Drag force on quasi-axisymmetric scramjets at various flight Mach numbers: theory and experiment

The net axial force on a non-fuelled quasi-axisymmetric scramjet model designed for operation at Mach 6 was measured in the T4 Stalker tube at The University of Queensland using a single-component stress wave force balance. The design used was a variant of a model that was tested previously at Mach 6. The new model was equipped with a modified thrust nozzle that was designed to improve the performance of the nozzle. Tests were performed to measure the drag force on the model for Mach 6, Mach 8 and Mach 10 shock tunnel nozzles for a range of flow conditions. The nozzle-supply enthalpy was varied from 3 to 10 MJ/kg and the nozzle-supply pressure from 35 to 45 MPa. For the test model, the drag coefficient increased with increasing nozzle-supply enthalpy. The test results are compared with a force prediction method based on simple hypersonic theories and three-dimensional CFD. The test results are in good agreement with the predictions over the wide range of conditions tested. The re-designed model has a more efficient nozzle but this comes at the expense of increased drag associated with the modifications required for the cowl. The results indicate that this type of vehicle design is not likely to be suitable for flight above Mach 8.

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低马赫数下斜爆轰波的结构

利用Euler方程和两步化学反应模型,对低马赫数入流时的驻定斜爆轰波进行了数值模拟,并重点研究了斜爆轰波的驻定过程和结构。数值结果显示,当入流马赫数较低时,即使其本身是附体的,在诱导区后侧的高压区的作用下,斜爆轰波也会从其起始位置向来流方向运动。在这种情况下,斜爆轰波会驻定在靠近斜面前缘的位置,诱导区的长度仅有1 mm左右。通过设置初始条件,让斜爆轰波在斜面前缘附近被触发,则其将一直维持在靠近斜面前缘的位置。     

Drag measurements in a hypervelocity expansion tube

A technique is described for the measurement of aerodynamic drag in a hypervelocity expansion tube in which the test flow period may be as short as 50 s. The technique is an application of the stress wave force balance first proposed by Sanderson and Simmons (1991). The experiments were conducted in a test flow of partially dissociated Carbon Dioxide where the flow speed was in excess of 7 kms. The validity of the technique is first demonstrated by comparing the forces measured on a range of sharp cones with those expected theoretically. Agreement to within 10% is achieved. Two re-entry type heat shield geometries were then tested with the experimental drag forces being compared with a Modified-Newtonian prediction. In both cases agreement to within 11% was obtained. Received 12 December 1995 / Accepted 29 April 1996     

Drag measurements on planar riblet surfaces at high subsonic speeds

This paper presents the results of an investigation of riblet performance at high subsonic Mach numbers, and Reynolds numbers of about 20 000 based on the momentum thickness, in both zero and adverse pressure gradient boundary layers. The maximum length Reynolds number of the ribbed section was 3.4×10⁷ so the results were directly relevant to flight applications on the engine nacelles of civil airliners. Seven different sizes of riblets with heights h (equal to spacing s) ranging from 0.0007 (0.0178mm) to 0.006 (0.1524 mm) have been studied, covering a range of h+, s+ from 10 to 106. The maximum percentage skin friction reduction, as deduced from velocity profiles measured at the downstream end of the riblet surfaces, under nominally zero pressure gradient conditions was 5.5±1; rather less than that recorded in low speed studies, but consistent with a recent theoretical analysis of the effect of Reynolds number. The values of h+ required for maximum and zero skin friction reduction agreed closely with other data. In addition subsequent floating element drag balance measurements revealed little effect of yaw angles up to 15°, again in line with other findings, and also suggested that the extent of the initial development length on, and recovery length behind, the riblets was approximately 5. The adverse pressure gradient studies indicated that riblet performance was essentially unaffected by mild gradients (=0.25), but diminished to zero in a more severe gradient (=0.5).     

Steady energy deposition at Mach 5 for drag reduction

Experiments addressing the effect of energy deposition via arc discharge on $15^\circ $ half angle-truncated cone-cylinder configurations at Mach 5 flow were carried out. The arc discharge was accomplished using a setup that consisted of a power supply, a high voltage unit and tungsten electrodes. Discharge-on tests were compared to discharge-off tests to evaluate the net effect of the energy deposition. Flow visualisation revealed the presence of a heated wake downstream of the energy spot. Compression waves were observed on top of the wake of the heated channel, which were oscillatory in nature. The deposited energy of 7 W shows a repeatable influence on the measured drag force for all the models at close arc-to-nose distances.     

