Medium Mach Number Research Articles

A new correlation of average temperature and maximum heat flux for turbulent supersonic flow in a large size channel up to Mach 5

Supersonic compressible turbulent flow through a large size channel is studied numerically. The flow is modeled by the Favre averaged Navier-Stokes (FANS) equation with k−ω as turbulence model, the resulting governing equations are solved by employing an in-house unsteady state density based solver developed using sixth order accuracy compact finite difference schemes. The effect of Mach number and different wall thermal boundary conditions influencing, the variation of velocity, temperature and density across the channel height are reported in the present study. In the present study, the height of the channel is considered as 10 mm and the bulk Reynolds number is in the range of 3.42×105 to 1.14×106 which is higher compared to previous studies. Furthermore, the present Reynolds number represents a fully turbulent flow scenario, common in many aerospace applications. The results indicate that for an adiabatic wall with higher Mach number, there is a substantial increase in the wall temperature. The flow characteristics for a heated wall carried at low and medium Mach numbers indicate that for higher wall temperature, the behaviour of flow characteristics shifts towards that of the adiabatic wall behaviour. However, for higher Mach numbers the flow characteristics behaves like that of isothermal wall condition. In the present work, mathematical correlations for average temperature and maximum heat flux based on the Mach number are developed for adiabatic and isothermal wall conditions, respectively. The present results are validated with direct numerical simulation (DNS) results reported in the literature.

He2+ dynamics and ion cyclotron waves in the downstream of quasi‐perpendicular shocks: 2‐D hybrid simulations

AbstractThe free energy provided by the ion temperature anisotropy is considered to be the source of ion cyclotron waves in the downstream of a quasi‐perpendicular shock. Besides the proton cyclotron waves excited by the proton temperature anisotropy, He2 + is decelerated differentially from the protons by the shock due to its different charge‐to‐mass ratio and forms a bunched ring‐like distribution in the immediate downstream of the quasi‐perpendicular shock. However, how the helium cyclotron waves associated with the anisotropic distribution of He2 + are excited is still in debate. In this paper, with two‐dimensional (2‐D) hybrid simulations, we investigate He2 + dynamics and its role in the ion cyclotron waves downstream of quasi‐perpendicular shocks (the proton plasma beta in the upstream is 0.4). A bunched ring‐like distribution of He2 + is formed in the immediate downstream of the quasi‐perpendicular shocks; then it evolves into a shell‐like distribution. At last, a bi‐Maxwellian distribution of He2 + is generated in the far downstream. In the medium and low Mach number shocks, besides the proton cyclotron waves excited near the shock front, there is another enhancement of the magnetic fluctuations in the downstream. The results show that the helium cyclotron waves can be driven directly by the bunched ring‐like distribution of He2 + in a low or medium Mach number quasi‐perpendicular shock. The relevance of our simulation results to the satellite observations is also discussed in this paper.

Aircraft Endurance Maximization at Medium Mach Numbers by Extremum Seeking

Aircraft endurance is maximized by optimizing the lift to drag ratio over a two-dimensional space spanned by the angle of attack and the Mach number, constrained to a one-dimensional curve on which the lift equals the weight of the aircraft. The gradient estimator used in the optimization is excited by atmospheric turbulence in the vertical and longitudinal directions. This new form of extremum seeking requires a reformulation of the standard gradient estimator used in extremum seeking to provide gradient estimates that are independent of the amplitude of the dither signal. A new gradient estimator based on an estimation error approach is presented to this end. Through stochastic averaging analysis, the estimator is shown to stabilize the aircraft to the optimal endurance speed, with a bias that is proportional to the square of the turbulence amplitude and thus is small when the turbulence is light. The controller is tested in a high-fidelity six-degree-of-freedom simulation provided by local industry. Simulation results show the maximization of aircraft endurance and even a slight improvement compared to flight at the nominal loiter speed of the aircraft being simulated.

Propagation and Stability Properties of Radio Jets in Cluster Cooling Flow Atmospheres

We present results from the first self-consistent, multidimensional simulations of perturbed radio jets in a realistic, cluster cooling flow atmosphere. The supersonic, steady state cooling flow atmosphere used in this work is unique in that it is evolved numerically from an isothermal, equilibrium state. Jets of varying Mach number are passed through this atmosphere and their ultimate rate is found to depend strongly on Mach number. Low Mach number jets (M j =3) effectively stagnate due to the ram pressure of the cooling flow atmosphere while medium Mach number jets (M j =6-12) become unstable and disrupt in the cooling flow to form amorphous structures. High Mach number jets (M j >50) manage to avoid disruption and are able to propagate through the cooling flow

Structure of medium Mach number quasi‐parallel shocks: Upstream and downstream waves

