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This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary conditions formulated recently, accounting for the crucial contributions of the nonlocal boundary layer. A slow-time perturbation scheme is established, leading to the reduced model for the Rayleigh wave field, comprised of a singularly perturbed hyperbolic equation for the longitudinal wave potential on the surface, acting as a boundary condition for the elliptic equation governing the decay over the interior. An equivalent alternative formulation involving a pseudo-differential operator acting on the loading terms, with parametric dependence on the depth coordinate, is also presented.

This study addresses performances and behaviors of the multi-cross-section HAWT blade design with and without fences. The FX66-S-196 V, FX63-137 S and SG6043, supercritical airfoils were used and distributed along the blade radius; further, the NACA4412 single-cross-section HAWT blade having the same dimensions was used to compare the behaviors and overall performances of all the blades. Analyses were then performed numerically using blade elements momentum BEM theory with a self-code (F.90) and CFD as well as experimentally with three multi-cross-section blades designed using SOLIDWORKS and 3D- printed with polylactic acid. the multi-cross-section HAWT blades show good performance compared with the single- cross-section blade, with an approximately 8% increase in power coefficient, i.e., 40 W, for a miniature wind turbine (127 cm diameter 500 W output power) and greater improvements for wind turbines with large diameters. The fences were designed using boundary layer theory and installed on multi-cross-section blades in experimentally determined positions. The fences showed high performance, with a 16% increase in total power coefficient and high flutter stability.

The paper presents an original approach to the study of the problem of internal friction arising from the motion of a rigid body in an incompressible fluid. This approach takes into account the spatial variability of molecular viscosity in the boundary layer region, and the solution of the problem is based on the use of an extreme for the fluid flow rate functional. The spatial variability of molecular viscosity in the boundary layer, by a well-known analogy with the theory of heat conduction, is based on the absence of a spatial isotropy of the medium. It is shown that molecular viscosity depends on the nature of the flow - on how many forces act on the fluid. So, if the flow is unsteady and non-gradient or steady and gradient, then both of these flows are subject to the action of two forces. In such flows, the molecular viscosity due to the extreme of the fluid flow rate is a constant value. It has been fond that the distribution of velocity in a gradient stationary boundary layer has a parabolic distribution law, and all existing theories are described by this law quite accurately, with an error of maximum 5%. At the same time, in a laminar non-gradient boundary layer, only the force of internal friction acts on the fluid. This causes the spatial variability of molecular viscosity: shear stress can be constant not only due to the linearity of the velocity distribution, which is not observed in the boundary layer, but also due to the variability of molecular viscosity. The resulting exponential velocity distribution in a non-gradient boundary layer is in complete agreement with those in the problems solved by Stokes, and is also confirmed experimentally. The paper also points out that the exponential law is consistent with modern data obtained by direct numerical simulation (DNS) for flows with Low Reynolds numbers – both single-phase and two-phase, in the presence of particles inside the fluid. Наведено новий підхід щодо аналітичного опису стаціонарного ламінарного примежового шару нестисливої рідини на нескінченій площині. Цей підхід базується на відмові, в загальному випадку, від припущення про сталість молекулярної в’язкості усюди в області течії. Новизна полягає у використанні варіаційного числення для замикання рівняння Нав’є-Стокса, в якому вже присутня нова невідома функція — молекулярна в’язкість. Для замикання використовується умова екстремуму втрати рідини крізь переріз примежового шару. Ця умова корелює із першим в історії варіаційним принципом (найменшої дії) П’єра Моперт’юі. В залежності від типу течії, - градієнтної чи без-градієнтної, -- вдалось показати, що при градієнтній течії рідини в’язкість є сталою усюди, а в без-градієнтній течії змінюється по всій товщі примежового шару. Ця відмінність пояснюється різною кількістю сил, що створюють течію рідини в без-градієнтному та градієнтному примежових шарах. Це відповідно одна та дві сили. Наявність другої сили, а саме повздовжнього градієнту тиску, відповідає за сталість молекулярної в’язкості. Відсутність інших, крім сили внутрішнього тертя, сил дозволяє молекулярній в’язкості, за умови сталості дотичних напружень, бути змінною величиною, а профілю повздовжньої швидкості відрізнятись від лінійної функції, яка не спостерігається у примежовому шарі. Наведено порівняння із існуючими класичними та сучасними теоріями ламінарного примежового шару. Згідно із цими теоріями, профіль швидкості має разючу схожість (відхилення не перевищує 5%) із параболічним законом, отриманим у даній роботі, а також забезпечує сталість молекулярної в’язкості в середині примежового градієнтного ламінарного шару нестисливої рідини. В цілому в роботі робиться висновок про відсутність аналогії між градієнтним та без-градієнтним стаціонарними примежовими шарами нестисливої рідини. Течії у цих шарах описується зовсім різними функціональними розподілами – параболічним і експоненціальним.&nbsp

