Experiments in transonic flow,

"Prepared by the California Institute of Technology, Pasadena, California, in June 1947, under AAF contract no. W33-038 ac-1717 (11592), supplemental agreement no. 6."

Transonic Aeroelastic Stability Predictions Under the Influence of Structural Variability

Flutter prediction as currently practiced is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognized that there can be significant structural variability, even for different flights of the same aircraft. The safety factor used for flutter clearance is in part meant to account for this variability. Simulation tools can, however, represent the consequences of structural variability in the flutter predictions, providing extra information that could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high-fidelity tools based on computational fluid dynamics is the computational cost. The current paper uses an eigenvalue-based stability method together with Euler-level aerodynamics and different methods for propagating structural variability to stability predictions. The propagation methods are Monte Carlo, perturbation, and interval analysis. The feasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and a generic fighter configuration.

Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation

A method is described to allow searches for transonic aeroelastic instability of realistically sized aircraft models in multidimensional parameter spaces when computational fluid dynamics are used to model the aerodynamics. Aeroelastic instability is predicted from a small nonlinear eigenvalue problem. The approximation of the computationally expensive interaction term modeling the fluid response is formulated to allow the automated and blind search for aeroelastic instability. The approximation uses a kriging interpolation of exact numerical samples covering the parameter space. The approach, demonstrated for the Goland wing and the multidisciplinary optimization transport wing, results in stability analyses over whole flight envelopes at an equivalent cost of several steady-state simulations.

On how structural model variability influence transonic aeroelasticity stability.

This paper considers the ways in which structural model parameter variability can in?uence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, Interval and Perturbation calculations to allow this question to be investigated. Three routes are identi?ed. The ?rst involves variable normal mode frequencies only. The second involves normal mode frequencies and mode shapes. Finally, the third, in addition to normal mode frequencies and mode shapes, also includes their in?uence on the static equilibrium. Previous work has suggested only considering route 1, which allows signi?cant gains in computational e?ciency if reduced order models can be built for the aerodynamics. However, results in the current paper show that neglecting route 2 can give misleading results for the ?utter onset prediction.

How Structural Model Variability Influences Transonic Aeroelastic Stability

This paper considers the ways in which structural model parameter variability can influence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, interval, and perturbation calculations to allow this question to be investigated. Three routes are identified. The first involves variable normal-mode frequencies only. The second involves normal-mode frequencies and shapes. Finally, the third, in addition to normal-mode frequencies and shapes, also includes their influence on the static equilibrium. Previous work has suggested only considering the first route, which allows significant gains in computational efficiency if reduced-order models can be built for the aerodynamics. However, results in the current paper show that neglecting the mode-shape variation can give misleading results for the flutter-onset prediction, complicating the development of reduced aerodynamic models for variability analysis.

Boundary layer and wake modifications to compressor design systems : the effect of blade-to-blade flow variations on the mean flow field of a transonic rotor : final report, 01 September 1976-31 August 1978 /

"AFAPL-TR-79-2010."

Model reduction for nonlinear aerodynamics and aeroelasticity using a Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by
a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted
by proper orthogonal decomposition (POD). The aeroelastic reduce order
model (ROM) is completed by introducing a nonlinear mapping function
between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using
a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil
and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit
cycle oscillations (LCO), which the model is able to predict. For all cases
tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow
field with sufficient accuracy at a fraction of the cost of full order CFD
model.

Active transonic aerofoil design optimization using robust multiobjective evolutionary algorithms

The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. The use of adaptive wing/aerofoil designs is being considered, as they are promising techniques in aeronautic/ aerospace since they can reduce aircraft emissions and improve aerodynamic performance of manned or unmanned aircraft. This paper investigates the robust design and optimization for one type of adaptive techniques: active flow control bump at transonic flow conditions on a natural laminar flow aerofoil. The concept of using shock control bump is to control supersonic flow on the suction/pressure side of natural laminar flow aerofoil that leads to delaying shock occurrence (weakening its strength) or boundary-layer separation. Such an active flow control technique reduces total drag at transonic speeds due to reduction of wave drag. The location of boundary-layer transition can influence the position and structure of the supersonic shock on the suction/pressure side of aerofoil. The boundarylayer transition position is considered as an uncertainty design parameter in aerodynamic design due to the many factors, such as surface contamination or surface erosion. This paper studies the shock-control-bump shape design optimization using robust evolutionary algorithms with uncertainty in boundary-layer transition locations. The optimization method is based on a canonical evolution strategy and incorporates the concepts of hierarchical topology, parallel computing, and asynchronous evaluation. Two test cases are conducted: the first test assumes the boundary-layer transition position is at 45% of chord from the leading edge, and the second test considers robust design optimization for the shock control bump at the variability of boundary-layer transition positions. The numerical result shows that the optimization method coupled to uncertainty design techniques produces Pareto optimal shock-control-bump shapes, which have low sensitivity and high aerodynamic performance while having significant total drag reduction.

