Propulsion system design with smart vortex generators

Transmission and reflection of acoustic and entropy waves through a stator–rotor stage

Thermoacoustic instabilities are a cause for concern in combustion applications as diverse as small household burners, gas turbines or rocket engines. In this work, a feedback mechanism is analyzed, which couples combustion chamber acoustics with convectively transported fluctuations of entropy (entropy waves) generated within a premixed flame. Essential elements of this thermo-acoustic feedback loop are fluctuations in fuel concentration, induced by acoustic disturbances at the location of fuel injection, convective transport of fuel inhomogeneities through the premixing section of the burner, modulations in heat release rate and hot gas entropy resulting from the consumption of fuel/air mixture with varying fuel concentration by the flame, and the generation of sound through entropy non-uniformities at the turbine inlet. From a qualitative analysis based on relative phases, it is concluded that depending on the various convective and acoustic time lags involved, entropy waves may couple constructively as well as destructively with combustor acoustics. However, such qualitative analysis does not indicate whether the coupling between entropy and acoustic waves is strong enough to significantly influence thermo-acoustic stability. Therefore, a linear model has been constructed to estimate the effect of entropy waves on the thermo-acoustic response and stability of a combustor with a choked exit nozzle, as it might be found in a gas turbine. Note that phenomena like dispersion of convective waves, distributed heat release, vortical velocities, etc., have not been taken into account, as they would burden the presentation with unnecessary complexity. Results obtained indicate that the interaction between combustor acoustics and entropy waves can be significant, especially for the lowest non-axisymmetric modes, and even at frequencies higher than those usually associated with convective waves. As expected, it was observed that the coupling between pressure and entropy waves at the exit nozzle can enhance as well as reduce the thermo-acoustic stability of a combustor, or the responsiveness to an external or internal fluid-mechanic excitation mechanism. It is concluded that comprehensive thermo-acoustic analysis of a premixed combustor with a choked exit must in general include generation and propagation of entropy waves and coupling with combustor acoustics.

Flow fields around asymmetrical micro vortex generators in supersonic flow

Compressible flow past thin wings and slender bodies are studied. First, subsonic flow past thin wings are analyzed by means of potential flow theory. The kernel function method is introduced for arbitrary planforms undergoing simple harmonic oscillations. The spanwise polynomial approximation and the chordwise trigonometric function approximations which automatically satisfy the Kutta condition and inherit the leading edge singularity are used. The Doublet-Lattice method as a more general numerical approach is given for the analysis of the flow past additional surfaces like tail or store surfaces, which are not necessarily in plane with the wing surface or surfaces having spanwise deflections. Airfoil response to the arbitrary unsteady motion is also given for subsonic flows. A brief review of shock waves and Mach waves in a supersonic flow is given. Afterwards, unsteady supersonic potential flow is studied for a simple harmonically oscillating point source. First, unsteady flow past an airfoil is considered. Then, supersonic flow about thin wings are analyzed using the Mach box technique. Introduction to supersonic kernel function method is briefly provided. Arbitrary unsteady motion of an airfoil in a supersonic flow is presented. Slender body theory is introduced to analyze the cross flow past bodies of considerable fineness where the cross flow is shown to be approximately incompressible under certain conditions. In connection with the slender body approximation, the Munk’s airship theory is utilized to predict the stability derivatives of missile like bodies.

Supersonic boundary-layer receptivity to different types of free-stream disturbance is studied for a Mach 4.5 boundary-layer flow over a flat plate by using the approaches of both direct numerical simulation and linear stability theory. This paper is Part 3 of a three-part study of the receptivity of supersonic boundary layers to free-stream disturbances. The present paper investigates receptivity to four types of different free-stream disturbances, i.e. slow and fast acoustic waves, entropy waves, and vorticity waves. A high-order shock-fitting scheme is used in the numerical simulation in order to accurately account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. Numerical results on the generation of fast acoustic waves by free-stream entropy waves or vorticity waves are compared with those of a linear theory. Good agreement is obtained in both wave angles and amplitudes immediately behind the bow shock. It is found that the second-mode receptivity to free-stream slow acoustic waves is several times stronger than that to free-stream fast acoustic waves. This is because free-stream slow acoustic waves can directly induce and interact with the first and second Mack modes, while free-stream fast acoustic waves cannot. Instead, the free-stream fast acoustic waves can only induce and interact with stable mode I waves, which in turn induce unstable Mack modes. In the cases of receptivity to free-stream entropy waves and vorticity waves, it is found that the oblique shock wave created by the displacement of the boundary layer plays an important role because boundary-layer disturbances are mainly induced by fast acoustic waves generated behind the shock by free-stream forcing waves. As a result, mechanisms of the receptivity to free-stream entropy and vorticity waves are very similar to those of the receptivity to free-stream fast acoustic waves.

