Nonlinear Flow Research Articles

Optimal scheduling of hydrogen blended integrated electricity–gas system considering gas linepack via a sequential second-order cone programming methodology

In the context of increasing global environmental pollution and constant increase of carbon emission, hydrogen production from surplus renewable energy and hydrogen transportation using existing natural gas pipelines are effective means to mitigate renewable energy fluctuation, build a decarbonized gas network, and achieve the goal of “carbon peak and carbon neutral” in China. Existing gas network modeling with hydrogen blended is divided into steady-state and dynamic. The steady-state modeling oversimplifies the physical process, while the dynamic modeling is computationally intensive. Thus, a quasi-steady-state modeling method of a hydrogen blended integrated electricity–gas system (HBIEGS) considering gas linepack is developed in this paper. The gas linepack refers to the gas stored in natural gas pipelines due to the compressibility of the gas. As a form of gas energy storage, linepack can enhance system flexibility by coping with wind power uncertainty. In the face of nonlinear gas flow equations in HBIEGS, conventional relaxation or approximate methods cannot provide a sufficiently feasible optimal solution. Therefore, a sequential second-order cone programming (S-SOCP) method is proposed to solve the developed model. It can effectively strike a balance between solution speed and the quality of the solution obtained. Finally, the modified IEEE-24-node power system and 12-node natural gas system are used to validate the effectiveness of the developed model and the proposed method. The optimization results show that the proposed method improves the computational efficiency by 91% compared with a general nonlinear solver.

Pore-scale insight into the effect of porous walls on fluid flow in rough-walled fractures

This study investigates the influence of porous walls on fluid flow behavior in single rough-walled fractures. A series of direct numerical simulations (DNS) were conducted to examine fluid flow through rough-walled fractures surrounded by porous walls under various hydraulic gradients. The simulation results clearly demonstrate the progressively significant impact of porous walls on flow characteristics as porosity increases. Regression analyses indicate that the Forchheimer's law, which characterizes the nonlinear flow of rock fractures, remains valid in the presence of porous walls. Moreover, increased porosity enhances fluid exchange and leads to an increased ability for single fractures to transmit fluid. Two double-parameter equations were established to quantitatively characterize the effects of porous walls on hydraulic conductivity of the fracture and fluid exchange between porous walls and the fracture. Further analysis revealed that the angle between the fracture profile and main flow direction profoundly influences the inflow/outflow exchange between the fracture and its adjacent porous walls. Moreover, the pore-scale results indicate that it is unreasonable to equate the effect of porous walls with slip boundaries as suggested in previous studies. The results and findings of this study deepen our understanding of flow behavior at the interface between the rough-walled fracture and adjacent porous walls, and they serve as a basis for accurately simulating large-scale fracture networks that consider the hydraulic contribution of fracture walls.

Numerical investigation on the hydrodynamic performance of a land-based OWC system with multi-chamber modules

Modular design of wave energy converters (WECs) can offer a promising scheme to improve the economic competitiveness of wave energy by reducing the levelized cost of energy. In this study, the hydrodynamic performance of a land-based oscillating water column (OWC) system with multi-chamber modules is evaluated to optimize the layout and design of the system, the OWC structure is extended to five-chamber modules. A two-dimensional wave flume is developed using the high-order boundary element method to simulate the interaction of the incident waves with the OWC device based on the fully non-linear potential flow theory. The proposed numerical model is validated by published experimental data. It is concluded that the two-chamber installation provides superior hydrodynamic performance compared with the single-chamber OWC. The five-chamber OWC system is more suitable for energy capture in low-frequency wave conditions, where the first and last chambers are dominant in energy extraction. From the perspective of energy conversion efficiency and economy, the two- and three-chamber systems are most suitable for targeting low and high frequency waves in the tested conditions, respectively. Additionally, the resonant frequency of the single-chamber module plays a decisive role in the energy capture of the OWC system, and a chamber with a low resonant frequency and a small orifice opening ratio should be selected as the module unit. This paper provides valuable guidance for the modular application of OWCs and the arrangement of multiple chambers.

Analysis of nonlinear poroviscoelastic flows with discontinuous porosities *

Abstract Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence of initial porosities with jump discontinuities are identified.

