The term “burnout” indicates a change in the boiling regime, the disturbance of contact between the liquid and the heated wall resulting in an abrupt drop of the heat transfer coefficient. If the surface heat flux is controlled (e.g., electrically or nuclear heated systems), burnout leads to an inordinate rise in the wall temperature. If there is a controlled temperature heat source (e.g., the tube is surrounded by hot fluid on the outside), the burnout is accompanied by a considerable reduction of heat flux carried away by the boiling fluid.
Burnout is the most important factor in designing steam generators for steam power and atomic power plants, systems for engine cooling, radio-electronic equipment, cryogenic systems and many other thermally stressed devices.
The mechanism for changing boiling regimes is rather diversified. Besides “burnout”, the terms “boiling crisis”, “departure from nucleate boiling (DNB)”, “critical heat flux (CHF)”, “maximum heat flux”, and “peak heat flux” are also used. The further term dryout suggests that the film of a liquid on the heated surfaces dries. The term burnout has received the widest acceptance.
The behavior of the wall temperature and the temperature of a liquid along the heated pipe ( = const) is shown in Figure 1. A cool liquid (TL(z = 0) < TSAT where TSAT is the saturation temperature) is supplied into the pipe, and a superheated steam leaves the pipe. Nucleate boiling begins in the pipe cross-section, where TWTSAT. After burnout occurs there exists a transition zone where an annular dispersed flow is replaced by a dispersed one. In the transition zone, drops of liquid fall out periodically onto the wall of the pipe. This is the zone of considerable pulsations of the wall temperature. After the transition zone, the liquid is concentrated in the flow core and does not come in contact with the wall.
In short pipes, not all the types of flow patterns shown in Figure 1 can be realized. Figure 2 illustrates how the burnout process differs with the rise in the vapor content of the flow with the motion along the vertical pipe.
(a) The mean-mass temperature of the flow is below the saturation temperature (Figure 2a). At large heat flows, the wall temperature can exceed the saturation temperature and in the boundary layer, bubbles are formed skipping over the heating surface. With the rise in heat flux, the number of bubbles increases and at the bubbles collapse together and form a continuous vaporous film. The burnout mechanism is approximately similar to the burnout in conditions of pool boiling (DNB). It usually occurs at the tube outlet, where the subcooling of the liquid relative to the saturation temperature is lowest. In the zone of film boiling, the flow presents a jet of cold on liquid separated from the wall by a continuous vaporous film. If x is close to zero, then a dispersed flow sets in.
(b) The slug or the plug flow (Figure 2b). The bubbles are formed on the wall and are entrained in the flow core. The bubbles are unevenly distributed along the flow section. At the boundary layer edge, the bubbles are accumulated. The burnout can occur as a result of evaporation of moisture in the boundary layer and of the formation of a vaporous film.
Dry spots on the wall formed as a result of film breakdown can cause burnout.
(c) Annular-dispersed flow. Steam generation occurs both as a result of evaporation on the surface of the film and vapor bubble formation on the wall. Moisture exchange between the film and the flow core takes place. The liquid is lost by the film due to boiling, evaporation from the film surface and separation of drops from the wave crests by action of the vapor. The film is filled up with moisture due to the fall-out of drops from the flow core. It thins along the heated pipe as the vapor content increases. Burnout occurs at the flow section in which the liquid flow rate in the film approaches zero.
(d) At large x, practically the entire liquid is concentrated in the flow core in the form of droplets. The wall is covered by a very thin film of liquid. Bubbles are not formed in the film; heat is removed by evaporation from the film surface. In this flow, are low and are determined by the intensity of droplets falling on the heated wall.
Burnout has been most thoroughly studied in water boiling. Here, depends on the flow’s vapor content (x), mass flux pressure (p) and the geometry of the channel. Typical dependencies (x) for fixed values of p and are given in Figure 3a, b.
As can be seen from the figures, the critical heat flux drops with the rise in x. The lines (x) showing different flow rates have a point of intersection, the point of inversion B (sometimes, this is a certain region rather than a point). To the left of the point, increases with the rise in ; to the right, decreases. Changes in the dependence of on can be explained by different mechanisms of burnout.
