Fluid Dynamic Phenomena Research Articles

Innovative simplified approach and numerical investigation for flow and heat transfer in internally threaded tubes

Internally threaded tubes exhibit exceptional heat transfer capabilities, holding paramount significance in enhancing energy efficiency, reducing energy consumption, and tackling thermal challenges across aerospace, automotive, and environmental domains. Nonetheless, their intricate structural features, software modelling intricacies, extensive grid requirements, and challenges in maintaining grid quality render numerical simulation investigations a demanding endeavor. This study elucidates the influence mechanisms of thread spacing on the distribution of single-phase and two-phase flows. It delves into the condensation heat transfer of the R32 refrigerant and the single-phase heat transfer of water within internally threaded tubes. At the same Reynolds number, the heat transfer rate can be improved by approximately 19.61% with the optimized internally threaded parameters. When the Reynolds number varies from 18,626 to 51,222, the heat transfer rate per unit length for Tube-5 remains around 2,478.9 W/m, with a variation of less than 5.19%. Furthermore, it presents a simplified numerical simulation approach tailored for internally threaded pipes. This method manipulates wall roughness and regulates wall rotation speed to mimic fluid dynamics phenomena akin to conventional numerical simulation techniques. The findings reveal that the proposed simplified numerical simulation approach yields heat transfer and pressure drop predictions with less than 3% discrepancies compared to traditional numerical simulation predictions. Simultaneously, compared to directly simulating threaded pipes through conventional means, this approach significantly mitigates grid generation complexities, slashing computational time costs by at least 85% and facilitating efficient thermal design and structural optimization processes.

Concentration and cavitation in the Riemann solutions to the Umami Chaplygin Euler equations

The concentration phenomena in fluid dynamics can be mathematically described by delta-shocks. With the introduction of flux-function, the Riemann problem for the Euler system with Umami Chaplygin gas equation of state is discussed. What Umami Chaplygin gas means is that the fluid obeys the pressure–density relation where the pressure is negative and is a new generalization of Chaplygin gas. The solutions with six kinds of structures are constructed. Unlike the Chaplygin gas, the delta-shock occurs in solutions, even though the system is strictly hyperbolic and two characteristic fields are genuinely nonlinear. The generalized Rankine–Hugoniot relation and entropy condition for delta-shock are clarified. Additionally, the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions are identified and analyzed as the Umami Chaplygin gas pressure and flux-function vanish simultaneously. It is proved that as the pressure and flux-function drop to zero, any solution consisting of two shocks tends to the delta-shock solution of the pressureless Euler system, and any solution consisting of two rarefaction waves tends to the vacuum Riemann solution of the pressureless Euler system. Finally, some numerical results exhibiting the processes of formation of delta-shocks and vacuum states are presented.

Properties of the hybrid solutions for a generalized (3 + 1)-dimensional KP equation

The Kadomtsev-Petviashvili (KP) equation is instrumental in characterizing nonlinear wave phenomena in fluid dynamics. With the incorporation of three-dimensional disturbances, the (3+1)-dimensional KP equation emerges. In this study, we employ the Hirota bilinear method to investigate a (3+1)-dimensional KP equation. We successfully derive both lump and lump-chain solutions for this equation. The characteristics of the resulting lump are thoroughly examined. It is observed that those lumps propagate along a specific ray direction, with the origin of these rays dependent on the imaginary part of σˆjk=σj−σk with 1≤j,k≤3 and j≠k. We have simultaneously obtained the propagation direction of these rays. The periodicity of those lumps is denoted as Tjk dependent on spectrum parameter. Furthermore, we explore two potential lines, including the characteristic line associated with the lumps, to gain a deeper understanding of the nonlinear waves controlled by this system.

Coanda Effect Displayed in a Giant Intracranial Aneurysm.

