The compressible laminar boundary layer with heat transfer on a yawed cone at small angle of attack

Perturbation method for calculating velocity, temperature profiles, skin friction, and heat transfer coefficients in compressible laminar boundary of supersonic strea

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves

Interaction between Tollmien-Schlichting waves and free-stream disturbances in boundary-layer flows

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small freestream disturbance and a small localized variation of the surface geometry has been carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the freestream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the Tollmien-Schlichting waves

Three dimensional boundary layers in internal flows

A numerical study of the effects of viscous-inviscid interactions in three-dimensional duct flows is presented. In particular interacting flows for which the oncoming flow is not fully-developed were considered. In this case there is a thin boundary layer still present upstream of the surface distortion, as opposed to the fully-developed pipe flow situation wherein the flow is viscous across the cross section

On the relation between adjacent inviscid cell type solutions to the rotating-disk equations

Over a large range of the axial coordinate a typical higher-branch solution of the rotating-disk equations consists of a chain of inviscid cells separated from each other by viscous interlayers. In this paper the leading-order relation between two adjacent cells will be established by matched asymptotic expansions for general values of the parameter appearing in the equations. It is found that the relation between the solutions in the two cells crucially depends on the behaviour of the tangential velocity in the viscous interlayer. The results of the theory are compared with accurate numerical solutions and good agreement is obtained

ON THE UNSTEADY SIMILARITY EQUATIONS FOR THE FLOW ABOVE A ROTATING DISC IN A ROTATING FLUID

The unsteady similarity equations for a large rotating disc immersed in an otherwise unbounded rigidly rotating incompressible fluid are investigated for several values of the parameter a, where a denotes the ratio of the angular velocity of the disc to that of the rigidly rotating fluid above it. Numerical computations for a =- 0- 5,-0-25,-0-20,- 0 1 5 and- 0 1 0 show that the appropriate steady-state solutions are not obtained even though they are known to exist. For a<—0-15 the computations break down for a finite value of fit * with all the velocity components as well as the displacement thickness becoming unbounded. However, for a = —0-10 and —0-15 a limit cycle solution is obtained. The results indicate that the steady-state similarity solutions are physically unacceptable for a«—0-10 since they cannot be reached via a time-dependent process. Further it is deduced that the concept of a rotating core of fluid with a thin unsteady boundary layer is destroyed and we can expect that thereafter the core flow must be modified in a serious way. 1