CFD MODELING OF SMOKE REVERSAL 

C. C. Hwang and J. C. Edwards 

NIOSH/ Pittsburgh Research Laboratory 

Pittsburgh, PA 15236 

ABSTRACT 

In the design for a fire or smoke emergency, a main concern is maintaining an evacuation path 

that is free of smoke and hot gases. In ventilated tunnel fires, smoke and hot gases may form a 

layer near the ceiling and flow in the direction opposite to the ventilation stream. The existence 

of the reverse stratified flow has an important bearing on fire fighting and evacuation of 

underground mine roadways, tunnels, and building corridors. In the present study, a 

computational fluid dynamics (CFD) program is used as a design tool to model floor-level fires 

in a ventilated tunnel. The fire is simulated by a diffusion flame of propane issuing from a 

circular hole on the tunnel floor. The computed profiles of velocity and temperature along 

channel cross sections are similar to those obtained experimentally. The computed reverse-flow 

layer length has been correlated with a densimatric Froude number with some success. A nondimensional parameter involving the source fire intensity is also used for the correlation. These 

analyses show that an appropriate ventilation air current must be maintained to provide an 

evacuation path from the source fire clear of smoke and hot gases. It is believed that CFD 

modeling, employed correctly and interpreted carefully, can be a useful design tool for fire 

protection. 

INTRODUCTION 

Although there has been increased attention to life safety during fire emergency in tunnels and 

mine roadways, there is no universally accepted design and operation of life safety systems for 

fire emergencies. In ventilated tunnel fires, smoke and other combustion products have been 

observed to fill the tunnel for a considerable distance on the intake side of a fire. Under certain 

flow and fire conditions, smoke may form a layer near the ceiling and flow in the direction 

opposite to the ventilation stream. The existence of reverse stratified layer of hot combustion 

products has an important bearing on fire fighting and evacuation of underground mine 

roadways, tunnels, and building corridors. It is of practical importance to understand the 

physical parameters and flow conditions under which the reverse stratified flow occurs. 

In the design for a fire or smoke emergency, a main concern is maintaining an evacuation path 

that is free of smoke and hot gases. Consider a scenario involving a stopped vehicle on fire in a 

tunnel, disrupting traffic and requiring worker and passenger evacuation. Another scenario 

involves a conveyer-belt fire in an underground mine entry, producing smoke and toxic 

combustion products. The design must focus on determining the ventilation required to maintain 

a single evacuation path from the fire source clear of smoke and hot gases. The risk from 

accidental fires as well as the subsequent smoke movement depends largely on these applied 

ventilation currents. 
When a fire is started on the floor of a straight channel without a ventilation (cross) flow, a hot 

plume rises above the fire and entrains the surrounding cold air into the plume. The plume, 

reaching the ceiling, forms two equal gas streams flowing in the opposite direction along the 

ceiling. The hot ceiling layer carries with it heat, carbon monoxide, smoke, and other 

combustion products. These layering streams eventually lose their buoyancy through heat loss to 

the strata or to the air beneath. The flow field is symmetric with respect to the plume axis. 

When a cross ventilation current exists, the symmetry in the rising plume and in the ceiling gas 

streams no longer exists. The ventilation current bends the plume and the length of the ceiling 

layer flowing against the ventilation current is reduced. It can be expected that the length of the

hot ceiling layer is a function of the fire intensity and the ventilation velocity. The temperature

of the layer decreases as the gas flows away from the region where the plume impinges the 

ceiling. Two mechanisms contribute to the temperature decrease. One mechanism is the heat

losses of the layer along the ceiling, and the other is cooling resulting from entraining the 

surrounding cold air into the layer. As a result, the temperature at the front region of the layer 

reaches the surrounding air temperature and the layer loses its buoyancy and identity. 

Previous workers employed simple empirical models to specify the critical velocity needed to

prevent upstream movement of smoke from a fire in a tunnel [1-6]. In general, these models 

consider the buoyancy head and the dynamic head in the system, and deduce appropriate 

quantities for correlation. Hwang et al. [7], Daish & Linden [8] and Charters et al. [9] employed 

phenomenological models that provide more detail than the simple empirical approaches. A

recent review of tunnel fires by Grant et al. [10] pointed out that existing experimental data still 

show an inadequate fundamental understanding of the interaction between buoyancy-driven 

combustion products and forced ventilation, the validity of extrapolating small-scale results to 

large scales, the influence of slopes on smoke movement and the effect of tunnel geometry. 

