A local solution method for shock boundary-layer interaction on a swept wing

Summary The paper describes a local solution method for the calculation of the interaction between a weak shock front and a turbulent boundary layer on a swept wing. A multiple-deck approach allows the simplification of the governing equations according to the physical character of each deck. The mathematical model is based upon small-perturbation theory. The final boundary-layer solution is given by an iterative coupling of the solutions for each domain. The results are compared with experiments and with other theoretical solutions.     

What makes the difference between shock boundary-layer interaction on an airfoil and on a swept wing?

Summary Swept wing flows are characterized by the curvature of the streamlines in the projection to the wing plan and by the skewing of the velocity profile in the boundary layer. The aerodynamic performance of supercritical wings at transonic speeds is trongly influenced by the interaction between a weak shock front and a turbulent boundary layer. The characteristic elements of this interaction are the precompression, the post-shock expansion, and the shock diffusion. The differences between the interactive flow over an airfoil and over a swept wing are elaborated by the comparison between the two-dimensional case and the flow with superposed tangential velocity.     

Insect-like flapping wing mechanism based on a double spherical Scotch yoke

We describe the rationale, concept, design and implementation of a fixed-motion (non-adjustable) mechanism for insect-like flapping wing micro air vehicles in hover, inspired by two-winged flies (Diptera). This spatial (as opposed to planar) mechanism is based on the novel idea of a double spherical Scotch yoke. The mechanism was constructed for two main purposes: (i) as a test bed for aeromechanical research on hover in flapping flight, and (ii) as a precursor design for a future flapping wing micro air vehicle. Insects fly by oscillating (plunging) and rotating (pitching) their wings through large angles, while sweeping them forwards and backwards. During this motion the wing tip approximately traces a "figure-of-eight" or a "banana" and the wing changes the angle of attack (pitching) significantly. The kinematic and aerodynamic data from free-flying insects are sparse and uncertain, and it is not clear what aerodynamic consequences different wing motions have. Since acquiring the necessary kinematic and dynamic data from biological experiments remains a challenge, a synthetic, controlled study of insect-like flapping is not only of engineering value, but also of biological relevance. Micro air vehicles are defined as flying vehicles approximately 150 mm in size (hand-held), weighing 50-100g, and are developed to reconnoitre in confined spaces (inside buildings, tunnels, etc.). For this application, insect-like flapping wings are an attractive solution and hence the need to realize the functionality of insect flight by engineering means. Since the semi-span of the insect wing is constant, the kinematics are spatial; in fact, an approximate figure-of-eight/banana is traced on a sphere. Hence a natural mechanism implementing such kinematics should be (i) spherical and (ii) generate mathematically convenient curves expressing the figure-of-eight/banana shape. The double spherical Scotch yoke design has property (i) by definition and achieves (ii) by tracing spherical Lissajous curves.     

Some indications from instability results about the effectiveness of wall heating as a control option for channel flow

This paper is a review of some of our recent work on the effect of wall heating on the stability of laminar flow in a channel. The summary of our results, some of them unexpected, is as follows. Viscosity stratification has very little effect on transient growth, whereas it results in linear mode stabilising or destabilising by an order of magnitude. It has hitherto been accepted that heat diffusivity does not affect stability. This is however true only for linear instability, transient growth is affected by an order of magnitude. Unusually, the growth is spanwise-independent and not in the form of streamwise vortices. It is also shown that flow is destabilised by secondary modes as the viscosity ratio increases. However, the viscosity ratio has no role in the selection of the pattern of Λ vortices.     

Unsteady compressible boundary layer flow on the stagnation line of an infinite swept cylinder

Summary Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wall enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.     

Navier-Stokes analysis of vortex flow over a cropped delta wing

Summary The vortex flow over a 65° cropped delta wing with round leading edge, atM =0.85 and Re=2.38×10⁶, has been analyzed for 10°, 20°, and 30° angles of attack. A vertex based finite volume code, JUMBO3D, with an algebraic turbulence model has been used to solve the Reynolds Averaged Navier-Stokes (RANS) equations. An H–O type grid generated by a hybrid elliptic-algebraic method has been used here, and a significant improvement of the results over an O–O type grid has been obtained. The results are compared with available experimental data. The complex physical phenomena due to interactions among the primary, secondary, and tertiary vortices, cross-flow and terminating shocks, and turbulent boundary layer, as visualized from the numerical solutions obtained are presented and discussed here.     

Crazing mechanism based on plastic instability

The mechanism of the nucleation of craze from the region of pre-formed voids is discussed on the basis of the finite elements analysis for an elastic plastic material containing a twodimensional array of cylindrical voids. Calculations are made for the two kinds of boundary conditions with respect to the constraint of the transverse strain under simple tension. The craze formation is considered to be an unstable concentration of plastic strain within the ligament between neighbouring voids. The present calculation shows that the constraint of the transverse strain is the essential factor in craze formation.     

