Shock Wave Parameters Research Articles

Investigation of the energy release characteristics and damage of thermobaric explosive under unconstrained conditions

To investigate the energetic release attributes and damage potential of a specific thermobaric explosive at atmospheric pressure, we had employed a pressure testing system, high-speed camera system, and thermal imager to elucidate the impact of explosive mass on the energetic release characteristics. Our findings underscored that thermobaric explosive can significantly enhance the after-burning effect. We noted a discernible positive relationship among the magnitude of the explosive force, post-detonation combustion effects, and the inherent quality of the given explosive. In addition, the resultant overpressure from the shockwave, positive pressure-area impulse, and the duration of the positive pressure, all markedly exceeded those produced by TNT, exhibiting increases of 38.9 %, 51.48 %, and 7 %, respectively. To quantify their explosive potency, empirical formulae were derived to account for the shock wave parameters of thermobaric explosive. Under equivalent mass conditions, the peak thermal radiation flux per unit area from thermobaric explosive substantially exceeded that of TNT. When the PROBIT (probability unit) model and the overpressure-impulse criteria were utilized to ascertain the damage potential of the respective explosives on human targets and structures, it emerged that TBX imparted superior destructive effects. This analysis underpinned the foundational assessment concerning the blast hazard presented by TBX.

Shock wave generated by composite energetic material driven by electrical non-penetrating wire explosion plasma.

Underwater shock wave technology can realize dynamic rock fracture, which is helpful to increase oil and gas reservoir permeability. It can realize the efficient exploitation of medium and low maturity oil and gas resources. In practical application, the shock wave parameters require not only high intensity but also safety and controllability. To meet these requirements, insensitive composite energetic materials driven by electrical wire explosion plasma were proposed, which is one of the most promising methods. However, when in use, the load assembly process containing wires and energetic materials is complex. In this paper, a new type of energetic material load is proposed, using non-penetrating wire to drive composite energetic material. It can simplify the production process of the energetic load and produce acceptable shock wave parameters. The test results show that both the energy deposition of the wire and the shock wave intensity decrease under a non-penetrating wire structure. However, the shock wave intensity is still higher than that of the underwater electrical wire explosion. Based on schlieren diagnosis, it is found that the composite energetic material is gradually driven, and the energy release is not concentrated. In addition, the "non-wire" structure driving condition was discussed in contrast. Under this condition, the process of ionization channel establishment in composite energetic materials is random. The shock wave intensity is weak because the composite energetic material is in the process of slow detonation.

Analysis of the building on the air shock wave by direct dy-namic method (with LIRA-FEM soft-ware)

Calculation of the impact of air shock waves on buildings is extremely important for our country, which is in a state of war. Studying the structural safety and survivability of load-bearing reinforced concrete structures under influence is an important task, especially for critical infrastructure facilities. A blast scenario can be carried out directly in an FEA program as a time history analysis evaluate varying levels of structural damage and to minimize loss of life.The article is devoted to the features of the calcula-tion of buildings under the influence of air shock waves using the finite element method using the LIRA-FEM software complex. The features of ex-plosive loads, typical shock wave parameters, and the order of analysis for explosive loads are taken into consideration. The primary distinctions be-tween shock or explosion impacts and regular loads are explained. In-depth consideration is given to the problems of determining shock wave parameters and how they affect structures. Also included are the techniques for evaluating structures for explosive impacts.Using LIRA-FEM software, a preliminary analysis of the explosion resistance of a one-story building with a metal frame and sheet metal wall infill is carried out. It is demonstrated how to define impulse loads from a shock wave to the side walls, roofs, rear walls, and walls facing the explosion. The article describes the peculiarities of the "Time History Analysis" system in the LIRA-FEM program for ex-plosion dynamics problems.This analysis helps in the assessment of risks in the design of protective structures, development of pro-ject solutions and conducting research in the field of explosion safety.

