A comparative numerical study of turbulence models for the simulation of fire incidents: Application in ventilated tunnel fires

Figures & data

Figure 1. Sketch of the tunnel and heat source.

Table 1. Coefficients of Equation 1 and constants values

Conservation equation	ϕ	Γϕ	Sϕ
Continuity	1	0	0
x-momentum	u	${\mathit{\nu }}_{\text{eff}}$	$-\frac{1}{\mathit{\rho }}\frac{\mathit{\partial }p}{\mathit{\partial }x}+\frac{\mathit{\partial }}{\mathit{\partial }{x}_j}\left({\mathit{\nu }}_{\text{eff}}\frac{\mathit{\partial }{u}_j}{\mathit{\partial }x}\right)$
y-momentum	v	${\mathit{\nu }}_{\text{eff}}$	$-\frac{1}{\mathit{\rho }}\frac{\mathit{\partial }p}{\mathit{\partial }y}+\frac{\mathit{\partial }}{\mathit{\partial }{x}_j}\left({\mathit{\nu }}_{\text{eff}}\frac{\mathit{\partial }{u}_j}{\mathit{\partial }y}\right)$
z-momentum	w	${\mathit{\nu }}_{\text{eff}}$	$-\frac{1}{\mathit{\rho }}\frac{\mathit{\partial }p}{\mathit{\partial }z}+\frac{\mathit{\partial }}{\mathit{\partial }{x}_j}\left({\mathit{\nu }}_{\text{eff}}\frac{\mathit{\partial }{u}_j}{\mathit{\partial }z}\right)+g{\mathit{\beta }}_{\mathrm{T}}\mathrm{\Delta }T$
Energy	T	$\frac{\mathit{\nu }}{Pr}+\frac{{\mathit{\nu }}_t}{P{r}_t}$	$\frac{{\dot{q}}_C}{\mathit{\rho }{C}_p}$
k-equation^a	k	$\mathit{\nu }+\frac{{\mathit{\nu }}_t}{{\mathit{\sigma }}_k}$	$p_k+G_k-\mathit{\epsilon }$
ε-equation	ε	$\mathit{\nu }+\frac{{\mathit{\nu }}_t}{{\mathit{\sigma }}_{\mathit{\epsilon }}}$	$[C_{\mathit{\epsilon }1}(P_k+C_{\mathit{\epsilon }3}{G}_k)-C_{\mathit{\epsilon }2}\mathit{\epsilon }]\frac{\mathit{\epsilon }}{k}$
k-equation^b	k	$\mathit{\nu }+\frac{{\mathit{\nu }}_t}{{\mathit{\sigma }}_k}$	$P_k+G_k-{\mathit{\beta }}^{*}\mathit{\omega }k$
ω-equation	ω	$\mathit{\nu }+\frac{{\mathit{\nu }}_t}{{\mathit{\sigma }}_{\mathit{\omega }}}$	$\mathit{\gamma }\frac{\mathit{\omega }}{k}{p}_k+C{D}_{\mathit{\omega }}+\mathit{\gamma }{C}_{\mathit{\epsilon }3}\frac{\mathit{\omega }}{k}{G}_k-\mathit{\beta }{\mathit{\omega }}^2$
${\mathit{\nu }}_{\text{eff}}=\mathit{\nu }+{\mathit{\nu }}_t,P_k={\mathit{\nu }}_t\left(\frac{\mathit{\partial }{u}_i}{\mathit{\partial }{x}_j}+\frac{\mathit{\partial }{u}_j}{\mathit{\partial }{x}_i}\right)\frac{\mathit{\partial }{u}_i}{\mathit{\partial }{x}_j},G_k=-\frac{{\mathit{\nu }}_t}{P{r}_t}g{\mathit{\beta }}_{\mathrm{T}}\frac{\mathit{\partial }\mathrm{T}}{\mathit{\partial }z},C{D}_{\mathit{\omega }}=2(1-f_1){\mathit{\sigma }}_{\mathit{\omega }2}\frac{1}{\mathit{\omega }}\frac{\mathit{\partial }k}{\mathit{\partial }{x}_j}\frac{\mathit{\partial }\mathit{\omega }}{\mathit{\partial }{x}_j}$
$\mathit{\rho }=1.18\frac{\text{kg}}{{\text{m}}^3},g=9.81\frac{\text{m}}{{\text{s}}^2},{\mathit{\beta }}_{\text{t}}=3.34·{10}^{-3}\frac{1}{\text{k}},cp=1,006\frac{\text{J}}{\text{kg}\text{K}},Pr=0.71,{Pr}_t=0.9,C_{\mathit{\epsilon }1}=1.44,C_{\mathit{\epsilon }2}=1.92,C_{\mathit{\epsilon }3}=1.0$

