Dorian P Jones

A structure-coupled CFD method for time-marching flutter analysis

Aeroelastic analysis is a critical area of the aircraft design process, as a good understanding of the dynamic behaviour of the wing structure is essential to safe operation of the vehicle. The inevitable inaccuracies present in the modelling of such phenomena impose mass penalties, as large safety margins are necessitated, which in turn lead to overly stiff designs. In an effort to reduce the uncertainty in analysis methods, fully coupled CFD and structural models are under widespread development. We describe the results produced by such a system for a series of test cases based on the AGARD445.6 and MDO wings

Prescribed velocity method for simulation of aerofoil gust responses

A new method for modeling the interaction of an aerofoil with a gust using a prescribed velocity approach, called the split velocity method is presented. This approach effectively rearranges the governing equations into a form that allows for more efficient calculation and includes both the effect of the gust on the aerofoil and the effect of the aerofoil on the gust. The convection of gusts, through the domain from the far field, is investigated using the new method for a range of 1-cosine gusts. The results obtained are compared to an existing prescribed velocity approach called the field velocity method, which neglects the effect of the aerofoil on the gust. The two prescribed velocity approaches agree well for longer gusts. For shorter gusts where the gust length is close to the chord of the aerofoil, the new approach produces better results. Details of a linearized version of the split velocity method are also given. The linearized version is shown to agree well with the full method for cases when th...

Aeroelastic analysis through linear and non-linear methods: a summary of flutter prediction in the PUMA DARP

This paper presents a comparison of linear and non-linear methods for the analysis of aeroelastic behaviour and flutter boundary prediction. The methods in question include NASTRAN and ZAERO, based on linear aerodynamics, and the non-linear coupled CFD-CSD methods RANSMB and PMB, developed at the Universities of Bristol and Glasgow respectively. The test cases used for this comparison are the MDO and AGARD 445.6 weakened wing. In general, it was found that the non-linear methods demonstrate excellent agreement with respect to pressure distributions, deflections, dynamic behaviour, and flutter boundary locations for both cases. This is in contrast to previous studies involving similar methods, where notable differences across the MDO span were found, and is taken to imply good performance of the CFD-CSD interpolation schemes employed here. While the linear methods produce similar flutter boundaries to the coupled codes for the aerodynamically simple AGARD 445.6 wing, results for the transonic ‘rooftop’ MDO wing design did not agree as well.

Reduced order modelling for aeroelastic aerofoil response to a gust

Results for the gust response of the FFAST aerofoil calculated using computational fluid dynamics (CFD) and reduced order models (ROM) constructed using the eigenvalue realization algorithm (ERA) are presented. The CFD results are calculated using the Split Velocity Method (SVM). The SVM method rearranges the Euler equations retaining all terms after splitting the velocity into a prescribed gust and the remainder. SVM allows for the capture of the effects of the gust on the aerofoil and the aerofoil on the gust. In addition to the full SVM method a linearized version, used to generate the data for producing the ROM, is also presented. For larger gusts with over 5 ◦ changes in effective angle of attack it was found that the non-linearities due to large shock motions, which are not captured by the standard ROM, became important. So in addition a version of the ROM corrected with steady state information is presented, this gives more accurate results for longer gusts particularly when used in aeroelastic simulations.

A two-dimensional linearized unsteady Euler scheme for pulse response calculations

Abstract An unsteady linearized Euler scheme for use on moving meshes is presented. This is derived from a scheme for the full non-linear unsteady Euler equations. This scheme is based on the Jameson cell-centred scheme, but is time-accurate and includes the necessary terms to account for grid motion. It is assumed that the unsteadiness in the flow and mesh is small. Using this assumption the discrete unsteady Euler equations are linearized about the full, non-linear, steady mean flow. The resulting equations are solved in the work presented here using a dual-time scheme. In the basic scheme no assumptions are made about the form of the perturbations other than that they are small. This permits the direct calculation of non-periodic flows, e.g. pulse responses. Linear pulse responses are a useful tool as they can be used to calculate the flow due to general inputs. The equations that would result from the assumption of harmonic flow are also derived. Results are presented for heave, pitch and ramp test cases and compared to full non-linear Euler results calculated using a dual-time scheme.

