In this article we will discuss about the small scale modelling of combined wind and buoyancy effects on buildings.
Introduction to Combined Wind and Buoyancy Effects:
The continuous and rapid growth of computer power creates many times a feeling and a hope that a comprehensive and rigorous Computational Fluid Dynamics model capable of solving all wind engineering problems will soon be available. A similar feeling existed a few decades ago among researchers that were busy solving the turbulent transport equation using the K-Theory. Such dreams ignore the inherent semi-empirical nature of all turbulent closures, which makes it necessary to validate predictions of new problems by comparison with experimental data.
The need to validate numerical models has been one of the major driving forces for the development of special wind tunnels for small-scale physical modelling, often called fluid modelling, of environmental and wind engineering phenomena. Indeed, the success of such modelling has been of great help in the development of better turbulent closures. But, it has also turned out that small-scale fluid models can be successfully used to get a better understanding of complex flows and to solve practical environmental and wind engineering problems.
This success, and the thrilling excitement of scaling-down and observing natural phenomena in small- scale models, should not hide the fact that fluid modelling, too, has its own inherent limitations and uncertainties. Some of them are related to the approximate nature of the similarity obtained in small-scale models and to the problem of determining the scaling criteria for such simulations, which is discussed below.
The Approximate Fluid Modelling Problem:
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To preserve similarity between a model (m) and a prototype (p), all the dimensionless numbers (∏i), that can be formed from all the independent variables and the boundary conditions associated with the studied phenomena, must be equal in the model and the prototype:
∏i(m) = ∏i (p). …(1)
This condition secures the desired similarity and determines the scaling criteria for the simulation, namely, the scaling laws for the different variables in the model.
In most fluid models, the values of some dimensionless parameters, whose effect is assumed to be relatively small, are not matched with their values in the prototype flow. Consequently, such models provide only approximate simulations of the studied phenomena.
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The accuracy of approximate simulations is not the same for different phenomena in the same flow field. It can also change considerably across the flow field.
Because of the interaction between the different regions of the flow, the overall accuracy of such simulations is not always clear, as shown below:
The Rossby number, U/LΩ, where Ω is the vertical component of the earth’s angular velocity, for example, cannot be matched, and thus, the relative effect of the Coriolis acceleration is not reproduced correctly in such models.
Similarly, it is impossible to match in small-scale models the Reynolds of the prototype flow. The Reynolds number is a measure of the importance of turbulent fluxes relative to molecular fluxes.
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Re > Recrit .…(2)
Thus, it is usually assumed that if the flow in the model is turbulent, namely the effect of molecular fluxes can be neglected. This assumption is valid, for example, when one focuses on transport processes within the turbulent region of the constant stress layer, say 30<zu*/v< 0.15δ, where δ is the boundary layer thickness and u* is the shear velocity.
Thus, in this region,
du/dz=(1/k)u*/z, …(3)
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Where k is a universal constant, independent of the viscosity and the small scale roughness of the ground surface.
Integration of (3) yields the logarithmic law:
u/u*=(1/k) In z + C …(4)
Near smooth walls, however, a viscous sublayer is formed. Its relative thickness increases as the Reynolds number of the model is decreased and, thus, one cannot simulate in small scale models transport phenomena across this sublayer.
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Moreover, although viscous effects above the sublayer are negligible, the value of C in Eq. 4 does depend on the viscosity of the fluid, and it is not reproduced correctly in such models. Fortunately, one can eliminate viscous effects above the sublayer by increasing the roughness in the model.
Besides possible Reynolds number effects on the mean velocities in certain regions of the model, a reduction of the Reynolds number attenuates the fluctuations of the kinetic turbulent energy of the small-scale eddies in the entire flow field. The resulting change in the turbulent energy spectrum is very significant whenever the studied phenomenon is affected by small-scale turbulence; relative diffusion near a small source, for example.
When a buoyancy emission is included in the boundary conditions, it is usually characterized by its exit velocity from the source, W, the diameter of the source, d, and the difference between its density and that of the ambient fluid, Δρ = ρa-ρs. The dimensionless numbers that describe the boundary conditions should also be equal in the model and prototype.
