ABSTRACT We investigate scavenging of gaseous pollutants in the atmosphere under the combined inf... more ABSTRACT We investigate scavenging of gaseous pollutants in the atmosphere under the combined influence of rain and varying temperature distribution that affects the rate of soluble gas scavenging. We employ a one-dimensional model of precipitation scavenging of gaseous pollutants having arbitrary solubility that is valid for small gradients and for non-uniform initial vertical distributions of temperature and soluble trace gases concentration in the atmosphere. It is showed that transient altitudinal distributions of temperature and concentration under the influence of rain are determined by linear wave equations that describe propagation of temperature and scavenging wave fronts. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of methanol ( \({\text{CH}}_{3} {\text{OH}}\) ) using measured initial distribution of methanol and temperature in the atmosphere. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for tritium oxide and sulfur dioxide are in good agreement with the available atmospheric measurements.
2010 14th International Heat Transfer Conference, Volume 8, 2010
ABSTRACT We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. I... more ABSTRACT We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. It is shown that below-cloud gas scavenging is determined by non-stationary convective diffusion equation with the effective Peclet number. The obtained equation was analyzed numerically in the case of log-normal droplet size distribution. Calculations of scavenging coefficient and the rates of precipitation scavenging are performed for wet removal of ammonia (NH3 ) and sulfur dioxide (SO2 ) from the atmosphere. It is shown that scavenging coefficient is non-stationary and height-dependent. It is found also that the scavenging coefficient strongly depends on initial concentration distribution of soluble gaseous pollutants in the atmosphere. It is shown that in the case of linear distribution of the initial concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient increases with height in the beginning of rainfall. At the later stage of the rain scavenging coefficient decreases with height in the upper below-cloud layers of the atmosphere.
ABSTRACT In this study we performed numerical analysis of heat and mass transfer during evaporati... more ABSTRACT In this study we performed numerical analysis of heat and mass transfer during evaporation and condensation of a stagnant cloud droplet in the presence of soluble polluted gases. It is assumed that gas absorption is accompanied by subsequent aqueous-phase equilibrium dissociation reactions. We considered liquid and gaseous phase controlled mass transfer. The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation and taking into account thermal effect of gas absorption. Using the material balance at the droplet surface we obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of gas absorption at the gas-liquid interface. We derived also boundary conditions taking into account the effects of gas absorption with subsequent dissociation reactions in the liquid phase and heat of absorption. Numerical analysis was performed for the case of sulfur dioxide dissolution in water droplet with pH values typical for atmospheric clouds. It was shown that thermal effect of absorption and Stefan flow result in the maximum of droplet surface temperature during the transient period of droplet evaporation and affect droplet size evolution. Comparison of the results obtained using the model of physical absorption of sulfur dioxide in water droplet (Elperin and Fominykh, 2005; Elperin et al., 2007) with the predictions of the present model that takes into account the subsequent equilibrium dissociation reactions showed that the model of physical absorption underestimates the droplet surface temperature and overestimates the average concentration of [SO2 · H2 O] at the transient stage of gas absorption. The developed model allows determining the dependence of pH vs. time for both evaporating and growing droplets. The performed calculations showed that the value of pH increase with the increasing relative humidity (RH).
In this study we investigated numerically simultaneous heat and mass transfer during evaporation/... more In this study we investigated numerically simultaneous heat and mass transfer during evaporation/condensation on the surface of a stagnant droplet in the presence of inert admixtures containing non-condensable solvable gas. The performed analysis is pertinent to slow droplet evaporation/condensation when Mach number is small (M<<1). The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation. Transport coefficients of the gaseous phase were calculated as functions of temperature and concentrations of gaseous species. Thermophysical properties of the liquid phase are assumed to be constant. Using the material balance at the droplet surface we obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of solvable gas absorption at the gas-liquid interface. We derived also boundary conditions at gas-liquid interface taking into account the effect of gas absorption. The governing equations were solved using a method of lines. Numerical calculations showed essential change of the rates of heat and mass transfer in water droplet-air-water vapor system under the influence of solvable species in a gaseous phase. Consequently, the use of additives of solvable noncondensable gases to enhance the rate of heat and mass transfer in dispersed systems allows to increase the efficiency and reduce the size of gas-liquid contactors.
