Search Results (1,203)

The inviscid, nonlinear shallow water model developed by Sun was applied to study the inverse of equatorial Rossby solitons, which can be represented by the Korteweg–De Vries equation (KdV equation). The model was integrated forward in time, then the results were used as initial conditions for backward integration by just changing time step from positive to negative. The detailed structure, secondary circulation, and propagating speed of waves from both integrations are in good agreement with analytic solutions. The total mass, energy, and enstrophy are also well conserved. The procedure is much simpler and the results are more accurate than other backward integrations of 2D nonlinear models, which require significant modification of the model and can be contaminated by unwanted diffusion in forward–backward integrations or time-consuming iterative methods. This paper is also different from the numerical method for solving the inverse of the KdV equation. Full article

A spillway is a hydraulic structure of major importance in dam safety, and its current analysis usually involves a hybrid approach combining CFD modeling with experimental research, either using well-known WES design charts or conducting new model experiments in the laboratory. Flow over spillway crests involves fluid accelerations, making irrotationality an adequate simplification of the Navier–Stokes (NS) equations. However, an efficient tool using this method is currently lacking for spillway flow, particularly for ogee spillway flow. This work focuses on this aspect of the problem, and a new method for computing irrotational flow solutions over ogee spillways is proposed by developing flow net computational solutions. The proposed method entails a new iterative procedure in the complex potential plane where free surface pressures are exactly set to zero, contrary to other methods, and an automatic determination of the critical point, the unknown energy head, and the free surface profile. The model generates solutions efficiently in only a few seconds on a personal workstation, permitting a fast estimate of spillway flow operation, and is thus an effective complement to experimental and NS-CFD modeling. The solutions produced are compared with observations of a high operational head equal to five times the design head of the ogee crest, resulting in reasonable agreement. The application of the new model to investigate the limitations of analytical equations used in spillway flow, like Jaeger’s theory, establishes limits for its use by relating its curvature parameter to the spillway chute slope. Full article

Smoothed particle hydrodynamics (SPH) is a state-of-the-art numerical simulation method in fluid mechanics. It is a novel approach for modeling and comprehending complex fluid behaviors. In contrast to traditional grid-dependent techniques like finite element and finite difference methods, SPH utilizes a meshless, purely Lagrangian approach, offering significant advantages in fluid simulations. By leveraging a set of arbitrarily distributed particles to represent the continuous fluid medium, SPH enables the precise estimation of partial differential equations. This grid-free methodology effectively addresses many challenges associated with conventional methods, providing a more adaptable and efficient solution framework. SPH’s versatility is evident across a broad spectrum of applications, ranging from advanced computational fluid dynamics (CFD) to complex computational solid mechanics (CSM), and proves effective across various scales—from micro to macro and even astronomical phenomena. Although SPH excels in tackling problems involving multiple degrees of freedom, complex boundaries, and large discontinuous deformations, it is still in its developmental phase and has not yet been widely adopted. As such, a thorough understanding and systematic analysis of SPH’s foundational theories are critical. This paper offers a comprehensive review of the defining characteristics and theoretical foundations of the SPH method, supported by practical examples derived from the Navier–Stokes (N-S) equations. It also provides a critical examination of successful SPH applications across various fields. Additionally, the paper presents case studies of SPH’s application in tunnel and underground engineering based on practical engineering experiences and long-term on-site monitoring, highlighting SPH’s alignment with real-world conditions. The theory and application of SPH have thus emerged as highly dynamic and rapidly evolving research areas. The detailed theoretical analysis and case studies presented in this paper offer valuable insights and practical guidance for scholars and practitioners alike. Full article

The occurrence of cavitation in marine propellers is a major source of noise in ships. Consequently, the occurrence and noise characteristics of cavitation must be better understood to control this issue. This study focuses on identifying the occurrence and noise characteristics of cavitating flow around two-dimensional (2D) hydrofoils. Using the commercial computational fluid dynamics software STAR-CCM+, a numerical analysis was conducted on the partial cavity flow occurring around 2D hydrofoils at specific angles of attack. In addition, the cavitation noise characteristics were analyzed by conducting a frequency analysis using the predicted pressure data obtained via a fluctuating pressure sensor positioned vertically above the hydrofoil. Consequently, the numerical results were compared with existing experimental data to validate the accuracy of the simulation. This study identifies the limitations of the Reynolds-averaged Navier–Stokes (RANS) method by closely comparing it with the large eddy simulation (LES) method for assessing noise characteristics in unsteady cavitating flow. Although RANS has limitations in qualitatively assessing periodic behavior compared to LES, it effectively predicts cavitation extent and is valuable for relative assessments in practical applications. Full article

