Axisymmetric shock wave interaction with a cone: a benchmark test

Results of the benchmark test are presented of comparing numerical schemes solving shock wave of M-s = 2.38 in nitrogen and argon interacting with a 43 degrees semi-apex angle cone and corresponding experiments. The benchmark test was announced in Shock Waves Vol. 12, No. 4, in which we tried to clarify the effects of viscosity and heat conductivity on shock reflection in conical flows. This paper summarizes results of ten numerical and two experimental applications. State of the art in studies regarding the shock/cone interaction is clarified.

Ultrasonic Viscosity Measurement Using the Shear-Wave Reflection Coefficient with a Novel Signal Processing Technique

Real-time viscosity measurement remains a necessity for highly automated industry. To resolve this problem, many studies have been carried out using an ultrasonic shear wave reflectance method. This method is based on the determination of the complex reflection coefficient`s magnitude and phase at the solid-liquid interface. Although magnitude is a stable quantity and its measurement is relatively simple and precise, phase measurement is a difficult task because of strong temperature dependence. A simplified method that uses only the magnitude of the reflection coefficient and that is valid under the Newtonian regimen has been proposed by some authors, but the obtained viscosity values do not match conventional viscometry measurements. In this work, a mode conversion measurement cell was used to measure glycerin viscosity as a function of temperature (15 to 25 degrees C) and corn syrup-water mixtures as a function of concentration (70 to 100 wt% of corn syrup). Tests were carried out at 1 MHz. A novel signal processing technique that calculates the reflection coefficient magnitude in a frequency band, instead of a single frequency, was studied. The effects of the bandwidth on magnitude and viscosity were analyzed and the results were compared with the values predicted by the Newtonian liquid model. The frequency band technique improved the magnitude results. The obtained viscosity values came close to those measured by the rotational viscometer with percentage errors up to 14%, whereas errors up to 96% were found for the single frequency method.

Isentropic Exergy and Pressure of the Shock Wave Caused by the Explosion of a Pressure Vessel

An accidental burst of a pressure vessel is an uncontrollable and explosion-like batch process. In this study it is called an explosion. The destructive effectof a pressure vessel explosion is relative to the amount of energy released in it. However, in the field of pressure vessel safety, a mutual understanding concerning the definition of explosion energy has not yet been achieved. In this study the definition of isentropic exergy is presented. Isentropic exergy is the greatest possible destructive energy which can be obtained from a pressure vessel explosion when its state changes in an isentropic way from the initial to the final state. Finally, after the change process, the gas has similar pressure and flow velocity as the environment. Isentropic exergy differs from common exergy inthat the process is assumed to be isentropic and the final gas temperature usually differs from the ambient temperature. The explosion process is so fast that there is no time for the significant heat exchange needed for the common exergy.Therefore an explosion is better characterized by isentropic exergy. Isentropicexergy is a characteristic of a pressure vessel and it is simple to calculate. Isentropic exergy can be defined also for any thermodynamic system, such as the shock wave system developing around an exploding pressure vessel. At the beginning of the explosion process the shock wave system has the same isentropic exergyas the pressure vessel. When the system expands to the environment, its isentropic exergy decreases because of the increase of entropy in the shock wave. The shock wave system contains the pressure vessel gas and a growing amount of ambient gas. The destructive effect of the shock wave on the ambient structures decreases when its distance from the starting point increases. This arises firstly from the fact that the shock wave system is distributed to a larger space. Secondly, the increase of entropy in the shock waves reduces the amount of isentropic exergy. Equations concerning the change of isentropic exergy in shock waves are derived. By means of isentropic exergy and the known flow theories, equations illustrating the pressure of the shock wave as a function of distance are derived. Amethod is proposed as an application of the equations. The method is applicablefor all shapes of pressure vessels in general use, such as spheres, cylinders and tubes. The results of this method are compared to measurements made by various researchers and to accident reports on pressure vessel explosions. The test measurements are found to be analogous with the proposed method and the findings in the accident reports are not controversial to it.

