Steady natural convection of non-Newtonian power-law fluid in a trapezoidal enclosure

Numerically investigation of free convection heat transfer in a differentially heated trapezoidal cavity filled with non-Newtonian Power-law fluid has been performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is maintained as uniformly cooled. The top and bottom surfaces are kept adiabatic with initially quiescent fluid inside the enclosure. Finite volume based commercial software FLUENT 14.5 is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 10^5 to 10^7, Prandtl number, Pr of 100 to 10,000 and power index, n of 0.6 to 1.4. Outcomes have been reported in terms of isotherms, streamline, and local Nusselt number for various Ra, Pr, n and inclined angles. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

Voltage unbalance improvement in low voltage residential feeders with rooftop PVs using custom power devices

Voltage unbalance is a major power quality problem in low voltage residential feeders due to the random location and rating of single-phase rooftop photovoltaic cells (PV). In this paper, two different improvement methods based on the application of series (DVR) and parallel (DSTATCOM) custom power devices are investigated to improve the voltage unbalance problem in these feeders. First, based on the load flow analysis carried out in MATLAB, the effectiveness of these two custom power devices is studied vis-à-vis the voltage unbalance reduction in urban and semi-urban/rural feeders containing rooftop PVs. Their effectiveness is studied from the installation location and rating points of view. Later, a Monte Carlo based stochastic analysis is carried out to investigate their efficacy for different uncertainties of load and PV rating and location in the network. After the numerical analyses, a converter topology and control algorithm is proposed for the DSTATCOM and DVR for balancing the network voltage at their point of common coupling. A state feedback control, based on pole-shift technique, is developed to regulate the voltage in the output of the DSTATCOM and DVR converters such that the voltage balancing is achieved in the network. The dynamic feasibility of voltage unbalance and profile improvement in LV feeders, by the proposed structure and control algorithm for the DSTATCOM and DVR, is verified through detailed PSCAD/EMTDC simulations.

Similarity solutions for flow and heat transfer of non-Newtonian fluid over a stretching surface

Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

CFD simulations of flow and heat transfer through the porous interface of a metal foam heat exchanger

This paper offers numerical modelling of a waste heat recovery system. A thin layer of metal foam is attached to a cold plate to absorb heat from hot gases leaving the system. The heat transferred from the exhaust gas is then transferred to a cold liquid flowing in a secondary loop. Two different foam PPI (Pores Per Inch) values are examined over a range of fluid velocities. Numerical results are then compared to both experimental data and theoretical results available in the literature. Challenges in getting the simulation results to match those of the experiments are addressed and discussed in detail. In particular, interface boundary conditions specified between a porous layer and a fluid layer are investigated. While physically one expects much lower fluid velocity in the pores compared to that of free flow, capturing this sharp gradient at the interface can add to the difficulties of numerical simulation. The existing models in the literature are modified by considering the pressure gradient inside and outside the foam. Comparisons against the numerical modelling are presented. Finally, based on experimentally-validated numerical results, thermo-hydraulic performance of foam heat exchangers as waste heat recovery units is discussed with the main goal of reducing the excess pressure drop and maximising the amount of heat that can be recovered from the hot gas stream.

On the effect of Reynolds number for flow past three side-by-side square cylinders for unequal gap spacings

Flow patterns and aerodynamic characteristics behind three side-by-side square cylinders has been found depending upon the unequal gap spacing (g1 = s1/d and g2 = s2/d) between the three cylinders and the Reynolds number (Re) using the Lattice Boltzmann method. The effect of Reynolds numbers on the flow behind three cylinders are numerically studied for 75 ≤ Re ≤ 175 and chosen unequal gap spacings such as (g1, g2) = (1.5, 1), (3, 4) and (7, 6). We also investigate the effect of g2 while keeping g1 fixed for Re = 150. It is found that a Reynolds number have a strong effect on the flow at small unequal gap spacing (g1, g2) = (1.5, 1.0). It is also found that the secondary cylinder interaction frequency significantly contributes for unequal gap spacing for all chosen Reynolds numbers. It is observed that at intermediate unequal gap spacing (g1, g2) = (3, 4) the primary vortex shedding frequency plays a major role and the effect of secondary cylinder interaction frequencies almost disappear. Some vortices merge near the exit and as a result small modulation found in drag and lift coefficients. This means that with the increase in the Reynolds numbers and unequal gap spacing shows weakens wakes interaction between the cylinders. At large unequal gap spacing (g1, g2) = (7, 6) the flow is fully periodic and no small modulation found in drag and lift coefficients signals. It is found that the jet flows for unequal gap spacing strongly influenced the wake interaction by varying the Reynolds number. These unequal gap spacing separate wake patterns for different Reynolds numbers: flip-flopping, in-phase and anti-phase modulation synchronized, in-phase and anti-phase synchronized. It is also observed that in case of equal gap spacing between the cylinders the effect of gap spacing is stronger than the Reynolds number. On the other hand, in case of unequal gap spacing between the cylinders the wake patterns strongly depends on both unequal gap spacing and Reynolds number. The vorticity contour visualization, time history analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and force statistics are systematically discussed for all chosen unequal gap spacings and Reynolds numbers to fully understand this valuable and practical problem.

