Turbulent heat mixing of a heavy liquid metal flow in the MEGAPIE target geometry—The heated jet experiment

The MEGAPIE target installed at the Paul–Scherrer Institute is an example of a spallation target using eutectic liquid lead–bismuth (Pb⁴⁵Bi⁵⁵) both as coolant and neutron source. An adequate cooling of the target requires a conditioning of the flow, which is realized by a main flow transported in an annular gap downwards, u-turned at a hemispherical shell into a cylindrical riser tube. In order to avoid a stagnation point close to the lowest part of the shell a jet flow is superimposed to the main flow, which is directed towards to the stagnation point and flows tangentially along the shell.The heated jet experiment conducted in the THEADES loop of the KALLA laboratory is nearly 1:1 representation of the lower part of the MEGAPIE target. It is aimed to study the cooling capability of this specific geometry in dependence on the flow rate ratio (Q_main/Q_jet) of the main flow (Q_main) to the jet flow (Q_jet). Here, a heated jet is injected into a cold main flow at MEGAPIE relevant flow rate ratios. The liquid metal experiment is accompanied by a water experiment in almost the same geometry to study the momentum field as well as a three-dimensional turbulent numerical fluid dynamic simulation (CFD). Besides a detailed study of the envisaged nominal operation of the MEGAPIE target with Q_main/Q_jet = 15 deviations from this mode are investigated in the range from 7.5 ≤ Q_main/Q_jet ≤ 20 in order to give an estimate on the safe operational threshold of the target.The experiment shows that, the flow pattern establishing in this specific design and the turbulence intensity distribution essentially depends on the flow rate ratio (Q_main/Q_jet). All Q_main/Q_jet-ratios investigated exhibit an unstable time dependent behavior. The MEGAPIE design is highly sensitive against changes of this ratio.Mainly three completely different flow patterns were identified. A sufficient cooling of the lower target shell, however, is only ensured if Q_main/Q_jet ≤ 12.5. In this case the jet flow covers the whole lower shell. Although for Q_main/Q_jet ≤ 12.5 the flow is more unstable compared to the other patterns most of the fluctuations close to the centerline are in the high frequency range (>1 Hz), so that they will not lead to severe temperature fluctuations in the lower shell material. In this case the thermal mixing occurs on large scales and is excellent.For flow rate ratios Q_main/Q_jet > 12.5 complex flow patterns consisting of several fluid streaks and vortices were identified. Since in these cases the jet flow does not fully cover the lower shell an adequate cooling of the MEGAPIE target cannot be guaranteed and thus temperatures may appear exceeding material acceptable limits.All conducted experiments show a high sensitivity to asymmetries even far upstream. A comparison of the numerical simulation, which assumed a symmetric flow, with the experimental data was due to the experimentally found asymmetry only partially possible.     

Single and multiple discharge from a stratified two-phase region through small branches

Experimental data are presented for the mass flow rate and quality during single, dual and triple discharge from a stratified air–water region through small side branches (d=6.35 mm) installed on a semicircular wall. Dimensions of the semicircular wall and branches were chosen such that interaction among the branches is possible under certain flow conditions. All the branches were adjusted to have the same hydraulic resistance (R=1000 (kg m)^−1/2) and for the cases of dual and triple discharge, the same pressure drop ΔP was imposed across all active branches. Tests were conducted at two system pressures P₀=316 and 517 kPa and the pressure drop was varied within the range 40≤ΔP≤235 kPa. Data analysis is presented with emphasis on the effect of wall curvature and also the effect of additional discharges on the flow from a certain branch. The present data can serve as benchmark data for testing numerical safety codes and they should guide future research on the flow from two-phase headers.     