Wind-farm parameterizations in weather models can be used to predict both the power output and farm effects on the flow; however, their correctness has not been thoroughly assessed. We evaluate the wind-farm parameterization of the Weather Research and Forecasting Model with large-eddy simulations (LES) of the wake performed with the same model. We study the impact on the velocity and turbulence kinetic energy (TKE) of inflow velocity, roughness, resolution, number of turbines (one or two), and inversion height and strength. We compare the mesoscale with the LES by spatially averaging the LES within areas correspondent to the mesoscale horizontal spacing: one covering the turbine area and two downwind. We find an excellent agreement of the velocity within the turbine area between the two types of simulations. However, within the same area, we find the largest TKE discrepancies because in mesoscale simulations, the turbine-added TKE has to be highest at the turbine position to be advected downwind. Within the downwind areas, differences between velocities increase as the wake recovers faster in the LES, whereas for the TKE both types of simulations show similar levels. From the various configurations, the impact of inversion height and strength is small for these heights and inversion levels. The highest impact for the one-turbine simulations appears under the low-speed case due to the higher thrust, whereas the impact of resolution is low for the large-eddy simulations but high for the mesoscale simulations. Our findings demonstrate that higher-fidelity simulations are needed to validate wind-farm parameterizations.

A new one-dimensional 1.5-order planetary boundary layer (PBL) scheme, based on the K–ε turbulence closure applied to the Reynolds-averaged Navier–Stokes (RANS) equations, is developed and implemented within the Weather Research and Forecasting (WRF) Model. The new scheme includes an analytic solution of the coupled equations for turbulent kinetic energy and dissipation rate. Different versions of the PBL scheme are proposed, with increasing levels of complexity, including a model for the calculation of the Prandtl number, a correction to the dissipation rate equation, and a prognostic equation for the temperature variance. Five different idealized cases are tested: four of them explore convective conditions, and they differ in initial thermal stratification and terrain complexity, while one simulates the very stable boundary layer case known as GABLS. For each case study, an ensemble of different large-eddy simulations (LES) is taken as reference for the comparison with the novel PBL schemes and other state-of-the-art 1- and 1.5-order turbulence closures. Results show that the new PBL K–ε scheme brings improvements in all the cases tested in this study. Specifically, the more significant are obtained with the turbulence closure including a prognostic equation for the temperature variance. Moreover, the largest benefits are obtained for the idealized cases simulating a typical thermal circulation within a two-dimensional valley. This suggests that the use of prognostic equations for dissipation rate and temperature variance, which take into account their transport and history, is particularly important with the increasing complexity of PBL dynamics.

We investigate the role of wildfire smoke on ozone photochemical production (P(O3)) and atmospheric boundary layer (ABL) dynamics in California's Central Valley during June–September from 2016 to 2020. Wildfire events are identified by the Hazard Mapping System (HMS) and the Hybrid Single Particle Lagrangian Integrated Trajectory Model (HYSPLIT). Air quality and meteorological data are analyzed from 10 monitoring sites operated by the California Air Resources Board (CARB) across the Central Valley. On average, wildfires were found to influence air quality in the Central Valley on about 20 % of the total summer days of the study. During wildfire-influenced periods, maximum daily 8 h averaged (MDA8) O3 was enhanced by about 5.5 ppb or 10 % of the median MDA8 (once corrected for the slightly warmer temperatures) over the entire valley. Overall, nearly half of the total exceedances of the National Ambient Air Quality Standards (NAAQS) where MDA8 O3 > 70 ppb occur under the influence of wildfires, and approximately 10 % of those were in exceedance by 5 ppb or less indicating circumstances that would have been in compliance with the NAAQS were it not for wildfire emissions. The photochemical ozone production rate calculated from the modified Leighton relationship was also found to be higher by 50 % on average compared with non-fire periods despite the average diminution of j(NO2) by ∼ 7 % due to the shading effect of the wildfire smoke plumes. Surface heat flux measurements from two AmeriFlux sites in the northern San Joaquin Valley show midday surface buoyancy fluxes decrease by 30 % on average when influenced by wildfire smoke. Similarly, afternoon peak ABL heights measured from a radio acoustic sounding system (RASS) located in Visalia in the southern San Joaquin Valley were found to decrease on average by 80 m (∼ 15 %) with a concomitant reduction of downwelling shortwave radiation of 54 Wm−2, consistent with past observations of the dependence of boundary layer heights on insolation.

We examine katabatic flow driven by a non-uniformly cooled slope surface but unaffected by Coriolis acceleration. A general formulation is given, valid for non-uniform surface buoyancy distributions over a down-slope length scale $$L\gg \delta _0$$ L ≫ δ 0 , where $$\delta _0=\nu /(N\sin \alpha )^{1/2}$$ δ 0 = ν / ( N sin α ) 1 / 2 is the slope-normal Prandtl depth, for a kinematic viscosity $$\nu$$ ν , buoyancy frequency N and slope angle $$\alpha$$ α . We demonstrate that the similarity solution of Shapiro and Fedorovich (J Fluid Mech 571:149–175, 2007) can remain quantitatively relevant local to the end of a non-uniformly cooled region. The usefulness of the steady similarity solution is determined by a spatial eigenvalue problem on the L length scale. Broadly speaking, there are also two modes of temporal instability; stationary down-slope aligned vortices and down-slope propagating waves. By considering the limiting inviscid stability problem, we show that the origin of the vortex mode is spatial oscillation of the buoyancy profile normal to the slope. This leads to vortex growth in a region displaced from the slope surface, at a point of buoyancy inflection, just as the propagating modes owe their existence to an inflectional velocity. Non-uniform katabatic flows that detrain fluid to the ambient are shown to further destabilise the vortex mode whereas entraining flows lead to weaker vortex growth rates. Rayleigh waves dominate in general, but the vortex modes become more significant at small slope angles and we quantify their relative growth rates.

