Numerical research on the hydrodynamic characteristics of a non-Newtonian ballast-type floating breakwater using a fully particle-based method

The primary purpose of the present study is to investigate the unsteady flow and heat transfer characteristics of non-Newtonian power-law fluid over an oscillating flat plate. The power-law fluid model is employed to distinguish the non-Newtonian fluid behavior, which has wide applications in nature and technology, such as crude oil exploitation, polymer processing and some bio applications. In this work, the governing equations are set up using the non-Newtonian fluid model. The radial basis function collocation method (RBFCM) and the finite element method (FEM) are used to solve the coupled equations. The numerical results of the fluid velocity and fluid temperature fields are analyzed in detail. For authentication of the proposed schemes, the results are compared with earlier research works. To further verify the validity of the FEM and the RBFCM results, the flow behavior of crude oil was studied and the obtained results were found to be consistent with each other using both methods. Our results provide further guidance for evaluation aspects dealing with crude oil in a pipe, which are basic tools in oil and gas explorations.

The primary purpose of the present study is to investigate the unsteady flow and heat transfer characteristics of non-Newtonian power-law fluid over an oscillating flat plate. The power-law fluid model is employed to characterize the non-Newtonian fluid behavior, which has wide applications in nature and technology, such as crude oil exploitation, polymer processing and some bio applications. In this study, the coupled governing equations are set up using the non-Newtonian fluid model. The radial basis function collocation method (RBFCM) and the finite element method (FEM) are used to solve the coupled equations. The simulation results on the fluid velocity and temperature distribution are analyzed in detail. For authentication of the proposed schemes, the numerical results are compared with earlier research works. To further verify the validity of the FEM and the RBFCM results, the flow behavior of crude oil was studied and the obtained results were found to be consistent with each other using both methods. Our results provide further guidance for evaluation aspects dealing with crude oil in a pipe, which are basic tools in oil and gas explorations.

Study on Heat Transfer of Non-Newtonian Power Law Fluid in Pipes with Different Cross Sections

Comprehensive experimental and numerical studies have been undertaken to investigate wave energy dissipation performance and main influencing factors of a lower arc-plate breakwater. The numerical model, which considers nonlinear interactions between waves and the arc-plate breakwater, has been constructed by using the velocity wavegenerating method, the volume of fluid (VOF) method and the finite volume method. The results show that the relative width, relative height and relative submergence of the breakwater are three main influencing factors and have significant influence on wave energy dissipation of the lower arc-plate open breakwater. The transmission coefficient is found to decrease with the increasing relative width, and the minimum transmission coefficient is 0.15 when the relative width is 0.45. The reflection coefficient is found to vary slightly with the relative width, and the maximum reflection coefficient is 0.53 when the relative width is 0.45. The transmission and reflection coefficients are shown to increase with the relative wave height for approximately 85% of the experimental tests when the relative width is 0.19−0.45. The transmission coefficients at relative submergences of −0.04, −0.02 and 0 are clearly shown to be greater than those at relative submergences of 0.02 and 0.04, while the reflection coefficient exhibits the opposite relationship. After the wave interacts with the lower arc-plate breakwater, the wave energy is mainly converted into transmission, reflection and dissipation energies. The wave attenuation performance is clearly weakened for waves with greater heights and longer periods.