Transonic Properties of Accretion Disk Around Compact Objects

An accretion flow is necessarily transonic around a black hole.However, around a neutron star it may or may not be transonic, depending on the inner disk boundary conditions influenced by the neutron star. I will discuss various transonic behavior of the disk fluid in general relativistic (or pseudo general relativistic) framework. I will address that there are four types of sonic/critical point. possible to form in an accretion disk. It will be shown that how the fluid properties including location of sonic point's vary with angular momentum of the compact object which controls the overall disk dynamics and outflows.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Transonic Properties of Accretion Disk Around Compact Objects

An accretion flow is necessarily transonic around a black hole. However, around a neutron star it may or may not be transonic, depending on the inner disk boundary conditions influenced by the neutron star. I will discuss various transonic behavior of the disk fluid in general relativistic (or pseudo general relativistic) framework. I will address that there are four types of sonic/critical point. possible to form in an accretion disk. It will be shown that how the fluid properties including location of sonic point's vary with angular momentum of the compact object which controls the overall disk dynamics and outflows.

KFVS (Kinetic Flux Vector Splitting) on moving grids for unsteady aerodynamics

Accurate numerical solutions to the problems in fluid-structure (aeroelasticity) interaction are becoming increasingly important in recent years. The methods based on FCD (Fixed Computational Domain) and ALE (Alternate Lagrangian Eulerian) to solve such problems suffer from numerical instability and loss of accuracy. They are not general and can not be extended to the flowsolvers on unstructured meshes. Also, global upwind schemes can not be used in ALE formulation thus leads to the development of flow solvers on moving grids. The KFVS method has been shown to be easily amenable on moving grids required in unsteady aerodynamics. The ability of KFMG (Kinetic Flux vector splitting on Moving Grid) Euler solver in capturing shocks, expansion waves with small and very large pressure ratios and contact discontinuities has been demonstrated.

Aerodynamics of delta wings with flaps at hypersonic speeds

Control surface effectiveness is an important parameter for any aeroplane. For a hypersonic aircraft, though the power required to operate the flaps is determined by low speed flying conditions, it is imperative to know the effect of flaps at hypersonic speeds. Hence, studies have been done on this topic by aerodynamicists for over 40 years. In spite of this, only a limited data is available in the literature on this subject. This paper discusses the experimental study of the effect of sweep on the aerodynamic characteristics of thin slab delta wings with flaps at hypersonic speeds. For the purpose of this investigation, a novel special thin six-component balance, which has a thickness of 4mm and can be housed inside wings with 8mm thickness, has been designed. The wings had a sweep of 76degrees, 70degrees and 65degrees, t/c of 0.053 and flaps with 12% of wing area and 12% of wing chord. Testing were done at Mach 8.2, Re number of 2.13 x 10(6) (based on chord), from alpha = -12degrees to 12degrees and flap angle of 20degrees, 30degrees and 40degrees. Separation lengths, measured from Schlieren pictures, clearly show that there is 'no appreciable' effect of sweep on them. Also, using a simple local flow field calculation, the separation has been identified to be transitional in nature. These features of separation reflect in the force data. Because of the small separation length, the flaps (inspite of their small size) were very effective in generating additional C-N, C-M and C-l, which increased with increase in flap angle. In general, the C-N, C-M and X-CP were unaffected by sweep for symmetric flap deflection at positive incidences and asymmetric flap case, For symmetric flap case at negative incidences, only C-N was not influenced by the sweep but C-M decreased and X-CP moved upstream as the sweep is decreased, The wing with lower sweep produces higher CA and lower (L/D)(max) for both symmetric and asymmetric flaps. The rolling moment and adverse yaw increased with decrease in sweep for asymmetric flap deflection. Newtonian theory is shown to be incapable of predicting the effect of sweep on C-l, C-n and on the incremental values of C-N, C-M and C-A. In conclusion, it can be said that a small flap is generally adequate for hypersonic aeroplanes provided they operate at altitudes where transitional and turbulent separation can be expected to occur. This would make the flaps effective and thus enable ample control authority.