The Coanda effect is a fluid dynamics phenomenon in which a fluid jet adheres to a convex or flat surface. This effect occurs when a liquid or gas jet emerging from an orifice clings to an adjacent surface and entrains the surrounding fluid, creating a lower-pressure region along its path that maintains its attachment to the surface. The Coanda effect accounts for the behavior of blood flow in the fetal right atrium and the dispersion of eccentric mitral regurgitation jets along atrial walls. This series of interesting images depicting a large 4 × 3.75 cm saccular intracranial aneurysm suggests that the Coanda effect may play a role in the pathophysiology of intracranial aneurysms and could be an underlying factor in their formation, progression, or rupture.

Influence of Rotation and Viscosity on Parallel Rolls of Electrically Conducting Fluid

Rayleigh–Bénard convection is a fundamental fluid dynamics phenomenon that significantly influences heat transfer in various natural and industrial processes, such as geophysical dynamics in the Earth’s liquid core and the performance of heat exchangers. Understanding the behavior of conductive fluids under the influence of heating, rotation, and magnetic fields is critical for improving thermal management systems. Utilizing the Boussinesq approximation, this study theoretically examines the nonlinear convection of a planar layer of conductive liquid that is heated from below and subjected to rotation about a vertical axis in the presence of a magnetic field. We focus on the onset of stationary convection as the temperature difference applied across the planar layer increases. Our theoretical approach investigates the formation of parallel rolls aligned with the magnetic field under free–free boundary conditions. To analyze the system of nonlinear equations, we expand the dependent variables in a series of orthogonal functions and express the coefficients of these functions as power series in a parameter ϵ. A solution for this nonlinear problem is derived through Fourier analysis of perturbations, extending to O(ϵ8), which allows for a detailed visualization of the parallel rolls. Graphical results are presented to explore the dependence of the Nusselt number on the Rayleigh number (R) and Ekman number (E). We observe that both the local Nusselt number and average Nusselt number increase as the Ekman number decreases. Furthermore, the flow appears to become more deformed as E decreases, suggesting an increased influence of external factors such as rotation. This deformation may enhance mixing within the fluid, thereby improving heat transfer between different regions.

[formula omitted]-adaptive discontinuous Galerkin solution of transonic viscous flows with variable time step-size

The discontinuous Galerkin methods demonstrated to be well suited for scale resolving simulations of complex configurations, characterized by different fluid dynamics phenomena, such as transition, separation, shock/boundary layer interaction. Unfortunately, solvers based on these methods cannot yet reach the computational efficiency of well-established standard solvers, e.g., based on finite volume methods. To reduce the computational cost and the memory footprint, while not spoiling the accuracy, different approaches were investigated, which act on the spatial or the temporal discretization, and on the linear algebra. The above approaches have been extensively investigated, but rarely considering their mutual interactions. In this work, a p-adaptation algorithm is coupled with a time step-size adaptation algorithm to mitigate robustness issues arising after each adaptation cycle, probably related to the projection of the old solution on the new polynomial orders distribution. Moreover, this strategy is able to control the transient phase before each adaptation cycle, and can handle also the presence of initial steady solution, when the mesh is too coarse and the polynomial degree has not yet compensated for the lack of spatial accuracy. The effectiveness and accuracy of the proposed algorithm are demonstrated on transonic viscous flows with shock-wave/boundary-layer interaction.

Concentration and cavitation phenomena of Riemann solutions for the generalized Chaplygin gas equations under the flux approximation

In this paper, we investigate the concentration and cavitation phenomena of Riemann solutions for the generalized Chaplygin gas equations in the presence of flux approximation. The concentration and cavitation are fundamental and physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves and vacuums (or constant density states), respectively. The main objective of this paper is to rigorously investigate the formation of delta shock waves and constant density states and observe the concentration and cavitation phenomena. First, the Riemann problem for the generalized Chaplygin gas equations under the flux approximation is solved constructively. Although the system is strictly hyperbolic and its two characteristic fields are genuinely nonlinear, the delta shock wave arises in Riemann solutions. The formation of mechanism for delta shock wave is analyzed, that is, the 1-shock wave curve and the 2-shock wave curve do not intersect each other in the phase plane. Second, it is rigorously proved that, as the pressure vanishes, the Riemann solutions for the generalized Chaplygin gas equations under the flux approximation tend to the two kinds of Riemann solutions to the transport equations in zero-pressure flow under the flux approximation, which include a delta shock wave formed by a weighted δ-measure and a constant density state.

