Theoretical and Computational Fluid Dynamics最新文献

The problem of the detachment of a free streamline from a smoothly shaped body is considered taking into account the effect of surface tension. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational and stationary in the body-fixed frame. We employ the Brillouin-Villat criterion to determine the position of the free streamline detachment. Using the integral hodograph method, we derive expressions for the complex velocity and the derivative of the complex potential, both defined in an auxiliary parameter plane. A system of singular integral equations, formulated in terms of the velocity magnitude along the free surface and the slope of the body, is derived by applying the dynamic and kinematic boundary conditions. The numerical method is highly efficient, as it only requires the evaluation of these two nonsingular functions. Numerical results demonstrate the effect of surface tension on the free streamline detachment, the drag force and the free surface shape for a wide range of Weber numbers. It is shown that the surface tension generates capillary waves due to the distortion of the magnitude of the inflow velocity at the detachment point, which propagate along the free streamline in the freestream reference frame.

This study investigates the onset of convection in a uniformly rotating fluid layer by varying the Taylor number ((textrm{Ta})), solute Rayleigh number ((mathrm {Ra_S})), Prandtl number ((textrm{Pr})), Schmidt number ((textrm{Sc})), and boundary conditions. The control parameters are varied over the ranges (textrm{Ta} in [0, 10^5]), (textrm{Pr} in (0, 10]), (textrm{Sc} in (0, 10^3]), and (mathrm {Ra_S} in [-3 times 10^3, 3 times 10^3]). Using a staggered grid Chebyshev spectral collocation method, the analysis reveals that rotation brings stability to the system and reduces the cell size at the onset of convection. Rotation also suppresses zero critical wave number convection and concavity of stationary neutral stability curve towards the origin under the non-identical temperature and concentration boundary conditions, as discussed by D. A. Nield [“The thermohaline Rayleigh-Jeffreys problem,” J. Fluid Mech. 29(3):545-558, 1967] in the absence of rotation. It is observed that a positive solute Rayleigh number promotes stationary convection, whereas a negative solute Rayleigh number tends to favor an oscillatory onset, depending on the fluid properties. Under no-slip velocity boundaries, three transition regimes are identified: oscillatory-stationary (O-S), stationary (S), and stationary-oscillatory (S-O). In contrast, only stationary convection occurs at onset when water-ethanol is confined between two stress-free plates at fixed rotation rate and concentration gradients. Moreover, reversing the solute boundary conditions does not affect the onset threshold when both plates are perfectly thermally conducting.

This study presents a numerical investigation of the dynamic response of a Newtonian fluid interface subjected to mixed oscillatory deformations. A slender cylindrical probe, floating horizontally at a water–air interface and partially submerged by capillary forces, is driven sinusoidally in the direction perpendicular to its axis. The interface exhibits shear, dilatational, and extensional viscosities, and the system is modeled using the finite volume method within the OpenFOAM framework. The governing equations are nondimensionalized and solved for a wide range of Marangoni numbers ((Ma in [1, 10^5])) and dilatational-to-shear viscosity ratios ((Theta in [1, 10^5])). The simulations enable the decomposition of the total interfacial force into its constituent components, revealing distinct regimes dominated by Marangoni, dilatational, or extensional stresses. The results demonstrate the feasibility of isolating these contributions under specific conditions, offering insights into the design and interpretation of interfacial rheometry experiments. The influence of geometric parameters and oscillation characteristics is also explored, confirming the robustness of the observed force dynamics.

The study presents a numerical investigation of unsteady plane channel flows of an elasto-viscoplastic material using the Herschel-Bulkley variant of the Saramito elasto-viscoplastic model [1] (SRM-HB), which incorporates both viscoelastic and viscoplastic behaviour. Yield stress fluids exhibit a dual nature, behaving as solids below a critical stress threshold and flowing as non-Newtonian fluids above it. This duality is crucial for numerous industrial applications and remains an area of active research. By examining the unsteady flow dynamics driven by steady and unsteady pressure gradients in a plane channel, this work evaluates the performance of the SRM-HB model against experimental data obtained with Carbopol gels. The findings highlight the significant role of elasticity in the yielding process and the resulting flow characteristics. Various flow scenarios, including creep tests, unsteady pressure ramps, and large-amplitude oscillatory flows, are analyzed to elucidate the complex interplay between elastic and plastic responses. The results demonstrate that the SRM-HB model effectively captures the transient flow behavior and hysteresis phenomena observed experimentally, providing insight into the material’s yielding and flow mechanisms.