They also pointed out that CFD-based models represent the best way forward for prediction 

purposes, because CFD models make few prior assumptions about the gross flow character.

CFD models are based on the fundamental conservation equations in fluid mechanics, and 

provide, in theory, fine resolution of the problem in terms of both space and time for all the

parameters of interest. With increasing availability of powerful computers, considerable

attentions are given to CFD modeling of fire in buildings and ventilated tunnels [11-16]. 

In the present study, a CFD program is used as a design tool to model floor-level fires in a

ventilated tunnel. The fire is simulated by a reacting fuel issuing from a hole on the floor of a

channel. The shape of the hole may be circular or rectangular. The tunnel has a rectangular 

cross section with sufficient length upstream to accommodate formation of reverse-layer flow. 

The fire is simulated by a diffusion flame of propane (mass fraction unity) issuing from a circular 

hole on the tunnel floor. A commercial program CFD2000 by Adaptive Research1

 is employed 

for the flow field computations. A four-step finite rate reaction scheme is used to represent a

realistic fire-ventilation interaction in the plume zone. The standard k-ε turbulence model is 

used in the three-dimensional channel flow. The subsequent development of hot-gas layers is 

three-dimensional. Re-circulating flow patterns, movement of the ceiling-layer front, and 

distributions of gas temperature and velocity are studied under various fire parameters. 

 

1 Reference to a specific product does not imply endorsement by NIOSH. 
MODEL DESCRIPTION 

The governing equations for the flow field are expressed as partial differential equations. 

mass conservation 

 ( ) 0 i

i

U

t x

∂ρ ∂ ρ + = ∂ ∂ (0.1) 

momemtum conservation 

( ) Ui

t

∂ ρ

∂

+ ( ) i j

j

U U

x

∂ ρ

∂ = ij

Ui

i j

p S

x x

∂ ∂τ − − +

∂ ∂ (0.2) 

energy conservation h

t

∂

∂

( ) j

j

U h

x

∂ ρ

+

∂

 = p

t

∂

∂

 + 

j

j

p U

x

∂

∂

+ 

j x

∂

∂ Pr Pr

t

h

j t

h S

x

μ ∂ μ

∂

      + +

     (0.3) 

species conservation Yi

t

∂ρ

∂

 + ( ) j i

j

U Y

x

∂ ρ

∂

 = t i

j t j

Y

x Sc Sc x

μ μ ω

∂     ∂   + +

∂ ∂      

&  (0.4) 

gas equation of state p = R

M

T (0.5) 

or turbulence modeling, the standard two-equation k -ε turbulence model was employed [17], in 

which additional equations for the kinetic energy of turbulent fluctuations ( k ) and the rate of

dissipation of turbulence energy (ε ) are solved. The empirical constants appearing in the 

equations are c 0.09, 1.44, μ = 1 c = 2 c = 1.92, Prk =1.0, Pr

ε =1.3. This set of constants is 

adopted from Launder and Spalding [17]. It may be noted that a modified k -ε model has been 

used by Woodburn & Britter [14] to include the effects of buoyancy and wall damping on the 

turbulence. The following boundary conditions are used in this work. At the upstream (inflow)

side of the channel, a uniform air velocity u is specified (forced ventilation) with v in = 0 and 

. The entering air temperature T is 300K and for the entering species the mass fractions

are , , for other species. For the turbulence inlet conditions,

 and 

w = 0

YO

in k =

in

2 = 0.233

0.02 m

2 =

in

0.767

0.02

YN

2 3 /s

Y = 0

ε = . At the downstream (outflow) side of the channel a 

uniform pressure is specified. The value of u is computed and no-source condition is 

specified for the other variables. The channel walls are assumed to be impervious, adiabatic, and 

non-slip. A program-supplied turbulence wall function is used. The modeling of a floor fire and 

its boundary conditions are described in the next section. 

3 3

m /s

out
Modeling a Floor Fire 

The fuel employed in the reaction process is propane (C H ). To realistically simulate the

burning process, the fuel reacts with air in a 4-step finite rate reaction scheme as shown in the 

following equations [18]: 

3 8

C H3 8 + → 1.5O2 3CO + 4H2 with 11 4 10 , Af = x n = 0, J/kmol 4 E =1.5105x10

C H3 8 + → 3 3 H2O CO + 7H2 with 8 3 10 , Af = x n = 0, J/kmol 4 E =1.5105x10

CO + → H2O CO2 + H2 with 9 2.75 10 , Af x = n = 0, J/kmol 4 E =1.017x10

2 2 H O + 0.5 → H2O with 15 8.5 10 , Af x = n = −1, J/kmol 4 E = 2.014x10

where Af is the Arrhenius coefficient, n is the collision factor exponent, and is the activation 

energy. The number of the chemical species involved are C H , , , , , 

E

3 8 O2 H2 CO CO2 H2O , and 

. At the source fire, the mass fractions of all species are zero except that of C H which is set 

. The fuel velocity is taken to be 0.1-0.3 m/s (u

N2

3 8 Yc H

3 8

=1.0 win = 0 , v = 0 ) and T K. The 

fuel velocity is approximately equal to the burning rate of the liquid fuels in open trays [19]. 