Continuous and explosive synchronization transition in turbulent combustors

Thermoacoustic instabilities in turbulent combustors have disastrous consequences and present notorious challenges in their modeling, prediction, and control. Such instabilities are characterized by self-excited periodic oscillations, arising from a positive feedback between the acoustic pressure and heat release rate fluctuations. We present a mean-field approach to model thermoacoustic transitions. The nonlinear flame response is modeled using an ensemble of phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. Starting from the acoustic wave equation coupled with the phase oscillators, we derive the evolution equations for the amplitude and phase for acoustic oscillations. The model captures abrupt and continuous transitions to thermoacoustic instability observed in disparate combustors. We also discover that continuous and abrupt transitions happen through paradigmatic continuous and explosive synchronization, respectively. Importantly, our approach explains spatiotemporal synchronization and pattern formation underlying the transition to thermoacoustic instability. The versatility of the model in capturing different types of transitions suggests promising prospects for its extension to encompass a wide range of fluid dynamics phenomena.

Passive Control of Vortices in the Wake of a Bluff Body

Vortices belong to the most important phenomena in fluid dynamics and play an essential role in many engineering applications. They can act detrimentally by harnessing the flow energy and reducing the efficiency of an aerodynamic device, whereas in other cases, their presence can be exploited to achieve targeted flow conditions. The control of the vortex parameters is desirable in both cases. In this paper, we introduce an optimization strategy for the control of vortices in the wake of a bluff body. Flow modelling is based on RANS and DES computations, validated by experimental data. The algorithm for vortex identification and characterization is based on the triple decomposition of motion. It produces a quantitative measure of vortex strength which is used to define the objective function in the optimization procedure. It is shown how the shape of an aerodynamic device can be altered to achieve the desired characteristics of vortices in its wake. The studied case is closely related to flame holders for combustion applications, but the conceptual approach has a general applicability to vortex control.

Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources

Abstract Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. This paper presents an enhanced exponential time integrator approach to dynamically simulate non-Newtonian boundary layer flow with spatially and temporally varying heat sources. We propose an explicit scheme with second-order accuracy in time, demonstrated to be stable through Fourier series analysis, for solving time-dependent partial differential equations (PDEs). Utilizing this scheme, we construct and solve dimensionless PDEs representing the flow of Williamson fluid under the influence of space- and temperature-dependent heat sources. The scheme discretizes the continuity equation of incompressible fluid and Navier–Stokes, energy, and concentration equations using the central difference in space. Our analysis illuminates how factors affect velocity, temperature, and concentration profiles. Specifically, we observe a rise in temperature profile with enhanced coefficients of space and temperature terms in the heat source. Non-Newtonian behaviours and geographical/temporal variations in heat sources are critical factors influencing overall dynamics. The novelty of our work lies in developing an explicit exponential integrator approach, offering stability and second-order accuracy, for solving time-dependent PDEs in non-Newtonian boundary layer flow with variable heat sources. Our results provide valuable quantitative insights for understanding and controlling complex fluid dynamics phenomena. By addressing these challenges, our study advances numerical techniques for modelling real-world systems with implications for various engineering and scientific applications.

Impact of variable viscosity, thermal conductivity, and Soret–Dufour effects on MHD radiative heat transfer in thin reactive liquid films past an unsteady permeable expandable sheet

