Conical Flow Research Articles

Axisymmetric-conical and locally conical flows without swirling

Axisymmetric steady conical and locally conical non-swirled flows of an ideal (inviscid and non-heat-conducting) gas are considered. Like two-dimensional conical flows, the examined onedimensional (axisymmetric) flows can be conically subsonic and supersonic. If the uniform flow is not considered as a conical flow, then the type of one-dimensional conical flows can change only on the shock wave, except for the junction of two one-dimensional conical flows of different types on the C + characteristic. C ± characteristics and streamlines are constructed for a number of locally conical flows and some already known and new conical flows.

Criteria of existence of nonviscous vortical structures in shock layers of supersonic conical gas flows

Criteria of existence of nonviscous vortical structures in shock layers of supersonic conical gas flows

Internal Conical Flow about Unyawed Cones at High Speeds

An approximate closed form solution to the internal conical, hypersonic flow about a circular cone at zero angle of incidence, has been obtained based on assumption that dissociation, and ionization etc. do not occur behind the shock wave. It has been shown that a singular line exists beyond which the solution is not valid.

A parameterized geometry design method for inward turning inlet compatible waverider

Intensive studies have been carried out on generations of waverider geometry and hypersonic inlet geometry. However, integration efforts of waverider and related air-intake system are restricted majorly around the X43A-like or conical flow field induced configuration, which adopts mainly the two-dimensional air-breathing technology and limits the judicious visions of developing new aerodynamic profiles for hypersonic designers. A novel design approach for integrating the inward turning inlet with the traditional parameterized waverider is proposed. The proposed method is an alternative means to produce a compatible configuration by linking the off-the-shelf results on both traditional waverider techniques and inward turning inlet techniques. A series of geometry generations and optimization solutions is proposed to enhance the lift-to-drag ratio. A quantitative but efficient aerodynamic performance evaluation approach (the hypersonic flow panel method) with lower computational cost is employed to play the role of objective function for optimization purpose. The produced geometry compatibility with a computational fluid dynamics (CFD) solver is also verified for detailed flow field investigation. Optimization results and other numerical validations are obtained for the feasibility demonstration of the proposed method.

Detached-eddy simulations on massively separated flows over a 76/40° double-delta wing

We investigated the flow past a 76/40° double-delta wing at angles of attack from 10° to 35° using SA-DES and a hybrid fourth-order scheme. Comparisons were made with the surface separation pattern, the pressure distribution and the location of vortex breakdown with experimental data, and acceptable agreement was obtained. Further discussions were made under the scenario of massively separated flows on topics such as the characteristics of conical flow, the structure of vortex breakdown and vortical substructures.

Formation of arbitrary axisymmetric relativistic beams

A new form of the solution to the exactly formulated problem of formation of arbitrary axisym-metric relativistic beams is obtained. This form includes the calculation of forming electrodes and the external magnetic field continuously matched with the field of the beam on the beam’s boundary. The problems of nonrelativistic cylindrical and conical beams, butt-end electrodes for a cylindrical diode, and toroidal Brillouin formations based on nonrelativistic conical and relativistic cylinder flows are considered.

The flow of a combustible mixture with a Chapman–Jouguet detonation wave around a cone

The flow around a circular cone under conditions of Chapman–Jouguet (CJ) self-sustaining detonation is investigated in the classical formulation of an infinitely thin detonation wave (DW) in an inviscid and non-heat conducting combustible mixture. Such conditions for flow around a cone are remarkable in several respects. In 1959, Chernyi and Kvashnina had already shown that, for supersonic flows of a combustible mixture around a cone, CJ detonation, as in the case of a wedge, is not only possible for a strictly fixed cone angle (the “CJ” angle) but also for angles smaller than this (including a zero angle, that is, when there is no cone). In the case of flow around a wedge with an angle that is less than the corresponding CJ angle, a centred rarefaction wave that turns the supersonic flow in the required direction borders on the CJ DW. In the case of a cone, a conical rarefaction flow also borders on the CJ DW. However, if, in the plane case, a uniform supersonic flow adjoins the centred rarefaction wave along its boundary C+-characteristic then the conical rarefaction flow is bounded by a conical shock wave (SW), bordered up to the surface of the cone by a conical compression flow. Only for a zero cone angle does the SW degenerate into the C+-characteristic and the conical compression flow degenerates into a uniform supersonic flow. The configuration obtained in the general case became the first example of a self-similar solution with two SW of “one family” (the first of them is the DW) diverging from a single point. The results of calculations carried out in this paper with the construction of streamlines and the characteristics of the two families give a fairly complete representation of the above mentioned features of the flows considered.

