Computational analysis of fluidic compression in supersonic flowfields

Air-breathing propulsion has been regarded in recent years as the future solution for spacecraft launchers. Hypersonic flight of vehicles designed for horizontal take-off remains nevertheless a challenging task. Especially the propulsion unit must work over a broad range of flight Mach number: efficiency can be guaranteed only with a system integrating conventional and air-breathing engines and the latter have to be suitable for dualmode operation. The Institute of Flight Propulsion of the Technische Universitat Munchen developed an air-breathing combustor concept, including a novel injection system. The combustion chamber consists of a constant cross section module hosting a strut injector followed by a diverging module which counteracts static pressure peaks consequent to combustion. Hydrogen and air are injected unlike-impinging into the strut wake, where a cylindrical pipe is inserted as flame-holder. The system allows creating a flow recirculation area. Combustion radicals are set free and promote further fuel reaction until a pilot flame stabilizes. Additional hydrogen or methane is injected through the strut sides, pre-mixes with the supersonic air flow (M=2.2) stoked to the combustor and is ignited by means of the pilot flame. The total temperature at the combustor entrance can be varied between 500K and 1200K. First results of wall static pressure measurements and Schlieren imaging demonstrated the possibility of dual-mode combustion. The transition between ramjet and scramjet modes showed to depend on the fuel total injection pressure. This paper presents the results of experiments carried out to define the fuel total injection pressure interval in which the transition occurs. Two injector versions of different thickness (i.e. 3mm and 5mm) have been used. This allowed evaluating the effects of the aerodynamic blockage due to the strut on the overall combustion process, particularly on the transition. ∗ Dipl.-Ing. Sara Rocci Denis, Research Assistant, Institute of Flight Propulsion † Professor Dr.-Ing. Hans-Peter Kau, Director, Institute of Flight Propulsion ‡ Dipl.-Ing. Armin Brandstetter, Systems Engineer, MT12 Mission Dynamics NOMENCLATURE MCC Combustor entrance Mach number MF Flight Mach number pCC Combustor entrance static pressure ptH2A Total pressure of hydrogen injected through system A pW Combustor wall static pressure TSS Flame-holder surface temperature TtCC Combustor entrance total temperature TtH2 Hydrogen injection total temperature φ Equivalence ratio

Results are presented of the calculation of the laminar boundary layer on infinitely long elliptic cylinders in a supersonic perfect gas flow at an arbitrary angle of attack. It was assumed that the Prandtl number is constant and equal to 0.7, the dynamic viscosity coefficient follows a power-law variation (μ ≈ T0.76) with temperature, and there is high heat transfer at the body surface (H1w=0.05). The calculations showed that a change of the body shape—the ellipticity coefficient δ=b/a—has a significant effect on the nature of the distribution and the magnitude of the local heat flux. In evaluating the thermal fluxes at the blunt leading edges, swept wings are usually considered as infinitely long yawed cylinders. In studying heat transfer at the surface of bodies of small aspect ratio at high angles of attack, wide use is made of the hypothesis of plane sections, when each section, orthogonal to the longitudinal axis of the body, is considered equivalent to a corresponding yawed infinite cylinder. By now quite detailed studies have been made of the behavior of the boundary layer on an infinitely long yawed circular cylinder with both the laminar and turbulent flow regimes for a compressible gas [1, 2]. However, there are no data on the heat transfer at the surface of a yawed infinite cylinder with arbitrary cross section, although the availability of such data is urgently needed, for example, for the proper selection of the form of the leading edges of the swept wing. This article presents the results of the calculation of the characteristics of the laminar boundary layer on the surface of infinite elliptic cylinders in a supersonic perfect gas flow. The calculations were made over a quite wide range of flight Mach number M, yaw angle λ, and ellipticity factor δ. The data presented on the distribution of the relative heat flux along the cylinder directrix may be used also for estimating the heat flux with account for the real properties of air if we know the corresponding value of the heat flux in the vicinity of the stagnation line.

