Variation Of Mach Number Research Articles

Over-expanded separation transitions of single expansion ramp nozzle in the accelerating and decelerating processes

Flow separation is a basic fluid-dynamics phenomenon that occurs in supersonic nozzles at low pressure ratios. In the over-expanded flowfield of nozzles, the subsonic area is formed, such as separation bubble, recirculation zone, and flow downstream Mach reflection. In static ambient, the recirculation zone is opened with the environment. When the external flow is not still, it will interact with the recirculation zone. As a result, the external flow will make significant influences on the over-expanded separation flowfield. This paper aims to present a detailed description of separation patterns transitions caused by external Mach number variation, analyze the mechanism of separation transitions. Accelerating and decelerating processes of a long flap single expansion ramp nozzle (SERN) is investigated by numerical simulation. Separation transitions and the performance of SERN influenced by the separation transitions have been discussed. In the accelerating process, free shock separation (FSS) is a stable separation pattern and lasts for a long time. The decelerating process is not just the inverse process because a new over-expanded flowfield pattern appears in the decelerating process. Meanwhile, there is an apparent hysteresis between the accelerating and decelerating processes.

Airfoil aerodynamics optimization under uncertain operating conditions

An aerodynamic robust optimization of a 2D airfoil is presented. Robust optimization aims to find a design which is less sensitive to small changes in uncertain quantities. Aerodynamic performance of airfoil is studied under variation of Mach number and angle of attach as operational uncertainties. The optimal aerodynamic shape of airfoil is computed by maximizing lift and drag coefficient ratio. Airfoil aerodynamic perfomance is evaluated using XFOIL solver. NACA 0012 is adopted as a basic airfoil design and optimized for robustness using Taguchi method. Signal-to-Noise ratio (S/N) of Taguchi method for larger the better is applied as robustness index. Nine of eleven variables of PARSEC airfoil parameters with 3 levels for each factors are selected as design variables and distributed using L27 fractional orthogonal array as the design of experiment. The optimization process does not only increase the average performance of lift-to-drag ratio but also decrease the standard deviation. The optimization strategy significantly improves the aerodynamic performance of the basic NACA 0012 from 21.76 to 36.79 or improves 69% of the robustness index.

Design and investigation of equal cone-variable Mach number waverider in hypersonic flow

A new design idea is put forward to adapt the design requirement of wide-speed range vehicle in the paper. The novel points are that the design Mach number and shock flowfield are variable continuously in the design methodology. The design process is introduced about the wide-speed waverider and the repeatability function is achieved systematically by means of the parameterized modeling. In order to validate the advantages of the new approach during the wide-speed range, the flowfield characteristics are investigated numerically in the paper. The numerical method is validated by comparing the simulation results with wind tunnel experiment data. The obtained results show that the wide-speed range waverider could be obtained easily by the parameterized modeling. For the variable Mach number waverider, the pressure drag accounts for the main part of total drag, about 60∼70%. The percentage of viscous drag increases and that of the rear drag decreases with the increase of flow velocity. The viscous L/D of Case 5 does not change obviously during the wide-speed range. The variable Mach number waverider holds the steady aerodynamic performance during the wide-speed range. This shows that the new design method is very useful for the integrated design of wide-speed hypersonic vehicles.

Some peculiarities of superheated water flow in contracting-expanding nozzles and their influence on droplet dimension distribution in an atomized water plume

New calculation data on superheated metastable water flow in atomizing Laval type nozzles is presented. The calculating model is discussed on the assumption of predominating nucleation role in liquid atomization. The Mach number variation is presented for diffuser part of the nozzle taking into account the sound velocity variation in a vapor-liquid system. The new criterion, based upon experimental and calculating data, which determines the reaching of full-flashing regime, is proposed for contracting-expanding nozzles. The submicron mass fraction is considered to be a function of dimensionless parameter, which is the critical radius bubble surface tension energy ratio to chemical potential of phase transition for critical bubble radius at certain pressure drop.

