Chaotic transients in spatially extended systems

Different transient-chaos related phenomena of spatiotemporal systems are reviewed. Special attention is paid to cases where spatiotemporal chaos appears in the form of chaotic transients only. The asymptotic state is then spatially regular. In systems of completely different origins, ranging from fluid dynamics to chemistry and biology, the average lifetimes of these spatiotemporal transients are found, however, to grow rapidly with the system size, often in an exponential fashion. For sufficiently large spatial extension, the lifetime might turn out to be larger than any physically realizable time. There is increasing numerical and experimental evidence that in many systems such transients mask the real attractors. Attractors may then not be relevant to certain types of spatiotemporal chaos, or turbulence. The observable dynamics is governed typically by a high-dimensional chaotic saddle. We review the origin of exponential scaling of the transient lifetime with the system size, and compare this with a similar scaling with system parameters known in low-dimensional problems. The effect of weak noise on such supertransients is discussed. Different crisis phenomena of spatiotemporal systems are presented and fractal properties of the chaotic saddles underlying high-dimensional supertransients are discussed. The recent discovery according to which turbulence in pipe flows is a very long lasting transient sheds new light on chaotic transients in other spatially extended systems.     

微波消解-微波等离子体矩原子发射光谱法测定乳胶管中的铁、钙、镍、镁、锌

本文研究了用HNO3-H2O2微波消解样品,微波等离子体矩原子发射光谱(MPT-AES)测定乳胶管中铁,钙,镍,镁,锌的含量方法。详细考察了测定铁、钙、镍、镁、锌的最佳实验条件,以及介质酸、共存离子的影响。本方法测定铁、镍、镁、钙、锌的检出限分别为77.80、7.55、2.70、275.87、46.23 ng/mL,方法的精密度分别为3.10%、2.19%、2.22%、1.27%、2.90%,线性范围分别为0.08~2 mg/L0、.06~2 mg/L0、.001~3 mg/L、0.005~2 mg/L、0.05~1 mg/L,加标回收率分别在97.7%~107.8%、96.0%~106.7%、98.0%~106.2%、92.3%~108.8%、98.7%~106.8%范围。     

Turbulent pipe flow of a drag-reducing rigid “rod-like” polymer solution

Fully developed turbulent pipe flow of an aqueous solution of a rigid “rod-like” polymer, scleroglucan, at concentrations of 0.005% (w/w) and 0.01% (w/w) has been investigated experimentally. Fanning friction factors were determined from pressure-drop measurements for the Newtonian solvent (water) and the polymer solutions and so levels of drag reduction for the latter. Mean axial velocity u and complete Reynolds normal stress data, i.e. u′, v′ and w′, were measured by means of a laser Doppler anemometer at three different Reynolds numbers for each fluid. The measurements indicate that the effectiveness of scleroglucan as a drag-reducing agent is only mildly dependent on Reynolds number. The turbulence structure essentially resembles that of flexible polymer solutions which also lead to low levels of drag reduction.     

On the use of generalized Hamilton׳s principle for the derivation of the equation of motion of a pipe conveying fluid

In this paper, first, some pertinent studies are reviewed, undertaken to extend Hamilton׳s principle or Lagrange׳s equations to open systems, and continua including so-called non-material volumes; then, the corresponding mathematical formulations are reproduced and discussed using a uniform nomenclature. A typical flexible pipe conveying fluid system is considered next, and it is shown that the expression given by McIver for Hamilton׳s principle remains valid even in the presence of non-material volumes; the extra term due to the flux of kinetic energy through the control surface in the expression obtained by Casetta and Pesce vanishes.     

Entropy generation for pipe flow of a third grade fluid with Vogel model viscosity

The flow of fluid-solid mixtures in a pipe can be treated as non-Newtonian fluids of third grade. Depending upon the fluid viscosity, entropy generation in the flow system varies. In the present study, flow of third grade fluid in a pipe is considered. The Vogel model is introduced to account for the temperature-dependent viscosity. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that increasing viscosity parameter A reduces the entropy generation number and opposite is true for increasing viscosity parameter B.     

Turbulence Plus

This paper attempts to give a concise overview of the turbulence research performed at the Laboratory for Aero and Hydrodynamics of the Delft University of Technology under the guidance of Frans Nieuwstadt. Frans Nieuwstadt was appointed in 1986 as director of the laboratory, and he held this position until his sudden death in 2005. Frans’ principal interest was to investigate turbulence at a fundamental level, but also to consider turbulence and its role in other processes. He coined a name for this research: turbulence plus.     

A theoretical analysis of forced convection in a porous-saturated circular tube: Brinkman–Forchheimer model

Fully developed forced convection inside a circular tube filled with saturated porous medium and with uniform heat flux at the wall is investigated on the basis of a Brinkman–Forchheimer model. The matched asymptotic expansion method is applied at small Darcy numbers. For large Darcy numbers, the solution for the Brinkman–Forchheimer momentum equation is found in terms of an asymptotic expansion. Once the velocity distribution is determined, the energy equation is solved using the same asymptotic technique. The results for the two limiting cases of clear fluid and Darcy flow conditions show good agreement with those available in the literature.     

Numerical study of transition in a cylindrical pipe flow

We present numerical results of transition in a smooth cylindrical pipe by small periodical suction and blowing (PSB) at the inlet of a laminar pipe flow at Reynolds number 3000 based on the maximum velocity of the laminar flow and radius of the pipe. The spatial development of the PSB disturbance is simulated by means of pseudo-spectrum element method. The transitional process is described in the paper that the disturbances are growing rapidly in a short part of the pipe after they develop gradually in sufficient long distance. When the rapid growth of disturbances occurs the time step of integration should be decreased and then the flow transits to turbulent.     

Fully developed flow in a curved pipe of arbitrary curvature ratio

It is generally assumed in curved pipe flow analyses that the curvature ratio, δ, of the pipe is very small, in which case the flow depends on a single parameter, the Dean number. This is not the case if δ is not very small. To determine the importance of this effect we have numerically solved the full Navier-Stokes equations, in primitive variable form, for arbitrary values of δ. A factored ADI finite-difference scheme has been used, employing Chorin's artificial compressibility technique. The results show that the central-difference calculation on a staggered grid is stable, without adding artificial damping terms, due to coupling between pressure and velocity. A spatially variable time step is used with a fixed Courant number.     

A finite element method for transient compressible flow in pipelines

A finite element method is developed to solve the partial differential equations describing the unsteady flow of gas in pipelines. Excellent agreement is obtained between simulated results and experimental data from a fullscale gas pipeline. The method is used to describe very transient flow (blowout), and to determine the performance of leak detection systems, and proves to be very stable and reliable.