Numerical simulations of droplet train and free surface jet impingement

The cooling behavior of the impingement of a droplet train, and free surface jets over a heated and pre-wetted surface is explored employing an Algebraic Volume-of-Fluid methodology. The code is based on a modified version of the two-phase numerical solver interFoam (OpenFOAM) (Trujillo and Lewis, 2012). Two versions of the free surface jet are studied. The first consists of a fully-developed profile exiting the nozzle, and the second is characterized by a uniform velocity distribution. Results show that both jet configurations have higher cooling performance than the droplet train locally and globally, with the fully-developed case being the most effective of the two jet arrangements. Locally, the performance is measured by radial profiles of the boundary-layer-displacement thickness and heat transfer coefficient. Globally, the cooling effectiveness is directly proportional to the surface area that resides within the high-convection region, i.e. before the boundary layer separation point. On a temporal basis, the liquid film within the impingement region of the droplet train exhibits pronounced variations in velocity magnitude and film thickness. This is directly attributed to the nature of continuous droplet impacts affecting the impingement region, and gives rise to an unsteady cooling and heating of the fluid near the wall. In contrast for the jets, the film and the corresponding free surface are nearly steady with only minor perturbations.     

Experimental study on effect of relative humidity on heat transfer of an evaporating water droplet in air flow

Dispersed water droplets are often seen in environmental air flows in rain, cloud, mist, sea spray and so on. It is therefore of great importance to precisely estimate heat transfer between water droplets and atmospheric air in developing a reliable climate model. The purpose of this study is to fabricate the measurement system for the temperature of a small water droplet in air flow under the controlled relative humidity condition and to investigate the effect of relative humidity on heat transfer across the surface of an evaporating water droplet in air flow. The results show that the droplet temperature decreases in the low-relative-humidity condition, whereas it increases in the high-relative-humidity condition. Nusselt number on the droplet surface is not affected by the relative humidity.     

弓形折流板开孔位置的数值模拟研究

在相同的开孔面积和开孔数目前提下,本文数值研究在开孔位置不同时圆缺高度为0.2D(D为折流板直径)的单弓型折流板换热器的壳程换热与流动阻力问题。数值结果表明:在折流板压强高的“高压区”,均匀地开孔对减小换热器壳程压降效果更好,其综合换热性能的性能评价因子E值也更好;在壳程入口速度为0.1m/s时,通过改变开孔位置,壳程压降可优化3%左右。     

Experimental analysis of the local heat transfer coefficient of falling film evaporation with and without co-current air flow velocity

This paper presents the experimental results of the local heat transfer for falling film evaporation of water sheet by solving the inverse heat conduction problem. It is shown that the local heat transfer coefficients increase by increasing the air flow velocity, the film liquid flow rate or decreasing the inlet bulk film temperature. Correlations for the mean heat transfer coefficients in the absence of superimposed flow for the stagnation region, the thermally developed region and the bottom of the heated cylinder are proposed.     

Numerical and experimental analysis of flow and heat transfer in a fuel assembly mock-up with transverse flow above the rods

Thermal-hydraulic conditions in a partially uncovered nuclear fuel assembly mock-up are studied with particular focus on the influence of the horizontal air flow above the rod bundle. The investigations are performed at the ALADIN test facility, which models a boiling water reactor fuel assembly at a 1:1 scale both axially and radially. In the scenario studied, the main heat transfer mechanisms – conduction, convection and radiation – are strongly coupled and all are of similar importance. A combination of measurements and CFD simulations serves to analyze the heat transfer processes in detail. Contrary to previous studies in this field, all heat transfer mechanisms were considered in the simulation with sophisticated models. The numerical results show a good agreement with the measurements, given the inevitable differences between the approaches. Although the successive evaporation of cooling water in a fuel assembly is a transient, multiphase process, the steady, single-phase simulation yields acceptable results. While single effects are overestimated in the simulation, the important dependencies are predicted similarly. A general result is that the maximum cladding temperature rises with decreasing water level. Further results indicate an impact of the horizontal air flow on the residual heat removal for moderate rod powers. Higher horizontal velocities above the fuel assembly lead to slightly higher temperatures inside. A characteristic flow field forms in the test facility that prevails for all studied water levels and horizontal velocities. However, it has only a minor effect on the temperature distribution in the central rod bundle. By combining experiments and numerical simulations, the study provides important information about the decisive parameters for the heat exchange in a spent fuel pool in case of an accident with loss of cooling. The exposed length of the fuel rods is of much more importance than the magnitude of the horizontal velocity above the fuel assembly.     

