Axial Heat Flux Profiles Research Articles

Numerical investigation of two-component single-phase natural convection and thermal stratification phenomena in a rod bundle with axial heat flux profile

The most numerical investigations of the thermal-hydraulic phenomena following the loss of the residual heat removal capability during the mid-loop operation of the pressurized water reactor were performed according to simplifications and are not sufficiently accurate. To perform more accurate and more reliable predictions of thermal-hydraulic accidents in a nuclear power plant using computational fluid dynamics codes, a more detailed methodology is needed. Modelling results identified that thermal stratification and natural convection are observed. Temperatures of lower monitoring points remain low, while temperatures of upper monitoring points increase over time. The water in the heated region, in the upper unheated region and the pipe region was well mixed due to natural convection, meanwhile, there is no natural convection in the lower unheated region. Water temperature in the pipe region increased after a certain time delay due to circulation of flow induced by natural convection in the heated and upper unheated regions. The modelling results correspond to the experimental data. The developed computational fluid dynamics methodology could be applied for modelling of two-component single/two-phase natural convection and thermal stratification phenomena during the mid-loop operation of the pressurized water reactor or other nuclear and non-nuclear installations at similar conditions.

Development of a dimensionless rod-bundle CHF correlation based on stepwise regression method, Part II: determination of correction factors accounting for the effect of unheated guide tube and non-uniform axial heat flux profile

Correlation for rod-bundle critical heat flux (CHF) is of vital importance for design and assessment of a Pressurized Water Reactor (PWR). In our previous study, the basic form of a dimensionless rod-bundle CHF correlation has been developed based on stepwise regression with CHF data obtained in test bundles of uniform axial heat flux. It proves that stepwise regression is an effective method to develop simple, but reliable CHF correlation consisting of only dimensionless parameters with rigorous physical meanings. As a continuation of the previous investigation, revision of the basic form was conducted. Dimensionless correction factors accounting for the cold-wall effect due to unheated guide tube and the effect of non-uniform axial heat flux were developed. For the data set of 486 rod-bundle CHF points obtained in 7 test bundles, the average ratio of the measured to predicted CHF is 1.002 with a standard deviation from the mean of 5.51%.

Wall Heat Loads in a Cryogenic Rocket Thrust Chamber During Thermoacoustic Instabilities

A subscale, research rocket thrust chamber operating with cryogenic oxygen and hydrogen exhibits self-excited transverse-mode instabilities with amplitudes of more than 80% of the steady combustion chamber pressure (peak-to-peak) for some operating conditions. During unstable combustion, an increase in the integral heat flux into the water-cooled combustion chamber walls of 20–40% with respect to stable conditions was experienced. A model was derived to predict changes in the axial heat flux profile considering only the dependence of flame length on the amplitude of transverse acoustic oscillations. The model predicts an increase in heat flux in the upstream part of the chamber by up to a factor of 7. This drastic increase is in agreement with past observations of rocket engine failures due to instabilities, in which the structural damage is commonly observed on the faceplate and the walls adjacent to the injection plane. The model also predicts a peak increase in integral heat flux of up to about 25%. While falling short of the peak experimental value of 40%, it nevertheless suggests that flame length is the dominant influence on the distribution of thermal loads in this study.

Effect of Wall Temperature Profile Inputs on Thermal Hydraulic Characteristics in Long Vertical Steam Generator Tube

Flow boiling phenomenon in long vertical tubes at high pressure is of great importance in nuclear and thermal power plants. These tubes are associated with several complexities such as flow instabilities, flow-induced vibrations, pressure drop, dry out etc. which may lead to tube fatigue/damage (responsible for severe plant accident and safety issues). Therefore, precise modeling of complete flow boiling phenomenon (single phase liquid to single phase vapor including two-phase flow boiling region) is necessary to design boiler tube and to avoid complexities. Most of the work carried out in literature mostly deals with modeling of particular heat transfer region of the tube. The present work, effect of wall temperature profile inputs on the thermal hydraulic characteristics and pressure drop in 23 m long steam generator (SG) tube at 172 bar pressure has been studied. Wall temperature profile (TP) is given as input by two different ways. The TP-1 is obtained from DESOPT one-dimensional computer code. Linearly increasing TP-2 is given based on shell side bulk fluid temperatures. In our recent article, a new methodology for modeling of complete flow boiling of long vertical tube has been developed, the vertical tube is divided into four sections based on flow patterns (which are decided in terms of vapor fraction value) to model the complete flow boiling process. Simulations were carried out at 20 % and 60 % designed heat duties. The heat transfer coefficient and vapor fraction results with TP-1 shows shift in the peak in positive direction as that of TP-2. Also, TP-2 shows extra small peak in axial heat flux and heat transfer coefficient distribution profile. The magnitude of predicted pressure drop for both the temperature profiles is comparable. Overall, axial distribution profiles of thermal hydraulics parameters such as vapor fraction, heat transfer coefficient etc. showed almost same trend for both the temperature profile inputs.

