Computational Study of Mach Number Effects on Dynamic Stall

Design of a supersonic inlet with double S-bend diffuser was developed. Numerical simulation and wind tunnel experiment were carried out to investigate the aerodynamic performance and variable geometric rules of the inlet. The result indicates that the variable geometry scheme adopted solves the contradiction between starting performance at low Mach number and aerodynamic performance at high Mach number. The inlet works normally and stably over a wide speed range. At design point, the total pressure recovery coefficient reaches 0.47. In addition, two different kinds of inlets with double S-bend diffuser and single S-bend diffuser were studied. Compared with the double S-bend diffuser, the total pressure recovery coefficient of the single S-bend diffuser is higher at low Mach number (Ma0 < 3) and lower at high Mach number (Ma0 > 3). With the increase of backpressure, shock train mainly moves upstream along the low-energy flow region in the diffuser. For the double S-bend diffuser, shock train will first move along the lower corner and then along the upper corner. For the single S-bend diffuser, it will only move along the upper corner. The strong secondary flow of the double S-bend is the main reason for the above phenomenon.

In the combustor inlet diffuser section of gas turbine engine, high-velocity air from compressor flows into the diffuser, where a considerable portion of the inlet velocity head PT3 − PS3 is converted to static pressure (PS) before the airflow enters the combustor. Modern high through-flow turbine engine compressors are highly loaded and usually have high inlet Mach numbers. With high compressor exit Mach numbers, the velocity head at the compressor exit station may be as high as 10% of the total pressure. The function of the diffuser is to recover a large proportion of this energy. Otherwise, the resulting higher total pressure loss would result in a significantly higher level of engine specific fuel consumption. The diffuser performance must also be sensitive to inlet velocity profiles and geometrical variations of the combustor relative to the location of the pre-diffuser exit flow path. Low diffuser pressure losses with high Mach numbers are more rapidly achieved with increasing length. However, diffuser length must be short to minimize engine length and weight. A good diffuser design should have a well considered balance between the confliction requirements for low pressure losses and short engine lengths. The present paper describes the effect of divergence angle on diffuser performance for gas turbine combustion chamber using Computational Fluid Dynamic Approach. The flow through the diffuser is numerically solved for divergence angles ranging from 5 to 25°. The flow separation and formation of wake regions are studied.

Laminar–turbulent transition in hypersonic boundary layers significantly influences heat transfer, skin friction, and flow separation. To examine the combined effects of shock wave–boundary layer interaction (SBLI) and adverse pressure gradients on boundary layer transition under hypersonic conditions, a flared cone–swept fin configuration was designed. High-fidelity transition data were obtained through wind tunnel experiments utilizing temperature-sensitive paint (TSP), temperature sensors, and high-frequency pressure sensors from PCB Piezotronics (PCB). TSP measurements revealed a triangular high-heat-flux region at the rear of the model, induced by the interaction between SBLI and the adverse pressure gradient. Temperature sensors provided precise wall heat flux, capturing a distinct “growth-decrease-regrowth” heat flux distribution pattern along the flared cone, highlighting the complex interplay between flow structures and transition phenomena. PCB sensors identified dominant instability modes, including low-frequency disturbances and second-mode instabilities. Furthermore, numerical simulations validated the wind tunnel results by reproducing the basic flow structures. This study presents the comprehensive wind tunnel dataset on transition for a complex configuration influenced by both SBLI and adverse pressure gradients, assessing the effects of Reynolds and Mach numbers on the flared cone–swept fin configuration. The findings offer valuable insights for transition prediction and thermal protection design in hypersonic vehicles with complicate fin–body interactions.

The use of a monorail ro (; kE::t sled system is detailed and recomme nded as a method of obtaining aerodyna mic data in a regime of high Mach and Reynolds numbers .The aerodyna mic and mechanical design of the Sandia rocket sleds is described , and the data c ollection system discussed in detail.The system has been successfu lly used by Sandia Laborato ry t o a cquire pressure data on conecylinders .These data are compared with data from free-fligh t r ockP.ts, wind-tunn el tests, anrl computer calcula tions.A principal advantage of the sled testing method is the high degree of accuracy possible in determini ng actual test condition s, which include Mach number, static pressure , and static temperat ure .Explorato ry tests indicate that sleds may be used to collect other types of experiment al data such as heat-tran sfer and boundary -layer transition .The high-spee d sled testing technique appears to be the most promis ing method of simulatin g flight condition s at low altitudes at Mach numbers up to M = 8.To date, excellent data have been obtained at a velocity of 7430 ft/sec (M = 6.53) which to our knowledg e is the highest velocity ever attained by a ro cket sled.At this speed, and the Holloman Air Force Base track altitude, the Reynolds number was 42 x 106 per ft, and the -dynamic pressure, 55,000 lbs/ft2. I. Introduct ionDuring wind tunnel and f:;:-ee-fiigh t rocket tests of slightly blunted, slender ( 5 to 2 5 degree half-angle ) cone-cyli nder bodies, it was noted that at Mach numbers greater than 4, the surface pressure ratio, Pm/P cn (measure d surface pressure divided by free-stre am static pressure) , in the region just aft of the cone-cyli nder junction was a strong function of free-stre am Reynolds number.Attempts to gather wind tunnel data at Reynolds numbers over 107 per ft and Mach numbers over M = 4. 5 were thwarted by inadequat e high-pressure facilities and/ or inadequat e pressure measurin g capabiliti es to meet the accuracy requirem e nt of 2 percent of the pressure ratio .

