Theoretical and Computational Fluid Dynamics最新文献

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with spectral proper orthogonal decomposition. In this method, space-only proper orthogonal decomposition is first performed on velocity data to identify a subspace onto which the known equations of motion are projected, following standard Galerkin projection techniques. The resulting reduced-order model is then utilized to generate time-resolved trajectories of data. Spectral proper orthogonal decomposition (SPOD) is then applied to this model-generated data to obtain a prediction of the spectral content of the system, while predicted SPOD modes can be obtained by lifting back to the original velocity field domain. This method is first demonstrated on a forced, randomly generated linear system, before being applied to study and reconstruct the spectral content of two-dimensional flow over two collinear flat plates perpendicular to an oncoming flow. At the range of Reynolds numbers considered, this configuration features an unsteady wake characterized by the formation and interaction of vortical structures in the wake. Depending on the Reynolds number, the wake can be periodic or feature broadband behavior, making it an insightful test case to assess the performance of the proposed method. In particular, we show that this method can accurately recover the spectral content of periodic, quasi-periodic, and broadband flows without utilizing any temporal information in the original data. To emphasize that temporal resolution is not required, we show that the predictive accuracy of the proposed method is robust to using temporally-subsampled data.

In this study, shock stand-off distances for thermally and chemically non-equilibrium flows of nitrogen over wedges are computationally investigated via a hypersonic computational fluid dynamics solver, hyperReactingFoam by spanning a parameter space that consists of ranges of Mach number, 4–10, specific heat ratio, 1.40–1.61 and wedge angles, 60(^circ )–90(^circ ). Then, the space is reduced into the parameters of inverse density ratio across the shock and dimensionless wedge angle which will be used as variables for quadratic functions that represent shock stand-off distances. Besides the functions of shock stand-off distances, detached shock profiles of computationally modeled flows are represented by parabolic equations. The flows are observed to be chemically frozen for Mach number ranges of 4–5 regardless of the specific heat ratio value of the nitrogen mixture. Our results show that the shock stand-off distance decreases as Mach number is increased from 4 to 7, if the wedge angle and free-stream specific heat ratio are kept the same. On the other hand, if Mach number is increased beyond 7, the shock stand-off distance starts to extend due to the dissociation of nitrogen molecules behind the shock wave. At Mach 10, nitrogen completely dissociates over 90(^circ ) wedge for all specific heat ratios considered in the present study. Increased leading edge angle of the wedge or specific heat ratio of free-stream yields longer shock stand-off distance.

The linear stability of a compressible flow in a pipe is examined using a modal analysis. A steady fully developed flow of a calorifically perfect gas, driven by a constant body acceleration, in a pipe of circular cross section is perturbed by small-amplitude normal modes and the temporal stability of the system is studied. In contrast to the incompressible pipe flow that is linearly stable for all modal perturbations, the compressible flow is unstable at finite Mach numbers due to modes that do not have a counterpart in the incompressible limit. We obtain these higher modes for a pipe flow through numerical solution of the stability equations. The higher modes are distinguished into an “odd” and an “even” family based on the variation of their wave-speeds with wave-number. The classical theorems of stability are extended to cylindrical coordinates and are used to obtain the critical Mach numbers below which the higher modes are always stable. The critical Reynolds number is calculated as a function of Mach number for the even family of modes, which are the least stable at finite Mach numbers. The numerical solution of the stability equations in the high Reynolds number limit demonstrates that viscosity is essential for destabilizing the even family of modes. An asymptotic analysis is carried out at high Reynolds numbers to obtain the scalings, and solutions for the eigenvalues in the high Reynolds number limit for the lower and upper branches of the stability curve.

Steady, depth-averaged, shallow water vorticity transport equations including advection, surface and bed shear stresses, and turbulent diffusion effects are written out in vorticity-velocity and stream function formalisms. The Boussinesq approximation is used to represent turbulent stresses in the effective stress tensor. We consider two different forms of the curl of the effective stress tensor: its complete form and the commonly used form neglecting the terms expressing interaction with variable water depth. After deriving the two equations in vorticity-velocity formalism, we recast the equations into stream function formalism, revealing all the internal effects associated with variable water depth. We examine the differences between the models through analytical solutions of the stream function equations for simple but realistic flows. The solutions are validated with CFD simulations.

Flickering buoyant diffusion methane flames in weakly rotatory flows were computationally and theoretically investigated. The prominent computational finding is that the flicker frequency nonlinearly increases with the nondimensional rotational intensity R (up to 0.24), which is proportional to the nondimensional circumferential circulation. This finding is consistent with the previous experimental observations that rotatory flows enhance flame flicker to a certain extent. Based on the vortex-dynamical understanding of flickering flames that the flame flicker is caused by the periodic shedding of buoyancy-induced toroidal vortices, a scaling theory is formulated for flickering buoyant diffusion flames in weakly rotatory flows. The theory predicts that the increase of flicker frequency f obeys the scaling relation (left( f-f_{0} right) propto R^{2}), which agrees very well with the present computational results. In physics, the external rotatory flow enhances the radial pressure gradient around the flame, and the significant baroclinic effect (mathrm {nabla }ptimes mathrm {nabla }rho ) contributes an additional source for the growth of toroidal vortices so that their periodic shedding is faster.

