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.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 x 10(3) to 6.5 x 10(5) to study the effect of natural ventilation on the boundary layer separation and near-wake Vortex shedding characteristics. In the subcritical range of Re (<2 x 10(5)), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 x 10(5)), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag.

Dependence of the large-scale vortex instability on latitude, stratification and domain size

In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions for the onset of the instability were investigated in terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification, and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the colatitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.

A simple method for potential flow simulation of cascades

A simple method using a combination of conformal mapping and vortex panel method to simulate potential flow in cascades is presented. The cascade is first transformed to a single body using a conformal mapping, and the potential flow over this body is solved using a simple higher order vortex panel method. The advantage of this method over existing methodologies is that it enables the use of higher order panel methods, as are used to solve flow past an isolated airfoil, to solve the cascade problem without the need for any numerical integrations or iterations. The fluid loading on the blades, such as the normal force and pitching moment, may be easily calculated from the resultant velocity field. The coefficient of pressure on cascade blades calculated with this methodology shows good agreement with previous numerical and experimental results.

Unsteady laminar compressible swirling flow with massive blowing

THE study of swirling boundary layers is of considerable importance in many rotodynamic machines such as rockets, jet engines, swirl generators, swirl atomizers, arc heaters, etc. For example, the introduction of swirl in a flow acceleration device such as a nozzle in a rocket engine promises efficient mass flow control. In nuclear rockets, swirl is used to retain the uranium atoms in the rocket chamber. With these applications in mind, Back1 and Muthanna and Nath2 have obtained the similarity solutions for a low-speed three-dimensional steady laminar compressible boundary layer with swirl inside an axisymmetric surface of variable cross section. The aim of the present analysis is to study the effect of massive blowing rates on the unsteady laminar swirling compressible boundary-layer flow of an axisymmetric body of arbitrary cross section when the freestream velocity and blowing rate vary with time. The type of swirl considered here is that of a free vortex superimposed on the longitudinal flow of a compressible fluid with variable properties. The analysis is applicable to external flow over a body as well as internal flow along a surface. For the case of external flow, strong blowing can have significant use in cooling the surface of hypervelocity vehicles, particularly when ablation occurs under large aerodynamic or radiative heating, but there may not be such an important application of strong blowing in the case of internal flow. The governing partial differential equations have been solved numerically using an implicit finite difference scheme with a quasilinearization technique.3 High temperature gas effects, such as radiation, dissociation, and ionization, etc., are not investigated. The nomenclature is usually that of Ref. 4 and is listed in the full paper.

Vortex sheet simulation of a plane �canonical� mixing layer

Discrete vortex simulations of the mixing layer carried out in the past have usually involved large induced velocity fluctuations, and thus demanded rather long time-averaging to obtain satisfactory values of Reynolds stresses and third-order moments. This difficulty has been traced here, in part, to the use of discrete vortices to model what in actuality are continuous vortex sheets. We propose here a novel two-dimensional vortex sheet technique for computing mixing layer flow in the limit of infinite Reynolds number. The method divides the vortex sheet into constant-strength linear elements, whose motions are computed using the Biot-Savart law. The downstream far-field is modelled by a steady vorticity distribution derived by application of conical similarity from the solution obtained in a finite computational domain. The boundary condition on the splitter plate is satisfied rigorously using a doublet sheet. The computed large-scale roll-up of the vortex sheet is qualitatively similar to experimentally obtained shadow-graphs of the plane turbulent mixing layer. The mean streamwise velocity profile and the growth rate agree well with experimental data. The presently computed Reynolds stresses and third-order moments are comparable with experimental and previous vortex-dynamical results, without using any external parameter (such as the vortex core-size) of the kind often used in the latter. The computed autocorrelations are qualitatively similar to experimental results along the top and bottom edges of the mixing layer, and show a well-defined periodicity along the centreline. The accuracy of the present computation is independently established by demonstrating negligibly small changes in the five invariants (including the Hamiltonian) in vortex dynamics.

Modelling plane mixing layers using vortex points and sheets

We present here a critical assessment of two vortex approaches (both two-dimensional) to the modelling of turbulent mixing layers. In the first approach the flow is represented by point vortices, and in the second it is simulated as the evolution of a continuous vortex sheet composed of short linear elements or ''panels''. The comparison is based on fresh simulations using approximately the same number of elements in either model, paying due attention in both to the boundary conditions far downstream as well as those on the splitter plate from which the mixing layer issues. The comparisons show that, while both models satisfy the well-known invariants of vortex dynamics approximately to the same accuracy, the vortex panel model, although ultimately not convergent, leads to smoother roll-up and values of stresses and moments that are in closer agreement with the experiment, and has a higher computational efficiency for a given degree of convergence on moments. The point vortex model, while faster for a given number of elements, produces an unsatisfactory roll-up which (for the number of elements used) is rendered worse by the incorporation of the Van der Vooren correction for sheet curvature.

Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping

In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural damping, enabling the system to take on both negative and positive damping. This permits a systematic study of the effects of system mass and damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of mass–damping ($\alpha$), in the so-called ‘Griffin plot’. A principal result in the present work is the discovery that the data collapse very well if one takes into account the effect of Reynolds number ($\mbox{\textit{Re}}$), as an extra parameter in a modified Griffin plot. Peak amplitudes corresponding to zero damping ($A^*_{{\alpha}{=}0}$), for a compilation of experiments over a wide range of $\mbox{\textit{Re}}\,{=}\,500-33000$, are very well represented by the functional form $A^*_{\alpha{=}0} \,{=}\, f(\mbox{\textit{Re}}) \,{=}\, \log(0.41\,\mbox{\textit{Re}}^{0.36}$). For a given $\mbox{\textit{Re}}$, the amplitude $A^*$ appears to be proportional to a function of mass–damping, $A^*\propto g(\alpha)$, which is a similar function over all $\mbox{\textit{Re}}$. A good best-fit for a wide range of mass–damping and Reynolds number is thus given by the following simple expression, where $A^*\,{=}\, g(\alpha)\,f(\mbox{\textit{Re}})$: \[ A^* \,{=}\,(1 - 1.12\,\alpha + 0.30\,\alpha^2)\,\log (0.41\,\mbox{\textit{Re}}^{0.36}). \] In essence, by using a renormalized parameter, which we define as the ‘modified amplitude’, $A^*_M\,{=}\,A^*/A^*_{\alpha{=}0}$, the previously scattered data collapse very well onto a single curve, $g(\alpha)$, on what we refer to as the ‘modified Griffin plot’. There has also been much debate over the last three decades concerning the validity of using the product of mass and damping (such as $\alpha$) in these problems. Our results indicate that the combined mass–damping parameter ($\alpha$) does indeed collapse peak-amplitude data well, at a given $\mbox{\textit{Re}}$, independent of the precise mass and damping values, for mass ratios down to $m^*\,{=}\,1$.

Single Cavity Trapped Vortex Combustor Simulations

The present work describes steady and unsteady computation of reacting flow in a Trapped Vortex Combustor. The primary motivation of this study is to develop this concept into a working combustor in modern gas turbines. The present work is an effort towards development of an experimental model test rig for further understanding dynamics of a single cavity trapped vortex combustor. The steady computations with and without combustion have been done for L/D of 0.8, 1 and 1.2; also unsteady non-reacting flow simulation has been done for L/D of 1. Fuel used for the present study is methane and Eddy-Dissipation model has been used for combustion-turbulence interactions. For L/D of 0.8, combustion efficiency is maximum and pattern factor is minimum. Also, primary vortex in the cavity is more stable and symmetric for L/D of 0.8. From unsteady non-reacting flow simulations, it is found that there is no vortex shedding from the cavity but there are oscillations in the span-wise direction of the combustor.

Experimental and Numerical Studies in a Compact Trapped Vortex Combustor: Stability Assessment and Augmentation

Fundamental studies on a compact trapped vortex combustor indicate that cavity injection strategies play a major role on flame stability. Detailed experiments indicate that blow-out occurs for a certain range of cavity air flow velocities. An unsteady RANS-based reacting flow simulation tool has been utilized to study the basic dynamics of cavity vortex for various flow conditions. The phenomenon of flame blow-out at certain intermediate cavity air velocities is explained on the basis of transition from a cavity-stabilized mode to an opposed flow stagnation mode. A novel strategy is proposed for achieving flame stability at all conditions. This involves using a flow guide vane in the path of the main flow to direct a portion of the main flow into the cavity. This seems to result in a desirable dual vortex structure, i.e., a small clockwise vortex behind the vane and large counterclockwise vortex in the cavity. Experimental results show stable flame at all flow conditions with the flow guide vane, and pressure drop is estimated to be within acceptable limits. Cold flow simulations show self-similar velocity profiles for a range of main inlet velocities, and high reverse velocity ratios (-0.3) are observed. Such a high-velocity ratio in the reverse flow shear layer profile leads to enhanced production of turbulence imperative to compact combustors. Reacting flow simulations show even higher reverse velocity ratios (above -0.7) due to flow acceleration. The flame is observed to be stable, even though minor shear layer oscillations are present in the form of vortex shedding. Self-similarity is also observed in reacting flow temperature profiles at combustor exit over the entire range of the mainstream velocity. This indicates that the present configuration holds a promise of delivering robust performance invariant of the flow operating conditions.

Flow-acoustic Characterisation of a Cavity-based Combustor Configuration

This study concerns the flow-acoustic characterisation of a cavity-based combustor configuration. A well-validated numerical tool has been used to simulate the unsteady, two-dimensional reacting flow. Initially, a conventional flow over a cavity with dimensions and conditions corresponding to a compact cavity combustor was studied. Cavity mass injections in the form of fuel and air injections required for trapped vortex formation were then employed and the resonance features of this configuration were studied. The results indicate that the cavity depth mode resonance mechanism is dominant at the conditions studied in this work and that the oscillation frequencies do not change with cavity air injection. This observation is important since it implies that the only important variable which can alter resonant frequencies is the cavity depth. With combustion, the pressure oscillation amplitude was observed to increases significantly due to periodic entrainment of the cavity air jet and fluctuation of fuel-air mixture composition to produce highly fluctuating heat-release rates. The underlying mechanisms of the unsteady flow in the cavity combustor identified in this study indicate the strong dependence of the acoustics on the cavity injection strategies.