The interaction of shock waves with a contact surface between gases of different densities has been studied experimentally and theoretically. The basic mechanism for the instability of perturbations at the interface is baroclinic vorticity generation resulting from the misalignment of the pressure gradient of the shock and the density gradient of the interface. In the present study, the effects of interface density contrast and initial thickness, and incident wave strength on the development of the instability at the interface are investigated. The experiments were performed in a new vertical shock tube facility where the interaction of a shock wave with either a discontinuous interface, formed by a thin (0.5 µm) plastic membrane, or a continuous interface, created by retracting a metal plate initially separating the two gases, was studied. Air was used on one side of the interface and either helium, carbon dioxide, refrigerant-22 or sulphur hexafluoride was used on the other side as the test gas. Experiments to study the time evolution of quasi-sinusoidal perturbations on a continuous interface have shown that the growth rates are reduced as the interface thickness is increased. It has been observed that growth rates of perturbations of wavelength λ ~ 25 mm on interfaces of thickness δ ~ 10 mm are about three times smaller than those predicted by the linear theory for the impulsive acceleration of discontinuous interfaces. A new model that accounts for the growth rate reduction caused by the presence of a finite density gradient on the interface has been proposed, and good agreement was obtained with the present experimental results. Experiments were also performed to observe the schlieren visual thickness of plane discontinuous or continuous interfaces with random small-scale perturbations after interaction with the incident shock wave and its reverberations. The interface was initially located near the end wall of the shock tube to permit the observation of the development of the interface phenomena after the arrival of the incident shock and its reverberations. It is found that the interaction of a shock wave with a discontinuous interface causes the appearance of a turbulent mixing zone between the two gases, whose growth rate slows down as time increases, owing to a decrease in turbulence intensity and the action of viscosity. Because of the large uncertainty associated with the measurements a short time after the interaction with the incident shock, the accurate determination of a possible universal power law governing the thickening of the interface is not feasible. Results for the interaction of the first reverberation of the primary wave with the already turbulent interface have demonstrated that this growth is sensitive to the initial pre-growth state of the interface. It also appears that the thickening of the turbulent mixing zone is accomplished by the merging of large structures within the interface. However, since the energy available for the turbulent motions at the impulsively accelerated interface remains constant after the interaction with the shock and also depends on the wavelength of the initial perturbation, it is not certain whether the development of mixing at the interface achieves an asymptotic stage of self-similar turbulence independent of initial conditions, as has been observed for the gravity-driven interfaces. Also, it has been found that the growth rates measured in the present experiments with discontinuous interfaces are nearly an order of magnitude lower than those reported by previous investigators. The continuous interfaces formed by the retracting plate are smoothed by molecular diffusion, and thus the combination of low density gradient and small initial perturbations is such that they exhibit growth only after being perturbed by acoustic noise introduced by the reverberation of waves between the interface, the side walls and the end of the shock tube. The development of viscous boundary layers on the side walls of the test section can cause the bifurcation of waves reflected from the end wall of the shock tube, and, thereafter, the formation of wall bubbles and interface contaminating jets. Moreover, the generation of vortical structures by the baroclinic instability excited by the interaction of reflected waves with the distorted interface within the boundary layer has been demonstrated. Significant contamination of the test gas can by achieved by these structures, even if reflected-wave bifurcation is absent. Moreover, the strain induced by the vorticity in these wall structures tends to thin the interface; the magnitude of this effect on the growth rates in the present plane interface experiments is estimated to be of order 10% for discontinuous interfaces and 50% for continuous interfaces.

