LAMINAR DEVELOPING FLOW IN THE ENTRANCE REGION OF ROTATING CURVED PIPES

Three-dimensional laminar flow in the entrance region of rotating curved pipes was investigated. The governing equations were written in an orthogonal curvilinear coordinate system and solved with a fully three-dimensional numerical method. The development of secondary flow, axial velocity, local and average friction factors for different cases of rotation were given and discussed in detail. The results show that rotation influences the flow structure and friction factor greatly and that the secondary flow is sink-type in the early stage of development and then turns to vortex structure. The average friction factor and the intensity of secondary flow have drastic decrease near the entrance. At some proper rotation, the average friction factor can be noticeably reduced.

Prediction of Thermophoretic Deposition Efficiency of Particles in a Laminar Gas Flow along a Concentric Annulus： A Comparison of Developing and Fully Developed Flows

Thermophoresis is an important mechanism of micro-particle transport due to temperature gradients in the surrounding medium.It has numerous applications,especially in the field of aerosol technology.This study has numerically investigated the thermophoretic deposition efficiency of particles in a laminar gas flow in a concentric annulus using the critical trajectory method.The governing equations are the momentum and energy equations for the gas and the particle equations of motion.The effects of the annulus size,particle diameter,the ratio of inner to outer radius of tube and wall temperature on the deposition efficiency were studied for both developing and fully-developed flows.Simulation results suggest that thermophoretic deposition increases by increasing thermal gradient,deposition distance,and the ratio of inner to outer radius,but decreases with increasing particle size.It has been found that by taking into account the effect of developing flow at the entrance region,higher deposition efficiency was obtained,than fully developed flow.

Heat Transfer Augmentation in Developing Flow Through a Ribbed Square Duct

An experimental study is conducted to investigate the heat transfer augmentation in developing turbulent flow through a ribbed square duct. The duct is made of 16ram thick bakelite sheet. The bottom surface of the ribbed wall having rib pitch to height ratio of 10 is heated by passing a c current to the heater placed under it. The uniform heating is controlled using a digital temperature controller and a variac. The results of ribbed duct are compared with the results of a smooth duct under the same experimental conditions. It is observed that the heat transfer augmentation in ribbed duct is better than that of the smooth duct. At Re=5.0× 10^4 , the mean temperature of air flowing through the ribbed duct increases by 2.45 percent over the smooth duct, whereas in the fibbed duct Nusselt number increases by 15.14 percent than that of the smooth duct with a 6 percent increase in pressure drop.

LAMINAR FLOW AND HEAT TRANSFER IN THE DEVELOPING REGION OF HELICAL SQUARE DUCTS

Simultaneous development of the laminar flow and heat transfer in helicalsquare ducts was numerically studied. The governing equations were written in an orthogonal helicalcoordinate system and fully parabolized in the axial direction. Results were found out over a widerange of the governing parameters. Two axial velocity entries were taken into account. Thedevelopment of secondary flow, axial velocity and temperature distribution for the large Dean numberwere examined in detail and the effects of different governing parameters on the friction factorand- the Nusselt number were annlyzee. Many new and interesting conclusions were reached. Thepresent results reveal the nature of fluid flow and heat transfer in the developing region ofhelical square ducts.

Numerical Investigation of Developing Turbulent Flow in a Helical Square Ductwith Large Curvature

A fully elliptic numerical study has been carried out to investigate the three-dimensional turbulent developing flow in a helical square duct with large curvature. A two-layer zonal model is proposed and used, in which the whole region is divided into a viscosity-affected near wall layer and a fully turbulent region. A DSM closure is applied in the former, and a one-equation model is solved in the latter. The results presented in this paper cover a Reynolds number range of (l- 10) x 104. The development of flow is found to be dominated by radial pressure gradient and Dean-type secondary motion. The distribution of Reynolds stresses in fully developed flow exhibit a complex pattern of turbulence anisotropy The development of peripherally averaged friction factor and the distribution of local friction factor in fully developed flow are given and discussed.

THE NUMERICAL PREDICTION OF DEVELOPING TURBULENT FLOW IN 3-D RECTANGULAR DUCTS

Comparisons are made between experimental data and numerical predictions based on the k-e turbulent model of low Reynolds number applicable to developing turbulent flow in rectangular ducts of arbitrary aspect ratio.The numerical procedure utilizes the separated-layers finite-analytical method.The merits of the k-e turbulent model of low Reynolds number and the computation procedure are assessed by means of comparison with results,referred to that of the length-scale model and the full-Reynolds-stress model used in recent years.

