Heat Flux Correlation Research Articles

Effect of bend radius and insulation on adiabatic section on the performance of a single closed loop pulsating heat pipe: experimental study and heat transfer correlation

Pulsating heat pipes are a relatively newer generation of heat pipe which are wickless thus more economical and less fabrication-intensive. These devices are made of a capillary sized tube bent in a serpentine form to result in a closed system. In this study a single closed loop pulsating heat pipe made of 2 mm internal diameter copper tubing is experimentally investigated for two different bend radii. The performance comparison is made for two fluids – methanol and water, for varying heat loads from 10 W to 100 W, with various inclinations from vertical bottom heated mode to horizontal mode, for a constant fill ratio of 60%. The sharper bend, though making the device more compact, is found to reduce the performance. One of the bend geometries is further investigated for the effect of insulation on the adiabatic sections. The insulation is found to certainly widen the heat load range though a distinct performance improvement is not found. The variation of the frequency of pressure pulsations with respect to the fluid, heat load and inclination is also studied. Additionally, one of the geometry is tested with FC 72 fluid as well to arrive at a correlation for heat flux for varying fluids, heat fluxes and inclinations, covering 116 data points. The performance trends predicted by the correlation are in line with those reported in the literature.

Calculation and Analysis of Critical Heat Flux at LWR Passive Safety Design

Critical heat flux (MDNBR) is one parameter for safe nuclear reactor operation. The magnitude of MDNBR is determined by local heat flux. When it is sufficiently high, it will cause a change in heat equilibrium and deteriorate nuclear fuel structure. To obtain assurance for nuclear reactor safety in safe criteria, Calculation and analysis of Critical heat flux of 630 MWe passive LWR was carried out at steady state and transient condition. The study used COBRA IV-I sub channel program coupled with critical heat flux correlation of EPRI-Columbia and W-3. The program models the core into 1/8 sections, each of which is divided into 83 sub-channels in radial direction and 40 nodes in axial direction, including 8 sub-channels of the hottest assembly. Normalized coast down flow and reactor power decay at initial phase is 10 second after loss of flow accident (LOFA) caused by anticipated primary pump failure. The effects of all input parameters, such as radial nodes, axial nodes, mix coefficient, velocity of coolant mass entering the core and power variation, have been identified. Evaluation of the results of safety calculation indicates that MDNBR, cladding temperature, and hot channel temperature are 1.83, 349°C and 2033°C, respectively. As the licensing limits for those parameters are 1.3, 1850°C, and 2840°C, it is concluded that the design of 630 MWe passive LWR has met the licensing criteria of safety. Modelling for safety analysis of passive LWR employs COBRA IV-I program. The results show that this program can be used to calculate hydraulic safety parameters with sub-channel model.

Concurrent flame spread over vertically oriented paper sheet: The effect of sample thickness

SummaryPacking or printing paper made out of cellulose is widely produced and used in daily life. The thickness of thin material affects the burning process significantly. Concurrent flame spread is an effective approach when analyzing and evaluating the fire hazard for combustible materials. Conducting this work will provide further understanding of the flame spread mechanism and reduce fire hazard. It will also enable investigation of the effect of sample thickness on concurrent flame spreading over the thin paper sheets experimentally. Numerically examining concurrent flame spread over thin paper sheet with varied thicknesses is also performed using Direct Numerical Simulation, which can provide more details on flame spread process. Qualitatively, the model predictions agree reasonably with the experiment in terms of the flame contour, burn duration, and flame spread rate. The moving rates of the flame base and pyrolysis front decrease with sample thickness both experimentally and numerically. The relationship between net heat flux, flame standoff distance, and solid burning rate is analyzed, with the burning rate exhibiting a similar trend to that of the net heat flux. A correlation of the flame net heat flux with the normalized distance in the pyrolysis region is also established where the flame heat flux displays a decay trend with the normalized space.

