Panayotis C. Yannopoulos

The round vertical turbulent buoyant jet

Experiments on round vertical turbulent buoyant jet have been performed using tap water as the jet liquid and saltwater solution as the ambient liquid. Measurements were made of the centerline axial velocity and the centerline and radial concentrations. The integral forms of the momentum and tracer equations were integrated on the basis of an assumption concerning a function of the spreading coefficients. The validity of this assumption has been verified by the experimental results and the analysis led to unified analytical expressions concerning the axial velocity and concentration distributions along the jet axis. The present findings are discussed and compared with previously reported works.

Interaction of vertical round turbulent buoyant jets—Part II: Superposition method

Based on the superposition of pertinent fluxes of single jets or plumes, a model to predict the mean axial velocities and mean concentrations of the combined field due to merging is developed. The model equations are produced by the integral equations of momentum, tracer and kinetic energy for the mean flow, which are derived for any single jet or plume or the entire set assuming that turbulence contributes equally to the rate of kinetic energy flux for either a single or interacting plume. Superposition solutions are developed for sets of any number of jets or plumes and are applied to equally spaced identical jets or plumes in a row, assuming Gaussian profiles for mean axial velocities and mean concentrations of single fields. Predictions obtained by this method are compared to analytical and experimental findings described in Part I. The spatial mean dilution is determined using the integral continuity equation. Present results are discussed and compared with other reported works. The evolution of the flow and mixing fields is explained in detail, while the practical usage of the methods discussed in this paper and Part I, either for sea outfall design or laboratory simulation studies, is illustrated.

An improved integral model for plane and round turbulent buoyant jets

The integral momentum and tracer equations for the mean motion with the turbulence contribution in momentum and tracer fluxes are integrated on the centreline of either plane or round buoyant jets, using suitable assumptions for the spreading coefficients and a closing function, and unified first- and second-order solutions are derived in the entire buoyancy range for mean axial velocities and mean concentrations. Comparisons to experimental data in the literature validate the model and show that second-order solutions deviate less than first-order solutions. Both types are used in conjunction with the integral continuity and kinetic energy equations for the mean motion to determine the variation of the local Richardson and Froude numbers, dispersion ratio, bulk dilution, dilution ratio, entrainment coefficient and mean velocity, kinetic energy flux and its gradient for the mean motion; and the variations of these quantities are evaluated using reported experimental or theoretical data. Finally, the variation of the product of kinetic energy flux and the local Richardson number is examined and a universal constant for both plane and round buoyant jets is revealed, leading to a unified definition of the local Richardson number, which is independent of the flow and mixing geometry and could be useful. Simple computational programming and good overall agreement make the proposed model a very promising tool for laboratory and field studies, outfall design and validation of numerical models. The outfall discharge of wastewater or warm water into surface-water bodies or the chimney release of air pollutants and volcanic gas eruptions into the atmosphere are associated with complicated turbulent buoyant-jet phenomena; in depth knowledge of these relationships is required for environmental quality assessment and design optimization of the discharge structures, minimizing cost and providing environmental protection. The integral method is popular for solving buoyant-jet problems. It is based on simplified partial differential equations (continuity, momentum and tracer transport) by adopting commonly used approximations for such types of flow and mixing phenomena. The equations are integrated on the jet cross-section, applying the similarity assumption and actual boundary conditions to yield a system of ordinary differential equations, and then the system may be solved either analytically or numerically. There are two approaches to the final integration of the set of ordinary differential equations: (a) using the entrainment concept (Morton, Taylor & Turner 1956) and making suitable assumptions for the entrainment coefficient (Morton 1959; List & Imberger

Interaction of vertical round turbulent buoyant jets—Part I: Entrainment restriction approach

Experiments using two, three or five interacting identical round vertical turbulent buoyant jets were performed, using tap water as the jet liquid and salt water as the ambient liquid. Measurements were made of the centreline axial velocity and the centreline and transverse concentrations for each row of buoyant jets. Centreline values have been normalized by the single identical jet values measured at the same axial distances. The integral forms of the momentum and tracer equations were integrated on the reduced cross-sectional area with restricted entrainment periphery, utilizing the assumption used for single buoyant jets regarding the spreading coefficient function. The analysis led to unified analytical expressions concerning the normalized axial velocity and concentration distributions along the jet axis: (a) for one of a pair of buoyant jets and (b) for a jet of an infinite row of buoyant jets. The present findings are discussed and compared with other works reported in the literature. Findings should be useful for design purposes, laboratory simulation studies and verification of numerical models.

