scholarly journals Axisymmetric superdirectivity in subsonic jets

2012 ◽  
Vol 704 ◽  
pp. 388-420 ◽  
Author(s):  
André V. G. Cavalieri ◽  
Peter Jordan ◽  
Tim Colonius ◽  
Yves Gervais
Keyword(s):  
Mach Number ◽  
Strouhal Number ◽  
Acoustic Field ◽  
Sound Radiation ◽  
Polar Angle ◽  
Sound Field ◽  
Higher Order ◽  
Velocity Dependence ◽  
Axisymmetric Mode ◽  
Mach Numbers

AbstractWe present experimental results for the acoustic field of jets with Mach numbers between 0.35 and 0.6. An azimuthal ring array of six microphones, whose polar angle, $\theta $, was progressively varied, allows the decomposition of the acoustic pressure into azimuthal Fourier modes. In agreement with past observations, the sound field for low polar angles (measured with respect to the jet axis) is found to be dominated by the axisymmetric mode, particularly at the peak Strouhal number. The axisymmetric mode of the acoustic field can be clearly associated with an axially non-compact source, in the form of a wavepacket: the sound pressure level for peak frequencies is found be superdirective for all Mach numbers considered, with exponential decay as a function of $ \mathop{ (1\ensuremath{-} {M}_{c} \cos \theta )}\nolimits ^{2} $, where ${M}_{c} $ is the Mach number based on the phase velocity ${U}_{c} $ of the convected wave. While the mode $m= 1$ spectrum scales with Strouhal number, suggesting that its energy content is associated with turbulence scales, the axisymmetric mode scales with Helmholtz number – the ratio between source length scale and acoustic wavelength. The axisymmetric radiation has a stronger velocity dependence than the higher-order azimuthal modes, again in agreement with predictions of wavepacket models. We estimate the axial extent of the source of the axisymmetric component of the sound field to be of the order of six to eight jet diameters. This estimate is obtained in two different ways, using, respectively, the directivity shape and the velocity exponent of the sound radiation. The analysis furthermore shows that compressibility plays a significant role in the wavepacket dynamics, even at this low Mach number. Velocity fluctuations on the jet centreline are reduced as the Mach number is increased, an effect that must be accounted for in order to obtain a correct estimation of the velocity dependence of sound radiation. Finally, the higher-order azimuthal modes of the sound field are considered, and a model for the low-angle sound radiation by helical wavepackets is developed. The measured sound for azimuthal modes 1 and 2 at low Strouhal numbers is seen to correspond closely to the predicted directivity shapes.

Effect of Mach number on the acoustic field of 2:1 elliptic-slot jet

2001 ◽  
Vol 105 (1043) ◽  
pp. 9-16 ◽  
Author(s):  
S. B. Verma ◽  
E. Rathakrishnan
Keyword(s):  
Mach Number ◽  
Fundamental Frequency ◽  
Acoustic Field ◽  
Major Axis ◽  
Shock Structure ◽  
Minor Axis ◽  
Noise Levels ◽  
Underexpanded Jets ◽  
Barrel Shock ◽  
Mach Numbers

Abstract The shock-structure and the related acoustic field of underexpanded jets undergoes significant changes as the Mach number Mj is increased. The present investigation is carried out to study the effect of Mach number on an underexpanded 2:1 elliptic-slot jet. Experimental data are presented for fully expanded Mach numbers ranging from 1.3 to 2.0. It is observed that the ‘cross-over’ point at the end of the first cell at low Mach numbers gets replaced by a normal shock at a highly underexpanded condition resulting in the formation of a ‘barrel’ shock along the minor-axis side with a ‘bulb’ shock formed along the major-axis side. The above change in shock structure is accompanied by a related change in the acoustic field. The amplitude of fundamental frequency along the minor-axis side grows with Mj but falls beyond Mj = 1.75. Along the major-axis side, however, the fundamental frequency does not exist at low Mach numbers. It appears at Mj = 1.75 but then falls at Mj = 2.0. The related azimuthal directivity of overall noise levels (OASPL) shows significant changes with Mj.