Development of a dimensionless rod-bundle CHF correlation based on stepwise regression method, Part I: determination of the basic form with CHF data obtained with uniform axial heat flux profile

Accurate prediction of rod-bundle critical heat flux (CHF) is a main challenge in thermal-hydraulic design and safety assessment of Pressurized Water Reactor (PWR). The most widely applied approach is empirical correlation developed based on rod-bundle experiments carefully tested with geometry and power distribution representative to PWR working conditions. The standard procedure is to correlate the experimentally obtained CHF values as empirical functions of local thermal-hydraulic conditions obtained with subchannel analysis. However, up-to-date empirical correlations developed according to this manner are in general quite complicated with a number of dimensional coefficients and correction factors with less or non-physical meanings. In this study, stepwise regression method was used to develop a novel, dimensionless rod-bundle CHF correlation covering typical PWR working conditions. First, various dimensionless parameters affecting CHF were selected as candidate independent variables. With stepwise regression, the form and coefficients of the proposed CHF correlation were dynamically optimized and determined.

Applicability of one-body model to predict thermal distribution in spent nuclear fuel pool

An assumption system with a one-body model of spent nuclear fuel (SNF) assemblies was developed to predict the thermal distribution in the spent fuel pool (SFP) in the absence of external cooling system. It was based on the three-dimensional (3D) thermal hydraulic behaviour computed using the computational fluid dynamic (CFD) software, Fluent 18.0. This study aims to determine the applicability of the one-body model (average decay heat) by comparing it with the individuals-body model (variation of decay heat) computation results. The thermal distribution for both models were compared and evaluated, neglecting other effects such as position of the SNF assemblies, decay heat, and axial heat flux profile. It was found that the one-body model was applicable to predict the thermal distribution of the SFP during loss of active cooling system with error less than 1°C.

On nonlinear dynamics of density wave oscillations in a channel with non-uniform axial heating

A few nonlinear dynamics (Hopf bifurcations and limit cycles) of density wave oscillations of a two-phase flow channel are studied in this work. The effects of different non-uniform axial heat flux profiles (found to be a key factor) on the aforesaid non-linear stability behavior of the system are shown which is missing in existing studies. The novel outcomes of this study are presented by the change in Hopf bifurcation phenomena as the heat flux pattern and other design parameters are varied even though the total heat rate remains same. The innovative aspect of this study can be explained by the use of a nodalized reduced order model (NROM). The time-dependent spatial variations of the flow variables (enthalpy and quality) are approximated in-line to the provided heat flux profiles and corresponding steady state solutions. On one hand, this scheme is capable of analyzing both linear and nonlinear stability characteristics of the system over a wide range of axial heat flux profiles. On the other hand, in this model the node positions are defined in such a way that they vary automatically during the system evolution as per the provided heat flux profile. Hence, it acts as an auto-adaptive scheme and helps to minimize the computational effort required to achieve significant accuracy to capture the state variable variations. A few unique findings of the present work are as follows: i) although non-uniform axial heat flux is more linearly stable compared to uniform axial heat flux profile, it is less non-linearly stable. ii) single humped axial heat profiles are more linearly stable than double humped profiles, but they become less non-linearly stable.

