Steady Disturbances Research Articles

Modelling of Combustor Non-Uniformities Evolution Through a High-Pressure Turbine Stage

Abstract In modern gas turbines, the reduction of pollutant emissions can be achieved by employing lean-burn combustors. At the combustion chamber outlet, the flow is non-uniform and characterized by a residual swirl superimposed to steady (hot streak) and unsteady (entropy waves) temperature disturbances. During the transport from the combustor outlet to the turbine inlet, these disturbances are weakly dissipated and persist at the turbine inlet. Therefore, the interaction between the combustor non-uniformities and the turbine has to be deeply studied. To study combustor-turbine interaction experimentally, a common practice is to install combustor simulators on non-reactive turbine test facilities. For this purpose, a combustor simulator was designed and installed at Politecnico di Milano turbine test facility. This device can generate a combined steady/unsteady temperature disturbance and swirl profile at the turbine inlet. Using this layout, several experimental campaigns have been carried out changing the type of injected disturbance, the injection position and the turbine operating condition. In this paper, the data collected from these experiments have been used to develop simplified models to predict the transport and dissipation of combustor perturbations through a turbine first stage. In the open literature, few attempts are discussed regarding the modelling of combustor-turbine interaction that - in authors' opinion - represents an important tool for preliminary turbine design.

Surviving disturbances: A predictive control framework with guaranteed safety

Rejecting all disturbances is an extravagant hope in safety-critical control systems, hence surviving them where possible is a sensible objective a controller can deliver. In order to build a theoretical framework starting from surviving all disturbances but taking the appropriate opportunity to reject them, a sufficient condition on surviving disturbances is first established by exploring the relation among steady sets of state, input, and disturbance, followed by an output reachability condition on rejecting disturbances. A new robust safety-critical model prediction control (MPC) framework is then developed by embedding the quartet of pseudo steady input, output, state, and disturbance (IOSD) into the optimisation. Unlike most existing tracking MPC setups, a new and unique formulation is adopted by taking the pseudo steady disturbance as an optimisation decision variable, rather than directly driven by the disturbance estimate. This new setup is able to decouple estimation error dynamics, significantly contributing to the guarantee of recursive feasibility, even if the disturbance or its estimate changes rapidly. Moreover, towards optimal coexistence with disturbances, offset-free tracking of a compromised reference can be achieved, if rejecting the disturbance conflicts with safety-critical specifications. Finally, the benefits of the proposed method have been demonstrated by both numerical simulations and experiments on aerial physical interaction.

Effect of environmental disturbances on crossflow instability

Wind tunnel experiments on the receptivity of three-dimensional boundary layers were performed in a range of freestream turbulence intensities, Tu, from 0.01%—the lowest level ever achieved in this type of work—up to 0.41%. This work confirms that for Tu=0.01%, and presumably below this level, the transition process is dominated by stationary modes. These are receptive to surface roughness and generate Type-I and Type-II secondary instabilities that eventually cause the transition to turbulence. The saturation amplitude of these stationary waves is highly sensitive to the level of environmental disturbances; the former is here recorded to be the highest in the literature, with the latter being the lowest. Travelling modes are still present; however, their influence on the transition process is marginal. At matched surface roughness levels, when the level of environmental disturbance is enhanced to Tuge 0.33%, the travelling modes acquire more importance, strongly influencing the laminar/turbulent transition process, whilst the initial amplitude and growth of the stationary modes are hindered. For this level of Tu, is the interaction of steady and unsteady disturbances that produces highly amplified waves (Type-III), that quickly lead to nonlinear growth and anticipated turbulence. Finally, a simple rule of thumb is proposed, where the transition front was found to move forward by roughly 10% chord for an increase in one order of magnitude in the Tu levels.Graphical abstract

Effective aero-optical suppression by steady wall blowing and wall suction schemes for supersonic turbulent boundary layer

AbstractAs a basic flow model for engineering applications, wall-bounded turbulent flow has been widely studied in the field of aero-optics, but the flow control methods that could effectively suppress aero-optical effects are relatively rare. As an urgent requirement in engineering application, the concept of the steady wall blowing and suction is proposed by the author. Firstly, the author briefly described the flow model and physical method. Secondly, the choice of disturbance type is given. Then, the results of wall blowing-suction, suction and blowing ways based on steady and unsteady disturbance are compared. Finally, it is concluded that employing the high steady wall blowing disturbance (A = 0.2) could realise aero-optical suppression by around 20%. Besides, the steady wall suction scheme contributes to about 70%–80% reduction effect within a wide amplitude range (A = 0.2–1.0), which suppresses this effect by maintaining laminar state downstream contrasted by the baseline case.

