Wall-normal Heat Flux Research Articles

Unsteady conjugate heat transfer simulation of wall heat loads for rotating detonation combustor

Rotating detonation engines (RDEs) are the most promising pressure-gain combustion devices, but their long-duration operations are hindered by the harsh thermal environment inside the chamber. This study analyzes the instantaneous and average heat loads on chamber walls of RDEs based on the newly developed unsteady conjugate heat transfer (CHT) OpenFOAM solver named multiRegionBYRFoam. To enhance accuracy in predicting heat transfer characteristics compared to decoupled simulations focusing solely on fluid or solid behavior, three-dimensional CHT simulations are conducted for a premixed H2/air annular RDE coupling the detonation simulation with heat conduction in both inner and outer chamber walls. The transient time evolutions of wall heat flux in RDEs are numerically captured for the first time and agree well with experiments. The calculated peak wall heat flux is 1.98 MW/m2 at the inner wall and 2.63 MW/m2 at the outer wall when a single detonation wave propagates with a mass flow rate of 0.227 kg/s. By investigating the influence of inlet flow conditions and detonation modes, valuable guidelines on designing efficient thermal management systems for RDEs are obtained: larger mass flow rates and multi-wave modes result in higher average wall heat flux; the heat flux at the outer wall exceeds that at the inner wall while both walls require effective cooling for gas turbine engines with a rotating detonation combustor. Furthermore, a novel heat transfer model for RDEs is proposed based on a thermal operation map depicting total heat transfer rates to describe the nonlinear impact of mass flow rate and number of detonation waves, which can be employed to predict total wall heat loads under specific operation conditions of RDE.

Investigation of the thermal response characteristics of the loop thermosyphon under convective boundary conditions

The two-phase loop thermosyphon (TPLT) is a highly efficient passive heat transfer device that is widely applied in various fields. This paper experimentally and numerically investigates the thermal response performance of a large-scale TPLT under various convective boundary conditions. Experimental studies have been carried out to explore the effects of different working fluids, filling ratios, cold and heat source temperatures, and mass flow rates on the thermosyphon’s performance. Meanwhile, a two-dimensional Computational Fluid Dynamics (CFD) simulation model of the TPLT is established and validated. The results indicate that the start-up procedure of the TPLT is highly dependent on the heat source temperature and the working fluid. Normally, the TPLT can start when the heat source reaches a certain temperature. In general, using methanol as the working fluid is more favorable to start-up compared to the water and ethanol TPLTs. The experimental results also show that the heat transfer capacity of the TPLT increases with increasing heat source temperature while increasing cooling temperature decreases heat transfer capacity. The best heat transfer performance of a TPLT charging methanol is observed at a filling ratio of 70 % with a heating mass flow rate of 1 L/min. At that point, the convective heat transfer coefficient of outside the evaporator is 1036.7 W/(m2·K). Moreover, the simulation results reveal that the average wall heat flux of the TPLT’s evaporator initially decreases and then gradually stabilizes with time. During stable operation, the wall heat flux density of the evaporator exhibits an initial increase in the pool section followed by a subsequent decrease with increasing wall height. This work provides insight into the heat and fluid flow characteristics of the TPLT under convective boundary conditions.

Direct numerical simulation of thermal turbulence in an aero-engine blade channel

The flow and heat-transfer phenomena are simulated by direct numerical simulation in the NACA65 blade channel with a Reynolds number equaling to 1.367×105. Induced by the strong adverse pressure gradient, the flow separations are observed on the suction surface with the multi-scale and multi-layer vortices. The DNS results indicates that the backflow transition is triggered by the small-scale spanwise-vortex fluctuations due to the viscous linear instability, and thereafter is further stretched into the quasi-streamwise vortices due to the upper K-H rolls, which generates the typical coherent structures in the flow-separation region. The Reynolds shear stresses and turbulent heat flux are found very strongly and actively concentrating in the region bounded by the blade-wall and the upper boundary of separation where the variety of ejections and sweeps are observed. These ejections and sweeps promote the momentum and heat transfers, which results in the large temperature gradients in both the near-wall and flow-separation regions. Moreover, the separation and reattachment zones present the non-similarity distributions for both the wall-normal heat flux and Reynold shear stresses due to the strong adverse pressure gradient. Therefore, the diverse profiles of velocity and temperature can be found developing in streamwise along the suction surface. However, through applying the newly-developed wall-bounded law formulations, it is demonstrated that these wall-laws are even universally capable of accurately representing these diverse velocity and temperature profiles.