Analysis of local bifurcations in a channel subjected to non-uniform axial heating

The effect of non-uniform axial heating on density wave oscillations of a two-phase flow channel is studied. This study becomes relevant in view of designing and modelling of nuclear reactor heat removal systems as several reactor fuel rods (Boiling Water Reactors) exhibit non-uniform axial heat flux profiles. In this work a Nodalized Reduced Order Model (NROM) has been developed The unique feature of the model is that, using this model the stability behaviour of two-phase flow systems with a wide range of axial heat flux variations (single humped and double humped) can be studied. In addition to these, the model behaves as an auto-adaptive scheme, where the mesh sizes between consecutive nodes automatically vary during the system evolution according to the provided shape of axial heat flux. This helps to minimize the computational effort required to achieve significant accuracy to capture the state variable variations. The effects of single humped and various double humped axial heating profiles on local bifurcation have been studied. It has been observed in this study that in addition to the linear stability characteristic the nonlinear stability behaviour (depicted by the position of generalized Hopf points and occurrences of limit cycles) also changes significantly as the axial heat flux changes from uniform to non-uniform even though the total heat rate provided remains same. Moreover, a generalized description of the cause due to which these changes occur in stability behaviour of the system is also presented.

Analysis of flow induced density wave oscillations in the CANDU supercritical water reactor

In this paper, a 1-D thermal-hydraulic model, THRUST, is developed to simulate and analyze the CANDU supercritical water reactor (SCWR) from the thermodynamic point of view without considering the effect of neutronic coupling. THRUST, where a characteristic-based finite difference scheme is used, is validated against the available numerical results. The model is, then, used for the analysis of the CANDU SCWR with a primary focus to determine the conditions for potential density wave oscillations. Extensive numerical studies are performed to obtain the marginal stability boundary in the operating regime of the reactor. The effect of various parameters, such as mass flow rate, operating pressure, axial heat flux profile, local pressure drop coefficient, and friction factor, on the stability thresholds of the reactor have been investigated.

Reduction of angle splitting and computational time for the finite volume method in radiative transfer analysis via phase function normalization

The commonly implemented splitting of solid angles to ensure scattered energy conservation in the finite volume method does not exactly conserve phase function asymmetry factor after directional discretization, leading to significant changes in scattering effect for radiative transfer analysis in highly anisotropic scattering media. In addition, use of a large number of split sub-angles results in drastic increases in computational CPU time and computer memory. The phase function normalization approach considered in this study is found to guarantee accurate conservation of both scattered energy and asymmetry factor simultaneously after directional discretization as well as depress solid angle splitting, vastly reducing the computational convergence time with improved accuracy. As a test, radial and axial radiative heat flux profiles in a scattering cylinder generated both with and without the phase function normalization are compared among different levels of angle discretization and splitting as well as with the discrete-ordinates method. The effects of changes in optical thickness, angular resolution, scattering albedo, and phase function approximation are examined.

Thermal Aspects of Uranium Carbide and Uranium Dicarbide Fuels in Supercritical Water-Cooled Nuclear Reactors

Supercritical water-cooled nuclear reactors (SCWRs) are a Generation IV reactor concept. SCWRs will use a light-water coolant at operating parameters set above the critical point of water (22.1 MPa and 374°C). One reason for moving from current Nuclear Power Plant (NPP) designs to SCW NPP designs is to increase the thermal efficiency. The thermal efficiency of existing NPPs is between 30% and 35% compared with 45% and 50% of supercritical water (SCW) NPPs. Another benefit of SCWRs is the use of a simplified flow circuit, in which steam generators, steam dryers, steam separators, etc. can be eliminated. Canada is in the process of conceptualizing a pressure tube (PT) type SCWR. This concept refers to a 1200-MWel PT-type reactor. Coolant operating parameters are as follows: a pressure of 25 MPa, a channel inlet temperature of 350°C, and an outlet temperature of 625°C. The sheath material and nuclear fuel must be able to withstand these extreme conditions. In general, the primary choice for the sheath is a zirconium alloy and the fuel is an enriched uranium dioxide (UO2). The sheath-temperature design limit is 850°C, and the industry accepted limit for the fuel centerline temperature is 1850°C. Previous studies have shown that the maximum fuel centerline temperature of a UO2 pellet might exceed this industry accepted limit at SCWR conditions. Therefore, alternative fuels with higher thermal conductivities need to be investigated for SCWR use. Uranium carbide (UC), uranium nitride (UN), and uranium dicarbide (UC2) are excellent fuel choices as they all have higher thermal conductivities compared with conventional nuclear fuels such as UO2, mixed oxides (MOX), and thoria (ThO2). Inconel-600 has been selected as the sheath material due its high corrosion resistance and high yield strength in aggressive supercritical water (SCW) at high-temperatures. This paper presents the thermalhydraulics calculations of a generic PT-type SCWR fuel channel with a 43-element Inconel-600 bundle with UC and UC2 fuels. The bulk-fluid, sheath and fuel centerline temperature profiles, together with a heat transfer coefficient profile, were calculated for a generic PT-type SCWR fuel-bundle string. Fuel bundles with UC and UC2 fuels with various axial heat flux profiles (AHFPs) are acceptable since they do not exceed the sheath-temperature design limit of 850°C, and the industry accepted limit for the fuel centerline temperature of 1850°C. The most desirable case in terms of the lowest fuel centerline temperature is the UC fuel with the upstream-skewed cosine AHFP. In this case, the fuel centerline temperature does not exceed even the sheath-temperature design limit of 850°C.