Macro–Micro-Coupled Simulations of Dilute Viscoelastic Fluids

Modeling the flow of polymer solutions requires knowledge at various length and time scales. The macroscopic behavior is described by the overall velocity, pressure, and stress. The polymeric contribution to the stress requires knowledge of the evolution of polymer chains. In this work, we use a microscopic model, the finitely extensible nonlinear elastic (FENE) model, to capture the polymer’s behavior. The benefit of using microscopic models is that they remain faithful to the polymer dynamics without information loss via averaging. Their downside is the computational cost incurred in solving the thousands to millions of differential equations describing the microstructure. Here, we describe a multiscale flow solver that utilizes GPUs for massively parallel, efficient simulations. We compare and contrast the microscopic model with its macroscopic counterpart under various flow conditions. In particular, significant differences are observed under nonlinear flow conditions, where the polymers become highly stretched and oriented.

Experimental and numerical flutter analysis of a folding fin with multiple asymmetric free-plays

Experimental folding fin models with an adjustable free-play are tested in a wind tunnel. The fin structure is modeled using the free-interface component mode synthesis method, and its free-play is modeled as four independent nonlinear springs with asymmetric stiffness. A nonplanar unsteady vortex-lattice method considering compressibility is employed to address nonlinear deformation and high subsonic flow. Surface spline interpolation is improved through projection and partition. The aeroelastic characteristics of folding fins with different free-play magnitudes, initial conditions and elastic-axis positions are analyzed using an established time-marching method because of its relatively small computation scale and high precision. The results show good consistency among the presented method, the wind tunnel test and the harmonic balance method. There is a negative correlation between the critical speed of divergent motion and the ratio of the initial condition to the free-play magnitude. If either the free-play magnitude or the initial condition is extreme (tiny or vast), the system nonlinearity degenerates to linearity. Generally, the flutter prevention design of a linear model can be applied to a nonlinear model, such as moving the elastic-axis position aftward. The presented fin configuration exhibits an unstable limit cycle oscillation because the orders of coupled flutter modes do not change with variations in equivalent linear stiffness.

Complementarity reformulations for the optimal design of distributed energy systems with multiphase optimal power flow

The optimal design of grid-connected distributed energy systems (DES) has been previously investigated, but most studies exclude nonlinear multiphase optimal power flow (MOPF) constraints which capture imbalances in alternating current (AC) distribution networks. Previous DES design studies considering AC power flow assume balanced loads and networks, which is an assumption that does not hold for distribution networks that are often inherently unbalanced. This is the first study to present an optimisation framework for designing grid-connected DES while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution. This study proposes a new algorithm for obtaining DES designs subject to nonlinear multiphase power flow constraints with regularised complementarity reformulations for operational constraints containing binary variables. DES design models with either MOPF or OPF are tested using an unbalanced distribution network, where rooftop solar, gas boilers, and battery storage are considered as distributed resources. Despite the increased complexity, DES design with MOPF obtains the best solution, with 81% greater solar capacity and 6% lower total annualised cost when compared to DES with OPF. Designs from a commonly-used linear DES design framework based on direct current (DC) approximations produce the highest costs (8% more than initially predicted) when tested with MOPF. The proposed algorithm with complementarity reformulations achieves a 19% improvement in the objective value over a previous two-stage decomposition for DES with OPF, where the entire binary topology in the nonlinear model is fixed. The study therefore enables the acquisition of DES designs that can work symbiotically within unbalanced distribution networks.

A hybrid RSA-IPA optimizer for designing an artificial neural network to study the Jeffery-Hamel blood flow with copper nanoparticles: Application to stenotic tapering artery

