Shock Tube Flow Research Articles

Computational analysis of dense gas shock tube flow

Nonclassical phenomena associated with the classical dynamics of real gases in a conventional shock tube are studied. A TVD predictor-corrector (TVD-MacCormack) scheme with reflective endwall boundary conditions is used for the one-dimensional Euler equations to simulate the evolution of the wave field of a van der Waals gas. Depending upon the initial conditions of the gas, wave fields are produced that contain nonclassical phenomena such as expansion shocks, composite waves, splitting shocks, etc. In addition, the interactions of waves reflected from the endwalls produce both classical and nonclassical phenomena. Wave field evolution is depicted using plots of the flow variables at specific times and withx-t diagrams.

Computational analysis of dense gas shock tube flow

Computational analysis of dense gas shock tube flow

Stream function coordinate Euler formulation and shocktube application

In this paper, the stream function coordinate SFC Euler formulation for one-dimensional unsteady compressible flow with strong discontinuities has been developed. A conservative system of three equations has been formulated and solved numerically using Godunov's scheme in the computational plane. To illustrate the applicability of the method, a finite length shocktube flow problem has been successfully simulated. The calculated results show good agreement with the exact solution. The present SFC Euler formulation is more powerful than the SFC isentropic formulation and is able to locate exactly the positions and accurately predict the strengths of the shock wave and the contact discontinuity. In fact, only a single grid interval is needed to capture the contact discontinuity. Reflection of the shock wave and rarefaction wave from the tube ends and interaction between the reflected shock wave and the contact discontinuity are also accurately simulated.

隔膜開口過程における損失を考慮した衝撃波管流れに関する研究

隔膜開口過程における損失を考慮した衝撃波管流れに関する研究

Computations of axisymmetric flows in hypersonic shock tubes

A time-accurate two-dimensional fluid code is used to compute test times in shock tubes operated at supersonic speeds. Unlike previous studies, this investigation resolves the finer temporal details of the shock-tube flow by making use of modern supercomputers and state-of-the-art computational fluid dynamic solution techniques. The code, besides solving the time-dependent fluid equations, also accounts for the finite rate chemistry in the hypersonic environment. The flowfield solutions are used to estimate relevant shock-tube parameters for laminar flow, such as test times, and to predict density and velocity profiles. Boundary-layer parameters such as bar-delta(sub u), bar-delta(sup *), and bar-tau(sub w), and test time parameters such as bar-tau and particle time of flight t(sub f), are computed and compared with those evaluated by using Mirels' correlations. This article then discusses in detail the effects of flow nonuniformities on particle time-of-flight behind the normal shock and, consequently, on the interpretation of shock-tube data. This article concludes that for accurate interpretation of shock-tube data, a detailed analysis of flowfield parameters, using a computer code such as used in this study, must be performed.

Acceleration of a sphere behind planar shock waves

The paper presents the results of an investigation on the motion of a spherical particle in a shock tube flow. A shock tube facility was used for studying the acceleration of a sphere by an incident shock wave. Using different optical methods and performing experiments in two different shock tubes, the trajectory and velocity of a spherical particle were measured. Based upon these results and simple one-dimensional calculations, the drag coefficient of a sphere and shading effect of sphere interaction with a shock tube flow were studied.

Formation of argon clusters by homogeneous nucleation in supersonic shock tube flow

The formation of argon clusters by homogeneous nucleation of pure argon diluted in helium was investigated in the supersonic outflow of a shock tube, where the clusters were detected by laser light scattering from the particles in supersaturated states. The thermodynamic states for the onset of homogeneous nucleation varied between 48 and 85 K with corresponding argon partial pressures in the range 2–850 Torr. Values of adiabatic supercooling with respect to the argon phase equilibrium ranged between 3 and 10 K. The experiments are in agreement with previous investigations in subsonic shock tube and supersonic Ludwieg tube expansions but disagree with previous investigations in steady supersonic nozzle expansions. It is possible to explain qualitatively the observed differences in argon nucleation behavior on the basis of a thermodynamic and kinetic concept independent of the basic assumptions of existing nucleation theories.

Application of hot-wire anemometry in shock-tube flows

Several techniques associated with the use of hot wire anemometry in compressible turbulence measurements are described and tested in shock tube flows. These techniques include 1. in-situ calibration of the hot-wire probe by firing several shock waves of different strengths in the shock tube; 2. on-line analog frequency compensation or off-line digital compensation of the temperature-wire; 3. simultaneous acquisition of time-dependent flow velocity and temperature of the flow without invoking Morkovin's hypothesis of strong Reynolds analogy. The techniques were tested in two different shock tube facilities, where a grid generated turbulent flow interacting with a moving shock was set up.

Asymptotic solution of shock tube flows with homogeneous condensation

The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz–Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows.

Design and Performance of Quick Opening Shock Tube Using Rubber Membrnae. 2nd Report, Modification of the Facility and Analysis of Shock Tube Flow.