The present study shows by a linear hydrodynamic stability analysis that an unstable mixed-layer deep circulation can be generated in the dry convective well-mixed layer by the entrainment from the top. The newly identified instability arises under the two competing processes induced by the top entrainment: the destabilization by generating thermal perturbations and the damping by mechanical mixing. The former and the latter, respectively, dominate over the other in the limits of large and small scales. As a result, the instability is realized at the horizontal scales larger than the order of the mixed-layer depth (ca. 1 km), and the time scale for the growth is about 1 day. This study has been motivated from a question of whether the cloud-top entrainment instability (CTEI) can induce a transition of the stratocumulus-topped well-mixed boundary layer into trade cumulus. The present study intends to extend the previous studies based on the local parcel analyses to a full analysis based on the hydrodynamics. Unfortunately, being based on a dry formulation, the present result does not apply directly to the CTEI problem. Especially, the evaporative cooling is totally neglected. Nevertheless, the present result can still be applied to moist systems, to some extent, by redefining certain terms in the formulation.

Background: Non-newtonian fluids, especially shear thinning fluids, have several applications in the polymer industry, food industry, and even everyday life. The viscosity of shear thinning fluids is decreased by two or three orders of magnitude due to the alignment of the molecules in order when the shear rate is increased, and it cannot be ignored in the case of polymer processing and lubrication problems. Objective: So, the effects of viscosities at the low and high shear rates on the heat and mass boundary layer flow of shear thinning fluid over moving belts are investigated in this study. For this purpose the generalized Carreau model of viscosity relate to shear rate is used in the momentum equation. The Carreau model contains the five parameters: low shear rate viscosity, high shear rate viscosity, viscosity curvature, consistency index, and flow behavior index. For the heat flow, the expression of the thermal conductivity model similar to the viscosity equation due to the non-Newtonian nature of the fluid is used in the energy equation. Methods: On the mathematical model of the problem, boundary layer approximations are applied and then simplified by applying the similarity transformations to get the solution. The solution of the simplified equations is obtained by numerical technique RK-shooting method. The results are compared with existing results for limited cases and found good agreement. Results: The results in the form of velocity and temperature profiles under the impact of all the viscosity’s parameters are obtained and displayed in graphical form. Moreover, the boundary layer parameters such as the thickness of the regions, momentum thickness, and displacement thickness are calculated to understand the structure of the boundary layer flow of fluid. Conclusion: The velocity and temperature of the fluid are decreased and increased respectively by all viscosity’s parameters of the model. So, the results of the boundary layer fluid flow under rheological parameters will not only help engineers to design superior chemical equipment but also help improve the economy and efficiency of the overall process.

A velocity formula is proposed for flow over a mobile sediment bed induced by velocity-skewed waves and current. The formula is obtained by a separation of waves and current velocities and requires seven free variables related to free stream velocity and sediment characteristics. The formula includes two parts: (1) a wave part consisting of the free stream velocity and defect function, which considers phase lead, wave boundary layer thickness, and mobile bed level, and (2) a current part, which changes the wave part through the boundary layer thickness and mobile bed level, influenced by wave eddy viscosity. The wave part is superior to the current part such that the boundary layer characteristics are mainly determined by the waves. The wave process is divided into four quarter stages to model the asymmetries of parameters in velocity and acceleration. Under velocity-skewed waves and current conditions, velocity asymmetry and residual velocity are accounted for in the formula, especially the offshore residual velocity with a large phase lag and mobile bed effect with a small phase lag. Phase lead is shown to be non-constant in velocity-skewed oscillatory sheet flow and corresponds to an extra offshore residual velocity.

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

This study investigates the boundary stresses prescribed by the traction boundary condition on an incompressible magnetohydrodynamic Jeffery-Hamel flow of viscous fluid. The governing partial differential equations are transformed to a nonlinear ordinary differential equation (ODE) by the transformation obtained from continuity equation. We have modeled traction boundary conditions to solve the problem. We have not imposed flow symmetry condition and applied prescribed flow rate condition. We have computed analytical and numerical solutions of the problem. We have developed modified Adomian decomposition method based on Daun-Rach Approach (DRA) for general nonlinear third order ODE subject to Robin’s and integral boundary conditions. The governing equation is solved using the developed scheme. The Mathematica routine, NDSolve, is used to obtain numerical solution by first approximating the constant flow rate condition by Gauss-Lobatto integration formula of four and five points as well as by trapezoidal rule. Analytical and numerical results are compared and found in good agreement. The slip and no-slip scenarios are observed both for inertial and non-inertial flows. The back flow occurs both for convergent and divergent channel geometries. Flow bifurcations and boundary layer get strengthened due to presence of boundary stresses. The symmetric and asymmetric natures of flow are also captured due to presence of boundary stresses.