Effects of typical MH2 (M= Ti, Mg, Zr) on the detonation energy release characteristics of composite charge containing Al/PTFE reactive materials and RDX

To explore the effects of three typical metal hydride powders (TiH2, MgH2, ZrH2) on the detonation energy release characteristics of composite charge containing Al/PTFE reactive materials and RDX, a variety of composite charges containing Al/PTFE/MH2 ternary active materials and RDX were prepared. The effects of metal hydrides on detonation parameters of composite charges were studied by air blast experiments and the temperature distributions of explosion fireball were mapped using colorimetric thermometry technique. The experimental results indicated that the addition of metal hydrides had significantly positive effects on afterburning effect and detonation performance of composite charges, and the enhancement effect of MgH2 was superior to that of TiH2 and ZrH2. The fireball duration, maximum average temperature and shock wave parameters of the composite charges in air blast experiments all changed with the order of Al/PTFE/MgH2+RDX > Al/PTFE/TiH2+RDX > Al/PTFE/ZrH2+RDX > Al/PTFE + RDX. The results could offer theoretical references for the formulation design of high-power explosives.

Motion measurements of explosive shock waves based on an event camera

Shock wave measurement is vital in assessing explosive power and designing warheads. To obtain satisfactory observation data of explosive shock waves, it is preferable for optical sensors to possess high-dynamic range and high-time resolution capabilities. In this paper, the event camera is first employed to observe explosive shock waves, leveraging its high dynamic range and low latency. A comprehensive procedure is devised to measure the motion parameters of shock waves accurately. Firstly, the plane lines-based calibration method is proposed to compute the calibration parameters of the event camera, which utilizes the edge-sensitive characteristic of the event camera. Then, the fitted ellipse parameters of the shock wave are estimated based on the concise event data, which are gained by utilizing the characteristics of the event triggering and shock waves’ morphology. Finally, the geometric relationship between the ellipse parameters and the radius of the shock wave is derived, and the motion parameters of the shock wave are estimated. To verify the performance of our method, we compare our measurement results in the TNT explosion test with the pressure sensor results and empirical formula prediction. The relative measurement error compared to pressure sensors is the lowest at 0.33% and the highest at 7.58%. The experimental results verify the rationality and effectiveness of our methods.

Underwater electrical wire explosions under different discharge types: An experimental study with high initial energy storage

In this study, underwater electrical explosions of aluminum wires of various sizes were carried out with an initial energy storage of ∼53.5 kJ. Two piezoelectric probes were adopted to record the pressure waveforms. The experiments were divided into different discharge types, and the statistical properties of the electrical and shock-wave parameters of the different discharge types were compared. The experimental results show that there are three discharge types, called type A (breakdown type), type B (transition type), and type C (matched type). The three types differ in the resistance characteristics of the plasma channel during the plasma growth process, which are determined from the average electrical field strength and the remaining energy in the circuit at the peak voltage. Shock waves from type C discharges are more likely to exhibit a higher peak pressure, a larger impulse, and a higher energy density than the other types. However, using a matched wire that matches a specific discharge type, a high peak pressure, large impulse, and high energy density can also be achieved under type A or type B discharges. For example, the maximum peak pressures at ∼33 cm under type B and type C discharges are 38.7 and 42.4 MPa, respectively. These results provide significant guidance for load selection in underwater electrical wire explosion engineering applications.

Extracorporeal Shockwave Treatment as Additional Therapy in Patients with Post-Stroke Spasticity of Upper Limb-A Narrative Review.

Stroke is a severe injury of the central nervous system (CNS) and one of the leading causes of long-term disability and mortality. One of the main symptoms of neurological diseases is spasticity. This is defined as a motor condition characterized by a velocity-dependent increase in tonic stretch reflexes with exaggerated tendon jerks and resulting in the hyperexcitability of the stretch reflex. Rehabilitation after a stroke is focused on relearning lost skills and regaining independence. Many new methods in neurorehabilitation have been introduced. This review concentrates on the current evidence for extracorporeal shockwave therapy (ESWT) as a noninvasive alternative to treat spasticity. We present the effect of EWST and radial EWST interventions to post-stroke patients with spasticity in the upper limb. Our collected data suggest that different parameters of shockwaves can be used to achieve functional improvementsin the upper limb after a stroke. Our accumulated data imply that ESWT is safe and can be used for pain relief, reduced muscle tension, and an increased range of motion. According to many studies, complications after shockwave treatment are infrequent. Transient complications after shockwave therapy (ESWT) include redness, tingling, pain, and bruising. We reviewed clinical trials that present the possible benefits in upper-limb function after shockwave therapy for post-stroke patients. In this article, we used many database search engines, including PEDro. In the stroke rehabilitation literature, a key methodological problem is the design of double-blind studies, which very often are not feasible.