DEVELOPMENT OF A WIND OBSERVATION SYSTEM USING PHOTOGRAMMETRY

Abstract. Quantitative understanding of wind flow near the ground surface in all three dimensions onsite is extremely important for wind research.The objective of this research is to develop a system to quantitatively measure wind flow near the ground surface in both the horizontal and vertical directions (in other words, wind flow in three dimensions) using inertial photographic surveying or phototheodolite. In this method, a balloon (a no-lift balloon) with the same relative weight as air and soap bubbles were released as tracers. Their movements were captured using stereo-photography and single photographs, and then the path of particles was analyzed in three dimensions. For this document, wind flow near tall buildings, conical vortices flow on the rooftops of buildings and wind flow crossing over an embankment were measured. The results of the testing proved that the measurement methods were effective.

Swirled flows and their generalizations

New swirled flows (flows in channels, flows around bodies of revolution, and flows with a sink or source on the axis of symmetry) are studied. Group solutions constructed from a supergroup, which are generalizations of conical flows, are considered.

Parametric investigation of the pintle-perturbed conical nozzle flows

Thrust variation, flow structures and geometric factors of pintle-perturbed conical nozzle are studied experimentally and numerically under the condition of constant mass flow rate. Regulators and choking orifice are installed for constant mass flow rate and static pressure distributions along the nozzle wall, chamber pressure and thrust are measured. In order to prevent transfer of non-linear load to the load cell by the flexible tubes, the load cell for thrust measurement is calibrated. Roeʼs flux-difference splitting scheme is applied to resolve the flow discontinuities such as the lip shock, trailing shock and oblique shock typical in the pintle-perturbed nozzle flows. Three different turbulent models of k–ε, k–ω SST and Spalart–Allmaras are examined to assess their validity for resolving the turbulence. The predicted thrust by empirical method, which includes influence of deliverable thrust coefficient by flow separation, showed good agreement with measured thrust at the minimum and maximum throat area. Spalart–Allmaras model and k–ω SST model showed good agreement with experiment on predicting the thrust especially in the case that the flow separation occurs in the nozzle diverging section, and the Spalart–Allmaras model predicted wall separation point more accurately than the other models. Shock impinging point and the flow separation point induced by shock wave separation occur and move in the nozzle flow as the pintle inserted into the nozzle throat. Because, the dominant factor which determines thrust is chamber pressure, the pintle shape must be considered essentially in view of minimizing the force acting on the pintle.

Conical gas flows with shock waves and turbulent boundary layer separation

The results of a theoretical and experimental investigation of nonsymmetric flow around a V-wing with supersonic leading edges are presented. The range of the angles of attack and yaw, on which additional singular lines are formed on the windward cantilever of the wing, are experimentally determined using different techniques of flow diagnostics. These are one convergence line and two divergence lines in the transverse flow which were not previously observable in the calculations of ideal-gas flow around wings. It is established that the appearance of the three new alternating singular lines located between the central chord of the wing and a convergence line, exterior to them and occurring within the framework of the ideal gas model, is associated with the relation between the intensities of two contact discontinuities. One of these proceeds from the branching point of the bow shock above the leeward cantilever, while the second issues out of the triple point of a λ-shaped shock configuration accompanying developed turbulent-boundary-layer separation generated by an internal shock incident on the leeward cantilever surface. If the intensity of the contact discontinuity proceeding from the branching point of the bow shock is large as compared with that of the contact discontinuity of the λ-configuration, then the flow pattern realized on the windward cantilever is analogous to that obtained within the framework of the ideal gas model, that is, it includes one convergence line on the wing surface. Under these conditions, the results of the calculations within the framework of the ideal gas model are applicable for understanding the phenomena occurring in the wing shock layer in a considerable part of the control parameter range, including the regimes with intense internal shocks generating turbulent boundary layer separation from the leeward cantilever. Corrections should be made only for a carachteristic pressure distribution in the separation zone and, as a consequence of separation, for an elevated pressure level in the vicinity of the central chord which is the stagnation line of the transverse flow that has passed across the oblique and terminating shocks of the λ-configuration and possesses a higher stagnation pressure than the flow that has passed in an ideal gas across the internal shock incident normally on the leeward cantilever. This is possible only when the divergence line, at which the stream surface enclosing the turbulent boundary layer separation zone enters, does not go over from the leeward onto the windward cantilever.