Aerodynamic force measurement using 3-component accelerometer force balance system in a hypersonic shock tunnel

A new three-component accelerometer force balance has been designed, calibrated and tested in hypersonic shock tunnel (HST2) of Indian Institute of Science. The newly designed balance is able to measure aerodynamic forces (within test time of one millisecond) on test models at angles of attack from 0 to 12°. Two models, a blunt cone with after body and a blunt cone with after body and frustum are used to establish the accuracy of the force balance. The tests were conducted for the above two configurations with a constant Mach number of 8 and total enthalpy of 2.0 MJ/kg. The effectiveness of the balance is demonstrated by comparing the forces and moments of measured data with AGARD models. The flow fields around the test model are simulated using a 3D axisymmetric Navier–Stokes solver and the simulated results were compared with the measured values. Measured and computed force data are matched within ±10% for two different models tested here. The accuracy of the force balance is also estimated with the Newtonian theory and the values are approximately ±10% for the axial component and ±8% for the normal and pitching moment components.      

H2 injection and combustion in a Mach 5 air inlet through a Viscous Mach Interaction

Hydrogen injection has been investigated numerically in a flow configuration caused by strong shock–boundary layer interaction named Viscous Mach Interaction (VMI). The geometry that leads to this configuration is used as a hypersonic inlet. The subsonic zone, because of boundary layer detachment, allows hydrogen to be injected along the wall of the central body where combustion processes occur along a slip line when hydrogen is mixed with the incoming air flow far from the wall of the central body.     

Velocity measurements at high temperatures by ultrasound Doppler velocimetry using an acoustic wave guide

Ultrasound Doppler velocimetry (UDV) was used to measure flow velocities at temperatures up to 620^°C. To overcome the thermal restriction of the ultrasonic transducers an acoustic wave guide was used. The acoustic wave guide and the piezoelectric element are combined in the form of an integrated sensor. This approach allowed the first successful application of the ultrasound Doppler technique in liquid metals at temperatures above 200^°C. The feasibility of this integrated sensor concept was demonstrated in experiments with metallic melts. Measurements were performed in a PbBi bubbly flow and in CuSn.     

Shock wave standoff distance for a sphere slightly above Mach one

This paper describes a numerical simulation of bow shock formation ahead of a sphere at steady supersonic flow in the Mach number range of 1.025–1.20. Turbulent viscous flow results are presented using the Spalart–Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for a spherical projectile at slightly supersonic free flight speeds. Results are compared to experimental data, including double exposure holographic interferograms obtained from a 40 mm polycarbonate sphere launched by a light gas gun. The shock standoff distance was determined from the interferograms. The present numerical simulations were found to agree with previously published data, and reached down to M = 1.025—a range where almost no previously published data exists. The computed flow structure and shock wave locations agree well with recently obtained free-flight interferograms.     

基于扰动方程的超音速轴对称射流马赫波辐射研究

超音速不稳定波是导致剪切流失稳和转捩的主要不稳定模态,这种模态以马赫波的形式辐射到远场,从而产生强烈的声场。采用线性稳定性理论和非线性扰动方程(NLDE)分析,计算超音速轴对称射流不稳定波的扰动演化(Ma=2.1),对马赫波辐射进行研究,包括马赫波辐射方向、辐射源位置,以及随斯特劳哈尔数的变化情况。研究结果表明,在超音速轴对称射流中,马赫波沿固定方向辐射向远方,不稳定波相位沿另一方向传播,这两个方向相互正交;马赫波辐射源位置位于不稳定波压力幅值最大处;斯特劳哈尔数St越大,马赫波辐射的能力越强,辐射区域越集中。     

Drag measurements on long thin cylinders at small angles and high Reynolds numbers

Measurements of the drag caused by turbulent boundary layer mean wall shear stress on cylinders at small angles of attack and high length Reynolds numbers (8×10⁶<Re_L<6×10⁷) are presented. The use of a full-scale, high-speed towing tank enabled the development of turbulent boundary layers on cylinders made of stainless steel, aluminum, titanium, and polyvinyl chloride. The diameter of all cylinders in this experiment was 12.7 mm; two cylinder lengths, 3.05 m and 6.10 m, were used, corresponding to aspect ratio values L/a=480 and 960, respectively. Materials of various densities were towed at critical angles, resulting in linear cylinder geometry for tow speeds ranging from 2.6 m/s to 20.7 m/s and angles between 0° and 12°. Towing angles were measured with digital photography, and streamwise drag was measured with a strut-mounted load cell at the tow point. The measured tangential drag was very sensitive to small increases in angle at all tow speeds. A momentum thickness length scale is proposed to scale the tangential drag coefficient. The effects of the cross-flow resulting from the small angles of tow have a significant effect on the tangential drag coefficient values. A scaling for the orthogonal force on the cylinders was determined and provides a correction to published normal drag coefficient values for pure cross-flow. The presence of the axial turbulent boundary layer has a significant effect on these orthogonal forces.     

