Janek Laanearu

Experimental investigation on rapid filling of a large-scale pipeline

This study presents the results from detailed experiments of the two-phase pressurized flow behavior during the rapid filling of a large-scale pipeline. The physical scale of this experiment is close to the practical situation in many industrial plants. Pressure transducers, water-level meters, thermometers, void fraction meters, and flow meters were used to measure the two-phase unsteady flow dynamics. The main focus is on the water-air interface evolution during filling and the overall behavior of the lengthening water column. It is observed that the leading liquid front does not entirely fill the pipe cross section; flow stratification and mixing occurs. Although flow regime transition is a rather complex phenomenon, certain features of the observed transition pattern are explained qualitatively and quantitatively. The water flow during the entire filling behaves as a rigid column as the open empty pipe in front of the water column provides sufficient room for the water column to occupy without invoking air compressibility effects. As a preliminary evaluation of how these large-scale experiments can feed into improving mathematical modeling of rapid pipe filling, a comparison with a typical one-dimensional rigid-column model is made.

Some estimates of the Baltic deep-water transport through the Stolpe trench

ABSTRACT The subsurface flowof high-salinewater masses from the Bornholm Basin through the Stolpe Channel plays an important role for the renewal of the Baltic Central Basin deep waters. In order to determine whether rotating 112 -layer hydraulic theory is an appropriate tool for describing this process, maximal-transport estimates based on climatological data from the Bornholm and Gdansk Basins have been established. These were found to deviate considerably from observational realities, and hence similar hydraulic considerations were also applied to more-or-less synoptic field data from a Finnish field campaign carried through in the mid-1980s. Also in this case significant differences were found between calculated transport capacity and observations. Since it furthermorewas demonstrated that the characteristics of the observed crosschannel hydrographic structure could be explained using a frictional-balance model of the deep-water flow, it has been concluded that a hydraulic framework, although providing an upper bound of the transport, is of limited use when dealing with the Stolpe-Channel overflow. Although it cannot be excluded that the inflow is inviscid, but submaximal, it is more likely that the transport is governed by the combined effects of friction and wind forcing.

Emptying of large-scale pipeline by pressurized air

AbstractEmptying of an initially water-filled horizontal PVC pipeline driven by different upstream compressed air pressures and with different outflow restriction conditions, with motion of an air-water front through the pressurized pipeline, is investigated experimentally. Simple numerical modeling is used to interpret the results, especially the observed additional shortening of the moving full water column due to formation of a stratified water-air “tail.” Measured discharges, water-level changes, and pressure variations along the pipeline during emptying are compared using control volume (CV) model results. The CV model solutions for a nonstratified case are shown to be delayed as compared with the actual measured changes of flow rate, pressure, and water level. But by considering water-column mass loss due to the water-air tail and residual motion, the calibrated CV model yields solutions that are qualitatively in good agreement with the experimental results. A key interpretation is that the long air...

Topographically constrained deep-water flows in the Baltic Sea

Density-driven currents have a significant impact on the deep-water characteristics of the Baltic Sea since they account for the water exchange between the deeper parts of neighbouring basins. The essential quantitative problem is to determine the flow rates in relation to a set of external parameters such as the strait topography, the stratification, and the internal circulation of the upstream basin. Using hydraulic theory it is possible to accomplish this by analysing the dynamical constraints that limit the deep-water flux between adjacent basins. On the basis of these results, the deep-water flows through the Bornholm Channel and the Irbe Strait are compared.

Topographic control of rotating deep water flow through the combination of a sill and a horizontal constriction

Many subsurface passages connecting the deep parts of the oceans have a topography such that the location of the most pronounced horizontal constriction does not coincide with that of the sill. When applying rotating hydraulic theory to describe the deep water flow through channels of this type, a problematic situation emerges since the standard analysis assumes a well-defined controlling section. The present study demonstrates how the associated critical flow problem arising from the hydraulic model may be resolved on the basis of functional-theoretical analysis. The methodology is applied to the deep water flow into the Baltic proper through the Bornholm Channel, where multiple critical cross sections were found. These, as well as the associated critical transport predictions, are discussed, and it is found that only one of them serves de facto as a control with unidirectional flow.