A methodology for the performance prediction: flow field and thermal analysis of a helium turboexpander

Helium liquefaction systems are widely used in nuclear fission, superconductivity, space industries, and other scientific instruments. However, the efficiency of these systems is quite low due to the cryogenic operating temperature. In this regard, the one-dimensional design methodology of the helium turbine and nozzle (hereafter, renowned as turboexpander) is important to increase the efficiency of the system. This paper demonstrates the sensitivity analysis and optimal range of non-dimensional design variables on which the radial inflow turbine has maximum efficiency, minimum losses, and maximum power output using artificial intelligence techniques. On this basis, three turboexpander models are developed within the optimal range of predicted non-dimensional variables. After that, a comparative numerical study is carried out to highlight the flow field and thermal characteristics of helium fluid. The standard two equations \(k{-}\omega \) SST model is used to solve the three-dimensional incompressible flow inside the computational domain. The numerical results are validated with the available experimental data from the existing literature. The variation of Mach number, Reynolds number, Prandtl number, static entropy, static enthalpy, temperature, and pressure inside the turboexpander is significantly affected by blade profile which is enormously affected by the design methodology. The study also demonstrates the flow separation region, vortex formation, tip leakage flow, secondary losses, and its reasons along with the spanwise location. The results highlight the importance of the design methodology, sensitivity analysis, the prediction capability of the artificial intelligence network, numerical methodology, and development of the helium turboexpander prototype models.

Transonic flow hysteresis in divergent bent channels

This paper presents a numerical study of the 2D and 3D turbulent airflows in divergent 9°-bent channels. The incoming flow is supersonic, whereas the exit flow may be either supersonic or subsonic. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver ANSYS CFX using the Spalart-Allmaras and Shear Stress Transport k-ω turbulence models. The solutions reveal a significant hysteresis of the flow field under variations of the free-stream Mach number or exit pressure. At the ends of hysteresis bands, the flow pattern changes crucially due to instability of a shock wave formed near the bend of channel. The instability is caused by the shock foot interaction with an expansion flow developed over the convex wall of channel. Boundary conditions, in which the flow admits a double hysteresis, are figured out. The occurrence of non-unique flow regimes must be taken into account in the advanced intake design, as different losses of the total pressure may cause different trusts of an air breathing engine.

Quasi 3D Nacelle Design to Simulate Crosswind Flows: Merits and Challenges

This paper studies the computational modelling of the flow separation over the engine nacelle lips under the off-design condition of significant crosswind. A numerical framework is set up to reproduce the general flow characteristics under crosswinds with increasing engine mass flow rate, which include: low-speed separation, attached flow and high speed shock-induced separation. A quasi-3D (Q3D) duct extraction method from the full 3D (F3D) simulations has been developed. Results obtained from the Q3D simulations are shown to largely reproduce the trends observed (isentropic Mach number variations and high-speed separation behaviour) in the 3D intake, substantially reducing the simulation time by a factor of 50. The agreement between the F3D and Q3D simulations is encouraging when the flow either fully attached or with modest levels of separation but degrades when the flow fully detaches. Results are shown to deviate beyond this limit since the captured streamtube shape (and hence the corresponding Q3D duct shape) changes with the mass flow rate. Interestingly, the drooped intake investigated in the current study is prone to earlier separation under crosswinds when compared to an axisymmetric intake. Implications of these results on the industrial nacelle lip design are also discussed.

Computational Analysis of Mixing in Scramjet Combustor using Cross Flow Injection Technique

The prime issue in supersonic combustion is proper mixing within short duration of time. Computational study has been performed to analyse the mixing of air and fuel using cross flow injection technique. Cross flow injection is performed by placing the fuel injectors on the walls of the scramjet engine which is perpendicular to the flow. To enhance the mixing of fuel and air, cavities were introduced. The flow recirculation inside the cavity will enhance the mixing and combustion. The fuel injectors were placed just upstream of the cavity. Analyses were done by changing the injection angles. The air is allowed to enter at different Mach numbers and the changes were analysed using ANSYS software. The roles of cavity cross flow injection, pressure, temperature, velocity and Mach number variation were examined in this study and the obtained results were compared between various configurations.