Numerical study of wedge supported oblique shock wave-oblique detonation wave transitions

The results of a numerical study of premixed Hydrogen-air flows ignition by an oblique shock wave (OSW) stabilized by a wedge are presented, in situations when initial and boundary conditions are such that transition between the initial OSW and an oblique detonation wave (ODW) is observed. More precisely, the objectives of the paper are: (i) to identify the different possible structures of the transition region that exist between the initial OSW and the resulting ODW and (ii) to evidence the effect on the ODW of an abrupt decrease of the wedge angle in such a way that the final part of the wedge surface becomes parallel to the initial flow. For such a geometrical configuration and for the initial and boundary conditions considered, the overdriven detonation supported by the initial wedge angle is found to relax towards a Chapman-Jouguet detonation in the region where the wedge surface is parallel to the initial flow. Computations are performed using an adaptive, unstructured grid, finite volume computer code previously developed for the sake of the computations of high speed, compressible flows of reactive gas mixtures. Physico-chemical properties are functions of the local mixture composition, temperature and pressure, and they are computed using the CHEMKIN-II subroutines.

Mountain waves in two-layer sheared flows: Critical-level effects, wave reflection, and drag enhancement

Internal gravity waves generated in two-layer stratified shear flows over mountains are investigated here using linear theory and numerical simulations. The impact on the gravity wave drag of wind profiles with constant unidirectional or directional shear up to a certain height and zero shear above, with and without critical levels, is evaluated. This kind of wind profile, which is more realistic than the constant shear extending indefinitely assumed in many analytical studies, leads to important modifications in the drag behavior due to wave reflection at the shear discontinuity and wave filtering by critical levels. In inviscid, nonrotating, and hydrostatic conditions, linear theory predicts that the drag behaves asymmetrically for backward and forward shear flows. These differences primarily depend on the fraction of wavenumbers that pass through their critical level before they are reflected by the shear discontinuity. If this fraction is large, the drag variation is not too different from that predicted for an unbounded shear layer, while if it is small the differences are marked, with the drag being enhanced by a considerable factor at low Richardson numbers (Ri). The drag may be further enhanced by nonlinear processes, but its qualitative variation for relatively low Ri is essentially unchanged. However, nonlinear processes seem to interact constructively with shear, so that the drag for a noninfinite but relatively high Ri is considerably larger than the drag without any shear at all.

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

Material processing by plasma shock wave generated in an inverse Z-pinch plasma expander

The applicability of plasma shock wave for material processing was investigated using modified inverse Z-pinch device. Shock wave expanding speed and plasma spectral analysis were studied using an internal magnetic,probe and spatially collimated light spectroscopy. The material processing capability of the device was shown by many different surface analysis techniques such as AES, IRS, EPM and SEM. The interactions between a plasma shock wave of similar to4x10(6) cm/s speed with a Si substrate surface shows some ion implantation capability using a nitrogen plasma and thin film formation using a methane plasma.

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Ultrastructural and immunocytochemical evaluation of the effects of extracorporeal shock wave treatment in the hind limbs of horses with experimentally induced suspensory ligament desmitis

Objective-To evaluate the effects of extracorporeal shock wave therapy (ESWT) on affected ligaments in the hind limbs of horses with experimentally induced suspensory ligament desmitis by use of ultrasonographic, ultrastructural, and immunocytochemical techniques.Animals-10 horses.Procedure-Suspensory ligament desmitis was induced in both hind limbs of each horse by use of 2 collagenase injections (administered 2 weeks apart) in each suspensory ligament. Two weeks after the second injection, the right hind limb of each horse was treated with ESWT (3 treatments at 3-week intervals)- the left hind limb was not treated (control limb). Periodically during the study, the healing process was monitored ultrasonographically and the proportions of ligaments affected with lesions were assessed. Four weeks after the last ESWT treatment, biopsy specimens were collected from all ligaments for ultrastructural evaluation and immunocytochemical analysis of transforming growth factor beta-1.Results-The difference in the proportion of the lesion-affected ligament between ESWT-treated and control limbs was significant (P < 0.05) from 3 weeks after the second ESWT treatment to the end of the study. Compared with control ligaments, ESWT-treated ligaments had more small, newly formed collagen fibrils and greater expression of transforming growth factor beta-1 4 weeks after the last ESWT treatment was administered.Conclusions and Clinical Relevance-Results have indicated that ESWT appears to facilitate the healing process in horses with experimentally induced hind limb suspensory ligament desmitis.

