Dynamic leg-motion and its effect on the aerodynamic performance of cyclists

In this wind-tunnel based experimental study, the flow topology of the near wake of a generic anatomically accurate model cyclist is mapped for a range of reduced pedalling frequencies. Wake flow fields for both static leg and pedalling cyclists are compared over the full 360° rotation of the crank using both time- and phase-averaging. The primary wake flow structures and aerodynamic forces are quantified and analysed under dynamic pedalling conditions representative of an elite-level time-trial cyclist. Over the range of reduced pedalling frequencies studied, only minor variation was detected between the instantaneous drag and primary vortical structures of a pedalling cyclist compared to a stationary cyclist with the pedals in the same position. A simplified model of the aerodynamic forces acting on the legs under motion is presented to provide insight into how the motion of the legs influences aerodynamic drag. A comparison of predicted forces from this model with those from experiments provides a new perspective on how the aerodynamics of cyclists may be optimised.     

Global persistence of geometrical structures for the Boussinesq equation with no diffusion

Our main aim is to investigate the temperature patch problem for the two-dimensional incompressible Boussinesq system with partial viscosity: the initial temperature is the characteristic function of some simply connected domain with 𝒞^1,𝜀 Hölder regularity. Although recent results ensure that the 𝒞¹ regularity of the patch persists for all time, whether higher order regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue. We also study the higher dimensional case, after prescribing an additional smallness condition involving critical Lebesgue or weak-Lebesgue norms of the data, so as to get a global-in-time statement. All our results stem from general properties of persistence of geometrical structures (of independent interest), that we establish in the first part of the paper.     

A sharp‐interface immersed boundary framework for simulations of high‐speed inviscid compressible flows

A new finite‐volume flow solver based on the hybrid Cartesian immersed boundary (IB) framework is developed for the solution of high‐speed inviscid compressible flows. The IB method adopts a sharp‐interface approach, wherein the boundary conditions are enforced on the body geometry itself. A key component of the present solver is a novel reconstruction approach, in conjunction with inverse distance weighting, to compute the solutions in the vicinity of the solid‐fluid interface. We show that proposed reconstruction leads to second‐order spatial accuracy while also ensuring that the discrete conservation errors diminish linearly with grid refinement. Investigations of supersonic and hypersonic inviscid flows over different geometries are carried out for an extensive validation of the proposed flow solver. Studies on cylinder lift‐off and shape optimisation in supersonic flows further demonstrate the efficacy of the flow solver for computations with moving and shape‐changing geometries. These studies conclusively highlight the capability of the proposed IB methodology as a promising alternative for robust and accurate computations of compressible fluid flows on nonconformal Cartesian meshes.     

On power-law fluids with the power-law index proportional to the pressure

In this short note we study special unsteady flows of a fluid whose viscosity depends on both the pressure and the shear rate. Here we consider an interesting dependence of the viscosity on the pressure and the shear rate; a power-law of the shear rate wherein the exponent depends on the pressure. The problem is important from the perspective of fluid dynamics in that we obtain solutions to a technologically relevant problem, and also from the point of view of mathematics as the analysis of the problem rests on the theory of spaces with variable exponents. We use the theory to prove the existence of solutions to generalizations of Stokes’ first and second problem.     

An accurate pressure–velocity decoupling technique for semi‐implicit rotational projection methods

In this paper, an accurate semi‐implicit rotational projection method is introduced to solve the Navier–Stokes equations for incompressible flow simulations. The accuracy of the fractional step procedure is investigated for the standard finite‐difference method, and the discrete forms are presented with arbitrary orders or accuracy. In contrast to the previous semi‐implicit projection methods, herein, an alternative way is proposed to decouple pressure from the momentum equation by employing the principle form of the pressure Poisson equation. This equation is based on the divergence of the convective terms and incorporates the actual pressure in the simulations. As a result, the accuracy of the method is not affected by the common choice of the pseudo‐pressure in the previous methods. Also, the velocity correction step is redefined, and boundary conditions are introduced accordingly. Several numerical tests are conducted to assess the robustness of the method for second and fourth orders of accuracy. The results are compared with the solutions obtained from a typical high‐resolution fully explicit method and available benchmark reports. Herein, the numerical tests are consisting of simulations for the Taylor–Green vortex, lid‐driven square cavity, and vortex–wall interaction. It is shown that the present method can preserve the order of accuracy for both velocity and pressure fields in second‐order and high‐order simulations. Furthermore, a very good agreement is observed between the results of the present method and benchmark simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

A note on compressive limiting for two‐material flows

In this short note we describe a simple extension to the multi‐material shock‐capturing algorithm presented in (J. Comput. Phys. 2007; 223 :262–297) that can be used to maintain sharp material interfaces. The method takes the form of an artificial compression which is designed so that the material indicator jumps across only a few cells but which does not excite physical instabilities in the flow. The advantages of the approach include its simplicity and flexibility in that it provides a parameter that effectively determines the captured interface thickness. Copyright © 2009 John Wiley & Sons, Ltd.     

