Investigation of the cooling of hot walls by liquid water sprays

Abstract

An experimental study was conducted for the heat transfer from hot walls to liquid water sprays. Four full cone, swirl spray nozzles were used at different upstream pressures, giving mass fluxes impinging on the wall, G, from 8 to 80 kg m⁻² s⁻¹, mean droplet velocities, U, from 13 to 28 m s⁻¹ and mean droplet diameters, D, from 0.4 to 2.2 mm.

A target consisting of two slabs of beryllium–copper alloy, each 4×5 cm in size and 1.1 mm thick, was electrically heated to about 300°C and then rapidly and symmetrically cooled by water sprays issuing from two identical nozzles. The midplane temperature was measured by a fast response, thin-foil thermocouple and the experimental data were regularized by Gaussian filtering.

The inverse heat conduction problem was then solved by an approximation of the exact Stefan solution to yield the wall temperature T_w and the heat flux q_w transferred to the spray at temperature T_f. As a result, cooling curves expressing the heat flux q_w as a function of T_w−T_f were obtained. The single-phase heat transfer coefficient h and the maximum heat flux q_c were found to depend upon the mass flux G and the droplet velocity U, while the droplet size D had a negligible independent influence. Simple correlations for h and q_c were proposed.

Introduction

Cooling hot surfaces by liquid sprays is a very effective process, which may provide heat fluxes in excess of 10⁷ W/m², and thus is widely used in many industrial fields like metallurgy [1] , microelectronics [2] , nuclear safety [3] and aerospace engineering [4] .

Experimental techniques used for heat measurements can be classified in two categories: steady state and transient methods.

In steady state experiments, heat transfer rates are derived from a thermal balance between the (usually electric) power input into an appropriate sample and the heat transferred to the spray. Measurements are conducted over times which are large compared to the time constants of the system. The application of steady state techniques is severely limited by the maximum attainable power densities; for example, a 4×5 cm metal slab cooled from both sides by a heat flux of 10⁷ W/m² would require an electric power of 40 kW to be kept at a constant temperature! Moreover, in power-controlled systems it is practically impossible to maintain steady state conditions in the unstable region of the heat transfer curve (transitional, or partial film, boiling) . Because of these limitations, steady state methods have usually been confined to investigations involving low heat transfer rates.

In transient experiments, the target is typically heated to a uniform high temperature and then rapidly cooled by the spray while the temperatures at one or more locations within the sample are recorded. The surface heat flux and temperature can be calculated from the raw experimental data by various methods, usually involving smoothing and solving an inverse heat conduction problem. Transient techniques are the only viable ones when large heat flow rates are involved, and thus have been most commonly employed in real-scale spray cooling research.

Transient spray cooling tests are usually conducted under the assumption that, despite the time-dependent conditions of the measurements, the relation between wall temperature and wall heat transfer rates is the same that would be observed under steady state conditions. This is justified by the fact that the time constants characterizing the impact, spreading and vaporization of an individual droplet are usually much smaller than the time constants of the overall cooling transient.

For any given fluid the measured heat transfer rate is a function of wall and fluid temperatures, local spray mass flux G, droplet velocity U and size D, and nature and finishing of the cooled surface. An extensive review of theoretical and experimental results for liquid spray cooling up to the late Seventies is given, for example, by Bolle and Moreau [5] .

More recently, Choi and Yao [6] studied heat transfer to horizontal sprays. Typical values of the hydrodynamic parameters were G = 0.3–2 kg m⁻² s⁻¹, U = 3–4 m s⁻¹ and D = 0.5 mm. Maximum heat fluxes of up to 2×10⁶ W m⁻² were measured for wall temperatures of ∼140–160°C, while the Leidenfrost point temperature was about 250°C. The influence of air flow on heat transfer in pneumatic sprays was also discussed.

Bernardin et al. [7] assessed the influence of surface roughness on water droplet impact history and heat transfer regimes; they also presented high quality photographic records of the droplet spreading, taken at 1 ms intervals. In this study, a single stream of droplets was produced; the mass flux did not exceed a fraction of kg m⁻² s⁻¹, yielding maximum cooling rates of the order of 10²°C s⁻¹ and maximum heat fluxes well below 1×10⁶ W m⁻². The maximum heat flux was attained at temperatures of 105–110°C, while the Leidenfrost point temperature varied between 150–200°C. In a subsequent paper [8] , the same authors presented more detailed results for droplets impacting on a polished surface and discussed the features of the boiling curve and the way of obtaining it from time-temperature series.

In both the above studies, the Biot number was well below one, so that the target could be assumed to be isothermal at each instant (cooling transients typically lasted more than 30 s) , and no inverse heat conduction problem had to be solved.

Similar remarks hold for the work of Sawyer et al. [9] , who also considered a single stream of droplets and presented a correlation for the critical heat flux as a function of the droplet Weber number and Strouhal number (dimensionless impact frequency) . The mass flux did not exceed 1–2 kg m⁻² s⁻¹; maximum heat fluxes were found to be of the order of 5×10⁶ W m⁻² once adjusted for the actual wetted area after droplet spreading, and were attained at wall temperatures of only ∼120°C.

On the whole, most of the experimental studies presented so far have focused on relatively low mass flow rates or on the film boiling heat transfer regime (wall temperature above the Leidenfrost point T_L) , while data on nucleate boiling and single-phase heat transfer at high mass flow rates are comparatively scarce.

On the contrary, the present investigation focused on the latter conditions; mass fluxes up to 80 kg m⁻² s⁻¹ were considered, giving wall heat fluxes in excess of 10⁷ W m⁻² and cooling rates above 10³°C s⁻¹, while the wall temperature never exceeded 250–270°C (which, according to the above literature results, is close to the typical value of the Leidenfrost point temperature) . The study was motivated by previous research on the influence of rapid cooling on the structure and properties of polymeric films [10] , a subject of importance in connection with the injection moulding of macromolecular materials.