Wall-attached temperature structures in supersonic turbulent boundary layers

It is well known that low- and high-speed velocity streaks are statistically asymmetric. However, it is unclear how different the low- and high-temperature structures (T-structures) are even though they are strongly coupled with the streamwise velocity. Therefore, this paper identifies three-dimensional wall-attached temperature structures in supersonic turbulent boundary layers over cooled and heated walls (coming from direct numerical simulations) and separates them into positive and negative families. Wall-attached T-structures are self-similar; especially, the length and width of the positive family are linear functions of the height. The superposed temperature variance in both positive and negative families exhibits a logarithmic decay with the wall distance, while the superposed intensity of the wall-normal heat flux in the negative family shows a logarithmic growth. The modified strong Reynolds analogy proposed by Huang, Coleman, and Bradshaw [“Compressible turbulent channel flows: DNS results and modelling,” J. Fluid Mech. 305, 185–218 (1995)] is still valid in the negative family. The relative position between T-structures of opposite signs depends on the wall temperature and that in the cooled-wall case differs significantly from the relative position between low- and high-speed streaks, especially those tall ones. In the cooled-wall case, although positive temperature fluctuations below and above the maximum of the mean temperature can cluster to large-scale wall-attached structures, they are very likely dynamically unrelated.

A numerical simulation of tube geometry effect on the performance of regenerators in Organic Rankine Cycle systems using the Volume of Fluid method

In this work, the tube geometry effect on the performance of regenerators in ORC systems is numerically studied using the Volume of Fluid (VOF) method. Three tube geometries are investigated: normal, divergent, and convergent tubes. The divergent tube offers increasing space, which is beneficial to bubble growth and delay the tube clogging induced by the increasing bubble size. The delay of tube clogging in the divergent tube can benefit the boiling heat transfer performance. The decreasing flow velocity due to the increasing space can also reduce the friction pressure drop. As a result, the divergent tube induces smaller total pressure drop as well as less pressure fluctuation, which are good for pump efficiency. It is found that the pressure drop can be up to 34.5% lower in divergent tube while the averaged wall heat flux is 2.94% higher comparing with the normal one. The features of enhancing heat transfer performance and reducing total pressure drop with less pressure fluctuation of the divergent tube can be used as a novel design for the liquid side of regenerators. The convergent tube will induce higher pressure drop with higher heat flux before the tube is clogged by the bubbles. However, the heat flux decreases as the tube clogging occurs. Due to the higher pressure drop induced, the convergent tube might not be suitable for the design of the liquid side of regenerators. It is the first time to study the heat transfer problem with a single vapor bubble considering the geometric effect, and this work provides physical insights on heat transfer performance and pressure drop for a two-phase boiling flow. The optimized geometry can increase the energy efficiency, whch could profoundly impact many industrial applications.

Influence of viscosity on the thermal behavior of fluids in a sealed can

Homogeneous fruit juice in a sealed container available in the commercial market exhibits some degree of non-Newtonian behavior with a wide viscosity range. During thermal processing, it is necessary to understand the effect of viscosity on thermal behavior, which may guide insight into the choice of physics involved in the conservation law equations. In this context, the present study considered the Carboxyl Methyl Cellulose (CMC) solutions (a viscosity-enhancing agent) as model foodstuffs to understand the effect of viscosity on the heat transfer mechanism in the thermal treatment of canned liquid products. Computational Fluid Dynamics (CFD) was employed to analyze the thermal behavior of different concentrations of CMC solutions, estimated based on averaged wall heat flux, averaged heat transfer coefficient, volume-averaged temperature, and minimum temperature. The effect of the CMC solutions' rheological properties on the thermal behavior was evaluated by comparing it with the pure conduction simulations. The time–temperature history obtained from the simulations was coupled with the kinetic parameter of microbial destruction to predict the heating time. When the viscosity increases due to increasing the concentration of CMC solution, the natural convection is suppressed, which leads to the heat transfer in almost pure conduction mode.

