Variation Of Mach Number Research Articles

Modified Linear Theory Sonic Booms Compared to Experimental and Numerical Results

Sonic boom pressure profiles calculated by modified linear theory are evaluated. These methods transform parametric descriptions of aircraft into -functions, which are used to predict the pressure profiles after propagation through the atmosphere. Although Whitham’s -function equation is the most widely used method, it cannot be applied to aircraft that have discontinuities in their area profiles. Lighthill’s -function is explored as an alternative. Procedures are presented to adapt Lighthill’s method so that it can be used for numerical calculations. Sonic boom pressure profiles from wind tunnel experiments, computational fluid dynamics, and flight tests are compared to profiles from Lighthill’s method to explore its accuracy. In general, Lighthill’s method is able to predict the sonic boom shape, magnitude, and duration within 10% and account for variations in lift, Mach number, and propagation angle. Sonic boom predictions are presented for the XB-70 to demonstrate limitations in modified linear theory. Its complex shape is not easily transformed into an axi-symmetric area profile, reducing the accuracy of the pressure profile. However, this study demonstrates that modified linear theory is a fast and sufficiently accurate method to predict sonic booms and is appropriate for the preliminary and conceptual design stages of quiet sonic boom aircraft.

Nonlinear dynamics of ion acoustic waves in quantum pair-ion plasmas

The nonlinear properties of the ion acoustic waves (IAWs) in a three-component quantum plasma comprising electrons, and positive and negative ions are investigated analytically and numerically by employing the quantum hydrodynamic (QHD) model. The Sagdeev pseudopotential technique is applied to obtain the small-amplitude soliton solution. The effects of the quantum parameter$H$, positive to negative ion density ratio${\it\beta}$and Mach number on the nonlinear structures are investigated. It is found that these factors can significantly modify the properties of the IAWs. The existence of quasi-periodic and chaotic oscillations in the system is established. Switching from quasi-periodic to chaotic is possible with the variation of Mach number or quantum parameter$H$.

Effect of non-equilibrium condensation on lift divergence Mach number at transonic speeds

In the present paper, the effects of non-equilibrium condensation on the lift divergence Mach number with the angle of attack in a transonic 2-D moist air flow of NACA0012 are investigated using a numerical analysis with a total variation diminishing scheme. In the case of T0 = 298 K and α = 3°, the lift divergence Mach number Mld decreases with increasing Ф0 up to 40%, whereas beyond Ф0 = 40%, the lift divergence Mach number is nearly constant at Mld = 0.75. On the other hand, for the case of α = 6°, Mld increases with increasing Ф0 up to 47%, and then Mld begins to decrease with an increase in Ф0. Because of the attenuating effect of non-equilibrium condensation on the shock stall, for the case of α = 3°, CL generally decreases with an increase in Ф0, whereas for M∞ = 0.85, which is appreciably larger than the lift divergence Mach number, CL increases with an increase in Ф0. In the case of M∞ = 0.85, regardless of Ф0, it is shown that the location of the maximum Mach number at the upper wall side is nearly constant at x/c = 0.4. It is found that the Mach number for the minimum CL decreases with an increase in Ф0.

Mathematical modeling of fast filling process at CNG refueling stations considering connecting pipes

One of the most important parameter in design of a compressed natural gas refueling station is detailed modeling of fast filling process. In this work, a new mathematical model was developed to analyze the fast filling process at compressed natural gas refueling stations. This new model is unique because connecting pipes between reservoir tanks and on-board vehicle cylinder also were taken into account. To model the process, the equation of state, continuity, momentum and energy equations have been solved for different parts of the system. The results have been validated against the experimental data to investigate effects of connecting pipes. The mass flow rate numerical values are in good agreement with the experimental values. The study carried out for both cascade and buffer storage systems. Variations of pressure and Mach number at different parts of the system, effects of the initial reservoir tank temperature on natural gas vehicle in-cylinder pressure and temperature are presented. The results show that pressure loss through pipes is very important and should be considered. Mass flow rate between reservoir tank and on-board cylinder is nearly constant (as the flow is chocked) during filling. Temperature growth rate at the beginning of the process is higher for the buffer system. It is also found that there is a temperature rise around 85 K for ideal gas model.

