It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical

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The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

The role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations. Coherent motion is defined as a three-dimensional region of flow where at least one fundamental variable exhibits significant correlation with itself or with another variable over a space or time range significantly larger than the smallest local scales of the flow. Sections are then devoted to flow-visualization experiments, statistical analyses, numerical simulation techniques, the history of coherent-structure studies, vortices and vortical structures, conceptual models, and predictive models. Diagrams and graphs are provided.

Coherent Motions in the Turbulent Boundary Layer

The structure of energy-containing turbulence in the outer region of a zero-pressure-
 gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

Vortex organization in the outer region of the turbulent boundary layer

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Hairpin vortex organization in wall turbulencea)

Direct numerical simulations of unsteady channel flow were performed at low to moderate Reynolds numbers on computational boxes chosen small enough so that the flow consists of a doubly periodic (in x and z) array of identical structures. The goal is to isolate the basic flow unit, to study its morphology and dynamics, and to evaluate its contribution to turbulence in fully developed channels. For boxes wider than approximately 100 wall units in the spanwise direction, the flow is turbulent and the low-order turbulence statistics are in good agreement with experiments in the near-wall region. For a narrow range of widths below that threshold, the flow near only one wall remains turbulent, but its statistics are still in fairly good agreement with experimental data when scaled with the local wall stress. For narrower boxes only laminar solutions are found. In all cases, the elementary box contains a single low-velocity streak, consisting of a longitudinal strip on which a thin layer of spanwise vorticity is lifted away from the wall. A fundamental period of intermittency for the regeneration of turbulence is identified, and that process is observed to consist of the wrapping of the wall-layer vorticity around a single inclined longitudinal vortex.

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The minimal flow unit in near-wall turbulence

The durability of gas turbine engines is strongly dependent on the component temperatures. For the combustor and turbine airfoils and endwalls, film cooling is used extensively to reduce component temperatures. Film cooling is a cooling method used in virtually all of today's aircraft turbine engines and in many power-generation turbine engines and yet has very difficult phenomena to predict. The interaction of jets-in-crossflow, which is representative of film cooling, results in a shear layer that leads to mixing and a decay in the cooling performance along a surface. This interaction is highly dependent on the jet-to-crossflow mass and momentum flux ratios. Film-cooling performance is difficult to predict because of the inherent complex flowfields along the airfoil component surfaces in turbine engines. Film cooling is applied to nearly all of the external surfaces associated with the airfoils that are exposed to the hot combustion gasses such as the leading edges, main bodies, blade tips, and endwalls. In a review of the literature, it was found that there are strong effects of freestream turbulence, surface curvature, and hole shape on the performance of film cooling. Film cooling is reviewed through a discussion of the analyses methodologies, a physical description, and the various influences on film-cooling performance.

Gas Turbine Film Cooling

Film-cooling effectiveness was studied using a row of inclined holes that injected cryogenically cooled air across a flat, adiabatic test plate. The density ratio of the coolant to mainstream varied from 1.2 to 2.0. Surface temperatures were measured using a unique surface thermocouple arrangement free of conduction errors. Temperatures were obtained along the jet centerline and across a number of lateral locations. By independently varying density ratio and blowing rate, scaling of adiabatic effectiveness with mass flux ratio, velocity ratio, and momentum ratio was determined. Depending on the momentum flux ratio, the jet either remains attached to the surface, detaches and then reattaches, or is fully detached. For attached jets, the centerline effectiveness scaled with the mass flux ratio. However, for detached-reattached jets, a consistent scaling was not found although the general distribution of the centerline effectiveness scaled with momentum flux ratio. Laterally averaged effectiveness was found to be dependent on density ratio and momentum flux ratio. Decreases in density ratio and increases in momentum flux ratio were found to reduce the spreading of the film cooling jet significantly and thereby reduce laterally averaged effectiveness.

Film-cooling effectiveness downstream of a single row of holes with variable density ratio

An evaluation of the effectiveness of the VITA, Quadrant, TPAV, U -level, Positive slope, and VITA with slope burst-detection algorithms has been done by making direct comparisons with flow visualization. Measurements were made in a water channel using an X-type hot-film probe located in the near-wall region. Individual ejections from bursts which contacted the probe were identified using dye flow visualization. The effectiveness of each of the detection algorithms was found to be highly dependent on the operational parameters, i.e. threshold levels and averaging or window times. These parameters were adjusted so that the number of events detected by each of the algorithms corresponded to the number of ejections identified by flow visualization, while the probability of a false detection was minimized. Comparing the detection algorithm using these optimum parameter settings, the Quadrant technique was found to have the greatest reliability with a high probability of detecting the ejections and a low probability of false detections. Furthermore, it was found that the ejections detected by the Quadrant technique could be grouped into bursts by analysing the probability distribution of the time between ejections.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086002094

Burst detection with single-point velocity measurements

Film cooling effectiveness was studied experimentally in a flat plate test facility with zero pressure gradient using a single row of inclined holes, which injected high-density, cryogenically cooled air. Round holes and holes with a diffusing expanded exit were directed laterally away from the free-stream direction with a compound angle of 60 deg. Comparisons were made with a baseline case of round holes aligned with the free stream. The effects of doubling the hole spacing to six hole diameters for each geometry were also examined. Experiments were performed at a density ratio of 1.6 with a range of blowing ratios from 0.5 to 2.5 and momentum flux ratios from 0.16 to 3.9. Lateral distributions of adiabatic effectiveness results were determined at streamwise distances from 3 D to 15 D downstream of the injection holes. All hole geometries had similar maximum spatially averaged effectiveness at a low momentum flux ratio of I = 0.25, but the round and expanded exit holes with compound angle had significantly greater effectiveness at larger momentum flux ratios. The compound angle holes with expanded exits had a much improved lateral distribution of coolant near the hole for all momentum flux ratios.

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Film Cooling With Compound Angle Holes: Adiabatic Effectiveness

Heat transfer coefficients have been measured for film cooling injection from a single row of holes laterally directed with a compound angle of 60 deg. Two hole configurations were tested, round holes and holes with a diffusing expansion at the exit. Streamwise-directed round holes were also tested as a basis for comparison. All the holes were inclined at 35 deg with respect to the surface. The density ratio was 1.0, momentum flux ratios ranged from I = 0.16 to 3.9, and mass flux ratios ranged from M = 0.4 to 2.0. Results are presented in terms of h{sub f}/h{sub 0}, the ratio of film cooling heat transfer coefficient to the heat transfer coefficient for the undisturbed turbulent boundary layer at the same location. Results indicate that for the streamwise directed holes, the heat transfer rates are close to the levels that exist without injection. Similarly, at low momentum flux ratio, holes with a large compound angle had little effect on heat transfer rates. However, at high momentum flux ratios, holes with a large compound angle had significantly increased heat transfer levels. The results were combined with adiabatic effectiveness results to evaluate the overall performance of the three geometries. It ismore » shown that for evaluation of film cooling performance with compound angle injection, especially at high momentum flux ratios, it is critical to know the heat transfer coefficient, as the adiabatic effectiveness alone does not determine the performance. Compound angle injection at high momentum flux ratios gives higher effectiveness values than streamwise-directed holes, but the higher heat transfer levels result in poorer overall performance.« less

David G. Bogard

Papers

Gas Turbine Film Cooling

Film-cooling effectiveness downstream of a single row of holes with variable density ratio

Burst detection with single-point velocity measurements

Film Cooling With Compound Angle Holes: Adiabatic Effectiveness

Film Cooling With Compound Angle Holes: Heat Transfer