Maximum Mach Number Research Articles

Numerical Investigation of Influence of Entropy Wave on the Acoustic and Wall Heat Transfer Characteristics of a High-Pressure Turbine Guide Vane

As an indirect noise source generated in the combustion chamber, entropy waves are widely prevalent in modern gas turbines and aero-engines. In the present work, the influence of entropy waves on the downstream flow field of a turbine guide vane is investigated. The work is mainly based on a well-known experimental configuration called LS89. Two different turbulence models are used in the simulations which are the standard k-ω model and the scale-adaptive simulation (SAS) model. In order to handle the potential transition issue, Menter’s ð-Reθ transition model is coupled with both models. The baseline cases are first simulated with the two different turbulence models without any incoming perturbation. Then one forced case with an entropy wave train set at the turbine inlet at a given frequency and amplitude is simulated. Results show that the downstream maximum Mach number is rising from 0.98 to 1.16, because the entropy waves increase the local temperature of the flow field; also, the torque of the vane varies as the entropy waves go through, the magnitude of the oscillation is 7% of the unforced case. For the wall (both suction and pressure side of the vane) heat transfer, the entropy waves make the maximum heat transfer coefficient nearly twice as the large at the leading edge, while the minimum heat transfer coefficient stays at a low level. As for the averaged normalized heat transfer coefficient, a maximum difference of 30% appears between the baseline case and the forced case. Besides, during the transmission process of entropy waves, the local pressure fluctuates with the wake vortex shedding. The oscillation magnitude of the pressure wave at the throat is found to be enhanced due to the inlet entropy wave by applying the dynamic mode decomposition (DMD) method. Moreover, the transmission coefficient of the entropy waves, and the reflection and transmission coefficients of acoustic waves are calculated.

Dynamics of unsteady compressible cavitating flows associated with the cavity shedding

The main purpose of this work is to shed light on the physics involved in the two distinct cavity cloud shedding mechanisms in cloud cavitating flows, namely re-entrant jet mechanism (RJM) and shock wave propagation mechanism (SWM). A compressible cavitating flow solver, which considers the compressibility effects of both liquid and vapor, is used to account for the wave dynamics in cavitating flows. The compressible Navier-Stokes equations, coupling the mass, momentum energy equations, and phase fraction transport equation, along with the thermodynamic equations of state for both liquid and vapor, Saito cavitation model and the SST-SAS turbulence model, are solved. Numerical results are presented for the conditions of both the re-entrant jet mechanism and shock wave mechanism around a NACA66 (mod) hydrofoil (Leroux et al., 2005), respectively, with emphasis on the process of re-entrant jet development and shock wave formation and propagation. The results show that the re-entrant jet can cause the attached cavity sheet breakup for both the two cavity cloud shedding mechanisms in both high and low angle of attack, while the shock wave formation and propagation process only occurs under shock wave mechanism at low angles of attack. Pressure evolution illustrates that in the re-entrant jet mechanism, cavity cloud collapse will induce high pressure load, while no shock wave and thus the corresponding rebound phenomenon are observed. In shock wave mechanism, during the whole process of the shock wave dynamics, namely generation, propagation and rebound process, pressure fluctuations increase sharply along with the generation of the pressure peaks with large amplitude and short time interval. Further study on the compressible characteristics involved in the two cavity shedding mechanisms illustrates that vapor fraction and mass transfer have a significant effect in sonic speed and Mach number characteristics. The average and standard derivation of maximum Mach number (Mamax) in shock wave mechanism is lower than that in re-entrant jet mechanism. Cavitating flows are characterized by low sonic speed value in the cavitation region and high sonic speed value in the pure liquid region and a sonic speed boundary layer exists between the two regions, the thickness of which is about the size of the local attached cavity sheet on foil surface. In the process of shock wave generation and rebound, cavity volume and cavity volume rate experience large fluctuations, showing strong cavitation instabilities in shock wave mechanism.

Theory, Analysis, and Applications of the Entropic Lattice Boltzmann Model for Compressible Flows.