Estimation of Wave Drag of Non-TransonicAirfoils Using Korn Equation

Approximation of Drag Divergence Mach number, Critical Mach Number and the Coefficient of Wave Drag of non-transonic airfoils using Korn equation are presented in this research paper. Due to the presence of the CFD factor which influences the aforementioned parameters heavily, transonic airfoils develop an undue advantage over non-transonic airfoils. A preliminary analysis of the behaviour of the airfoils is done using XFLR5 wherein the aerodynamic characteristics such as coefficient of lift, coefficient of drag, pitching moment, stall angle and aerodynamic efficiency of the airfoils are evaluated at low Reynolds Number. In order to observe the effect of camber and thickness on the performance of airfoils, airfoils of varying camber and thickness are chosen. The airfoils chosen for this research paper are NACA 0012, NACA 0018, MH 23, NLF 0115, FX 83 W108, FX 66 S196, UltraSport 1000 and Clark Y (smooth). The main objective of this paper is to computationally obtain an airfoil which can perform well under both transonic and low Reynolds number conditions.

Computational Fluid Flow Analysis of High Speed Cryogenic Turbine Using CFX

A turbo expander also referred as an expansion turbine, is a centrifugal or axial flow turbine through which a high pressure gas is expanded to produce work that is often used to drive a compressor. The low pressure exhaust gas from the turbine is at a very low temperature that is 120K or less depending upon the operating conditions. It is widely used as sources of refrigeration in industrial processes and liquefaction of gases such as oxygen, nitrogen, helium, argon and krypton. A cryogenic system needs many components, compressor, heat exchanger, expansion turbine, instrumentation, vacuum vessel etc. At present most of these process plants operate at medium or low pressure due to its inherent advantages. A basic component which is essential for these processes is the turbo expander. The main aim of this project to attain a minimum temperature and pressure and to study the variation of Mach number and entropy. This is done by computational fluid flow analysis of high speed rotating turbine. This involves with the three dimensional analysis of flow through a radial expansion turbine, using nitrogen as flowing fluid. The work is performed on various modules of Ansys that is BladGen, TurboGrid, CFX-Pre, CFX-Post. Bladegen is used to create the model of turbine using available data of hub, shroud and blade profile. Turbogrid is used to mesh the model. CFX-Pre is used to define the physical parameters of the flow through the Turbo expander. CFX-Post is used for examining and analyzing results. Using these results variation of different thermodynamic properties like Temperature, Pressure, Mach number, entropy etc. inside the turbine can be seen. Several graphs are plotted showing the variation of pressure, temperature, entropy and Mach number along streamline and span wise to analyze the flow through cryogenic turbine.

Numerical simulations of convergent-divergent nozzle and straight cylindrical supersonic diffuser

The flowfields inside a contour and a conical nozzle exhausting into a straight cylindrical supersonic diffuser are computed by solving numerically axisymmetric turbulent compressible Navier-Stokes equations for stagnation to ambient pressure ratios in the range 20 to 34. The diffuser inlet-to-nozzle throat area ratio and exit-to-throat area ratio are 21.77, and length-to-diameter ratio of the diffuser is 5. The flow characteristics of the conical and contour nozzle are compared with the help of velocity vector and Mach contour plots. The variations of Mach number along the centre line and wall of the conical nozzle, contour nozzle and the straight supersonic diffuser indicate the location of the shock and flow characteristics. The main aim of the present analysis is to delineate the flowfields of conical and contour nozzles operating under identical conditions and exhausting into a straight cylindrical supersonic diffuser.

Jet Dynamics of Co-Axial Dual Compressible Jets for Different Exit Velocity Ratios

The flow characteristics of jets emerging from a dual co-axial nozzle are investigated using Reynolds Averaged Navier Stokes calculations. The development of double shear layer from a dual compressible jet is compared with three exit velocity ratios, keeping a constant value for core exit velocity. The flow characteristics such as centreline velocity, velocity profiles in the jet development region, potential core length, turbulent kinetic energy fields, Vorticity, Mach number variation etc. are predicted from CFD simulations. The effect of secondary flow in the reduction of the growth rate of the primary shear layer, elongation of the primary potential core and the momentum transfer rate of the co-axial jet is compared. The core and secondary potential cores and the shear layers established between them are resolved together with the high turbulence regions between the shear layers. More over, vorticity in the vicinity of the primary and secondary nozzles in the three directions and the subsequent vortex dynamics studied. It is observed that the exit velocity ratio and inflow conditions have significant influence on physical mechanisms taking place within these jets. Co-axial jets exhibit complicated flow structures, depending on the mean-velocity ratio between the two streams. The study indicates that RANS calculations employing linear two-equation turbulence modelling, can predict the flow characteristics of co-axial dual jets reasonably well.