A typical example is the densimetric Froude number:
Fr=U/[(Δρ/ρa)gL]1/2 …(5)
According to Eq. 5, when Δρ/ρa is equal in the model and the prototype; the velocity scale reduction, λ(U), where λ(x)=xm/xp is equal to the scale reduction factor of the variable” x, is proportional to λ(L)1/2, and the Reynolds number is proportional to λ(L)3/2.
Now, it is generally agreed that the effect of Δρ/ρa on the flow field is small, as long as the densimetric Froude number and other dimensionless numbers describing the source remain constant. As seen from Eq. 5, by increasing the value of Δρ/ρa at the source, the value of the Reynolds number of the model can be increased.
Similarly, it appears that the exit velocity and/or the diameter of the source in the model need not always be modelled exactly, as long as the equality of more significant dimensionless numbers is maintained, which makes it possible to further increase the Reynolds number of the model.
It appears, however, that when such relaxations are made solely on the basis of intuitive arguments and analogies, the determination of the required scaling criteria for simulation becomes an incomplete problem. It is, thus, not surprising that researchers have proposed different criteria for simulating identical problems. As a result, the accuracy of approximate fluid modelling, which varies from one problem to the other and is not necessarily uniform across each flow field, also depends on the choice of the scaling criteria for each problem.
Scaling Criteria for Frequently Simulated Flows:
Plume Rise in a Neutrally Stratified Atmosphere:
The trajectory, z=f(x), of a buoyant plume rising from a vertical stack in a neutrally stratified atmosphere is determined by the characteristics of the ambient flow and the initial properties of the plume. The ambient flow field can be described by a characteristic length, L, such as the height of the stack, a reference velocity U, the mass density of the ambient air ρa, and M; dimensionless parameters describing the relative flow characteristics, boundary conditions and fluid properties.
These parameters include the Reynolds number, Rossby number, and Prandtl number of the flow. The parameters describing the stack and the initial properties of the plume are: the exit velocity, W, the initial plume density, ρs, the initial specific weight deficiency, Δρg, the initial plume diameter, d, as well as Ni dimensionless parameters that describe the relative properties of the plume gases and their initial distributions at the stack, if these are not uniform.
It follows, from dimensional considerations, that the plume trajectory can be described by the following relation:
z/x = F{ρaU2/(AρgL), W/U, d/L, Δρ/ρa, Wd/v, Mi, Ni} …(6)
An exact simulation of the flow field and the plume rise requires that the values of all the independent dimensionless parameters appearing on the right-hand side of Eq. (6) be equal in the model and prototype. This requirement cannot be fulfilled even when one attempts to simulate only the ambient flow. However, the role of the Rossby number may, in many cases, be ignored. When the Reynolds number of the flow in the model is sufficiently large, its effect, as well as those of the Prandtl number and the Schmidt number, may also be neglected.
In such cases:
z/x*= F[ρaU2/(ΔρgL), W/U, d/L, Δρ/ρa] .…(7)
Equation 7 implies that the required criteria for simulating plume rise is the equality of the four dimensionless numbers on its right hand side, namely:
λ[ρaU2/(ΔρgL]=1, λ(W/U)=1, λ(d/L)=1 and λ(Δρ/ρa)=1 …(8)
Simulations that satisfy these criteria are called exact simulations, although they do not fully reproduce all the molecular effects.
Now, although Eq. 7 may be formulated in an infinite number of forms, for example:
z/x= F{U3L/[(Δρ/ρa)gWd2], W/U, d/L, Δρ/ρa}, …(9)
The equality of the dimensionless numbers in Eq. (7) secures the equality of those in Eq. 9 and in any other form of this general relationship. When the requirement λ(Δρ/ρa)=1 is relaxed the number of the dimensionless numbers that have to be matched is reduced to three. It is observed, however, that the set of three numbers one obtains by neglecting Δρ/ρa in Eq. 7 is not the same as the set which one obtains if it is neglected in. Eq. 9. This example demonstrates that the required criteria for approximate simulations cannot be determined solely by dimensional analysis. Indeed, different criteria have been used by different investigators for the simulation of plume rise, as shown in Table 1.