The entropic lattice Boltzmann method for the simulation of compressible flows is studied in detail and new opportunities for extending operating range are explored. We address limitations on the maximum Mach number and temperature range allowed for a given lattice. Solutions to both these problems are presented by modifying the original lattices without increasing the number of discrete velocities and without altering the numerical algorithm. In order to increase the Mach number, we employ shifted lattices while the magnitude of lattice speeds is increased in order to extend the temperature range. Accuracy and efficiency of the shifted lattices are demonstrated with simulations of the supersonic flow field around a diamond-shaped and NACA0012 airfoil, the subsonic, transonic, and supersonic flow field around the Busemann biplane, and the interaction of vortices with a planar shock wave. For the lattices with extended temperature range, the model is validated with the simulation of the Richtmyer–Meshkov instability. We also discuss some key ideas of how to reduce the number of discrete speeds in three-dimensional simulations by pruning of the higher-order lattices, and introduce a new construction of the corresponding guided equilibrium by entropy minimization.

Plasma Collision in a Gas Atmosphere.

We present a study on the impact of a gas atmosphere on the collision of two counterpropagating plasmas (gold and carbon). Imaging optical Thomson scattering data of the plasma collision with and without helium in between have been obtained at the Omega laser facility. Without gas, we observed large scale mixing of colliding gold and carbon ions. Once ambient helium is added, the two plasmas remain separated. The difference in ionic temperature is consistent with a reduction of the maximum Mach number of the flow from M=7 to M=4. It results in a reduction of a factor ∼10 of the counterstreaming ion-ion mean free path. By adding a low-density ambient gas, it is possible to control the collision of two high-velocity counterstreaming plasma, transitioning from an interpenetrating regime to a regime in agreement with a hydrodynamic description.

2D Hypersonic Scramjet Inlet Geometry of Mach 7 using CFD

In the era of space transportations there is a huge demand on space technology to improve on cost reduction and take the heavy loads into space. Thus the load carrying capacities will be increase with this air breathing engines. This work gives a report on the design, analysis of optimal 2D scramjet engine inlet operating at Mach 7 without use of movable geometry. A computational study for scramjet inlet with different ramp angles is carried out. Several cases are considered to compress the air by rounding leading edge without moving the whole cowl up and down, by fixing the cowl lip and assuming axisymmetric inlet with rounded edge. The numerical tests are conducted to obtain maximum total pressure recovery, drag force and outlet Mach number for given flight condition. Two dimensional effects are studied with Navier-strokes approach to compute the pressure and Mach number at a different location. Oblique shock waves, expansion waves and shock wave interactions are primarily focused. Computational Fluid Dynamics (CFD) solver is used; steady flow simulations are carried out for inlet geometries with one, two, three and four ramps. Geometrical shape is redesigned based on oblique shock wave analysis. The corrected model is tested on Fluent with boundary layer considerations that the theoretical analysis is not able to cover. Lastly, a conclusion summarizing the design process is drawn and the optimal model is recommended for the Mach 7 inlet with different ramps with contraction ratio 10. It had been observed that two ramp scramjet inlet model has been preferred to use which has optimum pressure recovery and lower drag.

Analysis of the maximum flight Mach number of hydrocarbon-fueled scramjet engines under the flight cruising constraint and the combustor cooling requirement

Scramjet is the optimal propulsion system for hypersonic vehicles, and it is important to study its maximum flight Mach number. Upper limit and its influence factors of the flight Mach number of dual-mode scramjet used in hypersonic vehicles are investigated in this paper. Scramjet performance analysis model with the constant-area heating process, cooling requirement analysis model of the combustor and cruise model of the scramjet-powered hypersonic vehicle are established. Specific impulse of dual-mode scramjet engine with hydrocarbon fuel is similar to that of liquid oxygen kerosene rocket engine when the freestream Mach number is above 10. The ratio of hypersonic vehicle reference area to scramjet inlet capture area is introduced to establish the size relationship between the scramjet engine and the hypersonic vehicle. Considering the balance of thrust and drag, smaller ratio of hypersonic vehicle reference area to scramjet inlet capture area leads to higher flight Mach number that hypersonic vehicle can cruise. When the angle of attack is 10 degrees, the ratio of hypersonic vehicle reference area to scramjet capture area should be less than 5.5 to ensure that the vehicle can work at Mach 8. The maximum length to diameter ratio of the combustor is used to indicate active cooling requirements, and it is less than 5 under the cooling requirement when flight Mach number is above 9. Reducing the heat flux at the combustor wall and increasing the fuel heat sink is helpful to increase the allowable combustion chamber length, so as to increase the maximum flight Mach number of the scramjet engine on the premise of meeting thermal protection requirement.

