Evaluation of k-epsilon and RNG turbulence models for confined swirling and non-swirling flow

In a very recent study [1] the Renormalisation Group (RNG) turbulence model was used to obtain flow predictions in a strongly swirling quarl burner, and was found to perform well in predicting certain features that are not well captured using less sophisticated models of turbulence. The implication is that the RNG approach should provide an economical and reliable tool for the prediction of swirling flows in combustor and furnace geometries commonly encountered in technological applications. To test this hypothesis the present work considers flow in a model furnace for which experimental data is available [2]. The essential features of the flow which differentiate it from the previous study [1] are that the annular air jet entry is relatively narrow and the base wall of the cylindrical furnace is at 90 degrees to the inlet pipe. For swirl numbers of order 1 the resulting flow is highly complex with significant inner and outer recirculation regions. The RNG and standard k-epsilon models are used to model the flow for both swirling and non-swirling entry jets and the results compared with experimental data [2]. Near wall viscous effects are accounted for in both models via the standard wall function formulation [3]. For the RNG model, additional computations with grid placement extending well inside the near wall viscous-affected sublayer are performed in order to assess the low Reynolds number capabilities of the model.

Computation of confined swirling flow using RNG and k-epsilon turbulence models

In this work we numerically model isothermal turbulent swirling flow in a cylindrical burner. Three versions of the RNG k-epsilon model are assessed against performance of the standard k-epsilon model. Sensitivity of numerical predictions to grid refinement, differing convective differencing schemes and choice of (unknown) inlet dissipation rate, were closely scrutinised to ensure accuracy. Particular attention is paid to modelling the inlet conditions to within the range of uncertainty of the experimental data, as model predictions proved to be significantly sensitive to relatively small changes in upstream flow conditions. We also examine the characteristics of the swirl--induced recirculation zone predicted by the models over an extended range of inlet conditions. Our main findings are: - (i) the standard k-epsilon model performed best compared with experiment; - (ii) no one inlet specification can simultaneously optimize the performance of the models considered; - (iii) the RNG models predict both single-cell and double-cell IRZ characteristics, the latter both with and without additional internal stagnation points. The first finding indicates that the examined RNG modifications to the standard k-e model do not result in an improved eddy viscosity based model for the prediction of swirl flows. The second finding suggests that tuning established models for optimal performance in swirl flows a priori is not straightforward. The third finding indicates that the RNG based models exhibit a greater variety of structural behaviour, despite being of the same level of complexity as the standard k-e model. The plausibility of the predicted IRZ features are discussed in terms of known vortex breakdown phenomena.

Analysis of turbulent confined highly swirling flow

We report here a CFD model of highly swirling flow in a quarl burner using three versions of the k-epsilon model. Results for the recirculating zone, the bounding shear layer and the downstream flow are presented. We discuss, with suitable qualifications, how the model predictions can inform our understanding of this class of flows.

A numerical method for separation of stresses in photo-orthotropic elasticity

A numerical method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation for orthotropic case. The compatibility equation is written in terms of a stress parameter S analogous to the sum of principal stresses in two-dimensional isotropic case. The solution of this equation provides a relation between the normal stresses. The photoelastic data give the shear stress and another relation between the two normal stresses. The accuracy of the numerical method and its application to practical problems are illustrated with examples.

Velocity ratio-cum-transfer matrix method for the evaluation of a muffler with mean flow

The paper deals with a method for the evaluation of exhaust muffers with mean flow. A new set of variables, convective pressure and convective mass velocity, have been defined to replace the acoustic variables. An expression for attenuation (insertion loss) of a muffler has been proposed in terms of convective terminal impedances and a velocity ratio, on the lines of the one existing for acoustic filters. In order to evaluate the velocity ratio in terms of convective variables, transfer matrices for various muffler elements have been derived from the basic relations of energy, mass and momentum. Finally, the velocity ratiocum-transfer matrix method is illustrated for a typical straight-through muffler.

Nonsimilar incompressible laminar boundary layers with magnetic field.

The solution of the steady laminar incompressible nonsimilar magneto-hydrodynamic boundary layer flow and heat transfer problem with viscous dissipation for electrically conducting fluids over two-dimensional and axisymmetric bodies with pressure gradient and magnetic field has been presented. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for flow over a cylinder and a sphere. The results indicate that the magnetic field tends to delay or prevent separation. The heat transfer strongly depends on the viscous dissipation parameter. When the dissipation parameter is positive (i.e. when the temperature of the wall is greater than the freestream temperature) and exceeds a certain value, the hot wall ceases to be cooled by the stream of cooler air because the ‘heat cushion’ provided by the frictional heat prevents cooling whereas the effect of the magnetic field is to remove the ‘heat cushion’ so that the wall continues to be cooled. The results are found to be in good agreement with those of the local similarity and local nonsimilarity methods except near the point of separation, but they are in excellent agreement with those of the difference-differential technique even near the point of separation.