The Interplay Between the Alfeios (Greece) River Basin Components and the Exerted Environmental Stresses: a Critical Review

The characteristics (natural, socioeconomic and administrative/institutional) of Alfeios River basin, in Greece, are identified and presented, incorporating and critically reviewing all possibly found literature. The Alfeios River is a water resources system of great natural, ecological, social and economic importance for Western Greece, since it has the longest and highest flow rate watercourse in the Peloponnisos region. Moreover, the river basin was exposed in the last decades to a plethora of environmental stresses (such as hydrogeological alterations, intensively irrigated agriculture, surface and groundwater overexploitation and infrastructure developments), resulting in the degradation of its quantitative and qualitative characteristics. It is therefore necessary for the development of an integrated river basin management plan for this basin, to study and analyse the interplay between the river components and the exerted environmental stresses, taking into account the puzzle of various and conflicting water uses, including water supply, irrigation, hydropower generation, lignite thermal power production and recreation. Mitigative, preventive and control measures for the analysed environmental stresses are epigrammatically depicted. Focusing on the problematic features, the present work provides a concrete foundation for the determination and conceptualisation of management objectives and possible sustainable alternatives.

Superposition model for multiple plumes and jets predicting end effects

On the basis of integral forms of momentum, tracer, and kinetic energy equations for the mean flow, a superposition model is developed, which is able to predict end effects of multiple jet or multiple plume discharges. The general cases of inclined, single, or multiple buoyant jets in a row normal to a uniform ambient current or wind, and of equal or lower density than the ambient fluid, are being examined and the conditions under which the model can be applied are pointed out. The pertinent quantities describing the complicated field of interacting multiple plumes/jets are detected by comparing the integral equations produced for multiple discharges with the corresponding equations for single discharges. Provided that the single buoyant jet behavior is known, the model has been applied in problems of buoyant jet interaction, yielding analytical solutions, and it has been verified using literature data. The behavior of the limiting cases is also discussed, along with the pertinent explanations. Findings can be used in the design of disposal systems, that is, stacks, multiple cell cooling tower discharges, and multiport diffusers.

Particulate and Sulfur Dioxide Concentration Measurements in Patras, Greece

Abstract The purpose of this study was to obtain a better assessment of the Patras, Greece, air quality, in terms of the primary pollutants total suspended particulates (TSPs) and sulfur dioxide (SO2), because limited and short-duration measurements have been conducted in the past. Installation and operation of a mobile air monitoring station at two different locations in the Patras downtown area and one location in the outskirts of the city was undertaken and covered the periods July 1, 1994-January 30, 1995; March 18-August 23, 1995; and April 19-July 27, 1996, respectively. For both pollutants measured at each location, the monthly average concentrations and typical weekly variation of daily averages, as well as the diurnal variations and frequency concentration distributions in each month of the monitoring periods, were calculated and are presented in bar diagrams. The annual and winter period medians and the annual 98th percentile were also calculated and are compared with the limit and guide values provided by the European Economic Community Council Directive 80/779/EEC. In addition, comparison of SO2 values is made with the limit values adopted by the more recent Directive 1999/30/EC. It was found that the TSP and SO2 levels at all locations were very low and were lower than the levels found in Thessaloniki and Athens, Greece. An attempt to explain what had been measured is also undertaken. The data presented are considered essential for future reference and comparison purposes.

Round turbulent buoyant jets discharged vertically upwards forming a regular polygon

The simplified partial differential equations of momentum and tracer for the mean motion are integrated on the reduced cross-sectional area within the field of one buoyant jet from a group issued vertically upwards from a rosette-type riser. The solutions yield the dimensionless centerline axial velocities and concentrations. Mathematically, the one-jet field is separated from the entire group by employing the Entrainment Restriction Approach (ERA) applicable in interacting buoyant jets with symmetry planes. ERA was herein improved by incorporating the Second Order Approach (SOA). Interaction effects are highlighted by normalizing the mean-flow properties. The role of buoyancy on merging is introduced by a dynamic parameter, which combines proximity effects with buoyancy, thus termed dynamic proximity number. In addition, the distributions for mean dilution, kinetic energy flux and local Richardson number are also predicted, discussed, and compared with data reported in the literature. Findings may be useful for design purposes and environmental impact assessment.

A conceptual approach to model sand–gravel extraction from rivers based on a game theory perspective

Sand–gravel mining is a significant parameter of economic development and social welfare function in modern societies. As demand for aggregate increases in construction industry, conflicts for the availability of the resource and environmental impacts become more intense. The present paper describes the contested status quo in riverbed sand–gravel mining activities with an example from Greece, as a case study. The scope is to propose a methodology about good governance of the mining sector that promotes a sustainable sharing of aggregate resource by securing environment and safekeeping revenues in the mining trade market.

Unique Superposition Solution of Multiple Plumes’ Flow via Mean Kinetic Energy Fluxes

AbstractThis paper simplifies the partial differential equation (PDE) of total mean energy in the plumelike region of turbulent buoyant jets under the well-known distributions in the longitudinal a...