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In this paper, we present results from spontaneous ignition of aluminium particle clouds in a series of shock tube experiments. For all experiments, the shock propagates along a narrow pile of 40-$$\upmu $$ μ m aluminium particles. The study includes shock Mach numbers in the range from 1.51 to 2.38. The results are visualised using photographic techniques and pressure gauges. The combination of two Phantom high-speed video cameras and a beamsplitter allows a compact schlieren setup mounted together with a dark-film high-speed camera. While the schlieren technique allows the shock features to be identified, the dark-film camera is used to capture the ignition and burning of the aluminium particle clouds. Based on extensive image processing and shock tube relations for reflected shocks, spontaneous ignition of the aluminium particle cloud is found to take place for reflected shock gas temperatures above 635 K. For increasing Mach numbers, we find a decreasing trend for the ignition delay. Additionally, the burning time is observed to decrease with increasing Mach number, indicating that the burning process is more efficient with increasing gas temperature.

We investigate the shock-induced flow through random particle arrays using particle-resolved Large Eddy Simulations for different incident shock wave Mach numbers, particle volume fractions and particle sizes. We analyze trends in mean flow quantities and the unresolved terms in the volume averaged momentum equation, as we vary the three parameters. We find that the shock wave attenuation and certain mean flow trends can be predicted by the opacity of the particle cloud, which is a function of particle size and particle volume fraction. We show that the Reynolds stress field plays an important role in the momentum balance at the particle cloud edges, and therefore strongly affects the reflected shock wave strength. The Reynolds stress was found to be insensitive to particle size, but strongly dependent on particle volume fraction. It is in better agreement with results from simulations of flow through particle clouds at fixed mean slip Reynolds numbers in the incompressible regime, than with results from other shock wave particle cloud studies, which have utilized either inviscid or two-dimensional approaches. We propose an algebraic model for the streamwise Reynolds stress based on the observation that the separated flow regions are the primary contributions to the Reynolds stress., Comment: 33 pages, 23 figures, 3 tables

This study investigates the Reynolds-number dependence of shock-induced flow through particle layers at 10\% volume fraction, using ensemble-averaged results from particle-resolved large eddy simulations. The advantage of using large eddy simulations to study this problem is that they capture the strong velocity shears and flow separation caused by the no-slip condition at the particle surfaces. The shock particle cloud interaction produces a reflected shock wave, whose strength increases with decreasing particle Reynolds number. This results in important changes to the flow field that enters the particle cloud. The results show an approximate proportionality between the mean flow velocity and the flow fluctuation magnitudes. Maximum particle drag forces are in excellent agreement with previous inviscid studies, and we complement these results with statistics of time-averaged particle forces as well as the variation of temporal oscillations. The results of this work provides a basis for development of improved simplified dispersed flow models., Comment: 30 pages, 15 figures

In this paper we present work in progress and preliminary results from experimental studies of shock propagation through particle-laden gas columns. The experiments are conducted in a double-driver shock tube. The tube has a total length of 8.6 m. A setup with a double-driver chamber is chosen, as results clearly demonstrate high degree of repeatability. In order to obtain relatively short shock durations, the total length of the driver section is only 0.12 m. Pressure gauges and high-speed cameras are used to measure the results. A specially designed window section together with high-speed video cameras equipped with telecentric lenses and illuminators allows the shock-particle interaction in directions perpendicular to each other to be captured.

Necrotizing fasciitis of the head and neck is a rare and potentially fatal disease. It is a bacterial infection characterized by spreading along fascia planes and subcutaneous tissue resulting in tissue necrosis and likely death. It is commonly of dental or pharyngeal origin. Factors affecting the success of the treatment are early diagnosis, appropriate antibiotics and surgical debridement. Our study showed eight patients, five males and three females with mean age of 49.25 years (range 20-71 years). Clinical presentations were a rapidly progressing painful neck swelling, fever, dysphagia and trismus. The aetiology varied from idiopathic, pharyngeal/tonsillar infection, trauma and nasal malignancy. There were associated variable comorbidities (diabetes mellitus, HIV infection, hypertension and congestive cardiac failure). All the patients received early and aggressive medical treatment. The earliest time of surgery was 12 h after admission because of the poor financial status of patients. Three cases came in with complications of the disease and were not fit for extensive debridement under general anaesthesia. For them limited and reasonable bed side debridement was done. Mortality was 50 % from multiple organ failure, HIV encephalopathy, aspiration pneumonitis and septicemia. The duration of hospital stay for the patients that died ranged from 1 to 16 days and 4 to 34 days for the survivor. Our study heightens awareness and outlines the management challenges of necrotizing fasciitis of the head and neck in a poor resource setting.

