Confined buoyant plume

Underlying Flow Regime 4-09 © copyright ERCOFTAC 2004

References

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Cook, M.J. & Lomas, K.J. 1997 Guidance on the use of computational fluid dynamics for modelling buoyancy-driven flows. Proc. IBSPA. Vol. 3. ISBN. 80-01-01646-3.

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List of Figures

Figure 1. Schematic of the ‘filling box’ flow. Buoyant fluid rises vertically in the plume then collects in the upper part of the space forming a stratified layer (the horizontal lines represent constant density surfaces in the stratified layer). The leading ‘front’ of the stratified region, at height h_f, descends at speed u_f , until reaching the floor after some time. The plume entrains fluid from both the homogeneous and stratified regions. In the latter region, the entrainment produces a horizontal flow along constant density surfaces towards the plume. After the front has reached the floor, the stratification weakens and eventually the whole space becomes well mixed. Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 2. Definition sketch and schematic of the ‘emptying-filling box’ flow. Air at temperature T₀ enters the space through the bottom opening, of area a_b. The plume carries buoyant fluid from the plume source together with entrained ambient fluid into the upper layer. On reaching the upper layer the plume dissipates and maintains well-mixed conditions in the upper the layer at temperature T₀+ΔT. The interface between the two layers, at height h is quite sharp. Warm air in the upper layer leaves through the top opening, of area a_t. Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 3. Theoretical curves for 2D line-source plumes for a) interface height and (b) reduced gravity (equations 5 & 7). Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 4. Theoretical curves for 3D point-source plumes for a) interface height and (b) reduced gravity (equations 8 & 10). Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 5. Enhanced shadowgraph image of the flow in a typical salt-bath experiment showing the plume and the two well-mixed layers. The salt water entering from the plume is dyed. The dark vertical line on the right-hand side of the chamber is a screen to reduce mixing from the inflow. Here the inlets and outlets positioned vertically in the walls of the chamber rather than horizontally in the floor and ceiling (as in the CFD simulations and study of Linden et al. (1990)). As noted in the text, however, this difference is not thought to be of significance here. In the salt bath experiments a dense saline plume is used, so the flow is vertically inverted from that shown in Figure 2. (From Hunt & Linden 2001.) Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 6. Vertical density profiles in salt bath experiments averaged in the direction normal to the page, obtained by an optical image processing based technique in two salt-bath experiments a) buoyancy driving only (as Figure 5), b) buoyancy and wind driven ventilation (note that this case is not considered here). Note, again, the vertical inversion of the geometry from the standard case. (From Hunt & Linden 2001.) Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 7. Comparison of salt-bath experiment results with the theoretical model predictions for interface height and reduced gravity (equations 8 & 10). The theoretical curves have been plotted for three values of entrainment constant α = 0.083 (continuous line), α = 0.074 (dashed line) and α = 0.094 (dotted line). In all of the theoretical curves corrections for plume virtual origin offset and opening heights have been made. In the formulae for A* (equation 1) the values of discharge co-efficient used are C_t= 0.6, C_b= 0.5. (From Hunt & Linden 2001.) Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 8. The geometry of the room considered in the CFD simulations. In the 3D simulations the breadth of the room was 1.0m in the direction normal to the page. (Note the difference of notation from that used elsewhere in the paper; here a_t = a_u and a_b = a_l). Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 9. CFD model domain for 2D line-source plumes showing location and type of boundaries (Cook & Lomas 1998). Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 10. CFD model domain for 3D point-source plumes showing a) location and type of boundaries b) computational mesh (Cook & Lomas 1997). Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 11. Calculated flow fields (temperature contours and velocity vectors) for 2D line-source plume simulations for (a) plume source heat input, Q = 200 W, effective vent size =0.148, 'standard' k–ε turbulence model; (b) Q = 1000 W, =0.148, 'standard' k-ε turbulence model; (c) Q = 200 W, = 0.148, RNG k–ε turbulence model; (d) Q = 1000 W, = 0.148, RNG k–ε turbulence model; (e) Q = 200 W, = 0.075, RNG k–ε turbulence model; (f) Q = 200 W, =0.227, RNG k–ε turbulence model. Note that only half the room width is shown; the plume and symmetry plane are on the right-hand side of the region shown. (Cook & Lomas 1998) Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 12. Calculated flow fields (temperature contours and velocity vectors) for 3D point-source plume simulations (Cook & Lomas 1997) for (a) plume source heat input, Q = 200 W, effective vent area =0.0304, 'standard' k-ε turbulence model; (b) Q = 200 W, =0.0304, RNG k–ε turbulence model; (c) Q = 200 W, RNG k–ε turbulence model, plane normal to room major-axis plane 0.2m from the wall; (d) Q = 1000 W, =0.0304, RNG k–ε turbulence model. Note that in a), b) and d), only half the room width is shown; the plume and symmetry plane are on the right-hand side of the region shown. (Cook & Lomas 1998) Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 13. Measurements of a) interface height and b) reduced gravity for 2D line-source plumes, compared with the theoretical model and salt-bath experiments of Linden et al. (1990). In the theoretical curves the value of entrainment coefficient used is α = 0.1 has been used. Note that no-virtual origin corrections have been made and C_t= C_b= 1.0.) Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Figure 14. Measurements of interface height for 3D point-source plumes, compared with the theoretical model and salt-bath experiments of Linden et al. (1990). Theoretical curves for two different values of entrainment coefficient are shown: the typical value of α = 0.1 and the value inferred from the CFD measurements of α = 0.14. Note that no-virtual origin corrections have been made and C_t= C_b= 1.0. (From Cook 1998). Originals of all the figures in this UFR are in UFR4-09_Figures.pdf

Contributors: Jake Hacker - Arup