Search

Transition boiling heat transfer was studied for the case of internal flow of high-pressure water. Transition boiling results were determined from measurements from 138 steady-state tests conducted in a temperature-controlled facility. Water flowed vertically upward inside a tube with inside diameter = 10.1 mm and vertical length = 13.1 m, as it was heated by liquid sodium flowing countercurrent in a surrounding annulus. The water parameter range of the experiments was pressure 7–15.3 MPa and mass flux 0.7–3.2 Mg/m2•s. A mathematical model was developed that predicted the transition boiling heat transfer coefficient well over the entire parameter range.

Thermal fluctuations were measured in the tube wall in the transition boiling zone of a full-scale LMFBR sodium-heated steam generator tube. The tube had an inside diameter = 10 mm, wall thickness = 2.90 mm, heated length = 13.1 m, and material = 2 1/4 Cr-1 Mo steel. Water flowed vertically upwards inside the straight tube, and sodium flowed counter-currently in a surrounding annulus. Results of thermal, spectral, and thermal stress analyses are presented for a test within the normal operating range of LMFBR steam generators. Results of other tests are presented that show the effects and sensitivity of sodium temperature and water pressure on the severity of the thermal fluctuations.

Critical heat flux (CHF) experiments were performed in the Steam Generator Test Facility (SGTF) at Argonne National Laboratory for application to liquid metal fast breeder reactor steam generators. The test section consisted of a single, straight, vertical, full-scale LMFBR steam generator tube with force-circulated water boiling upwards inside the tube heated by sodium flowing countercurrent in a surrounding annulus. The test section tube parameters were as follows: 10.1 mm i.d., 15.9 mm o.d., material = 2 1/4 Cr–1 Mo steel, and 13.1 m heated length. Experiments were performed in the water pressure range of 7.0 to 15.3 MPa and the water mass flux range of 720 to 3200 kg/m2˙s. The data exhibited two trends: heat flux independent and heat flux dependent. Empirical correlation equations were developed from over 400 CHF tests performed in the SGTF. The data and correlation equations were compared to the results of other CHF investigations.

Models are presented for the inclusion of transition boiling heat transfer in the thermal analysis of liquid-heated boiling water heat exchangers. A relation was developed from experimental data for the prediction of the quality change in the transition boiling region. This quality relation was used alone and in conjunction with a transition boiling heat transfer coefficient to formulate two successful models. Predictions of heat exchanger heat transfer, including the transition boiling models, were compared with experimental results for high-pressure water in the range 7–15.3 MPa over a mass flux of 0.7–3.2 Mg/m2s.

Conservation equations are derived for the motion of a small inert gas bubble in a large flowing liquid-gas solution subjected to large thermal gradients. Terms which are of the second order of magnitude under less severe and steady-state conditions are retained, thus resulting in an expanded form of the Rayleigh equation. The bubble dynamics is a function of opposing mechanisms tending to increase or decrease bubble volume while being transported with the solution. Diffusion of inert gas between the bubble and the solution is one of the most important of these mechanisms included in the analysis. The analytical model is applied to an argon gas bubble flowing in a weak solution of argon gas in liquid sodium. Calculations are performed for these fluids under conditions typical of normal and abnormal operation of a liquid metal fast breeder reactor (LMFBR) core and the resulting bubble radius, internal gas pressure, and mass of inert gas are presented in each case. An important result obtained indicates that inert gas bubbles reaching the core inlet of an LMFBR will always grow as they traverse the core under normal and extreme abnormal conditions and that the rate of growth is quite small in all cases.

Sodium superheat experiments were performed in a forced convection facility employing system parameters in the range of interest for application to loop and pot-type liquid metal cooled fast breeder reactors. The test section was representative of a single reactor fuel element with sodium flowing vertically upward in an annulus heated indirectly from the inside wall only. Steady-state operating parameters prior to a flow coast down approach to boiling included: velocity, 17 fps; heat flux, 7 × 105 Btu/hr-ft2; test section inlet, 600 deg F; test section outlet to plenum, 900 deg F; plenum, 15 psia at 900 deg F and 700 deg F. Other important system variables controlled included sodium inert gas content and system pressure-temperature history. The axial location of boiling initiation in the test section was measured. Five test series encompassing 33 test runs were performed. Applicable superheat results were compared to predictions of the pressure-temperature history model including inert gas effects.

More than one steady-state solution is shown to exist for the problem of steady-state heat transfer across the walls of a duplex tube when the initial prestress between the inner and outer tubes is sufficiently low. This determination was used in explaining the apparently erratic heat-transfer performance of prestressed duplex tubes in the steam generating system of the Experimental Breeder Reactor II. The importance of the results lies not only in showing that nonuniqueness of steady-state solution applies to more complex geometries than heretofore analyzed, but also in demonstrating that such multiple steady-state conditions appear in practical situations.

An analytical method is presented which extends the series solution of the Laplace and Poisson equations with irregular boundary conditions to multi-cell problems. The method employs a least-squares technique of satisfying the boundary conditions on the irregular boundaries and eliminates the use of a finite number of boundary points to satisfy these conditions. The technique is applied to the calculation of the fully developed temperature distribution of a constant-velocity fluid flowing parallel to a semi-infinite square array of circular nuclear fuel rods. The bounding wall of the array is located such that the flow area of the cell associated with the rod adjacent to the wall is different from the (equal) areas of all the other cells. The series solution is compared to a finite-difference solution for a sample case of two cells. The results for the semi-infinite array indicate that while the array temperature distribution is markedly affected by the difference in flow areas, the Nusselt numbers of the rods are relatively unaffected. Typical results are presented for a pitch-to-diameter of 1.2; the flow area of the first cell is 3.67 percent greater than the area of the other cells.

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.