Mach number effects on the global mixing modes induced by ramp injectors in supersonic flows

AbstractModern injectors for supersonic combustors (hypermixers) augment the fuel–air mixing rate by energizing the perturbation in the mixing layer. From an instability point of view, the increased perturbation growth is linked to the increased complexity of the equilibrium base flow when compared to the axisymmetric mixing layer. Common added features are streamwise vortex streaks, oblique recompression shocks and Prandtl–Meyer expansions. One of the main effects of such distortions of the mean flow is to transform the instability responsible for the creation of fine scales from a local amplified mode to a global self-sustained fluctuation. The focus of the present research is on the flow distortion induced by flushed ramps for free-stream Mach numbers in the range 2.5–3.5. The principal mean flow features are the recirculation region due to the recompression of the flow after the ramp, the shear layer over the recirculation region and the vortex streaks propagating from the ramp corners. A global three-dimensional stability analysis and three-dimensional direct numerical simulations of small perturbations of the mean flow are performed. The growth and energy distribution of the dominant and subdominant fluctuations supported by the three-dimensional steady laminar base flow are computed. The main results are the growth rates of the self-sustained varicose and sinuous modes and their correlation to the variation in the free-stream Mach number. The complex three-dimensional wavemaker is investigated by evaluating the three-dimensional eigenfunctions of the direct and adjoint modes, and the effects of the axial vorticity generated by the ramp corners are discussed.

Large amplitude ion-acoustic double layers in warm dusty plasma

Large amplitude ion-acoustic double layer (IADL) is studied using Sagdeev's pseudo-potential technique in collisionless unmagnetized plasma comprising hot and cold Maxwellian population of electrons, warm adiabatic ions, and dust grains. Variation of both Mach number (M) and amplitude |φm| of large amplitude IADL with charge, concentration, and mass of heavily charged massive dust grains is investigated for both positive and negative dust in plasma. Our numerical analysis shows that system supports only rarefactive large amplitude IADL for the selected set of plasma parameters. Our investigations for both negative and positive dust grains reveal that ion temperature increases the mobility of ions, resulting in increase in the Mach number of IADL. The larger mobility of ions causes leakage of ions from localized region, resulting into decrease in the amplitude of IADL. Other parameters, e.g. temperature ratio of hot to cold electrons, charge, concentration, mass of heavily charged massive dust grains also play significant role in the properties and existence of double layers. Since it is well established that both positive and negative dust are found in space as well as laboratory plasma, and double layers have a tremendous role to play in astrophysics, we have included both positive and negative dust in our numerical analysis for the study of large amplitude IADL. Further data used for negative dust are close to experimentally observed data. Hence, it is anticipated that our parametric studies for heavily charged (both positive and negative) dust may be useful in understanding laboratory plasma experiments, identifying nonlinear structures in upper part of ionosphere and lower part of magnetosphere structures, and in theoretical research for the study of properties of nonlinear structures.

Propagation of Spherical Magnetogasdynamic Shock in a Radiative Gas

In this paper the propagation of explosion waves, in a conducting gas, produced on account of a point explosion into inhomogeneous self-gravitating gas sphere is considered. Radiation effects have been taken into account and the density of the gas is assumed to vary as r/sup -alpha/, r being the distance from the point of explosion. In order that the mass and pressure be positive in the equilibrium state, the choice of alpha is restricted between 1 and 3. The variation of Mach number of the shock and energy of the wave with time have been taken into consideration.

Starting characteristics of the hypersonic wind tunnel with the mach number variation

The scramjet engine test facility (SETF) of the Korea Aerospace Research Institute is a blow-down, high enthalpy wind tunnel with a free-jet test cell. The free-jet test sections can reduce choking and test larger models compared with solid wall test sections, but the facility needs an excessive starting pressure ratio and is highly unpredictable because of the free-jet space. An air ejector system was designed to simulate a Mach 3.5 test condition. Quasi one-dimensional and computational analyses of the ejector were performed. The test results of the ejector well agree with the analysis results. The SETF showed a normal-shock efficiency of 58% at the Mach 3.5 condition. The air ejector system was modified to conduct a scramjet intake test with a Mach 6.7 condition. The normal-shock efficiency of the SETF was 40% with the Mach 6.7 condition. There was almost no change in the starting pressure ratio due to blockage.