It may rightly be argued that the problem could be eliminated if the above assumption was confirmed in a careful tests, in which the other remaining dimensional parameters remained constant. Unfortunately, this is not the case. Supporters of the different criteria usually base their choice on partially intuitive arguments and a limited amount of experimental data.
Thus, until a comprehensive experimental verification program is carried out in relatively large-models, it would be difficult to rigorously prove which scaling criteria give more accurate simulations of a the plume rise, or any other similar phenomenon. It seems, however, that most researchers support the conclusion that approximate simulations of plume rise should ensure the equality of the dimensionless buoyancy flux and the dimensionless momentum flux of the source, which are the first numbers on the right hand side of Eq. (9).
Poreh and Kacherginsky (1981) have, thus, suggested, that only these two scaling criteria are required for approximate simulations, and that one should use a third condition X(W/U)=1, mainly to increase the Reynolds number of the flow in the model. Isyumov and Tanaka (1979), on the other hand, concluded that it is advantageous to use exact simulations even at the expense of somewhat reduced similarity of the overall flow region.
Plume Rise in Convective Boundary Layers:
The simulation of plume rise in a Convective Boundary Layer (CBL) is more difficult, because of the difficulties in simulating correctly the CBL itself and because the flow in the CBL is characterized by several velocity scales.
The breakthrough in the understanding of the nature of the CBL is primarily due to the water-tank experiments and numerical modelling in the Seventies by the joint works of Deardorff and Willis.
The averaged CBL is usually idealized as composed of several layers: The surface layer, where wind-shear plays a dominant role. The free convection layer, where wind-shear is no longer important but height z above the ground is a significant parameter. It usually extends to 0.1 Zi, where Zi is the thickness of the CBL.
The mixed layer, where the turbulence structure is independent of both height and shear and is primarily controlled by the convectively-generated turbulence. The interfacial layer, which separates the mixed layer and the usually stably-stratified air above.
The structure of the lower layers is best explained using the Monin-Obukhov (MO) similarity law. The buoyancy-induced local turbulent velocity scale w(z) is given by w(z)=(zσ)1/3, where σ is the buoyancy flux per unit area.
The mechanically generated turbulence in this layer is of the order of shear velocity, u*, and thus:
(w(z)/u*)3 = σz/u*3 = -z/(kLmo), …(10)
where Lmo,= -u*3/(kσ) is the MO Length and k=0.4 is von Karman’s constant. The MO similarity has been successfully used to formulate scaling criteria for wind- tunnel simulations of surface layers, as it secures the same ratio of w/u* for equal values of -z/Lmo in the model and the atmosphere.
One notes from Eq. 10 that the MO Length is also a measure of the thickness of the surface layer, as the mechanical turbulence in the CBL is dominant only in the layer z<ILmol. Thus, when -z/Lmo becomes large, the relative thickness of the surface layer decreases and the entire effect of the shear-generated turbulence on the structure of the CBL can be ignored. This is the basis for the convective scaling proposed by Deardorff (1970), which assumes that the turbulence characteristics of the CBL depend, primarily, on Zi and σ or, equivalently, on zi and the convective velocity scale, w*.
Which is defined as:
w*=(ziσ)1/3 …(11)
Water-tank simulations are then valid only when the role of the shear-produced turbulence is relatively small, which is usually the case for -zi/Lmo>10 or w*/u*>3. These conditions usually correspond to values of U/w*< 7, as it is usually assumed that u*=͠ 0.05 U. For rough surfaces, larger values of u*/U can be obtained, of the order of 0.1, and the effects of the mean wind and shear stresses would diminish only at values of U/w* <͠ 3.5.
It has also been suggested that surface roughness can affect the surface layer even when U/w* is small, as the large convective eddies induce local mean winds of random orientation and speed near the surface, which in turn produce shear and turbulent kinetic energy. These effects are not allowed for in either the convective similarity hypothesis or the M-0 similarity hypothesis. The convectively-mixed layfer similarity could also be affected by processes in the interfacial layer. For lack of space, such effects will be ignored in the following discussion.
