Scalar transport across the turbulent gas-liquid interface

 

The interest in turbulent scalar transport across the gas-liquid interface can be traced back to the 1930’s when Higbie (1935) tried to present a universal model to explain the phenomenon irrespective of the means of turbulence generation, whether originating from the gaseous or liquid sides. Many researchers followed on have made attempts to derive such a universal model but most models invariably involved parameters which are apparatus specific and hence are not simple or able to extend to more general applications. My interest follows that of my PhD work in our effort to relate the more generic turbulence on the liquid side to the bulk flow velocity and macro length scale and correlate it the associated scalar mass/heat transport across the interface [Khoo & Sonin (1992), Int. J. Heat Mass Trans., Vol. 35, pp 2233; Brown et al (1990), Int. J. Heat Mass Trans., Vol. 33, pp 2001]. This was met with limited success. Though the scalar transport is a function of the turbulence at/near the interface, it becomes apparent that the turbulence quantities taken w.r.t the fluctuating interface controls the transport rate. In the early 1990’s there is no commercial instrumentation that is able to measure the flow field and the fluctuating interface simultaneously, and PIV is still in its developmental stage. At NUS, we embarked to develop a PIV-based system including the necessary software routines to track and measure the liquid velocity field and the fluctuating interface velocity leading to two papers published [Khoo et al (1993), Exps Fluids, Vol. 13, pp 350; Law et al (1999), Exps Fluids, Vol. 27, pp 321]. (Even now, commercially available PIV system has to be modified to measure both fields simultaneously and the cost is rather high.)

 

Only with the required instrumentation problem solved, we were able to measure the linear vertical velocity gradient w.r.t. the interface (brms) and obtained a relation which correlates very well the scalar transport rate and brms for two vastly different flow conditions; one generated by turbulence solely from beneath the liquid via a submerged jet and the other via wind shear from above the interface [Law and Khoo (2002) (AIChE J., Vol. 48, pp 1856-1868]. Further experiments with gaseous stream above and liquid stream below in both co-current and counter-current directions performed confirmed the mentioned correlation obtained [Xu et al, 2006, AIChE J., Vol. 52, pp 3363-3374]. Because brms and related parameters describing the near-surface turbulence are not directly dependent on the particular means of generation, this gives the possibility that the said parameters identified in the relation are applicable to any other flows and hence the universality. In addition, as the said parameters are found in a very small region residing next to the interface, it further lends support to the small eddy model [first proposed by Lamont & Scott (1970), AIChE J., Vol. 16, pp 513] as opposed to the large eddy model and others. It may just be noted the relation is obtained from experiments without wave-breaking and generation of bubbles which can lead to two-regime behavior [Khoo & Sonin (1992), J. Geophy. Res., Vol. 97, pp 14413]; strictly if one can measure the variation of brms in entrained gas bubbles in the liquid, then there exists the possibility that the relation obtained for the scalar transport rate may yet be applicable. All these latter works were carried out at NUS and independent of my former thesis advisor at MIT who had moved on to pursue other research interest.

 

The importance and significance of the work are further supported by the following evidences:

(a) Invited to present a public seminar on “Turbulence structure at the air-water interface and its relationship to air-water mass transfer” at TUB (Technical University of Berlin) on 24th  February, 2000.

(b) BP International Limited (subsequently named as BP Amoco) has awarded a research grant in 1995 amounting to £38000 on “Transport across the turbulent air-sea interface” for a PhD scholarship tenable for a period of 3 years at NUS. This is a competitive grant application and is the first time awarded outside of the UK universities. Invited to present the research findings and a seminar entitled, “Turbulence structure at the air-water interface and its relationship to air-water mass transfer” at BP Amoco at Sunbury on Thames (where the Research HQ is located at that time) on 23 February 2000.