Based on the author's previous research, a novel hybrid grid generation technique is developed by introducing an Artificial Neural Network (ANN) approach for realistic viscous flow simulations. An initial hybrid grid over a typical geometry with anisotropic quadrilaterals in the boundary layer and isotropic triangles in the off-body region is generated by the classical mesh generation method to train two ANNs on how to predict the advancing direction of the new point and to control the grid size. After inputting the initial discretized fronts, the ANN-based Advancing Layer Method (ALM) is adopted to generate the anisotropic quadrilaterals in boundary layers. When the high aspect ratio of the anisotropic grid reaches a specified value, the ANN-based Advancing Front Method (AFM) is adopted to generate isotropic triangles in the off-body computational domain. The initial isotropic triangles are smoothed to further improve the grid quality. Three typical cases are tested and compared with experimental data to validate the effectiveness of grids generated by the ANN-based hybrid grid generation method. The experimental results show that the two ANNs can predict the advancing direction and the grid size very well, and improve the adaptability of the isotropic/anisotropic hybrid grid generation for viscous flow simulations.

This paper presents the investigation of airfoil turbulent boundary-layer trailing-edge noise reduction using a parametric airfoil design. The airfoil design tool performs a parametric design start...

Estimating heat-flux peak location and magnitude is important to efficiently design thermal protection systems of hypersonic vehicles, which are characterized by strict low-weight requirements. Thi...

Solving the problems of increasing highway fuel efficiency, throwing a better curve ball, and preventing an aircraft from stalling all have a common thread: controlling flow separation. Defined by the fast moving flow around an object detaching from the object, flow separation has implications for a broad number of engineering fields. Research regarding flow separation control has led to the understanding that the easiest method for delaying flow separation for a given shape is to vary how turbulent the flow around the object is. Varying this turbulence around an object may be achieved through various methods including changing the spin or surface roughness of the object. While spinning the object is seemingly straightforward, there are a myriad of options for varying the surface roughness. Further, how spin and surface features relate to each other is less understood. As a result, this study sought to understand how yet unexplored surface roughness patterns and spin interact as they relate to the boundary layer separation over a sphere. To identify where separation occurred, small particles were added to still air and illuminated in a thin sheet by a laser. Spheres were launched through the air and a digital camera captured images of the particles as the sphere passed through the field of view. These images allowed us to identify where the flow had separated. These separation points across a number of sphere roughness types and spin rates were mapped and compared to the known lift and drag on the spheres. Results show relationships between flow separation and lift/drag, demonstrating the potential for the surface roughness pattern to control the sphere aerodynamics.

The technique of swing bowling is used in the sport of cricket to gain an advantage over the batter, and improve a team’s chance of winning a match. The current best practice for swing bowling is based on anecdotal evidence, with little consensus on the optimal strategies. Bowling technique, the condition of the ball and atmospheric conditions are all considered important for swing, yet there is little quantification of these factors even in elite cricket. Previous experimental studies have not provided a description of swing that aligns with measurements of on-field swing made using ball-tracking technology. This research looks to provide clarity on the physical mechanisms behind swing bowling for new and used cricket balls. Appropriate boundary conditions are measured in field tests, and applied to experiments so that results represent on-field swing. Wind tunnel tests are performed which measure the changes in the aerodynamic force coefficient, CF. The relevant findings are related back to cricket through tools for use in the professional game. For new cricket balls, it is shown that conventional swing has a magnitude of 0.3

The proficiency of hybrid nanoparticles in augmenting the heat transfer has fascinated many researchers to further analysing the working fluid. The present paper is focused on the MHD hybrid nanofluid flow with heat transfer on a moving plate with Joule heating. The combination of metal (Cu) and metal oxide (Al2O3) nanoparticles with water (H2O) as the base fluid is used for the analysis. Similarity transformation reduces the complexity of the PDEs into a system of ODEs, which is then solved numerically using the function bvp4c from MATLAB for different values of the governing parameters. Two solutions are obtained when the plate is moved oppositely from the free stream flow. Analysis of flow stability unveils the first solution as the real physical solution, which is realizable in practice. From physical perspective, the real solution must be available for all cases of λ which affirms the finding from stability analysis. An upsurge of suction’s strength and magnetic parameter enhances the heat transfer operation and extends the critical value λ c . Meanwhile, there is no change on the critical value when the Eckert number is added. This study is important in determining the thermal behavior of Cu-Al2O3/H2O when the physical parameters like magnetic field and Joule heating are embedded. The results are new and original with many practical applications in the modern industry.

The effect of thermochemical kinetics modeling on hypersonic flow over a double-cone geometry is investigated. The double-cone is simulated using three different approaches based on the Park model:...

Hypothesis The boundary layer holds the key to solve the puzzle of the unusual stability of the nanobubbles in solution. The quantitative determination on its mechanical and structural properties has not been achieved due to its diffusive and dynamic nature, lack of distinctive interfaces, and difficult differentiation from bulk background. Therefore, it is necessary to investigate this boundary using more sensitive interface analysis technologies to effectively differentiate the water molecules at the interface from those in the bulk. Experiments An in-situ and non-deconstructive method, solvent relaxation nuclear magnetic resonance, was used to investigate the boundary layer on bulk nanobubbles, where the relaxation rate of the water in the layer and its thickness were measured by solvent relaxation NMR and the ratio between the water molecules at the bubble interfaces and those in the bulk and the corresponding boundary layer thickness were determined. Findings The spin-spin relaxation time for the water in the layer (∼101ms) is found to be two orders of magnitude lower than that of the free water (∼103ms). As the first attempt, the determined boundary layer thickness is around 35-45 nanometers and 17.0 %-8.7 % of the effective gaseous size of the nanobubbles, which increases with the decrease of the bubble diameter. As a result, a quantitative measurement model for bubble boundary layer has been established in order to better understand the interfacial properties and stabilization mechanism for bulk nanobubbles.

