Unidirectional Mean Research Articles

A two-chamber model of valveless pumping using the immersed boundary method

Abstract We present a new mathematical model of valveless pumping for a tube with two elastic chambers, which is motivated by the Liebau’s two-tank model. The tube consists of partially soft and partially (almost) rigid and the periodic pumping is applied at an asymmetric location of the soft tube. The immersed boundary method is used to investigate the important characteristics of valveless pumping as the previous experiments and mathematical models have been discovered. We have observed the existence of a unidirectional mean flow and the dependence of mean flows on the frequency and the compression duration of the periodic pumping. We are able to explain the occurrence of local maximum or minimum mean flows due to the resonances of the system.

A 1-D phenomenological model for soft tissue damage and repair

We present a new mathematical model of valveless pumping for a tube with two elastic chambers, which is motivated by the Liebau’s two-tank model. The tube consists of partially soft and partially (almost) rigid and the periodic pumping is applied at an asymmetric location of the soft tube. The immersed boundary method is used to investigate the important characteristics of valveless pumping as the previous experiments and mathematical models have been discovered. We have observed the existence of a unidirectional mean flow and the dependence of mean flows on the frequency and the compression duration of the periodic pumping. We are able to explain the occurrence of local maximum or minimum mean flows due to the resonances of the system.

On plume meandering in unstable stratification

Vertical plume meandering of gaseous pollutant is commonly experienced in the daytime atmospheric boundary layer (also know as convective boundary layer, CBL) that arose from the complicated interaction between buoyancy-generated turbulence and gravitational force. It leads to rapid pollutant mixing that cannot be accurately modeled by conventional Gaussian plume model. In the light of explaining the mechanism of plume rises and descents in CBLs, this study employs a direct numerical simulation (DNS) technique to compute the plume behaviors for pollutant emitted from line sources placed parallel to the spanwise direction in an unstably stratified turbulent open channel flow. The DNS results show that the plume meandering is due to the domination of uni-directional mean vertical pollutant fluxes above and below the mean plume height.

An efficient tool for accelerating the numerical solution of the stochastic subsurface flow problem using neural networks

An efficient numerical solution for the two-dimensional groundwater flow problem using artificial neural networks (ANNs) is presented. Under stationary velocity conditions with unidirectional mean flow, the conductivity realizations and the head gradients, obtained by a traditional finite difference solution to the flow equation, are given as input-output pairs to train a neural network. The ANN is trained successfully and a certain level of recognition of the relationship between input conductivity patterns and output head gradients is achieved. The trained network produced velocity realizations that are physically plausible without solving the flow equation for each of the conductivity realizations. This is achieved in a small fraction of the time necessary for solving the flow equations. The prediction accuracy of the ANN reaches 97.5% for the longitudinal head gradient and 94.7% for the transverse gradient. Head-gradient and velocity statistics in terms of the first two moments are obtained with a very high accuracy. The cross covariances between head gradients and the fluctuating log-conductivity (log-K) and between velocity and log-K obtained with the ANN approach match very closely those obtained by a traditional numerical solution. The same is true for the velocity components auto-covariances. The results are also extended to transport simulations with very good accuracy. Spatial moments (up to the fourth) of mean-concentration plumes obtained using ANNs are in very good agreement with the traditional Monte Carlo simulations. Furthermore, the concentration second moment (concentration variance) is very close between the two approaches. Considering the fact that higher moments of concentration need more computational effort in numerical simulations, the advantage of the presented approach in saving long computational times is evident. Another advantage of the ANNs approach is the ability to generalize a trained network to conductivity distributions different from those used in training. However, the accuracy of the approach in cases with higher conductivity variances is being investigated.

Specific discharge covariance in a heterogeneous semiconfined aquifer

In this study, covariance functions of specific discharge for both one‐dimensional and two‐dimensional flows in a semiconfined aquifer were derived with mean flow parallel to the formation bedding. Spectral theory was used to analyze a unidirectional mean flow field of infinite extent which is perturbed by one‐ and two‐dimensional statistically homogeneous hydraulic conductivity field. Relatively simple closed‐form analytical expressions requiring only some numerical integration for two‐dimensional flows were obtained for the longitudinal and transverse components of specific discharge covariance. The spatial, statistical structure of the specific discharge field was investigated in terms of the leakage factor and spatial structure of hydraulic conductivity field.

A LOW‐VOLUME FLOW TANK FOR MEASURING NUTRIENT UPTAKE BY LARGE MACROPHYTES1

ABSTRACTA recirculating flow‐tank was designed and tested to measure inorganic nutrient uptake by, and visualize the movement of seawater around, large macrophytes. The tank volume was small (46 L), and a propeller drive produced unidirectional mean flow. A turbulence reduction section dampened turbulence in the test section to a low level, so that water movement within this region was virtually laminar. The test section of the tank was wider than that of previous designs, allowing whole blades of Macrocystis integrifolia Bory and juvenile plants of Nereocystis luetkeana (Mert.) Post, et Rupr. to be placed in the flow, away from the influence of velocity boundary layers associated with the tank walls. The tank's use in macroalgae nutrient uptake and flow visualization experiments was demonstrated.