Whitham approach to Generalized Hydrodynamics

The formation of dispersive shock waves in one-dimensional Bose gas represents a limitation of Generalized Hydrodynamics (GHD) due to the coarse-grained nature of the theory. Nevertheless, GHD accurately captures long-wavelength behavior, thus indicating an implicit knowledge of the underlying microscopic physics. Such representations are already known through the Whitham modulation theory, where dispersionless equations describe the evolution of the slowly varying shock wave parameters. Here we study the correspondence between Whitham's approach to the Gross-Pitaevskii equation and GHD in the semiclassical limit and beyond. Our findings enable the recovery of the shock wave solution directly from GHD simulations, which we demonstrate for both zero and finite temperature. Additionally, we study how free expansion protocols affect the shock wave density and their implications for experimental detection. The combined picture of Whitham and GHD lends itself to additional physical interpretation regarding the formation of shock waves. Published by the American Physical Society 2024

Shock wave assisted intracellular delivery of antibiotics against bone infection with Staphylococcus aureus via P2X7 receptors

BackgroundTreatment of chronic osteomyelitis (bone infection) remains a clinical challenge; in particular, it requires enhanced delivery of antibiotic drugs for the treatment of intracellular Staphylococcus aureus (S. aureus), which prevents infection recurrence and resistance. Previous studies have found that noninvasive shock waves used to treat musculoskeletal diseases can alter cell permeability, however, it is unclear whether shock waves alter cell membrane permeability in chronic osteomyelitis. Furthermore, it remains unknown whether such changes in permeability promote the entry of antibiotics into osteoblasts to exert antibacterial effects. MethodsIn our study, trypan blue staining was used to determine the shock wave parameters that had no obvious damage to the osteoblast model; the effect of shocks waves on the cell membrane permeability of osteoblast model was detected by BODIPY®FL vancomycin; high performance liquid chromatography-mass spectrometry (HLPC-MS) was used to detect the effect of shock wave on the entry of antibiotics into the osteoblast model; plate colony counting method was used to detect the clearance effect of shock wave assisted antibiotics on S. aureus in the osteoblast model. To explore the mechanism, the effect of different pulses of shock waves on S. aureus was examined by plate colony counting method, besides, P2X7 receptor in osteoblast was detected by immunofluorescence and the extracellular ATP levels was detected. Furthermore, the effect of P2X7 receptor antagonists KN-62 or A740003 on the intracellular antibacterial activity of shock-assisted antibiotics was observed. Then, we used S. aureus to establish a rat model of chronic tibial osteomyelitis and investigated the efficacy and safety of shock-wave assisted antibiotics in the treatment of chronic osteomyelitis in rats. ResultsThe viability of the osteoblast models of intracellular S. aureus infection was not significantly affected by the application of up to 400 shock wave pulses at 0.21 mJ/mm2. Surprisingly, the delivery of BODIPY®FL vancomycin to osteoblast model cells was markedly enhanced by this shock wave treatment. Furthermore, the shock wave therapy increased the delivery of hydrophilic antibiotics (vancomycin and cefuroxime sodium), but not lipophilic antibiotics (rifampicin and levofloxacin), which improved the intracellular antibacterial effect. Afterwards, we discovered that shock wave treatment increased the extracellular concentration of ATP (the P2X7 receptor activator)， while KN-62 or A740003, a P2X7 receptor inhibitor, decreased intracellular antibacterial activity. We then found that 0.1 mL of 1 × 1011 CFU/mL ATCC25923 S. aureus was suitable for modeling chronic osteomyelitis in rats. Besides, the shock wave-assisted vancomycin treatment with the strongest antibacterial and osteogenic effects among the tested treatments was confirmed in vivo by imaging examination, microbiological cultures, and histopathology, with favorable safety. ConclusionsOur results suggest that shock waves can promote the entry of antibiotics into osteoblasts for antibacteria by changing the cell membrane permeability in a P2X7 receptor-dependent manner. Besides, considering antibacterial and osteogenic efficiency and a high degree of safety in rat osteomyelitis model, shock wave-assisted vancomycin treatment may thus represent a possible adjuvant therapy for chronic osteomyelitis.