Satellite observations of quasi‐parallel collisionless shocks document a complex behavior that has proven to be extraordinarily difficult to analyze and interpret. Recent data analyses and computer simulations, however, have revealed that these shocks can be unsteady and cyclically reforming, and have shed some light on the processes that are involved. Despite this progress, a number of issues regarding the ion thermalization at and re‐formation of quasi‐parallel shocks are still not well understood. Previous simulation studies at high Mach numbers have suggested either the convection of far upstream density perturbations into the shock or an instability at the shock interface as mechanisms contributing to the shock re‐formation. On the other hand, simulations at low Mach numbers have shown a steady shock. To understand the transition from steady low Mach number to unsteady high Mach number shocks, we have performed large‐scale one‐dimensional hybrid code simulations at increasing Mach numbers. We find that fast‐mode waves with wavelengths longer than phase‐standing whistlers are excited upstream from the shock by backstreaming ions. At increasing Mach numbers, the phase and group velocities of the dominant waves are reduced until they point back toward the shock. When there is sufficient energy flux in these waves, they lead to unsteady shock behavior and eventually to shock re‐formation. For typical solar wind conditions and an angle of θBn = 30° between the shock normal and the upstream magnetic field, we find the shock to become unsteady at MA ∼ 2.3. Various spectral diagnostics are employed to investigate the properties of the excited upstream and downstream waves. Fast‐mode wave energy that is convected through the shock is partially mode converted into downstream Alfvén and slow‐mode fluctuations. This mechanism may be responsible for some of the turbulence observed downstream of the the Earth's quasi‐parallel bow shock. An analysis of the shock dynamics indicates that there are no characteristic time scales associated with the unsteady medium Mach number shocks.

Shock Excitation of Powdered Solids. I. Spectroscopic Observations

Spectroscopic observations have been made in emission and absorption upon the luminosity which arises from the interaction between helium driven shock waves in argon and powdered solids. Astrophysically important metallic oxides, powdered meteorites, pure metals, and certain organic compounds have been subjected to shock excitation. The spectrum of the resulting luminosity is entirely molecular at low Mach numbers (4), entirely atomic at high Mach numbers (8), and mixed atomic and molecular at medium Mach numbers. Thus the shock tube appears to be an important new tool in the spectroscopic laboratory for the controlled excitation of spectra which are difficult to excite by more conventional means. Preliminary experiments which have been made using time resolved emission and time resolved absorption techniques have shown that the reflected shock wave is largely responsible for the excitation. The absorption experiments are also being performed to measure the oscillator strengths of bands of the metallic oxides.

On the Measurement of Supersonic Aerofoil Drag by Pressure Traverse

SummaryThe drag in two-dimensional flow is expressed in terms of the distributions of static and stagnation pressures along a traverse line downstream of the aerofoil. Sources of error are discussed with regard to their effect on the accuracy of drag measurement in small tunnels at medium Mach numbers.

Analytical treatment of two-dimensional supersonic flow. I. Shock-free flow

A solution is presented for the general, wave-interaction problem of steady, irrotational, homentropic flow of a perfect gas. It can be interpreted as a convergent process of successive approximations, based on the solution of linearized theory, for shock-free flow. It constitutes an approximate solution for flow with weak shocks. In part I, the equations of motion are transformed into linear equations in characteristic variables. Their solution is of different type according to whether the flow is near-sonic, hypersonic, or in between these extremes. Special attention is given to the types of boundary condition which occur in physical problems, and solution methods are devised to cope with these types in the medium Mach number range. The method of Riemann functions is used to calculate accurately the pressure distribution in the first interaction region of a jet expanding from a perfect nozzle. It is shown by the help of double power series that shock waves will always occur in the first period of such a jet, even for pressure ratios arbitrarily near unity. The Riemann function approach is also shown to be suitable for the approximate calculation of the flow past aerofoils of prescribed shape; when the requirements of accuracy are exacting, the method of double power series expansion presents the problem in a form suited to high-speed digital computers.

Characteristics of the Turbulent Boundary Layer on a Flat Plate in Compressible Flow from Measurements of Friction in Pipes

With the development of high-speed aerodynamics, the influence of compressibility on the boundary layer becomes of growing importance. In the case of laminar flow, this influence has been treated in numerous papers, while for the turbulent boundary layer, which is less convenient to treat analytically, the literature is rather scarce. From the practical standpoint, however, the latter is in all probability the more important, since the transonic and supersonic velocities achieved at the present time are, in general, connected with Reynolds Numbers that , according to experience with incompressible flow, should lie well in the turbulent range. In cases of extremely high supersonic speeds only, since they will be restricted to gases of low density, Reynolds Numbers will be low enough so that extensive laminar boundary layers can be expected. Hence, extensive turbulent boundary layers will mainly occur in the low and medium Mach Number ranges. Therefore, it seems to be worth while to approach the problem by starting with formulas for incompressible flow and to allow for the heat due to friction by introducing simplified thermodynamic relations. Attempts of this kind have been made by von Karman, Frankl, and Tetervin. They require, however, certain arbitrary assumptions regarding appropriate values for density and viscosity (values at the wall surface, in the free stream, or some mean values) which can be established only by experiments. The present paper attempts to eliminate the arbitrary character by applying the results of tests in pipes to the plate problem by a method analogous to that used first for the incompressible case by Prandtl and von Karman.