Hypersonic Mach Numbers Research Articles

Dynamic stability characterization of re-entry modules at hypersonic mach numbers

At the time of re-entry modules entering into the atmosphere from space, a small perturbation introduces dynamic oscillations on the vehicle because of their extreme traveling speed. The dynamic stability characteristics of re-entry modules at hypersonic Mach numbers is of considerable relevance to their initial design. In the present paper, the dynamic stability of blunt cone model about [Formula: see text] is examined with wide range of design parameters such as nose bluntness, semi-vertex angle and center of rotation through theoretical and experimental methods. Theoretical approximations are made over a model based on the standard Newtonian theory. Experiments are conducted at [Formula: see text] hypersonic wind tunnel at [Formula: see text] and the following trends are observed from the experimental analysis. Interestingly, the incremental higher nose bluntness, semi-vertex angle and center of rotation reduce the dynamic stability. At higher hypersonic Mach numbers [Formula: see text], dynamic stability characteristics of the re-entry module are insensitive to the free stream Mach number. However, it is observed that the dynamic stability is increased in proportion to the vibration amplitude at hypersonic speeds.

Turbulization of the Wake behind a Single Roughness Element on a Blunted Body at a Hypersonic Mach Number

Turbulization of the Wake behind a Single Roughness Element on a Blunted Body at a Hypersonic Mach Number

Pressure Fluctuations induced by a Hypersonic Turbulent Boundary Layer.

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially-developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analyzed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from the Taylor's hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The freestream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the freestream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Optimal Growth in Hypersonic Boundary Layers

The linear form of the parabolized linear stability equations is used in a variational approach to extend the previous body of results for the optimal, nonmodal disturbance growth in boundary-layer flows. This paper investigates the optimal growth characteristics in the hypersonic Mach number regime without any high-enthalpy effects. The influence of wall cooling is studied, with particular emphasis on the role of the initial disturbance location and the value of the spanwise wave number that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary-layer equations, mean flow solutions based on the full Navier–Stokes equations are used in select cases to help account for the viscous–inviscid interaction near the leading edge of the plate and for the weak shock wave emanating from that region. Using the full Navier–Stokes mean flow is shown to result in further reduction with Mach number in the magnitude of optimal growth relative to the predictions based on the self-similar approximation to the base flow.

Bow-Shock Instability and its Control in front of Hemispherical Concave Shell at Hypersonic Mach Number 7

Bow-Shock Instability and its Control in front of Hemispherical Concave Shell at Hypersonic Mach Number 7

Numerical study on aerodynamic heat of hypersonic flight

Accurate prediction of the shock wave has a significant effect on the development of space transportation vehicle or exploration missions. Taking Lobb sphere as the example, the aerodynamic heat of hypersonic flight in different Mach numbers is simulated by the finite volume method. Chemical reactions and non-equilibrium heat are taken into account in this paper, where convective flux of the space term adopts the Roe format, and discretization of the time term is achieved by backward Euler algorithm. The numerical results reveal that thick mesh can lead to accurate prediction, and the thickness of the shock wave decreases as grid number increases. Furthermore, most of kinetic energy converts into internal energy crossing the shock wave.

Dynamical separation of rigid bodies in supersonic flow

A computational investigation of the unsteady separation behavior of rigid bodies in Mach-4 flow is carried out. Two rigid bodies, a sphere and a cube, initially stationary, centroid axially aligned, are released and thereafter fly freely according to the aerodynamic forces experienced. During the separation process, the smaller cube can experience different types of movement and our principal interest here is the non-dimensional transverse velocity of it. The separation behavior is investigated for interactions between a sphere and a cube with different mass ratio and a constant initial distance between them. The qualitative separation behavior and the final transverse velocity of the small body are found to vary strongly with the mass ratio but less sensitive to the initial distance between the two bodies. At a critical mass ratio for a given distance, the smaller body transit from entrainment within the flow region bounded by the larger body’s shock to expulsion and the accumulated transverse velocity of the small body is close to maximum. This phenomenon is the so-called ‘shock-wave surfing’ phenomenon noted by Laurence & Deiterding for two spheres at hypersonic Mach numbers. Then we investigate the separation behavior of a sphere interaction with a rotary cube and with a non-rotary cube for a given mass ratio and different distance between them. The rotary is found to increase the likelihood of ‘surfing’. Only at a certain initial distance for a given mass ratio the rotary effect of cube can be neglectable.

