Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining

2007 ◽  
Vol 584 ◽  
pp. 301-335 ◽  
Author(s):  
SAVVAS XANTHOS ◽  
MINWEI GONG ◽  
YIANNIS ANDREOPOULOS
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Pressure Gradient ◽  
Shock Tube ◽  
Isotropic Turbulence ◽  
Strain Tensor ◽  
Velocity Fluctuations ◽  
Total Enthalpy ◽  
Expansion Waves ◽  
Custom Made

The response of homogeneous and isotropic turbulence to streamwise straining action provided by planar expansion waves has been studied experimentally in the CCNY shock tube research facility at several Reynolds numbers. The reflection of a propagating shock wave at the open endwall of the shock tube generated an expansion fan travelling upstream and interacting with the induced flow behind the incident shock wave which has gone through a turbulence generating grid.A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three-dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed the computations of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of kinetic energy term and full rate-of-strain tensor. The longitudinal size of the straining zone was substantial so that measurements within it were possible. The flow accelerated from a Mach number of 0.23 to about 0.56, a value which is more than twice the initial one.Although the average value of the applied straining was only betweenS11= 130 s−1andS11= 240 s−1and the gradient Mach number was no more than 0.226, the amplitude of fluctuations of the strain rateS11were of the order of 4000 s−1before the application of straining and were reduced by about 2.5 times downstream of the interaction. This characteristic of high-amplitude bursts and the intermittent behaviour of the flow play a significant role in the dynamics of turbulence.One of the most remarkable features of the suppression of turbulence is that this process peaks shortly after the application of the straining where the pressure gradient is substantial. It was also found that the total enthalpy variation follows very closely the temporal gradient of pressure within the straining region and peaks at the same location as the pressure gradient.Attenuation of longitudinal velocity fluctuations has been observed in all experiments. It appears that this attenuation depends strongly on the characteristics of the incoming turbulence for a given straining strength and flow Mach number. The present results clearly show that in most of the cases, attenuation occurs at large times or distances from the turbulence generating grids where length scales of the incoming flow are high and turbulence intensities are low. Thus, large eddies with low-velocity fluctuations are affected the most by the interaction with the expansion waves. Spectral analysis has indicated that attenuation of fluctuations is not the same across all wavenumbers of the spectrum. The magnitude of attenuation appears to be higher in cases of finer mesh grids.

Experiments of Compressible Homogeneous and Isotropic Turbulence Interacting With Expansion Waves

2003 ◽  
Author(s):  
Savvas S. Xanthos ◽  
Yiannis Andreopoulos
Keyword(s):  
Mach Number ◽  
Shock Tube ◽  
Total Pressure ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Pressure Fluctuations ◽  
Incident Shock ◽  
Expansion Waves ◽  
Curvature Effects ◽  
Homogeneous And Isotropic Turbulence

The interaction of traveling expansion waves with grid-generated turbulence was investigated in a large-scale shock tube research facility. The incident shock and the induced flow behind it passed through a rectangular grid, which generated a nearly homogeneous and nearly isotropic turbulent flow. As the shock wave exited the open end of the shock tube, a system of expansion waves was generated which traveled upstream and interacted with the grid-generated turbulence; a type of interaction free from streamline curvature effects, which cause additional effects on turbulence. In this experiment, wall pressure, total pressure and velocity were measured indicating a clear reduction in fluctuations. The incoming flow at Mach number 0.46 was expanded to a flow with Mach number 0.77 by an applied mean shear of 100 s−1. Although the strength of the generated expansion waves was mild, the effect on damping fluctuations on turbulence was clear. A reduction of in the level of total pressure fluctuations by 20 per cent was detected in the present experiments.

scholarly journals Design and Validation of a Probe for Spatially and Temporally Resolved Measurements of Vorticity and Strain Rates in Compressible Turbulence Interactions

10.14311/994 ◽  
2007 ◽  
Vol 47 (6) ◽  
Author(s):  
S. Xanthos ◽  
M. Gong ◽  
Y. Andreopoulos
Keyword(s):  
Isotropic Turbulence ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Compressible Turbulence ◽  
Expansion Waves ◽  
Custom Made ◽  
Homogeneous And Isotropic Turbulence ◽  
Total Temperature ◽  
Kinetic Energy Term

A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed computation of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of the kinetic energy term and full rate-of-strain tensor. The probe has been validated experimentally in low-speed boundary layers and used in the CCNY Shock Tube Research Facility, where interactions of planar expansion waves or shock waves with homogeneous and isotropic turbulence have been investigated at several Reynolds numbers. 

Shock Tube Simulation of the Transient Surge Phase Inside an Axial Compressor

2018 ◽  
Author(s):  
Paul Xiubao Huang ◽  
Robert S. Mazzawy
Keyword(s):  
Shock Wave ◽  
Shock Tube ◽  
High Speed ◽  
Transient Flow ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Dynamic Effect ◽  
Initiation Site ◽  
Flow Reversal ◽  
Expansion Waves

This paper is a continuing work from one author on the same topic of the transient aerodynamics during compressor stall/surge using a shock tube analogy by Huang [1, 2]. As observed by Mazzawy [3] for the high-speed high-pressure (HSHP) ratio compressors of the modern aero-engines, surge is an event characterized with the stoppage and reversal of engine flow within a matter of milliseconds. This large flow transient is accomplished through a pair of internally generated shock waves and expansion waves of high strength. The final results are often dramatic with a loud bang followed by the spewing out of flames from both the engine intake and exhaust, potentially damaging to the engine structure [3]. It has been demonstrated in the previous investigations by Marshall [4] and Huang [2] that the transient flow reversal phase of a surge cycle can be approximated by the shock tube analogy in understanding its generation mechanism and correlating the shock wave strength as a function of the pre-surge compressor pressure ratio. Kurkov [5] and Evans [8] used a guillotine analogy to estimate the inlet overpressure associated with the sudden flow stoppage associated with surge. This paper will expand the progressive surge model established by the shock tube analogy in [2] by including the dynamic effect of airflow stoppage using an “integrated-flow” sequential guillotine/shock tube model. It further investigates the surge formation (characterized by flow reversal) and propagation patterns (characterized by surge shock and expansion waves) after its generation at different locations inside a compressor. Calculations are conducted for a 12-stage compressor using this model under various surge onset stages and compared with previous experimental data [3]. The results demonstrate that the “integrated-flow” model closely replicates the fast moving surge shock wave overpressure from the stall initiation site to the compressor inlet.

Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

2014 ◽  
Vol 756 ◽  
Author(s):  
Jaiyoung Ryu ◽  
Daniel Livescu
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Isotropic Turbulence ◽  
Interaction Analysis ◽  
Longitudinal Velocity ◽  
Wave Structure ◽  
Turbulence Structure ◽  
Turbulent Structures ◽  
Linear Interaction ◽  
Third Invariant

AbstractThe interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

Experimental investigation of diaphragm material combinations in a small-scale shock tube

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anugya Singh ◽  
Aravind Satheesh Kumar ◽  
Kannan B.T.
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Production Capacity ◽  
Incident Shock ◽  
Small Scale ◽  
Content Type ◽  
Shock Mach Number ◽  
Reinforcing Material ◽  
Shock Wave Mach Number

Purpose The purpose of this study is to experimentally investigate the trends in shock wave Mach number that were observed when different diaphragm material combinations were used in the small-scale shock tube. Design/methodology/approach A small-scale shock tube was designed and fabricated having a maximum Mach number production capacity to be 1.5 (theoretically). Two microphones attached in the driven section were used to calculate the shock wave Mach number. Preliminary tests were conducted on several materials to obtain the respective bursting pressures to decide the final set of materials along with the layered combinations. Findings According to the results obtained, 95 GSM tracing paper was seen to be the strongest reinforcing material, followed by 75 GSM royal executive bond paper and regular 70 GSM paper for aluminium foil diaphragms. The quadrupled layered diaphragms revealed a variation in shock Mach number based on the position of the reinforcing material. In quintuple layered combinations, the accuracy of obtaining a specific Mach number was seen to be increasing. Optimization of the combinations based on the production of the shock wave Mach number was carried out. Research limitations/implications The shock tube was designed taking maximum incident shock Mach number as 1.5, the experiments conducted were found to achieve a maximum Mach number of 1.437. Thus, an extension to further experiments was avoided considering the factor of safety. Originality/value The paper presents a detailed study on the effect of change in the material and its position in the layered diaphragm combinations, which could lead to variation in Mach numbers that are produced. This could be used to obtain a specific Mach number for a required study accurately, with a low-cost setup.

Theory for producing a single-phase rarefaction shock wave in a shock tube

2001 ◽  
Vol 445 ◽  
pp. 37-54 ◽  
Author(s):  
S. H. FERGASON ◽  
T. L. HO ◽  
B. M. ARGROW ◽  
G. EMANUEL
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Single Phase ◽  
Van Der Waals ◽  
Small Region ◽  
Incident Flow ◽  
Global Theory ◽  
Rarefaction Shock ◽  
Shock Tube Experiment

Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.

A study of the impulsive wave discharged from the inclined exit of a tube

2003 ◽  
Vol 217 (2) ◽  
pp. 271-279 ◽  
Author(s):  
H-D Kim ◽  
Y-H Kweon ◽  
T Setoguchi
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Good Accuracy ◽  
Propagation Direction ◽  
Impulsive Wave ◽  
Compressible Euler ◽  
Computational Work ◽  
Initial Shock ◽  
Tube Exit

The propagation of the impulsive wave discharged from the inclined exit of a tube is investigated using a shock tube experiment and by numerical computations. The pressure histories and wavefront geometries of the impulsive wave propagating outside the exits of the tube with several different configurations are analysed for the range of an initial shock wave Mach number between 1.1 and 1.4. In the shock tube experiments, the impulsive waves are visualized by a Schlieren optical system for the purpose of validation of computational work. Computations using the two-dimensional, unsteady, compressible, Euler equations are carried out to represent the experimental impulsive waves. The results obtained show that the inclination angle of the tube exit reduces the magnitude of the impulsive wave and affects the wavefront geometry of the impulsive wave. It is also found that the propagation direction and magnitude of the impulsive wave depend on the Mach number of the initial shock wave, while the impulsive waveform does not significantly vary with the Mach number of the initial shock wave. The computed results obtained predict the experimental ones with quite good accuracy.

Estimation of Mach Number of Shock Wave Propagating in Pipe

2003 ◽  
Author(s):  
Takanori Yamazaki ◽  
Masaki Endo
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Dynamic Characteristic ◽  
Pressure Transducer ◽  
Shock Strength ◽  
Pressure History ◽  
Boundary Layer Interaction ◽  
Shock Mach Number

A useful way to estimate the local Mach number of shock propagating in a pipe is proposed in this paper. The shock Mach number, or the shock strength gradually decreases or increases as the shock propagates downstream in pipe due to the shock-boundary layer interaction. In general, the shock Mach number is estimated through the measurement of the time, which it takes for the shock to propagate between any two points along the pipe. This technique is very useful if the decreasing rate of the shock strength is given and it, after all, yields the average Mach number between the two points. In this paper the measurement of the local Mach number of shock in the shock tube is examined using one pressure transducer. The pressure history after the shock reaches the pressure tap is analyzed. The method to estimate the local Mach number is discussed considering the dynamic characteristic of the pressure transducer.

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