Theoretical analysis of convective heat flux structure in the incompressible turbulent boundary layer on a porous plate with uniform injection and suction

Although many experimental and numerical studies on thermal convection exist for turbulent transpiration boundary layer flows on a porous structure, the general convective heat flux formula is urgently needed to clarify the influence of injection or suction on the energy transfer mechanism of turbulent heat convection. The two-dimensional (2D) theoretical convective heat flux structure obtained previously is therefore applied to the incompressible turbulent thermal boundary layer on a porous flat plate with uniform injection and suction. The energy balance relationship between the streamwise and wall-normal heat flux components is established and the effects of injection and suction on turbulent convective heat fluxes are analyzed. The explicit analytical expressions of turbulent skin friction factor, convective heat transfer coefficient and Stanton number are obtained based on the heat flux theory and verified by the previously experimental measurements. The turbulence characteristics of convective heat transfer with uniform injection and suction are revealed by the proposed key parameters. A hybrid control volume analysis for energy transfer inside the porous media plate is performed and applied to the cases of transpiration cooling and enhancing heat transfer, respectively, and a novel calculation formula for convective heat transfer is proposed in the form of heat flux instead of the heat transfer coefficient. It is also found that the direction of the resultant convective heat flux combining the conduction with advection is not always to remain that of the negative temperature gradient, and it depends not only on the temperature difference direction as well as velocity direction, but also on the magnitude contrast of the conductive and advective heat fluxes.

Numerical parametric study on the burner arrangement design for hydrogen production in a steam methane reformer

A numerical parametric study on the burner arrangement design for a steam methane reforming reactor was conducted under three burner configurations: a single co-axial inside burner (SCIB), a single top burner (STB), and multiple top burners (MTB). The burner combustion gas inlet angle was changed to 25°, 45°, and 90° with respect to the horizontal plane. Moreover, the number of reformer tubes inside the reactor was changed to four, six, and eight tubes arrangements. Furthermore, the models were numerically evaluated for temperature distribution inside the combustion space and hydrogen mole fraction in the reactor by incorporating the Xu and Forment model using a user-defined function (UDF). The results show that the STB configuration is preferable over the SCIB and MTB configuration due to the uniform temperature distribution inside the combustion space and efficient heating from the combustion gas. Furthermore, the standard deviation of the temperature inside the combustion space was found to be lower for the STB arrangement. Moreover, the STB configuration reported a maximum temperature uniformity index of 0.92 for the eight-tubes reformer arrangement. The value of the average wall heat transfer coefficient and wall heat flux at the reformer tube surface for STB configuration was 396.6 W/(m2K) and 21.7 W/m2, respectively. The velocity inlet angle of the burner combustion gas also plays an important role in the methane steam reforming reaction. A burner combustion gas inlet angle of 45° was observed to have better hydrogen conversion than the 25° and 90° inlet angles due to the proper mixing, leading to more effective heat transfer to the reformer tubes.

Effects of Particle Stacking Angle on Heat Transfer Characteristics of Particles Close to the Wall

The primary energy demand increases, but a large amount of waste heat resources were not effectively used. To explore the influence of particle stacking structure on waste heat recovery process, CFD method was used to simulate. An unsteady heat transfer model of two particles was established, effect of particle stacking angle on heat transfer characteristics of the particles close to the wall under different initial temperature conditions was studied. Results show that: higher initial temperature, resulting in increased heat transfer time, the larger particle stacking angle causes the shortening of heat transfer time. When initial temperature is 1073 K, the average wall heat flux shows a trend of rapid decline first and then a slow one. At the same moment, the larger stacking angle causes smaller particle average temperature. The change of particle stacking angle shows a greater impact on the temperature of the particles close to adiabatic wall. The increase in the stacking angle resulting in better heat transfer characteristics between particles.