The rotation of a missile generates a side force perpendicular to the plane containing the attack angle and produces a yawing moment that tilts the body out of the plane, significantly affecting the flight stability of rotating missiles. The non-planar asymmetry of the wrap-around-fin rotating missile determines its more complex rotational effects. This study utilizes the dual time-step method to solve the unsteady Navier–Stokes equations, investigating the characteristics of the side force and yawing moment of the wrap-around-fin rotating missile under supersonic conditions and uncovering the mechanism behind the generation of the side force and yawing moment. The results reveal that the side force and yawing moment of the wrap-around-fin missile are composed of static values and induced values from rotation. The static side force and yawing moment of the wrap-around-fin missile are not zero, while those of the flat-plate-fin missile are zero. This difference is primarily caused by the non-axisymmetric nature of the wrap-around fin, resulting in the static side force and yawing moment of the wrap-around-fin missile being 40% greater than those of the flat-plate-fin missile. The rotation of the missile increases the effective angle of attack on the convex surface of the fin and decreases it on the concave surface, leading to an imbalance in the pressure changes on the windward and leeward sides. This is the main reason for the generation of the induced side force and yawing moment due to rotation. The induced values from rotation vary linearly with the rotation rate, and their magnitudes can be several times those of the static values. Full article

The prediction of separated flows at low Reynolds numbers is crucial for several applications in aerospace and energy fields. Reynolds-averaged Navier–Stokes (RANS) equations are widely used but their accuracy is limited in the presence of transition or separation. In this work, two different strategies for improving RANS simulations by means of field inversion are discussed. Both strategies require solving an optimization problem to identify a correction field by minimizing the error on some measurable data. The obtained correction field is exploited with two alternative strategies. The first strategy aims to the identification of a relation that allows to express the local correction field as a function of some local flow features. However, this regression can be difficult or even impossible because the relation between the assumed input variables and the local correction could not be a function. For this reason, an alternative is proposed: a U-Net model is trained on the original and corrected RANS results. In this way, it is possible to perform a prediction with the original RANS model and then correct it by means of the U-Net. The methodologies are evaluated and compared on the flow around the NACA0021 and the SD7003 airfoils. Full article

The influence of oblique currents in narrow and shallow channels causes the fluid flow around ships to become complex. To analyze the hydrodynamic characteristics of a ship in such channels, it is essential to examine the influence of oblique currents on the ship’s hydrodynamic characteristics. In this study, current direction, ship speed, current speed, and water depth were identified as determinants affecting the hydrodynamic characteristics of a ship. Numerical simulations were conducted on a large oil tanker to investigate the effects of these factors on the ship’s hydrodynamic characteristics. The viscous fluid flow was modeled using the unsteady Reynolds-averaged Navier–Stokes (URANS) equations in conjunction with the k-ε turbulence model. The URANS equations were discretized using the finite volume method. The numerical results indicate substantial differences in the hydrodynamic characteristics of ships under oblique current conditions compared to still-water conditions. At a current direction of β = −45°, the direction of the sway force is consistent with that of still water’s sway force, which is an attractive force. The yaw moment at β = −45° changes from a bow-out moment under still-water conditions to a bow-in moment. Conversely, at a current direction of β = 45°, the sway force shifts from an attractive force under still-water conditions to a repulsive force. The yaw moment acts as a bow-out moment, which is consistent with that observed in still-water conditions. Furthermore, the influence of hydrodynamic characteristics on a ship varies significantly with changes in ship speed, current speed, and water depth. To ensure the safe navigation of ships, it is essential to develop and apply comprehensive strategies and countermeasures that account for practical conditions. Full article