On the distribution of impulses in inviscid,incompressible flow — the induced downwash on a rotating wing

Summary We consider the prescribing of singularities in inviscid fluid flows by including Dirac delta functions in the Euler momentum equation. Examples are given of the modelling of the flows due to lifting bodies, in particular that due to a wing simultaneously translating and rotating and find the induced downwash due to the trailing vortex wake.With 2 Figures     

Transonic wing flow computations using the field-panel method with a shock-fitting technique

An integral equation field-panel scheme for solving the full-potential equation for compressible flows with and without shocks is presented. The full-potential equation is written in the form of the Poisson's equation. Compressibility is treated as non-homogeneity. The integral equation solution in terms of velocity field is obtained by Green's theorem. The solution consists of wing (or a general body) surface integral term(s) of vorticity/source distribution(s), wake surface integral term(s) of free-vortex sheet(s), a volume integral term of compressibility over a small limited domain around the source of disturbance, and a shock surface integral term of source distributions for the shock-fitting purpose. Solutions are obtained through an iterative procedure. Instead of using a grid (field-panel) refinement procedure, a shock-fitting technique is used to fit the shock. The present scheme is applied to non-lifting flows around both sharp and round leading edge rectangular wings at high-subsonic and transonic flow conditions.     

A note on the linear instability of the Blasius flow

Summary It is found that in a ribbon-excited Blasius boundary layer, a wave Reynolds number defined here on the basis of phase speed and wave number of the disturbance remains nearly independent of the local mean flow Reynolds number, and so also of the streamwise distance, under the parallel flow approximation. Consequently, a limited similarity feature of the Orr-Sommerfeld equation has been found to exist for the streamfunction in the outer region of the boundary layer.     

Effects of mass transfer on a resonance instability in the laminar boundary layer flow over a rotating-disk

In this paper the linear stability properties of the magnetohydrodynamic flow of an incompressible, viscous and electrically conducting fluid are investigated for the boundary-layer due to an infinite permeable rotating-disk. The fluid is subjected to an external magnetic field perpendicular to the disk. The interest lies also in finding out the effects of uniform suction or injection. In place of the traditional linear stability method, a theoretical approach is adopted here based on the high-Reynolds-number triple-deck theory. It is demonstrated that the nonstationary perturbations evolve in accordance with an eigenrelation analytically obtained.     

Rotational instability of the laminar flow of pseudoplastic fluids in a coaxial-cylindrical channel

Measurements of the stability limit of a spiral flow of a non-Newtonian fluid (n 1) in a coaxial-cylindrical channel are presented and substantiated.Z. P. Shul'man, a member of the editorial staff of Inzhenerno-Fizicheskii Zhurnal, arranged for the publication of this article.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 3, pp. 499–508, September, 1990.     

大气紊流作用下超音速二元机翼的脉动响应

以二元机翼为研究对象,研究大气紊流作用下系统的脉动响应。将气动力分解为简谐振动气动力和脉动气动力两部分,采用随机场的三角级数合成法得到作用在机翼上的脉动压力,运用随机理论对机翼均方根响应值进行分析,着重考查了平均来流速度、湍流尺度、湍流强度等对系统均方根响应的影响。结果表明,系统的均方根响应随速度的增大而增大,在流体速度小于线性临界颤振速度时,其变化很平缓,当速度超过临界颤振速度时,其均方根响应迅速增大。而均方根响应几乎随紊流强度的变化呈线性增长,但其对紊流尺度的变化不很敏感。     

Control of the flow over wing airfoils in transonic regimes by means of force action of surface elements on the flow

Mathematical modeling of the effect of force oscillations of surface elements of a wing airfoil on the shock-wave structure of the transonic flow over it is implemented. The qualitative and quantitative effect of the oscillation parameters on the airfoil wave drag is investigated.     

Some recent developments in the theory of boundary layer instability

The stability of boundary-layer flow over a flat-plate is investigated after taking into account the effects of boundary-layer growth. A critical review and analysis of earlier work is presented, mainly for those works that use an inhomogeneous Orr-Sommerfeld equation and a solvability condition to obtain corrections for the growth-rate based on the quasi-parallel (qp) approximation. During the course of this review and analysis an important result is proven; viz., for a ray, the basic spatial periodicity of the disturbance wave is indimensional space. Thereafter the energy integral equation is invoked, and an optimal monitorable property is found that has the same growth-rate as given by the eigensolution of the associated homogeneous problem. This also leads to the optimal normalisation of the eigenfunction at different downstream stations along the plate. A surprising result found is that the past non-parallel results can be virtually totally reproduced based on theqp-approximation and using the present methodology. And, by using the present methodology for the full non-parallel problem, the results obtained are in very much better agreement with past experimental results, and with the results of Smith based on the triple-deck theory. The students and co-workers who have worked on this problem are Dr T K Vashist and Ms R Verma.     

Some recent developments in the theory of boundary layer instability

The online version of the original article can be found at     

Nonlinear instability of mixed convection flow over a horizontal cylinder

Vortex shedding and instability of the mixed convection flow over a horizontal cylinder have been studied numerically for different flow directions with respect to the direction of buoyancy—with emphasis on assisting and opposing flows. Nonlinear instability and vortex shedding have been investigated with the help of the Landau equation—that is modified to identify critical Reynolds and Richardson numbers. Effects of flow direction are studied for a representative Richardson number. The average Nusselt number is estimated for all the cases to represent average heat transfer.     

Linear instability of flow over a semi-infinite plate in a stream with uniform shear

Summary The linear stability of a boundary layer flow with uniform free stream shear has been studied. The free stream shear is found to stabilize the flow.