The compressible turbulent shear layer: an experimental study

The growth rate and turbulent structure of the compressible, plane shear layer are investigated experimentally in a novel facility. In this facility, it is possible to flow similar or dissimilar gases of different densities and to select different Mach numbers for each stream. Ten combinations of gases and Mach numbers are studied in which the free-stream Mach numbers range from 0.2 to 4. Schlieren photography of 20-ns exposure time reveals very low spreading rates and large-scale structures. The growth of the turbulent region is defined by means of Pitot-pressure profiles measured at several streamwise locations. A compressibility-effect parameter is defined that correlates and unifies the experimental results. It is the Mach number in a coordinate system convecting with the velocity of the dominant waves and structures of the shear layer, called here the convective Mach number. It happens to have nearly the same value for each stream. In the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases rapidly with increasing convective Mach number, reaching an asymptotic value of about 0.2 for supersonic convective Mach numbers

Transonic flutter study of a 50.5 deg cropped-delta wing with two rearward-mounted nacelles

Transonic flutter characteristics of three geometrically similar delta-wing models were experimentally determined in the Langley transonic dynamics tunnel at Mach numbers from about 0.6 to 1.2. The models were designed to be simplified versions of an early supersonic transport wing design. The model was an aspect-ratio-1.28 cropped-delta wing with a leadingedge sweep of 50.5 deg. The flutter characteristics obtained for this wing configuration indicated a minimum flutter-speed index near a Mach number of 0.92 and a transonic compressibility dip amounting to about a 27-percent decrease in the flutter-speed index relative to the value at a Mach number of 0.6. Analytical studies were performed for one wing model at Mach numbers of 0.6, 0.7, 0.8, and 0.9 by using both doublet-lattice and lifting-surface (kernel-function) unsteady aerodynamic theory. A comparison of the analytical and experimental flutter results showed good agreement at all Mach numbers investigated

On the electron-ion temperature ratio established by collisionless shocks

Astrophysical shocks are often collisionless shocks. An open question about collisionless shocks is whether electrons and ions each establish their own post-shock temperature, or whether they quickly equilibrate in the shock region. Here we provide simple relations for the minimal amount of equilibration to expect. The basic assumption is that the enthalpy-flux of the electrons is conserved separately, but that all particle species should undergo the same density jump across the the shock. This assumption results in an analytic treatment of electron-ion equilibration that agrees with observations of collisionless shocks: at low Mach numbers ($<2$) the electrons and ions are close to equilibration, whereas for Mach numbers above $M \sim 60$ the electron-ion temperature ratio scales with the particle masses $T_e/T_i = m_e/m_i$. In between these two extremes the electron-ion temperature ratio scales as $T_e/T_i \propto 1/M_s^2$. This relation also hold if adiabatic compression of the electrons is taken into account. For magnetised plasmas the compression is governed by the magnetosonic Mach number, whereas the electron-ion temperatures are governed by the sonic Mach number. The derived equations are in agreement with observational data at low Mach numbers, but for supernova remnants the relation requires that the inferred Mach numbers for the observations are over- estimated, perhaps as a result of upstream heating in the cosmic-ray precursor. In addition to predicting a minimal electron/ion temperature ratio, we also heuristically incorporate ion-electron heat exchange at the shock, quantified with a dimensionless parameter ${\xi}$. Comparing the model to existing observations in the solar system and supernova remnants suggests that the data are best described by ${\xi} \sim 5$ percent. (Abridged abstract.)Comment: Accepted for publication in Astronomy and Astrophysics. This version is expanded with a section on adiabatic heating of the electrons and the effects of magnetic field

Interstellar Sonic and Alfv\'enic Mach Numbers and the Tsallis Distribution

In an effort to characterize the Mach numbers of ISM magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of patial increments of density, velocity, and magnetic field for fourteen ideal isothermal MHD simulations at resolution 512^3. In particular, we fit the PDFs using the Tsallis function and study the dependency of fit parameters on the compressibility and magnetization of the gas. We find that the Tsallis function fits PDFs of MHD turbulence well, with fit parameters showing sensitivities to the sonic and Alfven Mach numbers. For 3D density, column density, and position-position-velocity (PPV) data we find that the amplitude and width of the PDFs shows a dependency on the sonic Mach number. We also find the width of the PDF is sensitive to global Alfvenic Mach number especially in cases where the sonic number is high. These dependencies are also found for mock observational cases, where cloud-like boundary conditions, smoothing, and noise are introduced. The ability of Tsallis statistics to characterize sonic and Alfvenic Mach numbers of simulated ISM turbulence point to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques.Comment: 20 pages, 16 figures, ApJ submitte