=1200

RESULTS AND DISCUSSION 

The channel used in the modeling is 30 m long, 2.4 m wide, and 1.6 m high. For fixed channel 

geometry, the main parameters considered are the ventilation velocity u , the fuel-exit velocity 

, the fuel-exit diameter, and the channel inclination angle. The quantity is proportional to 

the rate of heat generation at the source fire. The fuel exits from a 0.8-m (or 0.4-m) diameter 

floor opening located at a distance 10 m from one end of the channel where ventilation air enters.

Figure 1 shows the geometry of the channel with grid distribution. A three-dimensional bodyfitted grid with 49×13×17 cells in the tunnel length, width and height direction was used for the 

0.8-m diameter fire. For the 0.4-m diameter fire, a grid with 51

in

win win

×13×18 cells was used. When

the reverse flow layer length exceeds 8 m, the ventilation flow was admitted from the end with a 

20-m leading distance to the fuel exit. It is assumed that the flow development at the entrance 

region has negligible effect on the flow reversal of the layer. 

The results are based on the computed flow field 30 seconds after the initiation of the fire. An 

initial plume rises to the ceiling and hot ceiling layers evolve during a transition period. It

appears that the flow field has attained a steady state at this time. When a reverse flow layer 

occurs, as shown in Fig. 2 the contour of zero axial velocity in channel cross sections upstream

of the plume is approximately parallel to the ceiling. This confirms an experimental observation 

that smoke layers are of uniform thickness at a channel cross section. This implies that the flow

along the ceiling layer is approximately two-dimensional. This observation may prompt a 

theoretician to approach the problem using a simplified analysis. In Fig. 2 the velocity vectors 

are also shown. It is noted that the magnitude of the vectors shown represents the component of 

the total vector in the y-z plane, and that the x-component of the velocity across the contour of 

U = 0 changes its sign. The hot gas in the central region of the layer flows into the ventilation
current below and a less amount of cold airflows into the layer near the wall regions. As a result 

the layer loses its buoyancy. 

The computed profiles of velocity and temperature along channel cross sections are shown in 

Figs. 3 and 4. These profiles are similar to those obtained experimentally in a fire tunnel by 

Hwang and Wargo [20]. Figure 5 shows vector plots in the x - plane at as a function

of . As the value of increases, the length of the reverse stratified layer decreases because of 

the increased counteracting effects of the ventilation current. 

z y = 0

uin uin

The channel inclination has considerable effects on the layer length of a reverse flow. When the 

ventilation flow has an upward component (positive inclination represented by +φ ), keeping 

other conditions fixed, the reverse-flow layer length decreases. When the ventilation flow has a 

downward component, the reverse-flow length increases. The computed reverse-flow layer 

length has been correlated with a densimetric Froude number with some success (Fig. 6). In

Fig. 6, is defined by 

Fr

Fr

,min

2

( ) in c

in in

gH

Fr

u

ρ ρ

ρ

− = , 

where ρc,min is the smallest value of the gas density in the ceiling layer. This corresponds to the 

highest temperature along the ceiling and is found at the region where the rising plume impinges 

on the ceiling. On the physical ground, represents the product of an interaction of a rising 

plume with a fire strength Q and a ventilation current with an average velocity u . As shown in 

Fig. 6, the effect of the channel inclination 

ρc,min

& in

φ is so pronounced that it is shown using separate 

lines. The effect of the size of the fuel exit (size of the source fire) on the reverse-layer length 

has been included by a parameter . The application of this type of correlation to a fire 

protection design needs the information on 

(D W/ )

1/ 2

ρc,min which cannot be found a priori, though some

estimate may be made from experimental data taken under similar conditions. 

