Blunt Cone Research Articles

On the Use of High-Order Accurate Solutions of PNS Schemes as Basic Flows for Stability Analysis of Hypersonic Axisymmetric Flows

Abstract High-order accurate solutions of parabolized Navier–Stokes (PNS) schemes are used as basic flow models for stability analysis of hypersonic axisymmetric flows over blunt and sharp cones at Mach 8. Both the PNS and the globally iterated PNS (IPNS) schemes are utilized. The IPNS scheme can provide the basic flow field and stability results comparable with those of the thin-layer Navier–Stokes (TLNS) scheme. As a result, using the fourth-order compact IPNS scheme, a high-order accurate basic flow model suitable for stability analysis and transition prediction can be efficiently provided. The numerical solution of the PNS equations is based on an implicit algorithm with a shock fitting procedure in which the basic flow variables and their first and second derivatives required for the stability calculations are automatically obtained with the fourth-order accuracy. In addition, consistent with the solution of the basic flow, a fourth-order compact finite-difference scheme, which does not need higher derivatives of the basic flow, is efficiently implemented to solve the parallel-flow linear stability equations in intrinsic orthogonal coordinates. A sensitivity analysis is also conducted to evaluate the effects of numerical dissipation and grid size and also accuracy of computing the basic flow derivatives on the stability results. The present results demonstrate the efficiency and accuracy of using high-order compact solutions of the PNS schemes as basic flow models for stability and transition prediction in hypersonic flows. Moreover, indications are that high-order compact methods used for basic-flow computations are sensitive to the grid size and especially the numerical dissipation terms, and therefore, more careful attention must be kept to obtain an accurate solution of the stability and transition results.

Stability analysis and transition prediction of hypersonic boundary layer over a blunt cone with small nose bluntness at zero angle of attack

Stability and transition prediction of hypersonic boundary layer on a blunt cone with small nose bluntness at zero angle of attack was investigated. The nose radius of the cone is 0.5 mm; the cone half-angle is 5°, and the Mach number of the oncoming flow is 6. The base flow of the blunt cone was obtained by direct numerical simulation. The linear stability theory was applied for the analysis of the first mode and the second mode unstable waves under both isothermal and adiabatic wall condition, and eN method was used for the prediction of transition location. The N factor was tentatively taken as 10, as no experimentally confirmed value was available. It is found that the wall temperature condition has a great effect on the transition location. For adiabatic wall, transition would take place more rearward than those for isothermal wall. And despite that for high Mach number flows, the maximum amplification rate of the second mode wave is far bigger than the maximum amplification rate of the first mode wave, the transition location of the boundary layer with adiabatic wall is controlled by the growth of first mode unstable waves. The methods employed in this paper are expected to be also applicable to the transition prediction for the three dimensional boundary layers on cones with angle of attack.

Experimental investigation of drag reduction by forward facing high speed gas jet for a large angle blunt cone at Mach 8

Substantial aerodynamic drag, while flying at hypersonic Mach number, due to the presence of strong standing shock wave ahead of a large-angle bluntcone configuration, is a matter of great design concern. Preliminary experimental results for the drag reduction by a forward-facing supersonic air jet for a 60° apexangle blunt cone at a flow Mach number of 8 are presented in this paper. The measurements are carried out using an accelerometer-based balance system in the hypersonic shock tunnel HST2 of the Indian Institute of Science, Bangalore. About 29% reduction in the drag coefficient has been observed with the injection of a supersonic gas jet.

Disappearance of holographic and interference fringes accompanies optical diagnostics of a supersonic bow shock flow

Preliminary results of optical diagnostics of bow shocks in a supersonic wind tunnel by applying dual-hologram shear interferometry technique are discussed. A strong refraction effect of the probing beam penetrating a region in the vicinity of a bow shock over a blunt nose cone model has been discovered. On a signal hologram the effect leads to the disappearance of holographic fringes in a narrow region attached to the shock wave front. A reconstructed interferogram in this region manifests the absence of an interference pattern. Computer simulations were performed for a part of the probing beam penetrating the area of high-density steep gradients of compressed air attached to the central part of the shock front of a bow shock. The compressed area was modeled as a hyperbolic cap. The bow shock was assumed axisymmetric. The simulations made it possible to evaluate angles of deflections and found conformity with reconstructed interferograms (shadowgraphs). It is concluded that in the above-indicated region of bow shocks probing light is deviated refractively into some angles, which could be large enough for light rays to be blocked out and never arrive at the detector (photo film). In the case when interferometric fringes disappear, the effect of strong refraction makes it impossible to measure air density gradients in some critical region.