In this study, the effects of copper nanoparticles are taken into account to create a new hybrid metaheuristic for solving the nonlinear MHD Jeffery-Hamel blood flow problem. Since copper nanoparticles are effective in lowering the hemodynamics of stenosis, the subject has scientific and biological implications. The coupled partial differential equations are converted to ordinary differential equations using suitable transformations. Considering an artificial neural network as a solution, the error function has been formed for the differential equations. A hybrid of the reptile search algorithm (RSA) and the interior point algorithm (IPA) is used to minimise the error function (≤10−05). The initial weights are first updated using the RSA algorithm (maximum 20 iterations), which is used as a tool for global search; later, IPA is used for quick local convergence. To validate the proposed technique’s accuracy, comparison studies are conducted using the fourth-order Runge-Kutta method and the hybrid PSO-IPA algorithm. Statistical analysis is provided using multiple performance indices to demonstrate the suggested approach’s precision, efficiency, and reliability. The research findings indicate that the outcomes achieved by the developed RSA-IPA technique exhibit superior performance compared to previously established methodologies, with an accuracy level of 10−04. The findings indicate that a rise in the volume fraction of cu-nanoparticles results in a decrease in the rate of blood flow. The research advances studies of blood flow in the medical sciences.

Dynamics of thin self-rewetting liquid films on an inclined heated substrate

In this paper, we investigate the quadratic Marangoni instability along with inertia in a self-rewetting fluid film that has a nonmonotonic variation of surface tension with temperature. The dynamics of such a thin self-rewetting fluid film flowing along an inclined heated substrate is examined by deriving an evolution equation for the film thickness using long-wave theory and asymptotic expansions. By adopting the derived long-wave model that includes the inertial and thermocapillary effects, we perform a linear stability analysis of the flat film solution. Two cases of the nonlinear flow are explored in depth using Tm (temperature corresponding to the minimum of surface tension) as the cutoff point. One is the case of (Ti,s−Tm)<0, and the other is (Ti,s−Tm)>0, where Ti,s is the interface temperature corresponding to the flat film. The Marangoni effect switches to the anomalous Marangoni effect as (Ti,s−Tm) shifts from a negative value to a positive value. Our calculations reveal that the Marangoni effect augments the flat film instability when (Ti,s−Tm)<0, whereas the stability of the flat film is promoted for (Ti,s−Tm)>0. Our further analysis demonstrates that the destabilizing inertial forces can be entirely compensated by the stabilizing anomalous thermocapillary forces. We verify the linear stability predictions of the long-wave Benney-type model with the solution to the Orr–Sommerfeld problem in the long-wave limit. Our time-dependent computations of the long-wave model establish the modulation of interface deformation in the presence of inertia and temperature gradients in the conventional Marangoni regime, whereas such deformations are suppressed in the anomalous Marangoni regime. A comparison of the numerical computations with the linear theory shows good agreement.

A study on aerodynamics of Ultra-efficient cars

Ultra-efficient cars (i.e. Formula One racing cars) are loaded with many different aerodynamic components. They interact to produce highly nonlinear flows, which have a very complex effect on the airflow around the racing car. Clearing up fluid phenomena makes it possible to optimize aerodynamic components effectively. This paper reviews the aerodynamic performance of currently used shapes, as well as the definition of the design constraints for the vehicle. The designs are inspired by formula one cars, especially by Honda F1 Team, but they are adjusted according to the limit conditions of CFD simulation software Ansys CFX, and parameters are scaled accordingly based on the space requirements of this test. A level of velocity at 40 km/h is tested, giving ideas of the full model performance. Results are then compared and discussed to obtain a comprehensive and valid conclusion about the potential improvement in the aerodynamics of road cars, which can be extracted from those ultra-efficient ones.

A new theoretical model for the nonlinear flow in a rough rock fracture under shear

Shear deformations significantly affect the nonlinearity of fluid flow in rock fractures. To estimate this nonlinear flow using the Izbash equation, it is necessary to determine the Izbash coefficients. However, their parametric expressions are rarely mentioned, particularly when the shear-flow process is involved. This study proposed an improved Izbash equation-based model by incorporating the Darcy–Weisbach equation, along with a friction factor. The proposed model considers two asymptotic cases. At low Re regime, the fluid flow regime is dominated by the viscous effect, and the proposed model can be approximated to the cubic law. When Re reaches a certain threshold (Res), the fluid flow transitions into a fully turbulent flow regime where the inertia force dominates the fluid behaviours. Consequently, the proposed model is equivalent to the quadratic term of the Forchheimer equation. The proposed model is verified with the experimental results conducted on 5 rough fracture surfaces with normal stress from 0.5 to 3 MPa. Good correlations between the experimental and analytical curves illustrated that the proposed model of strong theoretical foundation yielded good prediction signified by the Normalised Objective Function (NOF) and an average error (σ¯ave) within 0.18 and 15 %, respectively.

