Subsonic Freestream Mach Numbers Research Articles

Exploration of High-Frequency Actuation on Gust Response Using Large Eddy Simulation

Abstract Mitigation of gust-induced separation and aerodynamic loads using a high-frequency blowing/suction slot is demonstrated using high-order implicit large eddy simulation (LES). This approach was previously shown to be effective at alleviating dynamic stall on pitching wings. A NACA0012 wing section operating at a transitional chord-based Reynolds number of Rec=500,000, subsonic freestream Mach number of M∞=0.1, and angles of attack of α = 4 deg and 12 deg is subjected to discrete 1-cos transverse gusts. Gust-induced stall is demonstrated and then active flow control (AFC) is applied to cases vulnerable to gust-induced stall. The flow control strategy is shown to be effective at stall suppression during gust encounter, thereby providing partial alleviation of gust induced loads. This approach is most effective at attenuating pitching moment increment.

Numerička analiza tegljajućeg nadzvučnog dvokrilca u uslovima van projektovanja sa zaklopkom zadnje ivice

Supersonic biplanes can achieve low-boom and low-drag supersonic flights. In the present study, aerodynamic analysis of a two-dimensional stagger Bussmann biplane (staggered upper element by 0.5c) at zero degrees angle of attack with trailing edge flap was investigated with the help of computational fluid dynamics (CFD) tools. Due to the wave cancellation effect, the Busemann biplane delivers a positive drag reduction at design supersonic Mach values. However, when operating outside of its intended parameters, it performs worse, and the wave cancellation effect has no beneficial effects on reducing drag. Another issue with the Busemann biplane is flow chocking, which produces a potent bow shock wave in front of the aircraft. This paper attempts to address low aerodynamics efficiency problems during take-off through numerical simulation of a staggered Busemann biplane with trailing edge flaps at zero degrees angle of attack. It was confirmed that the staggered biplane airfoil with flap has better aerodynamic performance during take-off at lower subsonic free stream Mach numbers. In 2D wings, the effect of flow chocking and hysteresis as starting problems, which arise when the biplanes accelerate from low Mach numbers, is reduced by using the suitable dimension and angle of rotation of the flap, and the flap is effective in settling these issues.

Wake response downstream of a spanwise-oscillating hemispherical turret

An experimental Pressure Sensitive Paint (PSP) study of the unsteady pressure fields downstream of and on an oscillating hemispherical turret at subsonic freestream Mach numbers between 0.3 and 0.6 and Reynolds numbers of about 2 million is presented. The oscillating turret consisted of a hemispheric shell, mounted on an aluminum rectangular plate and is designed to oscillate in the spanwise direction at a single frequency, which lies within the frequency range of the dominant wake motion. The resonant-based aero-elastic response of the turret to the flow resulted in intermittent turret oscillations. Pressure fluctuations in the wake were found to be less energetic for the oscillating turret and the size of the recirculating region was increased, compared to the stationary turret. POD-based modal analysis of the pressure fields revealed that the wake dynamics is characterized by global anti-symmetric and symmetric shedding and showed that the oscillating turret primarily suppressed the global anti-symmetric shedding. The analysis of the unsteady forces acting on the turret demonstrated that the oscillating turret reduces the spanwise component of the unsteady force, while keeping other force components mostly unchanged. Intermittent nature of the spanwise force, which is responsible for the intermittent motion of the oscillating turret, was observed and discussed.

Properties of subsonic open cavity flow fields

Flow over an open cavity was studied for several different subsonic free stream Mach numbers ranging from 0.19 to nearly 0.73. Velocity field information was acquired through an application of particle image velocimetry, while the fluctuating surface pressure was acquired through a linear array of surface pressure sensors. These data were acquired on the centerline of the cavity which had a length to depth ratio of 6 and a turbulent boundary layer upstream of its leading edge. Over the range of free stream Mach numbers the fluctuating surface pressure spectra in the cavity exhibited different behavior ranging from no apparent resonance to resonance being dominated by the second or third Rossiter modes. The broadband levels of surface pressure spectra with strong resonant tones collapse with scaling by the flow dynamic pressure. Velocity measurements reveal that the center of circulation of the flow within the cavity moves from the aft wall towards the center of the cavity with increasing Mach number. The trend in the mean flow was also apparent in the mean square fluctuating velocities although to a lesser extent. Application of the proper orthogonal decomposition was performed independently on the velocity fields from each of the different free stream cases yielding a spatially dependent basis set. Using a similarity parameter between these spatial orthogonal basis functions it was shown that the first two modes for all of the cases were quantitatively similar. Furthermore this analysis showed some higher less energetic modes that were similar between the cases.