Transition of natural convection of liquid metal in an annular enclosure

Natural convection of a low-Prandtl-number fluid in an annular enclosure with a square cross section and radius ratio of the annulus of 0.5 is numerically studied using a finite-difference method in the cylindrical coordinate system. The fluid in the annular enclosure is heated from an inner vertical wall and cooled from an opposing vertical outer wall, both isothermally, whereas the two horizontal walls are adiabatic. Characteristics of the present natural convection are investigated in detail, with one of the annular computational domains divided into several equal parts. Three-dimensional (3D) regular oscillatory flow appears for a range of Rayleigh numbers when the computational domain angle is set to 90° or less. It is revealed that both the average Nusselt number and kinetic energy obtained from 3D flow are smaller than those obtained from a two-dimensional (2D) computation for the same Rayleigh number. When considered for an annular domain divided into 20 equal parts, flow transition of natural convection occurs gradually on the order of 2D steady, 3D regular steady, 3D regular oscillatory, and 3D irregular oscillatory flows, as the Rayleigh number increases. Most of the 3D regular oscillatory flows exhibit half-period symmetry in time and space. Both steady and oscillatory disturbance components coexist during the growing process from an initial state. In a fully developed stage of the 3D steady flow, only the steady disturbance component survives, whereas in that of the 3D regular half-symmetric oscillatory flow, only the oscillatory disturbance component survives.

Computation of static disturbances experienced by a launch vehicle during the flight

During its course from a launch site to an intended orbit, a launch vehicle faces an adverse environment and withstand a plethora of disturbances. The set of disturbance forces acting on each stage of the vehicle depends on the configuration of that stage. Different methodologies are used to predict the magnitude of static disturbances before the flight. To ensure the launch success, performance of a flight control system is validated using a high fidelity six degrees of freedom simulation testbed, in the presence of predicted magnitude of these disturbances. Magnitude experienced by the launch vehicle during its maiden flight, might vary from the predicted set. Actual magnitude of these disturbances is known only after the flight in post-flight exercise of matching launch vehicle dynamics using ground simulations. Correct information of the magnitude of these disturbances is of significant importance for subsequent developmental flights. Control power plant sizing, preflight actuator biasing to nullify lift-off disturbance and autopilot integrator limit setting are all dependent on the exact knowledge of these sources of disturbances. Flight data measurements of a launch vehicle offer a rich galore of information in this regard. This paper presents an analytical technique which uses flight measurements to compute static disturbances experienced during the flight by a launch vehicle. The main sources of steady disturbances considered in this paper are center of gravity, thrust-line offset and thrust misalignment.

Linear stability analysis of three-dimensional natural convection at low Prandtl number in an annular enclosure in the presence of a toroidal magnetic field

The natural convection of a liquid metal in an annular enclosure with a square cross section in the presence of a toroidal static magnetic field was investigated by linear stability analysis. Three-dimensional steady disturbances were obtained in an annular enclosure where the walls parallel to the gravitational field were heated and cooled. The Prandtl number Pr was set to 0.025 and the radius ratio of the enclosure κ was set to 0.5, while the Rayleigh number Ra, the Hartmann number Ha, and the angular wavenumber m were considered as parameters. The dimensionless governing equations were discretized by the finite difference method. Since the newly developed dual staggered grid was employed, the interpolation in the outer product terms was not required. The linear growth rate for a standing wave mode was amplified by increasing Ra and attenuated by increasing Ha. For any integer m, the neutral Rayleigh number Ran at Ha = 0 and the neutral Hartmann number Han for Ran ≤ Ra ≤ 200 000 were identified. Based on these, the neutral lines for a given m were obtained as Han ∼ (Ra − Ran)1/3. Furthermore, the critical values Rac, Hac, and mc were obtained, where mc was not necessarily limited to an integer. The distribution of mc was approximated by the power of Ra. The disturbances had symmetry in the azimuthal direction and constituted a pair of vortices rotating in opposite directions. These vortices were elongated along the main stream.

Interaction of Stationary Disturbances with Tollmien—Schlichting Waves in a Supersonic Boundary Layer

The possibility of controlling unsteady disturbances, traveling Tollmien—Schlichting waves, and stationary streamwise structures is studied. The investigation is performed for the flat-plate boundary layer at the freestream Mach number M = 2. The possible enhancement and suppression of the growth of these waves by stationary streaky structures of the stability eigenproblem of supersonic boundary layer is studied. The problem is solved in the local-parallel approximation within the framework of the three-wave resonance interaction. The pumping wave is a stationary, near-streaky formation. It is shown that even in the stability domain Tollmien—Schlichting waves grow under the influence of the streamwise structures. It is established that under certain conditions the effect of stationary disturbances on these waves can be considerable also in the instability domain and the Reynolds number ranges in which the steady disturbances suppress traveling waves are determined.

