Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

Modeling of Ammonothermal Growth of Gallium Nitride Single Crystals

Ammonothermal growth of GaN crystals with a retrograde solubility has been modeled and simulated here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow in the porous charge is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. For the case of retrograde solubility, the charge is put above the baffle. The temperature difference between the dissolving zone and growth zone is found smaller than that applied on the sidewall of autoclave. The baffle opening has a strong effect on the nutrient transport and supersaturation of GaN species in the growth zone.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Transport Phenomena in Ammonothermal Growth of Gallium Nitride

GaN can be used to fabricate blue/green/UV LEDs and high temperature, high power electronic devices. Ideal substrates are needed for high quality III-nitride epitaxy, which is an essential step for the manufacture of LEDs. GaN substrates are ideal to be lattice matched and isomorphic to nitride-based films. Bulk single crystals of GaN can be grown from supercritical fluids using the ammonothermal method, which utilizes ammonia as fluid rather than water as in the hydrothermal process. In this process, a mineralizer such as amide, imide or azide is used to attack a bulk nitride feedstock at temperatures from 200 - 500癈 and pressures from 1 - 4 kbar. Baffle design is essential for successful growth of GaN crystals. Baffle is used to separate the dissolving zone from the growth zone, and to maintain a temperature difference between the two zones. For solubility curve with a positive coefficient with respect to temperature, the growth zone is maintained at a lower temperature than that in the dissolving zone, thus the nutrient becomes supersaturated in the growth zone. The baffle opening is used to control the mixing of nutrients in the two zones, thus the transfer of nutrient from the lower part to the upper part. Ammonothermal systems have been modeled here using fluid dynamics, thermodynamics and heat transfer models. The nutrient is considered as a porous media bed and the flow is simulated using the Darcy-Brinkman-Forchheimer model. The resulting governing equations are solved using the finite volume method. We investigated the effects of baffle opening and position on the transport phenomena of nutrient from dissolving zone to the growth zone. Simulation data have been compared qualitatively with experimental data.

Basic equations for ferroelectrics

A set of new formula of energy functions for ferroelectrics was proposed, and then the new basic equations were derived in this paper. The finite element formulation based on the new basic equations was improved to avoid the equivalent nodal load produced by remnant polarization. With regard to the fundamentals of mathematics and physics, the new energy functions and basic equations are reasonable for the material element of ferroelectrics in finite element analysis.

Torsion fracture behavior of drawn pearlitic steel wires with different heat treatments

In this paper, torsion fracture behavior of drawn pearlitic steel wires with different heat treatments was investigated. Samples with different heat treatments was investigated. Samples with different heat treatment conditions were subjected to torsion and tensile tests. The shear strain along the torsion sample after fracture was measured. Fracture surface of wires was examined by Scanning Electron Microscopy. In addition, the method of Differential Scanning Calorimetry was used to characterize the thermodynamic process in the heat treatment. A numerical simulation via finite element method on temperature field evolution for the wire during heat treatment process was performed. The results show that both strain aging and recovery process occur in the material within the temperature range between room temperature and 435 degrees C. It was shown that the ductility measured by the number of twists drops at short heating times and recovers after further heating in the lead bath of 435 degrees C. On the other hand, the strenght of the wire increases at short heating times and decreases after further heating. The microstructure inhomogeneity due to short period of heat treatment, coupled with the gradient characteristics of shear deformation during torsion results in localized shear deformation of the wire. In this situation, shear cracks nucleate between lamella and the wire breaks with low number of twists.

Adiabatic shear localization: occurrence, theories, and applications

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

Development And Application Of Flexible Substrate Sensors In Instantaneous Heat Flux Measurement

A new type of sensor with the flexible substrate is introduced. It is applicable in measuring instantaneous heat flux on the model surface in a hypersonic shock tunnel. The working principle, structure and manufacture process of the sensor are presented. The substrate thickness and the dynamic response parameter of the sensor are calculated. Because this sensor was successfully used in measuring the instantaneous heat flux on the surface of a flat plate in a detonation-driven shock tunnel, it may be effective in measuring instantaneous heat flux on the model surface.