Calculation of transonic flows by a field integral equation method

A field integral equation method is developed to solve the two-dimensional compressible potential equation for transonic flow over airfoils with embedded shocks at subsonic freestream Mach numbers. The perturbation velocities are induced by linear internal source and vorticity distributions on the mean camber line of the airfoil and nonlinear field source distributions external to the airfoil surface. Derivatives are calculated in the computational plane, and those in the physical plane are determined by using the Jacobian of the transformation

On the first-mode instability in subsonic, supersonic or hypersonic boundary layers

The work, addressing subsonic, supersonic and hypersonic boundary-layer instability, is motivated by the need for more understanding of compressible transition at high global Reynolds numbers Re. In the supersonic case, the so-called ‘first modes’ of instability found/suggested by previous Orr-Sommerfeld computations can be identified as triple-deck oblique ones, directed outside the local wave-Mach-cone directions. Less oblique instability modes inside are not of Orr-Sommerfeld form since they are substantially affected by non-parallel flow effects. The maximum linear growth rates are determined for a range of supersonic and subsonic free-stream Mach numbers M∞, and comparisons are made with previous computations, showing fairly good agreement at moderate Mach numbers. A second mound of unstable wavenumbers and frequencies is also evident. In addition, the nonlinear version is set up and emphasized (with attention drawn to a recent paper by the author (1988a) showing the possibility of nonlinear break-up), and certain extremes are examined including those of transonic and hypersonic boundary layers. In the hypersonic limit a new regime is found (for many conditions, including the insulated plate), namely applies to the Orr-Sommerfeld approach. This is a very severe restriction in practice.

有限翼幅の亜音速揚力面理論を検証するに役立つ２次元“ＤＬＭ‐Ｃ”

In order to investigate accuracy and convergence characteristics of any unsteady lifting surface computation programs, it is found that DLM-C scheme for two-dimensional airfoils developed by us is quite useful. This scheme is reliable up to high reduced frequencies k and high subsonic free stream Mach numbers M. It has comparable efficiency with NASA 2-D, within the published k and M values. For a rectangular wing of aspect ratio ten chordwise lift distributions on the midspan section are computed by using some unsteady lifting surface programs, which are compared with DLM-C. The values of error-index parameters E are entered in a k vs M diagram, and constant E curves are drawn. This diagram shows clearly the upper limit of k where the scheme is efficient.

Axisymmetric transonic flow past slender bodies, including perforated wall interference effects