Critical Heat Flux (CHF) Correlations for Subcooled Water Flow Boiling at High Pressure and High Heat Flux

The subcooled water flow boiling is beneficial for removing the high heat flux from the divertor in the fusion reactor, for which an accurate critical heat flux (CHF) correlation is necessary. Up to now, there are many CHF correlations mentioned for subcooled water flow boiling in the open literatures. However, the CHF correlations’ accuracies for the prediction of subcooled water flow boiling are not satisfactory at high heat flux and high pressure for reactor divertor. The present paper compiled 1356 CHF experimental data points from 15 independent open literatures and evaluated 10 existing CHF correlations in subcooled water flow boiling. From the evaluation, the W-2 CHF correlation performs best for the experimental CHF data in all existing critical heat flux correlations. However, the predicted mean absolute error (MAE) of the W-2 correlation is not very ideal for all database and the MAE of the W-2 correlation is from 30% to 50% for some database. In order to enhance the CHF prediction accuracy in subcooled water flow boiling at high heat flux and high pressure, the present paper developed a new CHF correlation. Compared with other existing CHF correlations, the new CHF correlation greatly enhances the prediction accuracy over a broad range of pressures and heat fluxes which are desired in the cooling of high heat flux devices, such as those in the fusion reactor divertor. The validation results show that the new correlation has a MAE of 10.05% and a root mean squared error (RMSE) of 16.61%, predicting 68.1% of the entire database within ±10% and 81.5% within ±15%. The MAE of the new CHF correlation is 7.4% less than that of the best existing one (W-2 correlation), further confirming its superior prediction accuracy and reliability. Besides, the new CHF correlation works well not only for a uniform power profile but also for a non-uniform power profile in subcooled water flow boiling at high pressure and high heat flux.

Universal Critical Heat Flux (CHF) Correlations for Cryogenic Flow Boiling in Uniformly Heated Tubes

Experiments to determine critical heat flux (CHF) for cryogen flow in uniformly heated, round tubes have been performed throughout the globe during the past sixty years. However, experimental CHF data for cryogens are rarely published, remaining in the archives of authors, or in obscure technical reports of an organization or other inaccessible sources. In the present study, the Purdue University-Boiling and Two-Phase Flow Laboratory (PU-BTPFL) Cryogen Flow Boiling CHF Database is consolidated from world literature dating back to 1959. With 2312 data points for LH2, LHe, LN2 and LCH4, it represents the largest cryogen CHF database assembled to date. The database encompasses diameters from 0.5 to 14.1 mm, critical length-to-diameter ratios from 2.5 to 230.8 (term ‘critical’ refers to axial location where CHF is detected), system pressures from 0.01 to 4.07 MPa, reduced pressures from 0.1 to 0.93, mass velocities from 2.2 to 8203.9 kg m−2 s−1, inlet subcoolings from 0 to 78.9 K, inlet qualities from -2.06 to 0.95, critical subcoolings from 0 to 48.5 K, critical qualities from -1.23 to 1.00, critical void fractions from 0 to 1, and CHF values from 0.05 to 8203.9 kW m−2. The consolidated database represents an invaluable tool for development of CHF correlations – a primary goal for the present study – as well as future analytic and computational models. Using this database, new universal CHF correlations are constructed for two distinct CHF mechanisms, Departure from Nucleate Boiling (DNB) and Dryout, after careful physics-based segregation of the data. With mean absolute errors below 30%, the new CHF correlations are shown to provide good predictive agreement with the database.

AN EXPERIMENTAL INVESTIGATION ON RADIANT FLOOR HEATING SYSTEMS AT VARIOUS OPERATING CONDITIONS

In this study, heat transfer characteristics pertaining to a heated radiant floor are investigated experimentally. In order to achieve this aim, experiments have been conducted within extended supply water temperature ranging from 30 oC to 55 oC, and mass flow rate ranging from 0.056 kg/s to 0.125 kg/s according to experimental condition ranges in the relevant literature. Correlation comparison has been accomplished using a large number of experimental data including pioneer studies and international standards regarding with the determination of heat flux and heat transfer coefficients. Moreover, novel correlations providing convective, radiative and total heat fluxes have been derived, and it has been observed that most of the outcomes of correlations remain within deviation bands of ±15%, ±5% and ±20%, respectively. Apart from the literature, heat flux correlations corresponding to each heat transfer mechanisms are given and evaluated separately. Throughout experimental studies, the proportion of the radiative heat transfer to total one is found 60% approximately. Measured experimental data are given in the paper for other researchers validation problems on their theoretical and numerical works.

