A comparative analysis of approaches for investigating hypersonic flow over blunt bodies in a transitional regime

Hypersonic flows of a viscous perfect rarefied gas over blunt bodies in a transitional flow regime from continuum to free molecular, characteristic when spacecraft re-enter Earth's atmosphere at altitudes above 90-100 km, are considered. The two-dimensional problem of hypersonic flow is investigated over a wide range of free stream Knudsen numbers using both continuum and kinetic approaches: by numerical and analytical solutions of the continuum equations, by numerical solution of the Boltzmann kinetic equation with a model collision integral in the form of the S-model, and also by the direct simulation Monte Carlo method. The continuum approach is based on the use of asymptotically correct models of a thin viscous shock layer and a viscous shock layer. A refinement of the condition for a temperature jump on the body surface is proposed for the viscous shock layer model. The continuum and kinetic solutions, and also the solutions obtained by the Monte Carlo method are compared. The effectiveness, range of application, advantages and disadvantages of the different approaches are estimated.     

High level radiosonde ascents at hyderabad during January to April, 1961

The paper describes a new radiosonde developed at Poona for high altitude balloon soundings and the results of the high level radiosonde ascents taken at Hyderabad as part of the Indo-US Balloon Flight Programme—1961. The temperature data obtained during the programme are presented and compared with the results of the sounding balloon ascents made over Poona and Hyderabad during 1928–35.     

Radon concentration of air over the Eastern Arabian Sea

The radon concentrations of air samples collected during the South West monsoon period at altitudes up to 4 km over the Arabian Sea at two locations,i.e., 0–50 km and 300–400 km west of Bombay, are reported. Radon was extracted from air, using a simple single stage apparatus. The concentration of radon in the monsoon air mass was found to range around 80–100 dpm/m³ STP, indicative of its recent continental origin. The results suggest that the coastal monsoon air mass, up to 400 km west of Bombay coast, is generally homogeneous and vertically well mixed. During the post-monsoon condition, a strong gradient in the radon concentration in the vertical is observed. The concentration of radon decreases from 157 dpm/m³ at sea level to 35 dpm/m³ at about 3·7 km altitude, suggesting a vertical turbulent diffusion coefficient of ～6×10⁴ cm²/sec. In contrast, the near absence of vertical gradient of radon in the monsoon air mass indicates that the vertical turbulence is much stronger during the monsoon period.     

The excitation of tsunami by low-frequency non-stationary point and distributed centres of expansion

The elevation of the free surface of a liquid relative to the bottom is calculated for a layer of incompressible heavy liquid with a thickness fo 4 km located over an elastic half-space with a point or distributed centre of expansion acting on it at a depth of 40 km, the intensity of which undergoes stationary transient oscillations. The dependence of this elevation on the period of the source is investigated in the case when the period is greater than 2 minutes but less than 40 minutes. It is established that observable tsunamis are only excited by low frequency oscillations of the source.     

Effect of magnetic field dependent viscosity on ferroconvection in the presence of dust particles

This paper deals with the theoretical investigation of the effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of dust particles. For a flat ferromagnetic fluid layer contained between two free boundaries, the exact solution is obtained using a linear stability analysis and a normal mode analysis method. For the case of stationary convection, dust particles always have a destabilizing effect, whereas the MFD viscosity has a stabilizing effect on the onset of convection. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted but in the presence of MFD viscosity, non-buoyancy magnetization may have a destabilizing or a stabilizing effect on the onset of convection. The critical wave number and critical magnetic thermal Rayleigh number for the onset of stationary convection are also determined numerically for sufficiently large values of buoyancy magnetization parameter M ₁. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of dust particles. The oscillatory modes are introduced due to the presence of the dust particles, which were non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.     

On the unsteady three-dimensional boundary layer freely interacting with the external stream

Asymptotic equations that define unsteady processes in a three-dimensional boundary layer with self-induced pressure are derived. The pressure gradient under conditions of free interaction is, as usually, calculated not by the solution of the external problem of flow over a body, but on the assumption that it is due to growth of streamline displacement thickness near the body surface. Besides the principal terms, terms of second order of smallness are retained in asymptotic sequencies. If the characteristic dimensions of the free interaction region are the same in all directions in the plane tangent to the body surface, the system of equations defining the thin layer next to the wall must be integrated together with the system which defines the nonviscous stream.     