Analysis of Entropy Generation in a Rectangular Porous Duct

In this paper, we have considered a fully developed flow of a viscous incompressible fluid in a rectangular porous duct saturated with the same fluid. The duct is heated from the bottom for forced and mixed convection. The Brinkman model is used to simulate the momentum transfer in the porous duct. Using the momentum and thermal energy equations, the entropy generation has been obtained due to the heat transfer, viscous and Darcy dissipations. It is found from the mathematical analysis that the entropy generation is double when the viscous as well as the Darcy dissipations terms are taken in the thermal energy equation in comparison when the viscous as well as the Darcy dissipations terms are not taken in the thermal energy equation. This result clearly shows that there is no need of taking the viscous and Darcy dissipations terms in the thermal energy equation to obtain the entropy generation.

Flame development characteristics at variable swirl level inductions in a stratified CNG direct injection combustion engine

The study of flame development characteristics is crucial in the study of flame propagation, extinction, and for the investigation of combustion cyclic variability in SI engine. The aim of this study is to investigate the characteristics of flame development in a lean-stratified combustion of Natural Gas Engine （CNG） in a single cylinder direct injection （DI） engine at a specific motor speed, and fixed injection timing and air-fuel ratio by varying only the swirl level at the intake. The engine was set to run at 1800 rpm with half-load throttled. The ignition advance was set at 21.5 BTDC, and to create an overall lean and stratified mixture, injection timing was set at 61 BTDC with an air-fuel-ratio of 40.5 （λ=2.35）. Variable turbulent flow conditions near spark-plug were created by positioning the swirl control valves （SCV） at the intake port just before the two intake valves. This was done by setting one of the valves at full open position and the other one at 0% closed, 50% closed and 100% closed positions in order to achieve medium tumble （no swirl）, medium swirl and high swirl flows in the cylinder, respectively. An endoscope and CCD camera assembly was utilized to capture the flame images from the tumble plane at the intake side of the engine ever）, 2 CA degrees after ignition timing （AIT） for 40 CAs. It was observed that flame growth rate and flame convection velocity are increasing with increasing the swirl level. The total combustion duration is, thus, shorter in swirl induced combustion than without. However, COV in IMEP is greater in swirl induced flow cases than the medium tumble.

Large eddy simulation of a 3-D spatially developing turbulent round jet

A three-dimensional large eddy simulation （LES） of a spatially developing round jet is carried out in cylindrical coordinates using a dynamic subgrid model with strong inflow instability. Evolutions of large-scale vortex structures represented by tangential vortices are obtained and compared with flow visualization. Also presented are three-dimensional spatial evolutions of coherent structure, which are of quasi two-dimensional Kelvin-Helmholtz instability and vortex rings as well as breaking up of the vortex rings with fully three-dimensional characteristics. Predicted results of mean velocity and turbulent intensity agree well with experiments. They are also compared with the results predicted by LES using standard Smagorinsky model and show good self-similarity. Turbulence spectrum of the predicted velocity shows the -5/3 decay for higher wave number, as expected for turbulent round jet flows. In addition, fl-test and y-test are carded out for the instantaneous velocity, showing that the present LES method can successfully predict the hierarchical structure of round jet.

STEADY ENTRANCE FLOW IN A STRAIGHT CIRCULAR PIPE WITH SLOWLY VARYING CROSS SECTION

A pertubation method for the steady entrance flow through a convergingdiverging pipe, which can model an arterial stenosis at the initial stage, is presented. Aset of formulas for velocity, pressure and wall shear stress distributions are obtained. Results show that the flow patterns of entrance flow are considerably different from those ofdeveloped flow in a converging-diverging pipe: the velocity distribution at the stenosis issmoother, the centerline velocity decreases, and the wall shear stress and pressure gradient increase in the entrance region. The length of entrance flow for the pipe is slighty lower than that for a straight one with constant cross section. The results are checked by thefinite difference method.