In the previous paper, the design and performance of a diaphragmless shock tube which could generate, with a higher degree of repeatability, weak shock waves up to shock Mach number of 1.2 were reported. In the present paper, an experimental improvement of the facility, by which the pressure difference between the driver chamber and the driven channel can be increased to about 4 times higher than the previous system, was achieved so that the attainable shock Mach number was extended to Ms=1.6 at the initial atmospheric pressure. Higher shock Mach number up to 3 can also be readily obtained by decreasing the pressure in the driven channel. A numerical simulation and a theoretical analysis were perfomed in order to clarify the characteristics of this diaphragmess shock tube. Although the numerical simulation revealed that the flow near the rubber membrane is very complicated, however, with the help of simplified one-dimensional model, in which the varying cross-section is taken into account, shock Mach numbers achievable in this shock tube were well predicted as a function of the pressure ratio between the high-pressure chamber and low-pressure channel. Good agreement was obtained between the experimental results and theoretical prediction.

Numerical solution of the problem of shock tube flow development with transverse diaphragm withdrawal

The time-dependent two-dimensional perfect gas flow which occurs in a channel with a constant cross-section as a result of the transverse withdrawal of a diaphragm to provide an initial pressure difference is studied numerically using a second-order-accurate method. The evolution and interaction of the main wave disturbances is analyzed in detail on the basis of the solutions obtained.

One-Dimensional Interaction between Shock Wave and Low-Porosity Foam. 1st Report. Experiments.

Experimental studies on the interaction between a shock wave and a low-porosity foam are conducted by using a shock tube 125 mm in inner diameter and 10080 mm in length. The density of the experimental polyurethane foam is 284 kg/m3. Stress-strain relationships of the foam are investigated experimentally. The purpose is to investigate the effect of the impact of the gas dynamic shock wave on the unsteady deformation of the foam. One end of the foam is fixed to the end wall of the shock tube, and the shock tube flow is initiated by the quick acting valve. Experiments are conducted in the shock tube for incident shock Mach numbers of 1.7 and 1.9. Experimental time histories of the surface stress of the foam at the end of the shock tube show damping vibrations approaching the gas dynamic pressure of the reflected shock wave, and the peak stresses amount to several times the pressure of the reflected shock wave.

Two-line planar fluorescence for temporally resolved temperature imaging in a reacting supersonic flow over a body

An instantaneous temperature imaging technique for chemically reacting, supersonic flows over bodies is described and demonstrated in a H2/O2/Ar shock tube flow (M=1.3, 0.7 atm, 1760K freestream). Based on a planar fluorescence measurement, the approach uses a two-line rotational population ratio to infer temperature. The measured 2-d temperature profiles qualitatively match the expected flowfield structure around the blunt body, and the temperature increase across the bow shock in a single-shot measurement agrees within 5–10% of the prediction of a 1-d shock analysis. The significant systematic error sources for the technique are detailed, and the random error effects associated with shot-noise-limited fluorescence images are statistically analyzed to identify transitions which minimize the temperature errors for instantaneous and average measurements. Even for average temperature measurements, the analysis predicts errors which can be as large as 5–10% when noisy fluorescence images are used in conjunction with low temperature sensitivity. In general, temperature errors can be reduced by increasing sensitivity, i.e., the energy separation of the two rotational levels, until the fluorescence shot-noise rises to a value of 30–50% within the temperature range of interest.

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

A TVD scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock-tube flows; regular shock reflection; supersonic boundary layer; and shock boundary layer interactions. These numerical results compare well with the corresponding exact solutions or experimental data.

Thermo-chemical models for hypersonic flows

Abstract Investigations on the effects of high-temperature gas models have been performed by computing two-dimensional hypersonic flows. Thermal nonequilibrium effects are investigated by flow simulations around a vehicle of the Orbital Experiment along re-entry trajectory ranging from altitudes of 50 to 100 km, with the one-/two-temperature gas results being compared regarding the shock standoff distance, the heating rate and chemical species' concentrations. Additionally, calculations are performed for shock-tube flows in order to clarify the effects of the modelings included in the two-temperature model: the choice of chemical reaction constants, preferential dissociation and diffusive vibrational relaxation. Finally, a vibrational relaxation model for high-temperature gas without the need for information about immediately behind the shock wave is presented.

Planar laser-induced fluorescence imaging of shock-tube flows with vibrational nonequilibrium

Single-shot planar laser-induced fluorescence images of nitric oxide in shock-heated flows with vibrational nonequilibrium are reported. The results demonstrate that planar laser-induced fluorescence imaging is a promising diagnostic technique for multidimensional high-speed flows because of its ability to examine shock structure and to visualize and measure vibrational nonequilibrium. The flows studied were generated within a shock tube and were composed of dilute mixtures of NO in argon. A narrow-band ArF laser tuned to the D +- X (0,1) R2 (28.5) transition of NO at 193.346 nm was used as the excitation source. The broadband fluorescence was collected at 90 deg to the path of excitation using an intensified, two-dimensional photodiode array. Images presented include a normal incident shock, a normal reflected shock, and a four-image sequence of the development of high-temperat ure supersonic flow over a two-dimensiona l blunt body. The vibrational relaxation in the downstream region of the normal shocks is analyzed and compared with calculations based on known relaxation rates.