Numerical simulations of the Rayleigh-Bénard-Marangoni convections in a thin metallic layer

Within the context of nuclear power safety, the In-Vessel Retention (IVR) strategy consists in sustaining the integrity of the reactor pressure vessel by External Reactor Vessel Cooling (ERVC). However, due to the ablation of the vessel wall and the thermochemical effects, a thin metallic layer may be formed on top of the corium pool and lead to the vessel failure. In this article, numerical simulations of the thermal–hydraulic behavior of the thin metallic layer are carried out to reduce the uncertainties in the heat flux evaluation. Specifically, the Rayleigh-Bénard and Bénard-Marangoni convections are considered in the heat transfer models of the metallic layer. The TrioCFD code is validated for the Bénard-Marangoni convection, then applied into the numerical simulations of the metallic layer with different top boundary conditions: pure radiative heat transfer, and radiative heat transfer plus positive or negative Marangoni effects. The temperature profile, mean temperature and focusing effect of the metallic layer are evaluated and compared for various cases. Results show that the Marangoni effects have to be considered for small metallic layer thicknesses. Furthermore, the layer can be divided into two regions, of which the heat flux correlations can be evaluated independently, giving a better estimation of the heat flux profile.

Heat fluxes under the ceiling induced by wall fires with various burner aspect ratios in a channel

A detailed experimental investigation of wall fires in a channel was conducted to study the heat fluxes under the ceiling. Various burner aspect ratios and fire heat release rates were employed to simulate different wall fire scenarios. The effect of source-ceiling height was also examined. The results show that the distribution of heat flux under the ceiling from fires on rectangular burners was significantly influenced by the burner aspect ratio. As the burner aspect ratio increased, the heat flux under the ceiling at a given position perpendicular to the side wall increased. It was found that the existing heat flux correlation developed for a square burner could not capture such influence as it did not include the burner aspect ratio. A new predictive model based on the equivalent burner diameter concept was proposed incorporating the burner aspect ratio and was shown to predict well the heat flux for all the cases with different heat release rates, burner aspect ratios and source-ceiling heights. The model was also validated against available data in the literature which were not used in its derivation. Further analysis was also conducted for the temperature contours constructed from the temperature measurements under the ceiling.

Experimental correlation for critical heat flux in helical coils

The present work experimentally investigated the Critical Heat Flux (CHF) phenomena in helical coils. Literature on the CHF in helical coils is scarce. The centrifugal force and hence secondary flows of fluid is generated inside the coil due to its curvature. The Secondary flows of fluids may affect the heat transfer mechanism and hence, CHF inside helical coils. In present work, the experimental CHF data is compared with correlation available in literature. Fifteen empirical CHF correlations, that include correlation developed for straight horizontal tubes and helical coils, are compared with the experimental CHF databank. The CHF databank contains 413 CHF data of different helical coils. The data includes two fluids namely refrigerant R123 and water. Data covers the parameter range of tube diameter 5.5–10 mm, coil to tube diameter ratio 14–58, mass flux 92–2062 kg/m2s, heat flux 37–2984 kW/m2, density ratio 31–1352 and exit quality −0.1 to 1.2. The data mainly covers CHF in redeposition zone. The helical coil correlations are working reasonably well for long length helical coils but not working for short length helical coils. The straight tubes correlations are working reasonably well for all helical coils data. A generalised correlation is suggested for CHF in helical coils. The experimental data of CHF is published to contribute to the databank for helical coils.