In case of departure from nucleate boiling (DNB), the increase of is to be followed by the increase of because bubble departure from the heated surface is easier. If the burnout occurs as a result of liquid film drying out (Dryout), the increase in corresponds to liquid entrainment from the wall. Therefore, the film flow rate becomes lower and is lower too.
Lines (xc) may be divided into different parts, with each of them corresponding to a certain burnout mechanism or a certain flow pattern. Thus, within pressure range 3–15 MPa and 500 < < 3000 kg/m2s, five different parts can be distinguished (Figure 3a). Part 1 (AB), DNB takes place. Part 3 line CD, the burnout is connected to the liquid film drying out (Dryout); the annular dispersed flow is replaced by a dispersed one. There is some transition part, BC between 1 and 3, which corresponds to slug or churn flows.
In part 5 (EF), tube surface is covered with a thin liquid film. The value of is determined by droplet deposition onto the surface from the flow core.
The transition zone Part 4 (DE) has a particularity. In this region, the moisture exchange between the film and the flow core becomes negligible and ceases. The burnout occurs because the liquid in the film dries out. According to experimental data under conditions of no moisture exchange, the dessication occurs either at one and the same value of x, or independently of , or in the narrow range of Δx. Zone 4 is plotted in coordinates (x) either by a vertical line or by a strongly inclined line. The vapor content at which the moisture exchange ceases is called the boundary quality vapor, xb.
At high pressures (15 < P < 20 MPa) and high mass fluxes (3000 < < 6000 kg/m2s), zone 4 practically disappears and Parts 1 and 5 fill each other (Figure 3b).
The character of the dependence (x) varies with changes in pressure. The point of inversion moves to the zone of higher x with increase in pressure. At pressure over 18 MPa, it disappears.
The gradually drops in absolute value, beginning with p = 1–2 MPa, with the rise in pressure.
Data for the influence of the tube diameter (D) on the value are contradictory. Most of the investigators believe that decreased with the rise in D. The influence of the diameter can be accounted for under the formula:
Here D0 = 8 mm, 4 < D < 20 mm, (D), (D0) is the critical heat flux in the pipe with diameter D and 8 mm.
Pipe length only slightly affects . In long pipes (L/D > 20), qw does not depend on length. In short pipes (L/D < 20), increases with the decrease in length. The method of treatment of the wall surface, and the thermophysical properties of materials used in heat and power engineering slightly affect the value. The oxidation of the wall material and a slight deposition of scale leave unaffected.
The distribution of vapor and liquid along the channel cross-section depends on the heat flux density. The complicated and ambiguous effect of the above parameters on can be inferred from the entrainment diagram shown in Figure 4 obtained by Benett et al. Here, the entrained liquid flux is treated as a function of quality x. The distribution of liquid between the film and the flow core in a fully developed adiabatic flow is shown by line 1. A redistribution of liquid between the film and the flow core (line 2) occurs in a heated channel. The burnout is observed in the flow section in which the liquid flow rate in the film equals zero (dryout point). If there is a nonheated section in the central part of uniformly heated pipe, then in this section the phase equilibrium will tend to restore. If a nonheated section (line 3) lies to the left form point M (line 3), then the amount of moisture in the film will decrease and the burnout will occur at smaller x. If a nonheated section is to the right of the point M (line 4), then the amount of liquid in the film in the nonheated section will increase and xc increases [see Hewitt and Whaley (1989)].
There exist several ways for accounting for the effect of nonuniformity of heating along the channel length on burnout. For instance, we can take into account the effect of the previously discussed parameters with the help of the influence function:
where qc0 is the critical density of heat flux with uniform heating; (z) is the local density of heat flux in the z section; w(ξ, z) = exp [(ξ – z)/Lr]/Lr is the influence function: Lr is the length of influence relaxation of those parameters. In case of a cosinusoidal profile, L ≥ D and x ≥ 0.2, Lr = 40 D.