Investigation of Structural Modelling Methods for Aeroelastic Calculations

Flutter clearance and aeroelastic analysis of aircraft is of vital importance, as avoidance of the non-linear phenomena involved is critical to the safe operation of an aircraft. However, the complexity of the behaviour involved makes detailed analysis extremely dicult and, hence, in practise simplied linear methods have been used for all previous and current designs. However, the non-linear nature of the actual responses means that such methods have inherent inaccuracies, which requires the use of large safety margins, in turn imposing signican t weight penalties. Increasing computational power has allowed more complicated forms of analysis and, hence, fully coupled CFD and CSD solution methods are currently under development, allowing more accurate results to be generated. This paper considers a coupled full non-linear CFD solver and structural dynamic solver, and compares dieren t approaches to modelling the structural behaviour in this method. Specically mode extraction and mass and stiness matrix analysis are considered. The former is more commonly used, the latter more complex and computationally intensive. However, it is demonstrated here that for small to moderate structural grid sizes, the latter has signican t advantages in generality of approach and response accuracy and consistency, at negligible computational expense. The prediction and analysis of the aeroelastic behaviour of an aircraft is of critical importance, as any unstable response to time varying or impulsive loads (gusts, etc.) may rapidly lead to disastrous structural failure. This danger requires signican t safety margins, proportionate to the level of inaccuracy and uncertainty inherent in the prediction method used. This increased safety margin results in unnecessary stiness, and hence a higher structural weight. Methods currently common for aeroelastic analysis in industry involve the use of linear techniques for both utter and aeroservoelastic problems, allowing uncoupling of the aerodynamic and structural equations. This reduces the accuracy of the methods, particularly in the transonic igh t regime where the aerofoil thickness (usually neglected) plays a crucial role in the development and movement of shock waves. They are also inapplicable to non-linear instabilities such as control surface buzz and limit cycle oscillation. A new approach is therefore under widespread development, consisting of simulation by non-linear CFD analysis coupled to a dynamic structural representation of the body under investigation (e.g. references 1{14). This allows time-accurate non-linear analysis of dynamic behaviour, leading to much more accurate methods for utter investigation. The majority of such methods rely for prediction of structural motion on a summation of the displacement produced by a limited number of modes derived from an analysis of the structure by a commercial FE solver. Whilst this provides a simple method for producing a structural model within the main CFD algorithm that may be rapidly solved, it does mean that the delit y of the model is compromised, particularly at high frequencies. As an alternative, the full mass and stiness matrices may be extracted from the FE analysis, and once inverted, used to evolve the structure forward in time (this method is henceforth referred to as ‘MK’ for brevity). This increases the complexity of the analysis, but retains the higher frequency properties.

The use of pulse responses and system reduction for 2D unsteady flows using the Euler equations

This paper describes the application of the theory of pulse responses to a linearised Euler scheme on a moving grid. The impulse responses of such a linear system are memory functions or temporal representations of the manner in which, and the time over which a perturbation remains active in the response of the system. The exact response of the linear system to an arbitrary input can then be predicted via convolution. The linearised Euler scheme is derived from a full nonlinear Euler method based on Jameson’s cell-centred scheme which has been modified to make it time-accurate and has the necessary terms to account for grid motion. The discrete form of the full Euler equations are linearised about the corresponding nonlinear steady mean flow assuming the unsteadiness in the flow and grid are small. The resulting set of differential equations for the flow perturbations are solved at each time step using a dual-time scheme. These equations can be easily solved to obtain pulse responses, which capture the entire frequency content of the linear system. These pulse responses then provide a simple and efficient method for calculating the system response to many different inputs via convolution. A further use of the pulse responses is their potential to allow a reduced-order linear model to be constructed, which preserves some of the accuracy of the original system. Preliminary work carried out in this area is presented. Results of calculations for heave, pitch and ramp test cases are presented.