An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes

From a theoretical assessment of extensive critical heat flux (CHF) data under low pressure and low velocity (LPLV) conditions, it was found out that lots of CHF data would not be well predicted by a normal annular film dryout (AFD) mechanism, although their flow patterns were identified as annular–mist flow. To predict these CHF data, a liquid sublayer dryout (LSD) mechanism has been newly utilized in developing the mechanistic CHF model based on each identified CHF mechanism. This mechanism postulates that the CHF occurrence is caused by dryout of the thin liquid sublayer resulting from the annular film separation or breaking down due to nucleate boiling in annular film or hydrodynamic fluctuation. In principle, this mechanism well supports the experimental evidence of residual film flow rate at the CHF location, which can not be explained by the AFD mechanism. For a comparative assessment of each mechanism, the CHF model based on the LSD mechanism is developed together with that based on the AFD mechanism. The validation of these models is performed on the 1406 CHF data points ranging over P=0.1–2 MPa, G=4–499 kg m⁻² s⁻¹, L/D=4–402. This model validation shows that 1055 and 231 CHF data are predicted within ±30 error bound by the LSD mechanism and the AFD mechanism, respectively. However, some CHF data whose critical qualities are <0.4 or whose tube length-to-diameter ratios are <70 are considerably overestimated by the CHF model based on the LSD mechanism. These overestimations seem to be caused by an inadequate CHF mechanism classification and an insufficient consideration of the flow instability effect on CHF. Further studies for a new classification criterion screening the CHF data affected by flow instabilities as well as a new bubble detachment model for LPLV conditions, are needed to improve the model accuracy.     

Toughness investigation on simulated weld HAZs of SQV-2A pressure vessel steel

In order to get detailed information about weld HAZs toughness of SQV-2A steel and determine the optimum welding and heat treatment parameters, the toughness of simulated CGHAZs (coarse grained heat affected zone) and CGHAZs (intercritically reheated CGHAZ) were systematically investigated. The influence of tempering thermal cycles on weld ICCGHAZs toughness was clarified. The effect of post weld heat treatments (PWHT) on weld CGHAZs toughness was also determined. The results showed that high toughness (absorbed energy >200 J) of weld HAZs could be achieved by selecting the optimum welding and PWHT parameters (cooling time Δt_8/5: 6–40 s, PWHT: 893 K, 3.6–7.2 ks). Tempering thermal cycles with peak temperature of above 573 K could remarkably improve the toughness of deteriorated ICCGHAZs and reduce the hardness, when cooling time Δt_8/5(2) of the reheating thermal cycle was 6 s, which implies that welding of SQV-2A without PWHT is possible, provided that low heat input welding is adopted and welding procedure is correctly arranged. Metallography and fractography revealed that M–A constituents in weld HAZs played an important role in controlling weld HAZ toughness.     

Computations of post-trip reactor core thermal hydraulics using a strain parameter turbulence model

Coolant flows in the cores of nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be modified strongly from the forced convection condition by the action of buoyancy, in particular exhibiting impaired levels of heat transfer with respect to corresponding forced convection cases. The heat transfer performance of these ‘mixed convection’ flows is investigated here using two physically distinct eddy viscosity turbulence models: the recent ‘strain parameter’ (or k––S) model of Cotton and Ismael [A strain parameter turbulence model and its application to homogeneous and thin shear flows. Int. J. Heat Fluid Flow 19 (1998) 326] is examined against the benchmark low-Reynolds-number k– model of Launder and Sharma [Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1 (1974) 131]. Comparison is made with three sets of heat transfer data for ascending mixed convection flows, and it is demonstrated that both turbulence models are generally successful in resolving the Nusselt number distributions occurring along the lengths of mixed convection flow passages. The mechanisms by which the strain parameter model generates reduced turbulence levels, and hence impaired heat transfer rates, is explored in comparison with a fourth set of experimental data for mixed convection flow profiles.     

Experimental study of heat transfer enhancement in narrow rectangular channel with longitudinal vortex generators

In order to enhance heat transfer in cooling channels of plate-type fuel elements in reactor cores, the experimental research is conducted on the heat transfer and pressure drop in horizontal narrow rectangular channels with mounted longitudinal vortex generators (LVGs) for water flow with Prandtl number Pr = 4–5. The parameters examined were: flow velocity from 0.5 to 3.4 m/s, Reynolds number from 3000 to 20,000, heat flux 43.6 kW/m², maximum system pressure 1.3 atm, and viscosity ratio from 1.05 to 1.2. It is found that the LVGs could greatly improve the heat transfer rate by 10–45%. Thermal performance is compared under three constraints, i.e., identical mass flow rate (IMF), identical pressure drop (IPD) and identical pumping power (IPP). It is found that the heat transfer performance of channel with LVGs on two sides are better than those on one side. Application of LVGs to plate-type fuel element is a potential technique for next generation advanced nuclear reactors concepts.     

