3.1. Experiments with naturally-induced flow

From the results of the commissioning tests with pumped flow presented in preceding section, it was clear that the test facility was operating satisfactorily. Accordingly, a detailed programme of experiments was carried out with naturally-induced flow and uniform wall temperature. The power control and measurement system was used to achieve uniform values of wall temperature ranging from 60 to 300°C. Corresponding experiments with uniform wall heat flux were also performed keeping the total heat input the same as in the uniform wall temperature experiments. The matrix of conditions covered was as follows.

Wall temperature Tw (°С)	60	80	too	150	200	250	300
Corresponding wall heat flux qw (W/m2)	91.0	171.4	229.7	428.0	640.0	899.4	1130.0

Uniform heat flux boundary condition Re=29085 Qw=1910 W/m 2

FIG. 4(a). Commissioning test results with uniform heating for forced convection

Uniform heat flux boundary condition
Re= 10261 Qw=913 W/m2

FIG. 4(b). Commissioning test results with uniform heating for mixed convection with impaired heat transfer

In these experiments the flow rate induced through the system increased systematically as the thermal loading was increased. The variation of dimensionless flow rate (characterised by Reynolds number) with dimensionless heat loading (characterised by Grashof number) is shown in Figures 5(a) and 5(b) for the uniform wall heat flux and uniform wall temperature cases, respectively. The physical properties in these dimensionless parameters were evaluated at the inlet temperature and the characteristic dimension used was the tube diameter.

FIG. 5. Relationship between flow rate and thermal loading for naturally induced flow with (a) uniform heat flux, (b) uniform wall temperature

Figures 6(a) to 6(f) show the axial distributions of Nusselt number obtained in these experiments. The flow rates induced through the test section were used to determine the Reynolds numbers shown on the figures. In each case a curve is presented for forced convection with uniform heat flux evaluated at the Reynolds number for that case using the equation of Petukhov et al [5]. The main points to note are:

(i) The experimental values of Nusselt number all follow a similar general pattern. They lie well below the curves for forced convection calculated using the Petukhov equation.

(ii) The values of Nusselt number for the uniform wall temperature case are slightly lower than those for uniform wall heat flux in spite of the fact that the flow rates induced through the system are greater.

(iii) The Nusselt number curves for forced convection calculated using the Petukhov equation decrease slowly at a steady rate in the thermally fully developed region. This is due to the fact that the Reynolds number decreases as the bulk viscosity increases due to the rise of bulk temperature.

Figures 7(a) and 7(b) show the experimental results plotted in terms of local values of local Nusselt number, Nux, and Grashof number, Grx (evaluated using the distance x from the start of heating as the characteristic dimension). The fluid properties were evaluated at the local bulk temperature, calculated knowing the air temperature at inlet, the heat input and the flow rate of air induced through the system. As can be seen, this method of presenting the results does enable a good correlation of the data to be achieved.

The main conclusions which can be drawn from the naturally-induced flow tests are as follows:

Even though the flow rates achieved were such that in the absence of buoyancy influences the flow would have been turbulent, the effectiveness of heat transfer was seriously impaired in relation to that expected for conditions of turbulent forced convection at those flow rates. It is clear that under the conditions of all the experiments performed the turbulence structure was

significantly modified by buoyancy. In the experiments with uniform wall temperature the heat transfer behaviour did not change much as the temperature was increased. Furthermore, the behaviour was very similar in the corresponding experiments with uniform wall heat flux. Clearly, the results obtained in this study highlight the need for care to be exercised in the design of systems for cooling a steel containment shell by naturally-induced flow of air so as to ensure that the kind of buoyancy-influenced conditions which prevailed in the present experiments are avoided.

FIG. 6(b). Heat transfer results for naturally induced flow with Tw = 100°C

3.2. Experiments with pumped flow

After completing the naturally-induced flow experiments reported in the preceding sub-section, a programme of pumped flow experiments with uniform wall temperature was carried out. The conditions of heat transfer achieved in those experiments varied from forced convection with negligible influences of buoyancy to mixed convection with very strong influences of buoyancy. Inlet Reynolds number was varied in steps from about 30,000 down to 3,500 and values of wall temperature from 75°C to 300°C were covered. Again, corresponding experiments were performed with uniform heat input.

FIG. 7. Correlation of heat transfer results for naturally induced flow with (a) uniform wall heat flux, (b) uniform wall temperature

Some sample results for a wall temperature of 150°C are shown in Figures 8(a) to 8(d) along with the corresponding ones for uniform heat flux. The Reynolds numbers at inlet were about 29,000, 10,500, 5100 and 3500. The main points to note are:

(i) The heat transfer mechanism at the highest Reynolds number is turbulent forced convection. As can be seen from Figure 8(a), the results for the uniform heat flux case lie very close to the curve calculated using the Petukhov equation. Thus there are no significant influences of buoyancy. As expected, the results for uniform wall temperature lie slightly below those for uniform wall heat flux.

(ii) At the Reynolds number of 10,500, Figure 8(b), the mechanism of heat transfer is mixed convection with serious impairment of heat transfer due to influences of buoyancy on turbulence. The effect is much greater for uniform wall temperature than for uniform heat flux. The results for uniform wall temperature are similar to those obtained for naturally-induced flow with a wall temperature of 200°C (Figure 6(d)).

(iii) In the case of the experimental results shown in Figures 8(c) and 8(d) the conditions are those of mixed convection with progressively stronger influences of buoyancy leading to recovery and enhancement of heat transfer. Concentrated non-uniformities appear in the distributions of Nusselt number as a consequence of the development of the flow along the tube under the influence of strong buoyancy forces.

Figures 9(a) and 9(b) shows results from the pumped flow experiments for a large value of x/D presented in terms of Nusselt number ratio and buoyancy parameter. Experimental data for naturally induced flow are also included (in these cases the Reynolds number was evaluated using the value of flow rate induced through the system). The impairment of heat transfer which develops with increase of buoyancy parameter is strikingly apparent in both cases, as also is the recovery of heat transfer (in relative terms) when buoyancy influences become strong enough to restore turbulence production. As can be seen, when presented in this form the naturally-induced flow results map directly onto the pumped flow results.

Although the results obtained in the pumped flow experiments confirm that the general pattern of behaviour in buoyancy-aided mixed convection is the similar with uniform wall temperature and uniform wall heat flux, the impairment of heat transfer which develops with onset of buoyancy influences does occur more readily in the case of uniform wall temperature. The results highlight the fact that care is needed in the design of containment cooling systems to avoid conditions under which buoyancy-induced impairment of heat transfer might occur.