Solutions of the transonic small-perturbation equation for flow past slender bodies of revolution at subsonic freestream Mach numbers are presented in free air as well as in the presence of perforated walls. An artificial viscosity term which enables shock capture is added explicitly to the small-perturbation equation. The modified equation is then converted into an integral equation by the use of Green's theorem. Numerical solution to the integral equation is obtained by discretizing the region of integration into rectangular panels wherein the flow quantities can be considered uniform. Type-dependent operators are introduced in the calculation of the nonlinear source term. The resulting system of algebraic equations is then iteratively solved either by a single- step direct iteration scheme or a quasi-Newton scheme. HE finite difference relaxation procedure has been ap- plied to axisymmetric flow around bodies of revolution by Bailey 1 and Krupp and Mmrman2 and compared with the experimental data of McDevitt and Taylor.3'4 Using the method of split potential Sedin5 has devised a stable iterative scheme for the same problem. Both Bailey and Sedin have included tunnel wall interference effects. They have used the classical homogeneous wall boundary condition developed by Baldwin et al. 6 to model the presence of a perforated wall. Bailey's theoretical calculations seem to confirm the validity of this formulation insofar as the theoretical pressure distribution shows good agreement with the measured values and the shock location is correctly predicted for the ex- perimentally determined value of the porosity parameter. Thus, the theoretical model on which the computation of axisymmetric transonic flow with tunnel wall boundaries is based appears to be reasonably effective in predicting the flow details. It is well known that the axisymmetric transonic small- perturbation equation (TSPE), together with the linearized boundary condition on the body surface and a vanishing far- field disturbance, can be converted into an integral equation by the application of Green's theorem to the flow domain exterior to the body.7 In this formulation, the body boundary condition appears as a line integral on the body contour. Because the line integral for the axisymmetric flow is in- dependent of the unknown nonlinear field source term, iterative readjustment of the boundary condition is not necessary. Since the accuracy with which the tangency con- dition is satisfied depends only on the accuracy of the evaluation of the line integral, choice of the grid details in the vicinity of the body is unimportant to the overall com- putation. Further, since the far-field conditions are implicitly satisfied by the integral equation, no matching is necessary at the far-field boundary as is generally the case in finite difference calculations. The grid boundary is chosen after carrying out numerical experiments to assess its influence on the surface pressure distribution; the number of grid points can thus be minimized. The presence of the wall gives rise to an additional line integral on the wall, with appropriate changes in the domain of integration for the field integral.

Transonic flow past thin wings

This paper is devoted to a discussion of steady inviscid transonic flow past thin wings, with subsonic free-stream Mach number M∞ < 1, by the integral equation method. The integral equation formulation is developed for a thin unsymmetric wing at small incidence. A simple approximate analytical solution is presented for shock-free supercritical flow past a thin symmetric wing at zero incidence. The direct iteration scheme of Niyogi and Chakraborty is then extended to the three-dimensional zero incidence case, which may be used to obtain more accurate solutions for shockfree flows as well as for flows with shocks. The question of the existence and the uniqueness of a solution has been studied by means of the Banach contraction mapping principle in the spaceL 2 (E3), which establishes the condition of convergence of the direct iteration scheme. Simultaneously it provides us with an error estimate for the solution.

Numerical solution of simplified Oswatitsch equation in transonic flow

HE simplified Oswatitsch equation is a one-dimensional nonlinear singular integral equation, occurring in transonic aerodynamics.l It is an approximate version of Oswatitsch's integral equation, whose kernel has a dipole singularity. According to transonic small perturbation theory, the Oswatitsch equation is the basic equation governing the steady inviscid irrotational flow of a perfect gas past a thin symmetric profile at zero incidence, with subsonic freestream Mach number Mx rstrud 4 and Nixon5 deserve special mention. In the present work, the simplified Oswatitsch equation has been solved by two different numerical procedures, viz., the direct iteration scheme (DIS) proposed by Niyogi and Chakraborty6 and by the recent perturbed iterative scheme (PIS) put forward by Dey7 for solving a system of nonlinear algebraic equations. Further, this nonlinear integral equation was used as a test case for studying the global convergence behavior of PIS. From computational results, it has been found that for a parabolic arc profile there exists a range of values for the reduced thickness ratio r (which is a transonic similarity parameter), where both the procedures lead to the same shock-free supercritical solution, and that in this range PIS converges much faster than DIS. However, for higher values of r beyond this range, there exists another range where, contrary to expectations, DIS converges but PIS fails to converge, indicating that DIS has a wider range of convergence.