Linear analysis of flow instabilities in an open two-phase natural circulation loop

This paper describes the instability maps for the excursive and the density wave instabilities which may occur in an open two-phase natural circulation loop. Criteria for the excursive and the density wave instability were obtained from the steady loopwise momentum equation and the characteristic equation, respectively. A simple, one-dimensional two-phase homogeneous equilibrium flow was assumed. Heat flux, inlet subcooling, inlet- and exit-line restrictions, condenser liquid level, loop height and the heater section length were taken as parameters. The results were summarized on the instability map in the plane of N_pch(Fr)^1/2 vs. N_sub. The stable region appears at the lower left part of the map, bounded by two boundaries; the excursive instability region appears at the upper right part of the map. From the map, it can be readily confirmed that the dynamic stability criterion automatically satisfies the excursive stability criterion. Effects of parameters on the stability of the system were also discussed in this paper. The upper boundary of the stable region was compared with the experimental results reported previously.     

A bulk tungsten divertor row for the outer strike point in JET

In the frame of the ITER-like wall project, a new row of divertor tiles has been developed which consists of 96 bulk tungsten load-bearing septum replacement plates (LB-SRP). Exposed to the outer strike point for most ITER-relevant, high triangularity configurations, they shall be subject to high power loads (locally 10 MW/m² and above). These conditions are demanding, particularly for an inertially cooled design as prescribed. The expected erosion rates are high as well as the risk of melting, especially with transients and repetitive ELM loads. The development is also a real challenge with respect to the inevitable excursions of the tungsten material through the so-called DBTT, ductile-to-brittle transition temperature.A lamella design has been selected to fulfil the requirements with respect to the thermo-mechanical and electromagnetic loads during disruptions (∂T/∂z ≤ 5 × 10⁴ K/m vertically, induction rate of change ∂B/∂t ≤ 100 T/s, and I_halo ≤ 18 kA/module). Care is taken to act on refractory metals solely with compressive forces to a large extent. The dedicated clamping concept is described. Results of a test exposure to an electron beam around 70 MJ/m² substantiate the resort to ‘high temperature’ materials like – among others – high-grade Nimonic^® alloys, molybdenum or ceramic coatings.     

Experimental and numerical investigations of the warm-prestressing (WPS) effect considering different load paths

The effect of warm prestressing has been investigated representative for the core weld metal of the RPV Stade. Model experiments on CT specimens show a significant rise of effective fracture toughness K_eff after warm prestressing and the conservative WPS hypothesis, ‘no failure, if ∂K_I/∂t≤0’, is verified. Partial unloading and reheating show no influence on the effective fracture toughness K_eff. The magnitude of the WPS effect as a function of warm prestress level and temperature, path of unloading and cooling can be predicted using a modified Beremin model with temperature dependent parameters. It is shown that the Weibull stress is an appropriate crack tip loading parameter for decreasing load paths.     

Critical flow and spurious solutions Part II. The case of n equations

This paper discusses the mathematical models used as a basis for the calculation of critical conditions in two-phase flow. In practice, solutions are obtained with the aid of discretized versions of such models. It has now been established that the portrait of solutions in the phase space of any analytic model does not stand in a one-to-one relation to the map of solutions of any discretized version of such a model. As a result, computer outputs may develop spurious solutions. Branches of such spurious solutions often depart from the correct analytic solution in a haphazard manner, and bear no relation to the correct solution. Such degenerate solutions do not differ from their correct counterparts by merely containing acceptable numerical or truncation errors, but fail to fit the correct solutions even approximately. In the case of the most common analytic models used in two-phase flows through channels of varying cross-sectional areas, spurious solutions develop when the correct solution passes through or close to the saddle point in phase space. The paper examines two modes of obtaining critical-flow solutions. In some cases, a steady-state version (∂/∂t = 0) of the more general model is used. In other cases, the full equation (∂/∂t ≠ 0) is used, and the solution contains a transient but converges to the steady-state mode. This paper shows that the implied critical cross-section locations are identical in either mode of operation. The reason for the occurrence of spurious solutions is found in a term which assumes the indeterminate singular form 0/0 in the steady-state version of the model. By a suitable transformation, it is shown that this term is also present in the factor of ∂σ/∂t in the time-dependent version. It has been shown earlier that solutions passing through the singular point can be obtained with the aid of the theory of dynamical systems. In order to exclude the possibility of the appearance of spurious solutions, the numerical code, in either version, must be so arranged as to start the integration with the singular point.     