Problems in flow acoustics

The research field acoustics is defined, and problems of current interest are discussed. The physical interpretation of fluid-mechanical sound sources for an acoustic medium, both at rest and in motion, is addressed. In the first case, it has been possible to relate the sound pressure field for low Mach numbers to sound sources that depend linearly on velocity; progress has been achieved by means of the causality correlation method with the application of laser-Doppler velocity measurements. In the theory of the acoustic medium in motion, it has been found that vortices downstream from a nozzle discharge can function as sound sinks; for a unidirectional mean flow, conditions for the sound sources are developed on the basis of the causality principle and the boundedness of the flow quantities. Experimental and theoretical results for flowfield oscillations in a high-velocity duct flow with sudden duct enlargement are discussed. Finally, some points concerning the influence of shear flow on sound propagation are described.

Massive Sandstone Facies in The Hawkesbury Sandstone, A Triassic Fluvial Deposit Near Sydney, Australia

ABSTRACT Massive sandstone is a common facies in the Hawkesbury Sandstone, a Triassic formation attributed to deposition by a large braided river. The massive sandstone occurs as sheets and in elongate depressions trending perpendicular to the paleoslope, as indicated by the unidirectional mean orientation of abundant cross-strata. Some of the depressions filled with massive sandstone also contain angular mudstone intraclasts, up to several meters in length. Massive sandstone is also associated with deformed cross-strata, formed by progressive loss of lamination during mass movement down foreset slopes. Foreset failure is attributed to liquefaction due to falling water level, or to collapse of adjacent mud banks. The latter mechanism resulted in rapid loading of bedform foresets, and introduce large mudclasts into the massive sand. Sand and mudclasts accumulated in transverse scours at the foot of the foreset slopes, but also travelled along the scours, or spilled out to form massive sheet sands. The abundance of massive sandstone in the Hawkesbury Sandstone is attributed to deposition in a large river, in which flood stage bedforms were probably up to 15 m high. Because of the size of the bedforms, large volumes of liquefied sand were generated when foreset slopes failed.

A Statistical Investigation upon the Eddy Viscosity in Incompressible Turbulence

Eddy-viscosity concept is examined in incompressible turbulence with arbitrary mean motions, in relation to the subgrid eddy viscosity frequently used in numerical simulations of turbulence. A general expression for the Reynolds stresses is derived by the use of a statistical approach (A. Yoshizawa: J. Phys. Soc. Jpn. 46 (1979) 669) developed for inhomogeneous turbulence with a unidirectional mean flow. As a result, the eddy viscosity is shown to be expressed in terms of a fourth-order tensor, whose components are evaluated from the inertial-range theory with the aid of the direct-interaction formalism.

Statistical Approach to Inhomogeneous Turbulence with Unidirectional Mean Flow. II. Mean Velocity Profile in a Channel Flow

This paper studies turbulent flow in a channel. From a general formula for Reynolds stress given in paper I, mean velocity profiles are examined in the equilibrium layer near the wall and in the central region, respectively. Results obtained are that (1) in the equilibrium layer with constant Reynolds stress, the logarithmic velocity profile is derived and (2) in the central region with constant energy dissipation, the flattened parabolic profile is found, with its flattening determined by the Reynolds number of turbulence.

Statistical Approach to Inhomogeneous Trubulence with Unidirectional Mean Flow: Evaluation of Reynolds Stress

Statistical analysis is made of the inhomogeneous turbulence with unidirectional mean flow in infinite fluid. The velocity is assumed to depend on the coordinate normal to the flow. Considering that the space variation of the mean flow is small compared with that of the fluctuating one, two space scales corresponding to mean and fluctuating flows are introduced into the Navier-Stokes equations. The direct-interaction approximation is applied to the equation thus found, and Reynolds stress is evaluated. Results obtained are applied to the calculation of grid-scale Reynolds stress used frequently in a numerical simulation of turbulent flows.

Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one‐ and three‐dimensional flows

The complex variation of hydraulic conductivity in natural aquifer materials is represented in a continuum sense as a spatial stochastic process which is characterized by a covariance function. Assuming statistical homogeneity, the theory of spectral analysis is used to solve perturbed forms of the stochastic differential equation describing flow through porous media with randomly varying hydraulic conductivity. From analyses of unidirectional mean flows which are perturbed by one‐and three‐dimensional variations of the logarithm of the hydraulic conductivity, local relationships between the head variance and the log conductivity variance are obtained. The results show that the head variance produced by three‐dimensional statistical isotropic conductivity perturbations is only 5% of that in the corresponding one‐dimensional case. The head variance is also strongly dependent on the correlation distance of the log conductivity covariance function. These results emphasize the importance of including spatial correlation structure and multidimensional effects in stochastic simulation of groundwater flow.