Dusty Supersonic Flow Past a Blunt Body: Viscous and Nonstationary Effects

High‐speed space‐ or aircrafts travelling through a dusty atmosphere may meet dust clouds in which the particles are often distributed very nonuniformly. Such nonuniformities may result in the onset of unsteady effects in the shock and boundary layer and (that is of prime interest) unsteady heat fluxes at the stagnation region of the vehicle. In the nearwall region of high‐speed dusty‐gas flow, there may take place regimes with and without particle inertial deposition, which require essentially different mathematical models for describing the heat transfer [1]. The present paper deals with two problems, considered within the framework of the two‐fluid model of dusty gas [2]: (i) determination of the limits of the particle inertial deposition regime and the distribution of dispersed‐phase parameters near the frontal surface of a sphere immersed in dusty supersonic flow (Mach number M = 6) at moderate flow Reynolds numbers (10² ≤ Re ≤ ∞); (ii) effect of free‐stream nonuniformities in the concentration of low inertial (non‐depositing) particles on the friction and heat transfer at the stagnation point of the body at high Re and M.     

Instability in Porous Layers with Depth-Dependent Viscosity and Permeability

The paper is concerned with a multicomponent porous horizontal layer L with depth-dependent viscosity and permeability, heated from below and salted partly from below and partly from above. The instability of the thermal conduction solution, due to the growth of the gradient of temperature or of the gradient of chemical species salting L from above, is investigated.     

Determination of the flux of primary cosmic ray hydrogen and helium nuclei near the geomagnetic equator using nuclear emulsions

Nuclear emulsions exposed to the cosmic radiation over Hyderabad, India, at an altitude of 31·3 km. for six hours, have been used to derermine primary cosmic ray deuteron flux. The flux of deuterons of rigidity ?16·9 GV at the top of the atmosphere is found to be <10 m.^?2 sec.^?1 sterad^?1; this may be compared with the proton fiux of 83±12 m.^?2 sec.^?1 sterad.^?1 in the same rigidity region over Hyderabad.     

Continuum models in problems of the hypersonic flow of a rarefied gas around blunt bodiest

All possible continuum (hydrodynamic) models in the case of two-dimensional problems of supersonic and hypersonic flows around blunt bodies in the two-layer model (a viscous shock layer and shock-wave structure) over the whole range of Reynolds numbers, Re, from low values (free molecular and transitional flow conditions) up to high values (flow conditions with a thin leading shock wave, a boundary layer and an external inviscid flow in the shock layer) are obtained from the Navier-Stokes equations using an asymptotic analysis. In the case of low Reynolds numbers, the shock layer is considered but the structure of the shock wave is ignored. Together with the well-known models (a boundary layer, a viscous shock layer, a thin viscous shock layer, parabolized Navier-Stokes equations (the single-layer model) for high, moderate and low Re numbers, respectively), a new hydrodynamic model, which follows from the Navier-Stokes equations and reduces to the solution of the simplified (“local”) Stokes equations in a shock layer with vanishing inertial and pressure forces and boundary conditions on the unspecified free boundary (the shock wave) is found at Reynolds numbers, and a density ratio, k, up to and immediately after the leading shock wave, which tend to zero subject to the condition that (k/Re)^1/2 → 0. Unlike in all the models which have been mentioned above, the solution of the problem of the flow around a body in this model gives the free molecular limit for the coefficients of friction, heat transfer and pressure. In particular, the Newtonian limit for the drag is thereby rigorously obtained from the Navier-Stokes equations. At the same time, the Knudsen number, which is governed by the thickness of the shock layer, which vanishes in this model, tends to zero, that is, the conditions for a continuum treatment are satisfied. The structure of the shock wave can be determined both using continuum as well as kinetic models after obtaining the solution in the viscous shock layer for the weak physicochemical processes in the shock wave structure itself. Otherwise, the problem of the shock wave structure and the equations of the viscous shock layer must be jointly solved. The equations for all the continuum models are written in Dorodnitsyn--Lees boundary layer variables, which enables one, prior to solving the problem, to obtain an approximate estimate of second-order effects in boundary-layer theory as a function of Re and the parameter k and to represent all the aerodynamic and thermal characteristic; in the form of a single dependence on Re over the whole range of its variation from zero to infinity.

