Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.

Transient flows in enclosures: A generalised approach for modelling the effects of geometry, heat gains and wind

Transient flows in a confined ventilated space induced by a buoyancy source of time-varying strength and an external wind are examined. The space considered has varying cross-sectional area with height. A generalised theoretical model is proposed to investigate the flow dynamics following the activation of an external wind and an internal source of buoyancy. To investigate the effect of geometry, we vary the angle of the wall inclination of a particular geometry in which a point source of constant buoyancy is activated in the absence of wind. Counter-intuitively the ventilation is worse and lower airflow rates are established for geometries of increasing cross-sectional areas with height. We investigate the effect of the source buoyancy strength by comparing two cases: (1) when the buoyancy input is constant and (2) when the buoyancy input gradually increases over time so that after a finite time the total buoyancy inputs for (1) and (2) are identical. The rate at which the source heat gains are introduced has a significant role on the flow behaviour as we find that, in case (2), a warmer layer and a more pronounced overshoot are obtained than in case (1). The effect of assisting and opposing wind on the transient ventilation of an enclosure of constant cross-sectional area with height and constant heat gains is examined. A Froude number Fr is used to define the relative strengths of the buoyancy-induced and wind-induced velocities and five different transient states and their associated critical Fr are identified. © 2010 Elsevier Ltd.

The unidirectional emptying box

A theoretical description of the turbulent mixing within and the draining of a dense fluid layer from a box connected to a uniform density, quiescent environment through openings in the top and the base of the box is presented in this paper. This is an extension of the draining model developed by Linden et al. (Annu. Rev. Fluid Mech. vol. 31, 1990, pp. 201-238) and includes terms that describe localized mixing within the emptying box at the density interface. Mixing is induced by a turbulent flow of replacement fluid into the box and as a consequence we predict, and observe in complementary experiments, the development of a three-layer stratification. Based on the data collated from previous researchers, three distinct formulations for entrainment fluxes across density interfaces are used to account for this localized mixing. The model was then solved numerically for the three mixing formulations. Analytical solutions were developed for one formulation directly and for a second on assuming that localized mixing is relatively weak though still significant in redistributing buoyancy on the timescale of the draining process. Comparisons between our theoretical predictions and the experimental data, which we have collected on the developing layer depths and their densities show good agreement. The differences in predictions between the three mixing formulations suggest that the normalized flux turbulently entrained across a density interface tends to a constant value for large values of a Froude number FrT, based on conditions of the inflow through the top of the box, and scales as the cube of FrT for small values of FrT. The upper limit on the rate of entrainment into the mixed layer results in a minimum time (tD) to remove the original dense layer. Using our analytical solutions, we bound this time and show that 0.2tE ≈tD tE, i.e. the original dense layer may be depleted up to five times more rapidly than when there is no internal mixing and the box empties in a time tE. © 2010 Cambridge University Press.

Urban canyon influence on building natural ventilation

The natural ventilation of a building, flanked by others forming urban canyons and driven by the combined forces of wind and thermal buoyancy, has been studied experimentally at small scale. The aim was to improve our understanding of the effect of the urban canyon geometry on passive building ventilation. The steady ventilation of an isolated building was observed to change dramatically, both in terms of the thermal stratification and airflow rate, when placed within the confines of urban canyons. The ventilation flows and internal stratifications observed at small scale are presented for a range of canyon widths (building densities) and wind speeds. Two typical opening arrangements are considered. Flanking an otherwise isolated building with others of similar geometry as in a typical urban canyon was shown to reverse the effect of wind on the thermally-driven ventilation. As a consequence, neglecting the surrounding geometry when designing naturally-ventilated buildings may result in poor ventilation. Further implications are discussed.

Ventilation effectiveness measures based on heat removal: Part 2. Application to natural ventilation flows

The three effectiveness measures based on the ability of a flow to flush buoyancy from a ventilated space proposed by Coffey and Hunt [Ventilation effectiveness measures based on heat removal-part 1. Definitions. Building and Environment, in press, doi:10.1016/j.buildenv.2006.03.016.] are applied to assess and compare two fundamental natural ventilation flows. We focus on the limiting cases of passive displacement and passive mixing ventilation flows during transient conditions. These transient flows occur when, for example, heat is purged from a building at night. Whilst it is widely recognised that mixing flows are less efficient at purging heat than displacement flows, our results indicate that, when a particular zone of a room is considered, displacement ventilation can result in lower effectiveness than mixing ventilation. When a room is considered as a whole, displacement ventilation yields higher effectiveness than mixing ventilation and we quantify these differences in terms of the geometry of the space and opening area. The proposed theoretical predictions are compared with effectiveness deduced from measurements made during laboratory experiments and show good agreement. © 2006 Elsevier Ltd. All rights reserved.

Ventilation effectiveness measures based on heat removal: Part 1. Definitions

The effectiveness of ventilation flows is considered from the perspective of buoyancy (or heat) removal from a space. This perspective is distinct from the standard in which the effectiveness is based on the concentrations of a neutrally buoyant contaminant/passive tracer. Three new measures of effectiveness are proposed based on the ability of a flow to flush buoyancy from a ventilated space. These measures provide estimates of instantaneous and time-averaged effectiveness for the entire space, and local effectiveness at any height of interest. From a generalisation of the latter, a vertical profile of effectiveness is defined. These measures enable quantitative comparisons to be made between different flows and they are applicable when there is a difference in density (as is typical due to temperature differences) between the interior environment and the replacement air. Applications, therefore, include natural ventilation, hybrid ventilation and a range of forced ventilation flows. Finally, we demonstrate how the ventilation effectiveness of a room may be assessed from simple traces of temperature versus time. © 2006 Elsevier Ltd. All rights reserved.

Heat source modelling and natural ventilation efficiency

We compare natural ventilation flows established by a range of heat source distributions at floor level. Both evenly distributed and highly localised line and point source distributions are considered. We demonstrate that modelling the ventilation flow driven by a uniformly distributed heat source is equivalent to the flow driven by a large number of localised sources. A model is developed for the transient flow development in a room with a uniform heat distribution and is compared with existing models for localised buoyancy inputs. For large vent areas the flow driven by localised heat sources reaches a steady state more rapidly than the uniformly distributed case. For small vent areas there is little difference in the transient development times. Our transient model is then extended to consider the time taken to flush a neutrally buoyant pollutant from a naturally ventilated room. Again comparisons are drawn between uniform and localised (point and line) heat source geometries. It is demonstrated that for large vent areas a uniform heat distribution provides the fastest flushing. However, for smaller vent areas, localised heat sources produce the fastest flushing. These results are used to suggest a definition for the term 'natural ventilation efficiency', and a model is developed to estimate this efficiency as a function of the room and heat source geometries. © 2006 Elsevier Ltd. All rights reserved.

Thermal stratification produced by plumes and jets in enclosed spaces

The airflow and thermal stratification produced by a localised heat source located at floor level in a closed room is of considerable practical interest and is commonly referred to as a 'filling box'. In rooms with low aspect ratios H/R ≲ 1 (room height H to characteristic horizontal dimension R) the thermal plume spreads laterally on reaching the ceiling and a descending horizontal 'front' forms separating a stably stratified, warm upper region from cooler air below. The stratification is well predicted for H/R ≲ 1 by the original filling box model of Baines and Turner (J. Fluid. Mech. 37 (1968) 51). This model represents a somewhat idealised situation of a plume rising from a point source of buoyancy alone-in particular the momentum flux at the source is zero. In practical situations, real sources of heating and cooling in a ventilation system often include initial fluxes of both buoyancy and momentum, e.g. where a heating system vents warm air into a space. This paper describes laboratory experiments to determine the dependence of the 'front' formation and stratification on the source momentum and buoyancy fluxes of a single source, and on the location and relative strengths of two sources from which momentum and buoyancy fluxes were supplied separately. For a single source with a non-zero input of momentum, the rate of descent of the front is more rapid than for the case of zero source momentum flux and increases with increasing momentum input. Increasing the source momentum flux effectively increases the height of the enclosure, and leads to enhanced overturning motions and finally to complete mixing for highly momentum-driven flows. Stratified flows may be maintained by reducing the aspect ratio of the enclosure. At these low aspect ratios different long-time behaviour is observed depending on the nature of the heat input. A constant heat flux always produces a stratified interior at large times. On the other hand, a constant temperature supply ultimately produces a well-mixed space at the supply temperature. For separate sources of momentum and buoyancy, the developing stratification is shown to be strongly dependent on the separation of the sources and their relative strengths. Even at small separation distances the stratification initially exhibits horizontal inhomogeneity with localised regions of warm fluid (from the buoyancy source) and cool fluid. This inhomogeneity is less pronounced as the strength of one source is increased relative to the other. Regardless of the strengths of the sources, a constant buoyancy flux source dominates after sufficiently large times, although the strength of the momentum source determines whether the enclosure is initially well mixed (strong momentum source) or stably stratified (weak momentum source). © 2001 Elsevier Science Ltd. All rights reserved.

Shroud heat transfer measurements from a rotating cavity with an axial throughflow of air

The paper discusses measurements of heat transfer obtained from the inside surface of the peripheral shroud. The experiments were carried out on a rotating cavity, comprising two 0.985-m-dia disks, separated by an axial gap of 0.065 m and bounded at the circumference by a carbon fiber shroud. Tests were conducted with a heated shroud and either unheated or heated disks. When heated, the disks had the same temperature level and surface temperature distribution. Two different temperature distributions were tested; the surface temperature either increased, or decreased with radius. The effects of disk, shroud, and air temperature levels were also studied. Tests were carried out for the range of axial throughflow rates and speeds: 0.0025 ≤ m ≤ 0.2 kg/s and 12.5 ≤ Ω ≤ 125 rad/s, respectively. Measurements were also made of the temperature of the air inside the cavity. The shroud Nusselt numbers are found to depend on a Grashof number, which is defined using the centripetal acceleration. Providing the correct reference temperature is used, the measured Nusselt numbers also show similarity to those predicted by an established correlation for a horizontal plate in air. The heat transfer from the shroud is only weakly affected by the disk surface temperature distribution and temperature level. The heat transfer from the shroud appears to be affected by the Rossby number. A significant enhancement to the rotationally induced free convection occurs in the regions 2 ≤ Ro ≤ 4 and Ro ≥ 20. The first of these corresponds to a region where vortex breakdown has been observed. In the second region, the Rossby number may be sufficiently large for the central throughflow to affect the shroud heat transfer directly. Heating the shroud does not appear to affect the heat transfer from the disks significantly.

Finite element analysis of compressor disc heat transfer using the transient conduction method with sparse boundary collocation points

Surface temperature measurements from two discs of a gas turbine compressor rig are used as boundary conditions for the transient conduction solution (inverse heat transfer analysis). The disc geometry is complex, and so the finite element method is used. There are often large radial temperature gradients on the discs, and the equations are therefore solved taking into account the dependence of thermal conductivity on temperature. The solution technique also makes use of a multigrid algorithm to reduce the solution time. This is particularly important since a large amount of data must be analyzed to obtain correlations of the heat transfer. The finite element grid is also used for a network analysis to calculate the radiant heat transfer in the cavity formed between the two compressor discs. The work discussed here proved particularly challenging as the disc temperatures were only measured at four different radial locations. Four methods of surface temperature interpolation are examined, together with their effect on the local heat fluxes. It is found that the choice of interpolation method depends on the available number of data points. Bessel interpolation gives the best results for four data points, whereas cubic splines are preferred when there are considerably more data points. The results from the analysis of the compressor rig data show that the heat transfer near the disc inner radius appears to be influenced by the central throughflow. However, for larger radii, the heat transfer from the discs and peripheral shroud is found to be consistent with that of a buoyancy-induced flow.