The amplification of weak shock waves in axisymmetric supersonic flow and their reflection from an axis of symmetry

The problem of the amplification of weak shock waves when a supersonic flow approaches the axis of symmetry and they are reflected from this axis is considered within the framework of an ideal (non-viscous and non-heat-conducting) gas model. A non-linear theory is developed to investigate the amplification of shock waves, and Euler's equations are integrated numerically with an explicit construction of the head shock wave – the boundary of the unperturbed flow. In the simplest linear theory, in contradiction with numerical results, the amplification of weak shock waves is independent of the Mach number M0 of the flow in front of the shock wave and of the adiabatic exponent of the gas. The non-linear theory is free from this drawback. In this theory, obtaining the dependence of the intensity of the shock wave on the distance to the axis of symmetry reduces to the numerical solution of several unconnected Cauchy problems for two ordinary differential equations. Here the limit of applicability of the theory is also determined. In addition to investigating the amplification of weak shock waves, by numerical integration of Euler's equations on grids that are finer towards the axis of symmetry, irregular reflection is calculated and the dimensions of Mach discs are determined for different M0 for low initial intensities of the shock waves. These results confirm the well-known assertions that the size of the Mach disc is negligibly small for a shock wave of low initial intensity. A non-linear theory is constructed and a number of features of conical flows and related proofs of the impossibility of regular reflection of stationary shock waves of any initial intensity from the axis of symmetry, that are of independent interest, are considered, as well as the supersonic flow at the trailing edges of solids of revolution with finite vertex angles.

Effects of Variable Thermal Conductivity and Chemical Reaction on Steady Mixed Convection Boundary Layer Flow with Heat and Mass Transfer Inside a Cone due to a Point Sink

The steady incompressible mixed convection boundary layer flow with variable fluid properties and mass transfer inside a cone due to a point sink at the vertex of the cone have been investigated. The fluid viscosity and thermal conductivity have been assumed to be temperature dependent. The governing fluid flow equations with boundary conditions have been transformed into set of coupled ordinary differential equations with the help of similarity transformations and solved Runge-Kutta method with shooting technique. The effects of Schmidt number, variable thermal conductivity parameter, mixed convection parameter, buoyancy parameter and chemical reaction parameter on velocity distribution, temperature distribution, concentration distribution, heat transfer rate and coefficient of skinfriction have been investigated. It is observed that concentration decreases with increasing Schmidt number and temperature increases with increasing values of thermal conductivity parameter. Also with increasing values of mixed convection parameter, velocity, temperature and concentration decreases. The present study is relevant in conical nozzle and diffuser flow problems exist in petroleum and chemical industries.

Structure of supersonic inviscid nonsymmetric conical flow around a V-wing

The shock wave structure of flow around a V-wing and its properties determining the conical flow topology are numerically investigated within the framework of the inviscid gas model on a wide range of the angles of attack and yaw when in the disturbed supersonic flow either nonsymmetric Mach interaction between the shocks attached to the leading edges of the wing or a shockless flow in the compressed layer on the windward cantilever is realized. The subranges of the angles of attack and yaw with the disturbed flow properties characteristic of the wing of the given geometry are determined. It is found that at high angles of attack, when the branching point of the bow shock beneath the leeward cantilever generates an intense contact discontinuity, the structure of the conical flow in the shock layer on the windward cantilever involves a singularity of a new type which can be characterized as a “vortical” Ferri singularity. It is located above the point of convergence of the streamlines proceeding from the leading edges of the wing, at the vertex of the corresponding contact discontinuity. Flow patterns with the point of convergence of the streamlines proceeding from the leading edges located in the elliptical flow region, which is placed at a local maximum of the pressure distribution over the surface are also found. The range of the angles of attack and yaw on which this new property of supersonic conical flows is realized in the presence of a branched shock system is determined.