An efficient numerical method of global iterations, previously developed for solving viscous shock-layer equations, can be used to solve problems of supersonic and hypersonic flows around the windward side of blunt bodies using a single hydrodynamic model of a viscous shock layer for all Re numbers, subject to the condition that the limit (k/Re)^1/2 → 0 is satisfied in the case of small Re numbers. An aerodynamic and thermal calculation using different hydrodynamic models, corresponding to different ranges of variation Re (different types of flow) can thereby, in fact, be replaced by a single calculation using one model for the whole of the trajectory for the descent (entry) of space vehicles and natural cosmic bodies (meteoroids) into the atmosphere.     

Radiation balance of the lower stratosphere

A study of the radiation balance of the atmosphere involves the determination of the absorption and emission of radiant energy due to the different constituents of the atmosphere. In the stratosphere below 50 km., these are mainly ozone, CO₂ and water vapour. The major part of the absorbed energy is from solar radiation, the actual absorption at different levels being determined by the absorption coefficients of these gases and their vertical distributions. In this paper, a detailed survey is made of all the available data and of the recent methods developed for using such data, and after proper selection, curves are prepared giving the solar energy absorbed by different quantities of O₃, CO₂ and H₂O. These are used to calculate the absorption of solar energy per unit volume and per unit mass in different 2 km. layers for certain vertical distributions of the constituents. It is seen that the mass density of absorption due to ozone above 50 km. becomes much larger than that due to CO₂ and H₂O while in the region below 30 km., they become comparable. Water vapour becomes more and more effective as we approach the earth.     

Rank Gradient and p-gradient of Amalgamated Free Products and HNN Extensions

We calculate the rank gradient and p-gradient of free products with amalgamation over an amenable subgroup and HNN extensions with an amenable associated subgroup. The notion of cost is used to compute the rank gradient of amalgamated free products and HNN extensions. For the p-gradient the Kurosh subgroup theorems for amalgamated free products and HNN extensions will be used.     

煤粉起动速度与粒径及湿度的关系

在煤码头和车站的煤堆积场上,煤粉的扬起是污染环境的主要原因之一.作者根据力学的基本原理,考虑颗粒和液滴重力、煤粉颗粒尺寸和湿度的影响,利用煤粉颗粒起动时的力平衡条件,推导出在风的作用下,具有一定湿度的煤粉颗粒开始扬起的起动风速的理论表达式.最后.根据煤粉起动速度与煤粉颗粒粒径及湿度的关系,将理论公式和风洞实验结果进行了比较,理论和实验结果符合得相当好.     

Effect of dust particles on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

The problem of the effect of dust particles on the thermal convection in micropolar ferromagnetic fluid saturating a porous medium subject to a transverse uniform magnetic field has been investigated theoretically. Linear stability analysis and normal mode analysis methods are used to find an exact solution for a flat micropolar ferromagnetic fluid layer contained between two free boundaries. In case of stationary convection, the effect of various parameters like medium permeability, dust particles, non-buoyancy magnetization, coupling parameter, spin-diffusion parameter and micropolar heat conduction parameter are analyzed. For sufficiently large values of magnetic parameter M₁, the critical magnetic thermal Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. It is also observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and dust particles.     

A pair of solar spike emissions

Using the 2.6–3.8 GHz solar radio spectrometer of the National Astronomical Observatories of China (NAOC), a pair of microwave millisecond spike (MMS) emissions were observed, and their frequency drift rate was measured. The separatrix frequency of the MMS pair was at 2900 MHz. Its emission layer was about 2×10⁴km above the photosphere. The polarization degree was wave-like variation with an average value of about 25% in LCP. An MMS pair differs greatly from the type III bursts pair. For the latter, in a certain frequency range, there is no emission around separatrix frequency. This phenomenon may help better understand the mechanism of MMS.     

