A fast and accurate algorithm for computing radial transonic flows

An efficient algorithm is described for calculating stationary one-dimensional transonic outflow solutions of the compressible Euler equations with gravity and heat source terms. The stationary equations are solved directly by exploiting their dynamical system form. Transonic expansions are the stable manifolds of saddle-point-type critical points, and can be obtained efficiently and accurately by adaptive integration outward from the critical points. The particular transonic solution and critical point that match the inflow boundary conditions are obtained by a two-by-two Newton iteration which allows the critical point to vary within the manifold of possible critical points. The proposed Newton Critical Point (NCP) method typically converges in a small number of Newton steps, and the adaptively calculated solution trajectories are highly accurate. A sample application area for this method is the calculation of transonic hydrodynamic escape flows from extrasolar planets and the early Earth. The method is also illustrated for an example flow problem that models accretion onto a black hole with a shock.     

Symmetric Gauss-Seidel multigrid solution of the Euler equations on structured and unstructured grids

The efficient symmetric Gauss-Seidel (SGS) algorithm for solving the Euler equations of inviscid, compressible flow on structured grids, developed in collaboration with Jameson of Stanford University, is extended to unstructured grids. The algorithm uses a nonlinear formulation of an SGS solver, implemented within the framework of multigrid. The earlier form of the algorithm used the natural (lexicographic) ordering of the mesh cells available on structured grids for the SGS sweeps, but a number of features of the method that are believed to contribute to its success can also be implemented for computations on unstructured grids. The present paper reviews, the features of the SGS multigrid solver for structured gr0ids, including its nonlinear implementation, its use of “absolute” Jacobian matrix preconditioning, and its incorporation of multigrid, and then describes the incorporation of these features into an algorithm suitable for computations on unstructured grids. The implementation on unstructured grids is based on the agglomerated multigrid method developed by Sørensen, which uses an explicit Runge-Kutta smoothing algorithm. Results of computations for steady, transonic flows past two-dimensional airfoils are presented, and the efficiency of the method is evaluated for computations on both structured and unstructured meshes.     

Limit cycle oscillation behavior of transonic control surface buzz considering free-play nonlinearity

The limit cycle oscillation (LCO) behaviors of control surface buzz in transonic flow are studied. Euler equations are employed to obtain the unsteady aerodynamic forces for Type B and Type C buzz analyses, and an all-movable control surface model, a wing/control surface model and a three-dimensional wing with a full-span control surface are adopted in the study. Aerodynamic and structural describing functions are used to deal with aerodynamic and structural nonlinearities, respectively. Then the buzz speed and buzz frequency are obtained by V-g method. The LCO behavior of the transonic control surface buzz system with linear structure exhibits subcritical or supercritical bifurcation at different Mach numbers. For nonlinear structural model with a free-play nonlinearity in the control surface deflection stiffness, the double LCO phenomenon is observed in certain range of flutter speed. The free-play nonlinearity changes the stability of LCOs at small amplitudes and turns the unstable LCO into a stable one. The LCO behavior is dominated by the aerodynamic nonlinearity for the case with large control surface oscillation amplitude but by the structural nonlinearity for the case with small amplitude. Good agreements between LCO behaviors obtained by the present method and available experimental data show that our study may help to explain the experimental observation in wind tunnel tests and to understand the physical mechanism of transonic control surface buzz.     

Open and closed-loop control of transonic buffet on 3D turbulent wings using fluidic devices

This paper presents an overview of the work performed recently at ONERA on the control of the buffet phenomenon. This aerodynamic instability induces strong wall pressure fluctuations and as such limits aircraft envelope; consequently, it is interesting to try to delay its onset, in order to enlarge aircraft flight envelop, but also to provide more flexibility during the design phase. Several types of flow control have been investigated, either passive (mechanical vortex generators) or active (fluidic VGs, fluidic trailing-edge device (TED)). It is shown than mechanical and fluidic VGs are able to delay buffet onset in the angle-of-attack domain by suppressing the separation downstream of the shock. The effect of the fluidic TED is different, the separation is not suppressed, but the rear wing loading is increased and consequently the buffet onset is not delayed to higher angles of attack, but only to higher lift coefficient. Then, a closed loop control methodology based on a quasi-static approach is defined and several architectures are tested for various parameters such as the input signal, the objective function or, the tuning of the feedback gain. All closed loop methods are implemented on a dSPACE device calculating in real time the fluidic actuators command from the unsteady pressure sensors data.     