Thermal and inertial parameters of the flow field of a scramjet engine

Heat flux and pressure were measured on the internal walls of a scramjet engine at a hypersonic Mach number of 8 in a shock tunnel. Temperature-time history was recorded on model walls using fast-response thermocouples and the wall heat flux was deduced thereon from the temperature records. Pressure was measured at the same locations as that of heat flux using high-frequency pressure transducers. The surface measurements were used to analyze the internal flow field of the engine. The heat flux measurements revealed the regions of peak heating that may require additional thermal protection during the operation; the regions being the beginning of the constant area duct and the nozzle. The pressure measurements and the pertinent analysis indicated an optimum compression at intake through shock waves with a viable flow separation in the combustion chamber. The experimental data indicated an optimum design of the engine for a possible fuelled operation in future.

Transition Analysis for the Ascent Phase of HIFiRE-1 Flight Experiment

The HIFiRE-1 flight experiment provided a valuable database for boundary-layer transition over a 7 deg half-angle, circular cone model from supersonic to hypersonic Mach numbers as well as a range of Reynolds numbers and angles of incidence. This paper reports the findings from a computational analysis of the measured in-flight transition behavior during the ascent phase. Given a nearly zero angle of attack, computations indicate that the most likely cause for transition during the flight window of 19 to 22.5 s is the amplification of second-mode instabilities in the laminar boundary layer, except in the vicinity of the cone meridian, where a roughness element was placed midway along the length of the cone. The growth of first-mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition across the aforementioned window is found to correlate with an average linear -factor, based on parabolized stability equations, of approximately 13.3. For times less than approximately 18 s into the flight, the peak amplification ratio for second-mode disturbances is too small to cause transition because of the lower Mach numbers at earlier times. Therefore, the observed transition at these times is attributed to an unknown physical mechanism that is potentially related to the step discontinuities in surface height near the changes in surface material.

Estimation of Skin Friction Drag on a Model in Hypersonic Shock Tunnel

Viscous drag on the internal surfaces of a notional scramjet engine model has been estimated through Reynolds analogy, using measured wall heat transfer rates, in a shock tunnel at a hypersonic Mach number of 8. The study has been carried out without fuel injection and at zero degree angle of incidence of the model with the freestream. The heat transfer rate measurements were carried out on the upper and lower internal surfaces of the engine employing fast response E-type thermocouples. Application of Reynolds analogy to the wall heat transfer rates yielded the skin friction coefficient, through which the viscous drag on the surfaces could be determined. The measurements predict the salient features of the flow field of the model and are a novel reference on the data to the researchers working in the area of slender-body, hypersonic aerothermodynamics.

Dynamical separation of spherical bodies in supersonic flow

AbstractAn experimental and computational investigation of the unsteady separation behaviour of two spheres in Mach-4 flow is carried out. The spherical bodies, initially contiguous, are released with negligible relative velocity and thereafter fly freely according to the aerodynamic forces experienced. In experiments performed in a supersonic Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads which are detached by the arrival of the flow. The subsequent sphere motions and unsteady flow structures are recorded using high-speed (13 kHz) focused shadowgraphy. The qualitative separation behaviour and the final lateral velocity of the smaller sphere are found to vary strongly with both the radius ratio and the initial alignment angle of the two spheres. More disparate radii and initial configurations in which the smaller sphere centre lies downstream of the larger sphere centre each increases the tendency for the smaller sphere to be entrained within the flow region bounded by the bow shock of the larger body, rather than expelled from this region. At a critical angle for a given radius ratio (or a critical radius ratio for a given angle), transition from entrainment to expulsion occurs; at this critical value, the final lateral velocity is close to maximum due to the same ‘surfing’ effect noted by Laurence & Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396–431) at hypersonic Mach numbers. A visualization-based tracking algorithm is used to provide quantitative comparisons between the experiments and high-resolution inviscid numerical simulations, with generally favourable agreement.

Measurement of yaw, pitch and side-force on a lifting model in a hypersonic shock tunnel

Yawing moment, pitching moment and side-force on a blunt, triangular, lifting model were measured in a shock tunnel using an accelerometer balance at a hypersonic Mach number of 8. The measurements were carried out at different angles of incidence of the model with the freestream. The balance was instrumented with accelerometers to sense the model acceleration in the desired directions, and was equipped with a soft suspension system such that the model had a free flight during the tests in the shock tunnel. Pressure measurements on the surfaces of the model were carried out using high frequency pressure transducers to validate the output of the force balance. The moment and force coefficients obtained through both the measurement techniques have a good agreement reciprocally. The force and moment coefficients for the test model were analytically estimated using Newtonian theory to compare with the measured coefficients. The comparison between theory and experiments has been found quite encouraging.

