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

Transition to turbulence in particle laden flows

Suspended particles can alter the properties of fluids and in particular also affect the transition from laminar to turbulent flow. In the present experimental study, we investigate the impact of neutrally buoyant, spherical inertial particles on transition to turbulence in a pipe flow. At low particle concentrations, like in single phase Newtonian fluids, turbulence only sets in when triggered by sufficiently large perturbations and, as characteristic for this transition localized turbulent regions (puffs) co-exist with laminar flow. In agreement with earlier studies this transition point initially moves to lower Reynolds number (Re) as the particle concentration increases. At higher concentrations however the nature of the transition qualitatively changes: Laminar flow gives way to a globally fluctuating state following a continuous, non-hysteretic transition. A further increase in Re results in a secondary instability where localized puff-like structures arise on top of the uniformly fluctuating background flow. At even higher concentration only the uniformly fluctuating flow is found and signatures of Newtonian type turbulence are no longer observed

Conspicious Consumption, Economic Growth, and Taxation: A Generalization

This paper studies the infuence of consumption externalities in the Ramsey model. In contrast to the recent literature, a quite general specification of preferences is used and the concept of the effective intertemporal elasticity of substitution is introduced. We give conditions for the observational equivalence between economies with consumption externalities and externality-free economies. An additional key result is that there exist several types of instantaneous utility functions in which the decentralized solution coincides with the socially planned one in spite of the presence of consumption externalities. The conditions for optimal taxation are also derived.Social status, Conspicuous consumption, Economic growth

Status Seeking in the Small Open Economy

In our modified version of the small open economy Ramsey model, we assume that agents have preferences over consumption and status which, in turn, is determined by relative wealth. This extension potentially eliminates the standard model's counterfactual result that an impatient country over time mortgages all of its capital and labor income. We show that the steady-state values of net assets and consumption, the speed of convergence and, in particular, the direction of adjustment during the transition depend crucially upon the degree of status consciousness. The latter also influences the economy's response to macro-economic shocks.Status seeking, Relative wealth, Open economy dynamics

Relative Consumption and Endogenous Labour Supply in the Ramsey Model: Do Status-Conscious People Work Too Much?

This paper introduces consumption externalities into a Ramsey-type model with endogenous labour supply and homogeneous agents. The instantaneous utility of any consumer is assumed to depend on work effort, own consumption and relative consumption, where the latter determines the individual's status in the society. Appropriate normality conditions with respect to consumption and leisure ensure that at least in the long run status-conscious individuals consume and work too much, compared to the social optimum, and that the capital stock is too high. Public policy can, however, induce the private sector to attain the social optimum by designing an optimal consumption tax policy.Status, Relative consumption, Work effort

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

Exceeding the asymptotic limit of polymer drag reduction

The drag of turbulent flows can be drastically decreased by addition of small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view we will show in the following that for an appropriate choice of parameters polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. However at higher polymer concentrations the laminar state becomes unstable, resulting in a fluctuating flow with the characteristic drag of the MDR asymptote. The asymptotic state is hence dynamically disconnected from ordinary turbulence.Comment: 6 pages, 6 figure

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

Dynamics of viscoelastic pipe flow in the maximum drag reduction limit

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so called "maximum drag reduction" (MDR) asymptote is universal, i.e. independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations using minimal sized channels appeared to support this view and reported long "hibernation" periods where turbulence is marginalized. In simulations of pipe flow we find that, indeed, with increasing Weissenberg number (Wi), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in Wi, the flow fully relaminarises, in agreement with recent experiments. At even larger Wi, a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial-turbulence (EIT).Comment: 18 pages, 5 figure

Prediction error identification of linear dynamic networks with rank-reduced noise

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of measured signals}, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramer-Rao lower bound in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in Automatica, 4 April 201