Adjoint wall functions: A new concept for use in aerodynamic shape optimization

The continuous adjoint method for the computation of sensitivity derivatives in aerodynamic optimization problems of steady incompressible flows, modeled through the k–ε turbulence model with wall functions, is presented. The proposed formulation leads to the adjoint equations along with their boundary conditions by introducing the adjoint to the friction velocity. Based on the latter, an adjoint law of the wall that bridges the gap between the solid wall and the first grid node off the wall is proposed and used during the solution of the system of adjoint (to both the mean flow and turbulence) equations. Any high Reynolds turbulence model, other than the k–ε one used in this paper, could also profit from the proposed adjoint wall function technique. In the examined duct flow problems, where the total pressure loss due to viscous effects is used as objective function, emphasis is laid on the accuracy of the computed sensitivity derivatives, rather than the optimization itself. The latter might rely on any descent method, once the objective function gradient has accurately been computed.     

Unsteady flow around impacting bluff bodies

The flow resulting from the collision without rebound of generic bluff bodies with a wall in a still viscous fluid is investigated both computationally and experimentally. Emphasis is on the case of a circular cylinder impact (two-dimensional geometry), but comparisons with the flow generated by the impact of a sphere (axisymmetric geometry) are included. For normal cylinder impacts, the two counter-rotating vortices forming behind the body during its motion continue their trajectory towards the wall after the collision, leading to the generation of opposite-signed secondary vorticity at the cylinder and wall surfaces. Secondary vortices forming from this vorticity at higher Reynolds numbers exhibit a short-wavelength three-dimensional instability. Comparison with the sphere impact reveals significant differences in the scales of the vortices after the collision, due to the additional vortex stretching acting in the axisymmetric geometry. This leads to a delay in the onset of three-dimensionality and to a different instability mechanism. Oblique cylinder impacts are also considered. For increasing impact angles, the wall effect is gradually reduced on one side of the cylinder, which favours the roll-up of the secondary vorticity and increases the rebound height of the vortex system.     

Experimental and computational study of the flow induced by a plasma actuator

A complementary experimental and computational study of the flow field evoked by a plasma actuator mounted on a flat plate was in focus of the present work. The main objective of the experimental investigation was the determination of the vector force imparted by the plasma actuator to the fluid flow. The force distribution was presently extracted from the Navier–Stokes equations directly by feeding them with the velocity field measured by a PIV technique. Assuming a steady-in-mean, two-dimensional flow with zero-pressure gradient, the imbalance between the convective term and the momentum equation’s right-hand-side terms reveals the desired resulting force. This force-distribution database was used afterwards as the source term in the momentum equation. Furthermore, an empirical model formulation for the volume-force determination parameterized by the underlying PIV-based model is derived. The model is tested within the RANS framework in order to predict a wall jet-like flow induced by a plasma actuator. The Reynolds equations are closed by a near-wall second-moment closure model based on the homogeneous dissipation rate of the kinetic energy of turbulence. The computationally obtained velocity field is analysed along with the experimental data focussing on the wall jet flow region in proximity of the plasma actuator. For comparison purposes, different existing phenomenological models were applied to evaluate the new model’s accuracy. The comparative analysis of all applied models demonstrates the strength of the new empirical model, particularly within the plasma domain. In addition, the presently formulated empirical model was applied to the flow in a three-dimensional diffuser whose inflow was modulated by a pair of streamwise vortices generated by the present plasma actuator. The direct comparison with existing experimental data of Grundmann et al. (2011) demonstrated that the specific decrease of the diffuser pressure corresponding to the continuous forcing was predicted correctly.     

Generalized Wall Functions for Rough Walls Based on Data Assimilation

We present a systematic identification method for the development of equivalent boundary conditions for turbulent flow simulation over rough walls in engineering applications where the typical roughness involved is known for a given application. After parameterizing the roughness and sampling of the parameter space, numerical simulations or experiences are used to generate a database which is used to identify the coefficients of a polynomial reduced-order model. These laws are parameterized by an a priori length scale for which we propose a new a posteriori criterion.     

