Supersonic Axial Flow Research Articles

On the Influence of Nonlinear Inertial Forces on the Limit Cycle Oscillations of an Inextensible Plate in a Supersonic Axial Flow

Abstract Recent results in the literature highlight the impact of nonlinear inertial forces on the post-flutter limit cycle oscillation (LCO) characteristics of highly deflected structures in supersonic axial flow. The current investigation examines how the ability to passively modulate nonlinear inertial forces may alter the overall aeroelastic response. The structural model is a one-dimensional nonlinear inextensible plate subject to nonlinear aerodynamic forces in accordance with a new, geometrically modified third-order Piston Theory. For the linear aeroelastic case, we find that nonhomogeneous mass distribution elicits discontinuous increases in the critical Mach number for flutter and several flutter mode-switching phenomena that are not observed when mass is added homogeneously. The existence of several different flutter mode mechanisms as a function of a concentrated mass location leads to different post-flutter LCO amplitude behavior. This is found to transition the underlying nonlinear structural dynamics to either be stiffening (when lower-order modes merge) or softening (when higher-order modes merge), which in turn alter the influence of nonlinear aerodynamic forces. We also address discrepancies in LCO amplitude trends due to the nonlinear inertial forces previously reported in the literature.

Rotating Detonation Engine Using a Wave Generator and Controlled Mixing

A rotating detonation engine with two unique features, a wave generator and radial injection of fuel and oxidizer, has been designed and tested. The wave generator, consisting of a number of equidistant, circumferentially placed spark plugs, emitted phased sparks to produce free radicals in specified circumferential sequence. This prompted the detonation waves to spin in the specified direction. The detonation waves were initiated quickly, reached a self-sustained state, and maintained orderly spin for the duration of the test. The repeatability of the experiments enabled systematic studies of various controlling parameters, the characterization of orderly structure of detonation waves, and the clarification of the role of acoustic waves. In contrast, a single spark was found to induce two counter- rotating waves, which persisted for the entire experiment. The second feature, radial propellant injection from sparsely distributed holes, enabled the control of the mixing rate of fuel and oxidizer to regulate the axial location of detonation zones. Oblique shock waves emanating from the detonation wave fronts were found to reach the front-end wall, and the corresponding static pressure measurements found that the front-end wall pressure was insensitive to the variations in backpressure during stable rotating detonation engine operation, confirming the presence of supersonic axial exhaust flow.

Performance and flow fields of a supersonic axial turbine at off-design conditions

The increasing demand of energy efficiency and the utilisation of small-scale energy sources require efficient, small and versatile turbines. Supersonic turbines have a high power density and therefore small size and fewer stages than the subsonic ones. However, the performance of a supersonic turbine can decrease rapidly when operating at off-design conditions. This raises a need for the improvement of the turbine off-design performance. In this article, a supersonic axial flow turbine is studied numerically to find the causes of efficiency decrement. This article presents the most thorough study so far about the reasons that lead to the decreased off-design performance with supersonic axial flow turbines and explains the loss sources individually for the stator and the rotor. Three operating conditions are studied, and it is suggested that at the lower than design pressure ratios, the shock losses of the stator decrease while simultaneously the stator secondary losses increase. The high positive incidence at the lowest modelled pressure ratio, mass flow and rotational speed caused a significant decrease in the rotor and stage performance. This highlights the importance of incidence even in shock-driven supersonic turbine flows.

Design and off-design performance of a supersonic axial flow turbine with different stator–rotor axial gaps

The effects of changing the stator–rotor axial gap on the performance and flow field of a low-reaction supersonic axial turbine are studied at design and off-design conditions. The objectives are gaining a better understanding of the effects and giving information and recommendations that a designer can use in his work. Three different axial gaps are modelled numerically with computational fluid dynamics at design and low off-design conditions. The geometry with the smallest axial gap is also measured at intermediate off-design conditions. The efficiency of the turbine decreases when the axial gap increases. The efficiency decrement is steeper at the off-design than the design conditions. It is concluded that the efficiency drop is mainly caused by the increased total pressure losses at the axial gap. It is recommended that the axial gap should be as small as possible. The smaller axial gap makes the rotor inlet flow angle distribution less curved, which is recommended to be taken in account when designing the turbine rotor for the studied turbine type. At the rotor outlet, the changing axial gap changes the absolute flow angle.

