J. D. Jackson, J. Li

University of Manchester, United Kingdom

Abstract. A fundamental study is reported of heat transfer from a vertical heated tube to air which is induced naturally upwards through it by the action of buoyancy. Measurements of local heat transfer coefficient were made using a specially designed computer-controlled power supply and measurement system for conditions of uniform wall temperature and uniform wall heat flux. The effectiveness of heat transfer proved to be much lower than for conditions of forced convection. It was found that the results could be correlated satisfactorily when presented in terms of dimensionless parameters similar to those used for free convection heat transfer from vertical surfaces provided that the heat transfer coefficients were evaluated using local fluid bulk temperature calculated utilising the measured values of flow rate induced through the system. Additional experiments were performed with pumped flow. These covered the entire mixed convection region. It was found that the data for naturally-induced flow mapped onto the pumped flow data when presented in terms of Nusselt number ratio (mixed to forced) and buoyancy parameter. Computational simulations of the experiments were performed using an advanced computer code which incorporated a buoyancy-influenced, variable property, developing wall shear flow formulation and a low Reynolds number k~e turbulence model. These reproduced observed behaviour quite well.

1. INTRODUCTION

Convective heat transfer from the outside surface of the steel containment vessel of a pressurised water reactor to a flow of air induced upwards by buoyancy through the space between the vessel and an external concrete shell has been proposed as a passive method of removing heat from the containment following a severe accident. Whilst there is no doubt that conditions of turbulent flow could be produced by this means, it is probable that the effectiveness of the heat transfer process would be poor. In view of the limited flow rate likely to be achieved, the heat transfer process within the passage will be buoyancy-influenced as well as buoyancy-driven. The mechanism of heat transfer will therefore be mixed free and forced convection. Published work on mixed convection heat transfer in vertical passages has been reviewed in a number of papers (see, for instance, Reference [1]). Some surprising trends have been identified. In the case of upward flow in a heated vertical passage, buoyancy aids the motion but contrary to expectation the values of heat transfer coefficient achieved can be lower than for conditions of turbulent forced convection. This is because the turbulence in the boundary layer is modified through the action of buoyancy with the result that the flow takes on the characteristics of one at lower Reynolds number. Impairment of heat transfer builds up gradually as the buoyancy influence is caused to become stronger, either by increasing the heat loading or reducing the flow rate. Eventually a very sharp reduction in the effectiveness of heat transfer is found to occur. With further increase of buoyancy influence, the process of heat transfer recovers. In contrast, for downward flow in a heated tube buoyancy opposes the motion, turbulence is increased and heat transfer is enhanced. The physical mechanism by which turbulent heat transfer is modified through the action of buoyancy influences in vertical passages was first identified by Hall and Jackson [2]. The contrasting influences on heat transfer for upward and downward flow are well described by a simple semi-empirical model of mixed convection developed by Jackson and Hall [3]. Figure 1 shows the predictions of that model for the case of a uniformly heated tube. These are found to be in good agreement with observed behaviour (see Reference [1]).

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It is of interest to consider whether impairment of heat transfer would be encountered under the conditions likely to be achieved in a buoyancy-driven flow system of the kind which has been proposed for passively cooling a nuclear reactor containment vessel. In this connection, a further matter needs to be considered. Most of the experimental studies of mixed convection reported to date have been carried out with a thermal boundary condition of uniform wall heat flux. However, in the case of a severe accident in a pressurised water reactor, where steam is released from the core into a steel containment vessel and is condensing on its inside surface, the vessel will take up a uniform temperature. Since the nature of the thermal boundary condition could certainly affect the process of heat transfer to the air, there is a need to consider whether the behaviour with uniform wall temperature will be similar to that with uniform wall heat flux.

The study reported here using a non-uniformly heated test section which can operate at uniform temperature was undertaken to clarity these matters. This naturally-induced cooling experiment (NICE) formed part of the DABASCO project funded by the European Commission to provide an experimental data base for containment thermal hydraulic analysis (see Reference [4]).