Effusion cooling is often regarded as one of the critical techniques to protect solid surfaces from exposure to extremely hot environments, such as inside a combustion chamber where temperature can well exceed the metal melting point. Designing such efficient cooling features relies on thorough understanding of the underlying flow physics for the given engineering scenarios, where physical testing may not be feasible or even possible. Inevitably, under these circumstances, modelling and numerical simulation become the primary predictive tools. This review aims to give a broad coverage of the numerical methods for effusion cooling, ranging from the empirical models (often based on first principles and conservation laws) for solving the Reynolds-Averaged Navier–Stokes (RANS) equations to higher-fidelity methods such as Large-Eddy Simulation (LES) and hybrid RANS-LES, including Detached-Eddy Simulation (DES). We also highlight the latest progress in machine learning-aided and data-driven RANS approaches, which have gained a lot of momentum recently. They, in turn, take advantage of the higher-fidelity eddy-resolving datasets performed by, for example, LES or DES. The main examples of this review are focused on the applications primarily related to internal flows of gas turbine engines. Full article

Natural rock fractures often exhibit non-matching characteristics at certain scales, leading to uneven aperture distributions that significantly affect fluid flow. This study investigates the impact of the mismatch between the upper and lower surfaces on the flow through three-dimensional rough fractures. By applying fractal theory, a rough upper surface of the fracture is generated, and different degrees of mismatch are introduced by adding random noise to this surface. This approach enables the construction of a variety of three-dimensional rough fracture flow models. Numerical simulations, which involve directly solving the Navier-Stokes equations, are used to simulate flow through a rough single fracture, assessing the effects of various degrees of mismatch between the surfaces. The study also examines how the inclusion of the matrix alters flow characteristics. The results demonstrate that the Forchheimer equation accurately describes the nonlinear flow behavior in fractures with different degrees of mismatch. The increased mismatch intensifies the uneven distribution of fracture apertures, causing the flow velocity to shift from uniform to discrete and the streamlines to become increasingly curved. The overall tortuosity of the flow path increases and the formation of ‘concave’ and ‘convex’ areas leads to vortex zones, promoting nonlinear seepage. The correlation between both viscous and inertial permeability with the degree of mismatch is negative, whereas the impact of matrix permeability on the flow capacity of the fracture shows a positive correlation with a mismatch. Full article

During the operational process of an axial-flow compressor, the blade structure is simultaneously subjected to both aerodynamic loads and centrifugal loads, posing significant challenges to the safe and reliable operation of the blades. Considering both centrifugal loads and aerodynamic loads comprehensively, a bidirectional CFD-CSD coupling analysis method for blade structure was established. The Navier–Stokes governing equations were utilized to solve the internal flow field of the axial-flow compressor. The conservative interpolation method was utilized to couple and solve the blade’s static equilibrium equation, and the deformation, stress distribution, and prestress modal behavior of compressor blades were mainly analyzed. The research results indicate that the maximum deformation of the blades occurred at the lead edge tip, while stress predominantly concentrated approximately 33% upward from the blade root, exhibiting a radial distribution that gradually decreased. As the rotational speed increased, the maximum deformation of the blades continuously increased. Furthermore, at a constant rotational speed, the maximum deformation of the blade exhibited a trend of first increasing and then decreasing with the increase in mass flow. In contrast, the maximum stress showed a trend of first increasing, then decreasing, and finally increasing again as the rotational speed continuously increased. Centrifugal loads are the primary factor influencing blade stress and natural frequency. During operation, the blades exhibited two resonance points, approximately occurring at 62% and 98% of the design rotational speed. Full article

This study investigates a dual-stage axial-flow fan within a specific power plant context. Numerical simulations encompassing both steady-state and stall conditions were conducted utilizing the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the Realizable k–ε turbulence model. The findings reveal that, under normal operating conditions, there exists a positive correlation between the mass flow rate and outlet pressure with gas density while displaying a negative correlation with dynamic viscosity. Regardless of the changes in air density, the volumetric flow rate at the maximum outlet pressure of the fan remains essentially the same. When a stall occurs, the volumetric flow rate rapidly decreases to a specific value and then decreases slowly. The analysis of the three-dimensional flow field within the first-stage rotor was performed before and after the rotational stall occurrence. Notably, stall inception predominantly manifests at the blade tip. As the flow rate diminishes, the leakage area at the blade tip within a passage expands, directing the trajectory of the leakage vortex toward the leading edge of the blade. Upon reaching a critical flow rate, the backflow induced by the blade tip leakage vortex obstructs the entire passage at the blade tip, progressively evolving into a stall cell, thereby affecting flow within both passages concurrently. Full article