Other important questions concerning possible effects of several parameters on the turbulent structure of the CBL and on the diffusion of buoyant plumes within this layer are still unanswered. Improvement of the state of the art depends on the availability of experimental data. Field data appears to be prohibitively expensive. Water-tank experiments, where both the mean motion and shear are missing, cannot answer some of these questions either.
On the other hand, it appears simulations in wind tunnels, where control of the convective and shear velocities, temperatures, gradients and the heat flux from the floor can be achieved, would be very helpful in depicting some of these effects that cannot be simulated in water tanks. However, their realization critically depends on the dimensions and the characteristics of these wind tunnels, and the choice of the scaling criteria for such simulations.
Obviously, these criteria should determine the scaling of the major characteristics of the CBL (U, u*, w*, and zi) and the characteristics of the buoyant emissions (W, Δρ, d, the momentum flux M, and the buoyancy flux B at the source). As the effect of Δρ/ρ in such simulations is neglected, one faces the problem of selecting the appropriate scaling criteria. However, this time, it is more complicated, as the CBL is characterized by at least two velocity scales, U and w*, rather than one. It will be assumed, for the moment, that u* is determined by U and that the effect of the interfacial layer can be neglected.
Meroney and Melbourne (1992), suggest that such simulations require the equality of:
MR = M/(ρU2 zi2), …(12)
where M is the momentum flux from the source, and of:
Frm = F/(U3d), …(13)
where F is the buoyancy flux from the source (proportionality constants in the definition of M and F will be ignored in this paper).
F*=F/(ziUw*2) …(14)
They noted, however, that the modified Froude number had been successfully used to characterize the motion of plumes in CBL. Clearly, unless a similarity of d/zi and w*/U is maintained, the equality of both Frm and F* is not secured. It is questioned by the author, whether an exact matching of d/zi is always essential for such simulations, as its value is usually a small number. The equality of w*/U might be desired, but it is clear from the success of the water-tank simulations, where U=0, that it is not really essential, certainly not for w*/U<0.1, unless an undistorted vertical/horizontal scaling of the motion in CBL is desired.
Melbourne et al. (1993), on the other hand, suggested to distinguish between two phases of diffusion. They proposed that similarity in the initial phase is secured by the matching of MR and;
F/(U3Zi). …(15)
For the second phase they proposed to match the value of MR and F*. These two requirements are satisfied simultaneously when a similarity of w*/U is maintained.
Poreh (1991) focused on wind-tunnel simulations of cases in which the effect of shear at ground level is significant, as other cases can be simulated in water- tanks. For such cases, it is essential to maintain the similarity of w*/u*. They proposed, however, to increase the ratio u*/U in the model by increasing the roughness of the wind tunnel. The distorted similarity of w*/U and of the vertical/horizontal scaling of the CBL, they suggested, should not effect the turbulent processes and would make it possible to examine the far field of diffusion in relatively short wind tunnels.
Lift-off of Buoyant Plumes:
The behavior of buoyant plumes from ground level sources is often similar to that of plumes from stacks. However, in many cases, the vertical momentum of the source is small and, in the presence of winds, the plume is carried downwind along the surface. It has been observed by Briggs (1973) and Meroney (1979), however, that at a certain distance from the source the buoyant plume lifts-off, as shown schematically in Fig. 1.
Since the ground level concentrations of pollutants from such sources decreases drastically downwind of the lift-off point, it is of great interest to determine whether and where lift-off occurs.
The results of only a few studies of lift-off have so far been reported. Perhaps, because the problem is also related to the behavior of accidental emissions from nuclear power plants. Both Meroney (1979) and Hall et al. (1980) have assumed that lift-off is controlled by the buoyancy flux from the source B, the wind speed U, and a suitable length scale L.
Thus, the dimensionless concentrations downwind the source were assumed to depend on B*=B/U3L:
C*=CUL2/Q=F[B/U3L] …(16)
Where Q is the strength of the source. An implicit requirement for simulation is that the Reynolds number of the model is sufficiently large. To satisfy this requirement, the buoyancy flux in the model should be increased. Since the maximum possible value of Δρ/ρa in wind-tunnel models, is of the order of 0.85, this is accomplished by increasing the exit velocity W.
