Methodology of a combined ground based testing and numerical modelling analysis of supersonic combustion flow paths

In the framework of the European Commission co-funded LAPCAT (Long-Term Advanced Propulsion Concepts and Technologies) project, the methodology of a combined ground-based testing and numerical modelling analysis of supersonic combustion flow paths was established. The approach is based on free jet testing of complete supersonic combustion ramjet (scramjet) configurations consisting of intake, combustor and nozzle in the High Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Center (DLR) and computational fluid dynamics studies utilising the DLR TAU code. The capability of the established methodology is demonstrated by applying it to the flow path of the generic HyShot II scramjet flight experiment configuration.     

The effect of the arrangement of the openings on the amplification factor during asymmetric gas blowing into a laval nozzle

In asymmetric blowing of a gas into the supersonic part of a nozzle the main flow is perturbed by the jet which is being blown. Two interaction regimes are distinguished. In the first the perturbation of the main flow does not extend to the side of the nozzle opposite to the blast: the central angle subtended by the perturbation of the exit section of the nozzle is 2_a < 180 ° (Fig. 1). This regime is characterized by the fact that the curvature of the nozzle has no effect on the magnitude of the lateral force. In the second regime the zone of the perturbed flow extends to the side of the nozzle opposite to the blast (2_a > 180 °), and this leads to a decrease in the gradient of the lateral force with respect to the flow rate of the gas which is being blown. The first regime has been studied in the most detail.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 136–141, November–December, 1984.     

Interaction of the vortex structures formed in parallel pulsed jets

The experimental investigation of the lateral interaction of the heads of pulsed jets and primary shock waves at various nozzle spacings and pressure ratio numbers is described. The various stages of formation of a composite pulsed jet issuing from a multinozzle block are classified and the flow development mechanisms are explored. It is shown for both a block and a single nozzle the shock wave travels with almost the same velocity, whereas the jet front formed at the exit from a single nozzle moves much more slowly than the jet front formed beyond a nozzle block. Long-lived lateral bursts of gas, whose dimensions are an order greater than those of the jet bursts, are detected. Their long period of existence considerably increases the stabilization time of the steady-state structure and parameters as compared with a single pulsed jet with the same flow rate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 153–159, November–December, 1987.     

Outflow of an unexpanded jet into counter supersonic and subsonic flows

The article gives the results of an experimental investigation of the geometric structure of an opposing unexpanded jet. It discusses flow conditions with interaction between the jet and sub- and supersonic flows. It is shown that, with the outflow of an unexpanded jet counter to a supersonic flow, there are unstable flow conditions. For stable flow conditions with one roll, dependences are proposed determining the form of a jet in a supersonic opposing flow. A generalized dependence is obtained for the distribution of the pressure at the surface of a body with a jet, flowing out counter to a subsonic flow. The range of change in the determining parameters are the following: Mach numbers at outlet cross section of nozzle, M _a = 1 and 3; Mach numbers of opposing flow, M = 0.6–0.9 and 2.9; degree of effectiveness of jet, n = p _a /p = 0.5–800 (p _a and p are the static pressures at the outlet cross section of the nozzle and in the opposing flow); the ratios of the specific heat capacities, _a = = 1.4; the drag temperatures of the jet and the flow, T_o = T_oa = 290°K.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 89–96, January–February, 1977.     