In this study we analyze a new type of electric dynamo caused by the rapid change of the distribu... more In this study we analyze a new type of electric dynamo caused by the rapid change of the distribution of the electric conductivity in heterogeneous conducting systems. It is demonstrated that there exist two types of electric dynamos, namely, the regular magnetic dynamo and the electric current dynamo. The magnetic dynamo is associated with the growth of the total energy of the magnetic field. The electric current dynamo is defined as the growth of the total electric current through some cross section of a conductor, whereby the choice of the cross section is determined by the symmetry of the excited electromagnetic field. We show that the condition for the excitation of the electric current dynamo is less restrictive than the condition for the excitation of the magnetic dynamo, and it can be satisfied even without a hydrodynamic flow. The existence of the hydrodynamic flow is cardinal for the excitation of the magnetic dynamo. In contrast to the turbulent magnetic dynamo which is associated with the fact that magnetic-field lines are ``frozen in'' to the fluid and thus can be excited at high magnetic Reynolds numbers, the laminar magnetic dynamo which is considered in the present study can be excited at the relatively low magnetic Reynolds numbers Rem>=1 depending upon the symmetry of the electromagnetic field. In this study we determined the dependence of the magnetic Reynolds number providing the excitation of the instability upon the symmetry of the electromagnetic field.
Two types of intermittency of passive scalar fluctuations (the intermittency in the systems with ... more Two types of intermittency of passive scalar fluctuations (the intermittency in the systems with and without external pumping) are analyzed. We have shown that in the systems without external pumping under certain conditions there is a self-excitation of fluctuations of passive scalar (number density of particles advected by turbulent flow), and higher moments grow faster than lower moments. This can result in intermittency, i.e., the appearance of sharp peaks in which the main part of the field intensity is concentrated. We have also shown that in the systems with external pumping the anomalous scalings appear already in the second moment of passive scalar field when the degree of compressibility (i.e., the ratio of the energies in compressible and incompressible component of the velocity) is more than 1 / 27 . The mechanism for both, the small-scale instability and the anomalous scalings is associated with the compressibility of fluid flow or with the inertia of particles which results in a divergent velocity field of particles.
The usual network reliability problem is: Suppose that edges of G are s-independently erased with... more The usual network reliability problem is: Suppose that edges of G are s-independently erased with probabilities q ( e ) , e E E. Let F denote the set of non-erased edges; the subgraph ( V J ) of G then appears with probability:
Motion of a small spherical heavy particle subjected to the Stokes drag force and the force of gr... more Motion of a small spherical heavy particle subjected to the Stokes drag force and the force of gravity in a nonstationary fluid flow is studied. An analytical solution of the equation of the particle motion at a short-time interval and conditions for validity of this solution are obtained. For the case of a long-time motion the velocity and the acceleration of the particle are found. The velocity is obtained up to the second-order terms with respect to the Stokes response time and the acceleration is obtained up to the first-order terms.
ABSTRACT We investigate scavenging of gaseous pollutants in the atmosphere under the combined inf... more ABSTRACT We investigate scavenging of gaseous pollutants in the atmosphere under the combined influence of rain and varying temperature distribution that affects the rate of soluble gas scavenging. We employ a one-dimensional model of precipitation scavenging of gaseous pollutants having arbitrary solubility that is valid for small gradients and for non-uniform initial vertical distributions of temperature and soluble trace gases concentration in the atmosphere. It is showed that transient altitudinal distributions of temperature and concentration under the influence of rain are determined by linear wave equations that describe propagation of temperature and scavenging wave fronts. Scavenging coefficient and the rates of precipitation scavenging are calculated for wet removal of methanol ( \({\text{CH}}_{3} {\text{OH}}\) ) using measured initial distribution of methanol and temperature in the atmosphere. Theoretical predictions of the dependence of the magnitude of the scavenging coefficient on rain intensity for tritium oxide and sulfur dioxide are in good agreement with the available atmospheric measurements.
2010 14th International Heat Transfer Conference, Volume 8, 2010
ABSTRACT We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. I... more ABSTRACT We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. It is shown that below-cloud gas scavenging is determined by non-stationary convective diffusion equation with the effective Peclet number. The obtained equation was analyzed numerically in the case of log-normal droplet size distribution. Calculations of scavenging coefficient and the rates of precipitation scavenging are performed for wet removal of ammonia (NH3 ) and sulfur dioxide (SO2 ) from the atmosphere. It is shown that scavenging coefficient is non-stationary and height-dependent. It is found also that the scavenging coefficient strongly depends on initial concentration distribution of soluble gaseous pollutants in the atmosphere. It is shown that in the case of linear distribution of the initial concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient increases with height in the beginning of rainfall. At the later stage of the rain scavenging coefficient decreases with height in the upper below-cloud layers of the atmosphere.
