Frank E. Marble

Investigation of a contoured wall injector for hypervelocity mixing augmentation

An experimental and computational investigation of a contoured wall fuel injector is presented. The injector was aimed at enabling shock-enhanced mixing for the supersonic combustion ramjet engines currently envisioned for applications on hypersonic vehicles. Three-dimensional flow field surveys, and temporally resolved planar Rayleigh scattering measurements are presented for Mach 1.7 helium injection into Mach 6 air. These experimental data are compared directly with a three-dimensional Navier-Stokes simulation of the flow about the injector array. Two dominant axial vorticity sources are identified and characterized. The axial vorticity produced strong convective mixing of the injectant with the freestream. Shock-impingement was particularly effective as it assured seeding of baroclinic vorticity directly on the helium/air interface. The vorticity coalesced into a counter-rotating vortex pair of a sense which produced migration of the helium away from the wall. The influences of spatial averaging on the representation of the flow field as well as the importance of the fluctuating component of the flow in producing molecularly-mixed fluid are addressed.

The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise

The theory relating to the interaction of entropy fluctuations (‘hot spots’), as well as vorticity and pressure, with blade rows is described. A basic feature of the model is that the blade rows have blades of sufficiently short chord that this is negligible in comparison with the wavelength of the disturbances. For the interaction of entropy with a blade row to be important, it is essential that the steady pressure change across the blade row should be large, although all unsteady perturbations are assumed small. A number of idealized examples have been calculated, beginning with isolated blade rows, progressing to single and then to several turbine stages. Finally, the model has been used to predict the low-frequency rearward-radiated acoustic power from a commercial turbojet engine. Following several assumptions, together with considerable empirical data, the correct trend and level are predicted, suggesting the mechanism to be important at low jet velocities.

Growth of a Diffusion Flame in the Field of a Vortex

A simple diffusion flame with fast chemical kinetics is initiated along the horizontal axis between a fuel occupying the upper half-plane and an oxidizer below. Simultaneously a vortex of circulation Γ is established at the origin. As time progresses the flame is extended and “wound up” by the vortex flow field and the viscous core of the vortex spreads, converting the motion in the core to a solid-body rotation.

Ignition and combustion in a laminar mixing zone

The analytic investigation of laminar combustion processes which are essentially two- or three-dimensional present some mathematical difficulties. There are, however, several examples of two-dimensional flame propagation which involve transverse velocities that are small in comparison with that in the principal direction of flow. Such examples occur in thc problem of flame quenching by a cool surface, flame stabilization on a heated flat plate, combustion in laminar mixing zones, etc. In these cases the problem may be simplified by employing what is known in fluid mechanics as the boundary-layer approximation, since it was applied first by Prandtl in his treatment of the viscous flow over a flat plate. Physically it consists in recognizing that if the transverse velocity is small, the variations of flow properties along the direction of main flow are small in comparison with those in a direction normal to the main flow. The analytic description of the problem simplifies accordingly. The present analysis considers the ignition and combustion in the laminar mixing zone between two parallel moving gas streams. One stream consists of a cool combustible mixture, the second is hot combustion products. The two streams come into contact at a given point and a laminar mixing process follows in which the velocity distribution is modified by viscosity, and the temperature and composition distributions by conduction, diffusion, and chemical reaction. The decomposition of the combustible stream is assumed to follow first-order reaction kinetics with temperature dependence according to the Arrhenius law. For a given initial velocity, composition, and temperature distribution, the questions to be answered are: (1) Does the combustible material ignite; and (2) how far downstream of the initial contact point does the flame appear and what is the detailed process of development. Since the hot stream is of infinite extent, it is found that ignition always takes place at some point of the stream. However, when the temperature of the hot stream drops below a certain value, the distance required for ignition increases so enormously that it essentially does not occur in a physical apparatus of finite dimension. The complete development of the laminar flame front is computed using an approximation similar to the integral technique introduced by von Karman into boundary layer theory.

Study of a Diffusion Flame in a Stretched Vortex

The time dependent interaction of a laminar diffusion flame with a single plane vortex and with a stretched line vortex is examined with the aim of determining the flame configuration and the augmentation to the reactant consumption rate resulting from the interaction. Elements of the resulting curved flame sheets behave essentially as isolated flames until the neighboring flame sheets become so closely spaced that they interact and consume the intervening reactant. This process creates a core of combustion products with external isolated flame surfaces. The augmentation of the reactant consumption rate results both from the local straining of the flame in its own plane and from the overall increase in flame surface area. Three examples are treated in detail. The first is the plane problem in which an initially straight flame is distorted by a vortex. In the second, the situation is similar except that the problem is expanded to three dimensions and the vortex line is being stretched along its own axis. Finally, the effects of the density change resulting from the heat release are examined.