The hypersonic flow field around a blunt cone was simulated using a high-order finite difference method. Fast acoustic waves, slow acoustic waves, entropy waves, and vortical waves were introduced into the free-stream to determine the influence of a free-stream with disturbances on the hypersonic flow field and boundary layer. The effect of disturbance type on the evolution of perturbations in the hypersonic boundary layer was analyzed. Fast Fourier Transform was adopted to analyze the effect of the disturbance type on the evolution of different modes in the boundary layer. A roughness element was introduced into the flow field to reveal the impact of the roughness element on hypersonic boundary layer receptivity. The results showed that a free-stream with disturbances affected the hypersonic flow field and boundary layer; acoustic waves had the greatest influence. The impact of slow acoustic waves on the flow field was mainly concentrated in the region between the shock and the boundary layer, whereas the influence of fast acoustic waves was mainly concentrated in the boundary layer. Multi-mode perturbations formed in the boundary layer were caused by the free-stream with disturbances, wherein the fundamental mode was the dominant mode of the perturbations in the boundary layer caused by fast acoustic waves, entropy waves, and vortical waves. The dominant modes of the perturbations in the boundary layer caused by slow acoustic waves were both the fundamental mode and the second harmonic mode. The roughness element changed the propagation process of different modes of perturbations in the boundary layer. In the downstream region of the roughness element, perturbations in the boundary layer caused by the slow acoustic waves had the greatest influence. The second harmonic mode in the boundary layer was significantly suppressed, and the fundamental mode became the dominant mode. The effects of fast acoustic waves and entropy waves on the boundary layer receptivity were similar, except the amplitude of the perturbations in the boundary layer caused by the fast acoustic waves was larger.

Fretting fatigue is a random process that continues to be a major source of damage associated with the failure of aircraft gas turbine engine components. Fretting fatigue is dominated by the fatigue crack growth phase and is strongly dependent on the magnitude of the stress values in the contact region. These stress values often have the most influence on small cracks where traditional long-crack fracture mechanics may not apply. A number of random variables can be used to model the uncertainty associated with the fatigue crack growth process. However, these variables can often be reduced to a few primary random variables related to the size and location of the initial crack, variability associated with applied stress and crack growth life models, and uncertainty in the quality and frequency of non-deterministic inspections. In this paper, an approach is presented for estimating the risk reduction associated with non-destructive inspection of aircraft engine components subjected to fretting fatigue. Contact stress values in the blade attachment region are estimated using a fine mesh finite element model coupled with a singular integral equation solver and combined with bulk stress values to obtain the total stress gradient at the edge of contact. This stress gradient is applied to the crack growth life prediction of a mode I fretting fatigue crack. A probabilistic model of the fretting process is formulated and calibrated using failure data from an existing engine fleet. The resulting calibrated model is used to quantify the influence of inspection on the probability of fracture of an actual military engine disk under real life loading conditions. The results can be applied to quantitative risk predictions of gas turbine engine components subjected to fretting fatigue.

Heat Recovery Steam Generator (HRSG) is a crucial component in the combined cycle power plant, which utilises gas turbine exhaust gases to heat water into further hot steam. Research is needed to improve the heat transfer process in the LP Evaporator. One way to increase the heat transfer is by adding a Vortex Generator (VG) to the LP evaporator. The Vortex Generator itself is a vortex generator that aims to make the fluid flow from the gas turbine not only hit the tube banks in the HRSG but also between the tubes installed a Vortex Generator, which functions to make the fluid flow that was previously laminar into turbulent so that the heat transfer that occurs in LP Evaporator just got better. The analysis consists to velocity contour, temperature contour, local Nu, heat transfer (q), and pressure drop. To determine fluid flow using 2D simulation with Computational Fluid Dynamics (CFD). From the geometry type. Variations made are geometric shapes and the VG arrangement, namely rectangular common flow down, delta winglet common flow down, delta winglet common flow up, and rectangular common flow up. The heat transfer rate value is 2271.34 W, 2333.27 W, 3340.334 W, 3090.747 W. The highest heat transfer rate value occurs on the delta winglet with the common flow up arrangement, and the lowest heat transfer rate value occurs on rectangular with the common flow down arrangement.