Particle velocity field measurements in a near-wall flow using evanescent wave illumination

Evanescent waves from the total internal reflection of a 488 nm argon-ion laser beam at a glass-water interface were used to measure velocity fields in creeping rotating Couette flow within 380 nm of the stationary solid surface. Images of fluorescent 300 and 500 nm diameter polystyrene and silica particles suspended in water recorded at 30 Hz were processed using cross-correlation particle image velocimetry to determine the two in-plane velocity components with an in-plane spatial resolution of 40Ꮀ µm over a 200 µm (h)쏦 µm (v) field of view. The results are in reasonable agreement with the exact solution for the corresponding single-phase Stokesian flow. These data are, to our knowledge, the first velocity field measurements with this small out-of-plane spatial resolution (in all cases less than 380 nm), and the first such measurements in this interfacial or near-wall region. This paper describes the novel experimental diagnostic technique used to obtain these results.     

Drag force on a sphere in creeping motion throug a carreau model fluid

In the report of Chhabra and Uhlherr [1], a theoretical formulation for the drag force on a sphere in a fluid governed by the Carreau viscosity equation was presented. The formulation gave a good representation of the drag force when compared with experimental measurements, although the experiments were carried out on fluids exhibiting both shear-thinning and elastic behaviour. In the present work the ‘boundary element method’ has been used to obtain a fully numerical solution for comparison with the theoretical predictions. The two sets of results agree closely. We also present a simple empirical relation which gives a good first approximation to the drag force (～ 10%).     

Mach reflection of a plane shock wave passing a mountain of 45° inclination

The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan^[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM _i is analyzed and the variations of the incidence angle ω _i of the impinging shock and the reflection angle ω _r with the distanceL ^* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya.     

Drag force on a free surface-piercing yawed circular cylinder in steady flow

The force distribution on a surface-piercing yawed cylinder surface differs significantly from that on a surface-piercing vertical cylinder. The established numerical model for flow past the surface-piercing yawed cylinder with yaw angles from −45° to 45° was solved by the standard large-eddy simulation (LES) methodology. Six cases at intervals of ±15° relative to the vertical were studied at the Reynolds number of 27 000 and the Froude number of 0.8 based on the cylinder diameter and free-stream velocity, among which the drag forces on four cylinders with yaw angles from −15° to 30° were tested for the validation of the LES approach. The results revealed that the time-averaged total drag coefficient for all cases increases with the increase of yaw angle compared to that of the surface-piercing vertical cylinder, even over 2.5 for the ±45°-yawed cylinders. The sectional drag coefficients for the negatively yawed cylinders are much greater than that for the vertical cylinder, and much less for the positively yawed cylinders. The unbalanced hydrostatic pressures on the inclined section are mainly responsible for those increment and decrement. Once the hydrostatic pressure was removed, the sectional drag coefficient on the mid-span of the positively yawed cylinder increases from the top section to the bottom, and decreases for the negatively yawed cylinder. The corresponding integrated total drag coefficient decreases with the increase of the yaw angle to ±15°, then increases with the further increase of the magnitude of yaw angle.     

Three-dimensional boundary-layer transition on a cone at Mach 3.5

A boundary-layer transition study on a sharp, 5° half-angle cone at various angles of attack was conducted at Mach 3.5. Transition data were obtained with and without significantly reduced freestream acoustic disturbance levels. A progressive downstream and upstream motion of the transition front on the windward and leeward rays, respectively, of the cone with angle of attack was observed for the high noise level data in agreement with data trends obtained in conventional (noisy) wind tunnels. However, the downstream movement was not observed to the same degree for the low noise level data in the present study. Transition believed to be crossflow dominated was found to be less receptive to freestream acoustic disturbances than first-mode (Tollmien-Schlichting) dominated transition. The previously-developed crossflow transition Reynolds number criterion, _tr,max 200, was found to be inadequate for the current case. An improved criterion is offered, which includes compressibility and flow-geometry effects.