Flow between torsionally oscillating noncoaxial cylinders

Abstract is not available.

Nonsimilar incompressible laminar boundary-layer flows in micropolar fluids

The solution of the steady laminar incompressible nonsimilar boundary-layer problem for micropolar fluids over two-dimensional and axisymmetric bodies has been presented. The partial differential equations governing the flow have been transformed into new co-ordinates having finite range. The resulting equations have been solved numerically using implicit finite-difference scheme. The computations have been carried out for a cylinder and a sphere. The results indicate that the separation in micropolar fluids occurs at earlier streamwise locations as compared to Newtonian fluids. The skin friction and velocity profiles depend on the shape of the body and are almost insensitive to microrotation or coupling parameter, provided the coupling parameter is small. On the other hand, the microrotation profiles and microrotation gradient depend on the microrotation parameter and they are insensitive to the coupling parameter.

Mean Flow Measurements in Turbulent Boundary Layers along Mildly Curved Surfaces

An experimental investigation of the mean flow characteristics of two-dimensional turbulent boundary layers over surfaces of mild longitudinal curvature is reported. The study covered both convex and concave walls of \d/Rw I « 0.013 (d being the boundary-layer thickness and Rw being the wall radius). It was found that, whereas the region close to the wall was not affected significantly by wall curvature, the outer region was very sensitive to even mild wall curvature. A detailed study of the wake region using present and other available data suggests a systematic effect of b/Rw on the wake structure. The paper also discusses in detail the effect of mild wall curvature on the boundary-layer development with particular emphasis on the difference in behavior of the boundary layer at short and long distances from the leading edge of the curved wall, an aspect which has not received sufficient attention in previous experimental investigations. An attempt has been made to explain this behavior from a consideration of the structure of turbulence in boundary layers over curved surfaces taken into account.

On the computation of two-dimensional compressible flow fields by the modified local stability scheme

The modified local stability scheme is applied to several two-dimensional problems—blunt body flow, regular reflection of a shock and lambda shock. The resolution of the flow features obtained by the modified local stability scheme is found to be better than that achieved by the other first order schemes and almost identical to that achieved by the second order schemes incorporating artificial viscosity. The scheme is easy for coding, consumes moderate amount of computer storage and time. The scheme can be advantageously used in place of second order schemes.

Method for evaluation of the acoustical impedance of a black box, with or without mean flow, measuring pressures at fixed positions

The transmission-line or the impedance-tube method for the measurement of the acoustic impedance of any termination involves a search for various minima and maxima of pressure. For this purpose, arrangement has to be made for the microphone to travel along the length of the impedance tube, and this complicates the design of the tube considerably. The present paper discusses a method which consists in evaluating the tube attenuation factor at any convenient frequency by making use of measured SPL's at two (or more) fixed locations with a rigid termination, calculating the tube attenuation factor and wave number at the required frequency of interest with or without mean flow (as applicable), and finally evaluating the impedance of the given termination by measuring and using SPL's at three (or more) fixed locations. Thus, the required impedance tube is considerably smaller in length, simpler in design, easier to manufacture, cheaper in cost and more convenient to use. The design of the tube is also discussed. Incidentally, it is also possible to evaluate the impedance at any low frequency without having to use a larger impedance tube.

Laminar hypersonic boundary-layer flow at a three-dimensional stagnation point with slip and mass transfer

Abstract is not available.

Is there an athermal region of plastic flow in metals at intermediate temperatures?

The question of the existence or otherwise of an athermal temperature region of plastic flow in metals is examined. It is suggested that the athermal region is absent in metals with large dislocation densities. Such an explanation is provoked by a fairly recent proposition that the unzipping of attractive junctions is a plausible rate-controlling mechanism at high temperatures.

A method for separation of stresses in Two- and three-dimensional photoelasticity

A method for separation of stresses in two and three-dimensional photo elasticity using the harmonisation ofjrst stress invariant along a straight section is deve- ,dped. For two-dimensions, the equations of equilibrium are reformulated in terms ojsum and difference of normal stresses and relations are obtained which can be used for harmonisation of the first invariant of stress along a straight section. A similar procedure is adopted for three-dimensions by making use of the Beltrmi-MicheN equations. The new relations are used in finite d~yerencefo rm to evaluate the sum of normal stresses along straight sections in a three-dimensional body. The method requires photoelastic data along the section as well ~rra djacent sections. This method could be used as an alternative to the shear d@erence method for separation of stresses in photoelasticity. 7he accuracy and reliability of the method is ver$ed by applying the method to problems whose solutions are known.

On plane-wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient

A theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented. The temperature variation in the pipe is taken to be a linear temperature gradient along the axis. The theoretical studies include the formulation of a wave equation based on continuity, momentum, and state equation, and derivation of a general four-pole matrix, which is shown to yield the well-known transfer matrices for several other simpler cases.