Interplay between Kelvin‐Helmholtz and Current‐driven Instabilities in Jets

We investigate, by means of three-dimensional compressible magnetohydrodynamic numerical simulations, the interaction of Kelvin-Helmholtz (KH) and current-driven (CD) instabilities in a magnetized cylindrical jet configuration. The jet has a supersonic axial flow, sheared in the radial direction, and is embedded in a helical magnetic field. The strength of the axial magnetic field component is chosen to be weak, in accord with the "weak field regime" previously defined by Ryu, Jones, & Frank for uniformly magnetized configurations. We follow the time evolution of a periodic section where the jet surface is perturbed at m = ±1 azimuthal mode numbers. A m = -1 KH surface mode linearly develops dominating the m = +1 KH one, in agreement with results obtained using an independent ideal stability code. This lifted degeneracy, because of the presence of the helical field, leads nonlinearly to clear morphological differences in the jet deformation as compared to uniformly magnetized configurations. As predicted by stability results, a m = -1 CD instability also develops linearly inside the jet core for configurations having a small enough magnetic pitch length. As time proceeds, this magnetic mode interacts with the KH vortical structures and significantly affects the further nonlinear evolution. The magnetic field deformation induced by the CD instability provides a stabilizing effect through its azimuthal component Bθ. This helps to saturate the KH vortices in the vicinity of the jet surface. Beyond saturation, the subsequent disruptive effect on the flow is weaker than in cases having similar uniform and helical magnetic field configurations without the CD mode. We discuss the implications of this stabilizing mechanism for the stability of astrophysical jets.

A numerical study of shock wave/boundary layer interaction in a supersonic compressor cascade

A numerical analysis of shock wave/boundary layer interaction in transonic/supersonic axial flow compressor cascade has been performed by using a characteristic upwind Navier-Stokes method with various turbulence models. Two equation turbulence models were applied to transonic/supersonic flows over a NACA 0012 airfoil. The results are superion to those from an algebraic turbulence model. High order TVD schemes predicted shock wave/boundary layer interactions reasonably well. However, the prediction of SWBLI depends more on turbulence models than high order schemes. In a supersonic axial flow cascade at M=1.59 and exit/inlet static pressure ratio of 2.21, k-μ and Shear Stress Transport (SST) models were numerically stables. However, the k-μ model predicted thicker shock waves in the flow passage. Losses due to shock/shock and shock/boundary layer interactions in transonic/supersonic compressor flowfields can be higher losses than viscous losses due to flow separation and viscous dissipation.

Compressibility and windspeed limits in tornadoes

Numerical simulations, with a compressible model, show transient tornadoes with an axial windspeed that exceeds the speed of sound. In general, and even when the flow is subsonic, compressibility decreases the extremes in the windspeeds, as compared with a corresponding incompressible numerical simulation. In theory, an isentropic axial flow will become locally supersonic (with respect to the surface or a stationary shock wave) when the core pressure drops below 53% of the external pressure. When such supersonic flow develops in the numerical simulations, a shock wave occurs within the vortex breakdown, where the supersonic axial jet terminates. The extreme low pressure and supersonic axial flow in these simulated suction vortices is not altogether unnatural. The associated radial inflow at the base of the suction vortex, just above the ground, is relatively tame by comparison, and in accord with observations of extreme tornado damage. In all compressible simulations, the radial inflow was less than 1.26 times the thermodynamic speed limit, which, even for a convective available potential energy (CAPE) of 5000 m2 s‐2, puts the radial inflow at less than about 126 m s‐1.

Supersonic Axial Flow Oscillating Cascade Shock Motion and Unsteady Aerodynamic Moment

Article Supersonic Axial Flow Oscillating Cascade Shock Motion and Unsteady Aerodynamic Moment was published on June 1, 1995 in the journal International Journal of Turbo & Jet-Engines (volume 12, issue 2).

Ｓｈｏｃｋｌｅｓｓ‐ｉｎ‐Ｒｏｔｏｒ型超音波軸流圧縮機の検討

The performances of a shockless-in-rotor supersonic axial flow compressor are discussed on the basis of one dimensional flow analysis. Some characteristics are derived as follows in comparison with an ordinary shock-in-rotor supersonic axial flow compressor having the same inlet Mach number. 1) Normal shock loss can be avoidable in the entire passage including both rotor and stator. 2) The exit flow from rotor is turned in the opposite direction to the rotational one of rotor. 3) The absolute total pressure ratio per stage is small. 4) The starting problem is relieved. 5) The supersonic multistages may be easily put into practical use.

Supersonic turbomachine rotor flutter control by aerodynamic detuning

A mathematical model is developed to analyze the flutter stability characteristics of an aerodynamically detuned rotor operating in a supersonic inlet flowfield with a supersonic axial component. Alternate-blade aerodynamic detuning is considered, accomplished by alternating the circumferential spacing of adjacent rotor blades. The unsteady aerodynamics are determined by developing an influence coefficient technique which is appropriate for both aerodynamically tuned and detuned rotor configurations. The effects of this detuning on the flutter stability characteristics of supersonic axial flow rotors are then demonstrated by applying this model to baseline 12-bladed rotors. Results show that, dependent on the specific blade row and flowfield geometry, alternate blade aerodynamic detuning is a viable flutter control mechanism for supersonic through-flow rotors.

Double Linearization Theory Applied to Three-Dimensional Cascades Oscillating under Supersonic Axial Flow Condition.

The double linearization theory is extended to a three-dimensional straight cascade between parallel-plane end walls operating at supersonic axial velocity. Numerical examples are presented to show unsteady aerodynamic responses and flutter boundaries in correlation with cascade parameters. The three-dimensional effects are evaluated by comparing them with the strip theory predictions. To attain a large steady loading on the stability boundary of the first bending vibration, it is advantageous to design blades with angle of attack and camber decreasing from hub to tip. The three-dimensional effects are small, and the strip theory was found to be a useful method for estimation of the unsteady aerodynamic work of the three-dimensional straight cascade.