Numerical Simulation of Internal Cavities Acoustic Trapped Modes With Mean Flow

2010 ◽  
Author(s):  
Kareem Aly ◽  
Samir Ziada
Keyword(s):  
Mach Number ◽  
Acoustic Field ◽  
Particle Velocity ◽  
Perturbation Equation ◽  
Duct System ◽  
Trapped Modes ◽  
Mean Flow ◽  
Phase Gradient ◽  
The Mean ◽  
Mach Numbers

Flow-excited acoustic resonance of trapped modes in ducts has been reported in different engineering applications. The excitation mechanism of these modes results from the interaction between the hydrodynamic flow field and the acoustic particle velocity, and is therefore dependent on the mode shape of the resonant acoustic field, including the amplitude and phase distributions of the acoustic particle velocity. For a cavity-duct system, the aerodynamic excitation of the trapped modes can generate strong pressure pulsations at moderate Mach numbers (M>0.1). This paper investigates numerically the effect of mean flow on the characteristics of the acoustic trapped modes for a cavity-duct system. Numerical simulations are performed for a two-dimensional planar configuration and different flow Mach numbers up to 0.3. A two-step numerical scheme is adopted in the investigation. A linearized acoustic perturbation equation is used to predict the acoustic field. The results show that as the Mach number is increased, the acoustic pressure distribution develops an axial phase gradient, but the shape of the amplitude distribution remains the same. Moreover, the amplitude and phase distributions of the acoustic particle velocity are found to change significantly near the cavity shear layer with the increase of the mean flow Mach number. These results demonstrate the importance of considering the effects of the mean flow on the flow-sound interaction mechanism.

Heat Transfer in Rotating Serpentine Coolant Passage With Ribbed Walls at Low Mach Numbers

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Shang-Feng Yang ◽  
Je-Chin Han ◽  
Salam Azad ◽  
Ching-Pang Lee
Keyword(s):  
Heat Transfer ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Transfer Coefficients ◽  
Low Mach Number ◽  
Heat Transfer Coefficients ◽  
Rotation Numbers ◽  
Wide Range ◽  
Mach Numbers

This paper experimentally investigates the effect of rotation on heat transfer in typical turbine blade serpentine coolant passage with ribbed walls at low Mach numbers. To achieve the low Mach number (around 0.01) condition, pressurized Freon R-134a vapor is utilized as the working fluid. The flow in the first passage is radial outward, after the 180 deg tip turn the flow is radial inward to the second passage, and after the 180 deg hub turn the flow is radial outward to the third passage. The effects of rotation on the heat transfer coefficients were investigated at rotation numbers up to 0.6 and Reynolds numbers from 30,000 to 70,000. Heat transfer coefficients were measured using the thermocouples-copper-plate-heater regional average method. Heat transfer results are obtained over a wide range of Reynolds numbers and rotation numbers. An increase in heat transfer rates due to rotation is observed in radially outward passes; a reduction in heat transfer rate is observed in the radially inward pass. Regional heat transfer coefficients are correlated with Reynolds numbers for nonrotation and with rotation numbers for rotating condition, respectively. The results can be useful for understanding real rotor blade coolant passage heat transfer under low Mach number, medium–high Reynolds number, and high rotation number conditions.

Aeroelastic Problems in connection with High-Speed Flight

1956 ◽  
Vol 60 (547) ◽  
pp. 459-475 ◽  
Author(s):  
E. G. Broadbent
Keyword(s):  
Mach Number ◽  
High Speed ◽  
The Other ◽  
Control Surface ◽  
The Past ◽  
Other Hand ◽  
Aerodynamic Derivatives ◽  
Mach Numbers ◽  
The One

SummaryA review is given of developments in the field of aeroelasticity during the past ten years. The effect of steadily increasing Mach number has been two-fold: on the one hand the aerodynamic derivatives have changed, and in some cases brought new problems, and on the other hand the design for higher Mach numbers has led to thinner aerofoils and more slender fuselages for which the required stiffness is more difficult to provide. Both these aspects are discussed, and various methods of attack on the problems are considered. The relative merits of stiffness, damping and massbalance for the prevention of control surface flutter are discussed. A brief mention is made of the recent problems of damage from jet efflux and of the possible aeroelastic effects of kinetic heating.

Measurements of Endwall Flows in Transonic Linear Turbine Cascades: Part II—High Flow Turning

2010 ◽  
Author(s):  
F. Taremi ◽  
S. A. Sjolander ◽  
T. J. Praisner
Keyword(s):  
Mach Number ◽  
Kinetic Energy ◽  
Flow Visualization ◽  
Flow Separation ◽  
Surface Flow ◽  
Streamwise Vorticity ◽  
Vortical Structures ◽  
Turbine Cascades ◽  
Mach Numbers ◽  
Surface Flow Visualization