Sandbars are commonly encountered in coastal environments, acting as natural protections during storm events. However, the sandbar response to waves and possible shear failure is poorly understood. In this research, a two–dimensional numerical model is settled to simulate the wave-induced sandbar soil dynamics and instability mechanism. The model, which is based upon the Reynolds-averaged Navier–Stokes (RANS) equations and Biot’s consolidation theory, is validated using available experiments. Parametric studies are then conducted to appraise the impact of the wave parameters and soil properties on soil dynamics. Results indicate that the vertical distribution of the maximum vertical effective stress in the sandbar is different from that in the flat seabed, which decreases rapidly along the soil depth and then increases gradually. The impact of soil permeability and saturation on the vertical effective stress distribution around the sandbar also differ from that in the flat seabed. Unlike the flat seabed, the vertical distribution of shear stress in the sandbar increases with an increasing wave period. The sandbar soil shear failure potential is discussed based upon the Mohr–Coulomb criterion. Results show that the range of shear failure around the sandbar is wider and the depth is deeper when the wave trough arrives. Full article

In this paper, we consider the flow of a nanofluid in an enclosed lid-driven cavity using a single-phase model. Two cases are considered: one in which the top and bottom walls are kept at adiabatic conditions, and a second case in which the left- and right-side walls are kept in adiabatic conditions. The impact of different viscosity models on the mixed convection heat transfer is examined, and numerical methods are used to obtain solutions for the Navier–Stokes equations for various parameter ranges. Using our robust methods, we are able to obtain novel solutions for large Reynolds numbers and very small Richardson numbers. Using water as the base fluid and aluminium oxide nanoparticles, our results suggest that heat transfer enhancement occurs with increasing particle concentration and decreasing Richardson numbers. There are also significant differences depending on the viscosity model used in terms of the impact of reducing corner recirculation regions in the cavity. Full article

This work focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier–Stokes equations are investigated to address the mathematical constraint of incompressible flows. Raviart–Thomas finite elements are employed for the achievement of a discrete free-divergence velocity. In particular, the proposed algorithm projects the velocity field into the discrete free-divergence space by using the lowest-order Raviart–Thomas element. This decomposition is applied in the context of the projection method, a numerical algorithm employed for solving Navier–Stokes equations. Numerical examples validate the approach’s effectiveness, considering different types of computational grids. Additionally, the presented paper considers an interface advection problem using marker approximation in the context of multiphase flow simulations. Numerical tests, equipped with an analytical velocity field for the surface advection, are presented to compare exact and non-exact divergence-free velocity interpolation. Full article

Transonic buffet flow is a classical complex and unstable flow that has a negative effect on aircraft fly safety. Therefore, it is crucial to study the unsteady characteristics of buffet flow. The numerical analysis method is very useful in achieving the aforementioned goal. In this paper, focused on the typical supercritical airfoil OAT15A in fixed and pitching conditions, unsteady Reynolds averaged Navier–Stokes (URANS) closed with the sst-kω turbulence mode, coupled with the structure dynamical equation, is utilized to investigate the transonic buffet flow. Firstly, from the perspective of coherent flow structure, flow velocity divergence snapshots constructed from unsteady flow solutions are used to analyze the feature of transonic buffets in the two cases mentioned. Then, DMD modes are extracted by the dynamic mode decomposition technique from the velocity snapshots and adopted to analyze the flow modes of the two distinct flow fields. The numerical simulation results show that, in the fixed case, the regular motion feature of the buffet is present, the shock oscillation is closely related to the vortex structure, and the durations of rearward and forward movements of the shock are both equal to half of the buffet period. In the pitching case, the duration of the rearward motion of the primary shock is approximately five eighths of one buffet period, and the secondary shock appears with the primary one moving downstream, and they interact with each other. The region of the shock movement is larger than that of the fixed case, and there is chaotic flow rather than periodic flow in its wake. Structural elastic oscillation changes the characteristics of the aerodynamic response, which is solely affected by the frequency of the pitching oscillation. Full article