We present the laminar boundary layer flow over the standard tori rotating in an otherwise quiescent incompressible fluid. The mean flow equations are derived by using a specific form of the toroidal-poloidal coordinate system. A pseudo-spectral collocation method mixed with the first-order Euler scheme is employed to solve the related steady mean flow equations. A fixed aspect ratio R is defined as the ratio of radii of the torus and its tube that distinguishes each fixed torus within the general family of standard tori. Tori of spindle type turn into a sphere when the aspect ratio R = 0 and thus the mean flow results for the rotating sphere are consistently reproduced. The influence of aspect ratio R on the steady mean velocity components and the wall shear stresses are presented in detail. In a precise manner, the mean flow results for each rotating torus are explainable in a consistent way to the already established case of steady laminar boundary layer flow over the rotating sphere. The significance of the current work is discussed in terms of the hydrodynamic instabilities of boundary layer flows over the family of rotating tori.

This article addresses the design problem of distributed event-triggered average tracking (DETAT) algorithms for homogeneous and heterogeneous multi-agent systems. The objective of DETAT problem is to develop a group of distributed cooperative control algorithms with event-triggered strategies for agents to track the average of multiple time-varying reference signals. Firstly, for homogeneous linear multi-agent systems, based on sampling measurements and model-relied holding techniques, a class of static-gain DETAT algorithms is proposed with a couple of local event-triggered functions for estimators and controllers, respectively. Compared with the existing distributed average tracking (DAT) algorithms, the static-gain DETAT algorithms greatly reduce the cost over communication networks and the frequency of control protocol updates. Secondly, to reduce the chattering phenomenon caused by non-smooth items in staticgain algorithms and requirements of the global information of networks, smooth dynamic-gain DETAT algorithms are introduced based on boundary layer approximation methods and self-adaptive principles. Thirdly, for heterogeneous linear multiagent systems

Turbulent flow over a wall-mounted cube presents an important canonical problem with applications in circuit design, urban building design, or aerodynamics. Flow over a cube placed in a fully devel...

We introduce a coordinate transformation of independent variable, such that the second-order nonlinear singularly perturbed boundary value problem (SPBVP) in the transformed coordinate is less stiff within the boundary layer. An initial value problem for a new dependent variable can be derived easily through the variable transformation. While the zero initial values are given, an unknown terminal value of the new variable at the right end is determined iteratively. We propose the modifications of the asymptotic solution and the uniform approximate solution of the SPBVP; hence, the modified analytic solutions can exactly satisfy both the boundary conditions at two ends. Some examples confirm that the novel methods can achieve better analytic and numerical solutions of the nonlinear SPBVP.

The viscoelastic fluid flow over a non linear stretching porous sheet is considered in this analysis. The case of suction and injection is also discuused. The effects of thermophoresis and brownain motion with viscous dissipation is taken into account. Under the flow assumptions, boundary layer approximation applied on the mathematical model and developed the partial differential equations. The similarity variable is applied on the partial differential equations which converted into ordinary differential equations. The dimensionless system further solved through numerical technique bvp4c method. The results of the current problem achieved after solving the problem which presented through graphs and table. Influence of numerous physical parameters on velocity function, concentration function and temperature function are manipulated through graphs. The tabular results are schemed to display skin friction and local Nusselt number. The higher values of N b which enhanced the velocity profile but declines velocity profile due to higher values of Ec . The thermal thickness enhances due larger values of γ and Pr but thermal thickness declines due to higher values of Ec and N t . The concentration profile enhances due to enhancing the values of Ec and Pr but concentration profile declines due to increasing the values of N t . Nusselt number enhaced due to higher values of Ec , S c and N t but declines of higher values of Pr .

Flow separation due to shock wave/boundary layer interaction is dominated in blade passage with supersonic relative incoming flow, which always accompanies aerodynamic performance penalties. A loss reduction method for smearing the passage shock foot via Shock Control Bump (SCB) located on transonic compressor rotor blade suction side is implemented to shrink the region of boundary layer separation. The curved windward section of SCB with constant adverse pressure gradient is constructed ahead of passage shock-impingement point at design rotor speed of Rotor 37 to get the improved model. Numerical investigations on both two models have been conducted employing Reynolds-Averaged Navier-Stokes (RANS) method to reveal flow physics of SCB. Comparisons and analyses on simulation results have also been carried out, showing that passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot for moderate adverse pressure gradient as well as suppression of boundary layer separations and secondary flow of low-momentum fluid within boundary layer. It is found that adiabatic efficiency and total pressure ratio of improved blade exceeds those of baseline at 95%-100% design rotor speed, and then slightly worsens with decrease of rotatory speed till both equal below 60% rated speed. The investigated conclusion implies a potential promise for future practical applications of SCB in both transonic and supersonic compressors.

