Cone In Supersonic Flow Research Articles

Numerical study of freestream turbulence effects on the nose cones in supersonic flow

PurposeThis paper aims to numerically investigate the influence of shock wave and freestream turbulence interaction on the parabolic and spherically blunted nose cones at supersonic speed.Design/methodology/approachUsing density-based solver, the three-dimensional steady-state simulation is carried out. The working fluid is calorically perfect that obeys ideal gas law and the no-slip boundary conditionis given to the surface of the nose cone. Pressure far-field boundary condition is imposed at the boundary of the computational domain by giving freestream Mach number, freestream static pressure and temperature.FindingsThe growth rate of the boundary layer is faster on the spherically blunted nose cone, hence, the overall drag force is higher than the parabolic nose cone. Temperature at the edge of the boundary layer is increased due to the early ampli-fication of instabilities by the upstream disturbance. In this sense, the effects of freestream turbulence depend on its level, freestream conditions, strength and type of shock wave and zone of influence.Research limitations/implicationsSimulations are carried out for the flow Mach number 2.0 at zero angles of attack for the freestream conditions of the flow at an altitude of 10,000 m.Practical implicationsThe phenomenon of shock wave–turbulence interaction occurs in flow regimes from transonic to hypersonic speeds and finds a wide range of applications, especially in the design of aircraft and missiles configurations.Originality/valueThe phenomenon of compression wave and freestream turbulence interaction around the commonly used nose cones in the case of aircraft, missiles, etc., is investigated. The performance characteristics such as aerodynamic drag, boundary layer dynamics and the nature of flow around the different nose cones at zero angle of attack are illustrated.

Processing and visualization of the results of parametric numerical calculations

In modern problems of mathematical modeling in computational gas dynamics, it is increasingly necessary to implement parametric studies. In these cases, the key factors of the problem under consideration vary with the chosen step within the given ranges. Calculations of this kind can be effectively carried out by constructing a generalized computational experiment. A generalized computational experiment is a computational technology that combines the solution of mathematical modeling problems, parallel technologies, and visual analytics technologies. The results of a generalized computational experiment are multidimensional arrays, where the dimension of the arrays corresponds to the number of key factors. Processing and visual presentation of such arrays requires solving a number of separate tasks. The processing and visual presentation of the results are carried out for target functionals represented as a function of many variables. The report presents an examples of solving specific processing and visualization problems based on the implemented generalized computational experiment for 3D cone in supersonic flow.

Design and analysis of a Ventral Diverterless Supersonic Inlet

The diverterless supersonic inlet (DSI) has the advantages of good stealth performance and light structure weight. In this paper, the Bump surface is designed based on the flow field obtained by Taylor-Maccoll equation solving the supersonic conical flow, and a ventral diverterless supersonic inlet is given by the method. Numerical simulation is used to study the mechanism of the Bump surface for diverting the boundary layer. Results indicates: (1) the lateral pressure gradient created by the shock wave at the leading edge of the Bump surface is the main reason of pushing the boundary layer away; (2) the total pressure loss due to the shock wave will be small for better combination of the Bump surface and the lip; (3) it is necessary to design the duct of the DSI inlet with refinement to achieve low distortion.

Compressible Euler equations on a sphere and elliptic–hyperbolic property

Abstract In this work, we systematically derive the governing equations of supersonic conical flow by projecting the 3D Euler equations onto the unit sphere. These equations result from taking the assumption of conical invariance on the 3D flow field. Under this assumption, the compressible Euler equations reduce to a system defined on the surface of the unit sphere. This compressible flow problem has been successfully used to study the steady supersonic flow past cones of arbitrary cross section by reducing the number of spatial dimensions from three down to two while still capturing many of the relevant 3D effects. In this paper, the powerful machinery of tensor calculus is utilized to avoid reference to any particular coordinate system. With the flexibility to use any coordinate system on the surface of a sphere, the equations can be more readily solved numerically when a structured mesh is used by defining the mesh lines to be the coordinate lines. The type of the system of partial differential equations would be hyperbolic or elliptic based on whether the crossflow Mach number is supersonic or subsonic.