Catalytic Cracking and Heat Sink Capacity of Aviation Kerosene Under Supercritical Conditions

Catalytic cracking of China no. 3 aviation kerosene using a zeolite catalyst was investigated under supercritical conditions. A three-stage heating/cracking system was specially designed to be capable of heating 0.8 kg kerosene to a temperature of 1050 K and pressure of 7.0 MPa with maximum mass flow rate of 80 g/s. Sonic nozzles of different diameters were used to calibrate and monitor the mass flow rate of the cracked fuel mixture. With proper experiment arrangements, the mass flow rate per unit throat area of the cracked fuel mixture was found to well correlate with the extent of fuel conversion. The gaseous products obtained from fuel cracking under different conditions were also analyzed using gas chromatography. Composition analysis showed that the average molecular weight of the resulting gaseous products and the fuel mass conversion percentage were a strong function of the fuel temperature and were only slightly affected by the fuel pressure. The fuel conversion was also shown to depend on the fuel residence time in the reactor, as expected. Furthermore, the heat sink levels due to sensible heating and endothermic cracking were determined and compared at varying test conditions. It was found that at a fuel temperature of similar to 1050 K, the total heat sink reached similar to 3.4 MJ/kg, in which chemical heat sink accounted for similar to 1.5 MJ/kg.

Heat Transfer of Aviation Kerosene at Supercritical Conditions

The heat transfer characteristics of China no. 3 kerosene were investigated experimentally and analytically under conditions relevant to a regenerative cooling system for scramjet applications. A test facility developed for the present study can handle kerosene in a temperature range of 300-1000 K, a pressure range of 2.6-5 MPa, and a mass How rate range of 10-100 g/s. In addition, the test section was uniquely designed such that both the wall temperature and the bulk fuel temperature were measured at the same location along the flowpath. The measured temperature distributions were then used to analytically deduce the local heat transfer characteristics. A 10-component kerosene surrogate was proposed and employed to calculate the fuel thermodynamic and transport properties that were required in the heat transfer analysis. Results revealed drastic changes in the fuel flow properties and heat transfer characteristics when kerosene approached its critical state. Convective heat transfer enhancement was also found as kerosene became supercritical. The heat transfer correlation in the relatively low-fuel-temperature region yielded a similar result to other commonly used jet fuels, such as JP-7 and JP-8, at compressed liquid states. In the high-fuel-temperature region, near and beyond the critical temperature, heat transfer enhancement was observed; hence, the associated correlation showed a more significant Reynolds number dependency.

Bubble Behavior and Heat Transfer in Quasi-Steady Pool Boiling in Microgravity

Pool boiling of degassed FC-72 on a plane plate heater has been studied experimentally in microgravity. A quasi-steady heating method is adopted, in which the heating voltage is controlled to increase exponentially with time. Compared with terrestrial experiments, bubble behaviors are very different, and have direct effect on heat transfer. Small, primary bubbles attached on the surface seem to be able to suppress the activation of the cavities in the neighborhoods, resulting in a slow increase of the wall temperature with the heat flux. For the high subcooling, the coalesced bubble has a smooth surface and a small size. It is difficult to cover the whole heater surface, resulting in a special region of gradual transitional boiling in which nucleate boiling and local dry area can co-exist. No turning point corresponding to the transition from nucleate boiling to film boiling can be observed. On the contrary, the surface oscillation of the coalesced bubble at low subcooling may cause more activated nucleate sites, and then the surface temperature may keep constant or even fall down with the increasing heat flux. Furthermore, an abrupt transition to film boiling can also be observed. It is shown that heat transfer coefficient and CHF increase with the subcooling or pressure in microgravity, as observed in normal gravity.

