Mathematical Model of Fog Flow Source Strength and Diffusion in Flood Discharge Atomization

doi:10.11988/ckyyb.20230561

Abstract

Abstract:

In the process of flood discharge atomization, a large number of water droplets will be generated by the collision between the jetted water tongue and the downstream water cushion pond. The droplets carried by the airflow form a fog flow, which affects slope stability and traffic safety. To predict the distribution of fog flow in the downstream space, the interaction process between the jetted water tongue, air, and downstream water was simulated, and a background field for fog flow generation and transport was constructed. Based on the fog source generation mechanism and dimensional analysis methods, a calculation formula for fog flow source strength is proposed, and a mathematical model for fog flow source strength and diffusion is established. The fog flow process of the 3^# spillway hole discharge at the Manwan hydropower station is simulated using this model. The comparison shows that the distribution of fog flow source strength and the location of the fog source generation are consistent with prototype observation. The distribution of fog flow concentration distribution in the downstream space is in line with the prototype observation, and the calculated values of fog flow concentration at observation points match the trend of the original observed values. The comparison results verify the applicability of this model, providing a new method for predicting the distribution of fog flow in downstream spaces of flood discharge atomization.

Key words: flood discharge atomization, fog flow concentration, fog flow source strength, fog flow diffusion, Manwan hydropower station

CLC Number:

TV135.2泄水建筑物水力学

HE Gui-cheng, ZHANG Hua, PENG Yan-xiang. Mathematical Model of Fog Flow Source Strength and Diffusion in Flood Discharge Atomization[J]. Journal of Yangtze River Scientific Research Institute, 2024, 41(11): 109-117.

Figures/Tables 16

Fig.1 Schematic diagram of the droplet leaving the liquid

Fig.2 Flowchart of the numerical calculation process

Fig.3 Contour terrain and plane layout of Manwan hydropower station[31]

Table 1 Flood discharge conditions of Manwan hydropower station

闸门情况	库水位/m	下游水位/m	流量/(m³·s^-1)
3^#表孔全开	984.96	887.5	940

Fig.4 Fog flow generated by flood discharge of Manwan hydropower station

Fig.5 Schematic diagram of computing domain

Fig.6 Initial volume fraction of the water

Table 2 Parameters for the simulation

g/ (m·s^-2)	μ_w/ (Pa·s)		μ_a/ (Pa·s)	ρ_w/ (kg·m^-3)	ρ_a/ (kg·m^-3)	u_g/ (m·s^-1)
9.81	1.01×10^-3		14.8×10^-6	1 000	1.29	(0,0,5)
σ/ (N·m^-1)		d_s/m	λ₁/ (m²·s^-1)	c₂	c₃		c₄
72.75×10^-3		0.87×10^-4	0.6~1.7	(2.59~ 3.28)×10^-9	12~23		0.06~ 0.13

Fig.7 Flow pattern and turbulent kinetic energy distribution of water tongue and surface

Fig.8 Mass flow rate at the boundary and fog flow concentration at the measuring point

Fig.9 Schematic diagram of computational domain grid and four encrypted regions

Fig.10 Fog flow concentration at the measuring point under different grids

Fig.11 Spatial distribution of fog source intensity

Fig.12 Spatial distribution of water phase volume fraction

Fig.13 Spatial distribution of fog flow concentration

Fig.14 Calculated and observation values of fog flow concentration at measuring points

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