<sec>The study of surface wave dispersion equations in viscoelastic non-Newtonian fluids is the foundation for characterizing the thermophysical properties by using surface light scattering techniques. Unlike Newtonian fluids, non-Newtonian systems have the complex viscosity with nonlinear frequency behavior and stress relaxation time-dependent behavior. Consequently, the development of constitutive models capable of accurately capturing these complex viscosity characteristics is critical. Based on the multi-relaxation-time Maxwell framework, this work establishes a method of explicitly solving the surface wave dispersion equation through modal decomposition of the total power spectrum, which can systematically analyze the influence of relaxation time parameters on surface wave mode distributions. This study quantitatively correlates the number of relaxation time parameters in the constitutive model with the nonlinear response capacity of the system. These findings provide a theoretical foundation for precisely determining the surface wave characteristics in non-Newtonian fluids and advance the application of surface light scattering method to the measurement of thermophysical properties in viscoelastic fluid systems.</sec><sec>Based on a multi-relaxation-time Maxwell model, the complex viscosity is formulated by combining multiple stress relaxation time. Utilizing non-depersonalization and polynomial decomposition, we derive the governing equations for surface wave dispersion and the associated power spectrum. By systematically varying the parameter <i>n</i> and dimensionless variables, the roots of the dispersion equations are analyzed to study surface wave modes—including capillary, elastic waves, and overdamped modes—and their spectral signatures. A partial fraction expansion method is employed to decouple the total power spectrum into explicit modal contributions. This method demonstrates how the relaxation parameters determine the distribution of surface wave modes, thereby clarifying the inherent multimodal relaxation dynamics of complex fluids.</sec><sec>The proposed framework extends the classical Maxwell model by integrating multiple relaxation times, with a focus on surface wave dispersion behavior and spectral response. Theoretically, it quantifies the influence of relaxation time on the number and topological properties of roots in the complex plane. Furthermore, by correlating the dynamic behaviors of these roots with physical constraints, this study establishes criteria for the existence of different surface wave modes and evaluates their relative contributions to the power spectrum.</sec><sec>When the elastic modulus is low and approaches Newtonian fluid behavior, increasing the number of relaxation time parameters <i>n</i> will increase the critical threshold for surface wave mode transition. This simultaneously generates <i>n</i> purely imaginary roots corresponding to overdamped modes. At higher elastic modulus, the critical threshold vanishes and is replaced by an oscillation-dominated regime requiring power spectrum analysis to solve surface wave dynamics problems. Larger <i>n</i> values reduce the spatial extent of this oscillatory regime.</sec><sec>In systems with low elastic modulus, <i>n</i> mainly modulates the peak amplitudes in the power spectrum rather than changing its overall shape. Near the oscillation region, the power spectrum clearly distinguishes the contributions from capillary waves, elastic waves, and overdamped modes. Increasing <i>n</i> can enhance the strengths of elasticity and overdamped mode while suppressing the dominance of capillary wave. By incorporating additional relaxation time, the model gains enhance the resolution of multimodal relaxation dynamics, enabling precise characterization of viscoelasticity in complex non-Newtonian fluids.</sec><sec>We improve the complex viscosity model by increasing the number of stress relaxation time parameters <i>n</i>. Through the theoretical analysis of parameter variations under different conditions, the surface wave characteristics of non-Newtonian viscoelastic fluids are systematically investigated. The main conclusions are shown below. First, increasing the number of relaxation time parameters <i>n</i> will increase the number of roots in the dispersion equation, introducing additional relaxation modes manifested as low-frequency overdamped behavior. Second, increasing stress relaxation time <i>τ</i> will induce a critical oscillation regime, at which point power spectrum analysis is required for surface wave dynamics. Increasing <i>n</i> can reduce the spatial extent of this regime or even enables its complete avoidance. Third, under identical parameters, higher <i>n</i> suppresses surface tension-driven capillary wave intensity while enhancing elastic wave dominance. Variations in <i>n</i> quantitatively reflect the viscoelastic heterogeneity of polymer networks. Fourth, selecting appropriate <i>n</i> values can tailor the ability of model to resolve specific relaxation modes, making it suitable for different viscoelastic non-Newtonian fluids.</sec>

The heat transfer in a steady laminar stagnation point flow of an incompressible non-Newtonian micropolar fluid impinging on a permeable stretching surface with heat generation or absorption is investigated. Numerical solution for the governing nonlinear momentum equations and the inhomogeneous energy equations is obtained. The effect of the characteristics of the non-Newtonian fluid, the surface stretching velocity, the heat generation/absorption coefficient, and Prandtl number on both the flow and heat transfer is presented and discussed.

The steady laminar flow through a porous medium of an incompressible non-Newtonian Rivlin-Ericksen fluid impinging normal to a plane wall with heat transfer is investigated. A numerical solution for the governing nonlinear momentum and energy equations is obtained. The effect of the porosity of the medium and the characteristics of the non-Newtonian fluid on both the flow and heat transfer is outlined.

