Non-uniform Heat Flux Distribution Research Articles

A new semi-analytical model for studying the performance of deep U-shaped borehole heat exchangers

In deep geothermal exploitations, the U-shaped borehole heat exchanger (UBHE) has a longer fluid retention time and a larger contact area with the formation. In order to improve the utilization efficiency of geothermal energy, it is becoming increasingly important to accurately evaluate the performance of the deep UBHEs. In this study, the authors develop a new semi-analytical model for characterizing the heat transfer behavior of the deep UBHE geothermal system. In this developed model, the temperature change within the wellbore is numerically simulated by the finite difference method, whereas the temperature change between the formation and the wellbore is analytically simulated by the Green's-function. Besides, the non-uniform heat flux distribution along the horizontal section is considered to characterize three-dimensional heat transfer behaviors. By means of this model, the influences of developing strategies and well configurations on the outlet temperature and total thermal power are investigated. The calculation results indicate that the traditional assumption of uniform temperature along the horizontal section can induce significant errors in evaluating the performance of the UBHE geothermal systems; the horizontal section length is more conducive to improving the extraction performance in a shallower geothermal formation, and a longer horizontal section leads to a higher outlet fluid temperature, together with a larger total thermal power; a higher injection rate, as well as a lower injection fluid temperature, is more favorable for improving the total thermal power; an insulation casing with a length equaling the depth of injection point can lead to the maximum thermal power of the UBHE geothermal system.

Hydrothermal performance assessment of a parabolic trough with proposed conical solar receiver

Parabolic Trough Collectors (PTCs) are commonly employed in both industrial and residential settings for the purpose of harnessing solar energy. Several techniques have been implemented to improve performance, such as altering the geometry of the absorber tube, enhancing the selective coatings of the receiver envelope, and utilizing nanofluids. This study proposes a new method for enhancing the thermal-hydraulic efficiency of PTCs through the utilization of non-uniform heat flux distribution on conical solar receiver. The effectiveness of this approach is evaluated through numerical simulations conducted using Ansys Fluent with the aid of optical simulation performed using TracePro. The geometry under consideration is assessed at various diameter ratios (DR) spanning from 1.25 to 2 and Reynolds number (Re) ranging from 20000 to 100000, with increments of 20000. This evaluation is conducted at three distinct inlet temperatures: 150 °C, 250 °C, and 350 °C. The studied parameters include-the Nusselt number (Nu), friction coefficient (f), thermal efficiency (ηth), exergetic efficiency (ηex), and thermal enhancement factor (TEF). Furthermore, a comparative analysis is conducted between the newly proposed geometric design and a traditional straight absorber and glass structure. The findings indicated that a conical receiver generally enhances system heat transfer by a minimum of 7 % and up to 65 %, resulting in improved thermal and exergetic efficiencies. Decreasing the pipe outlet diameter from DR = 1.25 to DR = 2 led to a significant exponential rise in the friction coefficient. The TEF demonstrated that a diameter ratio of 1.25 and 1.5 resulted in maximum values of 1.19 and 1.11, respectively, at high Re and an inlet temperature of 350 °C. The results suggested that incorporating conical receivers in PTCs can greatly improve their performance. To minimize the friction coefficient and associated pumping power, it is crucial to carefully evaluate the reduction of the diameter of the absorber outlet. The results offered valuable insights for the development and improvement of PTCs in both industrial and power generation settings, promoting the adoption of renewable energy and supporting long-term sustainability.

Thermal performance of Parabolic Trough Solar Collector

The research progress of numerical simulation of parabolic trough solar collector was introduced. Especially the numerical simulation studies of the internal flow field in the collector tube and the external flow field of the concentrator were reviewed. In the study of the internal flow field in the collector tube, the type of heat transfer fluids and the characteristics of optical concentration have a significant effect on the heat collection performance and thermal stress distribution, especially in the water/steam medium heat collection loop. The unique gas-liquid two phase flow superposition of the non-uniform heat flux distribution outside the tube may lead to serious thermal stress bending deformation of the collector tube. In the study of the external flow field of the concentrator, due to the high actual wind speed and the low structural strength of the ultra-thin lens, the concentrator is subjected to wind load deformation, resulting in the loss of optical efficiency, and even leading to the failure of the parabolic trough collector structure, which directly affects the normal operation of the whole collector field.