Computational aeroelastic investigation of a transonic limit-cycle-oscillation experiment at a transport aircraft wing model

Aeroelastic measurements of a three-dimensional wing model, the so-called Aerostabil wing, were conducted in the Transonic Windtunnel Göttingen. This clean, backward-swept wing allowed the experimental investigation of limit cycle oscillations in a certain transonic parameter range. In this paper, a detailed insight into the observed physical phenomena, especially the measured limit cycle oscillations, is presented by means of CFD–CSM coupled simulations. These simulations on the basis of a detailed structural finite element model reveal the specific properties of the Aerostabil wing and furthermore allow investigating the unstable behavior of this windtunnel model for transonic flow settings. The aerodynamic characteristics include a two-shock system and large flow separation areas, further increasing the complexity of the aeroelastic problem. A structural single degree-of-freedom system is used for the prediction of the experimental stability range and the limit cycle oscillation investigations. Due to the good agreement of simulation and experiment the limit cycle oscillations can be explained by means of nonlinear aerodynamic effects.     

A collocated finite volume method for predicting flows at all speeds

An existing two-dimensional method for the prediction of steady-state incompressible flows in complex geometry is extended to treat also compressible flows at all speeds. The primary variables are the Cartesian velocity components, pressure and temperature. Density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm, which in the limit of incompressible flow reduces to its well-known form. Special attention is paid to the numerical treatment of boundary conditions. The method is verified on a number of test cases (inviscid and viscous flows), and both the results and convergence properties compare favourably with other numerical results available in the literature.     

Formation of multiple shocklets in a transonic diffuser flow

Multiple shocklets are frequently generated in transonic diffuser flows. The present paper investigates the formation of these shocklets with a high-speed CCD camera combined with the schlieren method. It is observed that compression waves steepen while propagating upstream, and eventually become new shock waves. The ordinary shock wave is found to move upstream beyond the nozzle throat or to disappear while moving downstream depending on the pressure ratio across the nozzle. This phenomenon is also analyzed with the one-dimensional Euler equations by assuming a pressure disturbance given by the sine function at the channel exit. The calculated results are found to reproduce quite well the experimental behavior of the shocklets. The effect of the frequency of disturbance is also studied numerically, and it is shown that the multiple shocklet pattern appears when the amplitude of disturbance is not large and the diverging part of the channel downstream of the ordinary shock wave is long. Received 26 June 1998 / Accepted 15 March 1999     

Application of particle image velocimetry to a transonic centrifugal compressor

As part of an ongoing research project the performance and internal flow field of a high-pressure ratio centrifugal compressor is being investigated. Based on previous, primarily, point-wise laser-optical measurements the compressor was redesigned and resulted in an improved impeller and diffuser with a single-stage pressure ratio of 6:1 at 50,000 rpm. Current research activities involve the use of particle image velocimetry (PIV) to analyze and further improve the understanding of the complex flow phenomena inside the vaned diffuser given the capability of PIV of capturing spatial structures. The study includes phase-resolved measurements of the flow inside a diffuser vane passage with respect to the impeller blade position. Both, instantaneous and phase-averaged velocity fields are presented. The flow field results obtained by PIV are to be used for future validation of the related CFD calculations, which in turn are expected to lead to further improvements in compressor performance. In addition, the potential of stereo PIV for this type of turbomachinery application could be successfully demonstrated.     

Conservative calculations of non-isentropic transonic flows

The classical potential formulation of inviscid transonic flows is modified to account for non-isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second-order mixed-type equation derived via differentiating the momentum equations. The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge. Results for the present conservative calculations are presented for non-lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.     

Cavity Tones by Computational Aeroacoustics

The flow past open cavities is a problem that is encountered in many engineering applications and can result in intense acoustic tones. The flow physics and acoustics of cavity configurations are complex and computational simulation techniques provide an opportunity to gain further understanding and provide a tool to predict not only cavity tone frequencies but their amplitude. In this paper, we describe the available techniques for performing computational aeroacoustic simulations of cavity flows, and review recent applications for the prediction and control of cavity tones in subsonic, transonic and supersonic regimes.