The prediction of airloads and the corresponding structural response in high-speed forward flight of rotors poses a significant challenge to predictive rotorcraft aeromechanics methods. One of the issues identified in the flight test data of the Puma and Black Hawk aircraft is the phase difference between the minimum lift coefficient and the minimum of the blade pitch on the advancing side of the rotor during high-speed forward flight. This is commonly referred to as the advancing-side lift-phase delay. In the present work, the unsteady three-dimensional flowfield on the advancing side of a helicopter rotor is analyzed using computational fluid dynamics in an attempt to quantify contributions to the preceding effect. Time-dependent two-dimensional computational fluid dynamics simulations of blade sections with combined pitch/freestream Mach number oscillation were carried out to isolate the contribution to the phase difference of pitch angle and Mach number variations in the absence of the complex rotor-induced flowfield, sideslip, and rotor blade dynamics. The results for the freestream Mach number oscillations show that the lift coefficient lags the Mach changes at outboard stations, but this effect is reduced for combined pitch/Mach number oscillations. Finite span and sideslip contributions to the phasing were quantified by investigating the chordwise extent of supersonic flow on the advancing side for two nonlifting rotors in high-speed flight. Finally, the UH-60A rotor in high-speed forward flight was considered. By comparing results for rigid blades with results for a prescribed blade torsional deflection, the contribution of the blade torsion to the advancing-blade lift phasing was also quantified. Furthermore, rigid-blade simulations with different flapping schedules demonstrated the sensitivity of the lift phasing to trim-state variations. It was found that Mach number effects are dominant and the lift phasing depends primarily on the encountered Mach number and pitch schedule. Further, the elastic torsional deflection of the blades effectively changes the pitch schedule of the blade sections and also plays a role in the phasing of the lift and pitching moment coefficients.

Compressible potential flows over nonlifting, hovering helicopter blades are described by suitable linear and nonlinear equations of motion for subsonic and transonic cases, respectively. Analytical and numerical results are presented for the linearized subsonic three-dimensional flow in the tip region. When the tip Mach number is transonic, the flowfield is calculated using a computational method that is a formal extension to three dimensions of recently developed nonlinear two-dimensional relaxation schemes. Calculations are presented for rectangular blades with 6% thick biconvex sections. Calculations show the relative importance of tip Mach number and aspect ratio on the growth and extent of shock waves in the tip region, and indicate a significant reduction in shock strength with decreasing aspect ratio. ELICOPTER rotor blades that can operate at high tip Mach numbers without the penalties usually associated with super-critical flow would permit high-forward speeds at relatively low-advance ratios. As the advance ratio decreases, the portion of the retreating blade that is stalled would be diminished, the portion of the retreating blade that is unstalled could operate at smaller angles of attack, and the advancing blade could generate lift without also generating an excessive rolling moment. Vibratory loads would be diminished, and severe unsteady pitching moments on the lifting portion of the retreating blade would decrease if that portion could usefully operate at higher tip speeds and smaller angles of attack. The design of rotor blade geometries that can support a transonic flowfield that is nearly shock-free requires a method for computing the detailed pressure distribution on the blade for a specified rotor geometry and advance ratio. However, the unsteady aerodynamic environment of a lifting rotor that is operating at or near the critical Mach number is extremely complicated. It is easy to appreciate the difficulty of describing such flowfields when one recalls that we do not yet have an adequate model for describing the details of the flow about a lifting, hovering rotor operating in an essentially incompressible flow. Our purpose here is therefore to focus on a portion of the high-speed rotor problem that is sufficiently limited to allow for some analytical and numerical treatment, but which retains important linear and nonlinear features of the flow. We consider a two-bladed nonlifting and hovering rotor operating in the range of tip Mach numbers where compressibility effects are important. The pressure distribution near the rotor tip is studied. In this region, the flowfield is fully three-dimensional, and blade element (strip) theory is in no sense a reasonable approximation to the rotor aerodynamics. It is assumed that the flow is inviscid. The flow is steady relative to a coordinate system attached to the blades. Analytical and numerical results presented here are based on suitable approximations to the full three-dimensional potential equation for compressible flow. When the tip Mach number is subcritical, the potential equation is the usual acoustic