The structure of particle-laden,underexpanded free jets

Underexpanded, supersonic gas-particle jets were experimentally studied using the shadowgraph technique in order to examine the influence of the dispersed particles on the shape of the free jet and the structure of the imbedded shock waves. The particle mass loading at the nozzle exit was varied between zero and one, and two sizes of particles (i.e. spherical glass beads) with mean number diameters of 26 and 45 m were used. It was found that the Mach-disc moves upstream towards the orifice with increasing particle loading. The laser light sheet technique was also used to visualize the particle concentration distribution within the particle jet and the spreading rate of the particle jet. Furthermore, the particle velocity along the jet centerline was measured with a modified laser-Doppler anemometer. These measurements revealed that the particles move considerably slower than the gas flow at the nozzle exit. This is mainly the result of the particle inertia, whereby the particles are not accelerated to sonic speed in the converging part of the nozzle.In order to further explore the particle behavior in the free jet, numerical studies were performed by a combined Eulerian/Lagrangian approach for the gas and particle phases, including full coupling between the two phases. The numerical results showed that the application of different particle velocities at the nozzle exit as the inlet conditions, which were below the sonic speed of the gas phase has a significant influence on the free jet shape and the configuration of the shock waves. These results demonstrate that the assumption of equilibrium flow (i.e. zero slip between the phases) at the nozzle exit which has been applied in most of the previous numerical studies is not justified in most cases. Furthermore, the numerical calculations of the free jet shape and the particle velocity along the jet axis were compared with the measurements. Although correlations for rarefaction and compressibility effects in the drag coefficient were taken into account, the particle velocity along the center line was considerably overpredicted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Experimental investigation of liquid jet injection into Mach 6 hypersonic crossflow

The injection of a liquid jet into a crossing Mach 6 air flow is investigated. Experiments were conducted on a sharp leading edge flat plate with flush mounted injectors. Water jets were introduced through different nozzle shapes at relevant jet-to-air momentum–flux ratios. Sufficient temporal resolution to capture small scale effects was obtained by high-speed recording, while directional illumination allowed variation in field of view. Shock pattern and flow topology were visualized by Schlieren-technique. Correlations are proposed on relating water jet penetration height and lateral extension with the injection ratio and orifice diameter for circular injector jets. Penetration height and lateral extension are compared for different injector shapes at relevant jet-to-air momentum–flux ratios showing that penetration height and lateral extension decrease and increase, respectively, with injector’s aspect ratio. Probability density function analysis has shown that the mixing of the jet with the crossflow is completed at a distance of x/d _j  ~ 40, independent of the momentum–flux ratio. Mean velocity profiles related with the liquid jet have been extracted by means of an ensemble correlation PIV algorithm. Finally, frequency analyses of the jet breakup and fluctuating shock pattern are performed using a Fast Fourier algorithm and characteristic Strouhal numbers of St = 0.18 for the liquid jet breakup and of St = 0.011 for the separation shock fluctuation are obtained.     

自然超空泡与尾喷流相互作用的数值模拟

认识带尾喷流和自然超空泡的水下高速航行体流体动力特性并发展其预报与控制方法仍是水动力学领域极具挑战性的课题．本研究采用CFD方法对尾喷流和自然超空泡之间的相互作用进行了数值研究．针对发动机欠膨胀超音速喷流,采用现有实验结果验证了基于两方程湍流模型的二维轴对称流动数值模型的可靠性．尾喷流在空气和蒸汽环境中流动的数值计算结果表明,由于蒸汽环境中背压较低,欠膨胀尾喷流无法及时形成压缩波,使得蒸汽环境中尾喷流的过膨胀区和气相扩散区的体积比空气中大;尾喷流很难形成规则的激波格栅,波系结构相对简单．针对携尾喷流的平头航行体超空泡流状态的数值模拟结果表明,尾喷流注入超空泡后迅速充满航行体周围的空腔区域;尾喷流与超空泡尾迹区域形成的回射流相互作用最终导致超空泡断裂,断裂过程中伴随着燃气泡的下泄现象;受空泡壁面约束,尾喷流难以在狭窄的超空泡空腔内完全膨胀,尾喷流的激波波系结构有显著的变化：在喷嘴附近受到压缩,在远离喷嘴区域受到超空泡水汽掺混的破坏;空泡内压强基本维持在饱和蒸汽压附近,没有显著增加．     

Choking of ideal-gas flow in convergent nozzles and integral nozzle characteristics

The results of a numerical and theoretical investigation of the local and integral characteristics of convergent nozzles are presented. It is shown that self-similar (choked) nozzle flow, when the gas flow rate does not depend on the external pressure, may occur at subcritical values of the pressure ratio _c . If the nozzle contour consists of the contour of the conical nozzle and the convergent part corresponds to the boundary of the emerging jet, then on a certain interval of _c this nozzle will have a higher thrust coefficient than the initial conical nozzle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–157, November–December, 1994.     