Coupled combustion characteristics of the base-bleed propellant and the igniter under transient depressurization based on detailed chemical kinetics

The coupled combustion process of AP/HTPB propellant and ignition jet in the base-bleed device is studied and analyzed by numerical simulation under transient depressurization. Two-dimensional axisymmetric simulation was established using Navier-Stokes equations, Realizable k-ε turbulence model and finite-rate chemical reaction model. The chemical reaction process of AP/HTPB, using 37 components and 127 chemical reaction equations, simulates the actual process of AP/HTPB combustion. The temperature field, velocity field and concentration field of components were obtained by solving, the analysis of the development process of the ignition jet realized the coupled combustion process of the AP/HTPB with ignition, an annular recirculation zone formed by multi-component blending was observed, and the interaction between the AP/HTPB combustion products and the ignition jet made the maximum Mach number reach to 1.2 near the nozzle of base-bleed device during the process of transient depressurization. The flow development process of H2 and CO2 under the action of the ignition jet is analyzed. It is known that H2 mainly flows near the AP/HTPB burning surface, while most of the CO2 is mixed in the ignition jet. After analyzing the reactants, products and intermediates in the H2 and CO2 reaction, the reason why the H2 and CO2 components are almost completely opposite is explained: the main combustion products H2 and CO are concentrated near the burning surface, while CO2 mainly reacts reversibly with CO. Therefore, the concentration distribution of CO2 is basically opposite to CO. Through the calculation and analysis of the transient depressurization process in the combustion chamber of the base-bleed device under multiple working conditions, it is known that the initial combustion pressure has a great impact on the depressurization in the combustion chamber before t = 1 ms. After t = 2 ms, the effect of initial combustion pressure on the depressurization is almost negligible.

Effects of steady and pulsed discharge arcs on shock wave control in Mach 2.5 flow

The effects of the steady and pulsed arc discharge on the oblique shock wave control are explored through an experimental study in a supersonic wind tunnel with the maximum design Mach number of 2.5. The oblique shock is formed by a compression ramp with an angle of 7 degree mounted on the floor of the wind tunnel. Four electrodes are placed upstream of the compression ramp and spaced equally in the spanwise direction to generate the discharge arcs. The steady discharge is generated between the electrodes and downstream ramp corner, forming streamwise arcs. The arc length can be modulated between 10 mm and 40 mm by moving the electrodes in the streamwise direction. With a High Frequency Switch (HFS), the pulsed discharge is achievable with a frequency range from 5 kHz to 50 kHz. The pulsed discharge is generated between two adjacent electrodes, forming so-called transversal arcs, which are blown downstream by the main flow. Results show that the steady discharge arcs act like a uniformly distributed conductor. With an increase of the arc length, the arc power increases, and the weakening effect on the shock is enhanced. For the pulsed discharge arcs, the shorter arcs are observed with higher discharge frequency, which implies a lower arc power. Overall, the weakening effect of the steady arcs on the shock is more effective with shock strength reduced by 4%, compared to the pulsed ones with only 0.35% reduction.

Thermodynamic performance evaluation of a turbine-less jet engine integrated with solid oxide fuel cells for unmanned aerial vehicles

The performance of conventional turbine engines for unmanned aerial vehicles (UAVs) is limited by the combustor exit temperature and the concept of turbine-less jet engines was proposed. For the engine, compressors are powered by a battery in the current study. The endurance and thrust-weight ratio of UAVs equipped with the turbine-less jet engines are strongly affected by the performance of batteries. In order to improve the performance of UAVs, the feasible scheme of turbine-less jet engines integrated with a solid oxide fuel cell (TLFC engine) is put forward. For the TLFC engine, reformed gas is provided to the solid oxide fuel cell (SOFC). The SOFC produces electric power to drive the compressor by a motor. Then, the extra fuel and SOFC exhaust enter into the combustor. The combustor exhaust expands and produces propulsion power in the nozzle. In order to evaluate the performance of the TLFC engine, the thermodynamic analysis model is built. The effects of pressure ratios, combustor exit temperature, flight Mach number and flight altitude on the TLFC engine are studied. The preliminary results are as follows. The TLFC engine has obvious advantages over the traditional turbojet engine in specific thrust and specific impulse. The increment of the specific thrust ranges from 27% to 55%. The maximum pressure ratio and Mach number are 33 and 0.89, respectively.