Hydraulic control of two-layer flow in quadratic -type channels

Previous treatments of two-layer exchange flow in a rectangular channel have been extended to consider the effects of channel geometry upon the hydraulics of such flows. Attention has been focussed on exchange flows in “quadratic” channels, defined as flow cross-sections having a single width maximum w0 at the surface and a single depth maximum D (not necessarily located at the centre of the channel cross section). The analysis shows that the effects of channel cross sectional geometry can be quantified satisfactorily in terms of a shape parameter ξ representing the ratio of the cross-sectional area of the channel to that of the equivalent rectangular channel having the same values of w0 and D. Specifically, the analysis shows that suitable definitions of the Froude numbers of the two fluid layers in terms of the shape parameter ξ enables the familiar general criticality condition G2 = 1 to be formulated for the composite Froude number. Furthermore, the application of the so-called functional approach to this type of channel problem is demonstrated to show excellent quantitative consistency with the results of the hydraulic model for two reference examples (the horizontal constriction and the sill) already studied intensively for rectangular channels. Finally, an analysis is presented to show the effects upon the exchange flow of changes in ξ in the along-channel direction.

Gravity currents in rotating, wedge-shaped, adverse channels

Results are presented from a series of parametric experimental and analytical studies of the behaviour of dense gravity currents along rotating, up-sloping, wedge-shaped channels. High resolution density profile measurements at fixed cross- and along-channel locations reveal the outflowing bottom gravity currents to adjust to quasi-steady, geostrophically-balanced conditions along the channels, with the outflow layer thickness and cross-channel interface slope shown to scale with the inlet Burger number for all experimental conditions tested. A general analytical solution to the classic rotating hydraulics problem has been developed under the assumption of inviscid, zero-potential-vorticity conditions to model dense water flow through a triangular constriction and thus simulate the vee-channel configurations under consideration. Predictions from this zero-PV model are shown to provide good overall quantitative agreement with experimental measurements obtained both under hydraulically-controlled conditions at the channel exit and for subcritical conditions generated along the channel length. Quantitative discrepancies between measurements and analytical predictions are attributed primarily to assumptions and limitations associated with the zero-PV modelling approach adopted, as well as the to the rapid adjustment in outflow characteristics as the channel exit is approached, as characterised by the along-channel variation in densimetric Froude number for the outflows.

Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines

Improved one-dimensional (1D) models ? compared to previous work by the authors ? are proposed which are able to predict the velocity, length and position of the liquid column in the rapid emptying and filling of a pipeline. The models include driving pressure and gravity, skin friction and local drag, and holdup at the tail and gas intrusion at the front of the liquid column. Analytical and numerical results are validated against each other, and against experimental data from a large-scale laboratory setup.

Dynamics of dense gravity currents and mixing in an up-sloping and converging vee-shaped channel

Detailed velocity and density measurements are used to investigate dense water dynamics in an inclined, silled channel of triangular cross-section with varying side slope α and adverse bed slope φ. For the steeper channel configuration considered (φ=3.6°), the dense-water bottom current is shown to be frictionally-controlled, with an internal flow structure characterized by a sharp pycnocline and decreasing isopycnal separation in the along-channel direction. For the milder up-sloping channel (φ=1.7°), the dense water outflow is shown to be hydraulically-controlled as the channel sill section is approached, with internal flow dynamics characterized by increasing isopycnal separation in the along-channel direction. Analysis of the gradient Richardson number Rig of the flow confirms that hydraulically-controlled flows dilute the active bottom water due to interfacial mixing. A gradually-varying internal flow model and a two-layer hydraulic modelling approach are shown, respectively, to represent adequately the outflow behaviour for these two bed slope conditions.

An optimal solution of thermal energy usage in the integrated system of stormwater collection and domestic-water heating

Abstract A solution is proposed to make use of the rainwater thermal energy in highly urbanised areas. It is demonstrated that the stormwater heat represents an additional on-site renewable energy available for hot water production. The proposed solution increases multi-functionality in the urban infrastructure that is essentially used to mitigate impacts from extreme climate events. The integrated system model applications correspond to local area conditions in the north-eastern Baltic region. This study considers the optimal collection of stormwater through maximizing the water absorbed heat usage in relation to hot water consumption in different building types (residential, public and commercial). Two key parameters, ‘stormwater volume in storage tank’ and ‘rainwater catchment area’, are determined. A genetic algorithm finds a number of storage tank fillings corresponding to rainfall statistics and the hot water consumption of buildings. System cumulative expenses are related to the stormwater storage and the rainwater harvesting expenses.