Robust optimization for a wing at drag divergence Mach number based on an improved PSO algorithm

In this study, an improved PSO (particle swarm optimization) algorithm is proposed and applied to the robust optimization of a wing at drag divergence Mach number. In order to reduce the number of design variables, a six-order CST (class/shape function transformation) method is employed for airfoil parameterization. For the purpose of improving the optimization efficiency, Delaunay graph mapping method is adopted for mesh deformation in each iteration of the airfoil optimization, and NURBS (non-uniform rational B-splines)-FFD (free-form deformation) method is employed for mesh deformation in each iteration of the wing optimization. For improving the standard PSO algorithm, CVTs (centroidal Voronoi tessellations) method is introduced to generate original positions of the particles more dispersedly, a second-order oscillating scheme is used and an FDR (fitness distance ratio) item is added for updating velocities and positions of the particles. By virtue of the improved PSO algorithm, single point optimization and robust optimization are conducted for both airfoil and wing. The results indicate that, comparing with the single point optimizations, the robust optimizations not only reduce drag coefficients of the airfoil and the wing at cruise Mach numbers, but also attenuate the drag increments as the Mach number increases up to drag divergence Mach numbers.

Novel osculating flowfield methodology for wide-speed range waverider vehicles across variable Mach number

In order to guarantee the good aerodynamic performance of the waverider vehicle in the wide-speed range, the variable Mach number osculating flowfield waverider design theory based on conical basic flowfield is put forward. The shape and aerodynamic characteristics of the variable Mach number osculating flowfield waverider and osculating cone waverider are compared and analyzed. And the inviscid numerical simulation method is used to verify the correctness of the theory and the validity of the design method. The obtained results show that the osculating flowfield waverider has good waverider properties under the conditions of wide-ranged flight Mach numbers. Furthermore, the comparison of osculating flowfield waverider and osculating cone waveriders indicates that the variable Mach number osculating flowfield waverider has balanced internal loading capacity and aerodynamic performance, which is more suitable for wide-speed flight.

Geometric shapes effect of in-duct perforated orifices on aeroacoustics damping performances at low Helmholtz and Strouhal number.

In this work, experimental studies are conducted to measure the aeroacoustics damping performances of 11 in-duct perforated plates in a cold-flow pipe with a variable Mach number. These in-duct plates have the same porosities but different number N and geometric shaped orifices. Here six shapes are considered, i.e., (1) triangle, (2) square, (3) pentagon, (4) hexagon, (5) star, and (6) circle. It is shown that the orifice shape has little influence on power absorption Δ and reflection coefficient R at a lower Helmholtz number He ≤ 0.0903. However, as He is increased, the in-duct plate with a star-shaped orifice is shown to be with much lower Δ in comparison with that of other plates with different shape orifices. In addition, the perforated orifice with the same shape and porosity but a larger N is shown to be associated with 20% more power absorption at approximately He = 0.1244. Δmax is observed to be approximately 85% at about He = 0.0244, as Ma≈0.029. To gain more insights, the quasi-steady model is applied, depending on the Strouhal number Sr. The transition from quasi-steady flow behaviors to unsteady behaviors occurs at approximately Sr = 0.45. The measured minimum reflection coefficient Rmin occurs at Ma ≈ 0.024. This experimental finding is consistent with the quasi-steady prediction.

Wall-pressure fluctuations induced by a compressible jet flow over a flat plate at different Mach numbers

The wall-pressure fluctuations induced by a compressible subsonic jet over a flat plate are experimentally investigated. Measurements were performed in a semi-anechoic environment, where a compressible jet facility, whose nozzle diameter (D) was 12 mm, is installed. The position of the flat plate was fixed at H/D = 2, where H is the radial position of the flat plate from the jet axis. The study was carried out for several jet Mach numbers spanning the range from 0.5 to 0.9. An overall aerodynamic characterization of the plate effect on the jet plume is provided by means of Pitot tube measurements. The wall-pressure fluctuations acting on the flat plate were measured by a couple of cavity-mounted pressure transducers, providing pointwise pressure signals in the streamwise and in the spanwise directions. A statistical and spectral characterization of the wall-pressure fluctuation field is provided addressing the effect of the jet Mach number variation and of the spatial evolution along the streamwise and spanwise directions. Implications for wall-pressure fluctuations modelling are discussed by the application of the Corcos’ model. Scaling laws with respect to the different jet flow conditions for the wall-pressure spectra are finally presented.