Comprehensive analysis method of acquiring wall heat fluxes in rotating detonation combustors

Accurate perception of the combustor thermal environment is crucial for thermal protection design of a rotating detonation combustor (RDC). In this study, a comprehensive analysis method is established to calculate the non-uniform heat flux distribution of the RDC by utilizing the measured temperature distribution of the combustor outer wall obtained by the high-speed infrared thermal imager. Firstly, a physical model based on the geometric characteristics of the RDC is constructed and its thermal conductive process is simulated, given by different heat flux boundary conditions. The analysis results indicate that the method used in current research for computing the heat flux of RDC leads to significant discrepancies, particularly in regions of obvious axial heat flux gradients near the top of the combustor. Then the Levenberg-Marquardt (L-M) method for inversely solving non-uniform heat flux is developed based on the two-dimensional heat conduction equation, and the wall heat fluxes are inversely calculated by the L-M method based on the above numerical data. Results show that the L-M method can obtain more accurate heat flux distribution even in the zones with large heat flux gradients, considering the axial heat conduction within the combustor outer wall caused by the non-uniform heat flux. Finally, the wall heat flux distribution is analyzed coupling the L-M method together with the experimental measurements in kerosene two-phase RDC. The analyses show that the wall heat flux exhibits non-uniform distributions both circumferentially and axially, with axial non-uniformity being particularly pronounced. The highest temperature of combustor outer surface and the highest wall heat flux occurs within the region of 20 mm from the combustor head, which corresponds to nearly 14 % of the combustor length. The heat flux peak and thermal heat rate are positively correlated with the combustor equivalence ratio in the range between 0.44 and 0.64. In this study, the distribution of wall temperature field in the two-phase RDC is obtained for the first time and the wall heat flux is calculated inversely by L-M method. This work provides a more accurate method for calculating heat flux in RDC and offers references for thermal protection designs in RDCs.

Improvement of temperature uniformity by using novel guide vanes in solar external receiver tubes

The heat flux sustainability in solar external receiver tubes is limited by the non-uniformity of the temperature distribution and the maximum achievable temperature of the molten salt flow. In this paper, the external receiver tubes were equipped with novel guide vanes to enhance the heat transfer inside the tube and improve the uniformity of the temperature distribution on the tube surface. The geometric structures of guide vanes were optimized under non-uniform heat flux distributions. Firstly, the numerical models of tubes with different guide vanes (different wrap angles at trailing angle and different number of blades) were developed. Secondly, the numerical calculation of each case was carried out by using the fine meshing method, and was carried out by means of the commercial software ANSYS Fluent 19.2 on the High-Performance Computing. The SST k-ω turbulence model was used to predict the flow field inner the tube. The temperature, pressure loss, velocity and Nusselt number of these models predicted by CFD were analyzed and compared. Finally, the effect of different geometric parameters on the heat transfer enhancement and for improving the uniformity of temperature distribution were studied. It was observed that the guide vane is very effective to enhance the heat transfer inside the tube and improve the uniformity of temperature distribution on the tube surface. By optimizing the design of two parameters (wrap angles and number of blades), better heat transfer performance and improved uniformity can be obtained. For enhancing the heat transfer, and for improving the temperature uniformity and the flow resistance in the tube, a value of θTE = 82° is should be chosen. With the increase of the blade number, the flow separation will be better controlled, and the swirling strength will increase gradually. To increase the number of blades helps to enhance the heat transfer and improve the temperature uniformity. A higher blade number will increase the system resistance and affect the thermal hydraulic performance, and increase the design head and power of the pump. The most convenient blade number is N = 6. In addition, it was observed, that by adding the guide vanes, the flow resistance increases and this affects the thermo-hydraulic performance of the receiver tube. This study will provide theoretical basis and technical support for the efficient and reliable operation of solar collector heat exchanger tubes.