Optimal suppression of a separation bubble in a laminar boundary layer

By means of nonlinear optimization, we seek the velocity disturbances at a given upstream position that suppress a laminar separation bubble as effectively as possible. Both steady and unsteady disturbances are examined and compared. For steady disturbances, an informed guess based on linear analysis of transient perturbation growth leads to significant delay of separation and serves as a starting point for the nonlinear optimization algorithm. It is found that the linear analysis largely captures the suppression of the separation bubble attained by the nonlinear optimal perturbations. The mechanism of separation delay is the generation of a mean flow distortion by nonlinear interactions during the perturbation growth. The mean flow distortion enhances the momentum close to the wall, counteracting the deceleration of the flow in that region. An examination of the effect of the disturbance spanwise wavenumber reveals that perturbations maximizing the mean flow distortion also approximately maximize the peak wall pressure, which is beneficial for lowering form drag. The optimal spanwise wavenumber leading to maximal peak wall pressure is significantly larger than the one maximizing the shift in separation onset. For unsteady disturbances, the mechanism of separation delay relies on enhancing wall-normal momentum transfer by triggering instabilities of the separated shear layer. It is found that Tollmien–Schlichting waves obtained from linear stability theory provide accurate estimates of the nonlinearly optimal disturbances. Comparison of optimal steady and unsteady perturbations reveals that the latter are able to obtain a higher time-averaged peak wall pressure.

Size of a steady disturbance source affects the frequency of a target wave

Controlling the frequency of a target wave is an important issue in the dynamics of pattern formation. A common method for controlling is to apply a local disturbance to the media, such as a periodic disturbance source which is not always valid in practice. In the present study, we proposed a method to control the frequency of a target wave by the application of a steady disturbance. We found that the size of a steady disturbance source affects the frequency of the chemical wave by the numerical simulations of three mathematical models. The simulation results are confirmed by theoretical analysis. Our theory and method shed light in the controlling frequency of the oscillatory media.

Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g., see Lamb’s Treatise, 1879). With traces back to Russell’s experimental observations of the Great Wave of Translation in 1834, Korteweg and de Vries (1895), and others, derived an unforced equation to describe the balance between nonlinearity and dispersion required to model the solitary wave. More recently, Akylas (1984) derived a forced KdV equation to model a pressure distribution on the free-surface (e.g., a ship). Since then, the forced KdV equation has been shown to be a useful model approximation for two-dimensional flow past disturbances in an open channel. In this paper, we review the stationary solutions of the forced KdV equation for four types of localised disturbances: (i) a flat plate separating two free surfaces; (ii) a compact bump, or dip in the channel bottom topography; (iii) a compact distribution of pressure on the free surface and (iv) a step-wise change in the otherwise constant horizontal level of the channel bottom topography. Moreover, Dias and Vanden-Broeck (2002) developed a phase plane method to analyse flow over a bump, and this general approach has also been applied to the three other types of forcing (see Binder et al., 2005–2015, and others). In this study, we use eleven basic flow types to classify the steady solutions of the forced KdV equation using the phase plane method. Additionally, considering solutions that are wave-free both far upstream and far downstream, we compare KdV model approximations of the uniform flow conditions in the far-field with exact solutions of the full problem. In particular, we derive a new KdV model approximation for the upstream dimensionless flow-rate which is conveniently given in terms of the known downstream dimensionless flow-rate.

Droplets generator: Formation and control of main and satellite droplets

The continuous-ink-jet printing technology is of great importance in many fields of the industrial and scientific applications due to its low-cost, simplicity, and flexible to a wide variety of material, which entail important technological advantages over existing technology. The perturbation imposed on the surface of the jet-flow is one of the primary parameters to control droplets formation. Therefore, a simple method for producing steady disturbance is presented in this article for further development the technology of continuous-ink-jet printing. Using high-speed photography technology along with image processing, the formation of droplets are investigated at different nozzle diameter and disturbance frequency. The results showed that the droplets formation experienced different breakup modes at different nozzle diameters. The satellite droplet was produced by breakup of jet-tip at the nozzle diameter of 0.15 mm. When the nozzle diameter was increased to 0.33 mm, the satellite droplet was produced by breakup of the trailing of primary droplet. The vibration region of uniform droplets could be controlled by the change of the gas pressure. The wavelength of surface wave decreased with the rose of the disturbance frequency, and a model was established to illuminate the relationship between the disturbance frequency and the wavelength of surface wave. The diameter of droplets decreased with the rose of the disturbance frequency.