GAS-SOLIDS FLOW BEHAVIOR WITH A GAS VELOCITY CLOSE TO ZERO

In a 9.3 m high and 0.10 m i.d. gas-solids downflow fluidized bed （downer）, the radial and axial distributions of the local solids holdups and particle velocities along the downer column were measured with the superficial gas velocity set to zero. A unique gas-solids flow structure was found in the downer system with zero gas velocity, which is completely different from that under conditions with higher gas velocities, in terms of its radial and axial flow structures as well as its micro flow structure. The gas-solids flow pattern under zero gas velocity conditions, together with that under low gas velocity conditions, can be considered as a special regime which differs from that under higher gas velocity conditions. According to the hydrodynamic properties of the two regimes, they can be named the ＂dense annulus＂ regime for the flow pattern under zero or low gas velocity conditions and the ＂dense core＂ regime for that under higher gas velocity conditions.

Truncation method for calculating the resistance of ventilation air-conditioning duct systems under nonfully developed flow boundary conditions

Calculating the resistance of ventilation air-conditioning ducts under nonfully developed flow is a crucial problem that must be addressed. Based on the characteristics of the resistance in ventilation air-conditioning ducts, the truncation method-a computational method that is appropriate for nonfully developed flow boundary conditions-was proposed in this study. The resistance distributions in the upstream and downstream ducts from typical local components, including reducers, bends and tee ducts, were investigated. Using the resistance values of the local components under fully developed flow, the resistances that did not belong to nonfully developed flow were truncated and removed. Finally, the calculation steps of the proposed method were discussed, an engineering case study was presented, and the accuracy of the developed model was analyzed. The results showed that for the local components in the system (reducers, bends and tee ducts), their proportions of the total resistance exhibited similar trends under different width-to-height ratios. The resistance of these local components included upstream resistance, downstream resistance and their own resistance. The upstream resistance accounted for 2%–6% of the total resistance, whereas the downstream resistance of the reducers, bends and tee ducts accounted for 40%–60% of the total resistance. A functional relationship was established between the local resistance and cutoff distance of the reducers, bends and tee ducts. Hence, the truncation method can calculate the local resistance from the cutoff distance. Moreover, in the presented engineering case study, the error between the actual measured resistance values and those simulated with the truncation method was only 4.28%, which was far less than that of the results simulated with the traditional calculation methods (53.64%).

Natural convection flow in a vertical annulus with time-periodic thermal boundary conditions

This paper presents an analytical solution for natural convection flow in a vertical annulus due to time-periodic heating of annulus surfaces.Closed-form expressions for velocity,temperature,skin-friction,mass flow rate and rate of heat transfer which is expressed as Nusselt number are obtained by solving the present mathematical model after separating into steady component and periodic regime.The effects of pertinent parameters such as Strouhal number(St),Prandtl number(Pr)and radius ratio(λ)are shown with the aid of contour and line graphs.Results indicate that the role of Strouhal number and Prandtl number is to decrease fluid velocity,temperature and skin-friction.Furthermore,increase in Strouhal number increases the temperature phase-lag.

Numerical Simulation of Unidirectional Stratified Flow by Moving Particle Semi Implicit Method

Numerical simulation of stratified flow of two fluids between two infinite parallel plates using the Moving Particle Semi-implicit(MPS)method is presented.The developing process from entrance to fully development flow is captured.In the simulation,the computational domain is represented by various types of particles.Governing equations are described based on particles and their interactions.Grids are not necessary in any calculation steps of the simulation.The particle number density is implicitly required to be constant to satisfy incompressibility.The weight function is used to describe the interaction between different particles.The particle is considered to constitute the free interface if the particle number density is below a set point.Results for various combinations of density,viscosity,mass flow rates,and distance between the two parallel plates are presented.The proposed procedure is validated using the derived exact solution and the earlier numerical results from the Level-Set method.Furthermore,the evolution of the interface in the developing region is captured and compares well with the derived exact solutions in the developed region.

Some developments of hot accretion flow theory in the past ten years

The hot accretion flow model was re-discovered in 1994 by Narayan and collaborators.Intensive theoretical works have been conducted and significant progresses have been achieved.In this paper,we review several developments in the past ten years.This mainly includes the finding of outflow and convection and its dynamical effect on inflow;the direct electron heating by viscous dissipation;the effect of large scale toroidal magnetic fields in the inner region of the accretion flow;and the effect of global Compton scattering.Their observational applications are also introduced very briefly.

THE APPLICATION AND DEVELOPMENT OF TURBULENCE MODELS IN BUOYANT RECIRCULATING FLOWS

In this paper, a modified κ-ε turbulence model, a simplified algebraic stress model and a developed two-fluid model have been presented based on numerical modeling of turbulent buoyant recirculating flows. The calculated results by these models are in good agreement with experiments. However, the last model is much better for simulating gravity-stratified flows.