Identification of the running status of membrane walls in an opposed fired model boiler under varying heating loads

To understand the running status of membrane walls in an opposite firing boiler, a scale-down model furnace was established, and the temperature, heat flux, strain and stress distributions are investigated under four heating loads. Results show that the average membrane wall temperature and heat flux present a continuous increase from 42 °C and 16 W/m2 to 96 °C and 50 W/m2, respectively, with the heating load increase from 25% to full load. The average strain and stress also rise from 88.7 µm and 0.094 MPa to 152.5 µm and 0.148 MPa when the heating load increases from 25% to 50%, but then they keep stable when further increasing the heating load. General distribution patterns of each tested parameter are found relatively similar under varying heating loads. High strain and stress distributions are always detected at the middle left zone of side walls and the middle of the rear wall, where wall temperatures are measured high. External fixed constraints and high-temperature thermal strain is found jointly affecting the strain and stress distribution of the membrane wall. A simplified mechanism of how the strain and stress on boiler membrane walls evolve is proposed after comprehensive discussion of the measurement results.

Turbulent Heat-Transfer Enhancement in Boundary Layers Exposed to Free-Stream Turbulence

Direct numerical simulations (DNS) are performed to study the effect of free-stream vortical forcing on a thermal turbulent boundary layer. In presence of external perturbations, the heat-transfer rate from the wall is increased relative to the unforced case. An explanation is provided, and starts from the free-stream forcing which enhances the Reynolds stresses inside the boundary layer, and in particular the wall-normal component. As a result, the wall-normal heat flux is also increased, which has the dual effect of distorting the base temperature profile and enhancing the production of scalar variance; both contribute to the increase in the wall heat-transfer rate. In addition, the flow sustains higher thermal fluctuations, even though the free-stream forcing is only vortical, and not thermal. These changes are accompanied by modification of the spectra of the thermal field in the outer region of the boundary layer, where large-scale thermal structures are formed in response to the large-scale velocity motions. In the near-wall region, the thermal structures are modulated by the outer hydrodynamic field and are strengthened relative to the unforced flow.

CFD analysis of the combustion process in a boiler of a 160 MWe power plant: leakage influence

This paper presents a developed and validated CFD model of a boiler with the objective of studying a presumed defective actual operating condition, that is, air leakage into the furnace. Three cases were assessed, concerning the amount of air leakage across the boiler water seal. The base case considered the actual operational condition of 5% air leakage. Case 1 assumed 10%, and Case 2 simulated a more extreme leakage of 25%. The influence of the air leakage was analyzed with emphasis on temperature profiles, flow, wall heat flux, O2, CO, NOx, Soot and CO2 formation. Eddy dissipation together with finite rate chemistry models were used to model the combustion process, while the k-ω approach was considered to predict the turbulence effect. Brazilian pulverized coal type CE3100 was adopted as fuel, burning in atmospheric air. The conservation equations of mass, momentum, energy and chemical species were solved by Finite Volume Method using Ansys CFX commercial software. As main results, it has been observed that air leakage across the water seal has influence over the profiles of temperature and concentration of oxygen and carbon dioxide. Significant amounts of air leakage can induce the plant staff to change the amount of air to be fed through the burners, changing the burning condition, thus impairing energy generation. Although the simulated case concerns a specific operational condition of a given thermal power plant, the results demonstrate the capability of CFD as a decision support tool. It has been found that even a small drop in the flue gas temperature in the combustion chamber due to air leakage in the water seal significantly affects the radiation heat transfer from flue gases to the chamber walls. The overall reduction in average wall heat flux was − 0,3% and − 1,81% of base case for cases 1 and 2, respectively. This situation alters the boiler behavior related to the formation of pollutants, especially NOx, also reduces the burning efficiency, increasing the concentration of CO and CH4 in the exit region.

Numerical analysis of hollow droplet impacts on a dry flat surface

Hollow droplet impacting on a dry fat surface has obvious difference in its dynamics and heat transfer behaviors comparing with continuous dense droplet impact. In the present research, a numerical model based on coupled level set and volume of fraction (CLSVOF) method is applied to investigate dynamics and heat transfer of a hollow droplet impact on a dry flat surface. Dynamics and heat transfer of hollow droplet with high and atmospheric cavitation-bubble pressure are compared with that of continues dense droplet. Both atmospheric-cavitation-pressure (ACP) and high-cavitation-pressure (HCP) hollow droplet appear obvious spreading and central counter-jet features after impact. However, the central counter jet is not observed in a continuous dense droplet impact. Pressure difference inside hollow droplet is the main reason leading to droplet spreading and central counter jet formation. HCP hollow droplet expands before impact and the diameter increasing is found to be closely related to Re. HCP hollow droplet has a smaller spread factor and average wall heat flux, while a larger dimensionless height of counter jet than those of ACP hollow droplet. Moreover, compared with continuous dense droplet, hollow droplet has a smaller spread factor and average wall heat flux.