EXACT CONICAL-FLOW SOLUTIONS are available only for circular cones at zero angle of attack. For nonaxisymmetric cones or cones at angle of attack, only approximate methods exist. These methods are generally quite complicated and further limited to certain body shapes or certain Mach-number ranges.* 3 A great need was therefore felt for a simple approximate method applicable to any arbitrarily shaped conical body at zero incidence as well as at angle of attack. Such a method has been developed recently at Lockheed and is presented here in abbreviated form. The method is based on the theory. This theory determines the pressure on a conical body utilizing information for a symmetric cone at zero angle of attack with the same normal component of the free stream with respect to the surface as the local element of the body considered. This method works relatively well a t high Mach numbers. However, it is quite inconsistent at lower Mach numbers, especially for bodies which deviate considerably from circular cones. The equivalent-cone method does not give satisfactory results, mainly due to the fact that it considers only the local surface element on the body independent of the other body elements in the Newtonian-theory manner. These interference effects between the different surface elements have been taken into account in the newly developed method by adding to the equivalent-cone value of pressure an additional correction term for the pressure exchange along the surface of the body. This new method may be called the improved equivalent-cone method. I t covers the whole supersonic\Mach number range for which the conical flow conditions with attached shock at the apex of the body are fulfilled. The assumptions made for the correction term are that the pressure exchange along the surface is proportional to the pressure difference between the equivalent cone and circular cone. This reference circular cone is a cone having a pressure equal to the

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

Many loss parameters are used in the turbomachinery field for correlating the effects on losses of numerous geometric and aerodynamic variables associated with blade rows. The parameter most common to these correlations is the ratio of a loss parameter to a velocity parameter, here called the loss coefficient. Such loss coefficients of different forms used for compressors by Howell and the NACA and those used for turbines by Ainley and Soderberg, plus an additional one, are compared explicitly for possible use in both compressors and turbines. Over a range of Mach numbers, loss coefficient values are compared with loss levels fixed and for representative blading cascade test data, and pressure recoveries and stage efficiencies are compared with loss coefficient values fixed. It is shown that for a low Mach number the different parameters are equal and interchangeable; however, as the Mach number increases, differences appear and grow larger, so that a given combination of loss coefficient value and Mach number implies different entropy-rise values depending upon which parameter is being used. The criteria used here for comparing the different parameters are that one loss coefficient is better than another a– if its loss coefficient values corresponding to test data vary less over a significant range of Mach number, and b– if the stage efficiency implied by a fixed loss coefficient value varies in a more realistic way over a range of Mach number. The Soderberg parameter was found to be better for both compressors and turbines than the other loss coefficients investigated.

Research on fluid dynamics and flow-induced noise at low Mach numbers (M<0.3) holds significant scientific importance. However, conventional numerical simulations for low Mach number flows often assume incompressible fluids, although the medium is compressible to allow sound wave propagation. In this study, we investigated sound generation from canonical flow configurations at low Mach numbers ranging from 0.05 to 0.30: flow around a cylinder, gust–airfoil interaction, and turbulence–airfoil interaction. Both incompressible and compressible numerical models were employed to assess their performance in predicting fluid dynamics and acoustic fields. Furthermore, the Ffowcs Williams and Hawkings (FW–H) equation is also employed to predict far-field noise radiation, which is further compared to direct numerical simulations. Our findings reveal that the incompressible model is able to predict drag and lift force but fails to capture sound wave propagation. Consequently, near-field sound sources from the incompressible model are unsuitable for the permeable-surface FW–H equation. Although the solid-surface integral form of the FW–H equation provides an effective approach for noise prediction, it exhibits deficiencies in accurately resolving high-frequency (non-compact) acoustic components. In contrast, the compressible model consistently yielded excellent agreement with the reference data across the entire Mach number range, both in direct numerical simulations and FW–H-based acoustic computations.