AbstractSignificance of magnetohydrodynamic effect on a viscous (temperature‐dependent) and chemically reactive thin fluid film flow past an unsteady permeable stretchable plate with Soret–Dufour effects, nonlinear thermal radiative, and suction under the action of a convective type of boundary condition is analyzed. The problem consists of nonlinear governing basic equations that are highly nonlinear due to the existence of nonlinear thermal radiative terms in the energy equation. Analytical solutions are challenging to achieve for such types of problems, so a numerical scheme adopts the numerical solution. Computed solutions indicate that decreasing the Dufour number (and simultaneously increasing the Soret number) enhances heat flux, whereas the reverse trend is estimated for the concentration gradient field. The influence of magnetization indicates a decrement in the thin liquid film velocity distribution, whereas an increment is observed in temperature and solutal gradient profiles. Further, an enhancement in thermoradiative values focuses on decreasing the heat flux profiles, whereas a decreasing trend is determined in the solutal gradient by incrementing the Schmidt number. The variations of the velocity field, temperature, and concentration gradients are shown for the unsteady parameter lying in the range [0.8, 1.4]. Similarly, the range of different parameters utilized are [0.0, 1.0], [0.0, 2.0], [0.8, 1.5], [0.5, 2.0], [0.0, 1.0], [0.2, 3.0], [1.0, 2.0], [0.0, 3.0], [0.4, 1.0], and [0.4, 1.0]. The novelty of the present study lies in its analysis of complex fluid dynamics phenomena and their implications for various industrial processes and engineering applications, including coating processes, heat exchangers, microfluidics, and biomedical engineering. The insights gained from the study can contribute to developing more efficient and innovative research in these areas. Further, we have compared the present results with those available in the literature under some special cases and found them to be in excellent agreement.

Maximizing liquid-cooled heat sink efficiency with advanced topology-optimized fin designs

Direct-to-chip liquid cooling offers significant advantages in managing higher power densities compared to traditional air-cooling methods. This approach utilizes nearly half the power required by server fans and air conditioners, enhances cooling efficiency in data centers. The effectiveness of this cooling strategy is intricately linked to the layout of the cold plate fins. In this research, a density-based topology optimization method is implemented in generating free-forming and non-intuitive fin structures. A pseudo-optimization model, which approximates the 3D heat sink as two 2D thermally coupled problem is selected and optimized with ‘pressure drop’ and ‘average junction temperature’ as objective function and constraint, respectively. Several fin layouts with inlet flow velocities and temperature constraints are generated. Three-dimensional numerical simulations reveal that the average junction temperature with the topology-optimized fin pattern is ∼2°C higher, and the pressure drop is significantly lower compared to size-optimized straight channel. Building on this, an inverted topology-optimized design is introduced along the channel length, inspired by the wavy nature of sectional fins. The average junction temperature with the inverted TO design is 3 to 4°C lower compared to the straight design, with a similar pumping power of 0.023 W. The TO fin layout capitalizes on frequent re-initialization of boundary layers, secondary flow-induced mixing, and the formation of Dean vortices along the channel length. Further refinement leads to the derivation of drop-oblique-trapezoidal and oval-shaped (DOTO) fins. These fins reduce average junction and wall temperatures by ∼23% compared to the inverted TO design, owing to the persistent effects of fluid dynamic phenomena along the channel length. Comparison with benchmarked designs indicates that DOTO fins reduce the average junction temperature by 3 to 6°C compared to size-optimized offset strip fins and step fins, with a similar pumping power of 0.083 W. The study indicates that optimizing DOTO fins dimensions can further enhance heat sink performance.

Numerical solutions of boundary problems in partial differential equations: A deep learning framework with Green's function

This work introduces Green Networks (GreenNets), a novel class of neural network architectures designed to address a wide spectrum of boundary problems in partial differential equations (PDEs). Demonstrated versatility includes solving the Poisson equation, convection-diffusion equation, and unsteady incompressible Navier-Stokes equations. GreenNets comprises two specialized variants: Boundary Transformation Green Network (BT-GreenNet), focusing on transforming Dirichlet boundary conditions into source terms, and Boundary Integral Green Network (BI-GreenNet), considering boundary integral terms with shared weights between the boundary and source integrals. Comparisons with existing deep learning and traditional numerical methods underscore their accuracy and efficiency. BT-GreenNet excels in efficiency, and BI-GreenNet offers enhanced flexibility. The research pinnacle, Boundary Unified Green Network (BU-GreenNet), merges BT-GreenNet and BI-GreenNet to address coupled PDEs, specifically unsteady incompressible Navier-Stokes equations. BU-GreenNet stands out by surpassing traditional numerical approaches, offering remarkable computational efficiency while faithfully capturing the intricate evolution of fluid dynamics phenomena. This research redefines the means of solution to boundary problems in PDEs through innovative neural network architectures, emphasizing practical utility and computational efficiency.