Measurement of Heat Transfer Rate on Backward-Facing Steps at Hypersonic Mach Number

Two backward-facing models with step heights of 2 and 3 mm are used to measure the convective surface heat transfer rates by using platinum thin-film gauges, deposited on Macor inserts. Heat transfer rates have been theoretically calculated along the flat plate portion of a model using the Eckert reference temperature method. The experimentally determined surface heat transfer rate distributions are compared with theoretical and numerical estimations. Experimental heat flux distribution over a flat plate model showed good agreement with the reference temperature method at stagnation enthalpy range of 0.8-2 MJ/kg. Theoretical analysis has been used for downstream of a backward-facing step using Gai's nondimensional analysis. It has been found from the present study that approximately 10 and 8 step heights are required for the flow to reattach for 2 and 3 mm step height backward-facing step models, respectively, at a nominal Mach number of 7.6.

Kinetic simulations of thermal escape from a single component atmosphere

The one-dimensional steady-state expansion of a monatomic gas from a spherical source in a gravity field is studied by the direct simulation Monte Carlo method. Collisions between molecules are described by the hard sphere model, the distribution of gas molecules leaving the source surface is assumed to be Maxwellian, and no heat is directly deposited in the simulation region. The flow structure and the escape rate (number flux of molecules escaping the atmosphere) are analyzed for the source Jeans parameter λ0 (ratio of the gravitational energy to thermal energy of the molecules) and Knudsen number Kn0 (ratio of the mean free path to the source radius) ranging from 0 to 15 and from 0.0001 to ∞, respectively. In the collisionless regime, flows are analyzed for λ0=0-100 and analytical equations are obtained for asymptotic values of gas parameters that are found to be non-monotonic functions of λ0. For collisional flows, simulations predict the transition in the nature of atmospheric loss from escape on a molecule-by-molecules basis, often referred to as Jeans escape, to an organized outflow, often referred to as hydrodynamic escape. It is found that the structure of the flow and the escape rate exhibit drastic changes when λ0 varies over a narrow transition range 2-3. The lower limit of this range approximately corresponds to a critical Jeans parameter equal to 2.06, which is the upper limit for isentropic, supersonic outflow of a monatomic gas from a body in a gravity field. Subcritical, λ0≤2, flows are qualitatively similar to free outgassing in the absence of gravity, resulting in hypersonic terminal Mach numbers and escape rates that are independent of λ0 in the limit of small Knudsen numbers. Supercritical, λ0≥3, flows are controlled by thermal conduction and demonstrate qualitatively different trends. The ratio of the actual escape rate to the Jeans escape rate at the source surface is found to be a non-monotonic function of Kn0 spanning the range from ∼0.01 to ∼2. At λ0≥6, the ratio of the actual escape rate to the Jeans escape rate at the exobase is found to be ∼1.4–1.7. This is unlike the predictions of the slow hydrodynamic escape model, which is based on Parker’s model for the solar wind and intended for the description of the atmospheric loss at λ0>∼10. At λ0<6, the actual escape rate can be well approximated by a modified Jeans escape rate, which accounts for non-zero gas velocity.

The hypersonic Mach number independence principle in the case of viscous flow

The hypersonic Mach number independence principle of Oswatitsch is important for hypersonic vehicle design. It explains why, above a certain flight Mach number (M∞ ≈ 4−6, depending on the body shape), some aerodynamic properties become independent of the flight Mach number. For ground test facilities this means that it is sufficient for the Mach number in the test section to be high enough, that Mach number independence exists. However, the principle was derived for calorically perfect gas and inviscid flow only. In this paper a theoretical study for blunt bodies in the case of viscous flow is presented. We provide numerical results which give insight into how attached viscous flow behaves at high Mach numbers. The flow past an axisymmetric configuration is analysed by applying a coupled Euler/second-order boundary-layer method. Wall boundaries are treated by assuming an adiabatic or radiation-adiabatic wall for laminar flow. Calorically perfect or equilibrium air is accounted for. Lift, drag, and moment coefficients, and lift-to-drag ratios are given for several combinations of flight Mach number and altitude, i.e. Reynolds number. For blunt bodies considered here, which are pressure dominated, Mach number independence occurs for the adiabatic wall, but not for the radiation-adiabatic wall assumption.