There are a great many experimental data on critical heat fluxes on water boiling in pipes. Tables for and xc, which embrace practically the entire range of parameters p and ρw used in power engineering [see IVTAN (1980), Groeneveld et al. (1986)], have been compiled from experimental observations. Numerical relationships have also been suggested, but since these relationships are valid only for a small range of operating conditions and their accuracy is less than that of the tabulated data, the data given in the tables are preferred.
In case of nonuniform heating along the channel length, the critical heat output of the channel and the place of burnout can be determined as follows. The dependence = f(xc) for the given type of channel with the given rate and pressure (line ABC, Figure 5) is plotted on the basis of experimental data and design recommendations. Given the vapor content at the inlet, the profile of heat flux density is plotted versus vapor content (DEF). By gradually increasing the power delivered to the channel, the GHI profile can be plotted, which will be in contact with the line ABC. As can be seen from the figure, the burnout will occur at the point of contact H. The critical power of the channel will correspond to the GHI profile. The burnout margin can be determined as the ratio. However, in some cases, this procedure can lead to large errors. It may be better to use an analytical prediction [Hewitt and Whalley, (1989)].
Large values of and a high saturation pressure for water present certain difficulties for investigation. Therefore, in order to simplify the experiment in designing new steam-generating device, it is advisable to perform simulations using refrigerants. Such refrigerants have lower latent heats and thus require less power. In this simulation, geometric and hydrodynamic similarity must be observed. If the same vapor content xW =xF is maintained at the outlet of the channel with water and of the channel with the refrigerant fluid, and the subcooling at the channel inlet is taken to be proportional to the heat of vaporization KΔh = Δhw/ΔhF = hlg,w/hlg,F, then the lengths of boiling sections for both heat transfer agents will be the same. The pressure of water and freon is chosen such that the condition pL,W/pG,W = pL,Ref/pG,Ref is fulfilled. These conditions make it possible to fulfill the conditions of hydrodynamic similarity, to obtain the equality of volume rate and true vapor contents in channels with water and refrigerant. Experimentally, the mass velocity ratio is been selected so that the condition is met.
An annular channel can be heated either from one side (inner or outer surface) or from both sides. Usually, the critical densities of heat flux for unilateral and bilateral heatings are about the same, all other factors being equal. The dependence (xc) is similar to that for circular pipes. The effect of annular gap width within the range of 1–4 mm on is small. At smaller gaps, is reduced. An influence of the channel length is observed for L/DH < 100. The occurrence of eccentricity reduces .
In nuclear power reactors, the fuel pins are combined into clusters. Inside the cluster, the position of the rods is fixed by means of spacer grids. A two-phase flow moves along parallel “subchannels” formed by the adjacent pins. In this case, boiling differs from that in a single-pipe because of constant exchange between the coolant paths. The quantity depends on such factors as the heat flux distribution, the relative position of the fuel pins, the conditions of coolant input, etc. It is natural that the critical conditions will be achieved first in the subchannels with higher local and with high local vapor content of the flow.
There are a number of computer programs available which allow the estimation of the local parameters of the flow and the critical power of the cluster. In order to define local parameters of the flow the entire space between the fuel pins and the shell surrounding them is divided into parallel subchannels. The boundaries of the channels are drawn through the centers of the adjacent pins or around separate pins. The cluster is divided axially into several sections. The axial and radial changes of enthalpy and of mass velocity are determined by solving the conservation equations of mass, energy and momentum for each subchannel. The conservation equations take into account the transverse transfer of the coolant, and also the exchange of heat and momentum between subchannels due to turbulent mixing. The local conditions are compared with available empirical relationships for . The solutions are made for a series of regimes, with power supplied to the cluster increasing in succession. The power at which the local critical heat flux is reached is determined.
Full-scale tests are carried out in order to develop and validate the design procedures. The cluster of heat-releasing fuel elements is simulated by a set of hollow cylinders, through which electric current passes. By adjusting the distribution of the electric resistance of the cylinders, nonuniform heat release along the length and the radius of the reactor core, and also the different stages of fuel burnup can be replicated. The wall temperature is measured by a sensing transducer. By gradually increasing power supply the initial temperature rise in the wall due to burnout is detected and the burnout location, the local parameters of the flow and the local heat flux at the burnout location are determined as well as the total power of the assembly.