Some problems for bundle CHF prediction based on CHF measurements in simple flow geometries

A comparison of critical heat flux (CHF) fuel bundles data with CHF data obtained in simple flow geometries was made. The base for the comparison was primary experimental data obtained in annular, circular, rectangular, triangular, and dumb-bell shaped channels cooled with water and R-134a. The investigated range of flow parameters (pressure, mass flux, and critical quality) in R-134a was chosen to be equivalent to modern nuclear reactor water flow conditions (p=7 and 10 MPa, G=350–5000 kg (m² s)⁻¹, x_cr=−0.1–1). The proper scaling laws were applied to convert the data from water to R-134a equivalent conditions and vise versa. The effects of flow parameters (p, G, x_cr) and the effects of geometric parameters (D, L) were evaluated during comparison. The comparison showed that no one simple flow geometry can be used for accurate and reliable bundle CHF prediction in wide range of flow parameters based on local (critical) conditions approach. The comparison also showed that the limiting critical quality phenomenon is unique characteristic for each flow geometry which depends on many factors: flow conditions (pressure and mass flux), geometrical parameters (diameter or surface curvature, gap size, etc.), flow obstructions (spacers, appendages, turbulizers, etc.) and others.     

A flow boiling critical heat flux correlation for water and Freon-12 at low mass fluxes

An empirical correlation has been developed for calculating critical heat flux (CHF) at low mass fluxes for vertical upflow in uniformly heated tubes. The correlation is based upon dimensionless groups. It compares favourably with experimental CHF data for both Freon-12 and pressurized water. When solved iteratively in conjunction with the heat balance equation, an overall mean ratio of predicted to experimental CHF of 0.986 was obtained with a root means square (r.m.s.) error of 7.0%, for the 233 low flow rate data sets examined.The boundary between the high flow rate correlation developed in earlier work and the proposed low flow rate correlation can be specified by a dimensionless factor δ₁. For values of δ₁ greater than 0.07, the low flow correlation is valid whereas for values less than 0.07 the high flow correlation applies.Development of this correlation and a means of defining its range of validity enables the prediction of CHF levels to be made over an increased range of coolant flow conditions. This is important in the analysis of postulated loss-of-coolant accidents in water-cooled nuclear reactors.     

Numerical investigation of boiling regime transition mechanism by a Lattice–Boltzmann model

A numerical study has been performed to investigate the hydrodynamic aspects of the pool boilingon horizontal-, vertical- and downward-facing surfaces. The FlowLab code, which is based on a Lattice–Boltzmann (LB) model of two-phase flows, is employed. Macroscopic properties, such as surface tension (σ) and contact angle (β), are implemented through the fluid–fluid (G_σ) and fluid–solid (G_t) interaction potentials. The model is found to express a linear relation between the macroscopic properties (σ, β) and microscopic parameters (G_σ, G_t). The simulation results on bubble departure diameter appear to have the same parametric dependence as the empirical correlation. Hydrodynamic aspects of two-phase flow regime transition mechanism are investigated for different surface–coolant configurations. Results of the LB simulation clearly demonstrate that not only the bubble nucleation site density (related, e.g. to the heater surface condition and heat fluxes), but also the surface position have a profound effect on the flow regime (pool boiling) characteristics. The results of the LB simulation of hydrodynamics of two-phase flow on the horizontal surface provide the pictures quite similar to the experimental observation for saturated pool boiling. Two mechanisms of flow (boiling) regime transition on the vertical surface are predicted for the local bubble coalescence at bubble generation site and the downstream bubble coalescence. On the downward-facing surfaces, friction between bubbles and the surface wall is found to significantly enlarge the bubble size prior the bubble slip upwards. This behavior is responsible for the earlier bubble coalescence, and therefore, lowers the maximum heat removal rate, in a similar regime of nucleate boiling on a downward-facing surface.     

Critical heat flux in a vertical tube at low and medium pressures. Part II — new data representation

An analysis of the physical processes taking place in a dispersed-annular flow which govern dry-out type CHFs has been carried out. The analysis has shown that the number of variables required to describe the critical phenomena can be reduced by the introduction of a new parameter: the length over which dispersed-annular flow takes place, L_dan. In this case only, for a given tube diameter, pressure and mass flux, the critical heat flux may be expressed in terms of a single variable: L_dan. A correlation which may be used to determine this length has also been developed. The representation of the CHF data obtained at low pressures in terms of the coordinate system (L_dan, q″_cr) has shown that the dispersion of the data about the regression curves is considerably reduced as compared with the traditional presentation of the critical heat flux as a function of the thermodynamic quality at the end of the heated length.     