Conjugate forced convection and heat conduction in circular microchannels

The effects of axial heat conduction in the solid walls of microchannels of circular cross-sections are analyzed here. A systematic approach is adopted, with the aim of pointing out the influence of geometrical parameters and of solid wall thermal conductivity on microchannel heat transfer. The reliability of a commonly adopted criterium, based on the so-called axial conduction number, to assess the relevance of axial heat conduction is also discussed. Numerical simulations concern the simultaneously developing laminar flow of a constant property fluid in microchannels of different length, wall thickness and wall material, heated with a uniform heat flux at the outer surface, for different values of the Reynolds number. Moreover, since often in experimental tests the two end sections of the microchannel wall are not perfectly insulated, the effects of heat losses through these sections are also considered. A hybrid finite element procedure, which implies the step-by-step solution of the parabolized momentum equations in the fluid domain, followed by the solution of the energy equation in the entire domain, corresponding to both the solid and the fluid parts, is used for the numerical simulations.     

Numerical analysis of the transient conjugated heat transfer in a circular duct with a power-law fluid

We treat numerically in this paper, the transient analysis of a conjugated heat transfer process in the thermal entrance region of a circular tube with a fully developed laminar power-law fluid flow. We apply the quasi-steady approximation for the power-law fluid, identifying the suitable time scales of the process. Thus, the energy equation in the fluids is solved analytically using the well-known integral boundary layer technique. This solution is coupled to the transient energy equation for the solid where the transverse and longitudinal heat conduction effects are taken into account. The numerical results for the temporal evolution of the average temperature of the tube wall, _av, is plotted for different nondimensional parameters such as conduction parameter, , the aspect ratios of the tube, and ₀ and the index of power-law fluid, n.     

Evaporation of thin liquid droplets on heated surfaces

We carry out combined experimental and theoretical studies of liquid droplet evaporation on heated surfaces in a closed container filled with saturated vapor. The droplets are deposited on an electrically heated thin stainless steel foil. The evolution of droplet shapes is studied by optical methods simultaneously with high-resolution foil temperature measurements using thermochromic liquid crystals. A mathematical model is developed based on the assumptions that the droplet surface has uniform mean curvature and the contact line is pinned during evaporation. Both the dynamics of liquid–vapor interface and the temperature profiles at the foil are shown to be in good agreement with the experimental data.     

Inertia dominated flow and heat transfer in liquid drop spreading on a hot substrate

The present work deals with computational modeling of the fluid flow and heat transfer taking place in the process of impact of a cold liquid drop (T_d = 20-25 °C) onto a dry heated substrate characterized by different thermophysical properties. The computational model, based on the volume-of-fluid method for the free-surface capturing, is validated by simulating the configurations accounting for the conjugate heat transfer. The simulations were performed in a range of impact Reynolds numbers (Re = 2000-4500), Weber numbers (We = 27-110) and substrate temperatures (T_s = 100-120 °C). The considered temperature range of the drop-surface, i.e. liquid-solid system does not account for the phase change, that is boiling and evaporation. The model performances are assessed by contrasting the results to the reference database originating from the experimental and complementary numerical investigations by Pasandideh-Fard et al. [Pasandideh-Fard, M., Aziz, S., Chandra, S., Mostaghimi, J., 2001. Cooling effectiveness of a water drop impinging on a hot surface. International Journal of Heat and Fluid Flow, 22, 201-210] and Healy et al. [Healy, W., Hartley, J., Abdel-Khalik, S., 2001. On the validity of the adiabatic spreading assumption in droplet impact cooling. International Journal of Heat and Mass Transfer, 44, 3869-3881]. In addition, the thermal field obtained is analyzed along with the corresponding asymptotic analytical solution proposed by Roisman [Roisman, I.V., 2010. Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition. Journal of Fluid Mechanics, 656, 189-204]. Contrary to some previous numerical studies, the present computational model accounts for the air flow surrounding the liquid drop. This model feature enables a small air bubble to be resolved in the region of the impact point. The reported results agree reasonably well with experimental and theoretical findings with respect to the drop spreading pattern and associated heat flux and temperature distribution.     

Modeling the evolution of droplet size distribution in two-phase flows

A theoretical model is developed in the present study to simulate droplet motion and the evolution of droplet size distribution (DSD) in two-phase air/dispersed water spray flows. The model takes into account several processes which influence DSD and droplet trajectory: droplet collision and coalescence, evaporation and cooling, gravitational settling, and turbulent dispersion of dispersed phase. The DSDs determined by the model at different locations in a two-phase flow are evaluated by comparing them to experimental observations obtained in an icing wind tunnel. The satisfactory coincidence between simulation and experimental results proves that the model is reliable when modeling two-phase flows under icing conditions. The model is applied for two particular examples in which the modification of DSD is calculated in two-phase flows under conditions describing in-cloud icing and freezing drizzle.     