<p>Floating breakwaters have been used to protect shorelines, marinas, very large floating structures, dockyards, fish farms, harbours and ports from harsh wave environments. A floating breakwater outperforms its bottom-founded counterpart with respect to its environmental friendliness, cost-effectiveness in relatively deep waters or soft seabed conditions, flexibility for expansion and downsizing and its mobility to be towed away. The effectiveness of a floating breakwater design is assessed by its wave attenuation performance that is measured by the wave transmission coefficient (i.e., the ratio of the transmitted wave height to the incident wave height or the ratio of the transmitted wave energy to the incident wave energy). In some current design guidelines for floating breakwaters, the transmission coefficient is estimated based on the assumption that the realistic ocean waves may be represented by regular waves that are characterized by the significant wave period and wave height of the wave spectrum. There is no doubt that the use of regular waves is simple for practicing engineers designing floating breakwaters. However, the validity and accuracy of using regular waves in the evaluation of wave attenuation performance of floating breakwaters have not been thoroughly discussed in the open literature. This study examines the wave transmission coefficients of floating breakwaters by performing hydrodynamic analysis of some large floating breakwaters in ocean waves modelled as regular waves as well as irregular waves described by a wave spectrum such as the Bretschneider spectrum. The formulation of the governing fluid motion and boundary conditions are based on classical linear hydrodynamic theory. The floating breakwater is assumed to take the shape of a long rectangular box modelled by the Mindlin thick plate theory. The finite element – boundary element method was employed to solve the fluid-structure interaction problem. By considering heave-only floating box-type breakwaters of 200m and 500m in length, it is found that the transmission coefficients obtained by using the regular wave model may be smaller (or larger) than that obtained by using the irregular wave model by up to 55% (or 40%). These significant differences in the transmission coefficient estimated by using regular and irregular waves indicate that simplifying assumption of realistic ocean waves as regular waves leads to significant over/underprediction of wave attenuation performance of floating breakwaters. Thus, when designing floating breakwaters, the ocean waves have to be treated as irregular waves modelled by a wave spectrum that best describes the wave condition at the site. This conclusion is expected to motivate a revision of design guidelines for floating breakwaters for better prediction of wave attenuation performance. Also, it is expected to affect how one carries out experiments on floating breakwaters in a wave basin to measure the wave transmission coefficients.</p>

The floating breakwater is important in protecting the safety of coastal buildings. Among them, water-ballasted floating breakwaters (WBFB) also have good performance, but the hydrodynamic characteristics and wave attenuation performance of WBFBs are less studied. Therefore, the physical model experiment and numerical simulation were combined, and the motion response was analyzed by DeepLabCut in this article. Under different wave conditions and five different ratios (f 1/D 1 = 0, f 2/D 2 = 0.2, f 3/D 1 = 0.3, f 4/D 1 = 0.4, f 5/D 1 = 0.5) of internal ballast water height (f) to box height (D), the wave attenuation performance and hydrodynamic characteristics of WBFB were studied by comparing several important parameters. Meanwhile, the effect of the number of cabins was also studied. The findings demonstrate that, for a given wave period, the WBFB has stronger motion responsiveness and superior wave attenuation performance. The increase in internal ballast water leads to a decrease in the transmission coefficient, especially when f 5/D 1 = 0.5, the best overall wave attenuation performance is achieved. In addition, splitting the WBFB into two cabins does not have a significant wave attenuation effect, but is effective in reducing surge and pitch wave motion responses.

Experimental results of the settling of spherical particles in flowing non-Newtonian fracturing fluids show that Stokes Law based on 'Power Law' viscosities is insufficient to predict particle fall rates in both flowing and quiescent fluids. In a stagnant fluid the experimental settling velocities are more than an order of magnitude higher than those calculated, while in a flowing fluid, settling is lower than that calculated. These phenomena can be explained by extending the 'Power Law' model with a zero shear viscosity and by assuming an anisotropic viscosity in a flowing fluid. Anisotropy in the viscosity only becomes important above shear rates of, say, 25 s-1, and so will not play a role in the majority of fracturing treatments where average shear rates in the fracture will be below this value.