We investigate the error scaling and computational cost of wall-modeled large-eddy simulation (WMLES) for external aerodynamic applications. The NASA Juncture Flow is used as representative of an aircraft with trailing-edge smooth-body separation. Two gridding strategies are examined: i) constant-size grid, in which the near-wall grid size has a constant value and ii) boundary-layer-conforming grid (BL-conforming grid), in which the grid size varies to accommodate the growth of the boundary-layer thickness. Our results are accompanied by a theoretical analysis of the cost and expected error scaling for the mean pressure coefficient ($C_p$) and mean velocity profiles. The prediction of $C_p$ is within less than $5\%$ error for all the grids studied, even when the boundary layers are marginally resolved. The high accuracy in the prediction of $C_p$ is attributed to the outer-layer nature of the mean pressure in attached flows. The errors in the predicted mean velocity profiles exhibit a large variability depending on the location considered, namely, fuselage, wing-body juncture, or separated trailing-edge. WMLES performs as expected in regions where the flow resembles a zero-pressure-gradient turbulent boundary layer such as the fuselage ($, arXiv admin note: text overlap with arXiv:2101.00331

Implicit large-eddy simulations of reflecting shock-wave turbulent boundary-layer interactions at a freestream Mach number of 2.05 were carried out for sweep angles of 0, 20, and 40 deg. The simula...

High-temperature high-velocity steam exposures of (0001) sapphire coupons were performed at temperatures of 1200 °C–1450 °C to determine the quantitative capability of the steamjet apparatus. Recession results were compared to calculated values of Al(OH)3 (g) mass transfer rates based on laminar flow models and available thermodynamic data for Al(OH)3 (g). Linear material volatilization rates and a strong gas velocity dependence on the reaction depth confirmed that the Al2O3 reaction was controlled by a gas-phase diffusion process. The temperature dependence for the steam reaction agreed with thermodynamic calculations and with the literature, confirming that Al(OH)3 (g) transport through a gas boundary layer represents the rate-limiting step for Al2O3 volatilization in steam. The steamjet experimental setup can thus be utilized for determination of steam-oxide reaction thermodynamics given known steam flow conditions. Steamjet test recession results for simple oxides are discussed for comparison with behavior of complex oxides that form porous product layers, which are not yet well understood.

Fluids like hybrid nanofluids have great potential that present exceptional thermal behavior and thermophysical properties as compare to ordinary nanofluids. Hybrid nanofluids are obtained by the mixture of two different nanoparticles in a base fluid. Many scholars stated that hybrid-nanofluids could be replaced by conventional coolants, especially fluids which work at high temperature. Therefore, these kinds of nanofluids are less damaging for environmental impact and also lead to save energy. The main idea of hybrid nanofluids is to develop performance of heat transfer and its advantages has directed to comparatively good hope for its applications. The objective of present article is to examine 3D stagnation point flow of hybrid nanofluid passes along a stretchable heated wavy cylinder under the impact of variable thickness and slip conditions. For this purpose we consider alloy particles of AA7075 + AA7072 and AA7072 which are suspended in methanol liquid. The alloy particles merged in this analysis are entirely manufactured materials as well as possessing higher heat transfer characteristics. Alloy AA7072 is a combination of zinc and aluminum in ratio 1:98 with addition of metals like silicon, copper and ferrous. Similarly, alloy AA7075 is a combination of zinc, aluminum, copper and magnesium in ratio −6, −9, −1 and −3 respectively with addition of metals like silicon, magnesium and ferrous. The scenario of this model is scrutinized mathematically by captivating induced magnetic field with in the domain of thermal boundary layer. Similarity transformations are deployed to change the governing equations into nonlinear ODEs and consequently solved this system through bvp4c solver. The impact of emerging parameters on velocity, induction and energy distributions are examined through graphical depiction. Furthermore, heat transfer rates and drag forces near the boundary are designed numerically in tabular form.

Hypersonic high-enthalpy wind tunnels have been a challenge to ground tests in aerospace research area for decades and its test flow uniformity is one of the most important parameters for evaluating wind tunnel performances. Regarding to the performance requirement, theories and methods for designing hypersonic flow nozzles at high enthalpy conditions are quite difficult, but very interesting topics, especially when air molecule dissociations take place in wind tunnel test gas reservoirs. In this paper, fundamental theories and important methods for nozzle designs are briefly reviewed with the emphasis on two-dimensional axisymmetric nozzles for hypersonic high-enthalpy wind tunnels, including the Method of Characteristics (MOC), the graphic design method, the Sivells method, the theory for boundary correction, and the CFD-based design optimization methods. These theories and methods had been proposed based on several physical issues, respectively, which play important roles in nozzle flow expansion processes. These issues cover the expansion wave generation and reflection, the boundary layer development, the real gas effect of hypersonic high-enthalpy flows. Difficulties arising from applications of these methods in hypersonic high-enthalpy nozzle design are discussed in detail and the state of the art of the nozzle design technologies that have reached for decades is summarized with some brief comments. Finally, the prospect for the hypersonic nozzle design methods, and its numerical and experimental verifications are provided with from authors’ viewpoint for readers’ reference.