Coupling of 3D thermal with 1D thermohydraulic model for single-phase flows of direct steam generation in parabolic-trough solar collectors

Estimating 3D temperature distribution around the heat collector element (HCE) is an essential matter for the safety and efficiency of parabolic-trough solar collectors (PTC) due to non-uniform heat flux distribution (NUHFD). Particularly in 2nd and 3rd generation PTC systems, such as direct steam generation (DSG), because of the higher thermal stress around the absorber. 3D HCE thermal models linked to a 1D approach of fluid flow appear as the fastest alternative to study this phenomenon. However, there are still challenges such as the thermal coupling between HCE and heat transfer fluid (HTF) for accurately estimating the receiver thermal field. In this work, the coupling is studied in depth for single-phase flows of DSG in PTC, with a fast and realistic 3D HCE − 1D HTF model, which is validated with experimental data of the Direct Steam Solar (DISS) facility for heat transfer and absorber thermal field variables. Firstly, the inability of standard heat transfer coefficient (HTC) correlations to predict absorber thermal field is constated, being deviations greater than −36.1% for absorber cross-sections (CS) maximum thermal gradients. Assuming underestimated and constant thermophysical properties of the absorber, as former models did, underestimations of more than −29.6% are reported. Besides, the heat transfer variables are overestimated by around 14.3–15.9% for temperatures above 600 K. Secondly, a new correction factor (CF) for standard HTC is proposed involving the NUHFD. Considering this CF and the thermal dependence of the absorber thermophysical properties, deviations fall below 7.5% for heat transfer variables, whilst the absorber CS maximum thermal gradients are under 6.0%. This approach also improves the results reported by former models around 4.3–7.3% for heat transfer variables, without underestimating absorber CS maximum thermal gradients. These deviations are between 4.9–19.1% guaranteeing the safety of the absorber when the model is used during the design stage.

Numerical investigation on ballooning and rupture of a Zircaloy tube subjected to high internal pressure and film boiling conditions

Film boiling may lead to burnout of the heating element. Even though burnout does not occur, the heating element is subject to deformation because it is not sufficiently strong to withstand external loads. In particular, the ballooning and rupture of a tube under film boiling are important phenomena in the field of nuclear reactor safety. If the tube-type cladding of nuclear fuel ruptures owing to high internal pressure and thermal load, radioactive materials inside the cladding are released to the coolant. Therefore, predicting the ballooning and rupture is important. This study presents numerical simulations to predict the ballooning behavior and rupture time of a horizontal tube at high internal pressure under saturated film boiling. To do so, a multi-step coupled simulation of conjugated film boiling heat transfer and ballooning using creep model is adopted. The numerical methods and models are validated against experimental values. Two different nonuniform heat flux distributions and four different internal pressures are considered. The three-step simulation is enough to obtain a convergent result. However, the single-step simulation also successfully predicts the rupture time. This is because the film boiling heat transfer characteristics are slightly affected by the tube geometry related to creep ballooning.

Evaluation of Heat Flux Distribution on Flat Plate Compound Parabolic Concentrator With Different Geometric Indices

AbstractThe Compound Parabolic Concentrator (CPC), when coupled with the photovoltaic system, namely the Concentrated Photovoltaic Thermal System (CPVT), makes utilizing solar energy efficient. The major challenge that hinders the electrical and thermal performance of the CPC–CPVT system is the non-uniform heat flux distribution on the absorber surface. In the present paper, detailed ray-tracing simulations have been carried out to understand the heat flux distribution characteristics of CPC with different geometrical conditions, and those are concentration ratio, truncation ratio, incident angle, and average heat flux on the absorber surface. To have a thorough understanding, the analysis has been carried out in multiple steps. First, it is performed by analyzing the effect of concentration ratio and incident angle on heat flux distribution characteristics at a fixed truncation ratio. Second, investigations have been carried out to understand the heat flux distribution characteristics at different truncation ratios and different incident angles by keeping the concentration ratio constant. Local concentration ratio and non-uniformity index have been employed to quantify the non-uniformity of heat flux distribution on the absorber surface. It has been observed that the 0-deg incidence angle is the most effective angle to achieve uniform heat flux distribution on the absorber surface. This paper sheds insight into the heat flux distribution characteristics on the absorber surface of a CPC–CPVT system which can be used by the research community for designing an effective CPVT system from the perspective of uniform heat flux distribution on the absorber surface.