A nonlinear multi-period hydrothermal optimal power flow model for hydropower systems

Despite their social and climate benefits, renewable energy sources also present challenges such as intermittency, volatility and randomness, which may considerably reduce security and reliability of the system. Hydro units have the ability to provide flexible and rapid energy reserves, serving as an effective way of handling these challenges. Yet, many Hydrothermal Optimal Power Flow (HOPF) models in the literature often provide a simplified and sometimes inaccurate representation of the hydraulic aspects. In most HPOF models proposed in the literature, the representation of hydraulic aspects disregards important physical and operational hydro constraints. Such simplifications can curtail the potential benefits of hydro generation, especially concerning system security and reliability. In this paper, we investigate the impact of hydro constraints in the operation of hydrothermal systems by means of HOPF models. For such a purpose, we propose a nonlinear multi-period active–reactive HOPF model where hydro constraints are represented in detail, by means of a nonlinear framework. This model presents innovative formulations for hydro units, specifically designed to address pivotal non-differentiable constraints. The proposed multi-period HOPF model is used as a benchmark to assess inaccuracies present in linear or linearized HOPF model variants. The results using the IEEE 24-bus and 300-bus systems, adapted so they become hydropower systems, clearly identify significant impact of some hydro constraints which have been neglected in most models described in the literature, in the hydrothermal operational policy and scheduling.

Computation of flow rates in rarefied gas flow through circular tubes via machine learning techniques

Kinetic theory and modeling have been proven extremely suitable in computing the flow rates in rarefied gas pipe flows, but they are computationally expensive and more importantly not practical in design and optimization of micro- and vacuum systems. In an effort to reduce the computational cost and improve accessibility when dealing with such systems, two efficient methods are employed by leveraging machine learning (ML). More specifically, random forest regression (RFR) and symbolic regression (SR) have been adopted, suggesting a framework capable of extracting numerical predictions and analytical equations, respectively, exclusively derived from data. The database of the reduced flow rates W used in the current ML framework has been obtained using kinetic modeling and it refers to nonlinear flows through circular tubes (tube length over radius l∈[0,5]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l \\in [0,5]$$\\end{document} and downstream over upstream pressure p∈[0,0.9]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \\in [0,0.9]$$\\end{document}) in a very wide range of the gas rarefaction parameter δ∈[0,103]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\in [0,10^3]$$\\end{document}. The accuracy of both RFR and SR models is assessed using statistical metrics, as well as the relative error between the ML predictions and the kinetic database. The predictions obtained by RFR show very good fit on the simulation data, having a maximum absolute relative error of less than 12.5%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$12.5\\%$$\\end{document}. Various expressions of the form of W=W(p,l,δ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W=W(p,l,\\delta )$$\\end{document} with different accuracy and complexity are acquired from SR. The proposed equation, valid in the whole range of the relevant parameters, exhibits a maximum absolute relative error less than 17%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$17\\%$$\\end{document}. To further improve the accuracy, the dataset is divided into three subsets in terms of δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document} and one SR-based closed-form expression of each subset is proposed, achieving a maximum absolute relative error smaller than 9%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$9\\%$$\\end{document}. Very good performance of all proposed equations is observed, as indicated by the obtained accuracy measures. Overall, the present ML-predicted data may be very useful in gaseous microfluidics and vacuum technology for engineering purposes.