In doing so, the momentum flux from the source, which is proportional to ρsQW, is increased. It is obvious that an increase of the vertical momentum flux from the source would augment the lift-off in the model. Poreh and Cermak (1988) showed, however, that even a horizontal momentum flux at the source, which discharges the buoyant fluid in the direction of the wind, critically affects lift-off.
Figure 2 shows the effect of the dimensionless horizontal momentum flux M*=ρsUs2d2/(ρaU2L2) on the dimensionless concentration profiles, C*, at a given distance downwind of the source (xm=1.0 m; x/δ=1.67, where δ is the thickness of the BL) for two values of the dimensionless buoyancy flux B*= B/U3L. The data shows that the plume stays closer to the ground for larger values of M*.
Figure 3 shows that the ratio of the ground level concentration, C(0), to the maximum concentration, Cmax, at a given distance downwind from the source (xm=1.5 m; x/δ=1.67) depends on the ratio B*/(M*1/2).
Large Area Fires and Heat Islands:
The mechanics of Large Area Fires (LAFs), whether forest fires or urban fires, the motion of fire plumes, the strength of the fire generated winds, and the interaction of fire plumes with atmospheric winds and circulation, have been studied intensively during the Eighties, when a threat of a nuclear war and the possibility of a Nuclear Winter were suggested. During that period, the possibility of simulating the flow field induced by LAFs in small-scale fluid models was investigated by Poreh (1985, 1986,1988). Now, it had been shown by Williams (1969) that an exact small scale simulation of all the processes that take place in fires is impossible.
Poreh et al. (1985) observed, however, that the thickness of the combustion layer in LAFs is very small, relative to the horizontal length scale of such fires. In such cases, they claimed, the flow induced by the fire is similar to the flow induced by an area source of buoyancy, and neither the thickness of the combustion layer nor the method by which the buoyancy is produced is of importance.
The above assumption implies that the velocity and temperature field above the combustion layer is determined by only two parameters: The convective buoyancy flux from the fire, B, or equivalently the buoyancy flux per unit area s, and the size of the fire, say the radius, R, for a circular fire.
Namely:
Ui(xi)/(σR)1/3=F(xi/R) …(17)
and
g'(xi)/(σ2/3R1/3)=B(xi/R) …(18)
The above universal functions are valid, of course, for large Reynolds numbers only.
Poreh (1991) suggested that the flow above buoyancy sources is turbulent when the Reynolds number:
σ1/3R4/3/v > 6,000 …(19)
In the presence of ambient winds (Ua). atmospheric vorticity (ω), and atmospheric stratification G=(dθ/dz)g/θ.
where θ is the potential temperature), the scaling of these boundary conditions should be:
λ(Ua)=λ(σ)1/3λ(L)1/3,λ(ω)=λ(σ)1/3λ(L)-2/3,and λ(G) = λ(σ)2/3λ(L)-4/3 …(20)
To model the effect of swirling on the plume, it is required that centripetal accelerations acting on the lighter-than-air plume, Vф2/r, where Vф, is the circumferential velocity, be scaled in the model as g’.
This is satisfied when:
λ(Δρ/ρa)= 1, or λ(σ)2= λ(L) …(21)
The question when may the above requirement be relaxed is of great importance. Such a relaxation is accepted in horizontal flows when the densimetric Froude number, U/(g’h)1/2, is smaller than unity.
Replacing U by Vф, g’ by ρVф,2/R and L by R one finds that for rotating flows, this requirement may be relaxed when:
Δρ/pa < 1 …(22)
Three possible methods of creating small-scale area sources of buoyancy have been used in previous studies.
The use of hot plates for simulating area fires was proposed by Nielsen (1965) and Long (1967). Parker et al. (1968) have used a hot plate to simulate the 335 m by 320 m experimental Flamebeau Fire. The primary disadvantage of generating the buoyancy flux in small-scale models by hot plates is that an unknown portion of the heat supplied to the plate, as high as 42%, is lost by radiation.