A beam-forming algorithm is developed to identify noise source structures in low Mach number jets near the peak frequency. Pressure data from a conical phased microphone array are Fourier decomposed in the azimuthal direction, and the dominant eigenvectors of a cross-spectral matrix are extracted for each azimuthal mode; subsequently, a robust adaptive beam-forming technique is applied to a cross-spectral matrix reconstructed from the primary eigenmodes. The coherent sound signals are then decomposed into multipoles in spherical coordinates, and the primary mode and its axial position are identified for the axisymmetric and first two azimuthal modes. The proposed beam-forming algorithm is applied to an unheated round jet over a range of Mach numbers and frequencies. The result indicates that at low Mach numbers, the second zenithal mode (i.e., quadrupole) appears to be dominant for each azimuthal mode, and the source position slightly shifts downstream with increasing azimuthal mode number.

An overview of the aerodynami c characteristics, along with the process for developing an aerodynamic database for the Generic Hypersonic Vehicle (GH V), is presented in this paper. The experimental investigation of the aerodynamic characteristics for the blunt bo dy of the GHV has been used as the core of the simulation model . The gaps in the wind tunnel data have been filled using the best available CFD results. The CFD results are compared with the equivalent win d tunnel data for authenticity. The expressions for the aerodynamic f orces and the aerodynamic coeffic ients acting on the GHV are dev eloped. The aerodynamic database covers the range of flight Mach numbers, angles of attack, sideslip angles, a nd control surface deflections. The aerodynamic mo del is then used within the si mulation of the GHV. Nomenclature alt. = altitude, ft b = lateral -directional reference length, span, ft c = longitudinal reference length, mean aerodynamic chord, ft CD = total drag coefficient, n. d. CDa = drag increment coefficient for basic vehicle, n. d. CD-�a = drag increment coefficient for right elevon, n. d. CD-�e = drag increment coefficient for left elevon, n. d. CD-�r = drag increment coefficient for rudder, n. d. CL = total lift coefficient for basic vehicle, n . d. CLa = lift increment coefficient for basic vehicle, n. d. CL-�a = lift increment coefficient for right elevon, n. d. CL-�e = lift increment coefficient for left elevon, n. d. CL-�r = lift increment coefficient for rudder, n. d. CY = tota l side force, n. d. CY� = side force with sideslip derivative for basic vehicle, n. d. CY-�a = side force increment coefficient for right elevon, n. d. CY-�e = side force, increment coefficient for left elevon, n. d. CY-�r = side force, increment coefficient for rudder, n. d. Cl = total rolling moment coefficient, n. d.

Oblique detonation waves (ODWs) are hypersonic combustion phenomena induced by oblique shock waves. When applied to air-breathing engines, ODWs offer high thermal cycle efficiency, adaptability to a wide range of flight Mach numbers, and the advantage of a short combustion chamber, making them highly promising for hypersonic propulsion applications. Despite numerous numerical studies on the heat release and multi-wave flow mechanisms of ODWs, practical applications of oblique detonation engines (ODEs) remain limited due to several technical challenges. These challenges include generating the required high-velocity test environments, achieving effective fuel and oxidant mixing, and measuring the flow field structure in hyper-velocity and high-temperature flows. These limitations hinder the development of ODEs, underscoring the importance of experimental research, particularly for understanding the initiation and propagation mechanisms of ODWs. One of the primary experimental techniques involves inducing oblique detonation using high-velocity models. This method is extensively used to study the initiation process, shock structure, initiation criteria, and ODW propagation. It is advantageous because the state of the experimental mixture is controllable, and the model state can be precisely measured. This paper reviews studies on oblique detonation induced by hyper-velocity projectiles, presenting advances in experimental methods, detonation wave structures, unsteady processes, and initiation characteristics. Additionally, we discuss the deficiencies in existing studies, noting that the current measurement methods fall short of the requirements for observing the ODW initiation process, propagation process, and fine structure. The application of advanced combustion diagnostic techniques and the exploration of the relationship between initiation processes and criteria are crucial for advancing our understanding of ODW initiation and stabilization mechanisms. Finally, we summarize the current state of experimental facilities and measurement techniques, providing suggestions for future research on the measurement of shock waves and chemical reaction zones.