Third-order nonoscillatory schemes for the Euler equations

Two time-level third-order finite-difference shock-capturin g schemes based on applying the characteristic flux difference splitting to a modified flux that may have high-order accuracy and either monotonicity preserving or essentially nonoscillatory (ENO) property have been developed for the Euler equations of gas dynamics. Two ways to achieve high-order accuracy are described. One is based on upstream interpolation using Lagrange's formula with van Leer's smoothness monitors. The other is based on ENO interpolation using reconstruction via primitive function approaches. For multidimensional problems, dimensional splitting is adopted for explicit schemes, and standard alternating direction implicit approximate factorization procedures are used for implicit schemes. Numerical examples to illustrate the performance of the proposed schemes are given. ERY recently, a new class of uniformly high-order accurate, essentially nonoscillatory (ENO) schemes has been developed by Harten and Osher,1 Marten,2 and Harten et al.3'4 They presented a hierarchy of uniformly high-order accurate schemes that generalize Godunov's scheme5 and its secondorder accurate MUSCL extension6'7 and total variation diminishing (TVD) schemes8'9 to an arbitrary order of accuracy. In contrast to the earlier second-order TVD schemes that drop to first-order accuracy at local extrema and maintain second-order accuracy in smooth regions, the new ENO schemes are uniformly high-order accurate throughout, even at critical points. Theoretical results for the scalar coefficient case and numerical results for the scalar conservation law and for the one-dimensional Euler equations of gas dynamics have been reported with highly accurate results. Preliminary results for two-dimensional problems were reported in Ref. 2. In this paper, following van Leer,10'11 Harten,2 and Harten et al.3'4 we describe a class of third-order, essentially nonoscillatory shock-capturing schemes for the Euler equations of gas dynamics. These schemes are obtained by applying the characteristic flux-difference splitting to an appropriately modified flux vector that may have high-order accuracy and nonoscillatory property. Third-order schemes are constructed using upstream interpolation and ENO interpolation. Both explicit and implicit schemes are derived. Implicit schemes for two-dimensional Euler equations in general coordinates are also given. We apply the resulting schemes to simulate one-dimensional and two-dimensional unsteady shock tube flows and steady two-dimensional flows involving strong shocks to illustrate the performance of the schemes. In Sec. II, characteristic properties of the Euler equations related to the numerical advections are briefly summarized. Upstream interpolation using Lagrange's formula to generate a class of two time-level, 2p + 1 space point, (2p - l)thorder accurate schemes is described in Sec. III. In particular, a third-order scheme with smoothness monitors due to van Leer10 is described. In Sec. IV, the essentially nonoscillatory interpolation of Harten2 and Harten et al.3'4 using reconstruction via primitive function approach is employed to yield a third-order nonoscillatory scheme.

Continuous wave laser absorption techniques for gasdynamic measurements in supersonic flows

Line-of-sight measurements of velocity, temperature, pressure, density, and mass flux were performed in a transient shock tube flow using three laser absorption schemes. All methods employed an intracavity-doubled ring dye laser tuned to an OH transition in the A(2) summation operator(+) ? X(2)II (0,0) band at 306 nm. In the first scheme, the gas was labeled by 193.3-nm excimer photolysis of H(2)O, and the passage of the generated OH was detected downstream. In the second method, the laser was tuned at a rate of 3 kH(z) over the R(1)(7) and R(1)(11) line pair, and absorption was simultaneously monitored at 90 and 60 degrees with respect to the flow. Velocity was determined from the Doppler shift of the profiles and the temperature from the intensity ratio of the lines. Pressure was determined from both the magnitude of absorption and the collisional broadening. In the third method, the laser wavelength was fixed at a single frequency, and a continuous measurement of velocity and pressure was obtained using the signals from the two beam paths. All methods gave results which compare favorably to calculated values.

39 ホログラフィ法による三次元衝撃波現象の可視化

In the present paper, holographic interferometry was applied to visualize of three dimensional shock wave phenomena. One of the examples is a shock wave discharged from the open end of a square cross sectional shock tube. The experiments were conducted in 40mm×40mm cross sectional shock tube. Double exposure diffuse holographic interferometry was used for the flow visualization. The three dimensional shock configulation and the three dimensional flow behind the shock wave can be clearly observed. Other three dimensional observations in shock tube flows are also shown.

A215 シッョクチューブによる鈍い後縁を持つ翼の後流の流れの観察

The vortex shedding and near wake flows of blunt trailing edge NACA 0012 airfoils and flat plates having rectangular trailing edge cavities are observed in Mach 0.6 Shock tube flow with a Schlieren system.While the sharp trailing edge generates only one discrete vortex, strong many discrete vortices are generated from blunt trairing edges. On the other hand dull and weak vortices can be seemed for the segmented blunt trailing edge.Circular cylindrical waves are formed due to the generation of discrete vortices.For blunt trailing edge airfoils with angle of attack vortices are shedded from the portion near the lower corner of the trailing edge, and their mean rear stagnation points seem to be near here.It can be thought that this is a reason why blunt trailing edge airfoils have higher lift.