Similarity analysis of compressor tip clearance flow structure

A new approach is presented for analyzing compressor tip clearance flow. The basic idea is that the clearance velocity field can be (approximately) decomposed into independent throughflow and crossflow, since chordwise pressure gradients are much smaller than normal pressure gradients in the clearance region. As in the slender body approximation in external aerodynamics, this description implies that the three-dimensional steady clearance flow can be viewed as a two-dimensional, unsteady flow. Using this approach, a similarity scaling for the crossflow in the clearance region is developed and a generalized description of the clearance vortex is derived. Calculations based on the similarity scaling agree well with a wide range of experimental data in regard to flow features such as crossflow velocity field, static pressure field, and tip clearance vortex trajectory.

A mechanism for high-frequency oscillation in ramjet combustors and afterburners

An experimental investigation was made of the behavior of a small two-dimensional combustion chamber, burning a uniform mixture of air and fuel vapor under conditions of high-frequency oscillation or screech. Measurements were made of the limits of stable screech, the amplitude and frequency of pressure oscillations over a wide range of mixture ratio, inlet air temperature, and combustor flow rate. Spark schlieren photographs and high-speed motion pictures taken of the combustion process showed, in agreement with other investigations, that the high-frequency oscillation is accompanied by vortices shed periodically from the flameholder lip with the same frequency as the oscillation. The following mechanism of exciting the oscillations is suggested. A mode of transverse oscillation is excited as the result of periodic transport of combustible material, associated with the vortices, into the hot wake of the flameholder. The vortices, in turn, are generated at the flameholder lips by the fluctuating transverse velocity. When the ignition time delay lies in the proper range, the phase relationship between oscillations in transverse velocity and combustion intensity is such that the oscillation is amplified.

Endwall Blockage in Axial Compressors

This paper presents a new methodology for quantifying compressor endwall blockage and an approach, using this quantification, for defining the links between design parameters, flow conditions, and the growth of blockage due to tip clearance flow. Numerical simulations, measurements in a low-speed compressor, and measurements in a wind tunnel designed to simulate a compressor clearance flow are used to assess the approach. The analysis thus developed allows predictions of endwall blockage associated with variations in tip clearance, blade stagger angle, inlet boundary layer thickness, loading level, loading profile, solidity, and clearance jet total pressure. The estimates provided by this simplified method capture the trends in blockage with changes in design parameters to within 10 percent. More importantly, however, the method provides physical insight into, and thus guidance for control of, the flow features and phenomena responsible for compressor endwall blockage generation.

Enhanced mixing with streamwise vorticity

Abstract A quantitative description is presented of mixing augmentation mechanisms associated with embedded streamwise vortices. The specific context of interest is the flowfield downstream of convoluted (lobed) mixers, but the concepts developed apply to a range of devices that generate such vortices for enhanced mixing. Arguments are presented to illustrate the dependence of mixing augmentation on the strain field associated with the vortices; this strain field increases both the area available for mixing between two streams and the local gradients in fluid properties which provide the driving potential for mixing. Computations and experiments have been carried out to assess the influence of the streamwise vortices on both momentum interchange and mixing on a molecular level. Based on these investigations, scaling laws have been developed for the overall parametric trends of flow field structure and mixing rate as functions of lobe geometry, Reynolds number, stream-to-stream velocity ratio and Mach number.

The Effect of Strain Rate on a Premixed Laminar Flame

The structure of a strained premixed laminar flame is examined. The flame is formed in the vicinity of a stagnation point established by the counterflow of fresh mixture and hot combustion products. This ideal configuration analyzed by Libby and Williams [18] with activation energy asymptotics is here examined numerically. This allows an exact description of flame and flow structure and a calculation of the mass rate of reaction per unit flame area for the whole range of strain rates. Previous results obtained for intermediate and high strain rates are confirmed. However, for low strain rates the mass rate of reaction per unit flame area differs from that determined with large activation energy asymptotics. The present calculations also provide the exact value of the strain rate (or Damkiihler number) for which the partial extinction regime appears. If the strain rate is increased beyond that value the flame front develops on the hot side of the stagnation point. The reactive front first moves away from the stagnation point and then moves back toward that point for the very large values of the strain rate.