Hybrid Control Trajectory Optimization for Air-breathing Hypersonic Vehicle

A prime requirement in the design of a modem gas turbine combustor is good combustion stability, especially near lean blowout (LBO), to ensure an adequate stability margin. For an aeroengine, combustor blow-off limits are encountered during low engine speeds at high altitudes over a range of flight Mach numbers. For an industrial combustor, requirements of ultra-low NOx emissions coupled with high combustion efficiency demand operation at or close to LBO. In this investigation, a step swirl combustor (SSC) was designed to reproduce the swirling flow pattern present in the vicinity of the fuel injector located in the primary zone of a gas turbine combustor. Different flame shapes, structure and location were observed and detailed experimental measurements and numerical computations were performed. It was found that certain combinations of outer and inner swirling air flows produce multiple attached flames, a flame with a single attached structure just above the fuel injection tube, and finally for higher inner swirl velocity, the flame lifts from the fuel tube and is stabilized by the inner recirculation zone. The observed difference in LBO between co- and counter-swirl configurations is primarily a function of how the flame stabilizes i.e., attached vs. lifted. A turbulent combustion model correctly predicts the attached flame location(s), development of inner recirculation zone, a dimple-shaped flame structure, the flame lift-off height, and radial profiles of mean temperature, axial velocity, and tangential velocity at different axial locations. Finally, the significance and applications of anchored and lifted flames to combustor stability and LBO in practical gas turbine combustors are discussed.

For externally mounted supersonic ramjets , cooled principally by exposure to the surrounding free stream, heat transfer methods are used to predict temperatures attained by single-walled tailpipes during ground and air launch transients and at steady state condit ions in the range of flight Mach numbers up to 4 and alt i tudes up to 100,000 ft. It is concluded that single-walled metal tai lpipes, internally ceramic-coated where necessary, en counter a thermal barrier only in the high Mach n u m b e r low alt i tude region where more complex cooling means are required. A h igh performance variable-geometry paper ramjet was chosen as example, wi th internal gases at 4000 F throughout , near the m a x i m u m obtainable from hydrocarbon-air combust ion . Graphs show how the tai lpipe meta l temperature at thermally critical locations is affected by the major variables of steady state flight condit ions, ground and air launch transients , tailpipe exit geometry, wall thickness and wall material . Turbojet-afterburner tailpipes would experience the same thermal severity. Based on the analysis, engine size effects and thermal design factors for single-walled tai lpipes are discussed. Also, a survey of more complex cooling systems is included. The heat transfer a s s u m p tions, methods and data employed in the analysis are contained in the Appendix.

Scramjet vehicles, especially those used as part of an orbital launch system, must operate over a wide range of flight conditions. One component that has difficulty accommodating a range of Mach numbers is the inlet. In this article, only two-dimensional-type scramjet inlets are considered. Such an inlet with fixed geometry can be designed for a single Mach number (using approximately the shock-on-lip configuration) or a range of Mach numbers. However, the performance of the inlet tends to degrade as the size of the Mach number range increases. One method to improve this performance is to use a variable-geometry cowl. Three cowl motions are considered in this paper: moving the whole cowl up and down, moving the whole cowl forward and backward, and rotating the cowl lip. A low-order model designed for control-oriented applications is used to simulate wave interactions. The model is used to evaluate the benefits of each type of variable geometry, and an inlet designed for a wide range of Mach numbers is presented.

