Principle Of Conservation Of Momentum Research Articles

Comprehensive analysis of wave interactions and resulting spall damage in layered heterogeneous medium under impact

The effect of dynamic spall damage on the response of layered medium subjected to one-dimensional impact involving an impactor and a multi-layered target is investigated. The study examines the damage caused by elastic waves below the Hugoniot Elastic Limit (HEL) during impact events. Analytical expressions of stress and particle velocity derived from mass and momentum conservation principles are utilized to solve the wave interactions within the impactor-target system, considering reflections, transmissions, and wave interactions between layers. These analytical expressions, integrated into a computational framework, facilitate the monitoring of material responses following each wave interaction, thereby analysing the impact response of the layered medium. Wave interactions, resulting in tensile stresses, that can cause damage to the target have been identified. A strain-based damage initiation and evolution law is incorporated into the developed computer program to predict damage in each layer of a medium. Damage alters the medium’s impact behaviour by decreasing stress magnitude and inducing temporal delays in the response due to attenuated wave propagation speed. The occurrences of tensile stress are explored, analyzing spatial and temporal variations of multiple damage incidents within the layered medium. The tension at the interface between two layers can induce damage in one or both adjacent layers, leading to debonding between layers. The effect of damage on the impact response of the medium is analysed by comparing the results for the damaged and undamaged target scenarios. The impact behaviour of a single-layer and a multi-layer target obtained from the present model, in terms of stress and particle velocity, is verified through Finite Element simulations of the identical impact problems, where the damage evolution criterion is incorporated using a VUMAT subroutine. The outcomes derived from this study align closely with Finite Element (FE) results.

Theoretical investigation of hysteresis loops in free-surface flow under sluice gates for power-law channels

ABSTRACT In the present study, a new theoretical framework and analytical solutions to the problem of hysteresis loops due to hydraulic jump in power-law open channels under supercritical flows are introduced. This investigation primarily focuses on the flow dynamics encountered at a vertical sluice gate across channels of various shapes: rectangular, parabolic, and triangular. By the application of energy and momentum conservation principles, the dual flow configurations emerging under identical initial conditions are shown. An intensive analytical computational analysis led to the development of approximate theoretical models, facilitating the prediction of hysteresis loops for a wide range of Froude numbers and dimensionless channel geometry parameters. Several illustrative examples were treated and the results show a high degree of accuracy of the proposed models in predicting the hysteresis loops. The present research contributes to a novel methodology for enhancing predictions regarding the behavior of supercritical flows and the design of open channels for specific scenarios of the hysteresis phenomenon.

A model-based design approach for low-pressure axial fan blades considering the air flow system characteristics

The paper puts forward a computer methodology for designing low-pressure axial fan blades for small-capacity refrigeration applications. Based on the blade element theory (BET), the airfoil efficiency of the airfoil, the principles of mass and momentum conservation together with empirical correlations for the flow irreversibilities, a mathematical model was devised for screening the blade geometric parameters (e.g., radial chord and pitch variation, and hub radius) by varying the induction coefficient distribution for a given fan diameter, motor speed, and airflow system characteristic curve. The best blade configuration is selected by means of a tailor-made optimization algorithm and undergoes a series of linear transformations for translating the fan parametrization into a CAD drawing. Two new fan blades were designed, one for maximum blade efficiency (MBE) and another for maximum airflow rate (MAR). In comparison with the free-swirl design approach, a standard procedure adopted in the open literature, the proposed blades showed an efficiency and an airflow by 20 % (MBE) and 14 % (MAR) higher than the reference. The airflow characteristics of the new designs were also assessed by means of wind-tunnel testing, which confirmed an increase of 11 % in the case of MBE design, while an enhancement of 10 % was observed in the case of MAR design.

Effects of cushion gas pressure and operating parameters on the capacity of hydrogen storage in lined rock caverns (LRC)

Hydrogen storage in lined rock cavern (LRC) provides versatile site selection, safety, and stability, making it a crucial option. In this study, a thermodynamic mathematical model was established to describe hydrogen storage in LRC. This model is based on the principles of mass, momentum, and energy conservation while accounting for the authentic compressibility of hydrogen. The thermodynamic fluctuations throughout the seasonal cycle in LRC were computed using the COMSOL Multiphysics software. The results indicate that when the hydrogen storage reaches the operating pressure, the lower the cushion gas pressure, the greater the hydrogen injection amount, and the higher the utilization rate of storage capacity. With a cushion gas pressure of 3 MPa, the storage capacity utilization rate exceeds that at 15 MPa by 41 %. The injection rate of 0.5 kg/s results in a temperature increase of 12 °C compared to 0.27 kg/s, indicating twice the temperature rise at the 0.27 kg/s injection rate. An increase in injection temperature corresponds to higher temperature within the hydrogen storage cavern upon completion of gas injection, thereby reducing the time needed for gas injection to reach maximum operating pressure. A lower initial cavern temperature results in a longer time for hydrogen storage to reach maximum operating pressure.