MHD flow past a semi-infinite flat plate with heat transfer

Exact numerical solutions to the boundary layer similarity equations of MHD flow and heat transfer past a semi-infinite flat plate of an incompressible viscous fluid have been presented. The velocity of the fluid U and the magnetic field H₀ at a distance from the plate are both assumed to be uniform and parallel to the plate which is considered as isothermal. Velocity, magnetic and temperature fields have been shown graphically whereas the numerical values of ƒ′(0) and {−θ′(0)} are entered in tables. We observe that both ƒ′(0) and {−θ′(0)} decrease with increasing S (magnetic field parameter) and increase with increasing λ (ratio of magnetic diffusivity and viscous diffusivity).     

PWR annulus thermal hydraulics important to analysis of pressurized thermal shock

Analysis of plume mixing in the annulus of a pressurized water reactor (PWR) are presented. The plume mixing analysis is based on a simple two-dimensional model that accounts for the surrounding flow and confinement. A correlation for entrainment is presented and comparison with experiment is made.Mixed convection resulting from downflow between parallel heated plates is studied experimentally. The experimental system used to obtain the data is described with the scaling rationale for choosing the working fluid. Heat transfer results are presented in terms of a Nusselt number and a correlation is given. Results show an enhancement in heat transfer with increasing Gr_Dh/Re_Dh² due to an increase in turbulence intensity associated with the buoyant wall layer. The correlation obtained for Gr_Dh/Re_Dh² < 2.29 was found to be Nu_Dh/Nu_Dh,0 = 1 + 2.93 (Gr_Dh/Re_Dh²)^0.54, where where Nu_Dh,0 is given by the Dittus-Boelter correlation. Use of this correlation for Gr_Dh/Re_Dh² > 2.29 is not recommended due to an observed flow bifurcation in this neighborhood.     

Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality

Based on the one-dimension two-phase drift flow model, the numerical simulation of two-phase flow stability characteristic on the test loop (HRTL-5) for 5 MW heating reactor (developed by the Institute of Nuclear and New Energy Technology of Tsinghua University, Beijing) is performed with and without coupled point neutron kinetics. The density wave oscillation instability is analyzed in the system under low pressure at 1.5 MPa and low steam quality less than 10%. The effect of inlet subcooling and heating flux on the system instability is simulated under the system pressure P_sys = 1.5 MPa. The numerical results show that there exist two instability inlet subcooling boundaries at different heat flux. The numerical results show good agreement with the experimental results on HRTL-5 without consideration of point neutron kinetics. If coupled with point neutron kinetics, the system will exhibit little difference on instability boundaries from that without considering the nuclear characteristics. But the amplitude and the phase of the oscillation of the thermal hydraulic parameters of the system will be somehow affected in unstable zone if the system is coupled with point neutron kinetics.     

Heat flux on limiters in low-q discharges

Heat flux on the Doublet III limiters was measured with an infrared camera and thermocouples during low-q discharges. The total heat load to the limiters increases with in both Dee and circular plasmas. The peak heat flux on the limiters in low-q discharges of q_a^* ≈ 2 is ≈ 2 times higher than that in high-q discharges of q_a^* ≈ 4. Since a low-q discharge is essential in order to have a high-β tokamak reactor in the future, higher heat flux on the limiters may be an inevitable problem. It is proposed that the increase in peak heat flux during low-q discharges can be reduced by modification of the limiter to an asymmetric shape.     

Novel porous media formulation for multiphase flow conservation equations

Multiphase flows consist of interacting phases that are dispersed randomly in space and in time. An additional complication arises from the fact that the flow region of interest often contains irregularly shaped structures. While, in principle, the intraphase conservation equations for mass, momentum, and energy, and their initial and boundary conditions can be written, the cost of detailed fluid flow and heat transfer analysis with explicit treatment of these internal structures with complex geometry and irregular shape often is prohibitive, if not impossible. In most engineering applications, all that is required is to capture the essential features of the system and to express the flow and temperature field in terms of local volume-averaged quantities while sacrificing some of the details. The present study is an attempt to achieve this goal by applying time averaging after local volume averaging.Local volume averaging of conservation equations of mass, momentum, and energy for a multiphase system yields equations in terms of local volume-averaged products of density, velocity, energy, stresses, and field forces, together with interface transfer integrals. These averaging relations are subject to the following length scale restrictions:

dℓL,