1,721,006 research outputs found
A computer code for enclosed natural convection in the boundary layer regime
No full textA computer code is developed for the numerical prediction of natural convection\ud
in rectangular two-dimensional cavities at high Rayleigh numbers. The\ud
governing equations are retained in the primitive variable form. The numerical\ud
method is based on finite differences and an ADI scheme. Convective terms may\ud
be approximated with either central or hybrid differencing for greater stability.\ud
A non-uniform grid distribution is possible for greater efficiency. The pressure is\ud
dealt with via a SIMPLE type algorithm and the use of a fast elliptic solver for\ud
the solenoidal velocity correction field significantly reduces computing times.\ud
Preliminary results indicate that the code is reasonably accurate, robust and\ud
fast compared with existing benchmarks and finite difference based codes, particularly\ud
at high Rayleigh numbers. Extension to three-dimensional problems\ud
and turbulence studies in similar geometries is readily possible and indicated
Evaluation of k-epsilon and RNG turbulence models for confined swirling and non-swirling flow
No full textIn 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.\ud
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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\ud
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\ud
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\ud
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
Natural convection in rectangular cavities at high Rayleigh number
No full textNatural convection in rectangular two-dimensional cavities with differentially heated side walls is a standard problem in numerical heat transfer. Most of the existing studies has considered the low Ra laminar regime. The general thrust of the present research is to investigate higher Ra flows extending into the unsteady and turbulent regimes where the physics is not fully understood and appropriate models for turbulence are not yet established. In the present study the Boussinesq approximation is being used, but the theoretical background and some preliminary results have been obtained[1] for flows with variable properties
Flow of a micropolar fluid bounded by a stretching sheet
Full text linkWe consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS).\ud
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For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult
Solutions for the flow of a micropolar fluid in a porous channel
No full textHow various additives can increase some cardio-vascular diseases and effects of transport for albumin and glucose through permeable membranes are some important studies in biomechanics. The rolling phenomena of the leucocytes gives rise to an inflammatory reaction along a vascular wall. Initiated by Eringen [5], a micropolar fluid is a satisfactory model for flows of fluids which contain micro-constituents which can undergo rotation
Assessment in tertiary mathematics
No full textThere is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989)
Micropolar flow over a porous stretching sheet with strong suction or injection
No full textWe consider self-similar boundary layer flow of a micropolar fluid driven by a porous stretching sheet. For the limiting cases of large suction or injection, an order of magnitude analysis is used to obtain analytic results for the shear stress and the microrotation at the surface. Our analysis reveals how the wall shear stress is significantly affected by two of the parameters in the micropolar model and we indicate how our findings may be of use in technological applications involving micropolar flow
Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet
No full textSimilarity solutions for flow over an impermeable, non-linearly (quadratic) stretching sheet were studied recently by Raptis and Perdikis (Int. J. Non-linear Mech. 41 (2006) 527–529) using a stream function of the form ψ=αxf(η)+βx2g(η). A fundamental error in their problem formulation is pointed out. On correction, it is shown that similarity solutions do not exist for this choice of
Computation of turbulent flow in an IFRF quarl burner
No full textA 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.\ud
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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 \ud
predictions compared with the standard k-e turbulence model. A difficulty\ud
is that the flow considered here features a confined vortex breakdown\ud
which can be highly sensitive to flow behaviour both upstream and downstream\ud
of the breakdown zone. Nevertheless, the relatively simple confining geometry\ud
allows us to undertake a systematic study so that both\ud
grid-independent and domain-independent results can be reported.\ud
The systematic study includes a detailed investigation of the effects of\ud
upstream and downstream conditions on the predictions, in addition to\ud
grid refinement and other tests to ensure that numerical error is not\ud
significant.\ud
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Another important aim is to determine to what extent the turbulence model\ud
predictions can provide us with new insights into the physics of confined\ud
vortex breakdown flows. To this end, the computations are discussed in detail \ud
with reference to known vortex breakdown phenomena and existing theories.\ud
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A major conclusion is that one of the RNG k-e models investigated here\ud
is able to correctly capture the complex forward flow region inside the\ud
recirculating breakdown zone. This apparently pathological result is in\ud
stark contrast to the findings of previous studies, most of which have concluded\ud
that either algebraic or differential Reynolds stress modelling is needed to\ud
correctly predict the observed flow features. Arguments are given as to\ud
why an isotropic eddy-viscosity turbulence model may well be able\ud
to capture the complex flow structure within the recirculating zone for this\ud
flow setup.\ud
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With regard to the flow physics, a major finding is that the results obtained\ud
here are more consistent with the view that confined vortex breakdown is a\ud
type of axisymmetric boundary layer separation, rather than a manifestation\ud
of a subcritical flow state
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