Hysteresis of shock wave locations in divergent bent channels

The turbulent airflow in 2D and 3D channels with bends of opposite walls is studied numerically. The channels are slightly divergent in the longitudinal direction upstream and downstream of the bends. The flow is supersonic on the inlet and outlet boundaries of the computational domain. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate considerable hysteresis under variations of the free-stream Mach number or angle of attack. At the ends of hysteresis bands, the flow structure changes drastically due to instability of shock wave positions. Effects of 3D phenomena, turbulent viscosity, and thickness of walls on the hysteresis are discussed.

The Methods of Control of Stabilized Detonation Location in a Supersonic Gas Flow in a Plane Channel

ABSTRACT Using a detailed kinetic model of chemical interaction, we have studied detonation stabilization in a stoichiometric hydrogen–air mixture flowing at a supersonic velocity into a symmetric plane channel with constriction the outflow section of which exceeds the inflow one. In addition, we examined the possibility of control of stabilized detonation location in the flow. In case of detonation initiation by energy input, the investigation of conditions of formation of a thrust developing flow with a stabilized detonation wave in the channel was conducted. The structure of the stabilized detonation wave was studied. We examined the effect of variations of the inflow Mach number, dustiness of the inflowing gas mixture, and geometric parameters of the channel on stabilized detonation location with the goal of thrust increase. In addition, the possibility of formation of the thrust developing flow with stabilized detonation in the channel without any energy consumption has been detected.

Aerodynamic Design of Nozzles with Uniform Outflow for Hypervelocity Ground-Test Facilities

A method is proposed for the aerodynamic design of nozzles with uniform outflow for supersonic and hypersonic ground-test facilities. This method involves the coupling of an open-source Reynolds-averaged Navier–Stokes computational fluid dynamics solver, Eilmer, with the simplex optimization method of Nelder and Mead for the design of an expanding nozzle contour with the least variations in Mach number and flow angularity. Three nozzles were designed using this method to produce exit flows of Mach 4, Mach 7, and Mach 10. Numerical simulations of the flow in these optimized nozzle contours showed excellent flow uniformity in the core flow; typical Mach number variations were less than 0.5%, flow angularity variations were less than 0.05 deg, static temperature and flow velocity variations were less than 1%, and Pitot and static pressures variations were less than 2%. Experimental surveys of the Pitot pressures at several planes downstream of the exit of the three optimized nozzles showed excellent agreement with numerical simulations. The experimental measurements showed that there were good levels of uniformity in the core flow regions of all three nozzles, thus proving the validity of the proposed design method.

NUMERICAL SIMULATION OF SUBSONIC FLOW OVER A PROFILE

A methodology and software-methodical support for describing the processes of flow around a wing profile by a viscous compressible flow based on the Reynolds-averaged Navier – Stokes equations using the Spalart – Almaras turbulence model is developed. The effect of Mach number variation at constant Reynolds number on the profile performance coefficients is analyzed.

Impact of Flow Unsteadiness on Steady-State Gas-Path Stagnation Temperature Measurements

Steady-state stagnation temperature probes are used during gas turbine engine testing as a means of characterizing turbomachinery component performance. The probes are located in the high-velocity gas-path, where temperature recovery and heat transfer effects cause a shortfall between the measured temperature and the flow stagnation temperature. To improve accuracy, the measurement shortfall is corrected post-test using data acquired at representative Mach numbers in a steady aerodynamic calibration facility. However, probes installed in engines are typically subject to unsteady flows, which are characterized by periodic variations in Mach number and temperature caused by the wakes shed from upstream blades. The present work examines the impact of this periodic unsteadiness on stagnation temperature measurements by translating probes between jets with dissimilar Mach numbers. For conventional Kiel probes in unsteady flows, a greater temperature measurement shortfall is recorded compared to equivalent steady flows, which is related to greater conductive heat loss from the temperature sensor. This result is important for the application of post-test corrections, since an incorrect value will be applied using steady calibration data. A new probe design with low susceptibility to conductive heat losses is therefore developed, which is shown to deliver the same performance in both steady and unsteady flows. Measurements from this device can successfully be corrected using steady aerodynamic calibration data, resulting in improved stagnation temperature accuracy compared to conventional probe designs. This is essential for resolving in-engine component performance to better than ±0.5% across all component pressure ratios.