The wavelet-based adaptive implicit eddy-resolving simulation approach is demonstrated for linearly forced homogeneous isotropic turbulence at moderate Taylor-Reynolds number. The wavelet-filtered incompressible Navier-Stokes equations are solved using the adaptive multilevel wavelet collocation method for elliptic problems without employing any explicit modeling for the unclosed terms. Instead, the energy dissipation induced by the built-in low-pass filtering associated with the adaptive numerical scheme is effectively exploited, thus mimicking the effect of unresolved subgrid-scale coherent flow structures on the dynamics of the resolved ones. The results of various numerical simulations, performed at different spatial resolutions, and with different filtering strengths, prove both the feasibility and efficacy of the proposed no-model approach for wall-free turbulence, while addressing the corresponding limits of application.

The entropy layer in a hypersonic flow over a blunted body is investigated using a high-accuracy spectral shock-fitting algorithm that solves the Euler equations within the shock layer. The base flow is computed via a direct numerical solution of the nonlinear equations. The analysis pays particular attention to the physical phenomena that arise at geometric discontinuities in body curvature. The flow field around a blunted 30-degree half-angle wedge, used as a representative body, is examined in detail and compared to viscous direct numerical solutions to evaluate the effect of viscosity on the profile of the entropy layer. Instabilities associated with the generalized inflection point in the entropy layer are investigated using linear stability theory. The entropy layer instabilities are shown to exhibit Mach number independence under a proper normalization. Our findings may be particularly useful for relating experimental results at different Mach numbers where the cold flow (calorically perfect gas) assumption is applicable.

Proper Orthogonal Decomposition (POD) extracts an optimal orthonormal basis for reconstructing a sequence of data. This technique is widely used in fluid mechanics to construct reduced-order models for physical analysis, modelling, estimation, and control. However, when the number of snapshots is small and the spatial domain is large, convergence of the basis with respect to the number of samples is compromised. This often results in a degradation of the quality of the resulting reduced-order models. In this study, we propose a localisation procedure to mitigate convergence artefacts in the context of limited data. Specifically, we adapt Schur product-based localisation – commonly used in operational data assimilation – to the POD framework. We develop an algorithm that operates directly on the snapshots rather than on the large-scale correlation tensor. In addition, we introduce a family of partition-of-unity localisation functions to preserve the reconstruction properties of the localised POD basis. By artificially increasing the rank of the correlation tensor, we demonstrate that the localised POD, computed from a limited number of snapshots, can approximate the POD basis obtained from a larger dataset. This is illustrated using a wave field scattered by a turbulent jet in a rotating shallow water system. We further show that using smooth, overlapping localisation functions enables physically meaningful reconstructions. The reconstruction capabilities of the method are also demonstrated using a realistic internal wave field in the Gulf Stream region, based on a high-resolution numerical simulation.

We present an open-source, modular and highly scalable thin-film flow solver that can perform complex simulations of wetting and dewetting phenomena in the presence of substrate or environmental heterogeneities. The implementation is based on the thin-film approximation and circumvents the stress singularity at moving contact lines by assuming the presence of an ultra thin precursor film covering the whole surface. The solver is implemented within the open-source Basilisk library (http://basilisk.fr/), and is validated by comparing with the predictions of reduced-order models derived from matched asymptotics analyses for a number of representative cases with isolated droplets. The capabilities of the solver are demonstrated by simulating multiple interacting droplets sliding on an inclined and chemically heterogeneous substrate.

This study examines the asymptotic and numerical behaviour of Newtonian fluid flows in geometries with sharp corners and the influence of the Navier slip boundary condition. A new similarity solution for a reentrant corner flow is derived by introducing a modification to the classical Navier slip law, where the slip coefficient is modelled as a function of the radial distance along the walls from the reentrant corner. This spatially dependent slip coefficient interpolates between the well-known no-slip similarity solution and the constant slip coefficient case in which the walls behave locally as free surfaces. The stress and pressure singularities now depend on the slip coefficient and the similarity solution is validated numerically through flow simulations in an L-shaped domain. This modified slip coefficient is then used to numerically investigate the influence of the corner stress singularity on the global flow behaviours of two benchmark problems: the 4:1 planar contraction flow and the 1:4 planar expansion flow. Specifically, its effect on salient vortex size and intensity, Couette correction and the flow type (extensional, shear or rotation). This combined asymptotic and numerical framework provides new insights into the role of boundary conditions in controlling flow behaviour near singular geometries, which has not previously been investigated.