Lyon-Type Integral Forms of Wall Friction, Heat- and Mass Transfer Closure Relationships for Non-Equilibrium Two-Phase Flows: Generalization for Annular and Rod Cluster Geometries

The main goal of this paper is to describe new approach to constructing generalized closure relationships for pipe, annular and sub-channel transfer coefficients for wall friction, heat and mass transfer. The novelty of this approach is that it takes into account not only axial and transversal parameter distributions, but also an azimuthal substance transfer effects. These constitutive relations, which are primordial in the description of single- and two-phase one-dimensional (1D) flow models, can be derived from the initial 3D drift flux formulation. The approach is based on the Reynolds flow, boundary layer, and substance transfer generalized coefficient concepts. Another aim is to illustrate the validity of the “conformity principle” for the limiting cases. The method proposed in this paper is founded on the similarity theory, boundary layer model, and a phenomenological description of the regularity of the substance transfer (momentum, heat, and mass) as well as on an adequate simulation of the flow structures. With the proposed generalized approach it becomes possible to develop an integrated in form and semi-empirical in maintenance structure analytical relationships for wall friction, heat and mass transfer coefficients.

Monitoring of Polymer Plastication in the Injection Moulding Process

In injection moulding or in extrusion, plastication is the step during which polymer pellets are melted by the means of mechanical dissipation provided by a rotating screw and by thermal conduction coming from a heated metallic barrel. This step is crucial for melt thermal homogeneity, charge dispersion and fibre length preservation. Although there have been a large number of theoretical and experimental studies of plastication during the past decades, mostly on extrusion and mostly using the screw extraction technique, extremely few of them have dealt with trying to visualise plastication, let alone measuring the plastication profile in real-time. As a matter of fact, designing such an equipment is an arduous task. We designed an industry-sized metallic barrel, featuring 3 optical glass windows; each window possessing 3 plane faces itself to allow for visualisation and record by synchronised cameras and lightening by lasers. The images recorded can be further analysed by digital image processing. Preliminary results confirm the plastication theory and show a compacted solid bed and a melt pool side by side. The total plastication length is a direct function of screw rotation frequency as it is obvious from results on the melt pool width, which increases when the screw rotation frequency decreases. However, some evidence of solid bed breakage has been recorded, whereby the solid bed does not diminish continuously along the screw but is fractured in the compression zone.

Thermal Transport to Sessile Droplets on Superhydrophobic Surfaces With Rib and Cavity Features

This paper reports on measurements of thermal transport to solitary sessile water drops placed on heated superhydrophobic substrates at constant temperature. Data was obtained by heating the surfaces to specified constant temperatures and gently placing a single water droplet of nominally 3 mm diameter on the surface. The droplet was allowed to evaporate completely while two video cameras and one infrared camera imaged it during the evaporation process. The images were post-processed to yield transient geometric and thermal information, including droplet volume, projected droplet-substrate contact area, and droplet temperature. The total evaporation time and Nusselt and Grashof numbers were determined from the measurements. For all scenarios, the substrate temperature was maintained below the saturation temperature of water and was varied from 60 to 100 °C. Three different rib-patterned superhydrophobic substrates were investigated of 0.5, 0.8, and 0.95 cavity fraction, respectively. The rib features ranged in width from 2 to 30 μm and in height from 15 to 20 μm, while the cavities between the ribs ranged in width from 30 to 38 μm. Results were also obtained for a smooth hydrophobic substrate for comparison purposes. Droplet evaporation times increase with substrate cavity fraction and decrease with increasing substrate temperature. Heat transfer rates decrease with increasing substrate cavity fraction and increase with substrate temperature. The Nusselt number generally increases with the Grashof number raised to the 1/4 power, and Nusselt number is larger for lower cavity fraction substrates.

