A computer model for circular and linear bubble plumes

Abstract

The purposes of this research were to implement the circular plume model developed by Wuest et al. (1992) and to develop and verify a linear plume model based on the circular model. The linear model developed is the first that models a bubble plume generated by a linear source in thermally stratified water and considers the effects of gas transfer between the bubbles and surrounding water.

The basis for both models is eight differential flux equations which are solved numerically using Euler’s method. Knowledge of ambient temperature, dissolved solids, dissolved oxygen, and dissolved nitrogen profiles as well as gas input rate, diffuser dimensions, and initial bubble size are required to implement the models.

The implementation of the circular model was successful as the results obtained corresponded with those reported by Wuest et al. (1992). The linear model made predictions very similar to those made by the circular model and, therefore, was also considered to perform well. Comparisons of the linear model with available data met with limited success. Initially, the linear model’s predictions of laboratory scale plume velocity data resulted in overpredictions of 40 to 50 percent when compared to actual data. Error in predictions of laboratory scale oxygen transfer data were greater than 100 percent. The model fared better when its predictions were compared to full scale data; the predicted temperature was within 7 percent of that measured at three depths and the predicted oxygen concentration was within 4, 20, and 38 percent for the three depths. Some of the discrepancies in the data likely result from the fact that the Froude number used in the model to calculate initial velocity was derived for a circular, rather than a linear, source. Determination of the appropriate linear Froude number would likely improve the model’s predictions.