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

NUMERICAL COMPUTATION OF ONE- AND TWO-LAYER SHALLOW FLOW MODEL

In this research, we study a proficient computational model designed to simulate shallow flows involving one- and two-layer shallow flow. This numerical model is built upon the Saint Venant equations, which are widely used in hydraulics to depict the behavior of shallow water flow. The numerical scheme used here is constructed based on the conventional leapfrog technique implemented on a staggered grid framework, referred to as MCS. The primary objective of this research is to re-examine and implement the MCS in accurately modelling the free surface and interface waves produced by different flows passing through irregular geometries. Unlike the conventional MCS, we modify the momentum conservation principle to be more general, accommodating a non-negative wet cross-sectional area due to irregular geometry. We successfully conduct numerous numerical simulations by examining various scenarios involving one-layer and two-layer flow through irregularly shaped channels or structures. Our results show that the correct surface wave profile generated by a one-dimensional dam break through the triangular obstacle in the open channel can be simulated very well. Comparison with the existing experimental data seems promising although some disparities are being found due to dispersive phenomena with RMSE less than 5%. Furthermore, our scheme is successfully extended to simulate the steady sub-maximal exchange in two-layer flows using specific boundary conditions. The alignment between the submaximal numerical results with exchange flow theory is noticeable in the interface profile, characteristics of flow conditions and the flux values achieved when the steady situation occurs. These satisfying results indicate that our proposed numerical model can be used for practical needs involving various flow situations both one and two-layer cases

Viscous dissipation effects on time-dependent MHD Casson nanofluid over stretching surface: A hybrid nanofluid study

The study of MHD Couple stress Casson flow of a hybrid nanofluid is paramount due to its potential applications in advanced engineering systems, particularly in enhancing thermal management and efficiency in various industrial processes. In this report, the time-dependent MHD Couple stress Casson flow of a hybrid nanofluid, considering the impact of viscous dissipation over a stretching surface is presented. The main objective of this work is to enhance the transformation heat ratio to meet the requirements of the engineering and manufacturing industries. After conducting a continuity check, the issue is analyzed by applying the principles of momentum and energy conservation. This modeling process generates nonlinear partial differential equations (PDEs), which are subsequently converted into nonlinear ordinary differential equations (ODEs) using similarity transformation and thermophysical characteristics. To solve these ODEs, the Approximate Analytical Method HAM is employed, which is specifically designed for nonlinear problems. Velocity decreases with increasing values and higher nanoparticle volume fraction further slows the velocity. Increasing the couple-stress parameter reduces velocity; increasing the Casson parameter slows the velocity profile. Increasing magnetic parameter enhances temperature profile; profile escalates with Eckert number magnitude. These findings contribute significantly to understanding the structure, interactions, and dynamics of such liquids, aligning with the focus on exploring the fundamental properties of simple, molecular, ionic, and complex liquids.

An approach for multiscale two-phase flow simulation in the direct simulation Monte Carlo framework

To simulate multiscale gas flow with solid particles, Burt's model, based on the Direct Simulation Monte Carlo (DSMC) framework, is widely used to predict gas–solid interactions under the assumption of a negligibly small solid particle diameter compared to the local gas mean free path. However, Burt's model could become inaccurate when the solid particle is large relative to the local gas mean free path. This study introduces the Gas–Solid Synchronous (GSS) model, which predicts gas–solid interactions in continuum gas regions without assuming the local gas flow regime around a solid particle. Similar to Burt's model, the GSS model includes gas-to-solid and solid-to-gas interaction models to consider bidirectional interaction between two phases. The GSS gas-to-solid model is established by selecting accurate semi-empirical force and heat transfer models in comparison with DSMC simulation results. The GSS solid-to-gas model is developed based on the principles of momentum and energy conservation and validated against Burt's solid-to-gas model. The results show that Burt's model could overestimate the interphase force and heat transfer rates when its assumption on solid particle diameter does not hold, but it can reproduce non-equilibrium characteristics of two-phase flows where gas velocity distribution functions do not follow the Maxwell–Boltzmann distribution. By contrast, the GSS model can accurately predict gas–solid interaction in continuum gas flows, while it cannot capture the non-equilibrium nature of two-phase flows. The characteristics and limitations of the two models indicate that using a valid model for each gas–solid interaction could be crucial for accurate simulation of multiscale two-phase flows.