A non-dimensional parameter involving the fire source intensity is also used for correlating the 

computed reverse-flow layer length L . The relevant non-dimensional parameters are taken as 

. 3 , ( ) in in in p f in

L Q gH f H c A u T , T φ

ρ

 = 

 −  

& 





 (0.6) 

The first term in the bracket is the ratio of heat generation by the fire to the kinetic energy of the 

ventilation current. The second term in the bracket is the ratio of the potential energy to the 

thermal energy of the rising gas from the fire. The parameterφ is the channel inclination angle.

In Figure 7 the reverse-layer length is correlated with the fire strength and the channelinclination angle, where 

0.947

3

in in in

Q X

A u ρ

 

=    

&
and 

 ( )

0.398

1.705 1/3 1 (sin ) ( ) p f in

L gH Y

H c T T φ

  −

= −   −  

In this correlation, the experimental data of Guelzim et al. [4] are also included. In their smallscale experiment a 3 m long half cylinder with an inside diameter of 0.3 m was used to simulate 

an arched tunnel. Midway along the tunnel a propane gas burner 2 cm in diameter was located. 

Forced ventilation was imposed with a variable rotation speed fan. It is seen that the effect of φ

is successfully included in the correlation. 

To determine the ventilation required to maintain a single evacuation path from the fire source 

clear of smoke and hot gases, we may set 0 L

H

= in Figure 7 and solve for u . This value of u is

the critical ventilation velocity. From the correlation in Figure 7 it is determined that the critical 

velocity is proportional to the heat rate to the one-third power. 

in in

CONCLUSIONS 

A CFD code based on the standard k -ε turbulence model was used to model a floor-level fire in 

a ventilated channel. The result of computations showed a qualitative behavior of the movement 

of the combustion products in the fire channel. The profiles of the gas velocity and temperature 

along channel cross sections are similar to those experimentally observed. 

The inclusion of a finite-rate reaction scheme resulted in very long computations. It may be

possible to employ a simpler reaction scheme (such as the mixture-fraction model) and simulate 

a realistic fire scenario. This point requires further investigations. 

 

The present computations use a constant value of pressure at the channel exit and a uniform flow 

of ventilation air velocity at the channel entrance. In a real fire scenario, fans drive the 

ventilation air, and as a fire develops, the ventilation current is reduced because of an increased

flow resistance in the channel. Thus, the boundary conditions used in the present computations 

apply to the fire scenario at the steady state. 

In various analytical and experimental investigations, the tunnel shapes and sizes will vary 

considerably. Because of the lack of geometrical similarity among various studies, caution 

should be exercised in the comparison of results obtained under dissimilar geometries. The same

caution applies to the cases with dissimilar fire scenarios. 

 

It has been shown how CFD analysis can be used to determine a correlation between smoke

reversal length and tunnel ventilation. The resultant correlation can be used to provide guidance 

for smoke management control measures. For example, the correlations indicate that ventilation

current proportional to the one third power of the fire intensity must be maintained to provide an 

evacuation path from the fire source clear of smoke and hot gases. This is an example of how a 

CFD modeling employed correctly and interpreted carefully, can be a useful design tool for fire
protection. Future investigation with other CFD codes and additional experiments should result 

in improved reverse flow length correlations. 

NOMENCLATURE 

A

c

area, m 2

p

D

specific heat, J/kg/K 

diameter of fuel exit, m

E activation energy, J/kmol 

Fr Froude number 

A

 gravitational acceleration, m/ 2s

h

f Arrhenius coefficient 

g

specific enthalpy, J/kg 

H channel height, m

L length of reverse stratified layer, m

M molecular weight, kg/kmol 

n collision factor exponent 

p fluid pressure, N/ 2m

Pr laminar Prandtl number 

Pr

Q& turbulent Prandtl number trate of heat generation, kJ/s 

R universal gas constant, J/kmol/K 

Sc laminar Schmidt number 

t

heat production per unit volume h

S

Sc

S

 turbulent Schmidt number 

Ui th component of body force per unit 

volume (e.g., gravity) 

i

T local fluid temperature, K 

t time, s 

i

x -component of velocity, m/s 

U

u

 ith-fluid velocity component, m/s 

v y -component of velocity, m/s 

w z -component of velocity, m/s 

W channel width, m

i x position vector in the i th coordinate 

direction, m

Yi mass fraction of species i

ρ 3 local fluid density, kg/m

μ laminar dynamic viscosity, N⋅s/ 2m

μ 2

t turbulent dynamic viscosity, N⋅s/ m

ω& 3 species production rate, kg/s⋅m

τ i, j viscous stress tensor, N/ m

2

Subscripts

a air 

c ceiling 

f fuel

in entering 

min minimum 

REFERENCES 

1. Thomas, P.H., “Movement of Smoke in Horizontal Corridors against an Air Flow,” Inst. Fire

Engrs Q., Vol. 30, pp. 45-53, 1970. 