Numerical analysis of droplet impact and heat transfer on an inclined wet surface

A numerical model based on the coupled level set and volume of fraction (CLSVOF) method is developed to investigate the dynamics and heat transfer of a droplet impacting on an inclined wet surface. Numerical results show that the droplet shows spreading, edge jets and splashing upon impact with high velocities. The front spreading factor and liquid velocity are larger than the back-spreading ones. As the impact velocity increases, both the front and back spreading factors and velocities increase. Significant air entrapment is observed when the droplet approaches the liquid film on the solid surface. The pressure difference between the trapped air and the liquids leads to the formation of an air film underneath the droplet. The entrapped air also shows a dynamic process. It becomes a small bubble at the initial stage of droplet impact and reduces heat transfer from the liquid droplet to the surface. This effect diminishes when the trapped air escapes the liquids. The average wall heat flux is found to be closely correlated to the impact velocity, but that correlation weakens as the impact velocity increases. Results from this study provide better understandings of the fluid dynamics and heat transfer during droplet oblique impact on inclined wet surfaces.

Bubble Lifecycle During Heterogeneous Nucleate Boiling

Heterogeneous nucleate boiling over a flat surface has been studied through complete numerical simulations. During the growth and departure of the vapor bubble, the interface is tracked following a coupled level-set and volume of fluid approach. A microlayer evaporation model similar to Sato and Niceno [“A depletable microlayer model for nucleate pool boiling,” J. Comput. Phys. 300, 20–52 (2015)] has been deployed in this investigation. A detailed study of the changes in microlayer structure as a result of different modes of boiling scenario has been performed. The departure diameter is found to increase with an increase in substrate superheat. The predicted departure diameter has been compared with the available experimental and analytical results. A power-law curve has been obtained for depicting the growth rate of bubble depending on the degree of superheat at the wall. The space–time averaged wall-heat flux at different values of superheat temperature of substrate is obtained. Bubble growth during subcooled boiling at a low and intermediate subcooled degree has been observed through direct numerical simulations. The variations in bubble dynamics after departure in saturated and subcooled liquid states have been compared.

Combustion and heat transfer characteristics of co-firing biomass and coal under oxy-fuel condition

A numerical investigation was conducted on co-firing biomass and coal under oxy-fuel condition with the refined combustion model. The effects of gas-phase reactions caused by various volatiles of coal and biomass were considered. The influences of biomass fraction and combustion atmosphere on the reaction rate of volatile, the distribution of wall heat flux, and the burnout behavior were analyzed. The results show that the reaction is more active for the volatile of Paulownia wood chips than that of coal. The average wall heat flux suffers a decline when the combustion atmosphere is switched from air to oxy-fuel condition, while the O2 fraction is 24%. The wall heat flux of hopper rises by 29.97% to 162.7% as the biomass fraction increases from 10% to 30% under various atmospheres. Due to the variation in trajectories of fuel particles and the change of temperature within the furnace, the combustion atmosphere and the biomass share fraction affect the burnout performance to some extent. The working performances of all cases were evaluated, and the optimal operation conditions for co-firing different co-firing scenarios were recommended.

Quasi-direct numerical simulation of forced convection over a backward-facing step: Effect of Prandtl number

Quasi direct numerical simulations (quasi-DNS) of forced heat convection over a backward-facing step are performed to study the turbulent heat transfer of low Prandtl number fluids in complex flow regimes. Reynolds number based on step height and inlet bulk velocity equals 4805. The expansion wall is heating by uniform dimensionless heat flux density. Effects of Prandtl number (Pr = 0.01, 0.025, 0.1, 1.0) on mean temperatures, heat transfer coefficients, heat fluxes, turbulent Prandtl numbers and instantaneous velocity and temperature fluctuations, are compared with each other. For low Prandtl numbers, diffusion effect is prominent, thermal boundary layer is much thicker, Nusselt number is smaller and Stanton number is larger. The maximum heat transfer location moves upstream of the reattachment point for larger Prandtl numbers while it is at the reattachment point for low Prandtl numbers. Wall-normal heat flux decomposition shows the turbulent part is comparable to the molecular one in the recirculation zone even for low Prandtl numbers. Turbulent Prandtl number profiles are irregular in the recirculation zone but in the recovering zone they increase first and then decrease. Their peak values decrease as Prandtl number increases. Near-wall instantaneous fields for streamwise velocity and temperature fluctuations show that the streak structures disappear in the recirculation zone but exist in the recovering zone. These highly-resolved data with heat transfer could serve for the validation and improvement of turbulence heat transfer models for low Prandtl media in future.