Orbit-attitude coupled dynamics modeling and adaptive sliding mode control for detumbling large space debris

For non-cooperative large tumbling space debris, the use of detumbling techniques to reduce its angular velocity facilitates capturing and deorbiting operations. In our recent work, a new detumbling device combining three harpoons and a nanosatellite was designed. The device is released from the servicing satellite and attaches to the surface of the target. Then, the device's thrusters are actuated to reduce the target's angular velocity. In this paper, the dynamics and control issues involved in this strategy are further investigated. The collision model between the detumbling device and the target in the process of attachment is built based on the principle of momentum conservation. A high-precision orbit-attitude coupled dynamics model of the combined system during the detumbling mission is established, in which major external disturbances as well as inertial parameter variations due to the fuel consumption of the nanosatellite are taken into account. In addition, an adaptive sliding mode control scheme incorporating pulse-width pulse-frequency (PWPF) modulation is proposed for debris targets with parametric uncertainties and external disturbances. Finally, the effectiveness and robustness of the detumbling control scheme are demonstrated by numerical simulations. The results show that the detumbling device is capable of detumbling a large tumbling rocket upper stage within 4000s.

A new analytical wind turbine wake model considering the effects of coriolis force and yawed conditions

Wind turbine wakes significantly affect power production and impose higher loads on downstream turbines. Therefore, the development of accurate and efficient wake models is important for optimizing wind farm layouts and predicting wind turbine performance. This study introduces a novel analytical wake model for yawed wind turbines that incorporates the effects of the Coriolis force. The wake deflection in the far wake region is derived through the application of the principles of mass and momentum conservation. In the near wake, the deflection is assumed to be linear with distance. A Gaussian distribution is assumed for the velocity deficit within the wind turbine wake. Two approaches have been proposed to estimate the onset of the far wake region. While the first approach employs a simplified empirical formula, the second approach utilizes an iteration-based method. The proposed analytical wake model has been validated against computational fluid dynamics (CFD) results. Subsequently, the effects of several important parameters on the wake deflection have been systematically investigated. Overall, the simulation results showed a satisfactory agreement between the CFD results and those obtained from the proposed model. Furthermore, the study concluded that the Coriolis force can exert significant effects on wake deflection, particularly in the far wake region, confirming previous findings from numerical simulations. Due to its simplicity and computational efficiency, the proposed model can be readily used in several applications, including wind farm layout optimization, control and risk assessment.

Research on Scavenging Flow Dynamics of Marine Two-Stroke Engines With a CFD-Derived Quasi-Dimensional Model

The complex in-cylinder gas state and flow significantly affect fuel-air mixture, combustion efficiency and emissions. However, the scavenging CFD model of large bore marine engines in digital twin system requires substantial computational resources. Therefore, a fast-run phenomenological model of the scavenging process is built in this study. The model simulates the thermal states and flow dynamics of inlet and exhaust gas based on the energy and momentum conservation principles, considering the ideal in-cylinder swirl velocity profile with effects of air mass loss, wall friction, and swirl shear. The model’s accuracy is confirmed by comparing it with CFD simulations on different engines, showing an average relative error less than 3.5%. It also analyzes the impacts of intake pressure. The model provides accurate boundary conditions for subsequent fuel spray, combustion, and emission simulations and can be combined with these models in the future, thereby applied to engine design, diagnostics, and control.