Morphology evolution of a melting solid layer above its melt heated from below

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to$Ra=10^{11}$) and three-dimensional (achieving Rayleigh number up to$Ra=10^9$) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wanget al.(Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

Effect of peripheral nonuniform distribution of furnace heat flux on thermo-hydraulic characteristics and design of riser downcomer circuit of natural circulation boiler

The usual practice of design of riser tubes of natural circulation boilers is with an assumption of uniform furnace heat flux. Using the uniform diameter of riser tubes inside the furnace zone is also very common. The effect of peripheral nonuniform distribution of furnace heat flux on thermo-hydraulic characteristics and design of the riser downcomer circuit of a natural circulation boiler is presented here for the first time. As the riser tubes are exposed under substantially high heat flux, the tubes containing water-steam mixture are vulnerable and susceptible to overheating, particularly at high flux zone. From systematic analysis, it is proposed that using different diameters and the number of riser tubes at various sections can overcome the early occurrence of tube dry-out. An appropriate two-phase flow model is developed with flow regime mapping, tube wall temperature calculation, and identification of possible dry-out. The peripheral nonuniform distribution of furnace heat flux is implemented analytically in the model by introducing a distribution parameter estimated from the actual furnace data. Results reveal that with an average heat flux of 150 kW/m2, the dry-out occurs near a riser tube height of 44 m for a typical 210 MW capacity boiler. However, considering the nonuniform heat flux variation, the dry-out appears near a height of 32 m and 73 m for higher and lower heat flux zone, respectively. The present analysis shows that the implementation of larger size and lower size diameter of riser tubes, respectively, in higher and lower heat flux regions has a 9.45 % cost-benefit compared to the usual design practice with a consideration of uniform diameter tube and heat flux. The present work concludes that instead of using uniform tube diameter with average heat flux assumption, the use of different diameter of tubes in different heat flux zone not only avoid the early onset of possible dry-out but also has a cost-benefit.

Improvement of uniformity of irradiance on truncated compound parabolic concentrator by introducing the homogenizer ratio

A compound parabolic concentrator (CPC) with a flat absorber is widely used in low-concentrating photovoltaic thermal (CPVT) systems. CPC certainly develops non-uniform heat flux distribution over the absorber surface which is significantly reduced by the integration of homogenizer referred as Elongated CPC (ECPC). The objective of the present work is to analyse the effect of homogenizer ratios, truncation ratios and concentration ratios on the heat flux distribution characteristics of a CPC collector. In this paper, a ray tracing simulation is carried out to obtain the heat flux distribution profiles and the same is incorporated within CFD software to obtain the temperature distribution profiles. As a result, it is observed that the optimum truncation ratio would be 0.7 at which uniformity in flux distribution is improved by 3%, with just 2% reduction of average heat flux value. Furthermore, with optimized homogenizer ratio of −0.35 at concentration ratio of 3, 64% improvement in uniformity of flux distribution has been noticed. From the study, it has been concluded that for different concentration ratios of 1.5, 2, 3, 4, 5, 6, 7 and 8, the optimum homogenizer ratio is observed to be −0.9, −0.55, −0.35, −0.25, −0.2, −0.15, −0.15 and −0.05 respectively.

An approach to thermal modeling of power cables installed in ducts

The power cables laying in the urban areas require utilization of the protective ducts, mainly to facilitate the faulty section replacement. However, the use of cable ducts results in reduced capacity to dissipate generated heat to the surroundings. Thus, the thermal analysis of cables placed in ducts is very important for proper power cable operation. The thermal response of cables laid in mutual and in separate ducts, respectively, is considered at two values of current load. The full-scale field measurement setup is utilized to carry out the analysis of both steady-state and dynamic power cable heating under actual field conditions for the two backfill configurations. The measurement results provide the insight into the power cable heating dynamics related to the situations of a short-term over-loads and fault drive-through responses and also the opportunity to verify the proposed numerical approach based on the use of finite element method and the boundary conditions on the interior duct surface. The approach could be considered as a compromise between the standardized procedure and the tedious procedure involving the computational fluid dynamics simulations due to straightforward implementation and very good accuracy. The results obtained suggest that cables laid in mutual duct lead to a less favorable thermal situation when compared to cables laid in separate ducts. Also, the numerical results suggest that the use of non-uniform heat flux around the inner duct surface results in a significantly better agreement with measurements, compared to the purely numerical approach utilizing the concept of the effective thermal conductivity to model heat transfer in the air gap between cable and duct. Finally, the sensitivity analysis has been carried out to assess the effects of various backfill thermal conductivities and the ground surface temperature on the resulting thermal field. • Full scale field measurements. • Simplified approach for thermal field estimation when cabled are placed in ducts. • Nonuniform heat flux distribution along the cable duct is implemented. • Better agreement with measurements when non-uniform heat flux distribution is used. • Use of effective thermal conductivity results in notable temperature underestimation.

