scholarly journals A surface renewal model for unsteady-state mass transfer using the generalized Danckwerts age distribution function

2018 ◽  
Vol 5 (5) ◽  
pp. 172423
Author(s):  
Isabelle R. Horvath ◽  
Siddharth G. Chatterjee
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Wind Speed ◽  
Age Distribution ◽  
Gas Absorption ◽  
Process Time ◽  
Unsteady State ◽  
Dissolved Gas ◽  
Transfer Coefficients ◽  
Wind Speeds

The recently derived steady-state generalized Danckwerts age distribution is extended to unsteady-state conditions. For three different wind speeds used by researchers on air–water heat exchange on the Heidelberg Aeolotron, calculations reveal that the distribution has a sharp peak during the initial moments, but flattens out and acquires a bell-shaped character with process time, with the time taken to attain a steady-state profile being a strong and inverse function of wind speed. With increasing wind speed, the age distribution narrows significantly, its skewness decreases and its peak becomes larger. The mean eddy renewal time increases linearly with process time initially but approaches a final steady-state value asymptotically, which decreases dramatically with increased wind speed. Using the distribution to analyse the transient absorption of a gas into a large body of liquid, assuming negligible gas-side mass-transfer resistance, estimates are made of the gas-absorption and dissolved-gas transfer coefficients for oxygen absorption in water at 25°C for the three different wind speeds. Under unsteady-state conditions, these two coefficients show an inverse behaviour, indicating a heightened accumulation of dissolved gas in the surface elements, especially during the initial moments of absorption. However, the two mass-transfer coefficients start merging together as the steady state is approached. Theoretical predictions of the steady-state mass-transfer coefficient or transfer velocity are in fair agreement (average absolute error of prediction = 18.1%) with some experimental measurements of the same for the nitrous oxide–water system at 20°C that were made in the Heidelberg Aeolotron.

scholarly journals A frequency quantum interpretation of the surface renewal model of mass transfer

2017 ◽  
Vol 4 (7) ◽  
pp. 170103 ◽  
Author(s):  
Chanchal Mondal ◽  
Siddharth G. Chatterjee
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Frequency Distribution ◽  
Age Distribution ◽  
Gas Absorption ◽  
Bulk Liquid ◽  
Gas Transfer ◽  
Transfer Resistance ◽  
Surface Renewal ◽  
Two Parameter

The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies or liquid elements. Assuming that surface elements of a particular age have renewal frequencies that are integral multiples of a fundamental frequency quantum, and further assuming that the renewal frequency distribution is of the Boltzmann type, performing a population balance for these elements leads to the Danckwerts surface age distribution. The basic quantum is what has been traditionally called the rate of surface renewal. The Higbie surface age distribution follows if the renewal frequency distribution of such elements is assumed to be continuous. Four age distributions, which reflect different start-up conditions of the absorption process, are then used to analyse transient physical gas absorption into a large volume of liquid, assuming negligible gas-side mass-transfer resistance. The first two are different versions of the Danckwerts model, the third one is based on the uniform and Higbie distributions, while the fourth one is a mixed distribution. For the four cases, theoretical expressions are derived for the rates of gas absorption and dissolved-gas transfer to the bulk liquid. Under transient conditions, these two rates are not equal and have an inverse relationship. However, with the progress of absorption towards steady state, they approach one another. Assuming steady-state conditions, the conventional one-parameter Danckwerts age distribution is generalized to a two-parameter age distribution. Like the two-parameter logarithmic normal distribution, this distribution can also capture the bell-shaped nature of the distribution of the ages of surface elements observed experimentally in air–sea gas and heat exchange. Estimates of the liquid-side mass-transfer coefficient made using these two distributions for the absorption of hydrogen and oxygen in water are very close to one another and are comparable to experimental values reported in the literature.

scholarly journals DMS gas transfer coefficients from algal blooms in the Southern Ocean

2014 ◽  
Vol 14 (21) ◽  
pp. 28453-28482
Author(s):  
T. G. Bell ◽  
W. De Bruyn ◽  
C. A. Marandino ◽  
S. D. Miller ◽  
C. S. Law ◽  
...  
Keyword(s):  
Wind Speed ◽  
Southern Ocean ◽  
Eddy Covariance ◽  
Algal Blooms ◽  
Biologically Active ◽  
Gas Transfer ◽  
Transfer Coefficients ◽  
Transfer Velocity ◽  
Gas Transfer Velocity ◽  
Wind Speeds

Abstract. Air/sea dimethylsulfide (DMS) fluxes and bulk air/sea gradients were measured over the Southern Ocean in February/March 2012 during the Surface Ocean Aerosol Production (SOAP) study. The cruise encountered three distinct phytoplankton bloom regions, consisting of two blooms with moderate DMS levels, and a high biomass, dinoflagellate-dominated bloom with high seawater DMS levels (>15 nM). Gas transfer coefficients were considerably scattered at wind speeds above 5 m s−1. Bin averaging the data resulted in a linear relationship between wind speed and mean gas transfer velocity consistent with that previously observed. However, the wind speed-binned gas transfer data distribution at all wind speeds is positively skewed. The flux and seawater DMS distributions were also positively skewed, which suggests that eddy covariance-derived gas transfer velocities are consistently influenced by additional, log-normal noise. A~flux footprint analysis was conducted during a transect into the prevailing wind and through elevated DMS levels in the dinoflagellate bloom. Accounting for the temporal/spatial separation between flux and seawater concentration significantly reduces the scatter in computed transfer velocity. The SOAP gas transfer velocity data shows no obvious modification of the gas transfer-wind speed relationship by biological activity or waves. This study highlights the challenges associated with eddy covariance gas transfer measurements in biologically active and heterogeneous bloom environments.