Boiling heat transfer enhancement by using micro-pin-finned surface for electronics cooling

For efficiently cooling electronic components with high heat flux, experiments were conducted to study the flow boiling heat transfer performance of FC-72 over square silicon chips with the dimensions of 10 × 10 × 0.5 mm3. Four kinds of micro-pin-fins with the dimensions of 30 × 60, 30 × 120, 50 × 60, 50 × 120 μm2 (thickness, t × height, h) were fabricated on the chip surfaces by the dry etching technique for enhancing boiling heat transfer. A smooth surface was also tested for comparison. The experiments were made at three different fluid velocities (0.5, 1 and 2 m/s) and three different liquid subcoolings (15, 25 and 35 K). The results were compared with the previous published data of pool boiling. All micro-pin-fined surfaces show a considerable heat transfer enhancement compared with a smooth surface. Flow boiling can remarkably decrease wall superheat compared with pool boiling. At the velocities lower than 1 m/s, the micro-pin-finned surfaces show a sharp increase in heat flux with increasing wall superheat. For all surfaces, the maximum allowable heat flux, qmax, for the normal operation of LSI chips increases with fluid velocity and subcooling. For all micro-pin-finned surfaces, the wall temperature at the critical heat flux (CHF) is less than the upper limit for the reliable operation of LSI chips, 85◦C. The largest value of qmax can reach nearly 148 W/cm2 for micro-pin-finned chips with the fin height of 120 μm at the fluid velocity of 2 m/s and the liquid subcooling of 35 K. The perspectives for the boiling heat transfer experiment of the prospective micro-pin-finned sur- faces, which has been planned to be made in the Drop Tower Beijing/NMLC in the future, are also presented.

A block SPP algorithm for multidimensional tridiagonal equations with optimal message vector length

A parallel strategy for solving multidimensional tridiagonal equations is investigated in this paper. We present in detail an improved version of single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication cost. We show the resulting block SPP can achieve good speedup for a wide range of message vector length (MVL), especially when the number of grid points in the divided direction is large. Instead of only using the largest possible MVL, we adopt numerical tests and modeling analysis to determine an optimal MVL so that significant improvement in speedup can be obtained.

Two-phase flow and pool boiling heat transfer in microgravity

Researches on two-phase flow and pool boiling heat transfer in microgravity, which included groundbased tests, flight experiments, and theoretical analyses, were conducted in the National Microgravity Laboratory/CAS. A semi-theoretical Weber number model was proposed to predict the slug-to-annular flow transition of two-phase gas–liquid flows in microgravity, while the influence of the initial bubble size on the bubble-to-slug flow transition was investigated numerically using the Monte Carlo method. Two-phase flow pattern maps in microgravity were obtained in the experiments both aboard the Russian space station Mir and aboard IL-76 reduced gravity airplane. Mini-scale modeling was also used to simulate the behavior of microgravity two-phase flow on the ground. Pressure drops of two-phase flow in microgravity were also measured experimentally and correlated successfully based on its characteristics. Two space experiments on pool boiling phenomena in microgravity were performed aboard the Chinese recoverable satellites. Steady pool boiling of R113 on a thin wire with a temperature-controlled heating method was studied aboard RS-22, while quasi-steady pool boiling of FC-72 on a plate was studied aboard SJ-8. Ground-based experiments were also performed both in normal gravity and in short-term microgravity in the drop tower Beijing. Only slight enhancement of heat transfer was observed in the wire case, while enhancement in low heat flux and deterioration in high heat flux were observed in the plate case. Lateral motions of vapor bubbles were observed before their departure in microgravity. The relationship between bubble behavior and heat transfer on plate was analyzed. A semi-theoretical model was also proposed for predicting the bubble departure diameter during pool boiling on wires. The results obtained here are intended to become a powerful aid for further investigation in the present discipline and development of two-phase systems for space applications.