A CHARACTERISTICS-BASED IMPLICIT FINITE-DIFFERENCE SCHEME FOR THE ANALYSIS OF INSTABILITY IN WATER COOLED REACTORS

The objective of the paper is to analyze the thermally induced density wave oscillations in water cooled boiling water reactors. A transient thermal hydraulic model is developed with a characteristics-based implicit finite-difference scheme to solve the nonlinear mass, momentum and energy conservation equations in a time-domain. A two-phase flow was simulated with a one-dimensional homogeneous equilibrium model. The model treats the boundary conditions naturally and takes into account the compressibility effect of the two-phase flow. The axial variation of the heat flux profile can also be handled with the model. Unlike the method of characteristics analysis, the present numerical model is computationally inexpensive in terms of time and works in a Eulerian coordinate system without the loss of accuracy. The model was validated against available benchmarks. The model was extended for the purpose of studying the flow-induced density wave oscillations in forced circulation and natural circulation boiling water reactors. Various parametric studies were undertaken to evaluate the model's performance under different operating conditions. Marginal stability boundaries were drawn for type-I and type-II instabilities in a dimensionless parameter space. The significance of adiabatic riser sections in different boiling reactors was analyzed in detail. The effect of the axial heat flux profile was also investigated for different boiling reactors.

Optimization of Steam Reformers: Heat Flux Distribution and Carbon Formation

Optimal heat flux distributions along the axial position of steam reformer tubes are analyzed, aiming to maximize the outlet methane conversion without violating the upper bounds specified for the tube skin temperature, Tw(z) and the local heat flux, Q(z). The possible occurrence of the carbon deposition phenomenon is considered as an additional constraint in the optimization problem by means of a kinetic criterion which accounts for the rate of carbon formation (rC,net).The problem of finding the axial heat flux profile that leads to maximum methane conversion (or minimum tube skin temperature for specified production) without violating the upper limits imposed for Tw(z), Q(z) and rC,net is in principle a complex optimization process. In this work, a relatively simple semi-analytical method, that requires only iterative reactor simulations, is proposed.At conditions of fresh catalyst and for operations with typical feed compositions and temperatures, the carbon formation constraint is not active. For low values of the maximum allowable local heat flux (Qall), the optimal heating policies are monotonically increasing Tw(z) trajectories. Conversely, for higher Qall values the optimal Tw(z) shows an initial increase in the first tube section followed by an isothermal section. Decreasing axial wall temperature profiles or Tw(z) curves with maximum are clearly not optimal.When the catalyst is strongly deactivated, the optimal manipulation of Q(z), or Tw(z), is an appropriate procedure to achieve carbon free conditions. As this heating policy consists basically in reducing the firing in the top section of the reformer tube, it leads to unavoidable production losses.The shape of the catalyst activity axial profile has a considerable influence on the risk of carbon formation. Increasing activity distributions (similar to those found when sulfur poisoning takes place) may result in severe carbon formation in the reformer top. An optimal control of the heat input can contribute to minimize this practical operation problem.

A Semi-Analytical Model to Predict the Capillary Limit of Heated Inclined Triangular Capillary Grooves

This paper presents a one-dimensional, semi-analytical model for prediction of the wetted length supported by inclined triangular capillary grooves subject to heating from below. The model utilizes a macroscopic approach employing the concept of an apparent contact angle. Constant liquid properties are assumed and no specific account is taken of surface roughness. The concept of accommodation theory is introduced to account for the change in the radius of curvature of the liquid-vapor interface between the liquid reservoir and the groove proper. Empirical input is required in the form of the axial heat flux profile and the axial profile of the liquid height in the groove. To assist other researchers in the implementation of the model, this paper concludes with a series of design curves. These curves can readily be used to estimate the wetted length (capillary limit) in inclined heated triangular capillary grooves for a variety of operating conditions.