A direct multimode method for the reduction of vibration induced oscillations on force signals during “pseudo-rigid” water impact experiments

A new experimental method is proposed to improve the force measurements during water impact experiments (e.g. water entry or wave impact tests) carried out with “pseudo-rigid” mock-ups. Despite the efforts of making the mock-up as stiff as possible, the impulsive nature of water impact loads may induce a transient response of the mock-up with a broad frequency content and a perturbation of the force measurements. Using the principles of momentum conservation, it can be shown that the load cell signal is the sum of the hydrodynamic forcing term and of an additional inertial term directly related to the vibrations of the structure. In the present paper, we suggest to estimate the inertial term using several accelerometers which record the response of the structure at different locations. Assuming that the structure response can be approximated by a set of natural modes, we show that it is possible to estimate the inertial term by a linear combination of the acceleration signals. The coefficients of the linear combination may be identified a priori by performing hammer tests, but in certain cases they can also be identified a posteriori using a segment of the signal time series. The performance of the method is demonstrated by considering two experimental test cases of increasing complexity. The first test case is a hydrofoil of constant section impacting water at constant speed which exhibits two-dimensional beam-like vibrations. The second test case is a segmented model of a vertical cylinder impacted by a breaking wave whose segments exhibit three-dimensional vibrations. The proposed method is efficient, conceptually simple and very simple to implement from a signal processing point of view, which makes it promising not only for water impact problems but also for other unstationary fluid–structure interaction problems.

Double diffusive on powell eyring fluid flow by mixed convection from an exponential stretching surface with variable viscosity/thermal conductivity

This study delves into heat and mass transference in fluids with variable thermo-physical features, focusing on the Powell-Eyring fluid, a non-Newtonian substance with unique characteristics. Our aim is to understand the behaviour of this shear-thinning fluid when interacting with an exponentially stretchable surface, considering factors like mixed convection and thermal radiation. Our research endeavours to uncover novel findings in this intricate domain, with the primary objective of comprehending how this shear-thinning fluid behaves when it encounters an exponentially stretchable surface. To address the complexities, we employ the BVP4C technique in MATLAB, transforming governing equations into nonlinear partial differential equations (PDEs) based on mass, linear momentum, and energy conservation principles. The Homotopy method aids in navigating these equations, and numerical solutions are calculated using the powerful BVP4C technique for ordinary differential equations (odes). The research stands out for its comprehensive exploration of the interplay among diverse factors, including radiation, variable viscosity, mixed convection, and activation energy constraints. Findings are presented through tables and graphs, offering valuable insights into the intricate physical phenomena within this multifaceted field.

A productivity equation of horizontal wells in the bottom water drive reservoir with an interlayer

The interlayer can effectively prevent the ridge of bottom water and has a non-negligible influence on the flow dynamics of oil and gas in the reservoir. In view of the above problems, this paper studies the influence of a bottom water reservoir with an interlayer on the critical productivity of horizontal wells and establishes a coupling model of seepage and wellbore flow in a bottom water reservoir with an interlayer. The critical productivity of horizontal wells in a bottom water reservoir with an interlayer can be evaluated more accurately. Firstly, the three-dimensional seepage field is approximately decomposed into internal and external seepage fields, and the critical productivity formulas of internal and external seepage fields are solved, respectively. Using the equivalent seepage resistance, the critical productivity formula of horizontal wells in interlayer bottom water reservoirs is obtained. The results are compared with the calculation results of the traditional productivity formula and the simulation results of the commercial software ECLIPSE. Second, based on the mass conservation principle and momentum conservation principle, the wellbore-reservoir coupling mathematical model of a horizontal well is established by the discrete method. Finally, the sensitivity analysis of the selected parameters is discussed in detail. The results show that: (1) compared with the traditional productivity algorithm, the algorithm considers the influence of interlayers on productivity and gives a detailed theory, a specific calculation process, and the importance of accurate prediction of wellbore flow. (2) The model is calculated by an example, and the calculation results are compared with the traditional formula and the commercial simulator ECLIPSE. The results show that the horizontal well productivity formula considering the influence of interlayer is closer to the simulation results of commercial software ECLIPSE, and the relative error is 8.56%. (3) The established coupling model considers the influence of interlayer radius length and horizontal well length. The general trend is that productivity gradually increases with an increase in interlayer radius length or horizontal well length, but the growth rate gradually decreases.