Numerical Study of Single Bubble Growth on and Departure from a Horizontal Superheated Wall by Three-dimensional Lattice Boltzmann Method

A three-dimensional hybrid lattice Boltzmann method was used to simulate the progress of a single bubble’s growth and departure from a horizontal superheated wall. The evolutionary process of the bubble shapes and also the temperature fields during pool nucleate boiling were obtained and the influence of the gravitational acceleration on the bubble departure diameter (BDD), the bubble release frequency (BRF) and the heat flux on the superheated wall was analyzed. The simulation results obtained by the present three-dimensional numerical studies demonstrate that the BDD is proportional to $g^{\mathrm {-0.301}}$ , the BRF is proportional to $g^{\mathrm {-0.58}}$ , and the averaged wall heat flux is proportional to $g^{\mathrm {0.201}}$ , where g is the gravitational acceleration. These results are in good agreement with the common-used experimental correlations, indicating the rationality of the present numerical model and results.

Dropwise condensation patterns of bismuth formed on horizontal and vertical surfaces

Simulation of dropwise condensation of bismuth vapor on a subcooled hydrophobic surface is discussed in the present study. The process starts from nucleation of drops, followed by their growth and coalescence, resulting in drop instability that removes them from the surface. Fresh nucleation occurs at the exposed nucleation sites, thus creating a cycle of vapor condensation and liquid removal. The drop size distribution over the surface determines the instantaneous surface averaged wall heat flux. Wall shear stresses are generated during coalescence process and also when large drops start moving due to instability, which is gravitational in origin; hence, the largest drop diameter achieved depends on the surface orientation. Near-horizontal and vertical surfaces have been studied in the present work. Drop instability affects the periodicity of the condensation process and the average drop size and thus, the wall heat flux and wall shear stress. Coalescence of adjacent drops is a momentary step with a timescale of milliseconds, but the velocities generated are substantial. Coalescence velocities and time intervals have been determined by scale analysis, and the sensitivity of wall heat flux and wall shear stress to these ensuing velocities are delineated. The multiscale model developed is computationally intensive and has been simulated on large condensing surface areas using MPI on a parallel architecture. Bismuth condensation properties have been compared with water. Large heat fluxes and shear stresses are seen to be attained sporadically during coalescence for short time instants and do not contribute significantly to the surface-averaged values. On the other hand, wall shear stresses are found to be large enough to damage the hydrophobic coatings and degrade surface wettability, thereby hindering dropwise mode of condensation.

Slip effects on turbulent heat transport over post and ridge structured superhydrophobic surfaces

Forced convection and turbulent scalar transport over a structured superhydrophobic walls composed of periodic arrays of square posts and ridges textures are numerically investigated in a periodic channel. The flow physics and thermal transport within the fluid are studied using Direct numerical simulation (DNS), assuming the plastrons are flat. Slip velocities, Nusselt number, turbulent Prandtl number and turbulent heat fluxes are determined for both square posts and streamwise ridge shaped feature geometry configurations at a friction Reynolds number of Reτ=180. This article provides an insight that superhydrophobic surfaces enhance turbulent heat fluxes and thermal fluctuations in the laminar-sublayer region. With increasing feature wavelength, the turbulent heat fluxes in the buffer layer and outer layer drop for both square posts and streamwise ridges. When compared with a smooth no-slip channel, the diffusion term in the budget of thermal fluxes pointed to the role of organized lateral flow motions in enhancing wall-normal heat-flux, and a reduction in large scale transport of streamwise heat fluxes by near-wall coherent structures.