Discrete optimal designs for distributed energy systems with nonconvex multiphase optimal power flow

The optimal selection, sizing, and location of small-scale technologies within a grid-connected distributed energy system (DES) can contribute to reducing carbon emissions, consumer costs, and network imbalances. There is a significant lack of studies on how DES designs, especially those with electrified heating systems, impact unbalanced low-voltage distribution networks to which most DES are connected. This is the first study to present an optimisation framework for obtaining discrete technology sizing and selection for grid-connected DES design, while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution networks. An algorithm is developed to solve the resulting Mixed-Integer Nonlinear Programming (MINLP) formulation. It employs a decomposition based on Mixed-Integer Linear Programming (MILP) and Nonlinear Programming (NLP) and uses integer cuts and complementarity reformulations to obtain discrete designs that are also feasible with respect to the network constraints. A heuristic modification to the original algorithm is also proposed to improve computational speed. Improved formulations for selecting feasible combinations of air source heat pumps (ASHPs) and hot water storage tanks are also presented. Two networks of varying size are used to test the optimisation methods. Designs with electrified heating (ASHPs and tanks) are compared to those with conventional gas boilers. The algorithms outperform one of the existing state-of-the-art commercial deterministic MINLP solvers, which fails to find any solutions in two instances within specified time limits. While feasible solutions were obtained for all cases, convergence was not achieved for all, especially for those involving the larger network. Where converged, the algorithm with the heuristic modification has achieved results up to 70% faster than the original algorithm. Results for case studies suggest that including ASHPs can support up to 16% higher renewable generation capacity compared to gas boilers, albeit with higher ASHP investment costs, as local generation and consumption minimises network violations associated with excess power export. The results also show the importance of including nonlinear power flow constraints in DES design problems. The optimisation framework and results can be used to inform stakeholders such as policymakers and network operators, to increase renewable energy capacity and aid the decarbonisation of domestic heating systems.

Heat transfer analysis of Maxwell tri-hybridized nanofluid through Riga wedge with fuzzy volume fraction

This contribution aims to optimize nonlinear thermal flow for Darcy-Forchheimer Maxwell fuzzy left( {{text{Al}}_{{2}} {text{O}}_{{3}} + {text{Cu }} + {text{TiO}}_{{2}} {text{/EO}}} right) tri-hybrid nanofluid flow across a Riga wedge in the context of boundary slip. Three types of nanomaterials, {text{Al}}_{{2}} {text{O}}_{{3}} , Cu and {text{TiO}}_{2} have been mixed into the basic fluid known as engine oil. Thermal properties with the effects of porous surface and nonlinear convection have been established for the particular combination left( {{text{Al}}_{{2}} {text{O}}_{{3}} + {text{Cu}} + {text{TiO}}_{{2}} {text{/EO}}} right){.} Applying a set of appropriate variables, the set of equations that evaluated the energy and flow equations was transferred to the dimensionless form. For numerical computing, the MATLAB software's bvp4c function is used. The graphical display is used to demonstrate the influence of several influential parameters. It has been observed that flow rate decay with expansion in porosity parameter and nanoparticles volumetric fractions. In contrast, it rises with wedge angle, Grashof numbers, Darcy-Forchheimer, nonlinear Grashof numbers, and Maxwell fluid parameter. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increases in drag force for ternary hybrid nanofluid are 13.2 and 8.44 when the Modified Hartmann number takes input in the range 0.1 le {text{Mh}} le 0.3 and wedge angle parameters 0.1 le m le 0.3. For fuzzy analysis, dimensionless ODEs transformed into fuzzy differential equations and employed symmetrical triangular fuzzy numbers (TFNs). The TFN makes a triangular membership function (M.F.) that describes the fuzziness and comparison. This study compared nanofluids, hybrid nanofluids, and ternary nanofluids through triangular M.F. The boundary layer flow caused by a wedge surface plays a crucial role in heat exchanger systems and geothermal.

Experimental Study on the Influence of Hypergravity on the Nonlinear Flow Behaviour in Rock Fracture

Experimental Study on the Influence of Hypergravity on the Nonlinear Flow Behaviour in Rock Fracture

Bounding nonlinear stretching about spacecraft trajectories using tensor eigenpairs

Local linearization is often used to enable analytical methods in spacecraft dynamics, navigation, and control. However, the linear approximation becomes inaccurate at large distances from the linearization point and/or when the underlying dynamical system is strongly nonlinear. As a result, linearization-based methods like the finite time Lyapunov exponent (FTLE) can underestimate stretching in phase space. Alternatively, this paper presents a semianalytical method to quantify nonlinear stretching: the eigenpairs of higher-order tensors are used to bound the maximum stretching of a state deviation over time. The tenors in question are derived from the Taylor series expansion of a nonlinear solution flow about a reference trajectory, i.e., the state transition tensor (STT) expansion. It is well known that the eigenvalues of the Cauchy–Green tensor (CGT) bound the stretching of state deviations over time for a linear system, and the largest eigenvalue can be related to the FTLE. This paper will present higher-order, nonlinear analogs to the CGT and the FTLE to more accurately bound nonlinear stretching for applications in guidance, navigation, and control.