An experimental study has been conducted to evaluate the effects of solids on the drag reduction characteristics of polymeric drilling fluids, loaded with solids, through straight and coiled tubing. The polymers investigated were PHPA and XCD. These polymers were dissolved in brines which were prepared by mixing potassium chloride (KCl) and sodium formate (Naformate) in water. Various concentrations of polysaccharide gum (XCD) and partially hydrolyzed polyacrylamide (PHPA) polymers were dissolved in the KCl and Na-formate solutions. These fluids were pumped through straight pipes. Based on the results, it was established that the PHPA/KCl solution exhibited better drag reduction than PHPA/Na-formate, XCD/KCl, and XCD/Na-formate solutions in straight pipes. Thus, the PHPA/KCl solution was selected for further study. This polymer solution was then loaded with barite and bentonite to simulate solid cuttings. The fluid system was pumped through different sized coiled tubing and straight pipes. A correlation in terms of Fanning friction factor and generalized Reynolds number was developed, and percentage drag reduction was calculated. It was observed that, when clear polymeric solutions were loaded with solids, drag reduction decreases drastically. Finally, the effect of curvature on the flow of solidladen fluids was studied. It was observed that frictional losses in coiled tubing were almost twice those of frictional losses in straight tubing for the solid-laden polymeric fluids under investigation. Introduction In the past, various studies have been conducted on the flow of clean Newtonian and non-Newtonian fluids through straight pipes in turbulent flow. For the flow of Newtonian fluids through smooth pipes, von Karman(1), Nikuradse(2), and Prandtl(3) suggested correlations, but the most commonly used correlation was proposed by Drew et al.(4). Their correlation is valid for Reynolds numbers between 3,000 and 3,000,000. Similarly, for Newtonian fluids flowing through rough pipes in a turbulent flow regime, Moody(5), Nikuradse(2), Churchill(6), and Chen(7) developed correlations. Among these, Chen's correlation is the most widely used in the industry, as Chen's correlation is explicit for Fanning friction factor and correlates the Fanning friction factor, pipe roughness, pipe diameter, and Reynolds number. Although non- Newtonian fluids have not been studied as often as Newtonian fluids, they have been under intense examination for some time for flow effects through smooth and rough pipes. Dodge and Metzner(8), Melton and Malone(9), and Shah(10) presented extensive theoretical and experimental studies. Similarly for non- Newtonian fluids through rough pipes, Dodge(11) and Shah(10) correlations are widely used in the industry. As shown, numerous studies have been conducted in the past, especially in the case of Newtonian fluids. However, no study could be found in the literature regarding the effects of solids on the flow of non-Newtonian fluids through straight or coiled tubing. The objective of this project was to study the effects of solids loading on the drag reduction characteristics of commonly used polymeric drilling fluids flowing through straight and coiled tubing. This was achieved by first studying the polymeric fluids flowing through straight pipe without solids.

Numerical investigation on the hydrodynamics of a hybrid OWC wave energy converter combining a floating buoy

Non-Newtonian fluids are frequently encountered in daily life and engineering. The viscosity of non-Newtonian fluids depends on the shear rate, making the thermo-hydraulic behavior of these fluids more complicated than that of Newtonian fluids. This study explores how channel cross-section geometry influences fluid flow and heat transfer characteristics of Newtonian and non-Newtonian fluids using computational fluid dynamics simulations. The friction factor for both Newtonian and non-Newtonian fluids was evaluated under different channel geometries and flow conditions. While prior research has extensively characterized the thermal behavior of non-Newtonian fluids at constant wall temperature, the effects of constant wall heat flux have received relatively little attention. To address this gap, the Nusselt number of non-Newtonian fluids at both constant wall temperature and constant wall heat flux boundary conditions was assessed for different channel cross-section shapes and different power law indices. Key findings revealed that the Nusselt number decreases as the power law index increases. The circular channel exhibits the highest Nusselt number at constant wall heat flux, while the elliptical channel shows the highest Nusselt number at constant wall temperature. Specifically, at a power law index of 0.4, the circular channel achieves maximum Nusselt number value of 4.91 and the elliptical channel reaches maximum Nusselt number of 4.11.

Fluids exhibit diverse behaviors under applied forces, classified broadly into Newtonian and Non-Newtonian fluids. Newtonian fluids have a constant viscosity regardless of applied stress, while Non-Newtonian fluids display viscosity variations based on stress conditions. This paper explores the fundamental differences between these fluid types, emphasizing the unique characteristics of Non-Newtonian fluids. Ketchup, a widely used food product, serves as a primary example of a shear-thinning Non-Newtonian fluid. This study delves into its rheological properties, flow behavior, and industrial applications, highlighting its relevance in food processing, packaging, and material science. Keywords: Newtonian fluids, Non-Newtonian fluids, Ketchup, Shear thinning, Rheology, Applications

Experimental investigation on electrostatic breakup characteristics of non-Newtonian zeolite molecular sieve suspension fluid