Development of shock wave and vortex structures in unsteady jets

The paper deals with the formation of a gaseous jet behind a sonic nozzle. The nozzle was located at the end wall of a shock tube. A specially made two-direction shadow system, which ensured a simultaneous recording of side-on and head-on images of the jet, as well as a diffraction interferometer were used. On the basis of the data obtained, an analysis of the vortex structure of the jet was carried out, the amplitude of the azimuthal instability was measured and the spatial distribution of the density in the gaseous flow was obtained. Comparison between the experimental density distribution, numerical results and a nonself-similar point source blast wave model was conducted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Radiation in a hypersonic shock layer generated around a projectile

Radiation emitted from the shock layer generated around a hypersonic flight model is experimentally investigated by using a ballistic range (two-stage light-gas gun). A polyethylene projectile of 1.2 cm in diameter is launched in this facility at the velocity of 5 km/sec (M=15), and the emission from the induced shock layer around the projectile is observed with a spectroscope. As a result, molecular band-spectra from NO and N₂ are detected along with those from carboncontaining molecules. Total emission power is measured with a diode-type powermeter. In addition, dimension effect of the flight model is theoretically and numerically examined, and a scaling law on thermochemical structure of the shock layer is developed. It shows that the thickness of thermal boundary-layer formed on the model surface does not follow the conventional scaling law based on the reaction distance and on the energy relaxation distance. Finally, the radiative field around the projectile is numerically computed, and the total power emitted from the shock layer is estimated. From the comparison between computed and measured results, the validity of the calculation model is discussed.     

Selective control of flow coherence in triangular jets

The triangular jet was investigated for use as a passive device to enhance fine-scale mixing and to reduce the coherence of large-scale structures in the flow. The suppression of the structures is vital to the enhancement of molecular mixing, which is important for efficient chemical reactions including combustion. The sharp corners in the jet injector introduced high instability modes into the flow via the non-symmetric mean velocity and pressure distribution around the nozzle. Both aerodynamic and hydrodynamic flows showed the difference between the flow at the corner (vertex) and at the flat side. While highly coherent structures could be generated at the flat side, the corner flow was dominated by highly turbulent small-scale eddies. The flow characteristics were tested using hotwire anemometry for mean flow and turbulence analysis, and flow visualization in air and water.List of symbols D inlet duct diameter - D _e equivalent diameter - D _i inside diameter - E _v velocity fluctuation energy - f _F forcing frequency - f _j preferred mode frequency - L length - Re Reynolds number - R _e equivalent radius (same area) - r _0.5 jet half-width - R _1.2 cross-correlation factor - r radial coordinate (circular duct) - St _e most energetic Strouhal number - St _j preferred mode Strouhal number - U _m centerline (maximum) velocity in radial u-profile - U ₀ jet exit velocity - u local axial mean velocity - x axial coordinate - X ₁ axial position of first of two hot-wires for axial cross-correlation - + y _F lateral coordinate at flat side of triangular duct - - y _V lateral coordinate at vertex side of triangular duct - (E _V)_j preferred mode energy - X axial distance between hot-wires - r radial distance between two hot-wires (circular jet) - y lateral distance between two hot-wires (triangular jet) - P/P pressure amplitude - momentum thickness - time     