An experimental investigation of two low-turning (90°) transonic linear turbine cascades was presented in Part I of the paper. Part II examines two high-turning (112°) turbine cascades. The experimental results include total pressure losses, streamwise vorticity and secondary kinetic energy distributions. The measurements were made using a seven-hole pressure probe downstream of the cascades. In addition to the measurements, surface flow visualization was conducted to assist in the interpretation of the flow physics. The turbine cascades in Part II, referred to as SL1F and SL2F, have the same inlet and outlet design flow angles, but different aerodynamic loading levels: SL2F is more highly loaded than SL1F. The surface flow visualization results show evidence of small flow separation on the suction side of both airfoils. At the design conditions (outlet Mach number ≈ 0.8), SL2F exhibits stronger vortical structures and larger secondary velocities than SL1F. The two cascades, however, produce similar row losses based on the measurements at 40% axial chord lengths downstream of the trailing edge. Additional data were collected at off-design outlet Mach numbers of 0.65 and 0.91. As the Mach number is raised, the cascades become more aft-loaded. The absolute blade loadings increase, but the Zweifel coefficients decrease due to higher outlet dynamic pressures. Both profile and secondary losses decrease at higher Mach numbers; the main vortical structures and the corresponding peak losses migrate towards the endwall, and there are reductions in secondary kinetic energy and exit flow angle variations. The streamwise vorticity distributions show smaller peak vorticities associated with the passage and the counter vortices at higher exit Mach numbers. The corner vortex, on the other hand, becomes more intensified, resulting in reduction of flow overturning near the endwall. The results for SL1F and SL2F are compared and contrasted with the results for the lower turning cascades presented in Part I. The possible effects of suction-surface flow separation on profile and secondary losses are discussed in this context. The current research project is part of a larger study concerning the effects of endwall contouring on secondary losses, which will be presented in the near future.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

2011 ◽  
Vol 680 ◽  
pp. 511-533 ◽  
Author(s):  
SATHESH MARIAPPAN ◽  
R. I. SUJITH
Keyword(s):  
Mach Number ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Heat Release ◽  
Acoustic Field ◽  
Release Rate ◽  
Governing Equations ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
Acceleration Term

An analysis of thermoacoustic instability is performed for a horizontal Rijke tube with an electrical resistance heater as the heat source. The governing equations for this fluid flow become stiff and are difficult to solve by the computational fluid dynamics (CFD) technique, as the Mach number of the steady flow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore, an asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stiffness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic field and the other for the unsteady flow field in the hydrodynamic zone around the heater. In this analysis, the coupling between the acoustic field and the unsteady heat release rate from the heater appears from the asymptotic analysis. Furthermore, a non-trivial additional term, referred to as the global-acceleration term, appears in the momentum equation of the hydrodynamic zone, which has serious consequences for the stability of the system. This term can be interpreted as a pressure gradient applied from the acoustic onto the hydrodynamic zone. The asymptotic stability of the system with the variation of system parameters is presented using the bifurcation diagram. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD techniques for the hydrodynamic zone. The results confirm the importance of the global-acceleration term. Bifurcation diagrams obtained from the simulations with and without the above term are different. Acoustic streaming is shown to occur during the limit cycle and its effect on the unsteady heat release rate is discussed.

Shock Wave - Film Cooling Interactions in Transonic Flows

2001 ◽  
Author(s):  
P. M. Ligrani ◽  
C. Saumweber ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Waves ◽  
Film Cooling ◽  
Cross Flow ◽  
Injection Velocity ◽  
Film Cooling Effectiveness ◽  
Mach Numbers ◽  
Density Ratios ◽  
Film Cooling Holes

Interactions between shock waves and film cooling are described as they affect magnitudes of local and spanwise-averaged adiabatic film cooling effectiveness distributions. A row of three cylindrical holes is employed. Spanwise spacing of holes is 4 diameters, and inclination angle is 30 degrees. Freestream Mach numbers of 0.8 and 1.10–1.12 are used, with coolant to freestream density ratios of 1.5–1.6. Shadowgraph images show different shock structures as the blowing ratio is changed, and as the condition employed for injection of film into the cooling holes is altered. Investigated are film plenum conditions, as well as perpendicular film injection cross-flow Mach numbers of 0.15, 0.3, and 0.6. Dramatic changes to local and spanwise-averaged adiabatic film effectiveness distributions are then observed as different shock wave structures develop in the immediate vicinity of the film-cooling holes. Variations are especially evident as the data obtained with a supersonic Mach number are compared to the data obtained with a freestream Mach number of 0.8. Local and spanwise-averaged effectiveness magnitudes are generally higher when shock waves are present when a film plenum condition (with zero cross-flow Mach number) is utilized. Effectiveness values measured with a supersonic approaching freestream and shock waves then decrease as the injection cross-flow Mach number increases. Such changes are due to altered flow separation regions in film holes, different injection velocity distributions at hole exits, and alterations of static pressures at film hole exits produced by different types of shock wave events.