In addition, the size of the model must be very large and the surface temperature of the hot plate must be very high, to ensure a turbulent flow and sufficiently high velocities that can be readily measured. Close to the surface of a hot plate a conduction layer is formed, where heat transfer is controlled by the molecular diffusivity k. It can be shown that its relative thickness, hc/R is of the order of [(α3/σ)1/4]/R, where a is the thermal diffusivity. When Eq. (19) is satisfied, its value will be of the order of 0.001, and its effect on the rest of the flow can be neglected.
Small area sources of buoyancy can also be created by small fires. It is, however, necessary to ensure that the thickness of the combustion layer in the model is relatively small and that, at the same time, the induced velocity field is turbulent. Yokoi (1959) studied the temperature field above small-scale alcohol pool-fires and above a circular fire made out of many little wicks of alcohol lamps, which he termed discontinuous heat sources. Although the relative thicknesses of the combustion layers in these model-fires were not as small as desired, these fires produce a fair approximation of area sources of buoyancy.
Poreh et al. (1986) have modelled LAF by injection of helium through a porous plate at ground level. The thickness of the layer where the helium is mixed with less than six times air by mass, in such models, is relatively small, so that the effect of the value of Δρ of helium on the flow field can be assumed to be small. It has also been shown that the effect of the momentum flux in the models is limited to a very thin layer.
Figure 4 shows the distribution of the dimensionless parameter B along the vertical axis of various helium models and alcohol-fire models (The values of Bo denoted at the abscissa are for pure helium). The results support the basic thesis that the overall structure of the flow field above area sources of buoyancy-is determined by their size and intensity and is independent of the way this buoyancy is produced.
Now, it has been shown by Poreh (1992) that the flow and temperatures above urban heat islands are many times determined by the size and the buoyancy flux of the urban area. Thus, small scale models of LAF are also models of such heat islands. Using the results from LAF models, many new characteristics of heat islands were identified. It was also proposed that other types of heat islands could be simulated in small scale models, and the scaling criteria for such simulations were discussed.
Smoke Movement and Stack Induced Ventilation in Buildings:
The movement of smoke generated by fires in buildings is of considerable practical importance, as smoke is recognized as the major killer in fire situations. Smoke often migrates to building locations remote from the fire space, threatening life and damaging properties.
The movement of smoke also determines the response of alarm systems that use smoke or heat sensors. Now, the smoke movement is determined by a large number of parameters. For a given building configuration, the buoyancy flux generated by the fire is, usually, the most important parameter. The ambient wind speed, U, and its direction become important factors, however, for large wind speeds and relatively small buoyancy fluxes. The use of sprinkles, which cool the smoke plume, makes such cases quite frequent.
The prediction of smoke movement in buildings is usually done using simplified numerical models. Such models have basic shortcomings. Some of them may be overcome by small-scale physical models, that simulate the motion of the smoke in the building.
The principles of physical modelling of smoke movement in buildings have been discussed by Cannon and Zukoski (1976), Quintiere et al. (1988) and Poreh et al. (1992). It is clear from these studies that only approximate simulations of this movement is possible. The scaling criteria and shortcomings of such simulations will be reviewed below.
Assuming that the effective gravitational acceleration g = gΔρ/ρ and the velocity ui at each point are functions of the buoyancy flux B, a length scale L, the thermal diffusivity α, the Prandtl number, Pr=α/v, and the ambient wind speed U (and direction).
It may be written that:
g*=g’/(B2/3L-5/3)=F[U/(B1/3L-1/3), α/(B1/3L2/3),Pr], …(23)
The dimensionless velocity at each point, ui/(B2/3L-5/3), will also be a function of the same dimensionless variables. The number α/(B1/3L2/3) may be considered as a representative Peclet number of the heat flow. The Peclet and the Reynolds numbers in small-scale models cannot be matched with those in the prototype.
If it is assumed that the effect of both Re and Pr can be neglected, one may write that:
g*=F[U/(B1/3L-1/3)] …(24)
As it is impossible to maintain the same Reynolds numbers in the model and the prototype, the conductive heat transfer to the walls is not properly simulated. Clearly, the film resistance in the models will be larger than in the full scale building. Since loss of heat to walls may, in many cases, reduce the stack effect, small-scale models may give an over optimistic simulation of smoke removal by this effect.