A disturbance rejection and data rate trade-off in networked data flow control

The paper discusses a trade-off between the steady state disturbance rejection performance and the achievable end to end data rate of a non-linear networked data flow control system. The control system is subject to delay and saturation, caused by the interface delays and the one-directional data flow. The trade-off is derived from a requirement of global L2-stability, in the limit where the loop delay tends to infinity. More specifically, it is proved that when the product of the steady state disturbance rejection ratio and a data flow discard rate is lower than 1/2, then the Popov inequality prevents L2-stability to be proved. A numerical study is presented, using a networked wireless data flow controller suitable for regulation of the transmission buffer data volumes in fifth generation base stations. The numerical results support the derived trade-off and show that in the studied special case the Popov criterion provides a tight prediction of the L2-stability limit. The numerical results also quantify the conservativeness of the asymptotic trade-off.

Numerical Simulation of Plunging Wing Section at High Angles of Attack

In the near-stall regime, the shedding of coherent structures can result in large unsteady aerodynamic loads. Under such conditions, high-aspect-ratio wings will experience some degree of structural motion. Simulations and experiments for a chord-based Reynolds number of are carried out for a wing section with an X-56A airfoil to investigate the effect of a harmonic heaving/plunging motion on the unsteady aerodynamics. The reduced frequency of the structural motion is , and the amplitude is 3.2–9.6% based on chord length. For a plunging motion at a 10 deg mean angle of attack, the unsteady lift is in good agreement with the Theodorsen theory. As the mean angle of attack is increased up to 14 deg, the flow begins to separate intermittently from the suction side of the wing. The onset of flow separation and the shedding of the resultant stall vortex depend on the frequency and amplitude of the structural motion. Steady spanwise disturbances that are introduced at the leading edge are found to strengthen the stall vortex. For a 16 deg angle of attack, the wing section is fully stalled. However, when subjected to a low-amplitude plunging motion, the flow intermittently reattaches and the mean lift is increased.

Heat transfer modification induced by a localized thermal disturbance in a differentially-heated cavity

Numerical investigation of a natural convection flow with a localized thermal disturbance is presented here. The configuration of a differentially heated cavity is considered with air as working fluid. In this study, the initial flow regime is steady and close to the transition to unsteadiness. Different cases of local wall temperature disturbances are tested in a thin area at the onset of the hot vertical boundary layer. These cases are distinguished by the time-averaged temperature of this area (higher or lower than the hot wall temperature) and by their temporal evolution (steady or periodic). In cases with a periodic disturbance, the imposed frequency corresponds to the first frequency emerging in the unsteady regime. The results show the spread of temperature fluctuations across the whole cavity with the periodic disturbance, in particular near the upper corner of the cavity. The hot steady disturbance trigs the onset of time-dependent flow. Moreover, the local modification of the hot wall temperature has an impact on global heat transfer: about 16% downstream the disturbance area and about 2% on the opposite cold wall.

Swept-wing boundary-layer transition at various external perturbations: Scenarios, criteria, and problems of prediction

This experimental work is devoted to a parametric study of characteristics of the laminar-turbulent transition occurred in a model of a crossflow-dominated swept-wing boundary layer. The experiments are performed in 39 different regimes with low and elevated freestream turbulence levels both in the absence and in the presence of steady freestream vortices of various spanwise scales. The measurements are performed at several values of freestream velocity for two types of distributed surface roughness. Transition scenarios and criteria of turbulence onset are investigated and the problem of transition prediction is examined. It is shown that in all studied cases, the turbulence onset starts with the appearance of local high-frequency secondary instability of the base flow perturbed by primary instability modes. It is found that the 30% level of the threshold zero-to-peak amplitude of combined boundary-layer disturbances (i.e., the steady ones plus unsteady ones) can be used in all studied cases as a simplified turbulence-onset criterion, which was found in previous experiments at other flow and disturbance conditions. A very important, often decisive role of extremely weak steady free-steam disturbances produced by turbulence generating grids is investigated. A generalized combined variable N-factor method of transition prediction is suggested.

Transient Growth and Receptivity of Steady Disturbances to Irregular Rough Walls

Direct numerical simulations (DNS) are performed to investigate the transient growth of a steady disturbance induced by a numerically generated Gaussian rough wall in a laminar boundary layer. In the calculation of the interaction between the rough wall and the fluid, the multiple direct force and immersed boundary method (MDF/IBM) are adopted. The evolution of the streak structures and the energy of the disturbances generated by the rough wall are presented. A similar evolution into an almost sinusoidal modulation for the cylindrical roughness element is found for the current irregular rough wall, and the disturbance energy also undergoes the classical transient growth mode. Moreover, the influences of the skewness, kurtosis, and correlation length on the evolution of spanwise harmonics are also analyzed. The results show that the effects of skewness and kurtosis are on the distribution of energy among the wavelengths and the subsequent growth processes, while the wavelengths of the harmonics are linked to both the streamwise and spanwise correlation lengths of the rough wall.