CFD modeling of pressure drop and drag coefficient in fixed beds: Wall effects

Simulations of fixed beds having column to particle diameter ratio (D/dp ) of 3, 5 and 10 were performed in the creeping, transition and turbulent flow regimes, where Reynolds number (dp VLL/L ) was varied from 0.1 to 10,000. The deviations from Ergun’s equation due to the wall effects, which are important in D/d p<15 beds were well explained by the CFD simulations. Thus, an increase in the pressure drop was observed due to the wall friction in the creeping flow, whereas, in turbulent regime a decrease in t...     

Control of Wall Thickness and Extraordinarily High Hydrothermal Stability of Nanoporous MCM‐41 Silica

Wall thickness of siliceous MCM‐41 could be controlled systematically up to 36.1 Å. A reasonable model explaining formation of thicker MCM‐41 walls, not enlarging pore channel is proposed on the basis of TGA and ¹³C MAS NMR data of samples. Thermal restructuring process under mild basic condition favors the silica redeposition on silica wall and building up thicker wall. Most mesostructure of calcined MCM‐41 with thicker wall was retained even after hydrothermal treatment in boiling water for 14 days. To our best knowledge, the excellent hydrothermal stability of the MCM‐41 silica reported herein has not been described before and facilitates practical applications of mesoporous molecular sieves in future.     

From random sphere packings to regular pillar arrays: effect of the macroscopic confinement on hydrodynamic dispersion

Flow and mass transport in bulk and confined chromatographic supports comprising random packings of solid, spherical particles and hexagonal arrays of solid cylinders (regular pillar arrays) are studied over a wide flow velocity range by a numerical analysis scheme, which includes packing generation by a modified Jodrey-Tory algorithm, three-dimensional flow field calculations by the lattice-Boltzmann method, and modeling of advective-diffusive mass transport by a random-walk particle-tracking technique. We demonstrate the impact of the confinement and its cross-sectional geometry (circular, quadratic, semicircular) on transient and asymptotic transverse and longitudinal dispersion in random sphere packings, and also address the influence of protocol-dependent packing disorder and the particle-aspect ratio. Plate height curves are analyzed with the Giddings equation to quantify the transcolumn contribution to eddy dispersion. Confined packings are compared with confined arrays under the condition of identical bed porosity, conduit cross-sectional area, and laterally fully equilibrated geometrical wall and corner effects on dispersion. Fluid dispersion in a regular pillar array is stronger affected by the macroscopic confinement and does not resemble eddy dispersion in random sphere packings, because the regular microstructure cannot function as a mechanical mixer like the random morphology. Giddings' coupling theory fails to preserve the nature of transverse dispersion behind the arrays' plate height curves, which approach a linear velocity-dependence as transverse dispersion becomes velocity-independent. Upon confinement this pseudo-diffusive behavior can outweigh the performance advantage of the regular over the random morphology.     

基质固相分散提取桃儿七根中鬼臼毒苷和异鬼臼苦酮

采用基质固相分散提取桃儿七根中的鬼臼毒苷和异鬼臼苦酮,并用高校液相色谱法进行了测定,选择硅胶为分散剂和甲醇为洗脱剂对鬼臼毒苷进行提取,硅藻土为分散剂和甲醇为洗脱剂对异鬼臼苦酮进行提取,与回流提取法相比,提取率较高。     

Examination of wall damping for the k-ε turbulence model using direct simulations of turbulent channel flow

Handler, Hendricks and Leighton have recently reported results for the direct numerical simulation (DNS) of a turbulent channel flow at moderate Reynolds number. These data are used to evaluate the terms in the exact and modelled transport equations for the turbulence kinetic energy k and the isotropic dissipation function ε. Both modelled transport equations show significant imbalances in the high-shear region near the channel walls. The model for the eddy viscosity is found to yield distributions for the production terms which do not agree well with the distributions calculated from the DNS data. The source of the imbalance is attributed to the wall-damping function required in eddy viscosity models for turbulent flows near walls. Several models for the damping function are examined, and it is found that the models do not vary across the channel as does the damping when evaluated from the DNS data. The Lam-Bremhorst model and the standard van Driest model are found to give reasonable agreement with the DNS data. Modification of the van Driest model to include an effective origin yields very good agreement between the modelled production and the production calculated from the DNS data, and the imbalance in the modelled transport equations is significantly reduced.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

The present paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a (k-ε) turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ε is proposed as a numerical treatment for physically meaningless values of k and ε. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.