Large-amplitude flow disturbances, or gusts, can drastically alter the aerodynamic forces on an airfoil and are regularly investigated through wind tunnel (or water tunnel) experiments. The gusts generated in those experiments are often further analyzed using numerical simulations, but usually without fully accounting for the wind tunnel walls or gust generator. The current work investigates the wind tunnel effects on the predicted lift response and flow field using a computational framework that models the viscous flow around the airfoil but treats the tunnel walls and gust generation as inviscid boundary conditions. We apply this model to three examples and compare the predicted gust response with the responses predicted by a free-space viscous model and a classical unsteady aerodynamics model to highlight the wind tunnel effects. We find that the wind tunnel modeling introduces non-negligible effects depending on the airfoil and gust configurations. These effects include the confinement effect of the wind tunnel walls and the triggering of flow separation when it does not occur in the corresponding free-space model. In the last example, we also note that this virtual counterpart of an actual wind tunnel can be paired with experiments through data assimilation to increase the accuracy of the gust response or perform parameter estimation.

In simulating two-phase combustion, most Reynolds-averaged Navier–Stokes (RANS) simulation and large-eddy simulation (LES) used Eulerian–Lagrangian (E–L) modeling (Eulerian treatment of gas phase and Lagrangian treatment of particles/droplets) which needs much more computational time than the Eulerian–Eulerian (E–E) or two-fluid modeling. However, in the E–E modeling, the problem of how to reduce the computation time for poly-dispersed particles is encountered . To solve this problem, the present author proposed an Eulerian–Eulerian–Lagrangian (E–E–L) modeling of two-phase combustion for both RANS modeling and LES. The E–E–L modeling is an Eulerian treatment of gas phase and a combined Eulerian–Lagrangian treatment of particles/droplets, in which the particle velocity and concentration are solved by Eulerian modeling, and particle temperature and mass change due to reaction are solved by Lagrangian modeling. In this paper, a review is given for an E–E–L modeling of coal combustion, its application in RANS simulation and its possible application in LES. For E–E–L LES, an energy equation model of two-phase sub-grid scale (SGS) stresses accounting for the interaction between two-phase SGS stresses is suggested, and a second-order moment SGS (SOM-SGS) turbulence-chemistry model is adopted to simulate gas-phase reaction in two-phase combustion. These SGS models were separately assessed by comparison with experiments.

A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the interface between two fluids, are considered. The proposed numerical framework is based on a finite volume method and allows solving the problem numerically in bipolar cylindrical coordinates. In these coordinates, both the pipe wall and the unperturbed interface (of a constant curvature, e.g., plane interface, as considered in this work) coincide with the coordinate surfaces. Thereby, the no-slip as well as the interfacial boundary conditions can be imposed easily. It also enables investigation of the local behavior of the flow field and shear stresses in the vicinity of the triple points, where the interface contacts the pipe wall. The results obtained in the bipolar coordinates are verified by an independent numerical solution based on the problem formulation in Cartesian coordinates, where the pipe wall is treated by the immersed boundary method. Two representative examples of gas–liquid and liquid–liquid flows are included to demonstrate the applicability of the proposed numerical technique for analyzing the flow stability.

The influence of an inviscid planar wall on the temporal development of the long-wavelength instability of a trailing vortex pair is formulated analytically and studied numerically. The center positions and deformation perturbations of the trailing vortices are marched forward in time via the vortex filament method based on Biot–Savart induction. An optimal perturbation analysis of the vortex system determines the wavenumber and initial condition that yield maximum perturbation growth for any instant in time. Direct integration of the vortex system highlights its sensitivity to initial conditions and the time dependence of the optimal wavenumber, which are not features of the classical free vortex pair. As the counter-rotating vortex pair approaches the wall, the wavenumber for maximum growth shifts to a higher value than what is predicted for the Crow instability of vortices in an unbounded fluid. The present analysis demonstrates that the local suppression of the Crow instability near a planar wall may be described without recourse to viscous fluid arguments.

Both schooling behavior and burst-and-coast gait could improve fish swimming performance. The extent to which fish can improve their swimming performance by combining these two strategies is still unknown. By examining two self-propelled pitching foils positioned side-by-side at different duty cycles (DC), we examine swimming speed and cost of transport efficiency (CoT) using the open-source immersed boundary software IBAMR. We find that a stable schooling formation can only be maintained if both foils employ similar and moderate DC values. In these cases, vortex interactions increase foils’ lateral movements, but not their swimming speed or efficiency. Additionally, we examine vortex interactions in both “schooling" and “fission" scenarios (which are determined by DC). The research provides useful insights into fish behavior and valuable information for designing bio-inspired underwater robots.