Gas Origin in the Extended Narrow Line Region of Nearby Seyfert Galaxies

The Extended Narrow Line Region (ENLR) of Active Galactic Nuclei (AGN) is a conical or bi-conical region of highly ionized gas with a size of few up to 15–20 kpc and the apexes pointing towards the active nucleus. This region is also called ionization cones. These cones are an evidence of the Unified Model (Antonucci 1993) that predicts an anisotropic escape of ionizing photons from the nucleus confined in a conical flow by a dusty torus. Many details about the complex structure of the ENLR still remains unveiled. For example it is not clear which is the origin of the ionized gas. This is an important issue, being related to the fuelling of the active nucleus. The gas could be simply part of the interstellar medium of the host galaxy, ionized by the active nucleus or by shocks; or it could be intergalactic medium acquired by the surroundings of the host galaxy through gravitational interactions. Up to now only 25 Seyfert 2 galaxies with ionization cones are known and studied. The lack of cones in Seyfert 2 galaxies could be a selection effect, or it could be due to the absence of gas distributed over large scales in the host galaxy, but it can also indicate that some particular initial conditions are needed in order to form an ENLR. In this work we tackle the question of the origin of the gas, by combining the information obtained from IFU, longslit and echelle spectra. Being the IFU field of view typically small, in order to correctly interpret the spectroscopic results we analyse also broad band images. We reduced and analyzed the collected data from our observational campaign of nearby Seyfert galaxies. IFU spectra were taken with MPFS at SAO 6-mt telescope, longslit spectra with AFOSC at the 1.8-mt telescope of Asiago Astrophysical Observatory and the echelle spectra with MagE at 6.5-mt Magellan telescope. The broad band images were taken with SCORPIO at SAO 6-mt telescope and from the ING archive. This work is based on: (i) analysis of gas physical properties (density, temperature and metallicity), (ii) analysis of emission lines ratios, (iii) study of gas and stars kinematics, (iv) morphological analysis. We applied this method to two Seyfert galaxies showing extended [O III] emission, NGC 7212, a Seyfert 2 galaxy and MRK 6 a Seyfert 1.5 galaxy. We obtained strong proof of an external origin for the ionized gas in both cases. This is more likely to occur in NGC 7212 because it is in a strongly interacting system, however also in MRK 6 we found hints of a past merger. We took advantage of integral field data which allow to spatially sample the ENLR in 1×1 emission line sub-regions and we selected 12 Seyfert 2 galaxies to perform a statistical study of spectroscopic properties of a large number of these regions. From the analysis of about 850 sub-regions we pointed out that most of them share the properties generally observed in the NLR of Seyfert galaxies. All these results strongly suggest that particular initial conditions are mandatory in order to generate a kpc-size NLR.

貫流を伴う内壁が回転する凹型，凸型，円錐型環状流路内流れの2次元PTV計測

貫流を伴う内壁が回転する凹型，凸型，円錐型環状流路内流れの2次元PTV計測

Properties of the transsonic reverse stream of the turbulent-boundary-layer separation zone in supersonic conical flows

Properties of the transsonic reverse stream of the turbulent-boundary-layer separation zone in supersonic conical flows

Heat and fluid flow in cylindrical and conical annular flow-passages with through flow and inner-wall rotation

The flow and heat transfer in cylindrical and conical annular flow-passages with through flow and inner-wall rotation have been numerically simulated by using the large eddy simulation with a Lagrangian dynamic subgrid-scale model. Inlet through-flow Reynolds number was 1000 and the Taylor number was set at 0, 1000, 2000, and 4000. In the conical flow passage, when the inner-wall rotation speed was increased, at first spiral vortices in the downstream region and then much more complicated vortices appeared. The vortices for Ta = 4000 changed the structure in both through-flow and wall-normal directions in the downstream half of the passage. The flow structure and heat transfer of the conical case were completely different from those of the cylindrical case. It was because of the three factors: the expansion of the flow passage, the rotation radius change in the through-flow direction, and the centrifugally driven through-flow. The last factor is due to the acute angle between the centrifugal and through-flow directions.

EVIDENCE FOR GENTLY SLOPING PLASMA DENSITY PROFILES IN THE DEEP CORONA: TYPE III OBSERVATIONS

Type III radio bursts are produced near the local electron plasma frequency fp and near its harmonic 2fp by fast electrons ejected from the solar active regions and moving through the corona and solar wind. The coronal bursts have dynamic spectra with frequency rapidly falling with time, the typical duration being about 1-3 s. In the present paper, 37 well-defined coronal type III radio bursts (25-450 MHz) are analyzed. The results obtained substantiate an earlier statement that the dependence of the central frequency of the emission on time can be fitted to a power-law model, f(t) ∝ (t – t 0)–α, where α can be as low as 1. In the case of negligible plasma acceleration and conical flow, it means that the electron number density within about 1 solar radius above the photosphere will decrease as r –2, like in the solar wind. For the data set chosen, the index α varies in the range from 0.2 to 7 or bigger, with mean and median values of 1.2 and 0.5, respectively. A surprisingly large fraction of events, 84%, have α ≤ 1.2. These results provide strong evidence that in the type III source regions the electron number density scales as n(r) ∝ (r – r 0)–β, with minimum, mean, and median β = 2α of 0.4, 2.4, and 1.0, respectively. Hence, the typical density profiles are more gently sloping than those given by existing empirical coronal models. Several events are found with a wind-like dependence of burst frequency on time. Smaller power-law indices could result from the effects of non-conical geometry of the plasma flow tubes, deceleration of coronal plasma, and/or the curvature of the magnetic field lines. The last effect is shown to be too weak to explain such low power-law indices. A strong tendency is found for bursts from the same group to have similar power-law indices, thereby favoring the hypothesis that they are usually produced by the same source region.

New type of existence of the turbulent boundary-layer separation in shock layers of conical flows

New type of existence of the turbulent boundary-layer separation in shock layers of conical flows