Transonic Aerofoil Research Articles

Aerodynamic Optimization Using Analytic Descriptions of the Design Space

This paper discusses a strategy for performing aerodynamic single-point and multipoint optimization studies. The approach uses a combination of three methods: an Euler computational e uid dynamics (CFD) code that provides accurate information at one chosen point in the design space, a linear approximation method of the quasianalytic type that rapidly evaluates data at many design points, and a function-e tting algorithm that maps aerodynamic and geometric data across the whole design space. As the method proceeds, a good quality database of aerodynamic and geometric quantities is rapidly constructed at a fraction of the cost of using conventional methods. The availability of this database and the analytic representation of the quantities over the whole design space permits optimizations to be performed using constraints on specie c aerodynamic parameters, e.g., maximum surface Mach number and pressure gradients, over chosen regions of the aerofoil. The approach is also highly e exible, enabling optimization problems of increasing complexity to be built up quickly, and is easily integrated within modern engineering methods. Results are presented for a typical transonic aerofoil giving comparisons with individual CFD analyses.

Surface suction on aerofoil aerodynamic characteristics at transonic speeds

This paper presents a numerical study of the effects of an active flow control through surface suction on shock boundary layer interactions over transonic aerofoils. Two different aerofoils were studied. Firstly, for the purpose of validation, an NACA64A010 aerofoil with a trailing edge flap was investigated and the numerical results were compared with experimental data with and without suction for surface pressure distributions and lift and drag coefficients. Grid sensitivity has also been studied regarding the numerical accuracy. The second geometry was an RAE9647 aerofoil, which was designed for superior aerodynamic performance when applied to a helicopter rotor blade. An active surface was used to prevent or alleviate shock-induced separation. The suction strength and location were varied to determine the effect on aerodynamic performance and to provide an effective means of suppressing undesirable flow features. In both cases, increases in both lift and drag were observed when surface suction was applied. However, the benefit of suction appeared in the form of a substantial increase in the lift-drag ratio. It was also found that the shock location and strength are very sensitive to the suction location and strength. Two different mechanisms for active flow control over transonic aerofoils are discussed.

Rapid design space approximation for two-dimensional transonic aerofoil design

This paper presents a strategy for exploring the design space for use in aerodynamic optimization. This is achieved by perturbing the values of the geometric shape variables, angle of attack, and freestream Mach number for a 2D transonic aerofoil. The approach uses the ’quasi-analytical’ method, which arises from the direct differentiation of the nonlinear governing equations. Using only one traditional CFD analysis, the design space can be explored cheaply with little loss in accuracy for small perturbations. This approach is extended further by developing a new technique by applying the ’quasi-analytical’ method to provide information at selected positions in the design space and then to the approximation of the function for the aerodynamic quantities by a series of polynomials. This provides a significant cost reduction and simplifies the integration within modern engineering methods. Results are presented for a typical transonic airfoil, giving comparisons with individual CFD analyses. (Author)

Solution of the Reynolds-averaged Navier-Stokes equations for transonic aerofoil flows

SummaryA computational method to predict the viscous transonic flow development around two-dimensional aerofoil sections is described. The Reynolds-averaged Navier-Stokes equations applicable to turbulent flow are discretised in space using a cell-centred finite-volume formulation. A multi-stage, explicit, time-marching scheme is used to advance the unsteady flow equations in time to a steady-state solution. Turbulence closure is achieved using either the Baldwin-Lomax algebraic model, or a one-equation model based on the turbulent kinetic energy equation. This latter equation is solved using essentially identical procedures to those for the mean-flow equations. Results are presented for the RAE 2822, RAE 5225, CAST 7 and MBB-A3 transonic aerofoil sections. The relative performance and limitations of the two turbulence models are discussed.

Viscous-inviscid interaction schemes for external aerodynamics

For aerofoils a calculation, which involves the coupling of the external inviscid flow with the viscous flow in the boundary layer and the wake, still provides a worthwhile alternative to the solution of the ‘time-averaged’ Navier-Stokes equations. Classical viscous-inviscid interaction methods which can be extended to include flows with separations and significant pressure gradients across the boundary layer are described. Basic theoretical principles of interactive methods in two dimensions are discussed. The extension of the classical methods leads to generalisations of the concept of displacement thickness and the momentum integral equation. The boundary conditions for the equivalent inviscid flow (EIF) are also described and these also include the effect of normal pressure gradients. An integral method based on the lag-entrainment method for the calculation of the turbulent boundary layer is described. The correlations associated with the method are extended to include separated flow. Two methods of solving the boundary-layer equations through a separation region are described: the inverse method and the quasi-simultaneous method. Principles of techniques for coupling the flows are described and the properties of the direct, fully inverse, semi-inverse and quasi-simultaneous methods are discussed. Results from a method for incompressible flow about a stalled aerofoil, a method for compressible flow about a high-lift aerofoil and a method for compressible flow about a transonic aerofoil are compared with experimental results. The current situation regarding the development of viscous-inviscid interaction methods is briefly summarized and future possibilities are considered.

