An experimental investigation of the ELAC 1 configuration at supersonic speeds

Supersonic flight of aerospace planes is of marked interest since several flow regimes characterized by different local flow structures have to be flown through. This problem was investigated experimentally for the hypersonic research configuration ELAC 1. The aim of the study was to detect the influence of the rounded leading edge, of the thickness distribution prescribed, and of the Reynolds number, especially on the flow on the leeward side of the configuration. The experiments were carried out in the transonic wind tunnel of Aerodynamisches Institut of RWTH Aachen, at a freestream Mach number Ma _∞=2, a unit Reynolds number of Re _∞=13×10⁶, angles of attack between ?3°?α?10°, and in a wind tunnel of the Institute for Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The freestream Mach numbers covered in these experiments were varied between 2?Ma _∞?4, freestream Reynolds numbers per unit length between 25×10⁶?Re _∞?56×10⁶ and angles of attack between ?3°?α?10°. Flow visualization studies, measurements of surface pressure distributions and of aerodynamic forces were used to analyze the flow. The results, which will also be compared with numerical data, clearly indicate marked differences in the location of the separation and reattachment lines, and the formation of the primary, secondary and tertiary vortices, for the flow regimes investigated.     

Experimental study of the laminar-turbulent transition on a blunt cone

Results of an experimental study of the laminar-turbulent transition in a hypersonic flow around cones with different bluntness radii at a zero angle of attack, free-stream Mach number M _∞ = 6, and unit Reynolds number in the interval Re _∞,1 = 5.79 · 10⁶–5.66 · 10⁷ m^?1 are presented. Flow regimes in which a reverse of the laminar-turbulent transition (decrease in the length of the laminar segment with increasing bluntness radius) are studied. Heat flux distributions over the model surface are obtained with the use of temperature-sensitive paints. Lines of the beginning of the transition in the boundary layer are analyzed by using heat flux fields. The critical Reynolds number Re _∞,R ≈ 1.3 · 10⁵ beginning from which the laminar-turbulent transition substantially depends on uncontrolled disturbances, such as the model tip roughness, is found. In supercritical regimes, the line of the transition beginning is shifted in most cases toward the model tip (reverse of the transition). The results obtained are compared with available experimental data.     

Experimental study of a hypersonic shock layer stability on a circular surface of compressionL'étude expérimentale de la stabilité d'une couche de choc hypersonique sur une surface circulaire de compression

The method of electron-beam fluorescence is applied to study the evolution of natural and artificial periodic disturbances on a developed streaky structure in the shock layer on a circular compression surface model. The model is exposed to a hypersonic nitrogen flow with a Mach number M_∞=21 and unit Reynolds number Re_1∞=6×10⁵ m^?1. Data on the effect of surface curvature and temperature on disturbance characteristics are obtained. To cite this article: S.G. Mironov, V.M. Aniskin, C. R. Mecanique 332 (2004).     

Density and temperature ahead of a cylinder with a thermally insulated wall and a cooled wall in a rarefied hypersonic system

Results are presented of a measurement of density and temperature on the stagnation line of a cylinder in cross flow at Mach number M_∞=5, Knudsen number Kn_∞=0.06?0.33, and with temperature factor varying from 1 to 0.11. The effect of degree of rarefaction and the temperature factor on the structure of the perturbed region ahead of the cylinder has been investigated.     

Experimental study of the effect of a passive porous coating on disturbances in a hypersonic boundary layer 2. Effect of the porous coating location

The effect of the location of a passive porous coating on natural disturbances in a hypersonic boundary layer is studied experimentally. The experiments are performed in the flow around a sharp cone aligned at a zero angle of attack with the free-stream Mach number M_∞ = 5.8, stagnation temperature T ₀ = 370 ± 5 K, and unit Reynolds numbers Re_1∞ = 2.6 · 10⁶, 4.6 · 10⁶, 6.6 · 10⁶, and 10⁷ m^?1. The wave characteristics of the boundary layer are calculated with the use of the linear stability theory for flow parameters corresponding to experimental values. A comparison of experimental and predicted results shows that the presence of a porous coating in the region where the second mode is unstable leads to reduction of its amplitude at the measurement point, whereas the presence of a porous coating in the region of second mode stability leads to enhancement of the amplitude.     