Heat flux correlation models for spray evaporative cooling of vibrating surfaces in the nucleate boiling region

New empirical correlation models are constructed to characterise heat transfer associated with spray evaporative cooling of vibrating surfaces - a process involving complex two-phase physics well beyond current numerical simulation capabilities. The proposed correlation models, which account for dynamic, rather than just static surface conditions as in existing models, are constructed using dimensional analysis involving the Generalized Buckingham Π-Theorem. Experimentally-measured spray evaporative cooling data is used to fit the model using the Vibrational Reynolds number and a dimensionless acceleration number which better correlate the influence of surface frequency and amplitude in the nucleate boiling regime. Different coolant flow-rates through a full-cone spray nozzle are used to cool a flat circular test-piece acting as a horizontal surface. The test-piece surface is excited by a shaker through a range of low and high vibration frequencies and amplitudes. The results show that surface dynamic effects certainly influence nucleate boiling, but they also show that surface vibration does not have the same effect for all excess temperatures - dynamic effects can either increase or decrease heat transfer depending on the heat transfer mechanism. These new models are important for thermal management in several areas, particularly involving batteries, power electronics, and electrical machines in automotive and aerospace applications.

Analysis of Enhanced Pool Boiling Heat Transfer on Laser—Textured Surfaces

Enhancement of pool boiling heat transfer can be attained with a number of passive and active techniques. The paper experimentally analyses the impact of laser treatment of the copper surfaces on pool boiling heat transfer of distilled water and ethyl alcohol. The samples were modified with a laser beam to produce longitudinal grooves of highly developed microstructures in the laser textured area. Specimens of different groove depths, groove widths and micro-fin widths were produced. The results indicate a significant influence of laser processing on heat flux dissipated from the surfaces and heat transfer enhancement for all the samples tested. The experimental results have been generalized in the form of a heat flux correlation based on a modified model of enhanced pool boiling heat transfer.

Development of correlation for critical heat flux for vertically downward two-phase flows in round tubes

ABSTRACT Critical Heat Flux (CHF) is one of the catastrophic failure modes encountered in two-phase flows in nuclear, chemical, and power industries. Considerable research was carried on CHF in last few decades in horizontal, inclined, and vertically upward flows. Only limited information, mostly at atmospheric pressure conditions and including CHF enhancers like inlet throttling, was available on CHF in vertical pipes with flow directed downwards. The complexity associated with vertically downward two-phase flows, due to flow instabilities and premature tube burnout, dictates for stringent design considerations, especially, from CHF perspective. As a result, accurate estimation of CHF is a requirement not only from performance, but also more significantly from safety perspective. The objective of this paper is to develop a correlation for CHF in vertical tubes in which the fluid flow was directed downward. As part of these investigations, a versatile test rig was designed and developed. Experiments were conducted in the pressure range of 1 to 5 bar and a CHF correlation is proposed as a function of inlet fluid temperature, mass flux and pressure in the absence of inlet throttling or other similar effects. The new correlation developed agrees well with the data from current experiments with a mean deviation of 13.87% and standard deviation of 18.71%. The uncertainty analysis revealed a 90% confidence level on the CHF estimate due to variation in the input variables.

Investigation the nanofluid flow through a nanochannel to study the effect of nanoparticles on the condensation phenomena

In this paper, the effect of nanoparticles on the annular condensation flow of Argon-Copper nanofluid passing inside a nanochannel is investigated by molecular dynamic method. Simulation is performed in a computational domain with two solid Copper walls for different saturation conditions with focusing on the thermal conductivity and flow characteristics of condensation process. By considering appropriate correlation length for heat flux autocorrelation function (HFACF) to decay to zero, Green-Kubo relation is utilized for calculation of thermal conductivity. It has been observed that adding nanoparticle disfigures the density profile and drives the liquid film closer to the walls towards the center of the nanochannel. With more Copper nanoparticles, correlation of heat flux is increased and decayed to zero in longer time. Also, with more particles, less time is required for condensation flow to reach equilibrium. Thermal conductivity of condensation flow of Argon-Copper nanofluid is obtained at different saturated temperatures. The results show that at a constant volume fraction, increasing the diameter of the nanoparticle has a better effect on the enhancement of thermal conductivity of nanofluid condensation than the increasing the number of nanoparticles.