Nonsimilar analysis of forced convection radially magnetized ternary hybrid nanofluid flow over a curved stretching surface

This study focuses on analyzing the rheological properties of the Carreau–Yasuda ternary hybrid nanofluid model on a curved stretched sheet considering the molybdenum disulfide ( Mo S 2 ) , graphene oxide ( GO ) , and Nichrome ( NiCr ) immersed in the base fluid ethylene glycol ( EG ) . This study employs a radial magnetic force that is directed perpendicular to the direction of flow to manipulate the motion characteristics of a nonNewtonian fluid. Augmenting the value of the magnetic number leads to a decrease in the velocity of the flow as resistance is introduced against its principal direction. Thermal radiation and viscous dissipation effects are considered in the energy equation. Assumptions that are fundamental to fluid flow theories are incorporated into the mathematical formulation of this problem. Following this, the governing equations are transformed into dimensionless nonsimilar partial differential equation (PDE) by applying nonsimilarity transformation to a nonsimilarity transformation, and subsequently analyzed as ordinary differential equations utilizing the local nonsimilarity method up to second level of truncation. By using the MATLAB-integrated bvp4c solver, numerical solutions are obtained. The results of these various solutions are examined using visual and tabular representations to thoroughly evaluate the variances across different parameter settings. Furthermore, the flow velocity is reduced by the Lorentz force caused by a more curved surface, and we gain insight into the impact of different physical quantities under different parametric considerations related to the stretching curved surface, which adds to our knowledge of this complex fluid dynamic phenomenon.

Non-intrusive reduced order models for the accurate prediction of bifurcating phenomena in compressible fluid dynamics

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier–Stokes equations discretised with the Discontinuous Galerkin method. On the other side, from a numerical modelling point of view, two different non-intrusive reduced order modelling techniques are employed to predict the overall behaviour of the bifurcation. Both approaches showed good agreement with full-order simulations even in proximity of the bifurcating points where the solution is particularly non-smooth.

Solitons, nonlinear wave transitions and characteristics of quasi-periodic waves for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation in fluid mechanics and plasma physics

A (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation describing many nonlinear phenomena in fluid dynamics and plasma physics is considered. The N-solitons and breathers are obtained by basing on its Hirota’s bilinear form and taking the complex conjugate condition on parameters of N-solitons. What is more, breathers can be transformed into a series of nonlinear localized waves by the mechanism of breather transformation. Then through the multi-dimensional Riemann-theta function and the bilinear method, the high-dimensional complex three-periodic wave solutions are constructed systematically, which are the generalization of one-periodic wave and two-periodic wave solutions. By a limiting procedure, the asymptotic relations between the quasi-periodic waves and solitons are strictly established. Additionally, a novel analytical method of characteristic line is introduced to analyze statistically the dynamical characteristics of the quasi-periodic waves. The analytical method employed in this paper can be further extended to investigate the other complex high-dimensional nonlinear integrable equations.

The limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force

In this paper, we investigate the limiting behavior of Riemann solutions to the Euler equations of compressible fluid flow for modified Chaplygin gas with the body force as the two parameters tend to zero. The formation of delta shock waves and the vacuum states is identified and analyzed during the process of vanishing pressure in the Riemann solutions. The concentration and cavitation are fundamental and physical phenomena in fluid dynamics, which can be mathematically described by delta shock waves and vacuums, respectively. In this paper, our main objective is to rigorously investigate the formation of delta shock waves and vacuums and observe the concentration and cavitation phenomena. First, the Riemann problem of the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force is solved. Second, we rigorously confirm that, as the pressure vanishes, any two shock Riemann solution to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force tends to a δ-shock solution to the pressureless gas dynamics model with a body force, and the intermediate density between the two shocks tends to a weighted δ-measure that forms the δ-shock; any two-rarefaction-wave Riemann solution to the Euler equations of compressible fluid flow for the modified Chaplygin gas with the body force tends to a solution consisting of four contact discontinuities together with vacuum states with three different virtual velocities in the limiting situation.