First stages of aeronautical high-pressure turbines are subjected to significant inlet distortions generated by the combustor system. These disturbances are characterized by velocity and temperature fluctuations convected downstream by the flow. Such perturbations are commonly defined as vorticity and entropy waves and interact with the turbine stages affecting the aerodynamic performance, the heat exchange and generating indirect noise. Moreover, the presence of a swirling flow highly influences the convection and migration of the entropy wave, thus its interaction with the stage. The paper presents an in-depth study of the impact of the swirling flows on the entropy wave evolution by means of experimental campaigns and numerical simulations. Experimental campaigns have been carried out at Politecnico di Milano where a high-pressure turbine rig was equipped with a novel combustor simulator able to generate entropy waves and swirl profiles. Numerical simulations have been performed at the University of Florence by applying time accurate simulation schemes, including incoming disturbances, implemented in the CFD TRAF code. Two different entropy waves (featuring frequencies of 10 and 110 Hz) injected in a counterclockwise swirling region at midspan have been analyzed at two clocking positions: passage aligned and vane aligned. An excellent agreement is found between experimental acquisitions and numerical results: both show an important reduction of the temperature fluctuations through the stage and highlight the effect of the swirling profile on secondary flows and blade wakes. The extensive comparison reported in the paper validates the numerical approach (based on URANS simulations post-processed by a dedicated filtering technique) which has been further applied to study the impact of swirling flows with an opposite rotation (clockwise). The broad numerical investigation combined with the extensive experimental campaign leads to a deeper understanding of the aerodynamic, thermal, and acoustic implications related to entropy wave evolution in a swirling flow highlighting the interaction phenomena and suggesting how to minimize the impact of entropy waves by comparing the results of the different injection positions and swirling flow directions.

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the quiescent gas (hence subsonic). We proved that such a transonic characteristic discontinuity is structurally stable under small perturbations of the upstream supersonic flow in BV. The existence of a weak entropy solution and Lipschitz continuous free boundary (i.e., characteristic discontinuity) is established. To achieve this, the problem is formulated as a free boundary problem for a nonstrictly hyperbolic system of conservation laws; and the free boundary problem is then solved by analyzing nonlinear wave interactions and employing the front tracking method.

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M1, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM1 > 1.

The effect of a tetrahedral vortex generator on the shock-induced boundary-layer separation has been investigated experimentally at a nominal Mach number of 1.4. The unit Reynolds number was 16 x 10 6 per meter. Two pairs of vortex generators with different heights have been used to control the shock/boundary-layer interaction. Each pair of vertex generators has been placed upstream of the shock location at a fixed distance of 130 mm, which corresponds to 18 times the boundary thickness. Measurements consist of mean boundary-layer profile and streamwise distribution of wall static pressure and Preston pressure. Experimental results suggests that both tetrahedral vortex generators influence and reduce the extent of boundary-layer separation as compared with the baseline configuration, in which no tetrahedral vortex generators were present. Experiments also revealed that the tetrahedral vortex generator with a height of 0.7δ did not produce further reduction in the extent of separation region as compared with the smaller tetrahedral vortex generator with a height of 0.4δ. The experiments confirm that a thicker vortex generator produces more displacement thickness at the expense of a thicker boundary layer and a lower Preston pressure. In both cases, the shape factor of the boundary layer at the location of shock wave showed a decrease of about 46 % as compared with the baseline value.

Advanced high temperature sensors and instrumentation for potential aircraft gas turbine propulsion health monitoring has been explored through significant research and development in the laboratory in the past two decades [8–17]. With continued emphasis on safety, improving engine life cycle cost and fuel efficiency, and increasing durability and life, there is strong impetus to move these technologies out of the laboratory and onto the engines. The objective of this paper is to provide a perspective of the opportunities and challenges in implementing advanced nondestructive evaluation (NDE) and health monitoring techniques on aircraft gas turbine engine components, and to propose an approach for accelerating implementation to meet Air Force objectives.

Fretting fatigue is a significant source of damage for aircraft gas turbine engine components. When combined with high-cycle fatigue (HCF) loading, it is arguably one of the costliest sources of in-service damage in military aircraft engines, reducing component lifetimes by 60% or more. However, surface treatments can significantly reduce the damage associated HCF fretting fatigue. In this paper, a methodology is presented to assess the influences of combined LCF and HCF loading on the fracture risk of gas turbine engine components subjected to fretting fatigue for two surface treatment conditions. The methodology is based on an integration of a calibrated finite element model of the disk-blade assembly, numerical solution of the singular integral equations, and a calibrated risk assessment using the DARWIN probabilistic fracture mechanics code. The methodology is illustrated for an actual military engine disk under real life loading conditions.