(c)  Related to application of the research work is the invitation to present and publish a paper on “Coastal sediment transport and chemical spill modeling” at the International Chemical and Oil Pollution Conference & Exhibition 2001, held in Singapore in September 2001. (In this regard, the turbulent transport model is incorporated into the 3D POM on the water circulation to study the effect of an accidental chemical spills on the regional seas and Singapore Strait. Singapore Jurong Island is one of the important chemical hub in this part of the world straddling between Europe and Japan/China and Australasia.)

(d) The national A*STAR research institute ICES (Institute of Chemical Engineering Sciences) has awarded a PhD scholarship to Mr. Xu Zhifeng tenable at NUS starting 2003 to carry on work to further ascertain the general applicability of brms with other different means of turbulence generation.

 

Future work:

(a) The incorporation of the rate of scalar transport into the 3D water circulation model to study the effect of (passive) chemical spill (whether accidental or otherwise) in the regional seas in SE Asia. Some preliminary numerical work has been carried out by us on the 3D water circulation in the Singapore Strait [see Chen et al (2005), J. Coastal Res., Vol. 21, pp 960-972.]. This is important in view of the (chemical) Jurong Island being located at the busy Singapore Strait and is one of the world’s busiest shipping lanes.

(b) The establishment of (brms) as the dominant factor controlling the scalar transport across the turbulent gas-liquid interface provides for the motivation to extend it to the falling film which is very prevalent in the chemical industries.

 

List of relevant publications

Brown, J S, B C Khoo* and A A Sonin, "Correlation for Condensation of Pure Vapor on Turbulent, Subcooled Liquid". International Journal of Heat & Mass Transfer, 33, part. 9 (1990): 2001‑2018. (United Kingdom).

 

Khoo*, B C and A A Sonin, "Scalar rate correlation at a turbulent liquid free surface: A two‑regime correlation for high Schmidt numbers". International Journal of Heat & Mass Transfer, 35, part. 9 (1992): 2233‑2244. (United Kingdom).

 

Khoo*, B C and A A Sonin, "Augmented gas exchange across wind‑sheared and shear‑free air‑water interface". Journal of Geophysical Research, 97, part. C9 (1992): 14413‑14415. (United States).

 

Khoo*, B C, T C Chew, P S Heng and H K Kong, "Turbulence characterisation of a confined jet using PIV". Experiments in Fluids, 13 (1992): 350‑356. (United Kingdom).

 

Chen, M, B C Khoo* and E S Chan, “Three dimensional circulation model of Singapore coastal waters”. In Proceedings of Oceanology International 97 Pacific Rim, 12-14 May 1997, Singapore, pp. 281-291. (Singapore: Oceanology International).

 

Law, C N S, B C Khoo* and T C Chew, "Turbulence structure in the immediate vicinity of the shear‑free air‑water interface induced by a deeply submerged jet". Experiments in Fluids, 27 (1999): 321‑331. (United Kingdom).

 

Khoo*, B C and J. Lou, “Coastal sediment transport and chemical spill modeling”. International Chemical and Oil Pollution Conference & Exhibition (ICOPCE) 2001. Compiler: IBC Asia Limited (2001): pp. 1-15. (Singapore).

 

Khoo*, B C, J Lou and K Kumar, “A quasi-3D convention dispersion model for coastal sediment transport and chemical spill”. Singapore Maritime & Port Journal 2002, pp. 145-153. (Singapore).

 

Law, N S and B C Khoo*, "Transport across a turbulent air‑water interface". AIChE Journal, 48, no. 9  (2002): 1856‑1868. (United States).

 

Chen, M, K Murali, B C Khoo*, J Lou and K Kumar, "Circulation modelling in the Strait of Singapore". Journal of Coastal Research, 21, no. 5 (2005): 960‑972. (United States).

 

Xu, Z.F., B C Khoo* and K. Carpenter, "Mass transfer across the turbulent gas‑water interface". AIChE Journal, 52, no. 10 (2006): 3363‑3374. (United States).