Hélio Aparecido Navarro

Effectiveness-ntu computation with a mathematical model for cross-flow heat exchangers

Abstract - Due to the wide range of design possibilities, simple manufactured, low maintenance and low cost, cross-flow heat exchangers are extensively used in the petroleum, petrochemical, air conditioning, food storage, and others industries. In this paper a mathematical model for cross-flow heat exchangers with complex flow arrangements for determining e-NTU relations is presented. The model is based on the tube element approach, according to which the heat exchanger outlet temperatures are obtained by discretizing the coil along the tube fluid path. In each cross section of the element, tube-side fluid temperature is assumed to be constant because the heat capacity rate ratio C*=C min /C max tends toward zero in the element. Thus temperature is controlled by effectiveness of a local element corresponding to an evaporator or a condenser-type element. The model is validated through comparison with theoretical algebraic relations for single-pass cross-flow arrangements with one or more rows. Very small relative errors are obtained showing the accuracy of the present model. e-NTU curves for several complex circuit arrangements are presented. The model developed represents a useful research tool for theoretical and experimental studies on heat exchangers performance.

Thermal Performance of Multipass Parallel and Counter-Cross-Flow Heat Exchangers

Univ Sao Paulo, Escola Engn Sao Carlos, Dept Engn Mecan, BR-13566590 Sao Carlos, SP, Brazil

Numerical simulation of a radial diffuser turbulent airflow

Abstract In the present work are presented results from numerical simulations performed with the ANSYS-CFX® code. We have studied a radial diffuser flow case, which is the main academic problem used to study the flow behavior on flat plate valves. The radial flow inside the diffuser has important behavior such as the turbulence decay downstream and recirculation regions inside the valve flow channel due to boundary layer detachment. These flow structures are present in compressor reed valve configurations, influencing to a greater extent the compressor efficiency. The main target of the present paper was finding the simulation set-up (computational domain, boundary conditions and turbulence model) that better fits with experimental data published by Tabatabai and Pollard. The local flow turbulence and velocity profiles were investigated using four different turbulence models, two different boundary conditions set-up, two different computational domains and three different flow conditions (Rein – Reynolds number at the diffuser inlet). We used the Reynolds stress (BSL); the k–e; the RNG k–e; and the shear stress transport (SST) k–ω turbulence models. The performed analysis and comparison of the computational results with experimental data show that the choice of the turbulence model, as well as the choice of the other computational conditions, plays an important role in the results physical quality and accuracy.

The effect of numerical diffusion and the influence of computational grid over gas-solid two-phase flow in a bubbling fluidized bed

The numerical diffusion effects appear due to the discretization process of the convective terms of the transport equations. This phenomenon takes place also in the numerical simulation of gas-solid two-phase flows in bubbling fluidized beds (BFB). In the present work a comparative analysis of the numerical results obtained using two interpolation schemes for convective terms, namely FOUP (First Order UPwind) and a high order scheme (Superbee) is presented. The equations are derived by considering the Eulerian-Eulerian gas-solid two-fluid model and the kinetic theory of granular flows (KTGF) for modeling solid phase constitutive equations. For that purpose the MFIX (Multiphase Flow with Interphase eXchanges) code developed at NETL (National Energy Technology Laboratory, US Department of Energy) is used. The numerical diffusion is analyzed by considering a single bubbling detachment and its hydrodynamic process in a two-dimensional BFB. The bubble shape is used as a metric for the description of the results. The influence of the computational grid is also analyzed. It is concluded that the Superbee scheme produces better results and this scheme is recommended for discretizations of the convective terms in coarse grids. The FOUP scheme can be used only in fine grids but it requires a high computational effort. In this study it is also verified that the analysis about estimating uncertainty in grid refinement can be applied in specific points of the grid when a monotonic convergence in time and space occurs.

A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number

Abstract This paper presents numerical simulations of incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number. The equations governing the flow are the Navier–Stokes equations of fluid motion coupled with Maxwell’s equations of electromagnetics. The study of fluid flows under the influence of a magnetic field and with no free electric charges or electric fields is known as magnetohydrodynamics. The magnetohydrodynamics approximation is considered for the formulation of the non-dimensional problem and for the characterization of similarity parameters. A finite-difference technique is used to discretize the equations. In particular, an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows is presented. The discretized conservation equations are solved in stream function–vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient in simulating low Reynolds number and magnetic Reynolds number problems. Numerical results demonstrating the applicability of this technique are also presented. The simulation of incompressible magnetohydrodynamic fluid flows is illustrated by numerical solution for two-dimensional cases.

Influences of the load centre of gravity on heavy vehicle acceleration

The aim of this paper is to analyse the influence of the load centre of gravity on heavy vehicle acceleration. This analysis is done through a method in which a vehicle centre of gravity map is used. A model for the driving force is presented for bus, truck and tractor-semitrailer combinations. The proposed model takes into consideration the resistance forces (drag, rolling resistance, translation and rotation acceleration, climbing resistance) and the 4 X 2 traction system. The positions of the vehicle centre of gravity as a function of the position of the load centre of gravity are determined. The vehicle acceleration is calculated based on the position of the load centre of gravity. This study analyses the acceleration of one of the Mercedes-Benz do Brasil tractor-semitrailer vehicle. A comparison of the acceleration for different maximum adhesion coefficients and ramps are presented, showing new results. An example showing the variations of the load centre of gravity position with the acceleration time and distance is provided. The load centre of gravity position is important for vehicle safety and the efficiency and economy in the transportation of the load.

INFLUENCE OF THE GRANULAR TEMPERATURE IN THE NUMERICAL SIMULATION OF GAS-SOLID FLOW IN A BUBBLING FLUIDIZED BED

This article describes a mathematical model and numerical simulation of gas-solid flow in a bubbling fluidized bed (BFB), where the the two-fluid Eulerian-Eulerian model was used and the solid phase stress tensor was modeled considering both the friction between particles and the kinetic theory of granular flows. The code MFIX (Multiphase Flow with Interphase eXchanges) developed by NETL (National Energy Technology Laboratory, U. S. Department of Energy) was used for numerical simulations, and the results were obtained through computing the granular temperature by using a partial differential equation (PDE) or an algebraic expression. More realistic results were obtained when a PDE with boundary conditions of the partial slip was used. However, for computing the granular temperature in the case of fine grids, it is recommended to use the algebraic equation because it will save computational effort in simulations. Variation in the diameter of the particles (Group B and Group A/B) was also analyzed, and, consequently, it was observed that in future analysis a term for capturing the influence of cohesive forces should be added for particles of Group A/B. This study has revealed that a smooth transition between the viscous regime and the plastic regime is necessary for simulating a hydrodynamic bubbling fluidized bed.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

Abstract This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic–plastic-damage models.