The influence of buoyancy upon near wake pollutant dispersal

Many links have been drawn between increased pollution exposure and increased health risks, and WHO data shows that 99% of the world’s population exceed their guideline limits. Cities provide a complex flow environment with various sources of, often buoyant, pollution. One common flow feature is the wake, which is of particular interest since it is a region where pollutant is likely to accumulate and become trapped. Understanding the mechanisms of pollutant trapping within wakes, and how pollutant buoyancy might change this, is crucial to understand human exposure to the many sources of pollutant present within cities. This thesis focuses upon the interaction between a buoyant pollutant and two wake producing objects: a backward facing step, which acts a simple and canonic representation of a wake, and an Ahmed body, which acts as a simplified representation of a road passenger vehicle. There are six fundamental parameters which can be used to characterise the influence of buoyancy upon pollutant dispersal within a wake: the objects height and width (𝐻, 𝑊), the speed of the freestream flow 𝑈, the volumetric exhaust flow rate 𝑄_0 , the exhaust buoyancy 𝑔’_0 (which we relate to the relative density difference 𝑔_0 = 𝑔(𝜌 − 𝜌_0)/𝜌) and the kinematic viscosity of the working fluid 𝜈. We can form three dimensionless groups from these parameters: a Reynolds number 𝑅𝑒 𝐻 = 𝑈𝐻/𝜈, a dimensionless exhaust dilution rate 𝑞 ˆ 0 = 𝑄 0 /(𝑈𝑊 𝐻) and an adapted Froude number 𝐹𝑟 ′ = 𝑈/(𝑔’_0 𝑄_0 /𝑊) 1/3 . We consider flow in a Reynolds invariant regime, and also consider a small exhaust flow rate which allows the problem to be characterised by a single dimensionless group, the adapted Froude number 𝐹𝑟 ′. Analytic models, quantifying pollutant transport around the wake of the backward-facing step and the Ahmed body were constructed. Alongside this, small-scale experiments were performed to investigate the interaction between exhaust buoyancy and wake inertia, with the freestream velocity, exhaust volumetric flow rate and the exhaust buoyancy each varied separately. Near wake velocity profiles were found using particle image velocimetry and concentration profiles were found using dye attenuation. For a neutrally buoyant exhaust released into the wake of a backward-facing step, pollutant is well mixed into a region extending to 𝑥/𝐻 ∼ 2 and approximately the height of the step. Introducing buoyancy pushes the pollutant into a wall plume which extends up the face of the step and delivers pollutant directly into the shear layer. We find that the average pollutant concentration within an 𝐻 × 𝐻 region behind the step can be predicted well by the analytic model, with buoyancy reducing the average pollutant concentration behind the step. The results and analytic model for the backward-facing step outlined within this thesis have been published, see Charlwood et al. (2023). The experimental results of the Ahmed body showed similar general trends to that of the backward-facing step, with increased buoyancy pushing pollutant further towards the top of the recirculation bubble and the formation of a wall plume up the back of the vehicle. The general trend of the experimental data for the average pollutant concentration behind the Ahmed body matches the trend as predicted by the analytic model, however, the magnitudes predicted by the model were approximately double that found experimentally. Further to this, as predicted analytically, the experimental results did not fully collapse onto a single line but showed a dependence upon the exhaust flow rate. The dependence found experimentally was larger than what was predicted analytically. This disparity between the model and experimental data highlights the additional complexity of the Ahmed body wake in comparison to the backward-facing step flow. The agreement between the general trends indicates a general understanding of the guiding physical principles behind the transport of pollutant.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2023

Author dc:creator

• Charlwood, Samuel

Advisor dc:contributor.advisor

• Davies Wykes, Megan

• Buoyancy
• Dispersal
• Fluid Dynamics
• Wakes

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/688ae344-d3de-404c-a2f8-108bcca80619/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.108444

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/368116