Theoretical and Computational Fluid Dynamics最新文献

Normal shock trains are a flow phenomenon of significance to ramjet engines, but it remains unclear what its structure is decided by and how it evolves with the incoming Mach number. To seek a theoretical explanation, the minimum entropy production principle is generalized to the quasi-steady behavior of normal shock trains in two-dimensional straight channels with uniform incoming flow. Numerical simulations are also performed to validate the model together with the data collected from public literature. The analysis suggests that the flow parameters of a normal shock train depend on the inviscid shock-shock interactions rather than the local boundary-layer separations, though the angles of two incident shocks should still be equal as similar to the case that complies with the free-interaction theory. The shock feet’s positions, meanwhile, are allowed to be coincident or not, free from the entropy restriction. This freedom of position explains why both symmetric and partially asymmetric normal shock trains could be found previously. Further theoretical calculations reveal the inclinations of two incident shocks increase first and then decrease with the incoming Mach number, peaking at 48.570 degrees when the Mach number reaches 1.753. It is also indicated that the Mach number range allowing for a normal shock train is 1.652 to 2.254, giving evidence for past observations.

A numerical approach is proposed for the study of instabilities in helical vortex systems as found in the near-wake of turbines or propellers. The methodology has a high degree of generality, yet the present paper focusses on the case of one unique helical vortex. First, a method based on helical symmetry aimed at computing a three-dimensional base flow with prescribed parameters—helical pitch, helical radius, vortex circulation, core size and inner jet component—is presented. Second, the linear instability of this base flow is examined by reducing the three-dimensional instability problem to two-dimensional simulations with wavenumbers prescribed along the helix axis. Each simulation converges towards an exponentially growing or decaying complex state from which eigenfunctions, growth rate and frequency are extracted. This procedure is validated against a standard method based on direct three-dimensional numerical simulations of the Navier–Stokes equations linearized in the vicinity of the same helical base flows. Three illustrative base flows are presented with or without inner jet component, the instability of which is dominated, at the prescribed axial wavenumber, by unstable modes of three different types: long-wave instability, short-wave elliptic and curvature instabilities. Results from the new procedure and from the fully three-dimensional one are found in excellent agreement, which validates the new methodology. The gain in computational time is typically the one that is achieved while going from three-dimensional to two-dimensional simulations.

This study presents new analytical solutions for the dynamics and dispersion of particles laden in two-dimensional Taylor–Green vortex flows. Explicit solutions are found for the temporal evolution of free and forced particles under the viscous decaying vortical flow for low Stokes numbers. When placed in the vicinity of the vortex structure, forced particles may either trap within or escape the vortex cell, for which an explicit criterion is proposed. Using the same methodology, the trajectories of charged particles in a vortex flow in the presence of a magnetic field are solved. All cases are compared to numerical simulations demonstrating the validity of the proposed theoretical solutions. The explicit analytical solutions derived here provide fundamental insights into the complex phenomena of particle-vortex interactions and may be used to predict and control particle dispersion in various engineering and natural systems .

Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al. (J Fluid Mech 928:A27, 2021. https://doi.org/10.1017/jfm.2021.812), we focused on wall-shear-stress distributions as input, which are difficult to measure in experiments. In order to overcome this limitation, we introduce a model that can take as input the heat-flux field at the wall from a passive scalar. Four different Prandtl numbers (Pr = nu /alpha = (1,2,4,6)) are considered (where (nu ) is the kinematic viscosity and (alpha ) is the thermal diffusivity of the scalar quantity). A turbulent boundary layer is simulated since accurate heat-flux measurements can be performed in experimental settings: first we train the network on aptly-modified DNS data and then we fine-tune it on the experimental data. Finally, we test our network on experimental data sampled in a water tunnel. These predictions represent the first application of transfer learning on experimental data of neural networks trained on simulations. This paves the way for the implementation of a non-intrusive sensing approach for the flow in practical applications.

We study the pressure-driven steady gas flow, imposed by temperature or density gradients, over a backward-facing step in a two-dimensional microchannel. Focusing on the near-free-molecular regime of high Knudsen ((textrm{Kn})) numbers, the problem is analyzed asymptotically based on the Bhatnagar, Gross and Krook kinetic model, and supported by numerical Discrete Velocity Method and Direct Simulation Monte Carlo calculations. The wall conditions are formulated using the Maxwell model, superposing specular and diffuse surface conditions. The asymptotic solution contains the leading-order free-molecular description and a first-order integral representation of the near-free-molecular correction. Our results indicate that flow separation at the step can occur at arbitrarily large (yet finite) Knudsen numbers in channels with specular surfaces (i.e., having an accommodation coefficient of (alpha = 0)), driven by temperature differences between the inlet and outlet reservoirs. It is then shown that detachment is significantly suppressed by density variations between reservoirs and partially diffuse surfaces (with (alpha gtrsim 0.3)). While the mass flow rate in a specular channel decreases with decreasing (mathrm {Kngg 1}) in a density-driven setup (in line with the Knudsen Paradox), it increases in a temperature-driven flow. The results are obtained for arbitrary differences between the inlet and outlet reservoir equilibrium properties, and are rationalized using the linearized problem formulation.

A methodology to numerically assess wall-curvature effects in boundary layers is introduced. Wall curvature, which directly induces streamline curvature, is associated with several changes in boundary-layer flow. By necessity, a local radial pressure gradient emerges to balance mean flow turning. Moreover, a streamwise (wall-tangential) pressure gradient can appear for configurations with non-constant wall curvature or a particular freestream condition; zero pressure gradient is a special case. In laminar concave flow, the Görtler instability and the associated Taylor-Görtler vortices destabilize the flow and promote laminar-turbulent transition, whereas in the fully turbulent regime, unsteady coherent structures formed by the centrifugal instability mechanism dramatically redistribute turbulent shear stress. One difficulty of assessing centrifugal effects on boundary layers is that they often appear simultaneously with other phenomena, such as a streamwise pressure gradient, making their individual evaluation often ambiguous. For numerical studies of transitional and turbulent boundary layers, it is therefore beneficial to understand the interactive nature of such coupled effects for generic configurations. A methodology to do so is presented, and is verified using the case of a subsonic, compressible turbulent boundary layer. Four direct numerical simulations have been computed, forming a (2{times }2) matrix of turbulent boundary-layer states; namely with and without concave wall curvature, each having a zero and a non-zero streamwise-pressure-gradient realization. The setup and accompanying procedures to determine appropriate boundary conditions are discussed, and the methodology is evaluated through analysis of the mean flow fields. Differences in mean flow properties such as wall shear stress and boundary-layer thickness due to either streamwise pressure gradient or wall curvature are shown to be remarkably independent of one another.