Two-dimensional interaction between an incident shock and a turbulent boundary layer in the presence of an entropy layer

The results of an experimental and numerical investigation of flow and heat transfer in the region of the interaction between an incident oblique shock and turbulent boundary layers on sharp and blunt plates are presented for the Mach numbers M_∞ = 5 and 6 and the Reynolds numbers Re_∞L = 27×10⁶ and 14×10⁶. The plate bluntness and the incident shock position were varied. It is shown that the maximum Stanton number St _m in the shock incidence zone decreases with increase in the plate bluntness radius r to a certain value and then varies only slightly with further increase in r. In the case of a turbulent undisturbed boundary layer heat transfer is diminished with increase in r more slowly than in the case of a laminar undisturbed flow. In the presence of an incident shock the bluntness of the leading edge of the flat plate results in a greater decrease in the Stanton number than in the absence of the shock. With increase in the bluntness of the leading edge of the plate the separation zone first sharply lengthens and then decreases in size or remains constant.     

Linear approximation for the flow of a conducting gas with a high magnetic reynolds number through a channel

In this paper, we discuss the flow of a nonviscous and non-heat-conducting gas through a channel of variable cross section under the influence of a transverse magnetic field. For high magnetic Reynolds numbers, the flow is shown to consist of a core and current layers at the electrodes and at the fixed channel walls. The distributions of currents and other parameters in the core and in the current layers are found analytically, in a linear approximation. The Joule dissipation in the current layers may be more intense than that in the core. The longitudinal currents and Joule dissipation increase with increasing Hall parameter in the electrode layers. Zhigulev [1] has shown that magnetic boundary layers may form in the flow of a conducting gas when there is a high magnetic Reynolds number (R_m«1). He illustrated this situation by the shielding of a plasma flow from the magnetic fields produced near a plate which is electrically isolated from the plasma and through which a current is flowing. In an incompressible fluid, the layer thickness is proportional to R_m ^?1/2. Morozov and Shubin [2] have offered a linear-approximation treatment of the structure of the electromagnetic near-electrode layers which arise during the flow of a nonviscous plasma with a high R_m and a small “exchange” parameter ξ≈H/R_m, for flow transverse to a magnetic field and near a corrugated wall. They pointed out the possible formation of “dissipationless” near-electrode layers with thicknesses on the order of the Debye or electron Larmor radii, and a “dissipative” layer whose thickness increases along the length of the electrodes and is proportional to (R_mc_B ²/c_T ²)^?1/2, where c_B and c_T are the magnetic and thermal sound velocities. Morozov and Shubin studied the properties of dissipationless and dissipative electromagnetic layers at segmented accelerator electrodes through which a current is passing, for an arbitrary “exchange” parameter, in [2] and [3], respectively. The exchange parameter ξ was found in [4]. Such layers should also exist at solid electrodes and at the nonconducting walls of an accelerator channel. Study of the two-dimensional flow in a channel is significantly simplified when such layers are present.     

Excitation by sound of Tollmien-Schlichting waves in a supersonic boundary layer

The interaction of sound with a supersonic boundary layer is considered. Because of the dependence of the main flow on the longitudinal coordinate, a sound wave generates unstable oscillations within the boundary layer. Calculations made for Mach number M = 2.0 and dimensionless frequency 2πfv_e/U_e ² = 0.91·10^?4 showed that near the lower branch of the curve of neutral stability a Tollmien—Schlichting wave can be excited with an intensity 2–3 times greater than that of the external acoustic wave.     

Hypersonic flow past a flat-plate/beveled-whistle system

The results of an experimental and numerical investigation of unsteady hypersonic nitrogen flow (M_∞ = 21 and the unit Reynolds number Re_∞1 = 6×10⁵ m^?1) past an integrated flat-plate/beveled whistle model are presented. The calculations using the ANSYS Fluent package are carried out for different geometries of the whistle cavity and angles of incidence of the model. The conditions under which fluctuations occur in the whistle are determined and the fields of the mean flow and fluctuations in the shock layer on the plate are obtained. In the experiments performed in the T-327A hypersonic nitrogen wind tunnel of the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences the dependence of the pressure fluctuations on the plate surface on the angle of attack of the model are obtained. The calculated and measured results are compared.     

L2Roe: a low dissipation version of Roe's approximate Riemann solver for low Mach numbers

A modification of the Roe scheme called L²Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M_∞=0.001) to hypersonic (M_∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L²Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. Copyright © 2015 John Wiley & Sons, Ltd.     