^a Standard k–ε turbulence model is used.

^b k–ω SST turbulence model is used.

Table 2. Cases data and calculated results

Case	Ventilation velocity (m/s)	Total heat release rate (MW)	Numerical approach	Flame angle (°)	Back-layering length
1	U1 = 0.85	${\dot{Q}}_1$ = 2.57	Present solver	8	Till entrance
			Ansys Fluent	9	Till entrance
2	U2 = 2	${\dot{Q}}_2$= 2.29	Present solver	58	3.2 m
			Ansys Fluent	58	3.7 m

Figure 2. Numerical mesh used for the standard k–ε with wall functions simulations.

Notes: Section y = 2.7 m near the vicinity of the heat source (top figure). Cross-section x = 60 m (bottom figure).

Figure 3. Numerical mesh used for the low-Re k–ω SST simulations.

Notes: Section y = 2.7 m near the vicinity of the heat source (top figure). Cross-section x = 60 m (bottom figure).

Figure 4. Temperature isolines through time for case 1.

Notes: (a) Standard k–ε at 0.5 s; (b) Low-Re k–ω SST at 0.5 s; (c) Standard k–ε at 2 s; (d) Low-Re k–ω SST at 2 s; (e) Standard k–ε at 5 s; (f) Low-Re k–ω SST at 5 s; (g) Standard k–ε at 10 s; and (h) Low-Re k–ω SST at 10 s.

Figure 5. Temperature isolines through time for case 2.

Notes: (a) Standard k–ε at 0.5 s; (b) Low-Re k–ω SST at 0.5 s; (c) Standard k–ε at 2 s; (d) Low-Re k–ω SST at 2 s; (e) Standard k–ε at 5 s; (f) Low-Re k–ω SST at 5 s; (g) Standard k–ε at 10 s; and (h) Low-Re k–ω SST at 10 s.

Figure 6. Velocity vectors at characteristic sections and moments for case 1 predicted by the standard k–ε model (left column) and the low-Re k–ω SST model (right column).

Notes: Section y = 2.7 m near the heat source at 0.5 s (top row), cross-section x = 60 m at 1 s (middle row), and cross-section x = 60 m at 5 s (bottom row).

Figure 7. Velocity vectors at characteristic sections and moments for case 2 predicted by the standard k–ε model (left column) and the low-Re k–ω SST model (right column).

Notes: Section y = 2.7 m near the heat source at 0.5 s (top row), cross-section x = 62 m at 1 s (middle row) and cross-section x = 62 m at 5 s (bottom row).

Figure 8. Case 2, 20 s after fire breaking.

Notes: Vertical temperature profiles at a distance of 18 m (top figure) and 30 m (bottom figure) downstream from the heat source.

Figure 9. Convergence curve.

Notes: Temperature corrections in pseudo-time for three physical time steps with starting point t = 2 s.

Figure 10. Flame shape comparison for case 1.

Notes: Present solver with the k–ω model (top figure), Ansys Fluent with the k–ε model (bottom figure).

Figure 11. Flame shape comparison for case 2.

Notes: Present solver with the k–ε model (top figure), Ansys Fluent with k–ε model (bottom figure). Definition of flame angle.

Figure 12. Comparison of temperature profiles along height when steady state was reached.

Notes: Case 1 (top figure), and case 2 (bottom figure).

Figure 13. Velocity vectors at section y = 2.7 m and stagnation point (red circle).