In the present paper, we study the combined incompressible and fast rotation limits for the full Navier-Stokes-Fourier system with Coriolis, centrifugal and gravitational forces, in the regime of small Mach, Froude and Rossby numbers and for general ill-prepared initial data. We consider both the isotropic scaling (where all the numbers have the same order of magnitude) and the multi-scale case (where some effect is predominant with respect to the others). In the case when the Mach number is of higher order than the Rossby number, we prove that the limit dynamics is described by an incompressible Oberbeck-Boussinesq system, where the velocity field is horizontal (according to the Taylor-Proudman theorem), but vertical effects on the temperature equation are not negligible. Instead, when the Mach and Rossby numbers have the same order of magnitude, and in absence of the centrifugal force, we show convergence to a quasi-geostrophic equation for a stream function of the limit velocity field, coupled with a transport-diffusion equation for a new unknown, which links the target density and temperature profiles. The proof of the convergence is based on a compensated compactness argument. The key point is to identify some compactness properties hidden in the system of acoustic-Poincar\'e waves. Compared to previous results, our method enables first of all to treat the whole range of parameters in the multi-scale problem, and also to consider a low Froude number regime with the somehow critical choice $Fr=\sqrt{Ma}$, where $Ma$ is the Mach number. This allows us to capture some (low) stratification effects in the limit.

The effect of Mach number on the evolution of instabilities in the compressible mixing layer is investigated. The full time-dependent compressible Navier–Stokes equations are solved numerically for a temporally evolving mixing layer using a mixed spectral and high-order finite difference method. The convective Mach number Mc (the ratio of the velocity difference to the sum of the free-stream sound speeds) is used as the compressibility parameter. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers (Mc > 0.6) oblique waves grow more rapidly than two-dimensional waves. Simulations are then presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves. A change in the developed large-scale structure is observed as the Mach number is increased, with vortical regions oriented in a more oblique manner at the higher Mach numbers. At convective Mach numbers above unity the two-dimensional instability is found to have little effect on the flow development, which is dominated by the oblique instability waves. The nonlinear structure which develops from a pair of equal and opposite oblique instability waves is found to resemble a pair of inclined A-vortices which are staggered in the streamwise direction. A fully nonlinear computation with a random initial condition shows the development of large-scale structure similar to the simulations with forcing. It is concluded that there are strong compressibility effects on the structure of the mixing layer and that highly three-dimensional structures develop from the primary inflexional instability of the flow at high Mach numbers.

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

EFFECTS OF CHOKING ON THE AEROACOUSTICS OF AN AXISYMMETRIC SUPERSONIC INLET

Corresponding to Oswatitsch’s Mach number independence principle the Mach number of hypersonic inviscid flows, , does not affect components of various non-dimensional formulations such as velocity and density, pressure coefficients and Mach number behind a strong shock. On this account, the principle is significant in the development process for hypersonic vehicles. Oswatitsch deduced a system of partial differential equations which describes hypersonic flow. These equations are the basic gasdynamic equations as well as Crocco’s theorem which are reduced for the case of very high Mach numbers, . Their numerical solution can not only result in simplified algorithms prospectively utilized to describe the flow around bodies flying mainly in the lower stratosphere with very high Mach numbers. It also offers a deeper understanding of similarity effects for hypersonic flows. In this paper, a solution method for Oswatisch’s equations for perfect gas, based on a 4-step Runge-Kutta-algorithm, is presented including a fast shock-fitting procedure. An analysis of numerical stability is followed by a detailed comparison of results for different Mach numbers and ratios of the specific heats.