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method. The English text was polished byYunming Chen.     

燃气射流冲击传热特性的数值模拟

针对射流传热问题,利用基于RNGk-ε湍流模型的数值方法模拟了射流垂直冲击平板的流动过程,并与实验数据比较,验证了模型的可行性。在此基础上,以火箭喷管入口参数为入口条件,建立了超音速燃气射流垂直冲击平板和冲击浸没平板的计算模型,分析了不同冲击条件下努塞尔数分布规律和温度分布规律, 论述了超音速射流传热的特性及影响传热特性的因素。得到了冲击距离为(14~18)D的努塞尔数取值范围,并表明冲击距离和射流温度是影响传热效率的关键因素;冲击距离增加,传热效率降低,冲击平板表面的射流温度越高,传热效率越高。     

Numerical simulation of transient response of heat transfer from a hot-wire anemometer transducer

Both the steady state and transient response of the Nusselt number to variations in Reynolds number over the range 1 to 40 are given by the analysis of a time dependent numerical simulation of a hot-wire anemometer transducer described here. Transducer response can be modelled suitably by considering the system to consist of a phase independent non-linearity followed by a non-linear differential equation whose coefficient (approximate time constant) is Nusselt number dependent. Errors associated with slip flow and free convection constrain the minimum size of a hot-wire which may be used in calibration anemometry while the wire thermal inertia and, to a lesser extent, the response of the Nusselt number to Reynolds number limits the use of large diameter wires. Thus, although the tendency has been to use finer and finer wires, the basic fluid mechanics suggests that a compromise in the choice of the wire diameter is appropriate. Thus development of even more sophisticated hot-wire anemometer control systems as well as accurate calibration techniques for measurement in flows containing large amplitude high frequency turbulence is required     

A random simulation of droplet distribution in nozzle and plume flows

A simple entrainment model is used to estimate droplet streamlines, velocity and mass flux in rocket exhaust plumes. Since droplet mass flux constitutes only about 1% of the exhaust mass flux, the effect of droplet entrainment on the gas flow is neglected. The novelty of the present model is in obtaining the droplet distribution within the nozzle by assuming a small radial random velocity component for droplets at the throat. Gas flow in the nozzle is approximated as isentropic plus a correction for the boundary layer. The computed distribution of droplet mass flux is found to be in good agreement with experimental data. Received 15 January 1996 / Accepted 11 September 1996     

Aero-thermal optimization of in-flight electro-thermal ice protection systems in transient de-icing mode

Even if electro-thermal ice protection systems (IPS) consume less energy when operating in de-icing mode than in anti-icing mode, they still need to be optimized for energy usage. The optimization, however, should also take into account the effect of the de-icing system on the aerodynamic performance. The present work offers an optimization framework in which both thermal and aerodynamic viewpoints are taken into account in formulating various objective and constraint functions by considering the energy consumption, the thickness, the volume, the shape and the location of the accreted ice on the surface as the key parameters affecting the energy usage and the aerodynamic performance. The design variables include the power density and the activation time of the electric heating blankets. A derivative-free technique, called the mesh adaptive direct search (MADS) method, is used to carry out the optimization process, which would normally need a large number of unsteady conjugate heat transfer (CHT) calculations for the IPS simulation. To avoid such prohibitive computations, reduced-order modeling (ROM) is used to construct simplified low-dimensional CHT models. The approach is illustrated through several test cases, in which different combinations of objective and constraint functions, design variables and cycling sequence patterns are examined. In these test cases, the energy consumption is significantly reduced compared to the experiments by improving the spatial and temporal distribution of the thermal energy usage. The results show the benefits of the approach in bringing energy, safety and aerodynamic considerations together in designing de-icing systems.     

Trade-off analysis of high-aspect-ratio-cooling-channels for rocket engines

High performance liquid rocket engines are often characterized by rectangular cooling channels with high aspect ratio (channel height-to-width ratio) because of their proven superior cooling efficiency with respect to a conventional design. However, the identification of the optimum aspect ratio is not a trivial task. In the present study a trade-off analysis is performed on a cooling channel system that can be of interest for rocket engines. This analysis requires multiple cooling channel flow calculations and thus cannot be efficiently performed by CFD solvers. Therefore, a proper numerical approach, referred to as quasi-2D model, is used to have fast and accurate predictions of cooling system properties. This approach relies on its capability of describing the thermal stratification that occurs in the coolant and in the wall structure, as well as the coolant warming and pressure drop along the channel length. Validation of the model is carried out by comparison with solutions obtained with a validated CFD solver. Results of the analysis show the existence of an optimum channel aspect ratio that minimizes the requested pump power needed to overcome losses in the cooling circuit.     