The Peak Overpressure Field Resulting From Shocks Emerging From Circular Shock Tubes

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
A. J. Newman ◽  
J. C. Mollendorf
Keyword(s):  
Shock Tube ◽  
Horizontal Plane ◽  
Three Dimensional ◽  
Polar Angle ◽  
Field Measurements ◽  
Initial Development ◽  
Theoretical Predictions ◽  
Mach Numbers ◽  
Tube Exit ◽  
Semi Empirical

A simple semi-empirical model for predicting the peak overpressure field that results when a shock emerges from a circular shock tube is presented and validated. By assuming that the shape of the expanding shock remains geometrically similar after an initial development period, an equation that describes the peak overpressure field in the horizontal plane containing the shock tube’s centerline was developed. The accuracy of this equation was evaluated experimentally by collecting peak overpressure field measurements along radials from the shock tube exit at 0 deg, 45 deg, and 90 deg over a range of shock Mach numbers from 1.15 to 1.45. It was found that the equation became more accurate at higher Mach numbers with percent differences between experimental measurements and theoretical predictions ranging from 1.1% to 3.6% over the range of Mach numbers considered. (1) Shocks do propagate in a geometrically similar manner after some initial development length over the range of Mach numbers considered here. (2) The model developed here gives reasonable predictions for the overpressure field from a shock emerging from a circular shock tube. (3) Shocks are expected to be completely symmetric with respect to the shock tube’s centerline, and hence, a three dimensional overpressure field may be predicted by the model developed here. (4) While there is a range of polar angle at which the shock shape may be described as being spherical with respect to the shock tube’s exit, this range does not encompass the entirety of the half space in front of the shock tube, and the model developed here is needed to accurately describe the entire peak overpressure field.

scholarly journals Critical Mach Numbers of Flow around Two-Dimensional and Axisymmetric Bodies

Aerodynamics ◽  
2021 ◽  
Author(s):  
Vladimir Frolov
Keyword(s):  
Mach Number ◽  
Cross Section ◽  
Flow Simulation ◽  
The Body ◽  
Two Dimensional ◽  
Critical Mach Number ◽  
Method Of Integral Relations ◽  
Viscosity Factor ◽  
Mach Numbers ◽  
Axisymmetric Bodies

The paper presents the calculated results obtained by the author for critical Mach numbers of the flow around two-dimensional and axisymmetric bodies. Although the previously proposed method was applied by the author for two media, air and water, this chapter is devoted only to air. The main goal of the work is to show the high accuracy of the method. For this purpose, the work presents numerous comparisons with the data of other authors. This method showed acceptable accuracy in comparison with the Dorodnitsyn method of integral relations and other methods. In the method under consideration, the parameters of the compressible flow are calculated from the parameters of the flow of an incompressible fluid up to the Mach number of the incoming flow equal to the critical Mach number. This method does not depend on the means determination parameters of the incompressible flow. The calculation in software Flow Simulation was shown that the viscosity factor does not affect the value critical Mach number. It was found that with an increase in the relative thickness of the body, the value of the critical Mach number decreases. It was also found that the value of the critical Mach number for the two-dimensional case is always less than for the axisymmetric case for bodies with the same cross-section.

scholarly journals FLOW SIMULATION OVER REENTRY CAPSULE AT SUPERSONIC AND HYPERSONIC SPEEDS. THE COMPARE BETWEEN TWO REENTRY CAPSULES. PART 1

2020 ◽  
pp. 45-51
Author(s):  
Pavel Timofeev ◽  
◽  
Vladimir Panchenko ◽  
Sergey Kharchyk ◽  
◽  
...  
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Flow Direction ◽  
Numerical Algorithms ◽  
Flow Simulation ◽  
Ansys Fluent ◽  
Forward Shock ◽  
Hypersonic Speeds ◽  
Mach Numbers ◽  
Cfd Method

This study presents flow simulation over the reentry capsule at supersonic and hypersonic speeds. Numerical algorithms solve for the CFD method, which is produced using help ANSYS Fluent 19.2. The using GPU core to get a solution faster. The main purpose – flow simulation and numerical analysis reentry capsule; understand the behavior of supersonic and hypersonic flow and its effect on the reentry capsule; compare temperature results for the range Mach numbers equals 2–6. This study showed results on velocity counters, on temperature counters and vector of velocity for range Mach numbers equals 2–6. This study demonstrates the importance of understanding the effects of shock waves and illustrates how the shock wave changes as the Mach number increases. For every solves, the mesh had adapted for pressure gradient and velocity gradient to get the exact solution. As a result of the obtained solution, it is found that a curved shock wave appears in front of the reentry capsule. The central part of which is a forward shock. An angular expansion process is observed, which is a modified picture of the Prandtl- Mayer flow that occurs in a supersonic flow near the sharp edge of the expanding region. It is revealed that with an increase in the Mach number, the shock wave approaches the bottom of the reentry capsule, and there is also a slope of the shock to the flow direction, with an increase in the Mach number. The relevance and significance of this problem for the design of new and modernization of old reentry capsules.

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