Improved relaxation schemes for transonic potential calculations

AbstractA block relaxation scheme, grouped in a red‐black ordering, is applied to transonic aerofoil calculations using body‐fitted co‐ordinates. The scheme is simple and easily vectorizable. Detailed comparisons with the approximate factorization method (AF2) are presented and it is shown that the new scheme is competitive in all cases considered. Transonic results, of engineering accuracy, on an 0‐type grid of 149 × 30 points, are usually obtained within 200 iterations (≃ 40s on a Cyber 175).

Application of elliptic continuation method for transonic aerofoil design and experimental verification

AbstractWith the aid of the elliptic continuation method, transonic aerofoils for two different purposes have been optimized. The design process is described and it is shown that the optimization is more difficult for higher design Mach numbers. The results of experimental investigations confirmed the good aerodynamic performances of the designed aerofoils, although no real shock‐free pressure distributions could be achieved in the experiments and the highest aerodynamic efficiencies occurred always at higher lift coefficients, with pressure distributions already having shock waves.

The design of transonic aerofoils by a well‐posed inverse method

AbstractThis paper describes a numerical method for designing closed aerofoils that correspond to given surface speed distributions including flows with shock waves. The prescribed surface speed distribution in general contains three parameters whose values are found as part of the solution. The inverse aerofoil design problem is not well posed unless the prescribed speed satisfies three constraints that can be used to fix the value of the three adjustable parameters. The computational method is based on the numerical solution of the full potential equation in conservation form by an approximate factorization–multigrid scheme. The nature of the constraints and several strategies for introducing the necessary freedom in the prescribed speed are discussed along with typical solutions illustrating the method.

Inverse method with geometric constraints for transonic aerofoil design

AbstractAn engineering method for the design of aerofoils having a prescribed pressure distribution in subsonic or transonic flow is described. The method is based on an iterative procedure of ‘residual‐correction’ type. In each iteration step, the difference between a current and a target pressure distribution (residual) is determined by a fast (multi‐grid) finite‐volume full‐potential code. Corrections to the geometry driving the pressure residual to zero are determined by a global, inverse, thin‐aerofoil theory based method for the subsonic part of the flow field, and by means of a local, inverse, wavy‐wall theory based formula for the supersonic part of the flow field. The determination of the geometry correction has been formulated as a minimization problem in the sense that pressure distribution and geometry requirements may be balanced in a weighted least squares sense. The method is described briefly, including the basic mathematical/physical formulation and the main computational aspects. The capabilities of the method are illustrated by means of examples of aerofoil designs.

Adaptive grids in numerical fluid dynamics

AbstractA solution adaptive grid (SAG) method which redistributes the nodal points of a function according to its curvature is presented. A single, user‐selected step parameter, P, is available for controlling the maximum step size, allowing the application of the technique to a wide variety of problems. Three test cases are cited: (1) the 1‐dimensional inviscid Burgers equation, (2) the Falkner‐Skan equation and (3) the finite‐volume form of the Navier‐Stokes equations for transonic aerofoil flows. In all three cases, significant solution improvement in terms of accuracy and convergence acceleration were achieved.

Analysis of a symmetric transonic aerofoil with the finite element method: A new upwinding technique

AbstractThe non‐linear, small‐disturbance, velocity‐potential equation for steady flow over a thin, symmetric, non‐lifting aerofoil is solved by the finite element method. Pressure distributions are computed for flow regimes ranging from incompressible flow to transonic flow with weak shocks. The governing equation is linearized by a sequence of linear equations which is solved iteratively using Galerkin's method. The infinite flow domain is replaced by a finite but sufficiently large domain which is discretized by bilinear rectangular elements. Boundary conditions of the Neumann type are imposed along an approximate boundary in accordance with classical thin‐aerofoil theory. Dirichlet conditions are imposed along the far‐field boundary from an asymptotic solution valid in the far‐field.Convergence of solution algorithms occurs rapidly for all subsonic flows, but fails for transonic or mixed flows when the supersonic bubble is larger than one‐half on an element. For transonic flows a new upwinding scheme is used to modify the finite element formulations for elements within the supersonic bubble. The scheme, governed by two parameters, accounts for the proper zone of influence for those elements within the bubble by excluding the influence of iterative downwind forces on the solution at upwind nodes. The upwinding scheme permits convergence of the iterative solution algorithm and also captures the weak compression shock which forms automatically in the solution process without the need or use of shock elements.

Transonic Shock-Free Aerofoil Design by an Analytic Hodograph Method

A design method for transonic shock-free aerofoils using hodograph theory is sketched. The method is based on the approximate solution of Tricomi boundary value problems for the elliptic-hyperbolic hodograph equations of transonic aerofoil flows on a two-sheeted hodograph surface. Special attention is paid to a numerical approximation method generating nearly always closed aerofoils. The use of the computer programs in an aerodynamic design process is illustrated by an example. Several examples of computed aerofoils (some of them advanced) demonstrate that the method is flexible and powerful.

An empiric correlation of some transonic aerofoil characteristics.

For symmetrical aerofoils at zero incidence in transonic flows, use of a nozzle analogy led to good correlations for the critical Mach number, the stock wave position, the crest Mach number, and the slope of the Mach number distribution at the crest. The independent variables used were the stream Mach number, the aerofoil curvature at the crest, the chordwise crest position, and the aerofoil thickness. The latter is only important at the lower end of the transonic speed range.