Laplace transform solution of the time-dependent annular Couette flow with dynamic wall slip

The annular Couette flow has several industrial applications, particularly for the characterization of the fluid flow and deformation behavior of fluids. The inclusion of the dynamic wall slip into the flow boundary conditions seems to be necessary for an efficient continuum description of motion of nanofluidics as it reflects the importance of fluid–structure interface related phenomena. Dynamic wall slip introduces a dissipative boundary condition and thus increases the difficulties of finding solutions to related problems. In the present work we investigate the behavior of fluid flow between two infinitely long coaxial circular cylinders, when the inner cylinder is axially moving due to sudden constant velocity, while the outer cylinder is held stationary. The boundary condition on the outer cylinder is that of dynamic wall slip, in addition to the usual Navier slip. The medium considered here is a Newtonian viscous fluid. The solution of the governing equations, initial and boundary conditions for this flow is obtained using the Laplace transform technique and inversion by Laguerre polynomials. This method may be useful, when applied in conjunction with perturbation methods, to solve nonlinear Couette flow problems involving temperature changes. Numerical results are presented and discussed.

Analysis of Nonlinear Flow and Heat Transfer Issues in Nanofluid by Using RK-4th Order Method

Nanofluids, composed of a base fluid with dispersed nanoparticles, have gained significant attention due to their unique thermal and flow characteristics. Understanding the nonlinear flow and heat transfer phenomena in nanofluids is crucial for optimizing their performance in engineering applications. In this study, we propose using the Runge-Kutta 4th order (RK-4) numerical method to analyze these issues. The RK-4 method is known for its accuracy and efficiency in solving ordinary differential equations. By applying this method to the governing equations of fluid flow and heat transfer, we can accurately capture the nonlinear behavior of nanofluids. We investigate various nonlinear phenomena, such as boundary layer separation, flow instability, and heat transfer enhancement, considering factors like nanoparticle concentration, size, shape, fluid properties, Reynolds number, and temperature gradient. The RK-4 method provides accurate solutions, revealing critical parameters that affect flow and heat transfer behavior. Comparisons with experimental data and other numerical methods validate the approach, demonstrating its reliability. Parametric studies are conducted to optimize nanofluid characteristics for improved heat transfer and fluid flow. This research enhances our understanding of nonlinear flow and heat transfer in nanofluids and enables efficient numerical analysis, opening new avenues for improving nanofluid-based systems.

Grasping extreme aerodynamics on a low-dimensional manifold

Modern air vehicles perform a wide range of operations, including transportation, defense, surveillance, and rescue. These aircraft can fly in calm conditions but avoid operations in gusty environments, encountered in urban canyons, over mountainous terrains, and in ship wakes. With extreme weather becoming ever more frequent due to global warming, it is anticipated that aircraft, especially those that are smaller in size, will encounter sizeable atmospheric disturbances and still be expected to achieve stable flight. However, there exists virtually no theoretical fluid-dynamic foundation to describe the influence of extreme vortical gusts on wings. To compound this difficulty, there is a large parameter space for gust-wing interactions. While such interactions are seemingly complex and different for each combination of gust parameters, we show that the fundamental physics behind extreme aerodynamics is far simpler and lower-rank than traditionally expected. We reveal that the nonlinear vortical flow field over time and parameter space can be compressed to only three variables with a lift-augmented autoencoder while holding the essence of the original high-dimensional physics. Extreme aerodynamic flows can be compressed through machine learning into a low-dimensional manifold, which can enable real-time sparse reconstruction, dynamical modeling, and control of extremely unsteady gusty flows. The present findings offer support for the stable flight of next-generation small air vehicles in atmosphere conditions traditionally considered unflyable.