Radiation force characteristics of non-uniform chiral stratified particles in standing wave field

<sec> <b>Objective</b> With the development of optical technology, the investigation of light-field-particle interactions has gained significant momentum. Such studies find widespread applications in optical manipulation, precision laser ranging, laser gas spectroscopy, and related fields. In optical manipulation techniques, employing two or more laser beams proves more effective for capturing and manipulating particles than using a single beam alone. In addition, with the increasing demand for manipulating particles with complex structures, it is necessary to conduct in-depth research on the radiation force characteristics of double Gaussian beams on non-uniform chiral particles. This research aims to deepen our understanding of how optical fields influence particles, thereby offering fresh perspectives in manipulating and utilizing non-uniform chiral layered particles on both a microscale and a nanoscale.</sec><sec> <b>Method</b> Based on the generalized Lorentz-Mie theory (GLMT) and spherical vector wave functions (SVWFs), the total incident field of a double Gaussian beam can be expanded by using the coordinate addition theorem. The incident field coefficient and scattering coefficient of each region of the multilayer chiral sphere are obtained by enforcing boundary continuity and employing multilayer sphere scattering theory. The radiation force acting on non-uniform chiral layered particles within a double Gaussian beam is then derived through application of the electromagnetic momentum conservation theorem.</sec><sec> <b>Results and Discussions</b> The theory and programs in this paper is compared with those in existing literature. The influence of various parameters on the radiation force is analyzed in detail, such as the incident angle, polarization angle, beam waist width, beam center position, and internal and external chiral parameters. These results indicate that compared with a single Gaussian beam, counter-propagating Gaussian standing waves exhibit significant advantages in capturing or confining inhomogeneous chiral layered particles, offering enhanced particle manipulation capabilities. Additionally, by selecting an appropriate polarization state of the incident light, a delicate balance can be achieved among these parameters, effectively stabilizing the capture of inhomogeneous chiral particles.</sec><sec> <b>Conclusions</b> This study employs the generalized Lorenz-Mie theory and the principle of electromagnetic momentum conservation to derive analytical expressions for the transverse and axial radiation forces exerted by dual Gaussian beams on multi-layered chiral particles propagating in arbitrary directions. The research provides an in-depth analysis of how standing wave beams affect the radiation force behavior of non-uniform chiral particles. Numerical analysis reveals significant influences of beam waist, particle size, chiral parameters, polarization angle and mode, as well as particle refractive index on both transverse and axial radiation forces. This research is important in analyzing and understanding the optical properties of complex-shaped multilayer biological cells and realizing the applications in the micromanipulation of multilayer biological structures.</sec>

Exploring pressure, temperature, and flow patterns in ciliated microfluidic systems

The integration of cilia-induced flow, nanofluids, and the inclusion of cobalt ferrite particles holds significant promise in fluid dynamics, heat transfer, and nanotechnology, offering potential breakthroughs in various technological and material applications. We explore the behavior of cilia-induced flow in a nanofluid confined within an annular domain, employing the Williamson fluid model to characterize the behavior of cobalt ferrite (CoFe2O4) nanoparticles. Our analysis is based on a mathematical treatment rooted in fundamental mass, momentum, and energy conservation principles while considering physical constraints (low Reynolds number and long wavelength) and adopting a dimensionless approach. By applying regular perturbation techniques, we derive series solutions for velocity and temperature profiles, providing insight into the complex interplay among cilia-generated flow, nanofluid properties, and the influence of Cobalt ferrite nanoparticles within the annular configuration. In particular, we uncovered clear correlations among cilia length, amplitude ratio, flow rate, and the Prandtl number with temperature distribution. Also, we observed substantial reductions in temperature trends under Weissenberg numbers and particle volume fractions.

Two‐Phase Relative Permeability Curves of Bingham Heavy Oil Under Different Types of Wettability: A Theoretical Model

As an important and universal petrophysics of heavy oil reservoirs, the two‐phase flow ability inside porous medium is vital for heavy oil development. Utilizing the laminar flow theory and an ideal pore structure, especially cylinder model, the function of the relative permeability of heavy oil–water with water saturation is derived by incorporating the principles of momentum conservation and the characteristics of Bingham fluids, which was modified by validated experiment. Two‐phase relative permeability, considering heavy oil as non‐Newtonian fluid, is the function of water saturation, pore size, oil–water viscosity ratio, and yield stress. The results of the validated experiment show that the theoretical values calculated employing the modified equation exhibit better agreement with the experimental values, particularly when the viscosities of two‐phase fluid are great. The results of the modified two‐phase relative permeability show a decrease in water saturation interval corresponding to the two‐phase flow area and a smaller value of permeability at equal two‐phase relative permeability. The oil–water viscosity ratio in the hydrophobic pores affects the water‐phase relative permeability, although the magnitude of its influence diminishes as the viscosity ratio increases. The behavior of relative permeability in hydrophilic pores is the opposite of that in hydrophobic pores. This work can afford good application prospects for mobility control in multilayered reservoirs through the heterogeneous‐phase‐composite fluid. The saturations of the remaining oil and irreducible water also play a vital role in the prediction of permeability. The work can afford good application prospects for the flow behavior of Bingham heavy oil in pores with different types of wettability.