Investigation of aerodynamic characteristics of a hypersonic flow around bodies of revolution with a permeable tip

Results of experimental investigations of aerodynamic characteristics of models of high-velocity flying vehicles consisting of a combination of a blunt cone, a cylinder, and a conical tail fin are presented. The model forebody is cooled by porous blowing. The choice of such a configuration is determined by the necessity of optimizing the arrangement of high-velocity flying vehicles on the launcher and their aerodynamic characteristics under conditions of intense surface mass transfer (decrease in drag and heat transfer and increase in static and dynamic stability).

Effect of concentrated energy deposition on the aerodynamic drag of a blunt body in hypersonic flow

Experimental results on the effect of energy deposition using an electric arc discharge, upstream of a 60° half angle blunt cone configuration in a hypersonic flow stream is reported. Investigations involving drag measurements and high speed Schlieren flow visualization have been carried out in a hypersonic shock tunnel using air and argon as the test gases; and an unsteady drag reduction of about 50% (maximum reduction) has been observed in the energy deposition experiments done in argon environment. These studies also show that the effect of discharge on the flow field is more pronounced in argon environment as compared to air, which confirms that thermal effects are mainly responsible for flow alteration with discharge. It has also been observed that the interaction of the hypersonic flow with the discharge filament results in the development of an unsteady flow field.

Study of the aerodynamic stability of a blunt cone with a side flap in a hypersonic flow

The stationary and time-dependent aerodynamic coefficients of a slender blunt cone with a flap located near the base section of the model are experimentally investigated. The freestream parameters (M∞ = 6, Re L = 0.88 × 107, and γ = 1.4) ensured a turbulent regime of flow over the conical surface and the flap. At high angles of attack (α ∼ 10°) laminar-turbulent transition is observable in the separation zone on the leeward side of the body. Emphasis is placed on the determination of the trimming angles of attack for different positions of the center of rotation and the static and dynamic stability coefficients (the model oscillation damping coefficient).

Variation of the temperature factor of models on a ballistic range

A technique for variation of the temperature factor of free-flight models by varying their initial temperature is described. An experiment on a ballistic range is carried out with a free-flying supersonic blunt cone with a half-angle of 15° at a Mach number of 2.3. The flow at the cone base is studied in the transition range (from the laminar to turbulent flow) of Reynolds numbers. The base flow pattern is determined from the shadowgraphs of the flow about the models. The drag coefficient of the blunt cone at a zero angle of attack is found by processing trajectory data. It is found that the near wake geometries and the drag coefficients of the models tested at the laboratory temperature and a temperature of 120 K differ. Explanations of this effect are given.

Study of the aerodynamic stability of a blunt cone with a side flap in a hypersonic flow

Study of the aerodynamic stability of a blunt cone with a side flap in a hypersonic flow

Projectile Nosetip Thermal Management for Railgun Launch to Space

A major issue in achieving direct launch to space using electromagnetic railguns from the surface of the earth is that we are at the bottom of a gravity well, requiring very high launch velocities to achieve orbit insertion. The atmosphere is most dense at the earth's surface-this, combined with high velocity, leads to very stressing thermal conditions for the launch aerobody. To minimize aerodynamic losses, a typical hypersonic flight body is a blunt slender cone. The thermal loads are greatest on the nosetip of this cone, and for small bodies (<10 kg) the thermal loads may exceed the capabilities of present passive thermal protection systems, such as dense, ablative carbon phenolics. Even for launch from a high-altitude airborne platform, aerothermal loads can be considerable unless rocket assist is provided. This paper discusses aspects of the launch package and characteristics of the railgun needed to achieve orbit insertion velocities

Counterflow drag reduction by supersonic jet for a blunt body in hypersonic flow

Counterflow drag reduction by supersonic jet for a large angle blunt cone at hypersonic Mach number is investigated in a shock tunnel. The flowfields around the test model in the hypersonic flow with an opposing supersonic jet emanating from the stagnation point of the model are visualized by high speed schlieren technique. The aerodynamic drag force is measured using the accelerometer based force balance system. The experimental measurements show about 30%–45% reduction in drag coefficient for different jet pressures.