Low-density jets beyond a sonic nozzle at large pressure drops

The gas-dynamical structure of jets of a low-density diatomic gas beyond a sonic nozzle at large pressure drops under conditions of a transition from continuous medium processes to rarefied gas processes is examined on the basis of experimental data obtained in low-density gas-dynamical tubes using electron-beam diagnostics and the Pitot tube method. Isomorphism is shown in the density distribution and total pressure in all cross sections of the jet with respect to pressures at a constant value of the complex R_L=R_*/N^1/2(R_* is the Reynolds number in the critical cross section of the nozzle, and N is the ratio of the Pitot pressure and the pressure in the discharge chamber). It is shown on the basis of a comparison of local Reynolds numbers for all zones of the jet that this is an analog complex. The experimental data on the variation in the jet structure are presented as a function of the number R_L in the range of 5–600. For R_L> 100 the flow in the jet can be considered as continuous; for R_L< 5–10 the flow corresponds to a scattering process; the range of 5–10< R_L< 100 corresponds to a transitional state. Ranges of isomorphism of the jet with respect to R_* and N are indicated. Based on the results of the measurements, it is shown that the flow behind a Mach disk for R_L> 200 remains subsonic on the axis to a distance of several lengths of the primary cycle. A transition to supersonic velocity on the jet axis can occur with a decrease in the numbers R_L owing to ejection acceleration by the supersonic ring-shaped compressed layer.This word is apparently interchangeable with self-similarity-Translator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 64–73, March–April, 1973.     

Effect of the flow regime in an underexpanded jet issuing into a subsonic counterstream on the pressure distribution on a body

The pressure distribution on a cone with a half-angle =75°, from which a single central underexpanded jet issues into a subsonic counterstream, has been experimentally investigated. The effect of the flow regime in the jet on the pressure distribution is demonstrated. Generalized relations for the pressure on the body are obtained for various jet-flow momentum ratios J and flow Mach numbers M = 0.35–0.9; the Mach number M_a at the exit of the conical nozzle with half-angle _a=10° was equal to 2.9. The working medium of the jet and the flow was air with stagnation temperatures T_0a = T₀ 260–265°K. The ratio of the nozzle outlet radius to the radius of the maximum cross section of the cone _a/R_M=0.1.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 182–185, January-February, 1988.     

Experimental investigation of the flow in the mixing layer in the initial section of an underexpanded jet in a parallel stream

The results are given of an experimental investigation of the flow in the initial section of a turbulent underexpanded jet exhausting from a profiled nozzle with Mach number M _a = 2.56 at the exit into a parallel stream with Mach number M = 3.1. Analysis of the results of measurement of the fields of the total head p₀ and the stagnation temperature T₀ in conjunction with results of calculation of a jet of an ideal gas make it possible to construct the velocity profile in the mixing layer of the underexpanded jet in the parallel supersonic flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–163, January–February, 1981.     

Axisymmetric impingement of a hot jet on a flat plate: equilibrium flow analysis of high-temperature air

The flow structure of an underexpanded supersonic jet with high reservoir temperature impinging on a flat plate has been numerically investigated using a Total Variation Diminishing (TVD) scheme. When the temperature of the flow field is high enough to cause chemical reaction, the specific heat ratio,, is no longer equal to 1.4, nor constant. This explains the difference found in the literature between the flow properties of the calorically perfect gas and that of the chemically reacting flow. Under the equilibrium flow assumption the effect of high temperature gas on the impinging jet has been taken into account in the present paper by using specific heat ratio and speed of sound given by correlation polynomials of thermodynamic variables. The limiting case of cold jet calculation in the present numerical results agreed well with the existing experimental data. For the equilibrium jet with high reservoir temperature,T _o=1000K, qualitative support of the present result has been provided by means of the approximation theory.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Investigation of supersonic isobaric submerged turbulent jets

Turbulent supersonic submerged air jets have been investigated on the Mach number interval M_a = 1.5–3.4 and on the interval of ratios of the total enthalpies in the external medium and the jet i₀ = 0.01 – 1. Oxyhydrogen jets with oxidizer ratios = 0.3–5 flowing from a nozzle at Mach numbers M_a = 1 and 2.4 have also been investigated. When < 1 the excess hydrogen in the jet burns up on mixing with the air. Special attention has been paid to obtaining experimental data free of the influence on the level of turbulence in the jet of the initial turbulence in the nozzle forechamber, shock waves occurring in the nozzle or in the jet at the nozzle exit, and the external acoustic field. The jet can be divided into two parts: an initial part and a main part. The initial part extends from the nozzle exit from the section x, in which the dimensionless velocity on the jet axis u_m = u_x/u_d = 0.75. Here, u_x is the velocity on the jet axis at distance x from the nozzle exit, and u_a is the nozzle exit velocity. The main part of the jet extends downstream from the section x. For the dimensionless length of the initial part x_m = x/d_a, where d_a is the diameter of the nozzle outlet section, empirical dependences on M_a and i₀ are obtained. It is shown, that in the main part of the jet the parameters on the flow axis — the dimensionless velocity and temperature — vary in inverse proportion to the distance, measured in units of length x, and do not depend on the flow characteristics which determine the length of the initial part of the jet. The angles of expansion of the viscous turbulent mixing layer in the submerged heated or burning jet increase with decrease in i₀ and M_a and are practically independent of the afterburning process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza. No. 4, pp. 56–62, July–August, 1988.     

