Unsteady laminar boundary layers in a compressible stagnation flow

The unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time is considered. The governing partial differential equations, involving both time and the independent similarity variable, are transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one. The resulting equations are solved by converting them into a matrix equation through the application of implicit finite-difference formulae. Computations have been carried out for two particular unsteady free-stream velocity distributions: (1) a constantly accelerating stream and (2) a fluctuating stream. The results show that in the former case both the skin-friction and the heat-transfer parameter increase steadily with time after a certain instant, while in the latter they oscillate thus responding to the fluctuations in the free-stream velocity.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

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.

Computation of turbulent flow in an IFRF quarl burner

A computational model for isothermal axisymmetric turbulent flow in a quarl burner is set up using the CFD package FLUENT, and numerical solutions obtained from the model are compared with available experimental data. A standard k-e model and and two versions of the RNG k-e model are used to model the turbulence. One of the aims of the computational study is to investigate whether the RNG based k-e turbulence models are capable of yielding improved flow predictions compared with the standard k-e turbulence model. A difficulty is that the flow considered here features a confined vortex breakdown which can be highly sensitive to flow behaviour both upstream and downstream of the breakdown zone. Nevertheless, the relatively simple confining geometry allows us to undertake a systematic study so that both grid-independent and domain-independent results can be reported. The systematic study includes a detailed investigation of the effects of upstream and downstream conditions on the predictions, in addition to grid refinement and other tests to ensure that numerical error is not significant. Another important aim is to determine to what extent the turbulence model predictions can provide us with new insights into the physics of confined vortex breakdown flows. To this end, the computations are discussed in detail with reference to known vortex breakdown phenomena and existing theories. A major conclusion is that one of the RNG k-e models investigated here is able to correctly capture the complex forward flow region inside the recirculating breakdown zone. This apparently pathological result is in stark contrast to the findings of previous studies, most of which have concluded that either algebraic or differential Reynolds stress modelling is needed to correctly predict the observed flow features. Arguments are given as to why an isotropic eddy-viscosity turbulence model may well be able to capture the complex flow structure within the recirculating zone for this flow setup. With regard to the flow physics, a major finding is that the results obtained here are more consistent with the view that confined vortex breakdown is a type of axisymmetric boundary layer separation, rather than a manifestation of a subcritical flow state.

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.

Rapid distortion of axisymmetric turbulence

A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.

The structure of turbulent boundary layers along mildly curved surfaces

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers. (Published Online April 12 2006)

Motion of a bore over a sloping beach: an approximate analytical approach

The motion of a bore over a sloping beach, earlier considered numerically by Keller, Levine & Whitham (1960), is studied by an approximate analytic technique. This technique is an extension of Whitham's (1958) approach for the propagation of shocks into a non-uniform medium. It gives the entire flow behind the bore and is shown to be equivalent to the theory of modulated simple waves of Varley, Ventakaraman & Cumberbatch (1971).

Experiments on the fine structure of turbulence

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings. It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings. The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.

Response of a turbulent boundary layer to a step change in surface heat flux

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0 is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.

Effects of mould filling on evolution of the solid-liquid interface during solidification

This work presents a numerical analysis of simultaneous mould filling and phase change for solidification in a two-dimensional rectangular cavity. The role of residual flow strength and temperature gradients within the solidifying domain, caused by the filling process, on the evolution of solidification interface are investigated. An implicit volume of fluid (VOF)-based algorithm has been employed for simulating the free surface flows during the filling process, while the model for solidification is based on a fixed-grid enthalpy-based control volume approach. Solidification modeling is coupled with VOF through User Defined Functions developed in the commercial computational fluid dynamics (CFD) code FLUENT 6.3.26. Comparison between results of the conventional analysis without filling effect and those of the present analysis shows that the residual flow resulting from the filling process significantly influences the progress of the solidification interface. A parametric study is also performed with variables such as cooling rate, filling velocity and filling configuration, in order to investigate the coupled effects of the buoyancy-driven flow and the residual flow on the solidification behavior.

Mechanism design of ventricular assist device

This research presents an innovative design approach for the development of high efficiency Ventricular assist device that can be used for long-term support a heart failure patient. Computational fluid dynamics (CFD) techniques were applied to the development and intensive analysis to improve the performance and reliability of the pump. From the CFD analysis, a prototype pump was created and evaluated on the mock circulation loop that simulate the human circulatory system environment to evaluate its performance in support varying heart conditions.