On the flow of a dusty viscous liquid through a circular pipe

Analytical solution of the flow problem of a dusty viscous liquid through a circular pipe in case of axial symmetry is obtained when pressure gradient varies harmonically with time. It is found that the effect of the fine dust is to make the velocity of sedimentation zero and when dust is sufficiently coarse, the effect of the dust is equivalent to an extra frictional force proportional to the fluid velocity.     

Linear flow induced in fluid particle suspension by an infinite differentially rotating disk

The steady, axisymmetric laminar flow of a homogeneous incompressible fluid with suspended particles occupying the half-infinite space over a differentially rotating rigid plane boundary is analyzed in this paper. The effect of suspended particles is described by two parametersf and τ. The mass concentration parameterf is a measure of the concentration of suspended dust particles. The interaction parameter τ is a measure of the rate at which the velocity of dust particles adjusts to changes in the fluid velocity and depends upon the size of the individual particles. Due to Ekman suction, the particle density remains no longer a constant in the boundary layer but varies with the axial coordinate ξ. Flow characteristics and density variations are studied as functions off, τ and ξ. Possible limiting cases for τ≪1 and τ≫1 which correspond to the case of fine dust and coarse dust respectively are derived and discussed.     

Approximate formulas for heat flows towards an ideally catalytic surface near a plane of symmetry

The three-dimensional flow of a chemically unstable viscous gas near a plane of symmetry of blunt bodies streamlined at the angle of attack, is considered. The investigation is carried out using a model of a thin, viscous shock layer. To a first approximation of the method of successive approximations for a uniform gas simple formulas are obtained for the distribution of the heat flux over the surface, referred to its value at the stagnation point. It is shown that for a chemically unstable gas the distribution of the heat flux along an ideally catalytic surface depends only slightly on the conditions prevailing within the incident flow, is determined mainly by the geometrical characteristics of the body, and is described quite satisfactorily by the formulas obtained. The accuracy of these formulas is determined by comparison with numerical computations carried out for bodies of various shapes, moving at different angles of attack along a planing trajectory of re-entry into the Earth's atmosphere, and during re-entry into the atmosphere at a constant velocity.     

Free convection from a point heat source in a stratified fluid

A non-stationary problem of free convection from a point heat source in a stratified fluid is considered. The system of equations is reduced to a single equation for a special scalar function which determinos the velocity field, and the temperature and salinity distribution. Relations are found connecting the spatial and temporal scales of the phenomenon with the parameters of the medium and the intensity of the heat source. The magnitude of the critical source intensity at which the fluid begins to move in a jet-flow mode is established.The structure of convective flows above the heat sources depends, in the stratified media, essentially on the nature of the stratification /1/ which may be caused by a change in the temperature of the medium /2, 3/ or its salinity /4–7/, and by the form of the heat source. When a temperature gradient exists within the medium, an ascending jet forms above the point source, mushrooming outwards near the horizon of the hydrostatic equilibrium. In the case of a fluid with salinity gradient, the jet is surrounded by a sheet of descending salty fluid, and a regular system of annular convective cells is formed around it /1/.The height of the stationary jet computed in /2, 3/ on the basis of conservative laws agrees with experiment. However, this approach does not enable the temperature and velocity distribution over the whole space to be found and does not enable the problem of determining the flow to be investigated. A stationary solution of the linearized convection equations /8/ does not correspond to detail to the observed flow pattern /1, 5–7/. In this connection the study of the non-linear, non-stationary convection equations is of interest.The purpose of this paper is to construct a non-linear, non-stationary free convection equation above a point heat source, and to analyse the scales of the resulting structure and the critical conditions under which the flow pattern changes.     

Laminar mixing layer on the boundary of two flows in the presence of a longitudinal pressure gradient : PMM vol. 38, n 6, 1974, pp. 1133–1136

We consider, in a linear formulation, the problem concerning the laminar mixing layer on the boundary of two flows of an incompressible liquid with a small difference in their Bernoulli constants; we assume the presence of longitudinal pressure gradient. We determine the velocity distribution in the mixing layer, the magnitude of the displacement thickness and the momentum loss thickness. For the case in which there is no longitudinal pressure gradient we calculate the force effect of the one flow on the other.