Eulerian multiphase study of direct steam generation in parabolic trough with OpenFOAM

AbstractDirect steam generation (DSG) in parabolic trough solar collectors is a feasible option for economic improvement in solar thermal power generation. Three‐dimensional Eulerian two‐fluid simulations are performed under OpenFOAM to study the turbulent flow in the evaporation section of the parabolic trough receiver and investigate the phase change, and pressure drop of water as a heat transfer fluid. First, the model's validity has been tested by comparing the numerical results of a laboratory scale boiler with the available correlations and semi‐correlations of boiling flows from the literature. Simulations agreed well with Rouhani–Axelsson correlation for horizontal tubes, with a mean relative error of less than 7.1% for all studied cases. However, despite a mean relative error of less than 13.19% compared to the experimental data in the literature, the reported pressure drop factor remains valid; overprediction remains tolerable for most engineering applications. Second, the scaling effect on the mathematical model, from laboratory to commercial‐scale configuration, was tested with experimental data of the DISS test loop in Platforma Solar de Almeria, Spain. The Monte Carlo Ray Tracing method under the Tonatiuh package allowed for obtaining the nonuniform heat flux distribution. Due to the large size of the evaporation section in the DISS loop (eight collectors), each collector is considered independently in the simulations. Thus, simulations follow each other, taking the numerical results of each collector output as input data in the next collector and so on until the last. The numerical results showed an excellent agreement for the void fraction with 3.53% against the Rouhani–Axelsson correlation. Frictional pressure losses are within a 17.06% error of the Friedel correlation, in the range of previous work in the literature, and the heat loss is less than 4.69% error versus experimental correlation.

Local hotspot thermal management using metal foam integrated heat sink

Single phase liquid-cooled parallel micro/mini-channel heat sinks are commonly used for electronic cooling because of their superior thermal–hydraulic performance. However, heterogeneous integration of electronic chips, especially in 2.5D and 3D integrated circuits (ICs), results in highly non-uniform heat flux distribution and consequently generates localized hotspots. Conventional micro/mini-channel heat sinks often fail to suffice concentrated local hot spots due to the insufficient heat transfer area and local heat transfer coefficient. Therefore, in this paper, three novel water-cooled aluminum (Al) metal foam (MF) integrated compound heat sink layouts, namely solid fin-MF, rectangular fin-MF, and MF heat sink, have been proposed to mitigate local hotspot resulting from non-uniform heat generation. The main concept of the proposed compound heat sinks is to deploy MF in the hotspot region to take advantage of the superior thermal performance of metal foam with minimal pumping power. 3D computational fluid dynamics/heat transfer (CFD/HT) simulations have been performed to quantify and compare the effectiveness of the proposed compound heat sinks with conventional plate-fin heat sink over a wide coolant flow rates/pressure difference ΔP range within the laminar flow regime. Numerical results showed that the solid fin-MF layout provides the best thermal–hydraulic performance compared to all other layouts and offers the highest temperature uniformity, especially at a higher coolant flow rate. Moreover, for the solid fin-MF layout, an optimal porosity and pore density of MF has been identified as 0.9 and 5 PPI (pores per inch), respectively. Finally, at ΔP of 250 Pa and 400 Pa, the optimized solid fin-MF heat sink layout successfully dissipated ∼22.6% and ∼33.4% higher hotspot heat flux compared to the conventional solid fin layout with ∼21% and ∼18.3% lower pumping power penalty while maintaining the peak junction temperature below 85°C.