Computational study of the cavity flow over sharp nose cone in supersonic flow

Heat and drag reduction on the nose cone is a significant issue for increasing the speed of the supersonic vehicles. In this paper, computational fluid dynamic method is applied to investigate the thermal and drag coefficient on the sharp nose cone with different cavity shapes. In order to simulate our model, the CFD method with SST turbulence model is applied to study the flow feature and temperature distribution in the vicinity of the nose body. The effect of depth and length of the cavity on the thermal characteristic of the nose cone is comprehensively investigated. In addition, the influence of the number of the cavity in the thermal performance of the main body is studied. According to our results, increasing the length of the cavity highly efficient for the reduction of the drag at Mach = 3. As the Mach number is increased to 3, the number of the cavity becomes a significant role and it is observed that case 9 with four cavities is more efficient. Obtained results also show that increasing the cavity depth declines the temperature on the main body. Our findings confirm that the main source of the expansion is the edge of the cavity.

Criteria of existence of Ferry vortex singularities in supersonic conical flows in the absence of branch points of shock waves

Based on the results of a numerical study of the control of the flow structure near a diamond-shaped wing with conical conjugation consoles for sliding flow in regimes with supersonic leading edges, criteria are determined for the existence of Ferry vortex singularities in the absence of branch points of the head and internal shock waves.

Conditions of the existence of vortex Ferri singularities in supersonic conical flows

The parameters determining the properties of the branching points on shock waves in conical flows and responsible for the existence of inviscid vortex structures in shock layers are established. The quantitative data for these parameters corresponding to the generation of the vortex Ferri singularities are presented. They are based on the results of an analysis of the numerical calculations of inviscid flow around V-wings of different geometries at the Mach numbers from the 3 ≤ M ≤ 10 range with the bow shock corresponding to the Mach-type interaction between the shocks attached to the leading edges. It is shown that at about M ≤ 2.35 the vortex structures no longer exist in the shock layers of conical flows. It is established that in the particular flow regimes characterized by regular-to-Mach-type transition of the pattern of interaction between the shocks attached to the leading edges an increase of the “blow-up” type in the shock layer thickness can be observable. The experimental data confirm the existence of the vortex Ferri singularities at the corresponding values of the relevant parameters.

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

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.

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

Submerged shocks in conical gas flows in the presence of a mach shock-wave configuration

The results of a numerical study of a new type of singularities in the Mach shock-wave structure realized in supersonic nonsymmetric conical flows over V-wings with a bow shock attached to the leading edges are presented. Within the framework of the ideal gas model we study the changes in the shock system on transition, with increase in the sweep angle, from the region of nonsymmetric Mach interaction of the shocks attached to the leading edges of the wing to the region of special flow patterns, where on the windward cantilever surface a rarefaction flow is realized rather than a flow with an internal shock. It is shown, in particular, that in the region with special wing flow patterns a Mach system of shocks with a submerged shock proceeding from the branch point above the windward cantilever may exist.

Aerodynamic Heating of a Thin Sharp-Nose Circular Cone in Supersonic Flow

The assumption of flow symmetry is made to investigate a supersonic flow (M∞ = 5) past a thin circular cone with a half-angle θ c = 4° and an isothermal surface (T w0 = 0.5) by way of numerical integration of unsteady-state three-dimensional Navier-Stokes and Reynolds equations. The calculations are performed in a discrete range of variation of the Reynolds number (104 ≤ Re ≤ 108) and angle of attack (0° ≤ α ≤ 15°). The effect of the determining parameters of the problem on the structure of flow field and on aerodynamic heating of the body surface subjected to flow is demonstrated.

Conical flow breakdown in non-free shock-wave/boundary-layer interaction

The non-free interaction between a shock wave and the boundary layer on a swept plate set at incidence in the undisturbed flow is studied using different experimental methods including special laser techniques for visualizing supersonic conical gas flows. It is shown that under shock-layer conditions the non-free interaction can lead to conical flow breakdown before the incident shock reaches the leading edge of the plate.

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved.

Supersonic axisymmetric conical flow solutions for different ratios of specific heats

Supersonic axisymmetric conical flow solutions for different ratios of specific heats

