Influence of film cooling hole angles and geometries on aerodynamic loss and net heat flux reduction

Turbine design engineers have to ensure that film cooling can provide sufficient protection to turbine blades from the hot mainstream gas, while keeping the losses low. Film cooling hole design parameters include inclination angle (α), compound angle (β ), hole inlet geometry and hole exit geometry. The influence of these parameters on aerodynamic loss and net heat flux reduction is investigated, with loss being the primary focus. Low-speed flat plate experiments have been conducted at momentum flux ratios of IR = 0.16, 0.64 and 1.44. The film cooling aerodynamic mixing loss, generated by the mixing of mainstream and coolant, can be quantified using a three-dimensional analytical model that has been previously reported by the authors. The model suggests that for the same flow conditions, the aerodynamic mixing loss is the same for holes with different α and β but with the same angle between the mainstream and coolant flow directions (angle κ). This relationship is assessed through experiments by testing two sets of cylindrical holes with different α and β : one set with κ = 35°, another set with κ = 60°. The data confirm the stated relationship between α, β, κ and the aerodynamic mixing loss. The results show that the designer should minimise κ to obtain the lowest loss, but maximise β to achieve the best heat transfer performance. A suggestion on improving the loss model is also given. Five different hole geometries (α =35.0°, β =0°) were also tested: cylindrical hole, trenched hole, fan-shaped hole, D-Fan and SD-Fan. The D-Fan and the SD-Fan have similar hole exits to the fan-shaped hole but their hole inlets are laterally expanded. The external mixing loss and the loss generated inside the hole are compared. It was found that the D-Fan and the SD-Fan have the lowest loss. This is attributed to their laterally expanded hole inlets, which lead to significant reduction in the loss generated inside the holes. As a result, the loss of these geometries is ≈ 50 % of the loss of the fan-shaped hole at IR = 0.64 and 1.44. Copyright © 2011 by ASME.

Influence of film cooling hole angles and geometries on aerodynamic loss and net heat flux reduction

Turbine design engineers have to ensure that film cooling can provide sufficient protection to turbine blades from the hot mainstream gas, while keeping the losses low. Film cooling hole design parameters include inclination angle (a), compound angle (b), hole inlet geometry, and hole exit geometry. The influence of these parameters on aerodynamic loss and net heat flux reduction is investigated, with loss being the primary focus. Low-speed flat plate experiments have been conducted at momentum flux ratios of IR=0.16, 0.64, and 1.44. The film cooling aerodynamic mixing loss, generated by the mixing of mainstream and coolant, can be quantified using a three-dimensional analytical model that has been previously reported by the authors. The model suggests that for the same flow conditions, the aerodynamic mixing loss is the same for holes with different a and b but with the same angle between the mainstream and coolant flow directions (angle k). This relationship is assessed through experiments by testing two sets of cylindrical holes with different a and b: one set with k=35 deg, and another set with k=60 deg. The data confirm the stated relationship between α, β, k and the aerodynamic mixing loss. The results show that the designer should minimize k to obtain the lowest loss, but maximize b to achieve the best heat transfer performance. A suggestion on improving the loss model is also given. Five different hole geometries (α=35.0 deg, β=0 deg) were also tested: cylindrical hole, trenched hole, fan-shaped hole, D-Fan, and SD-Fan. The D-Fan and the SD-Fan have similar hole exits to the fan-shaped hole but their hole inlets are laterally expanded. The external mixing loss and the loss generated inside the hole are compared. It was found that the D-Fan and the SD-Fan have the lowest loss. This is attributed to their laterally expanded hole inlets, which lead to significant reduction in the loss generated inside the holes. As a result, the loss of these geometries is≈50% of the loss of the fan-shaped hole at IR=0.64 and 1.44. © 2013 by ASME.

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.

Structure of cryogenic flames at elevated pressures

This paper presents new experimental results on cryogenic jet flames formed by a coaxial injector at a pressure of 70 bar, which approaches the pressures found in rocket engines. This element, fed with liquid oxygen and gaseous hydrogen, is placed in a square combustion chamber equipped with quartz windows. The flame is examined via spectroscopy, OH* emission, and backlighting, the aim being to provide basic information on the flame structure. It is found that some of the OH* emission is absorbed by the OH radicals present in the flame. A detailed examination of this effect is presented, in which it is shown that, for this turbulent flame, the Abel transform gives the position of the intense reaction region, whether or not absorption is signficant. The flame is attached to the oxygen injector, as at low pressure. At high pressure, flame expansion is reduced compared with low pressure and is also less dependent on the momentum flux ratio between the hydrogen and the oxygen streams. An analysis of the relevant Damköhler numbers suggests that this is because the rate of combustion is mainly controlled by large-scale turbulent mixing at high pressure, and it is dominated by jet break-up, atomization, and vaporization at low pressures. Jet break-up is particularly dependent on the momentum flux ratio. Finally, the mean volumetric heat release rates and flame surface density in the experimental facility are estimated.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

