Numerical Solution Of Conservation Equations Research Articles

Numerical simulation and thermal performance of hybrid brick walls embedding a phase change material for passive building applications

Phase change materials (PCMs) have the ability to store/release huge latent heat during phase change. When used in the building envelope, the PCM wall panel can potentially enhance the building’s operation by reducing energy requirements to maintain thermal comfort, downsizing heating/cooling equipment, and shifting the peak load from the electrical grid. This work deals with the numerical simulation of the thermal performance of brick walls with embedded PCMs using an enthalpy-porosity approach. An implicit finite volume method is used for the numerical solution of conservation equations for mass, momentum, and energy. The results gathered have been judged in good agreement with the experiments. It turns out that incorporating PCM into brick masonry can both reduce maximum temperatures up to 3 °C and mitigate daily fluctuations. A higher PCM amount incorporated in a masonry wall reduces the energy consumption required to ensure a suitable comfort temperature. The inward heat transfer decreases if the PCM amount required for efficient storage is 20–30%. Finally, the proposed predictions seem to be useful for developing better storage of the heat energy and latent heat used in buildings to improve their overall energy efficiency.

Wall heat recirculation and exergy preservation in flow through a small tube with thin heat source

Theoretical studies have been made on heat transfer and exergy analysis of flow through a narrow tube with heat recirculating wall and embedded thin heat source. Heat transfer analysis is based on numerical solution of conservation equations of mass, momentum and energy, while the exergy analysis is based on flow exergy balance and entropy transport equation. It has been observed that the ratio of heat recirculation to heat loss (QR/QL) increases with increase in the ratio of thermal conductivity of solid wall to that of working fluid (ks/kg) and Peclet number of flow (Pe), while it decreases with an increase in external Nusselt number (NuE). The ratio QR/QL has a maximum with the ratio of wall thickness to tube radius (tw/R). The optimum value of tw/R depends only on ks/kg and reduces from a value of 0.2 at ks/kg=330 to a value of 0.125 at ks/kg=850, and then remains almost constant for any further increase in ks/kg. The volumetric entropy generation rate in the fluid flow reaches a maximum at a radial location close to the inner surface of the wall, while the entropy generation in solid wall, being more than that of the fluid, is radially uniform. The volumetric entropy generation is found to be confined within the upstream region of the heat source. Second law efficiency increases with a decrease in tw/R and NuE, but with an increase in Pe. It remains almost constant with ks/kg.

NUMERICAL AND EXPERIMENTAL INVESTIGATIONS OF EGR DISTRIBUTION IN A DI TURBOCHARGED DIESEL ENGINE

This paper presents the results of numerical and experimental investigations to evaluate the distribution of exhaust gas recirculation (EGR) between cylinders in a DI turbocharged diesel engine. The turbulent three-dimensional flow field was analyzed by the numerical solution of conservation equations with an appropriate turbulence model. EGR was applied to intake manifold with various rates at cooled and non-cooled states. The experiments were conducted on an MT4.244 turbocharged DI diesel engine under full load condition at 1900rpm. The model was validated by experimental data with a good agreement between experimental measurements and numerical predictions. Using this method, it is possible to control EGR distribution so as to reduce emissions formation as well as to improve performance.

A Modified Eulerian-Lagrangian Approach Applied to a Compact Down-Hole Sub-Sea Gas-Liquid Separator

This article presents a modified Eulerian-Lagrangian approach for solving multi-phase flow applied to a laboratory-scale gas-liquid separator designed for high gas content. The separator consists of two concentric pipes with a swirl tube in the annular space between the pipes. The gas-liquid mixture comes from a tangential side inlet and the system works with a combination of gravity and centrifugal forces to achieve a high-efficient gas-liquid separation. In the modified Eulerian-Lagrangian method, gas flow is coupled with the spray and wall film models. The spray model involves multi-phase flow phenomena and requires the numerical solution of conservation equations for the gas and the liquid phase simultaneously. With respect to the liquids phase, the discrete-droplet method (DDM) is used. The droplet-gas momentum exchange, droplet coalesces and breaks-up, and the droplet-wall interaction with wall-film generation and entrainment of the water droplet back into the gas stream are taken into account in this investigation. To be consistent with the experiments the experimental air water mixture on the liquid carry over (LCO) curve is used for the numerical investigation. The standard k-ϵ turbulence model is used for turbulence closure. The predicted results from the modified Eulerian-Lagrangian multi-phase model explain the complex flow behavior inside the separator and are in good agreement when compared with experiments.

Influences of nozzle flow and nozzle geometry on the shape and size of an air core in a hollow cone swirl nozzle

Theoretical and experimental studies have been carried out to determine the influences of nozzle flow and nozzle geometry on the shape and size of a fully developed air core in a hollow cone swirl nozzle. The theoretical study is based on the numerical solution of conservation equations for mass and momentum along with the volume fraction of the liquid phase. An interface capturing method has been adopted in the numerical simulation of free surface flow in the nozzle. Experiments have been carried out with a number of nozzles fabricated in Perspex material. The air core diameter has been measured from photographs taken by a camera outside the nozzle. It has been observed that the shape of the fully developed air core in a conical swirl nozzle is cylindrical with a considerable bulging at the entrance to the orifice, while in the case of a conical nozzle without a finite length of orifice, the air core is uniform throughout the nozzle. The values of the air core diameter in the swirl chamber ( da1) and in the orifice ( da2) of a nozzle increase sharply with an increase in inlet Reynolds number ( Re) below 1.1 × 104, but become almost independent of Re above this (up to 1.7 × 104). The air core diameter, both in the swirl chamber and in the orifice, increases with an increase in the value of the ratio of orifice to swirl chamber diameter and the cone angle of the swirl chamber and with a decrease in the value of the ratio of entry port to swirl chamber diameter and the ratio of orifice length to swirl chamber diameter.