2. Hinckley, P.L., “The Flow of Hot Gases along an Enclosed Shopping Mall: a Tentative 

Theory,” Fire Research Note No. 807, Fire Research Station, 1970. 

3. Heselden, A.J.M., “Studies of Fire and Smoke Behavior Relevant to Tunnels,” Proc. 2nd Int. 

Symp. On the Aerodynamics and Ventilation of Vehicle Tunnels, Cambridge, UK, pp. 23-25, 

March 1976, BHRA Fluid Engineering, 1976. 

4. Guelzim, A., Souil, J.M., Vantelon, J.P., Sou, D.K., Gabay, D., and Dallest, D., 1994, 

“Modelling of a Reverse Layer of Fire-Induced Smoke in a Tunnel,” Fire Safety Science – 

Proceedings of the Fourth International Symposium, pp. 277-288. 

5. Kennedy, W.D., Gonzales, J.A., and Sanchez, J.G., “Derivation and Application of the SES 

Critical Velocity Equations,” ASHRAE Transactions: Research, Vol. 102, no.2, pp. 40-44, 

1996. 

6. Oka, Y., Atkinson, G.T., “Control of Smoke Flow in Tunnel Fires, “ Fire Safety Jl Vol. 25, 

pp. 305-322, 1996. 

7. Hwang, C.C., Chaiken, R.F., Singer, J.M., and Chi, D.N.H., “Reverse Stratified Flow in Duct 

Fires: Two-Dimensional Approach,” 16th Symposium (International) on Combustion, pp. 

1385-1395, The Combustion Institute, Pittsburgh, PA, 1977. 
8. Daish, N.C. & Linden, P.F., “Interim Validation of Tunnel Fire Consequence Models: 

Comparison between the Phase 1 Trials Data and the CREC/HSE Near-Fire Model,” 

Cambridge Environmental Research consultants Report No. FM88/92/6, 1994. 

9. Charters, D.A., Gray, W.A. & McIntosh, A.C., “A Computer Model to Assess Fire Hazards in

Tunnels (FASIT),” Fire Technol., Vol. 30, 134-154, 1994. 

10. Grant, G.B., Jagger, S.F., and Lea, G.J., “Fires in Tunnels,” Phil. Trans. R. Soc. Lond., A 

356, pp. 2873-2906, 1998. 

11. Kumar, S. and Cox, G., “Mathematical Modelling of Fires in Road Tunnels,” Proc. Of 5th

Int. Symp. on the Aerodynamics and Ventilation of Vehicle Tunnels, Paper B1, Lille, France,

20-22 May, 1985. 

12. Simcox, S., Wilkes, N.S., & Jones, I.P., “Computer Simulation of the Flows of Hot Gases 

from Fire at King’s Cross Underground Station,” Fire Safety Journal, Vol. 18, pp. 49-82, 

1992. 

13. Rhodes, N., “Review of Tunnel fire and Smoke Simulations,” Proc. Of 8th Int. Conf. On the 

Aerodynamics and Ventilation of Vehicle Tunnels, pp. 471-486, 6-8 July, Liverpool, 1994. 

14. Woodburn, P.J. and Britter, R.E.,“CFD Simulation of a Tunnel Fire – Part I,” Fire Safety

Journal, Vol. 26, pp.35-62, 1996. 

15. Lea, C.J., Owens, M. & Jones, I.P.,“Computational Fluid dynamics Modelling of Fire on a 

One-third Scale Model of a Channel Tunnel Heavy Goods Vehicle Shuttle,” Proc. Of 9th Int. 

Conf. on Aerodynamics and Ventilation of Vehicle Tunnels, pp.681-692, 6-8 October, Aosta 

Valley, Italy, 1997. 

16. Edwards, J.C. and Hwang, C.C., “CFD Analysis of Mine Fire Smoke Spread and Reverse 

Flow Conditions,” Proceedings of the 8th U.S. Mine Ventilation Symposium, pp. 417-422, 

1999. 

17. Launder, B.E. and Spalding, D.B., “The Numerical Computation of Turbulent Flow,” Comp. 

Mech. In Appl. Mech. and Engr., Vol. 3, pp.269-289, 1974. 

18. Jones, W.P. and Lindstedt, R.P., “Global Reaction Schemes for Hydrocarbon Combustion,” 

Comb. & Flame, Vol. 73, p. 233, 1988. 