Penetration of steady fluid motions into an outer stable layer excited by MHD thermal convection in rotating spherical shells

Penetration of steady magneto-hydrodynamic (MHD) disturbances into an upper strongly stratified stable layer excited by MHD thermal convection in rotating spherical shells is investigated. The theoretical model proposed by Takehiro (2015) is reexamined in the case of steady fluid motion below the bottom boundary. Steady disturbances penetrate into a density stratified MHD fluid existing in the semi-infinite region in the vertical direction. The axis of rotation of the system is tilted with respect to the vertical. The basic magnetic field is uniform and may be tilted with respect to the vertical and the rotation axis. Linear dispersion relation shows that the penetration distance with zero frequency depends on the amplitude of Alfvén wave speed. When Alfvén wave speed is small, viscous diffusion becomes dominant and penetration distance is similar to the horizontal scale of the disturbance at the lower boundary. In contrast, when Alfvén wave speed becomes larger, disturbance can penetrate deeper, and penetration distance becomes proportional to the Alfvén wave speed and inversely proportional to the geometric average of viscous and magnetic diffusion coefficients and to the total horizontal wavenumber. The analytic expression of penetration distance is in good agreement with the extent of penetration of mean zonal flow induced by finite amplitude convection in a rotating spherical shell with an upper stably stratified layer embedded in an axially uniform basic magnetic field. The theory expects that the stable layer suggested in the upper part of the outer core of the earth could be penetrated completely by mean zonal flows excited by thermal/compositional convection developing below the stable layer.

Fuzzy Adaptive Repetitive Control for Periodic Disturbance with Its Application to High Performance Permanent Magnet Synchronous Motor Speed Servo Systems

For reducing the steady state speed ripple, especially in high performance speed servo system applications, the steady state precision is more and more important for real servo systems. This paper investigates the steady state speed ripple periodic disturbance problem for a permanent magnet synchronous motor (PMSM) servo system; a fuzzy adaptive repetitive controller is designed in the speed loop based on repetitive control and fuzzy information theory for reducing periodic disturbance. Firstly, the various sources of the PMSM speed ripple problem are described and analyzed. Then, the mathematical model of PMSM is given. Subsequently, a fuzzy adaptive repetitive controller based on repetitive control and fuzzy logic control is designed for the PMSM speed servo system. In addition, the system stability analysis is also deduced. Finally, the simulation and experiment implementation are respectively based on the MATLAB/Simulink and TMS320F2808 of Texas instrument company, DSP (digital signal processor) hardware platform. Comparing to the proportional integral (PI) controller, simulation and experimental results show that the proposed fuzzy adaptive repetitive controller has better periodic disturbance rejection ability and higher steady state precision.

Influence of weak and strong gyroscopic effects on light aircraft dynamics

Purpose The purpose of this study is to investigate the influence of gyroscopic effects on the dynamic stability and the response of light aircraft to manoeuvres following either a rapid deflection of the control surfaces or wind gust. Design/methodology/approach The analyses were conducted for several different mathematical models of aircraft motion, which allowed for the investigation of the relationship between introduced simplifying assumptions and the aircraft response, including non-linear terms in equations of motion expressing the influence of inertial coupling. The analytical and experimental methods (measurements in the wind tunnel for the scaled model and during flight tests of I-31T prototype aircraft) were used. Findings It was found that gyroscopic moments are induced mainly by the propeller, and their influence on dynamic stability of a light aircraft is negligible. However, these phenomena in manoeuvring flight investigation should not be excluded, although for general aviation (GA) aircraft, they are not strong. Hence, two types of gyroscopic effects depending on the level of steady flight disturbances were distinguished. The authors differentiated weak gyroscopic effects, corresponding to classical dynamic stability, and strong gyroscopic effects, corresponding to rapid manoeuvres. Practical implications Conclusions include some findings on the nature of gyroscopic effects (i.e. sensitivity of flight stability versus turboprop power unit parameters) and practical recommendations for aircraft designers dealing with new configurations of GA aircraft. Originality/value The analysis focuses on the assessment of the flight dynamics of light aircraft with a novel, compact, lightweight, fast-rotating turbopropeller engine and strong/weak gyroscopic effects.