Experimental investigation of hypersonic aerodynamics

An extensive series of ballistic range tests were conducted at the Ames Research Center to determine precisely the aerodynamic characteristics of the Galileo entry probe vehicle. Figures and tables are presented which summarize the results of these ballistic range tests. Drag data were obtained for both a nonablated and a hypothesized ablated Galileo configuration at Mach numbers from about 0.7 to 14 and at Reynolds numbers from 1000 to 4 million. The tests were conducted in air and the experimental results were compared with available Pioneer Venus data since these two configurations are similar in geometry. The nonablated Galileo configuration was also tested with two different center-of-gravity positions to obtain values of pitching-moment-curve slope which could be used in determining values of lift and center-of-pressure location for this configuration. The results indicate that the drag characteristics of the Galileo probe are qualitatively similar to that of Pioneer Venus, however, the drag of the nonablated Galileo is about 3 percent lower at the higher Mach numbers and as much as 5 percent greater at transonic Mach numbers of about 1.0 to 1.5. Also, the drag of the hypothesized ablated configuration is about 3 percent lower than that of the nonablated configuration at the higher Mach numbers but about the same at the lower Mach numbers. Additional tests are required at Reynolds numbers of 1000, 500, and 250 to determine if the dramatic rise in drag coefficient measured for Pioneer Venus at these low Reynolds numbers also occurs for Galileo, as might be expected

Note on the limits to the local Mach number on an aerofoil in subsonic flow

It has been noted in some experiments that the local Mach number just ahead of a shock wave on an aerofoil in subsonic flow is limited, values of the limit of the order of 1.4 are usually quoted. This note presents two lines of thought indicating how such a limit may arise. The first starts with the observation that the pressure after the shock will not be higher than the rain stream pressure. Fig.1 shows the calculated relation between local Mach number ahead of the shock (M„ 1 ), shock inclination (S), mainstream Mach number (M1) and pressure coefficient just aft of the shock. • (Cp) It is noted that, for given M1 , Cp and .5 ,two shocks are possible in general, a strong one for which Ms , > 1.48, and a weak one for which MS1 < 1.48, and it is argued that the latter is the more likely. The second approach is based on the fact that a relation between stream deflection (8) and Mach number for the flow in the limited supersonics regions on a number of aerofoils has been derived from some. experimental data. Further analysis of experimental data is required before this relation can be accepted as general. If it is accepted, however, then it indicates that the Mach numbers increase above unity for a given deflection is about one-third of that given by simple wave theory (Fig.2). An analysis of the possible deflections on aerofoils of various thicknesses (Fig.3) then indicates that deflections corresponding to local Mach numbers of the order of 1,5 or higher are unlikely except at incidences of the order of5 ° or more, and may then be more likely for thick wings than for thin wings. Flow breakaway will make the attainment of such high local Mach numbers less likely

Wind tunnel investigation of the aerodynamic characteristics of five forebody models at high angles of attack at Mach numbers from 0.25 to 2

Five forebody models of various shapes were tested in the Ames 6- by 6-Foot Wind Tunnel to determine the aerodynamic characteristics at Mach numbers from 0.25 to 2 at a Reynolds number of 800000. At a Mach number of 0.6 the Reynolds number was varied from 0.4 to 1.8 mil. Angle of attack was varied from -2 deg to 88 deg at zero sideslip. The purpose of the investigation was to determine the effect of Mach number of the side force that develops at low speeds and zero sideslip for all of these forebody models when the nose is pointed. Test results show that with increasing Mach number the maximum side forces decrease to zero between Mach numbers of 0.8 and 1.5, depending on the nose angle; the smaller the nose angle of the higher the Mach number at which the side force exists. At a Mach number of 0.6 there is some variation of side force with Reynolds number, the variation being the largest for the more slender tangent ogive

Measurements of sonic booms generated by an airplane flying at Mach 3.5 and 4.8

Sonic booms generated by the X-15 airplane flying at Mach numbers of 3.5 and 4.8 were measured. The experimental results agreed within 12 percent with results obtained from theoretical methods. No unusual phenomena related to overpressure were encountered. Scaled data from the X-15 airplane for Mach 4.8 agreed with data for an SR-71 airplane operating at lower Mach numbers and similar altitudes. The simple technique used to scale the data on the basis of airplane lift was satisfactory for comparing X-15 and SR-71 sonic boom signatures

The small-scale dynamo: Breaking universality at high Mach numbers

(Abridged) The small-scale dynamo may play a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Low Mach numbers may in particular lead to the well-known, incompressible Kolmogorov turbulence, while for high Mach numbers, we are in the highly compressible regime, thus close to Burgers turbulence. In this study, we explore whether in this large range of conditions, a universal behavior can be expected. Our starting point are previous investigations in the kinematic regime. Here, analytic studies based on the Kazantsev model have shown that the behavior of the dynamo depends significantly on Pm and the type of turbulence, and numerical simulations indicate a strong dependence of the growth rate on the Mach number of the flow. Once the magnetic field saturates on the current amplification scale, backreactions occur and the growth is shifted to the next-larger scale. We employ a Fokker-Planck model to calculate the magnetic field amplification during the non-linear regime, and find a resulting power-law growth that depends on the type of turbulence invoked. For Kolmogorov turbulence, we confirm previous results suggesting a linear growth of magnetic energy. For more general turbulent spectra, where the turbulent velocity v_t scales with the characteristic length scale as u_\ell\propto \ell^{\vartheta}, we find that the magnetic energy grows as (t/T_{ed})^{2\vartheta/(1-\vartheta)}, with t the time-coordinate and T_{ed} the eddy-turnover time on the forcing scale of turbulence. For Burgers turbulence, \vartheta=1/2, a quadratic rather than linear growth may thus be expected, and a larger timescale until saturation is reached.Comment: 10 pages, 3 figures, 2 tables. Accepted at New Journal of Physics (NJP