A computational study on the performance and wake development of a tilted H-Shaped VAWT rotor

Wind energy is expected to play a key role in achieving challenging decarbonization objectives set by the current green energy transition. VAWTs are well-suited for the emerging market of floating offshore wind and hold significant potential to decrease the levelized cost of energy for offshore platforms. However, the flow field around a VAWT rotor is unsteady and three-dimensional due to the interaction between blades and vortical structures. Computational Fluid Dynamics is a crucial tool to study complex flow structures and optimize the machines at a reduced cost. This study presents a comprehensive 3D CFD investigation of the performance and wakes development trends of a straight-blade H-shaped VAWT operating in a tilted condition, a typical configuration for floating offshore installations. The VAWT model is studied at peak power and off-design TSR values. The predictions are analyzed by considering the complex flow field and near-wake development. The study finds that the 3D flow originating from the struts, the finite blade effects, and the tilted operating condition critically impact the machine’s performance. The study provides an in-depth analysis of turbine aerodynamics and spanwise variations to investigate the fluid-dynamic phenomena and their implications on energy production.

Volume viscosity of inhomogeneous fluids: a Maxwell relaxation model

Volume viscosity is one of the most important and fundamental parameters in hydrodynamics. It measures the momentum loss caused by a volume deformation rather than shape deformation. So it is closely related to numerous phenomena in fluid dynamics. However, most of the existing related researches focus on the bulk fluids, but there is still a lack of in-depth understanding of the bulk viscosity of inhomogeneous fluids. In this work, a novel theoretical method is proposed for the inhomogeneous volume viscosity in the framework of Maxwell viscoelastic theory. In this proposal, the local relaxation time is calculated by using the viscous and elastic properties of the bulk fluids. Accordingly, the inhomogeneous volume viscosity can be obtained by combining the calculations of the local relaxation time and the local relaxation modulus. It is advantageous in the theoretical sense over the conventional LADM, because it takes into account the underlying correlation much better. On the one hand, the local infinite-frequency modulus is more accurate. On the other hand, by using an appropriate weight function to calculate the weight, the correlation effect can be better considered . As an application, the volume viscosity of the confined Lennard-Jones fluid in slit pore is investigated, and the influences of bulk density, temperature, pore width and adsorption strength are calculated and analyzed. The results indicate that these factors can significantly modulate the volume viscosity of the confined fluid. Specifically, the positive correlation between the volume viscosity and the local density leads to the oscillation of viscosity profile in the pore. Besides, the occurrence of capillary condensation in the cases of lower density and lower temperature makes the inhomogeneous viscosity rather different from that of bulk gaseous phase. Further, this study shows that the inhomogeneous volume viscosity usually increases with temperature decreasing, or with adsorption strength increasing. This is again the result of its dependence on the fluid structure in the pore. Furthermore, the influence of pore width on the inhomogeneous volume viscosity indicates that the excluded volume plays a decisive role. This can be attributed to the fact that it exerts a direct influence on the deformation of the fluid. Moreover, comparison between the volume and shear viscosity is also conducted and analyzed. In general, this study can be beneficial to deepening the understanding of volume viscosity in the confined fluids, and can provide reliable theoretical support for studying related issues in hydrodynamics.

Exact solutions to the fractional nonlinear phenomena in fluid dynamics via the Riccati-Bernoulli sub-ODE method

<p>The Riccati-Bernoulli sub-ODE method has been used in recent research to efficiently investigate the analytical solutions of a non-linear equation widely used in fluid dynamics research. By utilizing this method, exact solutions are obtained for the space-time fractional symmetric regularized long-wave equation. These results comprehensively understand the long wave equation widely used in numerous fluid dynamics and wave propagation scenarios. The approach to studying these phenomena and using conceptual representation to understand their essential characteristics opens the door to valuable insights that may help improve both the theoretical and applied aspects of fluid dynamics and similar fields. Thus, as these complex equations demonstrate, the suggested approach is a valuable tool for conducting further research into non-linear phenomena across several disciplines.</p>