Reduced-order modeling of gust responses

This paper describes two approaches to the construction of reduced-order models from computational fluid dynamics to predict the gust response of airfoils and wings. The first is a linear reduced-order model constructed using the eigensystem realization algorithm from pulse responses, and the second approach modifies the linear reduced-order model using steady-state data to introduce some nonlinearity into the reduced-order model. Results are presented for the Future Fast Aeroelastic Simulation Technologies wing and the Future Fast Aeroelastic Simulation Technologies crank airfoil. These show that for gusts of large amplitude in the transonic regime the response exhibits nonlinearity due to shock motion. This nonlinearity is not captured well by linear reduced-order models; however, the nonlinear reduced-order model shows better agreement with the full nonlinear simulation results.

An initial study of the flow around an aerofoil at high Reynolds numbers using continuation

Nonlinearities are an important feature of high Reynolds numbers flows about aircraft. Standard time stepping schemes, used in computational fluid dynamics simulations, are unable to capture the whole solution space, breaking down in the region of bifurcations. The extension of continuation techniques to such flows is therefore attractive. CFD schemes yield large systems of equations and the associated difficulties of applying continuation methods to such large systems need to be overcome. Whilst previous studies of fluids using continuation have been published, these are mainly limited to much lower Reynolds numbers. In high Reynolds number flows, inertial forces dominate and turbulence must be modeled. This study has shown that continuation can be used effectively for high Reynolds number flows demonstrated through the presentation of a number of test cases.

Moving Mesh CFD-CSD Aeroservoelastic Modelling of BACT Wing with Autonomous Flap Control

Initial results produced by aeroservoelastic simulations of the BACT (Benchmark Active Control Technology) wing are presented. This is a low aspect ratio wing with large trailing edge ap. A fully time-synchronised aeroelastic simulation tool has previously been developed at the University of Bristol, by coupling a 3D central-dierence, nite-v olume, muliblock structured, unsteady CFD code with a linear computational structural dynamics code, in the time-domain. This has recently been extended to account for control surface representation and igh t control system integration, and various aspects of aeroservoelastic simulation have been analysed. All control surface motion is driven through control laws acting on the structure, allowing both commanded and un-commanded deections and distortions in the body modelled. The simulated response of the BACT wing and mount to aerodynamic perturbations and ap angle demands are presented, and a number of key issues relating to the modelling of surface motion are identied, the most signican t of which being the need for consideration of structural and aerodynamic grid behaviour at hinge lines. I. Introduction The accurate prediction of various types of non-linear aeroelastic behaviour is an important area of aircraft design. Whilst utter is the most spectacular example of the dangers posed by unpredicted and uncontrolled oscillations, other phenomena, whilst posing a less immediate threat to vehicle integrity, can have serious eects in the long term due to structural fatigue. Such phenomena would include, for example, Limit Cycle Oscillations (LCO’s) of control surfaces. Methods currently common in industry for aeroelastic analysis involve the use of linear techniques, allowing uncoupling of the aerodynamic and structural equations. However, these methods are not applicable in the most demanding design areas, i.e. non-linear regimes such as transonic utter, control surface LCO’s, and buzz. This can lead to the need for signican t safety margins, creating over-sti and hence high mass designs. More signican tly, it is likely that any errors in design will only be picked up during either ground vibration, or more likely igh t testing. This extends the length of the igh t test program (typically at a cost of thousands of dollars an hour), as a lack of condence in the prediction means that the initial tests must be carried out well below the expected onset of the non-linear behaviour, and speed increased only gradually. Further, the cost of xing any errors encountered at this stage is considerably greater than would be the case if they were to be identied before prototype manufacture through accurate modelling. Prediction methods proven to be of greater accuracy will therefore lead directly to signican t cost savings, without requiring any advances in the underlying aerodynamic or structural design methodologies. For this reason, non-linear techniques are under widespread development (e.g. references 1{22) consisting of time-accurate CFD (Computational Fluid Dynamics) analysis of the o w, coupled to a Computational Structural Dynamics (CSD) structural model. This oers the potential for modelling both the structure and aerodynamics in a non-linear fashion, although admittedly at a far higher cost in terms of CPU time. These methods can also be used to obtain high delit y o w data in regions of particular interest. At the