PurposeThe paper, titled “Supersonic Flow Over Different Nose Cone Designs to Reduce Aerodynamic Characteristics: A Comparative Study,” aims to investigate the impact of various nose cone shapes on aerodynamic performance at supersonic speeds. This study examines multiple nose cone designs, comparing their effects on drag, lift and overall stability, to identify configurations that reduce aerodynamic resistance and improve efficiency. By analyzing these designs under supersonic conditions, the research provides insights into optimal nose cone shapes for high-speed vehicles, offering valuable data for aerospace engineering and future applications in aircraft and missile design.Design/methodology/approachThe study investigates the aerodynamic performance of various nose cone designs in supersonic flow to minimize drag and improve stability. A comparative analysis uses computational fluid dynamics simulations across different nose cone geometries. The methodology includes setting up flow conditions at a supersonic Mach number and examining parameters like pressure distribution, drag coefficient and flow separation. The approach evaluates these nose cone shapes to identify designs with the most favorable aerodynamic characteristics, aiming to enhance efficiency and control.FindingsThis study examines how nose cone shapes impact aerodynamic performance in supersonic flows. Computational simulations reveal that sharp-nosed cones reduce drag and enhance stability at high Mach numbers, while blunt designs increase drag. Findings highlight optimal nose shapes for improved fuel efficiency and durability in aerospace and defense applications.Originality/valueTo the best of the authors’ knowledge, this research provides original insights into nose cone design for supersonic flows, comparing various geometries to reduce aerodynamic drag and heat transfer. By examining specific shapes and their aerodynamic properties, this study contributes valuable data for optimizing nose cone designs, advancing efficient supersonic travel and supporting sustainable aerospace innovation.

The hypersonic Mach number independence principle of Oswatitsch is important for hypersonic vehicle design. It explains why, above a certain flight Mach number (M∞ ≈ 4−6, depending on the body shape), some aerodynamic properties become independent of the flight Mach number. For ground test facilities this means that it is sufficient for the Mach number in the test section to be high enough, that Mach number independence exists. However, the principle was derived for calorically perfect gas and inviscid flow only. In this paper a theoretical study for blunt bodies in the case of viscous flow is presented. We provide numerical results which give insight into how attached viscous flow behaves at high Mach numbers. The flow past an axisymmetric configuration is analysed by applying a coupled Euler/second-order boundary-layer method. Wall boundaries are treated by assuming an adiabatic or radiation-adiabatic wall for laminar flow. Calorically perfect or equilibrium air is accounted for. Lift, drag, and moment coefficients, and lift-to-drag ratios are given for several combinations of flight Mach number and altitude, i.e. Reynolds number. For blunt bodies considered here, which are pressure dominated, Mach number independence occurs for the adiabatic wall, but not for the radiation-adiabatic wall assumption.

This paper describes the improvement in combustion efficiency achieved using streamwise vorticity and fuel injections when using hypermixer struts at high Mach numbers. The effects of fuel injection conditions on combustion were investigated using numerical simulations of chemical reactive flows with a detailed reaction mechanism. Hydrogen fuel was injected from the trailing edges of a separation-resistant strut. Fuel injection at sonic speeds led to an enhancement in efficiency with an increased injection angle at Mach number 2.5, but this improvement was not observed at Mach number 3.5. It was found that hydrogen accumulated in the vortex core because of the strong circulation generated from the strut at high Mach numbers. With fuel injection at speeds exceeding the sonic speed, the efficiency increased, and it improved further with an increasing injection angle. From the results, an important indicator for combustion enhancement was derived from the streamwise vortex circulation, fuel injection velocity, and inflow Mach number. To increase the combustion efficiency using the strut, the indicator value should exceed a threshold. This is crucial for ensuring effective fuel consumption during combustion. These findings provide useful insights into a good design of hypermixer struts in supersonic combustion.

To explore the effects of airfoil-probe tubes and its installment position on the flow field of the compressor cascade, and find out the mechanism that how the airfoil-probes affect the aerodynamic characteristics of the compressor cascade, this paper performed both numerical and experimental works on the same compressor cascade. The experiment mainly focused on the cases of low Mach number (Ma = 0.1), and cases with different Mach numbers (0.1, 0.3, 0.7) and different incidence angles (-5, 0, 5) are investigated by the numerical method. The case without the airfoil-probe tube was referenced as the baseline, and other three cases with the airfoil-probe tubes installed in different chordwise positions (30%, 50%, 70% of the chord length) were studied. The diameter of the airfoil-probe tube is 3mm, which is configured as 300% amplification of some particular airfoil-probe according to the geometrical similarity principle. The results show that the airfoil-probe tubes have a negative influence on the flow capacity of the cascade at all investigation points. The separations and the large scale streamwise vortices that induced by the airfoil-probe tube on the pressure side cause most the losses at the high Mach number. The influence of the airfoil-probe tube on the flow field in the vicinity of the pressure side surface is local separation at the low Mach number. The airfoil-probe tubes also have a clearly effect on the leakage flow. It decreases the mass flow of the leakage flow and weakens the intensity of the leakage vortex, but enlarges the influence area. The total pressure loss of the case that the tube is installed at the half chordwise position is generally lower than other cases especially at the high Mach number, it can even decrease the losses compared with the basic case.