Unsteady Thin Airfoil Theory for Transonic Flows with Embedded Shocks

A simple modification of classical unsteady thin airfoil theory is presented which accounts for the presence and induced motion of the embedded partial chord shock waves which appear at supercritical transonic Mach numbers. The basic model is found to be divergent at zero frequency because of an unbounded growth of the shock excursion amplitude. This behavior is eliminated by introducing a term associated with the mean flow Mach number gradient near the shock. Numerical results are given for the loads induced by an oscillating flap. LASSICAL unsteady thin airfoil theory fails for low frequencies at the subsonic freestream Mach number at which local supersonic flow first occurs. The main cause of this sudden failure is the formation of a shock wave, which shields the forward region of the airfoil from aft generated disturbances. In the present study,l a simple modification of classical thin airfoil theory is given which accounts for the presence and induced motion of such shocks. Predicted airloads are shown to be in favorable agreement with both experimental observations and finite difference calculations. We assume that the unsteady flow is generated by in- finitesimal harmonic oscillations of an airfoil which is suf- ficiently thin and at sufficiently small mean angles of attack that the transonic small disturbance approximation is valid. The unsteady problem can then be linearized about the steady flow, taking due account of the (small amplitude) displacement of any embedded shocks. The linearized un- steady problem has been formulated for an arbitrary three dimensional planar lifting surface in an earlier paper.2 The linearized equations of motion depend through various coefficients on the steady local Mach number M0 (jc), which in general varies in some complicated way throughout the flowfield. Unless the functional form of M0 is very simple, the boundary value problem for the unsteady flow field must be solved by purely numerical techniques. This has been attempted using finite difference methods by Weatherill et al.3 and Traci et al. 4 However, neither of these studies properly accounted for the between the embedded shocks and the unsteady disturbance field. (Of course, this issue does not arise in nonlinear formulations of the unsteady problem, in which the interaction is implicit; flow with oscillating shocks has been successfully computed from the nonlinear small disturbance equation by, for example, Ballhaus and Goor jian.5) An alternative to direct numerical methods is to ap- proximate the steady Mach number distribution M0(x) in such a way that analytical or semianalytica l methods can be applied. Classical theory, where M0 is set equal to the freestream Mach number M^, is, of course, one example. The

Subsonic loads on wings having sharp leading edges and tips

A vortex-lattice method for predicting the aerodynamics of wings having separation at the sharp edges in incompressible flows is extended to compressible subsonic flows using a modified Prandtl-Glauert transformation. Numerical results showing the effect of freestream Mach number on the aerodynamic coefficients are compared with available experimental data for several planforms. It is shown that the proposed method is suitable for predicting the aerodynamic loads on low-aspect wings at moderate angles of attack for high subsonic freestream Mach number. The method is limited to angles of attack up to 12 deg for high subsonic freestream Mach number and to angles of attack up to 20 deg for Mach number not exceeding 0.5.

Calculation of plane steady transonic flows

Transonic small disturbance theory is used to solve for the flow past thin airfoils including cases with imbedded shock waves. The small disturbance equations and similarity rules are presented, and a boundary value problem is formulated for the case of a subsonic freestream Mach number. The governing transonic potential equation is a mixed (elliptic-hyperbolic) differential equation which is solved numerically using a newly developed mixed finite difference system. Separate difference formulas are used in the elliptic and hyperbolic regions to account properly for the local domain of dependence of the differential equation. An analytical solution derived for the far field is used as a boundary condition for the numerical solution. The difference equations are solved with a line relaxation algorithm. Shock waves, if any, and supersonic zones appear naturally during the iterative process. Results are presented for nonlifting circular arc airfoils and a shock free Nieuwland airfoil. Agreement with experiment for the circular arc airfoils, and exact theory for the Nieuwland airfoil is excellent.

Solution of the transonic airfoil problem through parametric differentiation.

The difficulties associated with the nonlinearity of the transonic small disturbance equation are avoided by considering the linear problem governing the rate of change of the flow velocity with respect to the airfoil thickness ratio parameter and integrating solutions of this problem over the thickness ratio. This procedure is equivalent to summing a series of perturbations in airfoil thickness and has the advantage of moving all the nonlinearity to a firstorder ordinary differential equation, where it causes little difficulty. Solutions for nonlifting airfoils exhibit all the commonly observed features of transonic flow, such as the formation and movement of a shock on the airfoil surface and the presence of a detached shock upstream of the airfoil for low supersonic Mach numbers. Numerical results are given for subsonic and supersonic flow and for flows at Mach number unity which are in general agreement with other theoretical results and with experiment. Preliminary results for mixed flows with subsonic freestream Mach numbers indicate a rearward movement of the shock impinging on the airfoil surface with increasing airfoil thickness and exhibit the commonly observed rapid acceleration behind the shock. Extensions to lifting and unsteady flows are also discussed, as well as possible applications of the method to other problems in fluid mechanics.