A wide range of coolants, from helium (TSAT = 4 K) to sodium (TSAT = 1150 K), has been studied. The boiling of nitrogen, hydrogen, freon, ammonia, nitrogen tetraoxide, potassium, cesium and other fluids have been included. It was found that for any fluid, as with water, burnout or the DNB or dryout types can be observed. By virtue of a considerable difference in the thermal properties of the fluids, only limited relationships can be obtained, which only describe burnout for a finite number of fluids and for a narrow range of parameters.
In boiling, the dependence (xc) for helium is about the same as of water. There exists an inversion area in which the different lines obtained for (xc) intersect. With an increase in pressure, xiknv increases. The existence of a vertical section xb of the dependence (xc) is noted as in Figure 3b. The size of the vertical section decreases with increases in pressure and mass velocity. At pressures above 0.16 MPa and mass velocities exceeding 160 kg/cm2s, the vertical section on the graph (xc) degenerates and the dependence is smooth.
Burnout with boiling liquid metals has a number of characteristic properties. Metals (sodium, potassium, cesium) differ from other heat transfer agents in their high boiling temperature. The pressures used are usually not high (P < 1 MPa). For boiling, considerable superheating of fluids is usually required. After boiling, an annular dispersed fluid flow sets in practically immediately. A thin fluid film moves along the wall of the channel. Due to the high thermal conductivity of liquid metal, the superheat of the liquid is negligible and gas bubbles do not form in the film. The processes of evaporation and droplet deposition from the flow core take place on the surface of the film. The burnout occurs due to dryout of the film.
In order to increase and to avoid overheating of the wall, an additional inflow to the wall must be ensured. Use can be made of flow swirl, which enhances the deposition of drops from the flow onto the wall because of centrifugal forces. Spiral twisted metal tapes placed at the end of the zone of developed boiling are used for this purpose. The twisted tapes operate well at high quality where the high vapor velocity gives rise to larger centrifugal forces. An alternative method for increasing the dryout quality is to use coiled tubes. Here, the droplets are deposited by centrifugal action and the liquid film is spread around the wall under the influence of circumferential shear stress and pressure gradient. By optimizing the ratio of coil diameter to tube diameter, burnout qualities near 100% can be obtained.
Flow turbulization by transverse or spiral corrugations, fins and inverts may also be used. For instance, in an annular channel with the inner surface heated, turbulizing projections may be attached to the channel. The projections release the liquid from the outer wall into the flow core, thus ensuring a strong inflow to the heated wall. In nuclear fuel pin assemblies, the spacer grids exert a turbulizing effect. They enhance the mixing of the two-phase flow and the levelling-off of the enthalpy between adjacent subchannels.
In order to increase both and the heat transfer coefficient, porous coatings can be applied to the wall. The coatings are made by sintering metal particles (copper, bronze, steel powders are used) to the wall. Porous coatings are most efficient in boiling a subcooled liquid. A more than twofold increase in w has been observed. Porous coatings can be used in cases when, in boiling, no scale is formed on the wall or no contaminants clog up the pores.
Hewitt, G. F. and Whalley, P. B. (1989) Vertical Annular Two Phase Flow, Chapter 2 of Multiphase Science and Technology, Vol. 4 (Ed. G. F. Hewitt, J. M. Delhaye and N. Zuber), Hemisphere Publishing Corporation.
IVTAN-I-57, (1980) Recommendation for Critical Heat Flux Transfer Calculation for Water Boiling in Tubes, Moscow
Groeneveld, D. C., Cheeng, S. C., and Doan, T. (1986) AECI-40 Critical Heat Flux Transfer Lookup Table, Heat Transfer Eng., Vol. 7, p. 46.
Groeneveld, D. C. and Leung, L. K. H. (1989) Tabular Approach for Predicting CHF and Post-Dryout Heat Transfer, Proc. NURETH-4, Vol. 1, pp. 109–114, Karlsruhe, FRG.