Wind turbines are mostly prone to reduced aerodynamic performance due to the inevitable occurrence of the roughness on blades. However, it may be possible to control the boundary layer by means of the right sort of roughness. In this study, distributed passive roughness is applied to the surface of NACA 63–415 airfoil. The influence of the roughness on the aerodynamic performance is numerically investigated by means of the TSST turbulence model for 103 ≤ Re ≤ 3 × 106 and for the angle of attack α = 6°. Results show that the effect of roughness on the airfoil performance is negligible for Re ≤ 104. However, for 5 × 104 ≤ Re ≤ 1.5 × 105, the surface roughness can significantly improve the aerodynamic performance. Furthermore, for Re = 2.5 × 105, the roughness still has a favourable effect until the roughness height of h = 0.1 mm. Moreover, it is observed that for 2.5 × 105

This article has the objective of examining to perform unstable magnetohydrodynamic flow over an inclined plate enclosed in a penetrable mechanism with Soret-aligned magnetic field and chemical reaction. Once momentum and energy and mass are equal, they can be combined using the diffusion equation to yield the dimensionless momentum/energy/mass model. Aligned Magnetic field, Jeffrey Parameter, Inclined angle, and Chemical Reaction Model outlines are used to study the effect of numerous physical parameters on boundary layer properties, including Soret temperature, chemical reaction velocity, Temperature and concentration on the resulting heat accumulation profile, are tested using parametric models. The findings derived from skin friction, Nusselt number, and Sherwood numbers are included in the tables provided for several parameters. It is observed from the results that the velocity profile increases with increase Thermal and Mass Grashof Numbers, Jeffery Parameter and Porous media but the opposite trends are seen with increase in the magnetic field parameter, inclined parameter and Aligned magnetic field parameter. One of the important findings of this analysis includes that intensification in the Newtonian heating effect causes a gradual downfall in the rate of heat transfer at the plate and the concentration of the fluid decreases under the impact of chemical reaction. Their physic- Chemical features have been dealt with in detail. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

Different types of rotating disk boundary layers were previously shown to be absolutely unstable. The present study checks if this is also true for the flow between narrowly spaced co-rotating disks with merged boundary layers and imposed throughflow. The described method is able to reproduce the absolute instability of the von Karman boundary layer and of radially outward flow between co-rotating disks with separated boundary layers. Nevertheless, no absolute instability is found for the case of narrow disk spacing with merged boundary layers for both radially inward and outward flow. The data does however show convective instability. Stability maps are provided for the analysed parameter space.

From the formal expansion of the solutions of Euler-Voigt equations in R + 2 with no-slip boundary conditions, the boundary layer equations of Euler-Voigt equations to Euler equations are obtained. In case of the analytic data, one obtains the local existence and uniqueness of the solutions for the boundary layer equations by abstract Cauchy-Kovalevskaya theorem.

The study focuses on the design and materialistic amendments for thermal performance evaluation of a heat sink which is a just modified version of the conventional heat sink used for processor Ryzen 5 3600, introduced by a company named Advanced Micro Devices (AMD) for cooling applications in High-Performance Gaming PCs. The enhancement of the cooling strategy is achieved within dimensional and cost constraints by modifying the parametric dimensions, increasing the surface area, and introducing metal to the air-fluid boundary layer aspects into it. In this study, the heat sink is designed with a core of cylindrical shape, keeping a height of 20 mm and a diameter of 90 mm. Also, the universal dimensional compatibility of this heat sink is considered for the performance evaluation, followed by design and angle of air-fin interaction, swapped center rectangle shape with a frustum to decrease the thermal hindrance and to increase the surface area without any increment in overall volume. Moreover, the fin density in the module of the heat sink has also been increased to enhance the convective heat transfer strategy from the surface. Both designing & simulation have been carried out on the FEM tool Autodesk Fusion 360 and based on the numerical investigation on the modified design as per the conventional design, although our design is much more complex to manufacture in the first place. It has been observed that the new design is capable of providing 64.23% convective heat dissipation from the surface as well as able to reduce 50.9% of CPU surface temperature in comparison to the existing design of heat sink.

The effect of the surface conductivity on the electrical and mechanical characteristics of the surface dielectric barrier discharge actuator has been numerically investigated in this study. Two typical AC-surface dielectric barrier discharge actuators, wire-to-plate and plate-to-plate have been considered to control airflow alongside a flat dielectric plate. A sinusoidal high voltage of varied frequencies and amplitudes is supplied to the active electrode, and the passive electrode, which is grounded, is encapsulated inside a dielectric plate. Two-species ion transport model, involving generic positive and negative ions, coupled to the electrostatics model is assumed. The electrostatic field is affected by both the space and the surface charges. The surface charge is accumulated due to ion deposition, but its distribution varies due to the surface ohmic conduction. The Navier-Stokes equations for the flow simulation, which include the time-averaged electrohydrodynamic body force determined from the discharge model, are solved to analyze the flow field and the boundary layer morphology. The numerical algorithm has been implemented in the COMSOL commercial package. The significance of the dielectric surface conductivity on the discharge behavior and the flow field has been shown. The dielectric surface conductivity behaves non-monotonically and affects the flow field by altering the EHD force strength, direction and distribution.

The paper focuses on a theoretically study of fluid flow and heat transfer of Eyring-Powell fluid in a boundary layer over a flat surface. For the first time, groups of symmetry transformations were obtained for the full rheological law of Eyring-Powell fluid. This enabled obtaining self-similar forms of nonlinear differential equations different from the classical Blasius forms, which describe the limiting case for the large values of the parameter A. At the same time, the self-similar Blasius forms correctly describe the transition from the velocity profiles for a Newtonian fluid to linear profiles for Eyring-Powell fluid. The velocity and temperature profiles become less full due to the increasing parameter A, so that finally these profiles exhibit a linear shape. The friction coefficients and the Nusselt numbers decrease with the increasing parameter А.