Mach number and energy loss analysis inside multi-stage Tesla valves for hydrogen decompression

Multi-stage Tesla valves in the reversed flow state can be applied during the hydrogen decompression process between the high pressure hydrogen storage vessel and the fuel cell. Under high-pressure turbulent hydrogen flow, severe aerodynamic noise may be caused and large energy loss inside Tesla valves may be generated, which can cause uncomfortable noise in vehicles. In this paper, the valve stage number and the pressure ratio between the inlet and the outlet are analyzed to investigate the possibility of the occurrence of aerodynamic noise and energy loss inside Tesla valves, and Mach number, turbulent dissipation rate, and exergy loss are used and evaluated as the criterion. The results show that both Mach number and exergy loss increase with the increasing of pressure ratio, but with the decrease of valve stage number, Mach number increases and exergy loss decreases. In addition, large turbulent dissipation rate at each valve stage appears near the bifurcation and the confluence between the straight channel and the bend channel of multi-stage Tesla valves. The correlation between the valve stage number, the pressure ratio, and the maximum Mach number is fitted, which can be used to estimate the possibility of the occurrence of aerodynamic noise.

Numerical investigation on effect of divergent angle in convergent-divergent rocket engine nozzle

In rocket, a nozzle is used to control mass flow rate, velocity distribution and pressure of the exhaust gas that emerges out from the combustion chamber. The nozzle is used to alchemize the chemical and thermal energy generated in the combustion chamber into thrust. The nozzle metamorphoses the high pressure, high temperature, low velocity gas in the combustion chamber into high velocity, low pressure and temperature. The design of nozzle is an important aspect for achieving the maximum Mach number and minimum turbulent intensity. In this study, the numerical investigation is done at different divergent angles to find the effect of divergent angle on Mach number and static pressure. The different divergent angles used for analysis are 9°, 12°, 15° and 18°. The inlet boundary conditions were specified according to the available experimental information. The results evaluated and compared with the help of different contours and graphs to figure out the optimum divergent angle with maximum Mach number.

Radiation pressure in galactic discs: stability, turbulence, and winds in the single-scattering limit

The radiation force on dust grains may be dynamically important in driving turbulence and outflows in rapidly star-forming galaxies. Recent studies focus on the highly optically-thick limit relevant to the densest ultra-luminous galaxies and super star clusters, where reprocessed infrared photons provide the dominant source of electromagnetic momentum. However, even among starburst galaxies, the great majority instead lie in the so-called "single-scattering" limit, where the system is optically-thick to the incident starlight, but optically-thin to the re-radiated infrared. In this paper we present a stability analysis and multidimensional radiation-hydrodynamic simulations exploring the stability and dynamics of isothermal dusty gas columns in this regime. We describe our algorithm for full angle-dependent radiation transport based on the discontinuous Galerkin finite element method. For a range of near-Eddington fluxes, we show that the medium is unstable, producing convective-like motions in a turbulent atmosphere with a scale height significantly inflated compared to the gas pressure scale height and mass-weighted turbulent energy densities of $\sim 0.01-0.1$ of the midplane radiation energy density, corresponding to mass-weighted velocity dispersions of Mach number $\sim 0.5-2$. Extrapolation of our results to optical depths of $10^3$ implies maximum turbulent Mach numbers of $\sim20$. Comparing our results to galaxy-averaged observations, and subject to the approximations of our calculations, we find that radiation pressure does not contribute significantly to the effective supersonic pressure support in star-forming disks, which in general are substantially sub-Eddington. We further examine the time-averaged vertical density profiles in dynamical equilibrium and comment on implications for radiation-pressure-driven galactic winds.