A Study of Spatially-Resolved Non-Equilibrium in Laser-Irradiated Graphene Using Boltzmann Transport Equation

Raman spectroscopy is typically used to characterize graphene in experiments and also to measure properties like thermal conductivity and optical phonon lifetime. The laser-irradiation processes underlying this measurement technique include coupling between photons, electrons and phonons. Recent experimental studies have shown that e-ph scattering limits the performance of graphene-based electronic devices due to the difference in their timescales of relaxation resulting in various bottleneck effects. Furthermore, recently published thermal conductivity measurements on graphene are sensitive to the laser spot size which strengthens the possibility of non-equilibrium between various phonon groups. These studies point to the need to study the spatially-resolved non-equilibrium between various energy carriers in graphene. In this work, we demonstrate non-equilibrium in the e-ph interactions in graphene by solving the linearized electron and phonon Boltzmann transport equations (BTE) iteratively under steady state conditions. We start by assuming that all the electrons equilibrate rapidly to an elevated temperature under laser-irradiation and they gradually relax by phonon emission and reach a steady state. The electron and phonon BTEs are coupled because the e-ph scattering rate depends on the phonon population while the rate of phonon generation depends on the e-ph scattering rate. We used density-functional theory/density-functional perturbation theory (DFT/DFPT) to calculate the electronic eigen states, phonon frequencies and the e-ph coupling matrix elements. We calculated the rate of energy loss from the hot electrons in terms of the phonon generation rate (PGR) which serve as an input for solving the BTE. Likewise, ph-ph relaxation times are calculated from the anharmonic lattice dynamics (LD)/FGR. Through our work, we obtained the spatially resolved temperature profiles of all the relevant energy carriers throughout the entire domain; these are impossible to obtain through experiments.

Vibration Effects on Surface Coke Deposition of Hydrocarbon Fuel at Supercritical Pressure Condition in Micro-Tubes

Experiments are performed to study vibration effects on surface coke deposition of aviation hydrocarbon RP-3 under supercritical pressure. The flowing RP-3 kerosene is stressed to 5MPa, and heated up from 127°C to 450°C in a stainless tube (1.8mm I.D., 2.2mm O.D., 1Cr18Ni9Ti) with a constant heat flux, and the mass flow rate is 3g/s. The working fluids flow downward through an 1800mm long tube. The vibration frequency is set from 100Hz to 600Hz, covering the main frequencies of the combustion chamber vibration when it works. Compared with stable condition, vibration effects have a distinct impact on the flow resistance and heat transfer. The amount of coke deposition reduced under all different frequencies with the maximize decline of 40.46%. Moreover, restraining efficiency is proportional to the vibration energy. Besides, vibration enhanced the heat transfer, the coefficient of which comes to a wave crest at the zone of second-order modes of response to the peak area with the biggest vibration energy.

Optimized Multi-Floor Throughflow Micro Heat Exchangers

Multi-floor networks of straight-through liquid cooled microchannels have been investigated by performing conjugate heat transfer in a silicon substrate of size 15×15×1 mm. Two-floor and three-floor cooling configurations were analyzed with different numbers of microchannels on each floor, different diameters of the channels, and different clustering among the floors. Thickness of substrate was calculated based on number of floors, diameter of floors and vertical clustering. Direction of microchannels on each floor changes by 90 degrees from the previous floor. Direction of flow in each microchannel is opposite of the flow direction in its neighbor channels. Conjugate heat transfer analysis was performed by developing a software package which uses quasi-1D thermo-fluid analysis and a 3D steady heat conduction analysis. These two solvers are coupled through their common boundaries representing surfaces of the cooling microchannels. Using quasi-1D solver significantly decreases overall computing time and its results are in good agreement with 3D Navier-Stokes equations solver for these types of application. Multi-objective optimization with modeFRONTIER software was performed using response surface approximations and genetic algorithm. Maximizing total amount of heat removed, minimizing coolant pressure drop, minimizing maximum temperature on the hot surface, and minimizing non-uniformity of temperature on the hot surface were four simultaneous objectives of the optimization. Pareto-optimal solutions demonstrate that thermal loads of 800 W cm−2 can be effectively managed with such multi-floor microchannel cooling networks. Two-floor microchannel configuration was also simulated with 1,000 W cm−2 uniform thermal load and shown to be feasible.