Flow resistance characteristics of hydrocarbon fuel at supercritical pressure under various heat fluxes in regenerative cooling channel with micro-ribs

Flow distribution of hydrocarbon fuel in regenerative cooling channels is vital for the performance and safety of thermal protection system for scramjet engines. The spatially non-uniform distribution of heat flux at super-high speed (>Mach 6) brings great complexities on flow distribution inside cooling channels. In order to weaken the flow mail-distribution and enhance the adaptability of cooling system to various thermal environments, basic flow resistance characteristics of hydrocarbon fuel flow at supercritical pressure are numerically studied under various heat fluxes. Besides, the regulation patterns of micro-rib on flow resistance of hydrocarbon fuel are also explored. Results show that with incremental heat flux, flow resistance of hydrocarbon fuel in regenerative cooling channels not only shows different trends but also varies in large ranges in different temperature regions. Besides, the flow resistance of hydrocarbon fuel is intensively sensitive to heat flux, especially in trans-critical and supercritical temperature regions and thermal cracking regions. As a useful heat transfer enhancement structure, micro-rib shows extraordinary potential to both eliminate the nonlinearity and reduce the sensitivity of flow resistance to various heating conditions. Two main reasons accounting for this are: Wall shear stress on heated interface is significantly reduced by micro-ribs especially in supercritical and trans-critical temperature regions and thermal cracking regions. Also, enhanced turbulent energy consumption in channel central increases to a limited level even though heat flux is changed up to 5 times. The results provide an innovative perspective that those heat transfer enhancement structures could also be used to regulate flow distribution in parallel cooling channels.

Analysis of phase change material thermal effects in large-scale proton-exchange membrane fuel cell based on open-source computational fluid dynamics

• A proton-exchange membrane fuel cell is thermally analyzed. • The latent heat of phase change material is used for thermal management. • A 3D transient model is developed in OpenFOAM for corresponding simulations. • Phase change materials can cool the system for more than 120 s. • The effect of heat flux distribution and coolant flow direction is evaluated. In recent years, solid–liquid phase change materials (PCM) have been used in various applications for thermal management. However, PCM thermal effects on proton-exchange membrane fuel cells (PEMFC) have not been investigated. In this study, the effects of PCMs on the thermal management of a PEMFC are evaluated using a novel 3D model based on an open-source computational fluid dynamics (CFD) software. In addition, metallic bipolar plates have been considered for this study. The results indicate that when the cooling system is turned off, PCMs can have a good cooling effect for more than 120 s. It is also observed that the temperature of the PCM-equipped model is uniform, contrary to the non-PCM model. Two types of boundary conditions, uniform and non-uniform heat flux, have been considered for this study. The results suggest that if PCM is embedded in anode section, non-uniform heat flux distribution leads to better thermal performance, whereas if PCM embedded in cathode section or in non-PCM design, it is the opposite. Moreover, it is figured out if PCM is located in cathode section, co-direction flows of coolant and reactants lead to lower thermal performance, while it is contrary for other designs. It is also demonstrated that the PCM can store a significant amount of waste heat.

Studies on thermal-hydraulic characteristics of supercritical CO2 flows with non-uniform heat flux in a tubular solar receiver

Supercritical CO2 (SCO2) Brayton cycle is one of the best approaches for concentrated solar power tower, with tubular solar receiver being one of the most attractive options to directly heat SCO2. The superposition of drastically variable properties of SCO2 and uneven distribution of solar irradiance flux poses a great challenge to the design and optimisation of solar receiver, thus the studies on thermal-hydraulic characteristics of SCO2 in solar receiver become crucial to deal with the challenge. In this study, the thermal-hydraulic characteristics of SCO2 in a vertical receiver tube under axially and circumferentially non-uniform heat-flux conditions are numerically studied with average heat flux ranging from 150 kW m−2 to 210 kW m−2 and mass flux ranging from 400 kg m−2 s−1 to 700 kg m−2 s−1, and the influences of buoyancy on the flow and heat transfer characteristics are evaluated. The non-uniform distribution of the axial heat flux leads to 1.2%–20.5% increase in the overall heat transfer coefficient, while more severe local heat transfer deterioration is observed. The buoyancy effect changes the flow structure, resulting in suppression of turbulence intensity and formation of thick momentum and thermal boundary layers, which is closely related to the severe heat transfer deterioration of SCO2 under non-uniform heat-flux conditions. Bo* could well predict the buoyancy effect in a vertical tube under non-uniform heat-flux conditions. Compared with upward flow, downward flow could effectively alleviate heat transfer deterioration and reduce wall temperature gradient especially for axially non-uniform heat-flux condition. The present work could provide guideline for the design and optimisation of tubular solar receiver and solar power system with SCO2 as heat transfer fluid.

