solver combines the use of an Euler flow solver characterized by an integral boundary-layer method and linear stability analysis using a approximation for transition prediction. In particular, a conical transformation is adopted, including the determination of the shock-wave position. The solver is implemented in a multidisciplinary design optimization (MDO) framework, including wing weight estimation and aircraft performance analysis. The framework consists of different modules: aerodynamics, structure, suction system analysis, and performance evaluation. Using a genetic algorithm and considering HLFC technology, wing MDO has been performed to find the optimum wing planform and airfoil shape. A backward-swept wing (BSW) aircraft, developed inside the Cluster of Excellence–Sustainable and Energy Efficient Aviation (A) is studied. Novel technologies such as active flow control, limited maximum load factors due to load alleviation, and novel materials allow a fuel weight reduction of 6%.

Analytical Method in the Linear Three-Dimensional Aerodynamics of a Thin Rectangular Wing

The paper develops an analytical method in the classical problem on a flow around a thin rectangular plate of large span. It is shown that with a specific expansion on an orthogonal system of functions with a weight defined by qualitative properties of the solution, the initial 2d integral equation is asymptotically equivalent to a set of independent 1d integral equations. For them, we construct an asymptotic method allied to a boundary layer method, which permits development of analytical representations for basic aerodynamic characteristics. Comparison with the numerical method of discrete vortices shows that precision of the obtained solution is good not only for large but also for medium span of the wing.

Observer-Based Dynamic Event-Triggered Tracking Consensus for Switched Multi-Agent Systems

This article discusses the event-triggered consensus problem for a switched multi-agent system (MASs) with switching topologies. An observer-based dynamic event-triggered (DET) controller with a discontinuous nonlinear term is designed to reduce arduous communication. With the designed approach, the error system can reach a tracking consensus. Then, a continuous observer-based DET protocol is created using the boundary layer method to prevent chattering effects. Moreover, by employing the Riccati equation and the switched Lyapunov function method, some sufficient criteria are put forward to guarantee the tracking consensus of the systems. The suggested observer-based DET protocol can also exclude the Zeno behavior. Finally, two examples verify the validity of the analysis.

Disturbance Observer-Based Terminal Sliding Mode Tracking Control for a Class of Nonlinear SISO Systems with Input Saturation

This paper focuses on the trajectory tracking control for general nonlinear single-input single-output (SISO) systems in which the output is not directly related to the control input. To address the tracking problem with the consideration of possible model uncertainty, external disturbance, and control input saturation, we employ the input-output feedback linearization technique and design a finite-time disturbance observer-based terminal sliding mode controller to improve the tracking performance and enhance the robustness. The stability analysis is carried out by using the Lyapunov method. To alleviate the chattering while achieving an acceptable control performance, a boundary layer method is adopted for the trade-off between the high-frequency control actions and the bounded unavoidable nonzero steady-state error. The proposed method is evaluated on the two typical nonlinear systems, which are fully linearizable and partially linearizable, respectively, and compared to the state-of-the-art method in terms of tracking and robustness through comprehensive numerical simulations. The results show that the proposed method not only renders the estimated disturbance error tends to be zero in finite time, but also has superiority in the fast reaction to disturbance and small tracking error without high-frequency chattering.