Zuber-Type Parameter Distributions for Non-Equilibrium Two-Phase Flows: Generalization for Annular Channel and Rod Cluster Geometries

This study presents the main results of the analysis of the previously developed generalized hierarchical closed system of analytical closure relations for the distribution parameters (DPs) Cks (k = f - fluid or g - vapor; s = 0,1,2,3 - mass, energy, momentum) that are used in quasi-one-dimensional form of the conservation laws for mass, momentum and energy in non-equilibrium two-phase flows. The current method has been expanded to account for non-uniform in cross-section profile of void fraction. The main assumptions of the received quadrature relationships for DP are: (a) the use of the drift flux model, (b) the quasi-steady-state approximation, and (c) the power-mode approximations of the local distribution profiles of the variables. These DPs Cks quadrature are expressed in terms of elementary functions, they directly reflect the principle of superposition, generalize and unify not only the Zuber-Findlay method, but also Hancox-Nicoll and Hibiki-Ishii methods. The revealed complementarity properties are particularly useful for the purposes of testing, validating and verifying DPs.

An Advanced Frequency-Domain Code for BWR Stability Analysis and Design

Density Wave Oscillations in BWRs are coupled with the reactor kinetics. A new analytical, frequency-domain tool that uses the best available models and methods for modeling BWRs and analyzing their stability is described. The steady state of the core is obtained first in 3D with two-group diffusion equations and spatial expansion of the neutron fluxes in Legendre polynomials. The time-dependent neutronics equations are written in terms of flux harmonics (nodal-modal equations) for the study of “out-of-phase” instabilities. Considering separately all fuel assemblies divided into a number of axial segments, the thermal-hydraulic conservation equations are solved (drift-flux, non-equilibrium model). The thermal-hydraulics are iteratively fully coupled to the neutronics. The code takes all necessary information from plant files via an interface. The results of the steady state are used for the calculation of the transfer functions and system transfer matrices using extensively symbolic manipulation software (MATLAB). The resulting very large matrices are manipulated and inverted by special procedures developed within the MATLAB environment to obtain the reactor transfer functions that enable the study of system stability. Applications to BWRs show good agreement with measured stability data.

Smoke and Heat Propagation Modeling in Transportation Interchange Stations Using LES and RANS Methods

A numerical study of smoke and heat transport from fires occurring in a large interchange bus station is presented. The ultimate goal of this type of study is to increase the fire safety level of the station by improving the design of fire protection systems and evacuation procedures. The phenomena involved in the fire are highly transient and three dimensional, and their modeling requires large computational resources. In the present work, we introduce several simplifications in the numerical model, mainly related to turbulence modeling and the boundary conditions used to reproduce the effects of the combustion process, which allow us capturing the essential features of the fire while keeping the memory requirements and the CPU time at a reasonable level. In particular, we are interested in describing in a realistic way the spread of smoke and heat in a typical fire scenario in the lobby of an interchange bus station. The numerical analysis is carried out with the aid of a general-purpose computer code, using two different approaches for turbulence modeling (RANS and LES) and several discretization schemes. The fire effects are reproduced in a simple way, describing the fire focus as a source of mass, heat and chemical species. Boundary conditions are imposed at the fire focus, by setting the inlet velocity, temperature and gas composition (combustion products) at a section of appropriate area. The values of these quantities are chosen to be consistent with the prescribed heat release rate, type of fuel (heptane) and fire spread area. A comparison of the results obtained with the different methods, along with the CPU time consumption and dependence on the computational mesh, is presented. The capabilities and limitations of unsteady RANS and LES methods to reproduce the main features of the smoke and heat propagation patterns are analyzed.

Role of Internal Radiation With or Without Melt Inclusions During Czochralski Sapphire Crystal Growth

Sapphire is the most popular substrate material for GaN thin-film crystal growth during the Light-emitting diode (LED) fabrication. The performance of GaN films is directly influenced by the quality of the substrates. The control of the growth front, i.e., solid /liquid interface, is critical to improve the quality of the sapphire. As a semi-transparent material, sapphire has an intermediate optical thickness, which requires considering of internal radiation for an accurate prediction of temperature field and interface shape. In the paper, a coupled model has been applied on the modeling of transport phenomena during the Czochralski (Cz) sapphire growth. Especially, the role of the internal radiation with or without melt inclusions has been examined carefully by Discrete Ordinates (DO) method. The interface convexity is influenced by the parameters of the models as well as by the melt inclusions. By setting the different optical properties at the inclusion regions, as observed in the experiments, the entrapment of gas or solid inclusions inside the crystal and its effect on the interface shape are examined.