Simulating the Dynamic and Steady State Response of a Rotor Resistive Controlled 1.5 MW Variable Speed Wind Turbine

2010 ◽  
Author(s):  
Jared B. Garrison ◽  
Michael E. Webber
Keyword(s):  
Steady State ◽  
Wind Speed ◽  
Dynamic Response ◽  
Wind Turbine ◽  
Power Output ◽  
Pitch Angle ◽  
Maximum Power ◽  
Variable Speed ◽  
Wind Speeds ◽  
Variable Speed Wind Turbine

Currently, wind and solar technologies only generate 0.77% and 0.014% of the U.S. electricity consumption, respectively [1]. Though only a small portion of total U.S. electricity production, both sources have seen significant growth recently. For instance, Texas has more than quadrupled its installed wind capacity over the period from 2005–2009 with new installations totaling over 9400 MW [2, 3]. These two resources are globally available and have the potential to generate massive amounts of electricity. As the amount of installed wind turbines continues to grow, gaining better knowledge of their operation and their dynamic response to changing wind conditions is important to ensure their smooth integration and safe operation. The goal of this research is to analyze the dynamic and steady state operations of a 1.5 MW variable speed wind turbine that uses an external rotor resistive control mechanism. The addition of the external generator rotor resistance allows for adjustment of the generator slip and employs a feedback controller that maintains constant power output at all air velocities between the rated wind speed and cut-out wind speed. Using the electronic programming language PSCAD/EMTDC the model simulates the dynamic response to changing wind conditions, as well as the performance under all wind conditions. The first task of the model was to determine which blade pitch angle produces a maximum power output of 1.5 MW. A sweep was used where the simulation runs over the entire range of wind speeds for a selected pitch angle to find which speed resulted in maximum power output. This sweep was used for numerous blade pitch angles until the combination of wind speed and pitch angle at 14.4 m/s and −0.663°, respectively, resulted in a maximum power of 1.5 MW. The second task was to evaluate the model’s dynamic response to changes in wind conditions as well as steady state operation over all wind speeds. The dynamic response to an increase or decrease in wind speed is important to the safety and life expectancy of a wind turbine because unwanted spikes and dips can occur that increase stresses in the wind turbine and possibly lead to failure. In order to minimize these transient effects, multiple controllers were implemented in order to test each ones’ dynamic response to increasing and decreasing changes in wind velocity. These simulations modeled the characteristics of a variable-speed wind turbine with constant power rotor resistive control. First, through calibrating the model the design specifications of blade pitch and wind speed which yield the peak desired output of 1.5 MW were determined. Then, using the method of controlling the external rotor resistance, the simulation was able to maintain the 1.5 MW power output for all wind speeds between the rated and cutout speeds. Also, by using multiple controllers, the dynamic response of the control scheme was improved by reducing the magnitude of the initial response and convergence time that results from changes in wind speed. Finally, by allowing the simulation to converge at each wind speed, the steady state operation, including generator power output and resistive thermal losses, was characterized for all wind speeds.

Evaluation of steady state and unsteady state mass transfer rate of Cr(VI) in immobilized Bacillus sp.

2015 ◽  
Vol 20 (2) ◽  
pp. 267-275 ◽  
Author(s):  
Mathur Nadarajan Kathiravan ◽  
Geun Ho Gim ◽  
Jaewon Ryu ◽  
Gui Hawn Han ◽  
Si Wouk Kim
Keyword(s):  
Mass Transfer ◽  
Steady State ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Bacillus Sp ◽  
Unsteady State

scholarly journals Dimethylsulfide gas transfer coefficients from algal blooms in the Southern Ocean

2015 ◽  
Vol 15 (4) ◽  
pp. 1783-1794 ◽  
Author(s):  
T. G. Bell ◽  
W. De Bruyn ◽  
C. A. Marandino ◽  
S. D. Miller ◽  
C. S. Law ◽  
...  
Keyword(s):  
Wind Speed ◽  
Southern Ocean ◽  
Eddy Covariance ◽  
Algal Blooms ◽  
Biologically Active ◽  
Gas Transfer ◽  
Transfer Coefficients ◽  
Transfer Velocity ◽  
Gas Transfer Velocity ◽  
Wind Speeds

Abstract. Air–sea dimethylsulfide (DMS) fluxes and bulk air–sea gradients were measured over the Southern Ocean in February–March 2012 during the Surface Ocean Aerosol Production (SOAP) study. The cruise encountered three distinct phytoplankton bloom regions, consisting of two blooms with moderate DMS levels, and a high biomass, dinoflagellate-dominated bloom with high seawater DMS levels (> 15 nM). Gas transfer coefficients were considerably scattered at wind speeds above 5 m s−1. Bin averaging the data resulted in a linear relationship between wind speed and mean gas transfer velocity consistent with that previously observed. However, the wind-speed-binned gas transfer data distribution at all wind speeds is positively skewed. The flux and seawater DMS distributions were also positively skewed, which suggests that eddy covariance-derived gas transfer velocities are consistently influenced by additional, log-normal noise. A flux footprint analysis was conducted during a transect into the prevailing wind and through elevated DMS levels in the dinoflagellate bloom. Accounting for the temporal/spatial separation between flux and seawater concentration significantly reduces the scatter in computed transfer velocity. The SOAP gas transfer velocity data show no obvious modification of the gas transfer–wind speed relationship by biological activity or waves. This study highlights the challenges associated with eddy covariance gas transfer measurements in biologically active and heterogeneous bloom environments.

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