Measurements of turbulent inclined plane dual jets

Measurements of mean velocities, flow direction, velocity fluctuations and Reynolds shear stress were made with a split film probe of hot wire anemometer to investigate the interactions created by two air jets issuing from two identical plane inclined nozzles. The reverse flow was detected by using the split film probe and observed by flow visualization. Experimental results with an inclined angle of 9° are presented in the paper. Some experimental results with an inclined angle of 27° are presented to investigate the effect of inclination on the flow field.Mean velocities approach self-preservation in both the converging region and the combining region. Velocity fluctuations and Reynolds shear stress approach self-preservation in the combining region only. The spreads of jet and the square of the decay of maximum mean velocity increase linearly as the distance from the nozzle exit increases.List of symbols D nozzle width - h nozzle height - J momentum of jet - J ₀ momentum of jet at nozzle exit - M mass flow rate - M ₀ mass flow rate at nozzle exit - S nozzle spacing - U, V mean velocities in the X and Y axis respectively - U _m maximum axial velocity - U ₀ axial velocity at nozzle exit - u, v velocity fluctuations in the X and Y axis respectively - u, v r.m.s. of u and v - Reynolds shear stress - X, Y Cartesian coordinates - X _m , Y _m coordinates at the location of maximum axial velocity - y _0.5 distance from the location of maximum axial velocity to the location where the velocity is half of maximum axial velocity - inclined angle - yY/S - Reynolds stress correlation coefficient - C.P combining point - max maximum value - M.P merging point - o nozzle exit plane - V.C vortex center     

Flow and acoustic features of a supersonic tapered nozzle

The acoustic and flow characteristics of a supersonic tapered jet were measured for free and shrouded flow configurations. Measurements were performed for a full range of pressure ratios including over- and underexpanded and design conditions. The supersonic tapered jet is issued from a converging-diverging nozzle with a 31 rectangular slotted throat and a conical diverging section leading to a circular exit. The jet was compared to circular and rectangular supersonic jets operating at identical conditions. The distinct feature of the jet is the absence of screech tones in the entire range of operation. Its near-field pressure fluctuations have a wide band spectrum in the entire range of measurements, for Mach numbers of 1 to 2.5, for over- and underexpanded conditions. The free jet's spreading rate is nearly constant and similar to the rectangular jet, and in a shroud, the pressure drop it is inducing is linearly proportional to the primary jet Mach number. This behavior persisted in high adverse pressure gradients at overexpanded conditions, and with nozzle divergence angles of up to 35°, no inside flow separation was observed.     

Experimental investigation of a turbulent jet carrying heavy particles of a disperse phase

The results are given of an experimental investigation of an immersed jet carrying heavy spherical particles in the case of uniform velocity fields of the particles and the gas and uniform concentration of the particles at the nozzle exit. The laser-optical method was used to measure the velocity fields of the gas and the particles and the concentration of the latter in the flow-rate concentration range of the additive from 0 to 1.5 and particle diameters from 35 to 67 m. It was found that the flow in the jet is essentially nonequilibrium, the disequilibrium and intensity of the mixing in the jet depending on the concentration of the additive and the diameter of the particles. The investigation of the initial section revealed a somewhat anomalous behavior of the jet at a comparatively small (₀=0.5) flow-rate concentration of the additive, and this indicates a need to take into account the prehistory of the flow in the construction of a method for calculating the initial section of a two-phase jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–31, September–October, 1981.