For zero or small wind speed one finds that when a steady state is reached:
g*=g’/(B2/3L-5/3)= constant …(25)
For time dependent conditions, g* will be a function of the dimensionless time:
t*=t/(B-1/3L4/3). …(26)
Figure 5a shows measurements of temperature rise versus time in two simulations with different values of U and B but with equal values of B1/3L-1/3. Figure 5b shows the same data in dimensionless variables.
When Eq. (25) is valid, the simulation of the flow and temperature fields for a given geometry can be made at a reduced geometrical scale and a desired value of B. The way B is produced is of no significance. In other words, as in the case of LAFs, the fire is assumed to be source of buoyancy, which drives the flow and, theoretically, the experimental methods described earlier for generating buoyancy sources, can be used in such simulations.
Now, some of the heat flux produced by a fire is converted into a convective heat flux. A large portion of it, 30-40%, may be transferred to the structure or be lost by radiation. The same is true in small-scale models, in which the prototype fire is simulated by a small scale fire or a heat source. However, as the ratio of the various heat fluxes in such models is not the same as in the prototype fire, such models do not offer any advantage in this respect.
One should also note that the size of the combustion region could be an important factor that might effect smoke motion both in the prototype building and the model. This is particularly true if the height of the hall or room, where the fire burns, is relatively small. When the size of the fire decreases and/or the burning rate increases, the height of the combustion region increases. The volumetric flux at a given height z, which is an important parameter in the design of smoke control systems, will also depend on these parameters.
An implicit assumption in the above dimensional analysis is that Δρ/ρ in the model and prototype need not be equal to each other for correct simulation. The limitations of such a relaxation have been discussed earlier, and it appears that they are not very significant in the modelling smoke movement in building.
A clear limitation of such small models is that the flow through small openings and cracks in the inner and outer envelopes of the different spaces in the building, which have small Reynolds numbers, cannot be correctly simulated. To overcome this limitation, one could use a single orifice to model all the cracks at each wall of a given space.
The size of the orifice is determined so that the effective leakage area in the building is scaled to match the total effective leakage area of each wall in the model at the representative Reynolds number of the experiment. Clearly, the modelling of these flows is very rough, however, it is should be recalled that the estimate of the effective leakage areas in real buildings is very poor too.
Cannon and Zukoski (1976) have tried to augment the heat losses to the wall in the model by cooling the walls of the walls. Such a method is not be included in most physical models, both due to difficulties in its implementation and due to estimates that it is relatively small after the first phases of the fire and smoke spreading.
The ventilation and heat removal from industrial buildings are many times governed by the same mechanism as the motion of smoke. As suggested by Poreh et al. (1992) wind tunnel simulations of wind and buoyancy induced ventilation of such buildings is possible if the total buoyancy flux inside the buildings is known. The scaling criteria for such simulations are identical to those proposed above.
Conclusion:
It has been shown that various complex flow phenomena, which are created or affected by buoyancy sources, have been simulated in small-scale models. It appears, however, that most of these simulations are not exact, and that the required scaling criteria for such approximate simulations cannot be rigorously determined.
As a result, different criteria are being used by different investigators for simulating identical problems, and the accuracy of the simulations, which varies from one problem to the other and is not necessarily uniform across each flow field, also depends on the choice of the scaling criteria.
It has been concluded that only an extensive experimental study, aimed at evaluating the proposed criteria for each case, will be able to rigorously prove which of them minimizes the inaccuracies of approximate simulations.
Now, the question rises, whether one could really depend on results obtained in approximate simulations. Clearly, a universal approval cannot be given to all approximate simulations. However, it should be realized that such simulations have a basic quality, which is not always shared by other methods of investigation. They might not have the desired values of all the dimensionless numbers required for an exact simulation of the particular full-scale flow one would like to study.
On the other hand, they always depict the characteristics of a real flow, and satisfy all the relevant laws of physics. Thus, they can always be used for validation of numerical models that could be executed at the exact conditions of these physical models. Experience indicates, that their use for studying real life problems is also justified, as the boundary conditions of such problems vary over a very wide range.
It remains, however, our duty to carefully asses the accuracy of each approximate simulation and try to improve it.