Vortical Solutions in Supersonic Corner Flows

Vortical solutions are investigated for inviscid supersonic steady flows, described by the steady-state Euler equations, that occur in the corner region generated by two orthogonal ramps. Complex shock interactions appear, with the formation of a vorticity field in the corner region and the vorticity itself converging into spiral singularities. Symmetric or asymmetric flow configurations are generated within symmetric corners. The investigation is carried out by a numerical technique based on a space-marching procedure with a finite volume approximation. The integration of the conservation laws allows for the correct numerical capturing of shocks and contact surfaces. A flux-differenc e-splitting procedure is used for the calculation of the fluxes on the side walls of the volumes, based on the hyperbolicity of the Euler equations for steady supersonic regimes. A high-order accuracy scheme is introduced founded on the essentially nonoscillatory (ENO) scheme. Numerical results are presented and discussed with reference to similar problems investigated by other authors. HIS paper analyzes inviscid, supersonic conical corner flows generated by two intersecting wedges. Such config- urations are typical of supersonic inlet flows and are similar to one of the four corners of the box-type inlets. The corner flows are conical if the two intersecting walls are plane. Then all flow variables (pressure, velocity, and entropy) will be independent of the spherical radial coordinate centered at the origin of the corner flow, and these flows will depend only on two space dimensions. Moreover, the topology of a conical flow is characterized by its conical or crossflow streamlines (the projections of the three-dimensional streamlines onto a spherical surface centered at the origin of the flow). Two possible shock configurations could be generated by the intersection of two compressive wedges. One is character- ized by a regular reflection and the other by the presence of a Mach disk (irregular reflection) at the intersection of the two- dimensional shocks produced by each wedge; Such possibili- ties have been investigated for a symmetrical geometry (two wedges of equal deflection), and the regular reflection shock configuration has been predicted using linearized theory.1 The Mach disk configuration has been detected experimentally2 and in the numerical solutions of the Euler equations using a shock-capturing approach3 and a shock-fitting approach.4 Figure 1 from Ref. 4 shows in the range of wall deflections (6) and upstream conditions (Mo,) where the regular or the Mach disk configuration is expected to occur. Note that, for deflec- tions above 5 deg, the only possible solution is- the Mach disk shock configuration. Contact surfaces are generated at points where shocks interact because of the different entropies pro- duced by the wave systems on either side of the interaction. However, in the present case of symmetrical geometry and for regular interaction, the strength of the contact surface van- ishes. Conversely, in the cases of irregular reflection, two symmetric contact surfaces are generated at the two triple points that bound the Mach disk. For moderate values of upstream Mach number and deflection, the two contact sur- faces converge on the corner. According to the results of the present study, when the Mach number or the deflection in- creases, the configuration may drastically change.

Numerical Simulations of Supersonic Flow with Dissociation and Recombination.

We performed numerical simulations of supersonic conical nozzle flows and supersonic flow past wedge-shaped test pieces. We used the point-implicit MacCormac scheme to solve the governing equations. Chemical source terms were calculated using the Park model. The equation of Millikan was used to calculate relaxation time of vibrational energy of diatomic molecules. We consider two reservoir conditions : design and experimental. From these numerical simulations, the following conclusions are obtained. (1) Due to the effect of the boundary layer in the nozzle flow, the Mach number at the exit becomes smaller compared with the inviscid one-dimensional result. (2) The flow field can be considered as chemically frozen downstream from the shock wave. (3) The behavior of vibrational energy downstream from the shock wave in the experimental conditions on the ground is different from that in flight conditions at high altitude.

Experimental investigation of the interaction between convergent axisymmetric shock waves and sharp and blunt cones in supersonic flow

The interaction between convergent axisymmetric shock waves and sharp and blunt cones has been experimentally investigated in a wind tunnel at M∞=4.67. During the experiments the effect of the conicity angle of the convergent shock wave, the shape of the model and its position relative to the shock-wave configuration on the structure of the flow and the pressure distribution on the model surface was explored.

Euler flows about arbitrary cross sections using a node centered finite volume scheme

An efficient numerical scheme is presented to solve the Euler equations for both 2-D transonic and supersonic conical flows. The approach utilizes a physical space, finite volume, central difference scheme with added dissipation and a multi-stage, Runge-Kutta integrator which is applied to the crossflow plane terms of the Euler equations. The finite volume scheme is a new node centered method as opposed to a cell centered approach. A carefully scaled dissipation is added for stability and capture of shock waves. The method is applied to a variety of 2-D and conical flows illustrating both shock vorticity induced and leading edge separation.

Vectorized schemes for conical potential flow using the artificial density method

A method is developed to determine solutions to the full-potential equation for steady supersonic conical flow using the artificial density method. Various update schemes used generally for transonic potential solutions are investigated. The schemes are compared for speed and robustness. All versions of the computer code have been vectorized and are currently running on the CYBER-203 computer. The update schemes are vectorized, where possible, either fully (explicit schemes) or partially (implicit schemes). Since each version of the code differs only by the update scheme and elements other than the update scheme are completely vectorizable, comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme's performance. Results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows.