Scaling of the turbulence transition threshold in a pipe

We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in $Re$. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as $O(Re^{-1})$.Comment: 4 pages, RevTex (submitted to Phys. Rev. Lett.

Experimental investigation of transitional flow in a toroidal pipe

The flow instability and further transition to turbulence in a toroidal pipe (torus) with curvature (tube-to-coiling diameter) 0.049 is investigated experimentally. The flow inside the toroidal pipe is driven by a steel sphere fitted to the inner pipe diameter. The sphere is moved with constant azimuthal velocity from outside the torus by a moving magnet. The experiment is designed to investigate curved pipe flow by optical measurement techniques. Using stereoscopic particle image velocimetry, laser Doppler velocimetry and pressure drop measurements, the flow is measured for Reynolds numbers ranging from 1000 to 15000. Time- and space-resolved velocity fields are obtained and analysed. The steady axisymmetric basic flow is strongly influenced by centrifugal effects. On an increase of the Reynolds number we find a sequence of bifurcations. For Re=4075 a supercritical bifurcation to an oscillatory flow is found in which waves travel in the streamwise direction with a phase velocity slightly faster than the mean flow. The oscillatory flow is superseded by a presumably quasi-periodic flow at a further increase of the Reynolds number before turbulence sets in. The results are found to be compatible, in general, with earlier experimental and numerical investigations on transition to turbulence in helical and curved pipes. However, important aspects of the bifurcation scenario differ considerably

A RECREATION OPTIMIZATION MODEL BASED ON THE TRAVEL COST METHOD

A recreation allocation model is developed which efficiently selects recreation areas and degree of development from an array of proposed and existing sites. The model does this by maximizing the difference between gross recreation benefits and travel, investment, management, and site-opportunity costs. The model presented uses the Travel Cost Method for estimating recreation benefits within an operations research framework. The model is applied to selection of potential wilderness areas in Colorado. This example is then extended to show the model's capability in budget analysis and in planning to meet recreation targets.Resource /Energy Economics and Policy,

Caravan Awnings: a Geometrical Problem

Two questions regardingthe design of caravan awnings were posed by a company.The company wishes to produce awnings with a pretty appearance. When an awning is attached to a caravan, some wrinkles could appear. We developed some methods to avoid the wrinkles. The problem is restricted to awnings which are made from one piece of cloth

How to Mix Molecules with Mathematics

In this paper we develop two methods to calculate thermodynamic properties of mixtures. Starting point are the basic assumptions that also form the basis for the COSMO-RS model. In this approach, the individual molecules are represented by their geometrical shape with an electrical charge density on their surfaces. Next, the surface is split up into surface segments each with its own charge. In COSMO-RS a strong reduction is introduced by treating the segments as if they are completely independent. In the present study we take into account that the coupling between two patches is essentially dependent on the charge distribution on neighboring segments and on the local geometrical structure of the surface. Two approaches are followed. The first one points out how the model equations, which comprise the optimization of the entropy and conservation of internal energy, can efficiently be solved in general, thus also if the dependency between segments and the local geometry is included in the expression for the coupling energy between segments. In the second method the configuration with maximal entropy and prescribed energy is sought via simulation. Successive molecular configurations of the mixture are simulated and updated via a genetic algorithm to optimize the entropy. The second method is more time consuming but very general

Subcritical versus supercritical transition to turbulence in curved pipes

Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen--Poiseuille flow if the amplitude of flow perturbations as well as the Reynolds number exceed a minimum threshold (subcritical transition). As the pipe curvature increases centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter $d/D$) is sufficiently large a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability thresholds in the $Re-d/D$ parameter space in the range $0.01\leq\ d/D \leq0.1$ by means of laser-Doppler velocimetry and determine the point where the subcritical and supercritical instabilities meet. Two different experimental setups were used: a closed system where the pipe forms an axisymmetric torus and an open system employing a helical pipe. Implications for the measurement of friction factors in curved pipes are discussed

Mass Spectrometric Characterization of Oligomers in Pseudomonas aeruginosa Azurin Solutions

We have employed laser-induced liquid bead ion desorption mass spectroscopy (LILBID MS) to study the solution behavior of Pseudomonas aeruginosa azurin as well as two mutants and corresponding Re-labeled derivatives containing a Re(CO)_(3)(4,7-dimethyl-1,10-phenanthroline)^+ chromophore appended to a surface histidine. LILBID spectra show broad oligomer distributions whose particular patterns depend on the solution composition (pure H_(2)O, 20−30 mM NaCl, 20 and 50 mM NaP_i or NH_(4)P_i at pH = 7). The distribution maximum shifts to smaller oligomers upon decreasing the azurin concentration and increasing the buffer concentration. Oligomerization is less extensive for native azurin than its mutants. The oligomerization propensities of unlabeled and Re-labeled proteins are generally comparable, and only Re126 shows some preference for the dimer that persists even in highly diluted solutions. Peak shifts to higher masses and broadening in 20−50 mM NaP_i confirm strong azurin association with buffer ions and solvation. We have found that LILBID MS reveals the solution behavior of weakly bound nonspecific protein oligomers, clearly distinguishing individual components of the oligomer distribution. Independently, average data on oligomerization and the dependence on solution composition were obtained by time-resolved anisotropy of the Re-label photoluminescence that confirmed relatively long rotation correlation times, 6−30 ns, depending on Re−azurin and solution composition. Labeling proteins with Re-chromophores that have long-lived phosphorescence extends the time scale of anisotropy measurements to hundreds of nanoseconds, thereby opening the way for investigations of large oligomers with long rotation times

On the transient nature of localized pipe flow turbulence

International audienceThe onset of shear flow turbulence is characterized by turbulent patches bounded by regions of laminar flow. At low Reynolds numbers localized turbulence relaminarizes, raising the question of whether it is transient in nature or becomes sustained at a critical threshold. We present extensive numerical simulations and a detailed statistical analysis of the lifetime data, in order to shed light on the sources of the discrepancies present in the literature. The results are in excellent quantitative agreement with recent experiments and show that turbulent lifetimes increase super-exponentially with Reynolds number. In addition, we provide evidence for a lower bound below which there are no meta-stable characteristics of the transients, i.e. the relaminarization process is no longer memoryless. Copyright © Cambridge University Press 2010