Heat transfer and flow structures of supercritical n-decane in a regenerative cooling channel loaded with non-uniform heat flux

A harsh and complex thermal environment in the combustor threatens safe working of scramjets. In this study, heat transfer and flow structures of supercritical n-decane under 3 MPa in a regenerative cooling channel loaded with non-uniform heat flux distributions are investigated, including uniform, sinusoidal, increased, and decreased heat flux distributions. A verified k–ω SST turbulence model was employed, and a corresponding mesh independence study was performed. From this work, the fluid temperature at the outlet of the heated channel is only determined by the averaged heat flux, and all the regenerative cooling channels achieve the same temperature although loaded with different heat flux distributions. Compared with the fluid temperature, the wall temperature distribution is more sensitive to the variations of heat flux distribution. The regenerative cooling channels loaded with the sinusoidal heat flux distributions exist in several high-temperature regions, and the channel loaded with linear distributions changes the trend of temperature distribution. A larger temperature gradient is found in the regenerative cooling channel wall with a lower thermal conductivity. This work provides a good insight into the characteristics of the flow and temperature field of regenerative cooling channels loaded with non-uniform heat flux considering the effect of conjugate heat transfer.

Effects of the Conjugate Heat Transfer and Heat Flux Strength on the Thermal Characteristics of Impinging Jets

A numerical study using the conjugate heat transfer approach has been performed to investigate the effects of boundary heat flux, conduction effect, and working fluid on the thermal characteristics due to the jet impingement process. Air and water are used in this study as working fluids. For the water jet, the volume of fluid method is used to capture and track the interface in the multiphase flow. It is found that the wall conduction may change the fluid-solid interfacial thermal characteristics compared with no conduction or pure convection process. The amount of influence depends on the working fluid, nozzle size, metal thermal conductivity, metal thickness, and boundary heat flux. The conduction inside the solid wall tends to reorganize the uniform heat flux distribution at the boundary to a non-uniform heat flux distribution at the fluid-solid interface. This is mainly attributed to the conjugate effect of the solid. For a given jet Reynolds number and boundary heat flux, the conjugate heat transfer results divulge that the convective heat flux removed from the stagnation point is higher for the air jet than for the water jet. Contrary to the air jet, the effect of thermal boundary on the stagnation Nusselt number profile is negligible for the water jet. The disc material and thickness have no obvious effect on the stagnation Nusselt number profile for both air and water fluids.

Evaluation of roll dry granulation process on the high‐viscosity melt solidification and heat recovery

AbstractHigh‐viscosity melt with temperature above 1600 K has great potential for energy saving. A mathematical model was proposed on the heat transfer between the rotating roll and melt in a roll dry granulation system, aiming at the efficient granulation and heat recovery of high‐viscosity melt. In the model, the relationship between the rotation angle and time was utilized to simplify the three‐dimensional dynamic process to a one‐dimensional static problem. Then, the influences of the roll material, dimension, rotational speed, and the melt shedding angle on the system performance were investigated. Simulation results indicated that increasing the thermal conductivity or decreasing the wall thickness will result in a higher cooling rate but a more nonuniform heat flux distribution. The possible vibration and thermal fatigue due to the nonuniform heat flux distribution will cause a poor working stability. Heat‐resistant steel is a better choice than copper alloy. The optimum wall thickness is about 19 mm, and the rotational speed should be kept below 17 rpm. The overall exergy efficiency increased from 37% to 59%, when the melt shedding angle changed from 120° to 28.8°. This study provides a further feasible method for the efficient granulation and heat recovery of high‐viscosity melt.