Application of the Skeleton Model of a Highly Porous Cellular Material in Modeling Supersonic Flow past a Cylinder with a Forward Gas-Permeable Insert

The supersonic (M_∞ = 4.85) flow past a cylinder with a forward insertmade of a highlyporous cellular material is numerically modeled within the framework of the Reynolds-averaged Navier–Stokes equations. The air flow in the gas-permeable insert is described on the basis of a skeleton model of a highly-porous medium, whose determining parameters are the porosity coefficient (95%) and the pore dimensions (1 mm) of the actual cellular material. The aerodynamic drag coefficients of the model with different lengths of the porous forward insert are calculated on the unit Reynolds number range from 6.9 × 10⁵ to 13.8 × 10⁶ m^?1. They are in agreement with the available experimental data, which indicates the adequacy of the proposed skeleton model in describing the actual properties of highly-porous materials.     

Quantifying the dynamics of flow within a permeable bed using time-resolved endoscopic particle imaging velocimetry (EPIV)

This paper presents results of an experimental study investigating the mean and temporal evolution of flow within the pore space of a packed bed overlain by a free-surface flow. Data were collected by an endoscopic PIV (EPIV) technique. EPIV allows the instantaneous velocity field within the pore space to be quantified at a high spatio-temporal resolution, thus permitting investigation of the structure of turbulent subsurface flow produced by a high Reynolds number freestream flow (Re _s in the range 9.8?×?10³?C9.7?×?10⁴). Evolution of coherent flow structures within the pore space is shown to be driven by jet flow, with the interaction of this jet with the pore flow generating distinct coherent flow structures. The effects of freestream water depth, Reynolds and Froude numbers are investigated.     

Supersonic viscous perfect-gas flow past a slender sharp elliptic cone

The supersonic M_∞ = 5 flow past slender elliptic cones with the semi-vertex angle in the plane of the major semi-axis ? _c = 4° and an isothermal surface is investigated under the assumption of the flow symmetry. Calculations on the basis of the time-dependent three-dimensional Navier-Stokes and Reynolds equations are carried out on the Reynolds number and angle of attack ranges 10⁴ ≤ Re ≤ 108 and 0 ≤ α ≤ 15° for cones with ellipticity coefficients 1/32 ≤ δ= b/a ≤ 1. The effect of the relevant parameters of the problem on the flowfield structure and the aerodynamic characteristics of the cones is demonstrated.     

Stabilization of plasma flow in a transverse magnetic field

Results are given of a theoretical and experimental investigation of the intensive interaction between a plasma flow and a transverse magnetic field. The calculation is made for problems formulated so as to approximate the conditions realized experimentally. The experiment is carried out in a magneto-hydrodynamic (MHD) channel with segmented electrodes (altogether, a total of 10 pairs of electrodes). The electrode length in the direction of the flow is 1 cm, and the interelectrode gap is 0.5 cm. The leading edge of the first electrode pair is at x = 0. The region of interaction (the region of flow) for 10 pairs of electrodes is of length 14.5 cm. An intense shock wave S propagates through argon with an initial temperature T_o = 293 °K and pressure p_o = 10 mm Hg. The front S moves with constant velocity in the region x < 0 and at time t = 0 is at x = 0. The flow parameters behind the incident shock wave are determined from conservation laws at its front in terms of the gas parameters preceding the wave and the wave velocity W_S. The parameters of the flow entering the interaction region are as follows: temperature T ₀ ¹ = 10,000 °K, pressure P ₀ ¹ = 1.5 atm, conduction ₀ ¹ = 3000 ^–1·m^–1, velocity of flow u ₀ ¹ = 3000 m·sec^–1, velocity of sounda ₀ ¹ = 1600 m·sec^–1, degree of ionization = 2%, 0.4. The induction of the transverse magnetic field B = [0, B_y(x), 0] is determined only by the external source. Induced magnetic fields are neglected, since the magnetic Reynolds number Re_m 0.1. It is assumed that the current j = (0, 0, jz) induced in the plasma is removed using the segmented-electrode system of resistance R_e. The internal plasma resistance is R_i = h(A)^–1 (h = 7.2 cm is the channel height; A = 7 cm² is the electrode surface area). From the investigation of the intensive interaction between the plasma flow and the transverse magnetic field in [1–6] it is possible to establish the place x* and time t* of formation of the shock discontinuity formed by the action of ponderomotive forces (the retardation wave R_T), its velocity W_T, and also the changes in its shape in the course of its formation. Two methods are used for the calculation. The characteristic method is used when there are no discontinuities in the flow. When a shock wave R_T is formed, a system of nonsteady one-dimensional equations of magnetohydrodynamics describing the interaction between the ionized gas and the magnetic field is solved numerically using an implicit homogeneous conservative difference scheme for the continuous calculation of shock waves with artificial viscosity [2].Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–118, September–October, 1977.     

Flow of rarefied gas past a “flat” pitot tube

The Monte Carlo method was used to calculate flow past flat Pitot tubes at angle of attack α = 0 for the following flow parameters: Mach number M_∞ = 5, 10, 20, temperature factor t_w = 1, 0.1, and Re₀ ε [0–40]. The calculations were made for two types of molecule: elastic spheres (μ ～ √T) and pseudo-Maxwellian molecules (μ ～ T). It was found that the pressure on the end in the Pitot tube has a strongly nonmonotonic dedependence on Re₀ for t_w = 0.1.     

Experimental study of shock waves from the interaction of a supersonic plasma jet with an ambient gas

Preliminary results of the interaction of a supersonic, radiatively cooled plasma jet with an ambient gas are presented. The experimental setup consists of a radial foil, a mum-thick aluminium disc held between two concentric electrodes and subjected to a 1.4 MA, 250-ns current pulse from the MAGPIE generator. The plasma flow, with typical velocities of ~70?C90?km/s, is produced by the J?× B force acting on the plasma ablated from the foil. A jet is formed from the convergence of this ablated plasma on the axis of the system. A new setup allows the jet to interact with an argon ambient (particle density N ~10^16-17 cm^?3) from a supersonic gas nozzle (Mach ~9). First results are characterised by the presence of several (previously unseen) shock structures, which are formed from the interaction of the jet with the argon ambient.     

Interaction of intersecting shocks with a flat-plate boundary layer in the presence of an entropy layer

Gas flow and heat transfer on the surfaces of sharp and blunt plates is experimentally investigated in the presence of two forward-looking wedges at the Mach numbers M = 5, 6, and 8 and the Reynolds numbers up to Re_∞L = 27×10⁶. It is shown that the entropy layer generated by a small bluntness of the leading edge of the plate can considerably change the heat transfer, the gas pressure, and the friction in the zone of interference of the shock with the plate boundary layer. Under certain conditions a small plate bluntness can also lead to a qualitative change in the flow structure. The effect of constriction of the channel between the wedges on the interference flow is studied.     

Symbolic computation of flow in a rotating pipe

A perturbation solution of the fully developed flow through a pipe of circular cross-section, which rotates uniformly around an axis oriented perpendicularly to its own, is considered. The perturbation parameter is given by R = 2Ωa²/ν in terms of the angular velocity Ω, the pipe radius a and the kinematic viscosity ν of the fluid. The two coupled non-linear equations for the axial velocity ω and the streamfunction ? of the transverse (secondary) flow lead to an infinite system of linear equations. This system allows first the computation of a given order ?_n, n ? 1, of the perturbation expansion ? = ∑ Rⁿ?_n in terms of ω_n-1, the (n-1)-th order of the expansion ω = ∑ Rⁿω_n, and of the lower orders ?₁,…,?_{n ? 1}. Then it permits the computation of ω_n from ω₀,…,ω_{n ? 1} and ?₁,…,?;_n. The computation starts from the Hagen–Poiseuille flow ω₀, i.e. the perturbation is around this flow. The computations are performed analytically by computer, with the REDUCE and MAPLE systems. The essential elements for this are the appropriate co-ordinates: in the complex co-ordinates chosen the two-dimensional harmonic (Laplace, Δ) and biharmonic (Δ²) operators are ideally suited for (symbolic) quadratures. Symmetry considerations as well as analysis of the equations for ω_n, ?_n and of the boundary conditions lead to general (polynomial) formulae for these functions, with coeffcients to be determined. Their determination, order by order, implies, in complex co-ordinates, only (symbolic) differentiation and quadratures. The coefficients themselves are polynomials in the Reynolds number c of the (unperturbed) Hagen–Poiseuille flow. They are tabulated in the paper for the orders n ? 6 of the perturbation expansion.