Development of critical heat flux correlation for In-vessel retention

ABSTRACT In-vessel retention (IVR) is a strategy for severe accident management in which the lower head of the reactor vessel is submerged in a water-flooded reactor cavity. Critical heat flux (CHF) data for IVR are important for estimating cooling capacity of the reactor vessel. The existing CHF data for IVR which were obtained for the specific geometries and thermal-hydraulic conditions of actual plants are difficult to be applied to plants with other specifications. Hence, the purpose of this study is to develop CHF correlations applicable to various pressurized water reactor plants in a wide range of thermal outputs based on newly obtained CHF data. A rectangular test section with a cross-section of 150 mm × 150 mm and length of 600 mm was used for simulating a cooling channel. The thermal-hydraulic conditions expected in actual plants were studied, and the results were used in the experiment. The effects of parameters such as pressure, mass flux, thermodynamic quality, and angle on CHF were investigated . Based on these results, we developed a CHF correlation formula that can be applied to a wider range than previously, up to a maximum heat flux of 3000 kW/m2, and that predicts CHF with an error of ± 10%.

Discussion of the Heat Flux Calculation Method During Pool Boiling on Meshed Heaters

Abstract The paper discusses nucleate boiling heat transfer on meshed surfaces during pool boiling of distilled water and ethyl alcohol of very high purity. It presents a correlation for heat flux developed for heaters covered with microstructural coatings made of meshes. The experimental results have been compared with the calculation results performed using the correlation and have been followed by discussion. Conclusions regarding the heat flux determination method have been drawn with the particular focus on the usefulness of the considered model for heat flux calculations on samples with sintered mesh layers.

Experimental study of jet fire radiation and a new approach for optimizing the weighted multi-point source model by inverse methods

The present study brings new experimental data on radiation from subsonic jet fires and proposes a new method for employing the inverse analysis technique to optimize the weighting coefficients of the multi-point model. First, detailed measurements of radiative heat flux distributions are obtained for different flame powers, injector diameters and sensor distances. All results fall onto a single curve with an adequate non-dimensionalization. A new correlation for the radiative heat transfer rate from these flames was obtained with a better performance compared to other options from literature. Then, an inverse method is employed to obtain the coefficients of the weighted multi-point model for predicting the radiative heat transfer from flames. By using the non-dimensional heat flux distributions, the inverse method became independent of the flame radiated fraction. A new optimization parameter that emerges from the non-dimensional model showed the consistency of the inverse method and leads to a correlation for the maximum heat flux as a function of the radial distance from the flame. Finally, the new weighting coefficients and the radiative heat transfer rate correlation were used to compute the dimensional radiative heat flux distributions. The comparison with the experimental data showed expressive improvements of the model prediction.

A new correlation of average temperature and maximum heat flux for turbulent supersonic flow in a large size channel up to Mach 5

Supersonic compressible turbulent flow through a large size channel is studied numerically. The flow is modeled by the Favre averaged Navier-Stokes (FANS) equation with k−ω as turbulence model, the resulting governing equations are solved by employing an in-house unsteady state density based solver developed using sixth order accuracy compact finite difference schemes. The effect of Mach number and different wall thermal boundary conditions influencing, the variation of velocity, temperature and density across the channel height are reported in the present study. In the present study, the height of the channel is considered as 10 mm and the bulk Reynolds number is in the range of 3.42×105 to 1.14×106 which is higher compared to previous studies. Furthermore, the present Reynolds number represents a fully turbulent flow scenario, common in many aerospace applications. The results indicate that for an adiabatic wall with higher Mach number, there is a substantial increase in the wall temperature. The flow characteristics for a heated wall carried at low and medium Mach numbers indicate that for higher wall temperature, the behaviour of flow characteristics shifts towards that of the adiabatic wall behaviour. However, for higher Mach numbers the flow characteristics behaves like that of isothermal wall condition. In the present work, mathematical correlations for average temperature and maximum heat flux based on the Mach number are developed for adiabatic and isothermal wall conditions, respectively. The present results are validated with direct numerical simulation (DNS) results reported in the literature.