Non-Newtonian mixed convection flow from a horizontal circular cylinder with uniform surface heat flux

Mixed convection laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is investigated from a horizontal circular cylinder with uniform surface heat flux using a modified power-law viscosity model, that contains no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid temperature distributions, rate of heat transfer in terms of the local Nusselt number.

Statistical modelling and power analysis for detecting trends in total suspended sediment loads

The export of sediments from coastal catchments can have detrimental impacts on estuaries and near shore reef ecosystems such as the Great Barrier Reef. Catchment management approaches aimed at reducing sediment loads require monitoring to evaluate their effectiveness in reducing loads over time. However, load estimation is not a trivial task due to the complex behaviour of constituents in natural streams, the variability of water flows and often a limited amount of data. Regression is commonly used for load estimation and provides a fundamental tool for trend estimation by standardising the other time specific covariates such as flow. This study investigates whether load estimates and resultant power to detect trends can be enhanced by (i) modelling the error structure so that temporal correlation can be better quantified, (ii) making use of predictive variables, and (iii) by identifying an efficient and feasible sampling strategy that may be used to reduce sampling error. To achieve this, we propose a new regression model that includes an innovative compounding errors model structure and uses two additional predictive variables (average discounted flow and turbidity). By combining this modelling approach with a new, regularly optimised, sampling strategy, which adds uniformity to the event sampling strategy, the predictive power was increased to 90%. Using the enhanced regression model proposed here, it was possible to detect a trend of 20% over 20 years. This result is in stark contrast to previous conclusions presented in the literature. (C) 2014 Elsevier B.V. All rights reserved.

Optimal hydrothermal load flow: Formulation and a successive approximation solution for fixed head systems

This paper deals with the optimal load flow problem in a fixed-head hydrothermal electric power system. Equality constraints on the volume of water available for active power generation at the hydro plants as well as inequality constraints on the reactive power generation at the voltage controlled buses are imposed. Conditions for optimal load flow are derived and a successive approximation algorithm for solving the optimal generation schedule is developed. Computer implementation of the algorithm is discussed, and the results obtained from the computer solution of test systems are presented.

Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Stream power criterion and design of sand bed channels at incipient motion

The critical stream power criterion may be used to describe the incipient motion of cohesionless particles of plane sediment beds. The governing equation relating ``critical stream power'' to ``shear Reynolds number'' is developed by using the present experimental data as well as the data from several other sources. Simultaneously, a resistance equation, relating the ``particle Reynolds number'' to the``shear Reynolds number'' is developed for plane sediment beds in wide channels with little or no transport. By making use of these relations, a procedure is developed to design plane sediment beds such that any two of the four design variables, including particle size, energy/friction slope, flow depth, and discharge per unit width in the channel should be known to predict the remaining two variables. Finally, a straightforward design procedure using design tables/design curves and analytical methods is presented to solve six possible design problems.

Probabilistic load flow for distribution systems with uncertain PV generation

Large integration of solar Photo Voltaic (PV) in distribution network has resulted in over-voltage problems. Several control techniques are developed to address over-voltage problem using Deterministic Load Flow (DLF). However, intermittent characteristics of PV generation require Probabilistic Load Flow (PLF) to introduce variability in analysis that is ignored in DLF. The traditional PLF techniques are not suitable for distribution systems and suffer from several drawbacks such as computational burden (Monte Carlo, Conventional convolution), sensitive accuracy with the complexity of system (point estimation method), requirement of necessary linearization (multi-linear simulation) and convergence problem (Gram–Charlier expansion, Cornish Fisher expansion). In this research, Latin Hypercube Sampling with Cholesky Decomposition (LHS-CD) is used to quantify the over-voltage issues with and without the voltage control algorithm in the distribution network with active generation. LHS technique is verified with a test network and real system from an Australian distribution network service provider. Accuracy and computational burden of simulated results are also compared with Monte Carlo simulations.