Lift and the leading edge vortex

Leading edge vortices are considered to be important in generating the high lift coefficients observed in insect flight and may therefore be relevant to micro-air vehicles. A potential flow model of an impulsively started flat plate, featuring a leading edge vortex (LEV) and a trailing edge vortex (TEV) is fitted to experimental data in order to provide insight into the mechanisms that influence the convection of the LEV and to study how the LEV contributes to lift. The potential flow model fits the experimental data best with no bound circulation, which is in accordance with Kelvin's circulation theorem. The lift-to-drag ratio is well approximated by the function 'cot α' for α > 15°, which supports the tentative conclusion that shortly after an impulsive start, at post-stall angles of attack, lift is caused non-circulatory forces and by the action of the LEV as opposed to bound circulation. Copyright © 2012 by C. W. Pitt Ford.

Excess pore pressures around underground structures following earthquake induced liquefaction

Underground structures located in liquefiable soil deposits are susceptible to floatation following an earthquake event due to their lower unit weight relative to the surrounding saturated soil. This inherent buoyancy may cause lightweight structures to float when the soil liquefies. Centrifuge tests have been carried out to study the excess pore pressure generation and dissipation in liquefiable soils. In these tests, near full liquefaction conditions were attained within a few cycles of the earthquake loading. In the case of high hydraulic conductivity sands, significant dissipation could take place even during the earthquake loading which inhibits full liquefaction from occurring. In the case of excess pore pressure generation and dissipation around a floating structure, the cyclic response of the structure may lead to the reduction in excess pore pressure near the face of the structure as compared to the far field. This reduction in excess pore pressure is due to shear-induced dilation and suction pressures arising from extensile stresses at the soil-structure interface. Given the lower excess pore pressure around the structure; the soil around the structure retains a portion of this shear strength which in turn can discourage significant uplift of the underground structure. Copyright © 2012, IGI Global.

The rhythm of fountains: The length and time scales of rise height fluctuations at low and high Froude numbers

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 ≤ Fr 0 ≤ 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr 0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Strtop, based on experimental measures of the fountain top, defined such that Strtop = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- Fr 0 fountains we find Strtop ≈ 0. 9. © 2013 Cambridge University Press.

The influence of room geometry on the overturning of smoke owing to a floor fire

The present paper explores the influence of room geometry on the overturning of smoke owing to a centrally located floor fire, and examines the implications on smoke filling times. The focus is on presenting practical design guidelines based on the theoretical predictions of the model of Kaye and Hunt. An engineering platform is developed for the prediction of smoke filling times, and a rational basis is provided by way of which smoke behaviour can be specified for simple room designs. The time taken for smoke to fill a room to a given height is critically affected by the room aspect ratio and the characteristic size of the buoyancy source. At large times, taller (small aspect ratio) rooms are shown to fill with smoke at a faster rate than wide (large aspect ratio) rooms owing to large-scale overturning and engulfing of ambient air during the initial transients. Larger area sources of buoyancy also decrease significantly the smoke filling times, with important implications for fire and smoke safety design. Simplified design curves incorporating the main findings have been developed for use as a tool by practising fire-safety engineers.

Scaling laws for planetary dynamos

We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect ratio of the columnar convection cells are all predicted to be power-law functions of two observable quantities: the magnetic dipole moment and the planetary rotation rate. The resulting scaling laws constitute a somewhat modified version of the scalings proposed by Christensen and Aubert. The main difference is that, in view of the small value of the Rossby number in planetary cores, we insist that the non-linear inertial term, uu, is negligible. This changes the exponents in the power-laws which relate the various properties of the fluid dynamo to the planetary dipole moment and rotation rate. Our scaling laws are consistent with the available numerical evidence. © The Authors 2013 Published by Oxford University Press on behalf of The Royal Astronomical Society.