Optimal Axisymmetric Noses of Bodies in a Flow. Calculations and Experiments

The distinctive features of directmethods for contouring axisymmetric noses of bodies in a supersonic flow are discussed. The nose of a body of revolution in a supersonic flow, optimal with respect to the wave drag, includes a forward-looking flat face adjoining through a bend a sloping region of given aspect ratio (length-to-base-radius ratio), which, in turn, adjoins, again through a bend, the main part of the body. The above-mentioned sloping region can have, depending on its length, some additional internal bends. The presence of bends in a contoured configuration can often be undesirable, owing to strength, thermal, or others restrictions. For this reason, in solving the optimal contouring problems by means of direct methods analytical approximations of the unknown contour are often used, which leads to an increase in the drag of the optimized configuration. The degree of the increase in the drag of the nose part of a body of revolution in the cases of the local smoothing of bends in the optimal configuration and the global variation of its shape on the basis of an analytical approximation is investigated. It is shown that an increase in the drag of the nose part of a body of revolution owing its ineffective approximation can be many times greater than the gain due to optimization. The results of calculations are confirmed by the experimental data obtained.     

Stability and Transition on a Swept Cylinder in a Supersonic Flow

Results of experimental investigations of the evolution of natural disturbances and laminar–turbulent transition in a supersonic boundary layer on the attachment line of a circular cylinder with a sweep angle of 68° and a freestream Mach number M = 2 are presented. The experimental studies are supplemented by calculations of the mean flow and stability characteristics. Flow regimes in the boundary layer on the attachment line are determined by a hotwire technique as functions of the Reynolds number and height of twodimensional roughness elements. The results are compared with NASA (Ames) experiments.     

Limits of the Inertial Particle Deposition Regime and Heat Transfer in Supersonic Viscous-Dusty-Gas Flow Past Bodies

Supersonic steady dusty-gas flow past a blunt body at moderate and large Reynolds numbers Re is considered. Using the complete Navier-Stokes equations for the carrier phase, the effect of viscosity on the limits of the inertial particle deposition regime and the two-phase flow pattern near the frontal surface of the body is studied numerically for 10² Re 10⁵. The dependence of the limits of the inertial particle deposition regime on the phase velocity slip ahead of the bow shock is investigated. For large Re, the flow near the stagnation point is studied in the boundary layer approximation. On the basis of numerical calculations over a wide range of variation of the Reynolds number and the particle inertia parameter, the maximum increase in the heat fluxes at the stagnation point due to the presence of dispersed particles in the free-stream is estimated.     

Drag of Bodies of Revolution in Supersonic Flow with Heat and Mass Addition to the Near Wake

It is shown experimentally that the base drag of bodies of revolution in Mach 1.15 to 3.0 flow can be completely eliminated using special techniques for injecting hydrogen and the products of incomplete combustion of pyrotechnic compounds into the near wake. The experimental data obtained are generalized.     

Investigation of a Gas Flow with Solid Particles in a Supersonic Nozzle

A two-phase flow with high Reynolds numbers in the subsonic, transonic, and supersonic parts of the nozzle is considered within the framework of the Prandtl model, i.e., the flow is divided into an inviscid core and a thin boundary layer. Mutual influence of the gas and solid particles is taken into account. The Euler equations are solved for the gas in the flow core, and the boundary-layer equations are used in the near-wall region. The particle motion in the inviscid region is described by the Lagrangian approach, and trajectories and temperatures of particle packets are tracked. The behavior of particles in the boundary layer is described by the Euler equations for volume-averaged parameters of particles. The computed particle-velocity distributions are compared with experiments in a plane nozzle. It is noted that particles inserted in the subsonic part of the nozzle are focused at the nozzle centerline, which leads to substantial flow deceleration in the supersonic part of the nozzle. The effect of various boundary conditions for the flow of particles in the inviscid region is considered. For an axisymmetric nozzle, the influence of the contour of the subsonic part of the nozzle, the loading ratio, and the particle diameter on the particle-flow parameters in the inviscid region and in the boundary layer is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 65–77, November–December, 2005.     

Development of a Parachute System for Deceleration of Flying Vehicles in Supersonic Regimes

Aerodynamic problems arising during design and development of braking systems for re-entry vehicles are analyzed. Aerodynamic phenomena and laws valid in a supersonic flow around a pair of bodies having different shapes are studied. Results of this research can be used in solving application problems (arrangement and optimization of experiments; design and development of various braking systems for re-entry vehicles moving with supersonic speeds in the atmosphere).     

Modeling of Supersonic Turbulent Flows in the Vicinity of Axisymmetric Configurations

Calculation results of turbulent flows in the vicinity of axisymmetric configurations of the cylinderflare type for Mach numbers M = 3, 5, and 7 are presented. The calculations are performed for conditions of real physical experiments. The mathematical model is based on the averaged Navier–Stokes equations supplemented by the Wilcox turbulence model. The calculated and experimental distributions of pressure on the body surface, velocity fields, and heattransfer coefficients are compared.     

Experimental Investigation of Vibrational Deactivation of CO Molecules in a Supersonic Gas Flow

The vibrational temperature and vibrational deactivation time of CO molecules in collisions with hydrogen atoms are measured using the broadband version of the coherent anti-Stokes Raman scattering technique (CARS). Carbon monoxide with hydrogen-containing admixtures (H₂, H₂O) heated in a reflected shock wave up to temperatures 2900–5100 K escaped through a supersonic wedge-shaped nozzle. The measurements demonstrate the high efficiency of hydrogen atoms in the vibrational deactivation of CO. A difference in the measured temperature dependences of the vibrational excitation and deactivation times of CO molecules in collisions with H atoms, which seems to be associated with a difference in the mechanisms of CO-H complex formation, is noted.     