Simultaneous measurement of aerodynamic and heat transfer data for large angle blunt cones in hypersonic shock tunnel

Aerodynamic forces and fore-body convective surface heat transfer rates over a 60° apex-angle blunt cone have been simultaneously measured at a nominal Mach number of 5.75 in the hypersonic shock tunnel HST2. An aluminum model incorporating a three-component accelerometer-based balance system for measuring the aerodynamic forces and an array of platinum thin-film gauges deposited on thermally insulating backing material flush mounted on the model surface is used for convective surface heat transfer measurement in the investigations. The measured value of the drag coefficient varies by about ± 6% from the theoretically estimated value based on the modified Newtonian theory, while the axi-symmetric Navier-Stokes computations overpredict the drag coefficient by about 9%. The normalized values of measured heat transfer rates at 0‡ angle of attack are about 11% higher than the theoretically estimated values. The aerodynamic and the heat transfer data presented here are very valuable for the validation of CFD codes used for the numerical computation of flow fields around hypersonic vehicles.

Modeling of Shock Tunnel Aeroheating Data on the Mars Science Laboratory Aeroshell

A series of shots are run in the T5 shock tunnel at California Institute of Technology to measure heating levels on a 70 blunt cone at angle of attack in an environment representative of the Mars Science Laboratory entry. Twenty shots are obtained in CO 2 over a range of enthalpies and pressures chosen to span the laminar and turbulent flow regimes. The data indicate that the lee side turbulent heating augmentation predicted by flight simulations is valid and must be accounted for during the design of the thermal protection system. Computational fluid dynamic simulations are generally in good agreement with the laminar data when employing a supercatalytic wall model, whereas turbulent simulations are in reasonable agreement when a noncatalytic wall model is used. The reasons for this discrepancy are unknown at this time. The turbulent heating augmentation is shown to be inversely related to freestream enthalpy. Changes in angle of attack between 11 and 16 are shown to have minimal impact on measured and computed heating. A transition criterion based on momentum thickness Reynolds number, analogous to that used in flight predictions, predicts onset with reasonable accuracy, although transition is observed to occur later than the current design criterion indicates.

Calibration parameters for the probing tip of a magnetic force microscope in the field of a test current loop

The subject of discussion is calibration of the tip of a magnetic force microscope using the field of a ring-shaped current loop. To calculate the calibration parameters, the magnetic contribution from the extended tip of the probe in the field of the current loop to the rigidity of the cantilever is approximated by the contribution from a point magnetic dipole and magnetic “charge” in terms of the theoretical model adopted. Three simplified models of the conic tip (with a sharpened, blunted, and rounded top) are considered. The calculated dependences of the effective calibration parameters on the radius of the current loop are compared with experimental data. It is found that the model of a uniformly magnetized tip in the form of a blunted cone provides the best fit to the experiment. The calculation results may be helpful in simulating images obtained with a magnetic force microscope and numerically testing magnetic objects.

The P1 and P2 approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere

The spherical harmonics method in the P1 and P2 approximations is used to analyze radiative heat transfer for a space vehicle entering a planet’s atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle’s flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of −5°.

Modeling of High-Speed Penetration Into Concrete Shields and Shape Optimization of Impactors#

We modified the model of Forrestal and Tzou (1997) for a case of an arbitrary impactor having a shape of a body of revolution with a plane bluntness and derived a formula for the depth of penetration (DOP) into semi-infinite concrete shield. The shape of the impactor that attains the maximum DOP for a given impact velocity is found through analytical investigation of a corresponding non-classical variational problem when the criterion of optimization is a function of integral functionals of the unknown solution. It is shown that the optimum shape is close to a blunt cone. The influence of the penetration model parameters on the optimum solution is studied. #Communicated by N. Banichuk.

Boundary-layer receptivity of Mach 7.99 flow over a blunt cone to free-stream acoustic waves

