The time-dependent behaviours of the shallow flow of hot fire products were studied by using the full scale corridors of different size (A: 13 m(L) × 1.5 m(B) × 2.5 m(H), B: 70 m(L) × 3.3 m(B) × 1.8 m(H)) and by taking the wood cribs as the model fire source. Those cribs were placed at the end of both corridors and were ignited by a small pilot-flame at the center of their bottoms to obtain the similarity for the growth of flame.
The weight and maximum burning rate of the cribs were 5 kg and 20 kg, 5 g/sec and 20 g/sec for A and B corridor respectively.
The smoke concentration (Cs) was defined by the turbidity in unit of 1/m. The gas concentrations were represented by the output of the gas-sensor (Cg) in unit of mV which were feasibly replaced by [CO] in the combustion gases in terms of the calibration curve. By taking CO as a labelled gas, the concentration of CO₂ were estimated from Cg on the basis of [CO]/[CO₂] at the fire source which were obtained the high precision I. R. measurement.
The origin for the horizontal flow corresponding to the point of the hydraulic jump was determined by the break of the logarithmic plots of T/Too vs. travelling distance, where Too was the temperature at the surface of the crib and T meant those along the center of the fire plume or those at 10 cm beneath the ceiling of the corridor. As results, starting position (X=0) was taken at 2.5 m apart from the center of the crib for B corridor. Then, cartesian co-ordinates (x, y) were taken with abcissa along the corridor and aforesaid starting position at origin and with ordinate to vertical direction (y=0 on the ceiling).
Following results were obtained;
(1) Relations in the equation (1) and (2) were obtained at and around the fire source among T_avf-, T_avo- and V_avo- irrespective of time,
(T_av0 − T_R )/(T_avf − T_R ) = 0.2       (1)
V_av0 / √(T_avf − T_R ) − T_c = 0.03       (2)
where T_avo-, T_avf-, T_av-and T_R-meant the height-average temperature of the fire plume, thickness-averaged temperature of the flow at X=0, the critical temperature for the efflux motion and the ambient temperature, respectively. V_avo- was the thickness-averaged velocity at X=0.
(2) The constancy of the flow thickness (δ_v) of ca. 0.2 m at X=0 and of ca. 0.3 m at arbitrary X (X—35 m) after the ignition).
was observed vs. time before the flow reached to the opposite end of the closed B corriodr (7min. after the ignition).
(3) Disymmetrical triangular-shaped profile was obtained for Y-distribution of velocity. However, top-hat like profile tailing exponentially toward the floor was observed for the temperature.
(4) It was estimated that the flow was relatively shallow on the base of equation (3).
B δ_υ/(B +2δ_υ) ≈ 0.2       (3)
(5) Exponential decrease of V and T at arbitrary y within δ_υ and of Cg at y=0.1 m were obtained along the corridor direction respectively.
(6) The flow behaviour of quantity along the corridor was discussed in terms of Y-averaged quantity which was defined by following equation.
A_av (X, t ) = 1⁄δ_υ ∫^δυ₀ A (X, y, t )dy       (4)
However, the stretcl-out of Cs-concentration terrace was observed vs. X itinerantly with time before 7 min. and the obvious accumulation of smoke around X=35 m was recognized after 7 min.

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In this Report, first of all it is mentioned how side flows which have ununiform velocity distributions as in fire influence on the flow characteristics of air shutters, and next how to design them.
Then, assuming push flow, pull one and side one to be two dimensional potential flow, three flows are combined theoretically.
The results are as follows:
(1) The mode of push-pull flow of the shutter varies according to the velocity distribution pattern of side flow, even if each volume flow rate is constant.
(2) In such cases, the nearer the position of the point where the velocity of side flow shows maximum situates at the suction side of the shutter, the stabler the flow becomes. In other words, the position of center of gravity of side flow influences at a great extent on the stability of push-pull flow.
(3) Furthermore, the smaller the maximum velocity of side flow is, the stabler the push-pull flow becomes, under the condition that the mean velocity and distance of center of gravity of side flow from the pull side of air shutter are constant.
Next, in order to confirm the conclusions described above, the experiment on the practical flow has performed by employing a model and the results coincide well with the conclusions (1)-(3) abovementioned.
Consequently, relating to the design of air shutter for fire protertion the concrete standards are obtained as follows.
(1) As the side flow of smoke which runs near the ceiling in fire is faster than the one which runs near the floor, the shutter ought to be designed so as the flow is inhaled in ceiling side, and this way is affirmed also from different regard that a smoke has a buoyancy because of its temperature.
(2)The volume rate of suction flow Q₃ can be culculated from next equation by “Flow Ratio Method”
Q₃ = Q₁(1+m · K_Buni )
where, Q₁ : Volume rate of push flow,       m³/min
m : Break safety factor determined accordingly velocity distribution pattern of side flow
K_Buni : Break limit flow ratio culculated by employing the mean velocity of side flow

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We shall treat the problem of a two-dimensional heat-flow of a viscous imcompresible fluid within a spuare cross section at the building fire. The governing epuations are continuity, motion and energy. Here the equation of motion is used to Navier-Stokes' law and Boussinesp approximation.
The numerical solutions of these equations are studied, that various methods are carried out on a digital computer. For investigating the mathematical and camputational stability of finite difference epuations, moreover, the physical phenomena and computational technipue, a finite-difference method is applied to solve these epuations numerically.
Attempt to solve partial differential epuations by finite-difference method forused to digital computer;
1] finite difference approximations to
i) stability   ii) convergence   iii) rate of convergence   iv) truncation error   v) mathematical and numerical error
2] Calculational solutions to
i) calculated real time (CPU-time)   ii) numerical methods for computer memory scale   iii) rounding off error   iv) elapsed time
3] physical treatment to
i) physical conservation of the epuations by the computational values   ii) apropriate to numerical values for physical investigation
iii) simulational models
In this paper, a finite difference epuation is reduced to a partial differential epuation by the backward implicit scheme and, central and upstream difference scheme. A simultaneous linear algebraic epuations by thismethod is solved by the succesive overrelaxation (S.O.R.) method with overrelaxation facter σ _ΔT/X ² (σ is nondimensionalcoefficient), where matrices are used Sparse Matrix out of the computer memory scale.
Initial and boundary values difined by the experiment, and this problem was solved on the IBM SYSTEM/370 Model 135-DHO for Re=10⁴, Gr=10⁸ and Pr=0.72
With this parameter values except for ε=10, CPU-time was about 28 min. and elapsed time about 32 min. to depict the motion of heat flow during 7 min. than a initiation used compiler is PL/I (F).

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