Impression creep of zinc and the rate-controlling dislocation mechanism of plastic flow at high temperatures

The impression creep behaviour of zinc is studied in the range 300 to 500 K and the results are compared with the data from conventional creep tests. The steady-state impression velocity is found to exhibit the same stress and temperature dependence as in conventional tensile creep with the same power law stress exponent. Also studied is the effect of indenter size on the impression velocity. The thermal activation parameters for plastic flow at high temperatures derived from a number of testing techniques agree reasonably well. Grain boundary sliding is shown to be unimportant in controlling the rate of plastic flow at high temperatures. It is observed that the Cottrell-Stokes law is obeyed during high-temperature deformation of zinc. It is concluded that a mechanism such as forest intersection involving attractive trees controls the high-temperature flow rather than a diffusion mechanism.

Transition of turbulent pipe flow

The velocity profile in turbulent pipe flow is usually divided into two regions, a wall or inner region and a core or outer region. For the inner region, the viscosity and wall shear stress are the important parameters governing the velocity distribution whereas for the outer region, the wall reduces the velocity below the maximum velocity independent of viscosity. In the present work, a velocity model is proposed for turbulent flow in the wall region of a pipe covering the entire transition from smooth to rough flows. Coupling this model for the wall region with the power law velocity model for the core region, an equation for the friction factor is obtained. The model constants are evaluated by using Nikuradse's experiments in the fully smooth and rough turbulent flows. The model shows good agreement with the friction factor and the velocity profiles obtained by Nikuradse for the transition region of turbulent flow.

Boundary-layer effects on internal flow choking in dual-thrust solid rocket motors

Theoretical studies have been carried out to examine internal flow choking in the inert simulators of a dual-thrust motor. Using a two-dimensional k-omega turbulence model, detailed parametric studies have been carried out to examine aerodynamic choking and the existence of a fluid throat at the transition region during the startup transient of dual-thrust motors. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second-order-implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-averaged, Navier-Stokes equations is employed. It was observed that, at the subsonic inflow conditions, there is a possibility of the occurrence of internal flow choking in dual-thrust motors due to the formation of a fluid throat at the beginning of the transition region induced by area blockage caused by boundary-layer-displacement thickness. It has been observed that a 55% increase in the upstream port area of the dual-thrust motor contributes to a 25% reduction in blockage factor at the transition region, which could negate the internal How choking and supplement with an early choking of the dual-thrust motor nozzle. If the height of the upstream port relative to the motor length is too small, the developing boundary layers from either side of the port can interact, leading to a choked,flow. On the other hand, if the developing boundary layers are far enough apart, then choking does not occur. The blockage factor is greater in magnitude for the choked case than for the unchoked case. More tangible explanations are presented in this paper for the boundary-layer blockage and the internal flow choking in dual-thrust motors, which hitherto has been unexplored.

Continuous-Flow Surface Aeration Systems

An aeration process in ail activated sludge plant is a continuous-flow system. In this system, there is a steady input flow (flow from the primary clarifier or settling tank with some part from the secondary clarifier or secondary settling tank) and output flow connection to the secondary clarifier or settling tank. The experimental and numerical results obtained through batch systems can not be relied on and applied for the designing of a continuous aeration tank. In order to scale up laboratory results for field application, it is imperative to know the geometric parameters of a continuous system. Geometric parameters have a greater influence on the mass transfer process of surface aeration systems. The present work establishes the optimal geometric configuration of a continuous-flow surface aeration system. It is found that the maintenance of these optimal geometric parameters systems result in maximum aeration efficiency. By maintaining the obtained optimal geometric parameters, further experiments are conducted in continuous-flow surface aerators with three different sizes in order to develop design curves correlating the oxygen transfer coefficient and power number with the rotor speed. The design methodology to implement the presently developed optimal geometric parameters and correlation equations for field application is discussed.