Determination of Drop Sizes in Annular Gas/Liquid Flows in Vertical and Horizontal Pipes

Measurement of drop sizes play vital role in applications dealing with gas/liquid flow mixtures. In the present work, drop sizes in vertical and horizontal pipe flows were determined using Malvern 2600HSD system that applies laser diffraction method. From the analysis of the experimental data obtained at two different pipe orientations, two separate expressions were developed to determine Sauter mean diameter, d ₃₂. Except for the 20 m/s superficial gas velocity in vertical flow case, a good agreement was found between the developed expressions and the experimental data.     

Isolation of three glucaric acids from Leonurus japonicus Houtt. by using high-speed countercurrent chromatography combined with semi-preparative high-performance liquid chromatography

The isomerism of glucaric acids and the complexity of the composition of Leonurus japonicus Houtt. increased the difficulty of the separation of glucaric acids from the herb. In the present study, three glucaric acids were isolated from Leonurus japonicus Houtt. by using high-speed countercurrent chromatography combined with semi-preparative high-performance liquid chromatography. Cation exchange resin chromatography was applied to remove the alkaloids and enrich the glucaric acid fractions. Preliminary separation of the glucaric acid extract by high-speed countercurrent chromatography was carried out at 45℃ by using an optimized solvent system of ethyl acetate/n-butanol/formic acid/water (1:1:0.01:2, v/v/v/v) with satisfied stationary phase retention and separation factor. The semi-preparative high-performance liquid chromatography was used for further separation and purification of the target fractions, and three monomeric compounds were obtained with purities of 90.0, 91.0, and 95.3%. UV spectroscopy, NMR spectroscopy, and mass spectrometry were employed to identify their structures, which were assigned as 2-syringyl glucaric acid, 2,4-disyringyl glucaric acid, and 3,4-disyringyl glucaric acid, respectively, and 2,4-disyringyl glucaric acid was reported for the first time.     

Scale-Up Preparation of Crocins I and II from Gardenia jasminoides by a Two-Step Chromatographic Approach and Their Inhibitory Activity Against ATP Citrate Lyase

Crocins are highly valuable natural compounds for treating human disorders, and they are also high-end spices and colorants in the food industry. Due to the limitation of obtaining this type of highly polar compound, the commercial prices of crocins I and II are expensive. In this study, macroporous resin column chromatography combined with high-speed counter-current chromatography (HSCCC) was used to purify crocins I and II from natural sources. With only two chromatographic steps, both compounds were simultaneously isolated from the dry fruit of Gardenia jasminoides, which is a cheap herbal medicine distributed in a number of countries. In an effort to shorten the isolation time and reduce solvent usage, forward and reverse rotations were successively utilized in the HSCCC isolation procedure. Crocins I and II were simultaneously obtained from a herbal resource with high recoveries of 0.5% and 0.1%, respectively, and high purities of 98.7% and 99.1%, respectively, by HPLC analysis. The optimized preparation method was proven to be highly efficient, convenient, and cost-effective. Crocins I and II exhibited inhibitory activity against ATP citrate lyase, and their IC₅₀ values were determined to be 36.3 ± 6.24 and 29.7 ± 7.41 μM, respectively.     

Aeolian transport of sand

The airborne transport of particles on a granular surface by the saltation mechanism is studied through numerical simulation of particles dragged by turbulent air flow. We calculate the saturated flux q_s and show that its dependence on the wind strength u_* is consistent with several empirical relations obtained from experimental measurements. We propose and explain a new relation for fluxes close to the threshold velocity u_t, namely, q_s=a(u_*-u_t)^α with α≈2. We also obtain the distortion of the velocity profile of the wind due to the drag of the particles and find a novel dynamical scaling relation. We also obtain a new expression for the dependence of the height of the saltation layer as function of the strength of the wind.