19. Burgess, D.S., Grumer, J. and Wolfhard, H.G., “Burning Rates of Liquid Fuels in Large and 

Small Open Trays,” Int. Symp. On the Use of Models in Fire Research, Nat. Acad. of Sci.-

Nat. Res. Council Publication 786, 1961. 

20. Hwang, C.C. and Wargo, J.D., ”Experimental Study of Thermally Generated Reverse 

Stratified Layers in a Fire Tunnel,” Combustion and Flame, V.66, pp.171-180, 1986. 
01 z

-10 0 10 20

x

-1

0

1

y

X

Y

Z

-101 y

-10 -5 0 5 10 15 20

x

0

0.5

1

1.5

z

Y X

Z

1 1

1 1 1

2 2

2 2

2

3

3

3 3

3 3

4

4 4

4

4 4 4

5 5

5

6

6

6

7 7

7

7

7

7 7

7

8 8

8

8 8

9

9

9

9

10

10

10

11

11

y

z

-1 0 1 0

0.5

1

1.5

Level

UVEL:

1

-1.2

2

-1

3

-0.8

4

-0.6

5

-0.4

6

-0.2

7

0

8

0.2

9

0.4

10

0.6

11

0.8

uin = 0.5 m/s, win = 0.2 m/s, φ = 0°

cut plane x = -1 m

contour of u

Figure 2. The contour of the axial velocity in the channel cross-section 

at x=-1 m. The region above level 7 is a reverse stratified layer. 

Figure 1. Channel geometry and grid distribution 
nt el c e

u, m/s

z,

m

-0.5 0 0.5 1 1.5

2

0.4

0.6

0.8

1

1.2

1.4

1.6

x=-1 m y=0 m

u, m/s

0 0.5 1 1.5 0

2

0.4

0.6

0.8

1

1.2

1.4

1.6

x=1 m y=0 m

u, m/s

0 0.5 1 1.5 0

2

0.4

0.6

0.8

1

1.2

1.4

1.6

x=3 m y=0 m

u, m/s

-0.5 0 0.5 1 1.5

2

0.4

0.6

0.8

1

1.2

1.4

1.6

x=-3 m, y=0 m x=-3 m

u, m/s

0 0.5 1 1.5 0

2

0.4

0.6

0.8

1

1.2

1.4

1.6

x=-5 m, y=0 m x=-5 m

Figure 2. The co our of the axial v ocity in the hannel cross s ction

at x=- 1 m. The region above level 7 is a reverse stratified layer 

0. 0. 0. 0. 0.

. 

 

Figure 3. Velocity distribution along z (height) in the plane y=0, at various 

values of x (axial distance).

T, K

300 350

x=-5 m

y=0 m

T, Kz,

m

300 350 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

x=-3 m

y=0 m

T, K

300 350

x=-1 m

y=0 m

T, K

300 350 400

x=3 m

y=0 m

T, K

300 400 500

x=1 m

y=0 m

Figure 4. Temperature distribution along z (height) in the plane y=0 at various 

values of x (axial position). 
x, m

z, m

-10 -5 0 5 10 0

0.5

1

1.5

y=0, uin=0.8 m/s, win=0.1 m/s, φ=0°

x, m

z, m

-10 -5 0 5 10 0

0.5

1

1.5

y=0, uin=0.7 m/s, win=0.1 m/s, φ=0°

x, m

z, m

-10 -5 0 5 10 0

0.5

1

1.5

y=0, uin=0.6 m/s, win=0.1 m/s, φ=0°

x, m

z, m

-10 -5 0 5 10 0

0.5

1

1.5

y=0, uin=0.5 m/s, win=0.1 m/s, φ=0°

 

Figure 5. Velocity vector plots showing the extent of reverse stratified layers for 

various flow conditions. 

 

F r (D /W )

1 /2

L/H

0 5 1 0 1 5 2 0 -2

0

2

4

6

8

1 0

1 2

D /W = 0 .3 3 3

D /W = 0 .2 5 0

− 5 °

0 °

+ 5 °

+ 1 0 °

φ = − 1 0 °

Figure 6. 

L

H versus for different values of the channel inclination angle 1/ 2 Fr( / D W ) φ .
y = 0.0247Ln(x) - 0.1353

R2

 = 0.8796

0.001

0.01

0.1

100 1000 10000

X

Y

CFD

GUEZIM ( ref 4)

Log. (CFD)

Figure 7. A correlation using parameters X and Y.