A forced convection subcooled boiling model for nonuniform axial heat fluxes

The modeling of convective subcooled boiling of water flowing in round tubes subjected to nonuniform axial heat fluxes is described. The effects of different axial heat flux profiles are modeled using a local hypothesis; i.e. flow and thermal development are assumed to occur very rapidly in the subcooled boiling (SCB) flow regime. A computer code has been developed to predict the pressure drop, heat transfer coefficient and wall temperature for nonuniform axial heat fluxes, starting with a well-validated code for uniform axial heat fluxes. The predictions for some common nonuniform axial heat profiles are compared to the uniform heat flux case.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part II. Mold heat transfer, mold flux behavior, formation of oscillation marks, longitudinal off-corner depressions, and subsurface cracks

Axial heat-flux profiles have been determined quantitatively from temperature measurements conducted on a slab mold under routine operating conditions. As in earlier studies, the heat flux was observed to have a maximum value at the meniscus and to decline with increasing distance down the mold. The mold heat flux increased with increasing casting speed and was greater with a mold powder having lower viscosity and melting point being applied as lubricant. The heat extraction was largest while casting 0.29 pet carbon steel and least for a 0.09 pet carbon grade; reducing the depth of the submerged entry nozzle increased the heat flux slightly in the upper region of the mold. Most significant was the higher heat flux observed at the meniscus of the outside-radius face, attributable to the locally greater copper plate thickness compared to that of the opposite broad face. All of the measurements can be explained straightforwardly by heat flow in the vicinity of the meniscus and the resulting behavior of the so-called slag rim adjacent to the mold wall. It is postulated that the difference in copper plate thickness between the two broad faces at the meniscus causes the slag rim to be smaller on the outside-radius face which gives rise to shallower oscillation marks, as observed, higher heat transfer, and a slightly thicker solid shell. The dissimilar behavior has implications for quality because the inside-radius shell, experiencing reduced heat extraction, cools and shrinks less than the outside-radius shell. Thus, for a given end-plate taper, the narrow face of the slab adjacent to the inside radius can push against the end plate, accelerating copper wear, and, owing to squeezing of the broad face, cause an off-corner depression and subsurface crack toward the mold exit. If this is correct, maintenance of the same copper plate thickness at the meniscus is fundamental to preventing such an occurrence. Moreover, adjustment of the heat extraction at the meniscus should be achievable by changing copper plate thickness, mold coating thickness/conductivity, cooling water velocity, cooling channel configuration, and mold flux composition for a given steel grade.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials, mold temperature measurements, and mathematical modeling

An extensive study has been conducted to elucidate mold behavior and its influence on quality during the continuous casting of slabs. The study combined industrial measurements, mathe matical modeling, and metallographic examination of cast slab samples. The industrial mea surements involved instrumenting an operating slab mold with 114 thermocouples in order to determine the axial mold wall temperature profiles for a wide range of casting conditions. A three-dimensional (3-D) heat-flow model of the mold wall was developed to characterize the heat fluxes in the mold quantitatively from the measured mold temperature data. Furthermore, heat-flow models were developed to examine steel solidification phenomena and mold flux behavior at the meniscus. Slab samples collected during the industrial trials were examined metallographically to evaluate the cast structure and defects. Owing to the length of the study, it is presented in two parts, the first of which describes the experimental techniques employed in the instrumentation of the mold together with the details of the industrial trials and mold temperature measurements. Also, the mathematical modeling technique applied to determine the axial heat-flux profiles from the measured mold temperature data is presented. It is shown that a fully 3-D model of the mold wall is needed to convert the measured temperatures to heat-flux profiles properly.

An experimental study of the effect of the axial heat flux distribution on the dryout conditions in a 3650-mm long annulus

Dryout measurements have been carried out for flow of boiling water in a 3650-mm long annulus. Eight different axial heat flux profiles, typical for BWRs, as well as one with uniform heat flux have been studied. It was found that for the present geometry the effect of the axial heat flux profile upon the total dryout power was rather small or in the range of ± 6 per cent.