Scalar Dispersion from Wall-Mounted Cylinders at Large Reynolds Number: Plume Transitions and Regime Classification

TL;DR

This work investigates scalar dispersion from the free end of wall-mounted cylinders in a high-Re turbulent boundary layer, focusing on transitions between elevated plumes, ground-level plumes, and ground-level sources. Through four geometries (GEOM1–GEOM4) spanning primary and secondary aspect ratios and a low momentum ratio $r$, the study quantifies how wall-flow interactions drive the EP–GLP–GLS transitions and assesses the Gaussian Dispersion Model and Wall Similarity Model against high-fidelity measurements. The authors provide a comprehensive dataset, develop an empirical data-informed framework to predict ground-level concentration and plume structure across geometry and momentum-ratio space, and offer guidance on model applicability and limitations. The work delivers actionable insights for regulatory dispersion modeling, urban and industrial hazard assessment, and validation targets for LES/RANS simulations in complex near-wall environments, with implications for improving near-wall pollutant predictions.

Abstract

This study presents a comprehensive experimental investigation of scalar dispersion from the free end of wall-mounted cylindrical obstacles immersed in a large-Reynolds-number turbulent boundary layer. A key focus is the characterization of transition behavior between distinct dispersion regimes: elevated plumes (EP), ground-level plumes (GLP), and ground-level sources (GLS). Experiments systematically vary the primary and secondary aspect ratios ($AR_1, AR_2$) and the velocity ratio ($ r$) to explore their effects on the evolution of scalar plumes. Plume classification is governed by the non-dimensional parameter $\tilde{h}_s / δ_{cz}$, which quantifies the progressive interaction between the plume and the ground. Here, $\tilde{h}_s$ denotes the effective source height and $δ_{cz}$, the vertical plume half-width. Detailed concentration measurements demonstrate that the EP--GLP--GLS transitions substantially modify both vertical and lateral dispersion characteristics. The measurements reveal systematic departures from classical dispersion-coefficient scaling. To assess the capability of existing models under these conditions, the experimentally determined dispersion coefficients are used to evaluate the Gaussian Dispersion Model (GDM) and a Wall Similarity Model (WSM). The GDM captures general trends but deviates in specific regimes, whereas the WSM offers improved representation under GLS conditions. The resulting dataset, grounded in systematic laboratory measurements, establishes a critical benchmark for validating numerical simulations and informing the development of next-generation predictive models. Finally, leveraging these results, a concise data-informed predictive framework is introduced that captures the EP--GLP--GLS transitions and provides first-order estimates of ground-level concentration across geometric and momentum-ratio parameter space.

Figures (21)

• Figure 1: (left) The normalized vertical location of peak concentration $z_M/\tilde{h}_s$ versus $\tilde{h}_s/\delta_{\mathrm{cz}}$ (black curve). The red dashed line is a derived analytical solution $\tilde{h}_s/\delta_{\mathrm{cz}} = \sqrt{ \tanh^{-1}(\hat{z}_M)/( 2 \ln(2) \, \hat{z}_M)}$ valid for $0 < z_M/\tilde{h}_s < 1$, where $\hat{z}_M = z_M/\tilde{h}_s$. (middle) $z_M/z_c$ versus $z_c/\delta_{\mathrm{cz}}$. (right) $\tilde{h}_s/\delta_{\mathrm{cz}}$ versus $z_c/\delta_{\mathrm{cz}}$. The green dotted line is the fit $\tilde{h}_s/\delta_{\mathrm{cz}} = 1.68 (z_c/\delta_{\mathrm{cz}} - \chi_\text{GLS})^{0.66}+ 0.05(z_c/\delta_{\mathrm{cz}} - \chi_\text{GLS})$, valid for $0 < z_c/\tilde{h}_s < 1.55$. The blue dotted line is $\tilde{h}_s/\delta_{\mathrm{cz}}$ = $z_c/\delta_{\mathrm{cz}}$ shown for reference.
• Figure 2: Schematic of the scalar release setup (GEOM2–GEOM4 shown). The inner dashed cylinder is the source (GEOM1). Measurement planes $P1,P2,P3$ capture plume development.
• Figure 3: Schematic of time-averaged flow over a finite-height circular cylinder (adapted from Sumner2013).
• Figure 4: Ensemble-averaged smoke images near the source: GEOM1 (top), GEOM3 (bottom). Columns: $r\simeq 0.46, 0.23, 0.16$. Black box: outer geometry; dashed white box: source (GEOM1).
• Figure 5: Mean concentration fields of GEOM1. Rows: $r\simeq 0.46, 0.23, 0.16$. Columns: $x/h_s\simeq 2.24, 5.82, 14.70$. Dashed isoline marks $C=C_M/2$. The colour map is $(C/C_o)\times10^4$, where $C_o$ is the source concentration.