Wave reflection at the end of a waveguide supported by a nonlinear spring

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Microvascular response to shock wave application in striated skin muscle

This study aims to quantify by intravital microscopy the microhemodynamic response after extracorporeal shock wave application (ESWA) to the physiologic microcirculation of the mouse dorsal skinfold chamber.

Radial extracorporeal shock wave therapy (rESWT) induces new bone formation in vivo: results of an animal study in rabbits

The aim of this study was to investigate if radial extracorporeal shock wave therapy (rESWT) induces new bone formation and to study the time course of ESWT-induced osteogenesis. A total of 4000 impulses of radial shock waves (0.16 mJ/mm²) were applied to one hind leg of 13 New Zealand white rabbits with the contralateral side used for control. Treatment was repeated after 7 days. Fluorochrome sequence labeling of new bone formation was performed by subcutaneous injection of tetracycline, calcein green, alizarin red and calcein blue. Animals were sacrificed 2 weeks (n = 4), 4 weeks (n = 4) and 6 weeks (n = 5) after the first rESWT and bone sections were analyzed by fluorescence microscopy. Deposits of fluorochromes were classified and analyzed for significance with the Fisher exact test. rESWT significantly increased new bone formation at all time points over the 6-week study period. Intensity of ossification reached a peak after 4 weeks and declined at the end of the study. New bone formation was significantly higher and persisted longer at the ventral cortex, which was located in the direction to the shock wave device, compared with the dorsal cortex, emphasizing the dose-dependent process of ESWT-induced osteogenesis. No traumata, such as hemorrhage, periosteal detachment or microfractures, were observed by histologic and radiologic assessment. This is the first study demonstrating low-energy radial shock waves to induce new bone formation in vivo. Based on our results, repetition of ESWT in 6-week intervals can be recommended. Application to bone regions at increased fracture risk (e.g., in osteoporosis) are possible clinical indications.

Histomorphologic evaluation of extracorporeal shock wave therapy of the fourth metatarsal bone and the origin of the suspensory ligament in horses without lameness

OBJECTIVE: To determine via histologic examination and scintigraphy the effect of focused extracorporeal shock wave therapy (ESWT) on normal bone and the bone-ligament interface in horses. ANIMALS: 6 horses without lameness. PROCEDURE: Origins of the suspensory ligament at the metacarpus (35-mm probe depth) and fourth metatarsal bone (5-mm probe depth) were treated twice (days 0 and 16) with 2,000 shocks (energy flux density, 0.15 mJ/mm2). One forelimb and 1 hind limb were randomly treated, and the contralateral limbs served as nontreated controls. Bone scans were performed on days -1 (before ESWT), 3, 16, and 19. Histomorphologic studies of control and treated tissues were performed on day 30. RESULTS: ESWT significantly increased the number of osteoblasts but caused no damage to associated soft tissue structures and did not induce cortical microfractures. A significant correlation between osteoblast numbers and radiopharmaceutical uptake was noticed on lateral views of the hind limb on days 3 and 16 and on caudal views of the forelimb on day 3. CONCLUSIONS AND CLINICAL RELEVANCE: Results suggested that ESWT has the potential to increase osteoblast numbers in horses. The correlation between increased osteoblast numbers and radio-pharmaceutical uptake 3 days and 16 days after the first ESWT suggested that stimulation of osteogenesis occurred soon after ESWT. No damage to bone or the bone-ligament interface should occur at the settings used in this study, and ESWT can therefore be administered safely in horses.