A flame surface density approach to large-eddy simulation of premixed turbulent combustion

The flame surface density approach to the modeling of premixed turbulent combustion is well established in the context of Reynolds-averaged simulations. For the future, it is necessary to consider large-eddy simulation (LES), which is likely to offer major advantages in terms of physical accuracy, particularly for unsteady combustion problems. LES relies on spatial filtering for the removal of unresolved phenomena whose characteristic length scales are smaller than the computational grid scale. Thus, there is a need for soundly based physical modeling at the subgrid scales. The aim of this paper is to explore the usefulness of the flame surface density concept as a basis for LES modeling of premixed turbulent combustion. A transport equation for the filtered flame surface density is presented, and models are proposed for unclosed terms. Comparison with Reynolds-averaged modeling is shown to reveal some interesting similarities and differences. These were exploited together with known physics and statistical results from experiment and from direct numerical stimulation in order to gain insight and refine the modeling. The model has been implemented in a combustion LES code together with standard models for scalar and momentum transport. Computational results were obtained for a simple three-dimensional flame propagation test problem, and the relative importance of contributing terms in the modeled equation for flame surface density was assessed. Straining and curvature are shown to have a major influence at both the resolved and subgrid levels.

Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Large eddy simulations for fan-OGV broadband noise prediction

The work in this paper forms part of a project on the use of large eddy simulation (LES) for broadband rotor-stator interaction noise prediction. Here we focus on LES of the flow field near a fan blade trailing edge. The first part of the paper aims to evaluate LES suitability for predicting the near-field velocity field for a blunt NACA-0012 airfoil at moderate Reynolds numbers (2× 10 5 and 4× 10 5). Preliminary computations of turbulent mean and root-mean-square velocities, as well as energy spectra at the trailing edge, are compared with those from a recent experiment.1 The second part of the paper describes preliminary progress on an LES calculation of the fan wakes on a fan rig. 2 The CFD code uses a mixed element unstructured mesh with a median dual control volume. A wall-adapting local eddy-viscosity sub-grid scale model is employed. A very small amount of numerical dissipation is added in the numerical scheme to keep the compressible solver stable. Further results for the fan turbulentmean and RMS velocity, and especially the aeroacoustics field will be presented at a later stage. Copyright © 2008 by Qinling LI, Nigel Peake & Mark Savill.

Addition of ferromagnetic CoFe2O4 to YBCO thin films for enhanced flux pinning

An attempt has been made to prepare a YBa2Cu3O 7-δ (YBCO) thin film doped with ferromagnetic CoFe 2O4. Transmission electron microscopy of the resultant samples shows, however, that Y(Fe, Co)O3 forms as a nanoparticulate dispersion throughout the film in preference to CoFe2O4, leaving the YBCO yttrium deficient. As a consequence, the superconducting properties of the sample are poor, with a self-field critical current density of just 0.25 MA cm-2. Magnetic measurements indicate however that the Y(Fe, Co)O3 content, together with any other residual phases, is also ferromagnetic, and some interesting features are present in the in-field critical current behaviour, including a reduced dependence on applied field and a strong c-axis peak in the angular dependence. The work points the way towards future attempts utilising YFeO3 as an effective ferromagnetic pinning additive for YBCO. © 2009 Elsevier B.V. All rights reserved.

Flux closure vortexlike domain structures in ferroelectric thin films

Enhanced piezoresponse force microscopy was used to study flux closure vortexlike structures of 90° ferroelastic domains at the nanoscale in thin ferroelectric lead zirconium titanate (PZT) films. Using an external electric field, a vortexlike structure was induced far away from a grain boundary, indicating that physical edges are not necessary for nucleation contrary to previous suggestions. We demonstrate two different configurations of vortexlike structures, one of which has not been observed before. The stability of these structures is found to be size dependent, supporting previous predictions. © 2010 The American Physical Society.

A general design method for electric machines using magnetic circuit model considering the flux saturation problem

This paper proposes an analytical approach that is generalized for the design of various types of electric machines based on a physical magnetic circuit model. Conventional approaches have been used to predict the behavior of electric machines but have limitations in accurate flux saturation analysis and hence machine dimensioning at the initial design stage. In particular, magnetic saturation is generally ignored or compensated by correction factors in simplified models since it is difficult to determine the flux in each stator tooth for machines with any slot-pole combinations. In this paper, the flux produced by stator winding currents can be calculated accurately and rapidly for each stator tooth using the developed model, taking saturation into account. This aids machine dimensioning without the need for a computationally expensive finite element analysis (FEA). A 48-slot machine operated in induction and doubly-fed modes is used to demonstrate the proposed model. FEA is employed for verification.