Galactic interstellar turbulence across the southern sky seen through spatial gradients of the polarization vector

Radio synchrotron polarization maps of the Galaxy can be used to infer the properties of interstellar turbulence in the diffuse warm ionized medium (WIM). In this paper, we investigate the spatial gradient of linearly polarized synchrotron emission ($|\nabla\textbf{P}|/|\textbf{P}|$) as a tracer of turbulence, the relationship of the gradient to the sonic Mach number of the WIM, and changes in morphology of the gradient as a function of Galactic position in the southern sky. We use data from the S-band Polarization All Sky Survey (S-PASS) to image the spatial gradient of the linearly polarized synchrotron emission ($|\nabla \textbf{P}|/|\textbf{P}|$) of the entire southern sky at $2.3$~GHz. The spatial gradient of linear polarization reveals rapid changes of the density and magnetic fluctuations in the WIM due to magnetic turbulence as a function of Galactic position; we make comparisons of these data to ideal MHD numerical simulations. In order to constrain the sonic Mach number ($M_{s}$), we apply a high order moments analysis to the observations and to the simulated diffuse, isothermal ISM with ideal magneto-hydrodynamic turbulence. We find that polarization gradient maps reveal elongated structures, which we associate with turbulence in the ISM. Our analysis corroborates the view of a turbulent WIM in a transonic regime $M_{s}\lesssim 2$. Filamentary structures with typical widths down to the angular resolution are seen and the observed morphologies match closely with numerical simulations and in some cases H$\alpha$ contours. The $|\nabla \textbf{P}|/|\textbf{P}|$ intensity is found to be approximately log-normal distributed. No systematic variations of the sonic Mach number are observed as a function of Galactic coordinates, which is consistent with turbulence in the WIM inferred by the analysis of H$\alpha$ data.

Quantification of initial-data uncertainty on a shock-accelerated gas cylinder

We quantify initial-data uncertainties on a shock accelerated heavy-gas cylinder by two-dimensional well-resolved direct numerical simulations. A high-resolution compressible multicomponent flow simulation model is coupled with a polynomial chaos expansion to propagate the initial-data uncertainties to the output quantities of interest. The initial flow configuration follows previous experimental and numerical works of the shock accelerated heavy-gas cylinder. We investigate three main initial-data uncertainties, (i) shock Mach number, (ii) contamination of SF6 with acetone, and (iii) initial deviations of the heavy-gas region from a perfect cylindrical shape. The impact of initial-data uncertainties on the mixing process is examined. The results suggest that the mixing process is highly sensitive to input variations of shock Mach number and acetone contamination. Additionally, our results indicate that the measured shock Mach number in the experiment of Tomkins et al. [“An experimental investigation of mixing mechanisms in shock-accelerated flow,” J. Fluid. Mech. 611, 131 (2008)] and the estimated contamination of the SF6 region with acetone [S. K. Shankar, S. Kawai, and S. K. Lele, “Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder,” Phys. Fluids 23, 024102 (2011)] exhibit deviations from those that lead to best agreement between our simulations and the experiment in terms of overall flow evolution.

The drag reduction study of the supercritical airfoil with shock control bump considering the robustness

The shock control bump of supercritical airfoil is numerically investigated by Computational Fluid Dynamics in present paper. The influence of the geometry parameters of the bump is studied by considering the drag reduction performance and robustness. The results show that, the bump location strongly affects on the drag reduction. The best performance is obtained when locating the bump crest at the shock position of the clean airfoil. Higher bump is worse for the drag reduction, while longer bump has good effect in a bigger height range. The bump can effectively weaken the shock wave, suppress the boundary layer separation, and extend the buffet onset boundary, but its working lift coefficient range is relatively narrow. The robustness is an important requirement of engineering application. The results of robustness analysis shows that, the longer and lower bump is more engineering acceptable than the shorter and higher bump, while it could not only improve lift-drag ratio in larger lift coefficient range insensitive to the changes of shapes and Reynolds number, but also increase the drag divergence Mach number.

Numerical analysis of the step jump structure of a scramjet flow by the DSMC method

Computations using the direct simulation Monte Carlo method are presented for hypersonic rarefied flow over a supersonic combustion ramjet (scramjet). The primary object of this study is to examine the geometrical effects of a step jump on flow field structures. The sensitivity of internal flow properties, including shock interaction, vortex, pressure and temperature distributions to free-stream Mach number and configuration variations, such as the step height and the ratio of isolator to combustor, is analyzed. Comparisons are made between cases with various configurations, based on surface pressure and temperature. It is shown that different isolator to combustor ratios and expansion ratios cause profoundly different results. The flow structures generated in the scramjet inlet directly affect vehicles operating at high speeds and high altitudes.