Evaporation of multicomponent liquid fuel droplets

A theoretical investigation on evaporation of a two-component liquid fuel droplet in high-temperature quiescent gaseous surroundings has been made from the numerical solution of conservation equations of heat, mass and momentum transports in the carrier and droplet phases. Liquid fuel droplets containing (i) components of widely varying volatilities, namely, n-hexane and n-hexadecane and (ii) components of closely spaced volatilities, namely, n-hexane and benzene, have been considered for the studies. The evaporation characteristics, namely mass depletion, droplet temperature and droplet composition histories with time, have been evaluated in terms of the pertinent input parameters, namely the initial composition of the drop constituents and the free stream temperature. The present studies have been made on the basis of both (i) the interdiffusion (finite diffusion in the droplet phase) model, and (ii) the rapid mixing (infinite diffusion in the droplet phase) model. The results from both the models have been compared to ascertain the accuracy of the rapid mixing model.

Computational fluid dynamics for chemical reactor engineering

Computational Fluid Dynamics (CFD) involves the numerical solution of conservation equations for mass, momentum and energy in a flow geometry of interest, together with additional sets of equations reflecting the problem at hand. In this paper the current capabilities of CFD for chemical reactor engineering are illustrated by considering a series of examples from industrial practice. These examples form the basis for the identification of future trends and potential stumbling blocks. Recent progress in the predictions of flow in baffled stirred tank reactors is reviewed. Improved turbulence modelling and high-performance computing have a particularly important part to play in the future applications of CFD to this type of reactor. In the next example, which concerns non-Newtonian, non-isothermal flow in an extruder, CFD turns out to be helpful in understanding the rôle of temperature profiles and residence time distribution in determining the product quality. In this application area limitations in available computing power and experimental validation of rheological models are both important. CFD simulations of gaseous turbulent flow with competing parallel and consecutive reactions constitute the third example. Apart from the need for accurate kinetic rates, the main problem in this case is the optimal choice of closure of chemical source terms in the mean transport equations for species mass fractions. Several models have been implemented in a commercial CFD code and validated with plant data, thus allowing CFD model calculations to contribute to an improved reactor design. Finally, a discussion of future needs and expectations of the chemical processing industry with respect to CFD modelling, mainly focussing on multiphase flow, is given.

Transport processes and associated irreversibilities in droplet combustion in a convective medium

A mathematical model of the combustion of a droplet surrounded by hot gas with a uniform free stream motion is made from the numerical solution of conservation equations of heat, mass and momentum in both the carrier and the droplet phases. The gas-phase chemical reaction between the fuel vapour and the oxidizer is assumed to be single-step and irreversible. The phenomenon of ignition is recognised by the sudden rise of temperature in the temperature/time histories at different locations in the carrier phase. To ascertain the process irreversibilities, the instantaneous rate of entropy production and its variation with time have been determined from the simultaneous numerical solution of the entropy conservation equations for both the gas and liquid phases. The relative influences of pertinent input parameters, namely the initial Reynolds number Rei, the ratio of the free stream to initial temperature T∞ and the ambient pressure on (i) the local and average Nusselt numbers, (ii) the life histories of burning fuel drops, and (iii) the entropy generation rate in the process of droplet combustion have been established.

A numerical solution for the turbulent flow of non-Newtonian fluids in the entrance region of a heated circular tube

Numerical solutions of conservation equations are obtained for turbulent flow of non-Newtonian fluids in a circular tube. The forward marching procedure of Patankar and Spalding 1 was implemented in order to obtain the simultaneous development of the velocity and temperature fields by using the apparent viscosity of fluids. Prandtl's mixing length concept is used to determine the apparent turbulent shearing stress. Furthermore, local and average Nusselt numbers are obtained in the entrance region, as well as in the fully developed region. For the case of the fully developed region, values of the Nusselt numbers are compared both with the experimental data and empirical correlations.

Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics

The propagation of waves in slightly inhomogeneous dispersive media is conveniently described by a geometrical or kinematic theory. In such frameworks the solution of the propagation problem is constructed by (a) deriving a dispersion relation and determining its characteristic lines and (b) solving an equation expressing the conservation of a field invariant like the wave action. This paper is concerned with the implementation of the last step under general field and boundary conditions. The method presented is based on the derivation of a variational system of differential equations for the geodesic elements of the wave front. The elementary cross-section of the wave front is obtained by integration and the principle of conservation of the field invariant directly yields the field amplitude. In addition, suitable jump conditions are derived for treating specular reflexions at solid boundaries. The method is illustrated by specific problems of interest in aeroacoustics.

Measurement and Calculation of Furnace-Flow Properties

Measurements of the three components of mean velocity, the corresponding normal stresses, mean temperature, and wall heat flux are reported in a model furnace; they were obtained with a coaxial burner with a 20° quarl angle and swirl numbers of 0.3 and 0.5. Particular attention is devoted to the influence of the profiles in the plane of the burner exit; it is shown, for example, that combustion results in large increases in the values of maximum positive and negative velocity in the near-burner region and that the two swirl numbers result in significantly different profiles of all the measured flow properties. The variations in local furnace properties, including the wall heat flux, are quantified for the two swirl numbers and shown to agree, in general terms, with previous calculations; the location of maximum heat flux, for example, is significantly closer to the burner exit for the larger swirl number. Calculations, obtained from the numerical solution of conservation equations in differential form, are presented and compared with the measurements. Particular attention is devoted to the uncertainties associated with density fluctuation correlation and with the specification of a probability density distribution of scalar fluctuations. An attempt is made to quantify the precision with which calculations of furnace flow properties can presently be calculated.