The experimental facility used in the present study is shown in Figure 2. The test section, which was made from stainless steel tube of inside diameter 72.9 mm and wall thickness 1.63 mm, is suspended vertically in a space of height 15 m. It can be used for experiments with either naturally-induced flow or pumped flow.

In the case of naturally induced flow, the entry box is absent and air passes from the laboratory into the bellmouth intake and upwards through an unheated flow development section of length 3 m and a heated section above it of length 6 m before discharging at the top. Motion occurs simply as a result of heat being applied to the test section. The velocity at inlet is measured using a calibrated hot film probe mounted in the centre of the bellmouth intake.

In the case of pumped flow, air is supplied to the entry box at the bottom of the test section by a blower and then flows upwards through the test section. The mass flow rate can be measured using a metering nozzle installed at the exit. The hot film probe was calibrated against this flow metering nozzle. Wall static pressure tappings are provided at the top and bottom of the heated section. The pressure difference is measured using a high precision electronic micro­manometer.

Numerous thermocouples attached to the outside of the heated length of the test section enable the wall temperature distribution to be measured in detail. The heated length is well lagged on the outside with pre-formed thermal insulation of low thermal conductivity to minimise heat transfer to the surroundings. The small loses which do occur can be accurately accounted for using data from calibration experiments which were performed at the commissioning stage. Heat can be applied to the test section either uniformly or non-uniformly by means of 40 separate, individually-controlled heaters distributed along its length. These were made using proprietary heater cable which was wound tightly around the outside of the stainless steel tube. Electrical power is supplied to the heaters from the mains via variable auto-transformers through the specially designed computer-based power control and measurement system shown in Figure 3. This supplies power to each heater at a rate needed to maintain the tube at a specified temperature at that location and also enables the power to be measured. The power is controlled by allowing a proportion of the half cycles of the incoming AC supply to pass to the heater. For each of the 40 heaters there is a control signal generator and a zero-crossing solid state relay. The former generates a control signal which enables the latter to pass a programmable number of half cycles from the supply to the heater during a specified time interval of 0.16 s. The signal generators are connected to a computer via a PC interface. The computer can write a number to each of the 40 signal generators under the action of software. The power to each heater is controlled by these numbers. Knowing this number, the voltage of the incoming supply and the electrical resistance of the heater, the power generated can be calculated. In operation, the computer reads temperatures using the Intercole data acquisition system. It then compares each wall temperature with a pre-set value, calculates a new number using the PID technique and sends it to the corresponding signal generator. The power supply system can also be operated in such a manner that a specified distribution of heat input is applied to the test section. A Pentium PC connected to a 208 channel data acquisition system is used for signal collection and processing. The software package which is used to drive the data logger and the power control and measurement system was developed and tested ‘in house’ using Visual Basic under the Windows 95 environment.

Initially, commissioning tests were performed on the test facility using the pumped flow arrangement to demonstrate that everything was operating satisfactorily. Friction factors determined from pressure drop measurements made under conditions of isothermal flow through the test section were compared with values calculated using the well-established correlation equation of Blasius for fully developed turbulent flow in a smooth tube. The maximum discrepancy was less than 6%.

Local values of Nusselt number were determined at various locations along the tube from experiments performed under conditions of forced convection with uniform heating. In Figure 4(a) the results are compared with the distribution of Nusselt number calculated using the established empirical correlation equation of Petukhov et al [5]. As can be seen, the agreement is very satisfactory.

Results from a mixed convection experiment with uniform wall heat flux are shown in Figure 4(b). The Reynolds number was about 10,000. Under such conditions heat transfer was found to be strongly impaired due to the influence of buoyancy. It can be seen that the local values of Nusselt number lie well below the curve for forced convection calculated using the Petukhov equation. The observed behaviour is very similar to that found in an earlier study by Li [6] using a uniformly heated test section of similar dimensions (see Jackson and Li [7]).