Supersonic piston synthetic jets with single/multiple orifice

We experimentally study a high-speed synthetic jet actuator consisting of a cylinder with an orifice plate at the top and a piston driven by a motor. The experiments are performed for four orifice plates with a single hole or multiple holes with different diameters. The characteristics of the synthetic jets are investigated with cylinder pressure measurement and flow visualization based on the shadowgraph method, where the Mach disks in the shadowgraph images are used for estimating the Mach number of supersonic synthetic jets. A total orifice area on the plate affects cylinder pressure and jet Mach number. The number of the orifices has a direct influence on the downstream region where the jets from different orifices interact with each other. A smaller total orifice area results in a higher jet Mach number, a larger spatial extent of Mach disks, and an earlier formation of the Mach disks in one cycle. The influences of total orifice area are well explained by larger/smaller values of maximum/minimum values of the cylinder pressure for a smaller total orifice area. It is also found that the maximum jet Mach number is represented as a function of the maximum cylinder pressure even for different orifice configurations. Furthermore, for a given operating frequency, the maximum cylinder pressure increases almost linearly with the stroke length divided by an effective diameter of the total orifice area independently of the number of the orifices.

Experimental Investigations on Microshock Waves and Contact Surfaces.

The present work reports on progress in the research of a microshock wave. Because of the lack of a good understanding of the propagation mechanism of the microshock flow system (shock wave, contact surface, and boundary layer), the current work concentrates on measuring microshock flows with special attention paid to the contact surface. A novel setup involving a glass capillary (with a 200 or 300 μm hydraulic diameter D) and a high-speed magnetic valve is applied to generate a shock wave with a maximum initial Mach number of 1.3. The current work applies a laser differential interferometer to perform noncontact measurements of the microshock flow's trajectory, velocity, and density. The current work presents microscale measurements of the shock-contact distance L that solves the problem of calculating the scaling factor Sc=Re×D/(4L) (introduced by Brouillette), which is a parameter characterizing the scaling effects of shock waves. The results show that in contrast to macroscopic shock waves, shock waves at the microscale have a different propagation or attenuation mechanism (key issue of this Letter) which cannot be described by the conventional "leaky piston" model. The main attenuation mechanism of microshock flow may be the ever slower moving contact surface, which drives the shock wave. Different from other measurements using pressure transducers, the current setup for density measurements resolves the whole microshock flow system.

On the error of the time–pulse method of measuring air consumption in mines

The derivation of a formula for the time during which a sound signal propagates between two given points A and B in a stationary gas flow is considered. It is shown that the gas flow changes the signal reception time by a quantity proportional to the consumption, regardless of the detailed velocity profile. The difference between the reception time of signals from point B to the point A and vice versa is proportional to air consumption with high accuracy. It is shown that the relative error of the obtained formula does not exceed the squared maximum Mach number in the gas flow. This allows measurement of the consumption of gas moving in a mine with an arbitrary stationary subsonic velocity field.

Mach Number Distribution and Profile Losses for Low-Pressure Turbine Profiles With High Diffusion Factors

The results of this investigation come from two linear cascades at high diffusion factors (DFs). The measurements presented for each low-pressure turbine (LPT) profile were conducted at midspan under a range of Reynolds- and exit Mach numbers. The exit Mach number was varied in a range covering low subsonic up to values where a transonic flow regime on the suction side of the blade could be expected. This work focuses on two profiles with a diffusion factor in a range of 0.18≤DF≤0.22, where values in this range are considered as a comparable for the two cascades. Profile A is a front-loaded design and has shown no obvious flow separation on the suction side of the blade. Compared to the design A, design B is a more aft-loaded profile which exhibits flow separation on the suction side for all Reynolds numbers investigated. The integral total pressure losses were evaluated by wake traverses downstream of the airfoil. To determine the isentropic Mach numbers and the character of the boundary layer along the suction side of the profile, the static pressure measurements and traverses with a flattened Pitot probe were carried out. A correlation between the position of maximum Mach number on the suction side and the integral total pressure losses has been successfully established. The results show that the optimum location of peak Mach number to minimize integral total pressure losses is significantly dependent on the Reynolds number. However, the correlation presented in this paper, which is based on the data of the integral total pressure losses of an attached boundary layer, is not able to predict the integral total pressure loss or the location of the maximum Mach number on the suction side of the blade when an open separation bubble occurs.