Kinetic theory analysis of explosive boiling of a liquid droplet

The process of rapid phase transition from highly superheated liquid to vapor is frequently so fast and violent that it is called explosive boiling. The paper uses the kinetic theory of evaporation to study growth of an internal vapor bubble produced by homogeneous nucleation within a highly superheated liquid droplet boiling explosively in a hot medium. Evaporation/condensation coefficient is estimated by comparing the predictions of the theory with available experimental data. We show that the value of the evaporation coefficient can be very low for high reduced temperatures (0.06 for butane at 378 K), in agreement with recent molecular dynamic simulations.     

Numerical simulation of thermally and chemically nonequilibrium flows and heat transfer in underexpanded induction plasmatron jets

The results of numerical simulation are presented for thermally and chemically nonequilibrium air plasma flows in a plasmatron discharge channel and underexpanded dissociated and partially ionized air jets flowing past a cylindrical model with a blunt leading edge and cooled copper surface under the experimental conditions realized in a VGU-4 100 kW induction plasmatron (Institute for Problems in Mechanics of the Russian Academy of Sciences) (see, for example, [1, 2]). The nonequilibrium excitation of the vibrational degrees of freedom of the molecules in the modal approximation and the difference between the electron and translational heavy-particle temperatures are taken into account in the calculations. The calculated data on the heat transfer and pressure at the stagnation point are compared with the results obtained within the framework of the thermally equilibrium model. Comparison with the experimental data obtained in the Institute for Problem in Mechanics of the Russian Academy of Sciences (Laboratory for interaction between plasma and radiation and materials) and kindly provided for comparison purposes gives satisfactory agreement.     

Conjugate heat transfer in the unbounded flow of a viscoelastic fluid past a sphere

This work addresses the conjugate heat transfer of a simplified PTT fluid flowing past an unbounded sphere in the Stokes regime (Re = 0.01). The problem is numerically solved with the finite-volume method assuming axisymmetry, absence of natural convection and constant physical properties. The sphere generates heat at a constant and uniform rate, and the analysis is conducted for a range of Deborah (0 ≤ De ≤ 100), Prandtl (10⁰ ≤ Pr ≤ 10⁵) and Brinkman (0 ≤ Br ≤ 100) numbers, in the presence or absence of thermal contact resistance at the solid–fluid interface and for different conductivity ratios (0.1 ≤ κ ≤ 10). The drag coefficient shows a monotonic decrease with De, whereas the normalized stresses on the sphere surface and in the wake first increase and then decrease with De. A negative wake was observed for the two solvent viscosity ratios tested (β = 0.1 and 0.5), being more intense for the more elastic fluid. In the absence of viscous dissipation, the average Nusselt number starts to decrease with De after an initial increase. Heat transfer enhancement relative to an equivalent Newtonian fluid was observed for the whole range of conditions tested. The dimensionless temperature of the sphere decreases and becomes more homogeneous when its thermal conductivity increases in relation to the conductivity of the fluid, although small changes are observed in the Nusselt number. The thermal contact resistance at the interface increases the average temperature of the sphere, without affecting significantly the shape of the temperature profiles inside the sphere. When viscous dissipation is considered, significant changes are observed in the heat transfer process as Br increases. Overall, a simplified PTT fluid can moderately enhance heat transfer compared to a Newtonian fluid, but increasing De does not necessarily improve heat exchange.     

Numerical simulation of MHD stagnation point flow and heat transfer of a micropolar fluid towards a heated shrinking sheet

A comprehensive study of magneto hydrodynamics two‐dimensional stagnation flow with heat transfer characteristics towards a heated shrinking sheet immersed in an electrically conducting incompressible micropolar fluid in the presence of a transverse magnetic field is analyzed numerically. The governing continuity, momentum, angular momentum and heat equations together with the associated boundary conditions are first reduced to a set of self similar nonlinear ordinary differential equations using a similarity transformation and are then solved by a method based on finite difference discretization. Some important features of the flow and heat transfer in terms of normal and streamwise velocities, microrotation and temperature distributions for different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The results indicate that the reverse flow caused due to shrinking of the sheet can be stopped by applying a strong magnetic field. The magnetic field enhances the shear stresses and decreases the thermal boundary layer thickness. The heat loss per unit area from the sheet decreases with an increase in the shrinking parameter. Micropolar fluids exhibit reduction in shear stresses and heat transfer rate as compared with Newtonian fluids, which may be beneficial in the flow and thermal control of polymeric processing. Copyright © 2011 John Wiley & Sons, Ltd.