Incident shock Mach number effects on Richtmyer-Meshkov mixing in a heavy gas layer

Experiments were performed at the horizontal shock tube facility at Los Alamos National Laboratory to study the effect of incident shock Mach number (M) on the development of Richtmyer-Meshkov instability after a shock wave impulsively accelerates a varicose-perturbed, heavy-gas curtain. Three cases of incident shock strength were experimentally investigated: M = 1.21, 1.36, and 1.50. We discuss the state of the mixing and the mechanisms that drive the mixing at both large and small scales by examining the time evolution of 2D density fields derived from quantitative planar laser-induced fluorescence measurements. Several differences in qualitative flow features are identified as a result of Mach number variation, and differences in vortex interaction, observed using particle image velocimetry, play a critical role in the development of the flow field. Several quantities, including mixing layer width, mixing layer area, interface length, instantaneous mixing rate, the density self-correlation parameter, probability density functions of the density field, and mixing progress variables are examined as a function of time. These quantities are also examined versus time scaled with the convection velocity of the mixing layer. A higher incident Mach number yields greater mixing uniformity at a given downstream location, while a lower Mach number produces a greater amount of total mixing between the two gases, suggesting possible implications for optimization in applications with confined geometries.

Numerical Investigation of Viscous Laminar Supersonic Flow Past an Asymmetric Biconvex Circular-Arc Aerofoil

A numerical investigation of two-dimensional unsteady, viscous and laminar compressible flow past an asymmetric biconvex circular-arc aerofoil in supersonic regime is carried out. The focus of the present work is to investigate the effects of variation of Mach number, at two different angles of attack, on the flow and force characteristics on NACA 2S-(50)(04)-(50)(20) aerofoil. The value of Reynolds number is taken as 5x105. The computations are carried out at Mach numbers of 1.25, 1.5 and 2.0 at an angle of attack of α=0° and α=10°. It is found that the aerofoil works well in the supersonic flow and, unlike the conventional symmetric biconvex aerofoil, generates finite lift at α=0° due to stronger shock waves at the lower surface. Moreover, the L/D ratio at α=10° is always found to be more than 2.5.

Axial Loss Development in Low Pressure Turbine Cascades

The objective of this work presented in this paper is to study the performance of low-pressure turbines in detail by extensive numerical simulations. The numerical flow simulations were conducted using the general purpose code ANSYS CFX. Particular attention is focused on the loss development in the axial direction within the flow passage of the cascade. It is shown that modern computational fluid dynamics (CFD) tools are able to break down the integral loss of the turbine profile into its components, depending on attached and separated flow areas. In addition, the numerical results allow one to show the composition of the loss depending on the Reynolds number. The method of the analysis of axial loss development presented here allows for a much more comprehensive investigation and evaluation of the quality of the numerical results. For this reason, the paper also demonstrates the capability of this method to quantify the influence of the axial velocity density ratio, the inflow turbulence level, the inflow angle, and the Reynolds number on the loss configuration and the flow angle of the cascade as well as a comparison of steady state and transient results. The validation data of this low pressure turbine (LPT) cascade have been obtained at the High Speed Cascade Wind Tunnel of the Institute of Jet Propulsion. For this purpose, experiments were conducted within the range of Re2th = 40,000 to 400,000. To gather data at realistic engine operation conditions, the wind tunnel allows for an independent variation of Reynolds and Mach number. The experimental results presented herein contain detailed pressure measurements as well as measurements with 3D hot-wire anemometry. However, this paper shows only integral values of the experimental as well as the numerical results to protect the proprietary nature of the LPT design.

Physical processes influencing acoustic radiation from jet engine inlets

AbstractNumerical simulations of acoustic radiation from a jet engine inlet are performed using advanced computational aeroacoustics algorithms and high-quality numerical boundary treatments. As a model of modern commercial jet engine inlets, the inlet geometry of the NASA Source Diagnostic Test is used. Fan noise consists of tones and broadband sound. This investigation considers the radiation of tones associated with upstream-propagating duct modes. The primary objective is to identify the dominant physical processes that determine the directivity of the radiated sound. Two such processes have been identified. They are acoustic diffraction and refraction. Diffraction is the natural tendency for an acoustic duct mode to follow a curved solid surface as it propagates. Refraction is the turning of the direction of propagation of a duct mode by mean flow gradients. Parametric studies on the changes in the directivity of radiated sound due to variations in forward flight Mach number, duct mode frequency, azimuthal mode number and radial mode number are carried out. It is found there is a significant difference in directivity for the radiation of the same duct mode from an engine inlet when operating in static condition versus one in forward flight. It will be shown that the large change in directivity is the result of the combined effects of diffraction and refraction.