Analysis of Heat Transfer in a Supersonic Rocket Head

Abstract Design of supersonic H1 rocket by the Rocketry Group of Students’ Space Association (SR SKA) requires an analysis of thermal phenomena occurring in the elements particularly exposed to the high temperature gas. This paper contains a description of the methodology and the results of numerical simulation of heat transfer in the elements of the rocket head. The starting points were the flight conditions (3 characteristic points defined by altitude and Mach number) and independently calculated adiabatic temperature field of the gas. ANSYS Fluent code was used to determine the temperature field on the surface of the rocket. Computed cases were viscous and inviscid flow (for comparison). Based on the results formulated for the viscous case heat transfer boundary conditions, the numerical model and the thermophysical properties of materials were defined. The model was limited to a brass top part of the head and a part of a composite dome. Analytical and empirical method of “intermediate enthalpy” determined distribution of the heat transfer coefficient on the rocket surface. Then the transient heat transfer was calculated with the ANSYS system. It included the range from the rocket launch, moment of maximum Mach number to sufficient structure cooling. The results of the analyses were conclusions relevant to the further development work. Excessive heating of composite structures during the flight has been shown.

Non-Linear Ion-Acoustic Solitary Waves in Electron-Positron-Ion Plasma with Non-Thermal Electrons

Ion-acoustic solitary (IAS) waves in electron-positron-ion (e-p-i) plasma have been of interest to many researchers probably due to their relevance in understanding the Universe. However, the study of non-linear ion-acoustic waves in e-p-i plasma with non-thermal electrons has not been adequately studied. A theoretical investigation on non-linear IAS waves in e-p-i plasma comprising of warm inertial adiabatic fluid ions and electrons that are kappa distributed, and Boltzman distributed positron is presented here using the Sagdeev potential technique. It was found that existence domains of finite amplitude IAS waves were confined within the limits of minimum and maximum Mach numbers with varying k values. For lower values of k, the amplitude of the solitary electrostatic potential structures increased as the width decreased, while for high values, the potential amplitude decreased as the width of the solitary structure increased.

Modeling for optimization of circular flat pad aerostatic bearing with a single central orifice-type restrictor based on CFD simulation

For a circular flat pad aerostatic bearing with a single orifice-type restrictor, flow field in the air film is numerically investigated. The formation process of sonic region and shock waves is studied and formation mechanism of the vortex is revealed. Based on flow analysis, the maximum Mach number is taken as the benchmark of bearing dynamic stability and used as a constraint in the optimization modeling, for which the rationality is verified through transient flow calculations. The mathematical model for optimization considering both stiffness and dynamic stability is established, and several cases of optimization are performed under different given loads. The results are compared and benefits of the design optimization are demonstrated.

Generation of Weak Double Layers and Low-Frequency Electrostatic Waves in the Solar Wind

We propose that the mechanism for the generation of weak double layers (WDLs) and low-frequency coherent electrostatic waves, observed by Wind in the solar wind at 1 AU, might be slow and fast ion-acoustic solitons and double layers. The solar wind plasma is modelled as a fluid of hot protons and hot $\alpha$ particles streaming with respect to protons, and suprathermal electrons having a $\kappa$ -distribution. The fast ion-acoustic mode is similar to the ion-acoustic mode of a proton–electron plasma and can support only positive-potential solitons. The slow ion-acoustic mode is a new mode that occurs due to the presence of $\alpha$ particles. This mode can support both positive and negative solitons and double layers. The slow ion-acoustic mode can exist even when the relative streaming, $U_{0}$ , between $\alpha$ particles and protons is zero, provided that the $\alpha$ temperature, $T_{i}$ , is not exactly equal to four times the proton temperature, $T_{p}$ . An increase of the $\kappa$ -index leads to an increase in the critical Mach number, maximum Mach number, and the maximum amplitude of both slow and fast ion-acoustic solitons. The slow ion-acoustic double layer can explain the amplitudes and widths, but not the shapes, of the observed WDLs in the solar wind at 1 AU by Wind spacecraft. The Fourier transform of the slow ion-acoustic solitons/double layers would produce broadband low-frequency electrostatic waves having main peaks between 0.35 kHz to 1.6 kHz, with an electric field in the range of $E = (0.01\,\mbox{--}\,0.7)~\mbox{mV}\,\mbox{m}^{-1}$ , in excellent agreement with the observed low-frequency electrostatic wave activity in the solar wind at 1 AU.