Aerodynamic and aerothermodynamic trade-off analysis of a small hypersonic flying test bed

This paper deals with the aerodynamic and aerothermodynamic trade-off analysis aiming to design a small hypersonic flying test bed with a relatively simple vehicle architecture. Such vehicle will have to be launched with a sounding rocket and shall re-enter the Earth atmosphere allowing to perform several experiments on critical re-entry technologies such as boundary-layer transition and shock–shock interaction phenomena. The flight shall be conducted at hypersonic Mach number, in the range 6–8 at moderate angles of attack. In the paper some design analyses are shown as, for example, the longitudinal and lateral-directional stability analysis. A preliminary optimization of the configuration has been also done to improve the aerodynamic performance and stability of the vehicle. Several design results, based both on engineering approach and computational fluid dynamics, are reported and discussed in the paper. The aerodynamic model of vehicle is also provided.

Numerical Study on Heat Reduction of Various Counterflowing Jets over Highly Blunt Cone in Hypersonic Flow

In this paper, the effectiveness of counterflowing jets as heat-reduction devices for large-angle blunt cones flying at hypersonic Mach numbers is numerically simulated with various coolant jets. Different jet conditions have been chosen to investigate the effect of the counterflow jet on the surrounding flow field of nose cone. The compressible, unsteady, axisymmetric Navier-Stokes equations are solved with SST turbulence model for free stream Mach number of 5.75 at 0° angle of attack with and without gas injection. The coolant gas (air, Carbon Dioxide, and helium) is chosen to inject into the hypersonic flow at the nose of the model. The numerical results presented the surface heat reduction for different coolant jets. According to the investigation of various conditions of opposing jets, important phenomena of flow field and some effective jet conditions are found.

Experimental Investigation of the Effects of Aerospike Geometry on Aerodynamic Drag and Heat Transfer Rates for a Blunt Body Configuration at Hypersonic Mach Numbers

The effects of aerospike geometry on the drag reduction and heat transfer rates for a large-angle blunt cone flying at hypersonic Mach numbers are investigated in a hypersonic shock tunnel. Two spike geometries are considered. The first is a plain spike with a conical tip and the second is a telescopic aerospike fitted with discs of decreasing diameter in the direction opposite to the flow direction. These aerospikes are fitted to a 120° apex-angle blunt cone and results are investigated at free stream Mach numbers of 5.75 and 7.9 for different angles of attack. The aerodynamic forces are measured using an accelerometer-based force balance system and the heat transfer rates are measured using platinum thin film sensors. It is found that the telescopic aerospike has better drag reduction performance at angles of attack beyond 2° while the performance of the plain aerospike is better for angles of attack closer to zero degrees.

Numerical simulation of hypersonic flow over highly blunted cones with spike

In this paper, effectiveness of aerodisk/aerospike assemblies as retractable drag-reduction devices for large-angle blunt cones flying at hypersonic Mach numbers is simulated numerically at various angles of attack. Different lengths of spike have been chosen to investigate the effect of the aerospike on the surrounding flowfield of nose cone. The compressible, 3-D full Navier–Stokes equations are solved with k − ω (SST) turbulence model for free stream Mach number of 5.75 and different angles of attack namely 3, 7, 10, and 12. The visualized shock structure and the computed drag on the blunt cone with aerospike agree well with the experimental result. The effect of reattachment of point on the surface convective heat-load reduction is investigated for different kind of spikes with varying length to diameter ratio. Additional modifications to the tip of the spike are examined in order to obtain different bow shocks, including a cut spike, and a flat and hemispherical aerodisk mounted on the tip of the spike. The numerical results presented the pressure distributions and the surface heat reduction for different type of spike. Some discrepancies existed, especially on the length of the recirculation region.

Investigation of Missile-Shaped Body with Forward-Facing Cavity at Mach 8

A blunt-nosed hypersonic missile mounted with a forward-facing cavity is a good alternative to reduce the stagnation heating rates. The effects of a forward-racing cavity on heat transfer and aerodynamic coefficients are addressed in this paper. Tests were carried out in hypersonic shock tunnel HST2, at a hypersonic Mach number of 8 using a 41 deg apex-angle blunt cone. The aerodynamic forces on the test model with and without a forward-facing cavity at various angles of attack are measured by using an internally mountable accelerometer force balance system. Heat flux measurements have been carried out on the test model with and without a forward-facing cavity of the entire surface at zero degree angle of attack with platinum sensors. A numerical simulation was also carried out using the computational fluid dynamics code (CFX-Ansys 5.7). An important result of this study is that the smaller cavity diameter has the highest lift-to-drag ratio, whereas the medium cavity has the highest heat flux reduction. Theshock structure around the test model has also been visualized using the Schlieren flow visualization technique. The visualized shock structure and the measured aerodynamic forces on the missile-shaped body with cavity configurations agree well with the axisymmetric numerical simulations.