This chapter presents experimental and numerical work in progress on shock propagation through dust columns in a shock tube environment. The shock tube consists of a short double driver chamber separated by membranes from the driven section. The shock tube is instrumented with pressure sensor and high-speed cameras. A specially designed window section allows Schlieren and shadow photography to be recorded simultaneously, in directions perpendicular to each other. The dust column is injected from below in the driven section, using a spark generator. The timing is such that the dust is in suspension before the shock arrives. The numerical method Regularized Smoothed Particle Hydrodynamics has been used to simulate shock–dust interaction problems, with a full multiphase description. Comparison with experimental data shows promising results for further studies on shock–dust interactions.

In this paper we present an approach to the implementation of a multi-phase description in the numerical Smoothed Particle Hydrodynamics method. The work is based on previous work, but has been modified to suit the applications of interest, in this case shock propagation through dusty gases. Theoretical models for multi-phase systems rely on the introduction of a number of terms describing the interaction between the different phases; drag and heat exchange are two examples. These terms contain parameters, the value of many of which must be determined empirically. We present results on the effect of changing values of some of the important parameters and compare our results to experimental and numerical results published in the literature. Our numerical results generally agree well with published results, taking uncertainties concerning accuracy in existing experimental data and details in the choice of parameters for numerical results into consideration. In particular, we find that a reduction in dust particle size is an efficient way of increasing shock retardation for a given dust loading.

In this paper we study shock ignition of reactive particles in a shock tube environment. When shock propagates through a dust cloud consisting of reactive particles, the cloud is shifted, compressed, and the internal cloud temperature increased. In most experimental studies a closed-end shock tube is used to allow the shock to reflect and propagate through the cloud a second time, further increasing the dust particle temperature. We use a multi-phase version of the numerical Regularized Smoothed Particle Hydrodynamics (RSPH) method [1], to study shock ignition, and discuss important parameters that affect the particle ignition process.

In the current work, we use the Constant Volume model and the numerical method, Regularized Smoothed Particle Hydrodynamics (RSPH) to study propagation and reflection of blast waves from detonations of the high explosives C-4 and TNT. The results from simulations of free-field TNT explosions are compared to previously published data, and good agreement is found. Measurements from height of burst tests performed by the Norwegian Defence Estates Agency are used to compare against numerical simulations. The results for shock time of arrival and the pressure levels are well represented by the numerical results. The results are also found to be in good agreement with results from a commercially available code. The effect of allowing different ratios of specific heat capacities in the explosive products are studied. We also evaluate the effect of changing the charge shape and height of burst on the triple point trajectory.

In many shock wave problems, the assumption of cylinder symmetry is useful, and allows 3D situations to be simulated with a 2D numerical code, thereby reducing computational cost, and increasing computational speed. In this paper we use the regularized smoothed particle hydrodynamics (RSPH) description for cylinder symmetry (Omang in “A numerical study of shock reflection phenomena. Exploring the capabilities of regularized smoothed particle hydrodynamics to handle shock waves”, 2005; Omang et al. in Shock Waves 14(4):293–298, 2005; Omang et al. in J Comput Phys 213(1):391–412, 2006) to study 3D shock reflection and shock interaction phenomena. In the first example we study the shock reflection pattern resulting from a torus-shaped shock reflecting both from the symmetry axis and from an object in the flow field. At the symmetry axis a characteristic Mach reflection is formed, with a triple point, a curved Mach stem, and a weak slip layer. The shock also interacts with the object, producing additional reflected shocks. The interactions between the different shock waves, resulting for instance in strong local pressure and density peaks, are studied in closer detail.

This paper investigates to what extent the numerical scheme regularized smoothed particle hydrodynamics (RSPH) is able to accurately describe multidimensional MHD shocks. The scheme can be viewed as an extension to smoothed particle hydrodynamics (SPH), which is widely used for astrophysical applications. In the first of two previous papers, the basic idea behind the RSPH scheme was introduced and tested, primarily on one-dimensional MHD shock problems. A new formulation of the momentum equation was also proposed to secure stability in the low-β regime. A two-dimensional, linear stability analysis of this formulation was presented in the second paper. The second paper also utilized recent developments of the RSPH scheme that improve the overall description of multidimensional problems in general. Based on the results from the linear stability analysis, adjustments to the momentum equation are made in the present work, which are also applicable to the nonlinear regime. These adjustments address the problem of asymmetries in the momentum equation, which in nonlinear problems can lead to small, yet systematic errors in postshock conditions. In addition, this paper describes the first application of the improved RSPH scheme to multidimensional MHD shocks. Comparisons are made with existing methods, in particular the related SPH method. Special attention is given to the scheme's ability to maintain the ∇ = 0 constraint and to what extent redefining the particle distribution affects the conservation of kinetic energy and angular momentum.

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.

New kernel functions for spherically, planar and cylindrically symmetric problems are developed, based on the fundamental interpolation theory of SPH. The Lagrangian formalism is used to derive the corresponding set of modified SPH equations of motion. The results show good agreement both with analytical and numerical results, in the case of the Sod shock tube test, the Noh infinite shock problem, and the Sedov point explosion test. The formulation has also been included in a 3D cylindrically symmetric problem of two colliding spherical shocks. For this latter problem, the results are presented allowing both a constant and a variable resolution. The results clearly demonstrate the capability of the new formulation to solve the singularity problem at the symmetry axis.