Technique of Allowing for Plastic Strains Under Unloading in Thermoplasticity Problems for Axisymmetric Bodies

International Applied Mechanics - The nonaxisymmetric elastoplastic stress–strain state of bodies of revolution under nonisothermal combined loading is analyzed with allowance for secondary...     

Construction of Equivalent Axisymmetric Bodies for Calculating Heat Transfer and Viscous Stress on Three-Dimensional Bodies at Incidence

An effective approximate technique for calculating heat transfer, viscous stress, and species components on the windward side of three-dimensional bodies at incidence in hypersonic flow is developed. Using the similarity method, the solution of the three-dimensional problem is reduced to the solution of an axisymmetric problem. For determining the heat flux on a real body, modified two-dimensional equations are solved for equivalent axisymmetric bodies, specially constructed for meridional planes of the original body. For an arbitrary three-dimensional geometry and angle of attack formulas are derived and a conversion program is developed. These make it possible to determine all the parameters of the equivalent body corresponding to a given meridional plane of the original body; then these parameters are used as input data for calculating the viscous flow past the body. The solutions of the two-dimensional equations for the equivalent bodies are in good agreement with more exact solutions of the three-dimensional equations.     

Investigation of the Flow in an Annular Cavity in a Cylindrical Body in a Supersonic Stream

The results of an experimental investigation of the flow over an annular cavity in a cylindrical body are presented; the cavity-to-body diameter ratio was 0.7 and the incident flow Mach number was 2.84. Using the data on the pressure distribution and optical measurements of the flow pattern, the structure of the flow inside the cavity was studied on the relative cavity length range from 0.5 to 14 including the regimes with both open and closed separation zones.     

Aerodynamic Characteristics of Slender Star-Shaped Bodies with Supersonic Leading Edges

A theory of the flow around slender conical bodies with a star-shaped cross-section in regimes with shock attachment along the length of the leading edges is developed. The aerodynamic characteristics of the slender star body, a single cycle of which represents a V-shaped wing, are obtained for different numbers of reflections of the disturbances proceeding from the leading edges of the cycles from the wing cantilevers, using superposition of the solutions of linear problems of flow around the V-wing.     

Axisymmetric Dynamic Problem of Coupled Thermoviscoplasticity

An axisymmetric dynamic thermoviscoelastic problem is formulated with allowance for the coupling of mechanical and thermal fields. The behavior of the material is described by the Bodner–Partom model. A technique for numerical solution of the problem is developed. The laws governing the stress–strain state and the temperature field of a circular disk under forced flexural vibrations are studied     

Linear Approximation for Supersonic Flow Past a Delta Wing

(Accepted June 13, 1996)     

Dynamic Effects Accompanying the Flow Past Oscillating Bodies Mounted with a Narrow Clearance in Pipes

The unsteady and steady flow past a sphere mounted with a very narrow clearance in a cylindrical pipe is experimentally investigated. The unsteady flow is studied for the case of regular transverse self-oscillations of the sphere accompanied by its impact interaction with the pipe wall. In the steady flow regime the center of the sphere is fixed on the pipe axis. The dependence of the local resistance due to the presence of the sphere and of the body drag coefficient on the relevant dimensionless parameters is determined. The dynamic characteristics for the steady and unsteady regimes are compared.     

Theoretical and Experimental Investigation of Supersonic Flow Past a Slender Sharp Circular Cone at Incidence

Supersonic M4 flow past a slender sharp circular cone with semi-vertex angle _c =4° at small and moderate angles of attack is investigated both theoretically and experimentally over the Reynolds number range from 1.69·10⁴ to 13.62·10⁶. The theoretical analysis is based on the numerical integration of the three-dimensional Navier-Stokes and Reynolds equations, while the experimental study was carried out in a wind tunnel of the Central Aerohydrodynamics Institute (TsAGI). The calculated and measured integral characteristics of the cone are compared.     

Numerical Solution of Three-Dimensional Stability Problems for Elastic Bodies

A solution in Cartesian coordinates to plane and spatial stability problems for composites is obtained within the framework of the second variant of the three-dimensional linearized theory of stability of deformable bodies. Two mechanical models are used: a homogeneous anisotropic medium with averaged mechanical characteristics and a piecewise-homogeneous medium with orthotropic linearly elastic components. To solve the problems, a mesh approach is applied. Discrete models are constructed using the concept of a base scheme. The calculated results are analyzed     

Electrical Fracture Diagnostics for Metal Bodies in a Gas Flow

New results of studying the electrical aspects of metal body fracture in a gas flow are obtained. The basis of the investigations and the diagnostic method developed is a fundamentally new effect discovered by the authors: most of the microparticles formed when metal specimens (rods) fracture have the same (positive) electric charge. When the specimen is immersed in a gas flow, the charged particles formed are carried out by the flow into the ambient space and the electric field generated by the particles can be recorded by special probe-antennas. The electric signals produced by fracturing rods made of different metals immersed in a high-temperature jet of combustion products are measured. An approximate theoretical dependence of the total charge on the particles formed as a result of fracture on the strength characteristics of the rod material is obtained.     

Nonlinear Group Interactions of the Taylor–Görtler Disturbances in Supersonic Axisymmetric Jets

The nonlinear group interaction of the Taylor-Görtler disturbances (streamwise vortices) at the initial section of a supersonic axisymmetric jet is numerically studied within the framework of the weakly nonlinear theory of stability. The experimentally observed spectrum of disturbances is considered. The regular and specific features of the streamwise dynamics of various wave components for a turbulent jet are studied. It is shown that such an interaction in the coupled mode in resonant group triplets allows one to describe the experimentally observed elevated growth of background components of the real spectrum.