Because a fluctuating incoming flow can affect with the unstable shock train movement, a numerical study was performed to analyze the effects. For the base flow with constant incoming and downstream flow conditions, the fundamental frequency and dominant role of the first separation shock are confirmed. The oscillations of the first separation shock are not always strengthened with an increase of the excitation amplitude at the resonant frequency. It is found that with a specific amplitude, the pressure peak in the shock wave/boundary layer interaction is enhanced, which can effectively suppress the upstream movement of the separation shock. However, a further increased excitation results in a wider oscillation region and greater pressure fluctuation. The non-negligible effects of the core flow enhance the oscillation of the separation shock.

We aim to address the consensus tracking problem for multiple-input-multiple-output (MIMO) linear networked systems under directed switching topologies, where the leader is subject to some nonzero but norm bounded inputs. First, based on the relative outputs, a full-order unknown input observer (UIO) is designed for each agent to track the full states' error among neighboring agents. With the aid of such an observer, a discontinuous feedback protocol is subtly designed. And it is proven that consensus tracking can be achieved in the closed-loop networked system if the average dwell time (ADT) for switching among different interaction graph candidates is larger than a given positive threshold. By using the boundary layer technique, a continuous feedback protocol is skillfully designed and employed. It is shown that the consensus error converges into a bounded set under the designed continuous protocol. Second, as part of the full states' error can be constructed via the agents' outputs, a reduced-order UIO is thus designed based on which discontinuous and continuous feedback protocols are, respectively, proposed. By using the stability theory of the switched systems, it is proven that the consensus error converges asymptotically to 0 under the designed discontinuous protocol, and converges into a bounded set under the designed continuous protocol. Finally, the obtained theoretical results are validated through simulations.

Two techniques are presented for characterisation of cloud-feeding coherent boundary-layer structures through analysis of large-eddy simulations of shallow cumulus clouds, contrasting conditions with and without ambient shear. The first technique is a generalisation of the two-point correlation function, where the correlation length-scale as well as the orientation can be extracted. The second technique identifies individual coherent structures and decomposes their vertical transport by the shape, size, and orientation of these objects. The bulk-correlation technique is shown to capture the elongation and orientation of coherence by ambient wind, but is unable to characterise individual coherent structures. Using the object-based approach, it is found that the individual structures dominating the vertical flux are plume-like in character (extending from the surface into cloud) rather than thermal-like, show small width/thickness asymmetry, and rise near-vertically in the absence of ambient wind. The planar stretching and tilting of boundary-layer structures caused by the introduction of ambient shear is also quantified, demonstrating the general applicability of the techniques for future study of other boundary-layer patterns.

In this paper, the linear finite element method on a Bakhvalov-type mesh is applied to a singularly perturbed problem with two parameters. The solution of the problem exists two exponential boundary layers. A new interpolation, which is simple in construction and analysis, is introduced for convergence analysis. Furthermore, we find a subtle relationship between the Bakhvalov-type mesh itself and the weaker exponential layer and obtain an interesting result. Finally, we prove a supercloseness result between the Lagrange interpolation and the numerical solution. Numerical tests confirm our theoretical results.

In this study, we present numerical and theoretical study of enthalpy and solar radiative heat transfer in a generalized Newtonian fluid flow induced by a flat plate. Our theoretical study depends on thermal diffusion coefficient, thermophoretic and viscous dissipation approach for modeling the steady boundary layer flow of heat and mass transfer over a flat surface. Impact of thermal diffusion coefficient with newly introduced enthalpy at heat and mass equations is considered. The boundary layer equations are transformed into system of ordinary differential equations by applying similarity variables and solved numerically by utilizing fifth-order Runge–Kutta integrator scheme with shooting technique. The physical results are explored by utilizing theoretical and numerical approaches. The numerical results acquired for different mechanisms are presented through tables and figures. The physical properties of the appearing parameters on the mean flow, temperature and concentration are presented through graphs and tables The comparative results are calculated for a limited case and good agreement is noted with previously published work.

Numerical modeling of turbulent fluid flow generally valid only for fully developed turbulent flow without consideration of laminar flow region. Generally in any flow past body consist of laminar flow region eventually it turn to turbulent over a finite length. The prediction of laminar to turbulent transition boundary flow is influence the boundary separation in the turbulent zone and its effects in delay of separation. In this paper transition flow is predicted by fully turbulent flow solved by turbulent Kinetic energy and Specific turbulent dissipation models, transition is modeled by coupling of turbulent scalars and kinetic energy of laminar fluctuations. Transition model is analyzed over flow past aerofoil.

A numerical simulation study of laminar hypersonic cold airflow over the backward-facing step (BFS) is performed at a freestream Knudsen number of 0.00009589 for resolving the flow field. The effects on the wall properties caused by the expansion of the flow and the separation of the boundary layer at the step corner have been investigated. The contributions of pressure and viscosity to the coefficients of lift and drag have been elucidated. It is seen that an increase in step height “nh” from n = 1 to 5 for a freestream flow at Mach 7.6 produces an incremental effect on the CL/CD ratio, whose range is between −1 to 1 for the variations in the step height simulated. The current study concludes that BFS yet remains a geometry that contributes to more drag than lift, however that effect can be minimized by increasing the step height during the design process of hypersonic vehicles for the above-mentioned Mach number.