Experimental exploration of inlet start process in continuously variable Mach number wind tunnel

The flow structures of the inlet in continuously variable Mach number inflow are studied experimentally to evaluate accurately the performance of scramjet inlet during acceleration/deceleration in ground experiments. To break the limitation in which majority of supersonic wind tunnels operate at a fixed Mach number condition, a continuously variable Mach number wind tunnel has been built. The running Mach number of the wind tunnel varies continuously from 2.0 to 3.0 under suction mode. The experiments of the inlet at fixed and variable Mach number inflows are conducted successively in the continuously variable Mach number wind tunnel. In the fixed Mach number experiment, the typical flow structures of the inlet under the unstart/start conditions are captured. The pressure distributions on the lower wall of the inlet, which were obtained from the experiments, are consistent with numerical ones. Thus, the effectiveness and accuracy of the experiments and numerical simulations were verified. In the continuously variable Mach number wind tunnel experiment, we found the inlet suffers from four flow structures. With the exception of typical unstart/start flow structures, the inlet undergoes pseudo unstart/start conditions under the influence of the wind tunnel unstart. By analyzing the pressure and Schlieren result, variations in the flow structures are observed in detail, which can provide useful references for the subsequent experiments in continuously variable Mach number wind tunnels. In particular, pseudo unstart/start conditions must be distinguished from real ones in the case wrong experimental data are obtained in the following experiments.

Aerodynamic Shape Optimization of Natural-Laminar-Flow Wing Using Surrogate-Based Approach

Aerodynamic shape optimization of a swept natural-laminar-flow wing in the transonic regime is still challenging. The difficulty is associated with reliable prediction of laminar–turbulence transition and reasonable compromise of viscous and wave drags. This paper proposes to use efficient global optimization based on surrogate models to address this problem. The Reynolds-averaged Navier–Stokes flow solver features automatic transition prediction via a full method, in which dual factors are used for Tollmien–Schlichting and crossflow instabilities, respectively. The optimizer is based on the kriging surrogate model and parallel infill-sampling method. The baseline natural-laminar-flow wing for short- and medium-range transport aircraft is designed at a cruise Mach number 0.75. Then, drag minimization with up to 42 design variables is carried out, and significant drag reduction (8.79%) has been achieved. A close examination of the optimal wing shows that the drag reduction mainly comes from shock-wave weakening on the upper surface and laminar flow extending via suppression of crossflow instability on the lower surface. Robustness of the optimal wing is investigated, and multipoint optimization is further exercised to improve the robustness to the Mach number variation. It is demonstrated that surrogate-based optimization is feasible and effective for aerodynamic shape optimization of transonic natural-laminar-flow wings.

Variable Mach number design approach for a parallel waverider with a wide-speed range based on the osculating cone theory

In the current study, a variable Mach number waverider design approach has been proposed based on the osculating cone theory. The design Mach number of the osculating cone constant Mach number waverider with the same volumetric efficiency of the osculating cone variable Mach number waverider has been determined by writing a program for calculating the volumetric efficiencies of waveriders. The CFD approach has been utilized to verify the effectiveness of the proposed approach. At the same time, through the comparative analysis of the aerodynamic performance, the performance advantage of the osculating cone variable Mach number waverider is studied. The obtained results show that the osculating cone variable Mach number waverider owns higher lift-to-drag ratio throughout the flight profile when compared with the osculating cone constant Mach number waverider, and it has superior low-speed aerodynamic performance while maintaining nearly the same high-speed aerodynamic performance.