Combustion noise is becoming increasingly important as a major noise source in aeroengines and ground based gas turbines. This is partially because advances in design have reduced the other noise sources, and partially because next generation combustion modes burn more unsteadily, resulting in increased external noise from the combustion. This review reports recent progress made in understanding combustion noise by theoretical, numerical and experimental investigations. We first discuss the fundamentals of the sound emission from a combustion region. Then the noise of open turbulent flames is summarized. We subsequently address the effects of confinement on combustion noise. In this case not only is the sound generated by the combustion influenced by its transmission through the boundaries of the combustion chamber, there is also the possibility of a significant additional source, the so-called ‘indirect’ combustion noise. This involves hot spots (entropy fluctuations) or vorticity perturbations produced by temporal variations in combustion, which generate pressure waves (sound) as they accelerate through any restriction at the exit of the combustor. We describe the general characteristics of direct and indirect noise. To gain further insight into the physical phenomena of direct and indirect sound, we investigate a simple configuration consisting of a cylindrical or annular combustor with a low Mach number flow in which a flame zone burns unsteadily. Using a low Mach number approximation, algebraic exact solutions are developed so that the parameters controlling the generation of acoustic, entropic and vortical waves can be investigated. The validity of the low Mach number approximation is then verified by solving the linearized Euler equations numerically for a wide range of inlet Mach numbers, stagnation temperature ratios, frequency and mode number of heat release fluctuations. The effects of these parameters on the magnitude of the waves produced by the unsteady combustion are investigated. In particular the magnitude of the indirect and direct noise generated in a model combustor with a choked outlet is analyzed for a wide range of frequencies, inlet Mach numbers and stagnation temperature ratios. Finally, we summarize some of the unsolved questions that need to be the focus of future research.

This paper summarizes the research on transonic turbine vane wake flows carried out in a Transonic Planar Cascade at the National Research Council of Canada between 1987 and 1995. The cascade used in the research is a large scale, continuously operating, inflow facility which was developed to study both flow phenomena and aerodynamics of turbine vanes. Research was initially directed at investigating the apparent redistribution of total temperature (energy) from the centre to the edge of the vane wake. This redistribution was found to be a real physical phenomenon that correlated extremely well with wake total pressure distributions indicating that the mechanism which redistributes the energy also has a direct effect on the losses associated with the vane wake. Both phenomena were found to be a function of Mach number in that the losses and the time-averaged total temperature difference between the centre and edge of the wake increased to a maximum as the Mach number approached 0.95 and then decreased by half as the Mach number was raised to 1.3. Following Kurosaka et al (1987) conclusion that the redistribution of energy behind a circular cylinder was caused by the vortices which were shed from the trailing edge an additional experimental program was initiated to study the details of the unsteady vane wakes by the use of high speed schlieren photographs and high frequency response transducers to measure unsteady static and total pressures. This research has confirmed that over the range of Mach numbers, from low to high subsonic, a von Karman vortex street is shed continuously from the vanes. What this research has revealed is that as the transonic regime is traversed, the von Karman vortex street still occurs but only as one of a number of different and highly transient vortex shedding patterns. This breakdown of the stable von Karman vortex street is associated with the migration of the origin of the vortices from the trailing edge of the vane to the nodal point formed by the trailing edge shock waves and the confluence of the two trailing edge shear layers. The cause of the redistribution of energy within the wake and of the high wake losses is the shedding of a continuous von Karman vortex street from the vane. In the subsonic flow regime the presence of a stable von Karman vortex street leads to high wake losses due to the depression of the base pressure while the redistribution of total temperature (energy) is caused by the combined pumping action of the vortices. The strength of the vortices and the above phenomena increase with increasing Mach number. As the transonic flow regime is encountered and the supersonic flow regime entered the coherent structures in the wake become unstable, less von Karman-like, and occur less frequently and the origin of the vortices migrates downstream. This leads to a significant elevation in base pressure and redistribution of energy, thereby implying that significant gains in engine stage efficiency can be realized by the destabilization or elimination of the von Karman vortex street from the vane wake.