A novel method to determine the multi-phase ejection parameters of high-density battery thermal runaway

The growing demands on high-performance energy systems for emerging technologies drive the advancement of high-density batteries. However, the issue of thermal runaway (TR), particularly in high-density battery, remains a major challenge worldwide. One of the primary hazards associated with TR is the emission of combustible ejections. Therefore, elucidating the TR ejection parameters holds significant meaning. In this study, we propose a novel method to determine the ejection parameters. Based on the principles of momentum conservation, the proposed method is applicable to high-density battery types. For the 52 A h ternary battery, our results indicate the following: 1) the ejection velocity reaches a peak of 210 m/s, a maximum mass loss rate of 0.041 kg/s and a maximum total pressure of 112.325 kPa; 2) the temperature of the particles is 200 °C higher than that of the gas. Furthermore, we have derived empirical formulas that encompass the ejection dynamics, thereby facilitating the modeling of TR degassing and ventilation within a battery pack. This approach overcomes the challenges associated with measuring the ejection parameters in high-density battery TR, such as the extreme temperature, flammability, and multiphase composition. Consequently, this method exhibits great potential to bolster the fire safety and structural design of battery packs.

Scientific exploring of Marangoni convection in stagnation point flow of blood-based carbon nanotubes nanofluid over an unsteady stretching surface

This study examines Marangoni convection in blood-based carbon nanotubes nanofluid's stagnation point flow over a time-dependent stretching surface. This study is inspired by the emerging importance of nanofluids in a variety of scientific and technical fields due to their unique and varied uses and effective thermal activities. Some examples of potential applications of these fluids include cancer treatment, magnetic refrigeration, drug delivery, and magnetic resonance imaging. Two types of nanoparticles are considered name is single wall carbon nanotube and multi wall carbon nanotube blood is takin as base fluid. Nonlinear partial differential equations are used to simulate the specified flow issue using momentum and energy conservation principles. Using a similarity transformation, the resultant is transformed into nonlinear with reduced dimensions. The relations for velocity profile and temperature distribution are calculated from the developed nonlinear ordinary differential equation by using an approximate analytical technique called the homotopy asymptotic method. Subsequently, these equations are implemented and executed within Mathematica software. The investigation focuses on significant outcomes such as momentum filed, energy filed, Skin friction coefficients, and Nusselt number. Graphs are used to interpret the effects of several factors, including the Marangoni parameter, nanoparticle volume friction, stretching parameter, slip parameter, and Prandtl number. The behavior of Nusselt's number and skin friction coefficient was also checked with the help of graphs and tables. The convergence of the solutions is checked with the help of auxiliary functions as well.

Numerical simulation of KVLCC2 self-propulsion with ducted propeller in head waves

In order to meet the Energy Efficiency Design Index (EEDI) requirements, consideration of reducing added power in waves is important for large tankers operating in ocean environments. In this study, the Reynolds-averaged Navier-Stokes (RANS) solver is employed in Computational Fluid Dynamics (CFD) method to simulate the self-propulsion of KVLCC2 model with a ducted KP458 propeller in head waves, especially for comparison with the non-ducted cases. Two methods are adopted for simulating the ducted propeller: the discretized propeller method and the improved body force ducted propeller method. The latter method incorporates an improved principle of momentum conservation to solve the advance speed of the ducted virtual disk precisely in real time, resulting in similar accuracy and higher efficiency compared to the former method. For some wavelengths, the ducted cases display higher propulsive efficiency and lower power than the non-ducted cases, especially under very short wavelength condition, where negative thrust deduction fraction is observed in the ducted case. With the increase of wave height, the effect of the duct becomes more pronounced, resulting in an increase in propulsive efficiency and a reduction in power, both of which can exceed 10%. Moreover, this research carefully analyzes the added values of self-propulsion factors in head waves, as well as flow fields, providing useful insights to inform the application of ducted propellers in ultra-large ocean-going tankers.