Experimental study on flow and heat transfer characteristics at onset of nucleate boiling in micro pin fin heat sinks

The micro pin fin heat sink has great application potential in the heat dissipation of high-power LED chips, phased array radars and semiconductor lasers. The onset of nucleate boiling (ONB) is a critical limit in designing heat dissipation systems. A simultaneous visualization and measurement study is conducted to investigate the ONB phenomenon of deionized water in circular, diamond, and oval micro pin fin heat sinks. Experiments are conducted under inlet subcooling of 29.6–49.5 °C, mass flux of 147.4–355.4 kg m−2 s−1 and heat flux of 4.8–55.8 W cm−2. Visualization result indicates that the ONB is always initiated at the surrounding region of a micro pin fin. The effects of additional nucleation sites caused by a micro pin fin and the temperature distribution of the surrounding region captured by an infrared camera can be used to explain the occurrence of the first bubbles. In this study, the effects of inlet subcooling, mass flux, and the cross-section shape of the micro rib on the ONB characteristics are investigated. Results show that the heat flux and wall superheat needed for the ONB increase as the mass flux and inlet subcooling increase. Moreover, the heat flux required for the ONB in the diamond and oval micro pin fin heat sinks is higher than that in the circular one. On the basis of the experimental data, the correlation of heat flux at the ONB in the micro pin fin heat sink is established, with 85.7% of the data falling within an error band of ±15%.

Jet quenching phenomena during emergency cooling of high temperature solid surface

In the case of loss of coolant accident, LOCA in nuclear reactor, heat removal can be successful only when water rewets the surface. Jet impingement is a highly potential technique of heat removal from high temperature solid surface. After the impingement of liquid jet on hot solid surface it is not capable to wet the surface immediately, it takes time (wetting delay) to get a favorable condition by the liquid to wet and then propagate over the surface. Generation of vapor and its explosion creates the barrier for the liquid front to move. An experimental investigation has been conducted during sub-cooled water jet impingement quenching of three different cylindrical blocks of copper, brass and steel. The jet velocity varied from 3 to15 m/s, jet sub-cooling was 5-80 K and initial block temperature was 250 to 600 ºC. The study was conducted to determine the dominating parameters of maximum heat flux, wetting delay, quench front movement, boiling region size and finally developed a correlation of maximum heat flux for steel. After elapsing the wetting delay period, a visible smaller boiling region was observed to move radially from the impinged centre. The leading edge of this boiling region is designated as the quench front. The boiling region is a vital region as the maximum heat flux occurred at this region during cooling. The boiling region increases with the movement of the quench front and therefore the position of maximum heat flux moves accordingly. The boiling region width increases with material conductivity and decreases with liquid sub-cooling and liquid velocity. The maximum heat flux increases with jet velocity, liquid sub-cooling, solid material conductivity and it is almost independent of solid initial temperature. Wetting delay increases with block initial temperature and decreases with jet velocity and liquid sub-cooling.

Investigation on building eave effect of fire-induced ejected plume from a room window and its heat flux imposing upon the facade wall

This paper investigates building eave effect of fire-induced ejected plume from a room window and its heat flux imposing upon the facade wall. Based on a 1:8 cubic model and Froude modeling, a series of reduced scale experiments are set up. The window dimensions and total heat release rate due to a room fire are changed during experiments. The eave upon the facade wall, made of noncombustible fiber board is installed horizontally above the window top, varying with different vertical heights (distance of the eave to the window top) and lengths (direction normal to the facade wall). The facade flame height is recorded by a CCD camera, while the heat fluxes imposing upon the facade wall are collected by five water-cooled heat flux gauges. Results show that the ejected flame with horizontal eave can be distinguished into the “free flame stage”, the “flame horizontal spread stage” and the “flame overflow stage”. The visible flame height and heat flux within the “flame overflow stage” are detailed discussed, revealing the physical mechanism of the vertical height and length of the horizontal eave effects. Finally, an implicit correlation in regarding with the visible flame height, the updated flame extension area beneath the horizontal eave as well as the vertical height of the horizontal eave to the window top is established. Taking the horizontal eave conditions into consideration, the heat flux correlation is well corrected and proposed. The results would provide theoretical basis for the fire-induced thermal protection in high buildings.