The receptivity phenomenon, which is the process of environmental disturbances initially entering the boundary layers and generating disturbance waves, is one of the important but not well understood mechanisms involving laminar–turbulent transition of hypersonic flows. This paper presents a numerical simulation study of the receptivity to weak free-stream fast acoustic waves for a Mach 7.99 axisymmetric flow over a half-angle blunt cone. In hypersonic boundary-layer flow over a blunt cone, the process of receptivity to free-stream disturbances is altered considerably by the presence of a bow shock and an entropy layer. In the present study, both steady and unsteady flow solutions are obtained by computing the full Navier–Stokes equations with a fifth-order shock-fitting finite-difference scheme, which is able to account for the effects of bow-shock/free-stream-disturbance interaction accurately. The current numerical results for the steady base flow are compared with previous experimental and numerical results. In addition, a normal-mode linear stability analysis is used to identify the main components of boundary-layer disturbances generated by forcing free-stream fast acoustic waves. It is found that neither the first mode nor the second-mode instability waves are excited by free-stream fast acoustic waves in the early region along the cone surface, although the Mack modes can be unstable there. Instead, the second mode is excited downstream of the second-mode Branch I neutral stability point. The delay of the second-mode excitation is because the hypersonic boundary-layer receptivity is governed by a two-step resonant interaction process: (i) resonant interactions between the forcing waves and a stable boundary-layer wave mode I near the leading-edge region; and (ii) resonant interactions between the induced stable mode I and the unstable second Mack mode downstream. The same receptivity mechanism also explains the results that no first Mack mode components are generated by the current receptivity process because there is no resonant interaction between fast acoustic waves and the first Mack mode.

Simulation models of click production in dolphins

The simulation model (SM) of dolphin click source originally presented by [Dubrovskiy and Giro, ‘‘Echolocation in Bats & Dolphins,’’ Chap. 10, 59–63 (2003)] was further developed by Gladilin, Dubrovskiy, Mohl, and Walberg, Acoust. Phys. 50, 463‐468 (2004). The SM describes movements of a solid sphere frozen in a compliant ring. A jet of air in a duct connecting air cavities brings the sphere into self‐oscillations. The SM allows calculating the waveform and sound pressure of the generated clicks. Here the mathematical and simulation model (MSM) of click production in dolphins is further developed. The MSM describes radiation of clicks by bodies comprising of waterlike tissue with different shapes (a ring, a blunted cone) pulsating and (or) oscillating under action of muscles tension. Calculations are made for the energy efficient case when acting force is consecutively applied not to the entire body but to its thin layer, which resulted in action of the progressing wave array. Directivity patterns of such a waterlike compliant body in main directions are similar to that of a rigid body with the same shape and dimensions. Comparisons are made of MSM predictions with properties of an actual radiation field of dolphins (in clicks wave forms, sound pressure levels, and directivity patterns) and dimensions of biological structures supposedly responsible for click production in dolphins.

Magnetohydrodynamic control of supersonic flow past bodies: Possibilities and undesirable effects

Basic problems of super-and hypersonic magnetohydrodynamics (MHD) associated with the determination of the integral characteristics of bodies and vehicles inside which there are systems generating a uniform magnetic field are considered. Three classes of flows, namely, flow in a hypersonic multimode fixed-geometry air-intake; internal and external flow in a model of a hypersonic vehicle containing an air-intake with an MHD generator, a combustion chamber, and a supersonic nozzle; and hypersonic flow past a blunt cone are studied using numerical simulation and theoretical analysis (on the basis of the complete averaged system of Navier-Stokes equations and the electrodynamic equations). Attention is concentrated on the presence of an additionalmagnetic force acting on the system generating themagnetic field and, consequently, on the body and initiating an additional drag (in the case of a vehicle-reducing its thrust). Attractive possibilities for MHD flow control, namely, an increase in the degree of flow compression in the air-intake, a reduction in the ignition length in the combustion chamber, and a decrease in the heat flux to the nose of the body, are noted, as well as negative effects associated with the action of the magnetic force on the bodies considered.

First description of an Arctic Loricifera – a new Rugiloricus-species from the Laptev Sea

This is the first discription of Loricifera-species from the Arctic Ocean. Rugiloricus polaris sp. n. was discovered along with other species of the genus in samples from the Laptev Sea (Arctica). The new species is described from clayish deep-sea bottoms at 1,210 m depth. Apart from of a single adult male two Higgins-larvae have been found. The adult of Rugiloricus polaris sp. n. is characterized e.g. by its small rounded distally blunt mouth cone; four small oral valves around the terminal mouth opening; broad clavoscalids with round bases and ventral jags distally; strongly transformed and spiny ventral pair of clavoscalids; type B scalids of fourth row with serrated claw-tips; two types of trichoscalids differing in length but not in structure. The Higgins-larvae differ from others e.g. by hook-like type B scalids with double hook-tips; extremely short toes; long anterior setae with fine setules scattered along their dorsal and ventral margins.