Aerodynamic detuning for control of supersonic rotor forced response

A mathematical model is developed to analyze the aerodynamically forced response characteristics of a detuned rotor operating in a supersonic inlet flow field with a supersonic axial component. Alternate blade aerodynamic detuning is considered, with the aerodynamic detuning accomplished by alternating the circumferential spacing of adjacent blades. The unsteady aerodynamics are determined by developing an influence coefficient technique which is appropriate for both aerodynamically tuned and detuned rotor configurations. Rotor forced response is then analyzed by combining this unsteady aerodynamic model with a single-degree-of-freedom structural model. The effects of this detuning on the forced response characteristics of supersonic axial flow rotors is then demonstrated by applying this model to baseline twelve bladed rotors.

Flutter of a Fan Blade in Supersonic Axial Flow

An application of a simple aeroelastic model to an advanced supersonic axial flow fan is presented. Lane’s cascade theory is used to determine the unsteady aerodynamic loads. Parametric studies are performed to determine the effects of mode coupling, Mach number, damping, pitching axis location, solidity, stagger angle, and mistuning. The results show that supersonic axial flow fan and compressor blades are susceptible to a strong torsional mode flutter having critical reduced velocities that can be less than one.

Off-Design Performance of Supersonic Compressors With Fixed and Variable Geometry

Regarding the extremely high pressure ratios of jet-engine compressors for the next decade, increasing interest belongs to the further development of supersonic compressors with supersonic relative flow at rotor inlet and supersonic absolute flow at stator inlet. In the past, different suitable design procedures for these components have been developed and tested successfully. However, there is a lack of information concerning the off-design performance of supersonic compressors. The present paper first systematically shows blading and flow path geometry of different experimentally investigated supersonic axial flow compressors. These investigations refer to combinations of characteristic rotors and stators with fixed and variable geometry. A comparison of these geometric data with the main characteristics of the flow pattern shows that, for the investigated stages, the three-dimensional passage geometry has an essential influence on the off-design performance. On the basis of this information semi-empirical models are established for a numerical description of the flow phenomena with predominant influence, as for example shock-, profile-, and endwall boundary layer losses and rotor-stator interactions. For the determination of the off-design performance, these models are incorporated into a streamline curvature calculation method. The computer model established is able to describe the off-design characteristics of the different investigated supersonic compressor stages in the most important operating range.

Application of Advanced Computational Codes in the Design of an Experiment for a Supersonic Throughflow Fan Rotor

Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The data base for components of this type is practically nonexistent; therefore, in order to furnish the required information for assessment of this type fan, a program has been initiated at the NASA Lewis Research Center to design, build, and test a fan rotor that operates with supersonic axial velocities from inlet to exit. This paper describes the design of the experiment using advanced computational codes to calculate the unique components required. The fan rotor has constant hub and tip radii and was designed for a pressure ratio of 2.7 with a tip speed of 457 m/s. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier–Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. A translating nozzle was designed to produce a uniform flow parallel to the fan up to the design axial Mach number of 2.0. The nozzle was designed with the three-dimensional Euler/interactive boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code, which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes.

Unsteady Supersonic Cascade in Subsonic Axial Flow

This paper presents an analysis for determining the unsteady flowfield produced by an oscillating cascade placed in a supersonic stream which has a subsonic velocity component normal to the cascade. The analysis is based on the assumptions of an inviscid, two dimensional, linearized flowfield. Solutions for the velocity potential and the blade pressure distributions which satisfy the blade-to-blade periodicity condition are developed explicitly in terms of disturbance functions distributed on blade and wake surfaces. The boundary conditions of flow tangency at blade surfaces and continuity of pressure across wake surfaces provide integral relations which can be solved numerically to evaluate the disturbance functions. Predicted blade pressure distributions are in good agreement with results determined from a previous finite cascade solution. Further, in the two limiting cases of sonic axial velocity and zero frequency, the present solution approaches the lower limit of Lane's solution for supersonic axial flow, and it reduces to an Ackeret type of steady-state solution, respectively. The numerical examples indicate that a single~degree- of-freedom torsional instability will exist over a broad range of cascade parameter values.

On the Supersonic Parts of Supersonic Axial Flow Compressor-Blade Sections

The supersonic cascade, in which a normal shock occurs and a flow is decelerated from supersonic to subsonic, is used in supersonic axial flow compressors. For cascades of this type, supersonic starting at the given inlet Mach number, high compression efficiency, larger deflection angles and thick blades enough not to be destroyed are required. Therefore it is considered to be hopeful that a blade section is divided into a supersonic part and a subsonic part, and the former gives most deflection angle to a flow and the latter gives little, consisting of straight surfaces. This report describes the method which dicides such a supersonic part of a blade section and the results of the analytical calculation about the obtainable deflection angles and compression efficiencies in the supersonic regions for the inlet Mach number from 1 to 2.