ABSTRACT In this study we performed numerical analysis of heat and mass transfer during evaporati... more ABSTRACT In this study we performed numerical analysis of heat and mass transfer during evaporation and condensation of a stagnant cloud droplet in the presence of soluble polluted gases. It is assumed that gas absorption is accompanied by subsequent aqueous-phase equilibrium dissociation reactions. We considered liquid and gaseous phase controlled mass transfer. The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation and taking into account thermal effect of gas absorption. Using the material balance at the droplet surface we obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of gas absorption at the gas-liquid interface. We derived also boundary conditions taking into account the effects of gas absorption with subsequent dissociation reactions in the liquid phase and heat of absorption. Numerical analysis was performed for the case of sulfur dioxide dissolution in water droplet with pH values typical for atmospheric clouds. It was shown that thermal effect of absorption and Stefan flow result in the maximum of droplet surface temperature during the transient period of droplet evaporation and affect droplet size evolution. Comparison of the results obtained using the model of physical absorption of sulfur dioxide in water droplet (Elperin and Fominykh, 2005; Elperin et al., 2007) with the predictions of the present model that takes into account the subsequent equilibrium dissociation reactions showed that the model of physical absorption underestimates the droplet surface temperature and overestimates the average concentration of [SO2 · H2 O] at the transient stage of gas absorption. The developed model allows determining the dependence of pH vs. time for both evaporating and growing droplets. The performed calculations showed that the value of pH increase with the increasing relative humidity (RH).
In this study we investigated numerically simultaneous heat and mass transfer during evaporation/... more In this study we investigated numerically simultaneous heat and mass transfer during evaporation/condensation on the surface of a stagnant droplet in the presence of inert admixtures containing non-condensable solvable gas. The performed analysis is pertinent to slow droplet evaporation/condensation when Mach number is small (M<<1). The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation. Transport coefficients of the gaseous phase were calculated as functions of temperature and concentrations of gaseous species. Thermophysical properties of the liquid phase are assumed to be constant. Using the material balance at the droplet surface we obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of solvable gas absorption at the gas-liquid interface. We derived also boundary conditions at gas-liquid interface taking into account the effect of gas absorption. The governing equations were solved using a method of lines. Numerical calculations showed essential change of the rates of heat and mass transfer in water droplet-air-water vapor system under the influence of solvable species in a gaseous phase. Consequently, the use of additives of solvable noncondensable gases to enhance the rate of heat and mass transfer in dispersed systems allows to increase the efficiency and reduce the size of gas-liquid contactors.
In this study we analyze a new type of electric dynamo caused by the rapid change of the distribu... more In this study we analyze a new type of electric dynamo caused by the rapid change of the distribution of the electric conductivity in heterogeneous conducting systems. It is demonstrated that there exist two types of electric dynamos, namely, the regular magnetic dynamo and the electric current dynamo. The magnetic dynamo is associated with the growth of the total energy of the magnetic field. The electric current dynamo is defined as the growth of the total electric current through some cross section of a conductor, whereby the choice of the cross section is determined by the symmetry of the excited electromagnetic field. We show that the condition for the excitation of the electric current dynamo is less restrictive than the condition for the excitation of the magnetic dynamo, and it can be satisfied even without a hydrodynamic flow. The existence of the hydrodynamic flow is cardinal for the excitation of the magnetic dynamo. In contrast to the turbulent magnetic dynamo which is associated with the fact that magnetic-field lines are ``frozen in'' to the fluid and thus can be excited at high magnetic Reynolds numbers, the laminar magnetic dynamo which is considered in the present study can be excited at the relatively low magnetic Reynolds numbers Rem>=1 depending upon the symmetry of the electromagnetic field. In this study we determined the dependence of the magnetic Reynolds number providing the excitation of the instability upon the symmetry of the electromagnetic field.
Two types of intermittency of passive scalar fluctuations (the intermittency in the systems with ... more Two types of intermittency of passive scalar fluctuations (the intermittency in the systems with and without external pumping) are analyzed. We have shown that in the systems without external pumping under certain conditions there is a self-excitation of fluctuations of passive scalar (number density of particles advected by turbulent flow), and higher moments grow faster than lower moments. This can result in intermittency, i.e., the appearance of sharp peaks in which the main part of the field intensity is concentrated. We have also shown that in the systems with external pumping the anomalous scalings appear already in the second moment of passive scalar field when the degree of compressibility (i.e., the ratio of the energies in compressible and incompressible component of the velocity) is more than 1 / 27 . The mechanism for both, the small-scale instability and the anomalous scalings is associated with the compressibility of fluid flow or with the inertia of particles which results in a divergent velocity field of particles.
The usual network reliability problem is: Suppose that edges of G are s-independently erased with... more The usual network reliability problem is: Suppose that edges of G are s-independently erased with probabilities q ( e ) , e E E. Let F denote the set of non-erased edges; the subgraph ( V J ) of G then appears with probability:
Motion of a small spherical heavy particle subjected to the Stokes drag force and the force of gr... more Motion of a small spherical heavy particle subjected to the Stokes drag force and the force of gravity in a nonstationary fluid flow is studied. An analytical solution of the equation of the particle motion at a short-time interval and conditions for validity of this solution are obtained. For the case of a long-time motion the velocity and the acceleration of the particle are found. The velocity is obtained up to the second-order terms with respect to the Stokes response time and the acceleration is obtained up to the first-order terms.
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Papers by Tov Elperin