In this paper we present an alternative generic kernel function for use in Smoothed Particle Hydrodynamics (SPH) based methods. The alternative kernel has been implemented in a standard Cartesian description, and the results for the Sod shock tube problem is presented both with the alternative kernel and the traditional B-spline kernel. Kernels for cylindrically symmetric systems are developed based on fundamental interpolation theory for the cylindrical symmetry. A set of modified equations of motions are further derived through the use of Lagrangian formalism. Previous results have shown that the use of the traditional B-spline kernel function as a generic kernel implies that the cylindrically symmetric solution must be solved by table interpolation. By introducing an alternative generic kernel function, we derive simple analytical solution also for cylindrically symmetric systems. When compared to the B-spline function, the computational efficiency has been increased and the results improved. The results show good agreement with the analytical solution both for the Noh infinite shock problem and the Sedov point source explosion.

Regularized Smoothed Particle Hydrodynamics (RSPH) has been proposed as an extension to Smoothed Particle Hydrodynamics (SPH). Its development has been motivated by the desire to improve the accuracy of the latter method by allowing the resolution to vary in time and space by orders of magnitude and by providing the means to avoid particle penetration. In the current work, an alternative technique for handling stepwise, spatially varying resolution, is proposed. A comparison is made between the original and new RSPH techniques. This includes test results from 2D simulations of linear sound waves as well as weak shocks. In addition, simulation results of two interacting, cylindrical blast waves are presented that provide a comparison between standard SPH with variable smoothing length and RSPH. The test results show that, using the new technique, a more accurate and robust description near steps in the resolution is obtained and that a significant improvement compared to standard SPH is achieved.

Smoothed particle hydrodynamics (SPH) is an N-body integration scheme widely used within the field of astrophysics. Unfortunately, the method has up until recently been facing serious problems concerning instabilities when applied to MHD problems. Regularized smoothed particle hydrodynamics (RSPH) was proposed as an extension to SPH with the aim of achieving high-accuracy modeling of hydrodynamic and magnetohydrodynamic problems. This work included a new formulation of the discrete MHD equations that is easily implemented into SPH and RSPH codes alike. In this paper, the stability properties of two-dimensional linear MHD waves using this formulation are investigated. The presented analysis shows that linear stability properties similar to that obtained for sound waves in the absence of a magnetic field is achieved also for MHD waves. This result is confirmed by the included test results using both standard SPH and RSPH.

Smoothed particle hydrodynamics (SPH) has proven to be a useful numerical tool in studying a number of different astrophysical problems. Still, used on other problems, such as the modeling of low-β MHD systems, the method has so far not performed as well as one might have hoped. The present work has been motivated by the desire to accurately model strong hydrodynamic and magnetohydrodynamic shocks, and a key issue has therefore been to achieve a near-optimal representation of the simulated system at all times. Using SPH, this means combining the Lagrangian nature of the method with a smoothing-length profile that varies in both space and time. In this paper, a scheme containing two novel features is proposed. First, the scheme assumes a piecewise constant smoothing-length profile. To avoid substantial errors near the steps in the profile, alternative forms of the SPH equations of motion are used. Second, a predictive attitude toward optimizing the particle distribution is introduced by activating a mass, momentum, and energy conservation regularization process at intervals. The scheme described has been implemented in a new code called regularized smoothed particle hydrodynamics (RSPH), and test results for a number of standard hydrodynamic and magnetohydrodynamic tests in one and two dimensions using this code are presented.

In this paper we present results from numerical simulations of high explosives, using a constant volume method and an axis-symmetric Regularized Smoothed Particle Hydrodynamics method. smoothed particle hydrodynamics method Empirical and numerical results show satisfactory agreement for 1 kg of detonating TNT charge. The method is further challenged with the study of shock propagation and shock reflection in complex geometries. The shock reflection pattern is altered by introducing barriers of different shapes. The effect of such barrier structures are studied.

Concerns regarding efficiency and accuracy of Smoothed Particle Hydrodynamics (SPH) compared to modern grid-based methods have been raised. Likewise, the extension of SPH to MHD problems has proven to be a challenge. In an attempt to improve the ability of SPH to treat shocks in general, and MHD shocks in particular, a modified version of SPH called Regularized Smoothed Particle Hydrodynamics (RSPH) has been presented [1]. This method allows a piecewise constant smoothing length profile to be used. Furthermore, the smoothing length profile is optimized at temporal intervals using a mass, momentum and internal erergy conserving regularization process. In this paper, we examine more closely the abilities of the RSPH method to treat MHD shocks. We present a simple stability analysis, as well as results from MHD shock tests in one and two dimensions.