Experimental analysis and numerical simulation of ignition delay time of diesel fuel using a shock tube

The present work consisted in developing a computational routine for prediction and characterization ignition delay time, pressure, temperature generated and energy released in the combustion process in a shock tube. Mathematical modeling considered the high-pressure region of the shock tube known as the conducted section. The Lazarus code compiler was used to generate the unstructured triangular meshes and to implement the computational routines to simulate the propagation of shock waves inside the shock tube. The mathematical modeling used the geometric parameters of the shock tube of the combustion laboratory of the Federal University of Minas Gerais and was based only on the displacement of the shock wave after the diaphragm rupture. The main objective of the work was the development of computational routines to characterize the shock wave parameters of the ignition delay times of conventional diesel to validate the experimental tests carried out in the shock tube conducted by Santana et al. [3] and compare it with the experimental tests and numerical simulations carried out by other authors available in the literature. A linear regression of the experimental tests conducted by Santana et al. [3] with conventional diesel was performed to obtain the Arrhenius equation for numerical simulation of the ignition delay time of diesel under the following conditions: temperatures from 880 to 1300 K, pressures 24 bar and equivalence ratio 1. The results show good prediction between experimental tests and numerical simulations. Were found delay times ranging from 425 to 1890 μs. Considering all temperature range, the difference between the experimental and simulated test was approximately 15%, this difference also can be explained by the measurement in the shock tube, that the ignition delay time was calculated by the time difference between the passage of the shock wave by the pressure sensor and the start of the ignition detected by the luminosity detection sensor. This work is relevant because it was developed computational routine in open software and the results achieved in the simulation were considered satisfactory, since they are in the same order of magnitude as the results found in the experimental tests carried out by Santana et al. [3] and other works.

Анализ параметров ударных волн на стенке взрывной полости при преломлении детонационных волн через воздушную и водную среду

Анализ параметров ударных волн на стенке взрывной полости при преломлении детонационных волн через воздушную и водную среду

Evolution of underwater shock wave in far-field regime of electrical wire explosion system over wide range of electric pulse energy

The parametric relationships between underwater shock waves (SWs) in far-field regime and electrically exploded wire under different charging voltages of a generator are investigated. Contributions of the vaporization and current restrike to the resulting SWs have been examined by means of electro-physical diagnostics, free-field pressure probe, and high-speed photography. In the experiment, a 6-μF pulse capacitor is adopted to provide a microsecond timescale pulsed current, exploding a 90/185-μm-diameter, 2-cm-long copper wire with the charging voltage ranging from 7.1 kV (stored energy ∼ 150 J) to 18.3 kV (∼1000 J). Experimental results indicate that as the increase of the charging voltage, the relationship between electro-physical and shock wave parameters shows a rather complex situation. When the charging voltage ranging from 7.1 kV (∼150 J) to 11.6 kV (∼400 J), the peak pressure of SWs (300 mm away from the explosion source) increases almost linearly from 1.16 ± 0.03 to 2.24 ± 0.05 MPa (90-μm wire), and 1.67 ± 0.17 to 2.87 ± 0.12 MPa (185-μm wire). Nevertheless, at a higher charging voltage between 11.6 kV (400 J) to 14.1 kV (600 J), the peak pressure stabilizes in a strange “plateau”. Until the residual energy after the explosion is sufficiently large (>600 J in this study) to induce a strong current restrike, the development of the plasma channel could further enhance the expansion of explosion products, as well as the intensity of measured SWs. In addition, high-speed photography has been applied for those explosions, providing the information of plasma channel expansion and initial SWs propagation.

Non-ideal explosive underwater explosion shockwave model

The non-ideal behavior of aluminized explosives significantly affects the characteristics of underwater explosion shockwaves, rendering the classical model for underwater explosion shockwaves difficult to apply. In this paper, we analyze the underwater explosion shockwave characteristics of a new generation of aluminized explosives and propose a non-ideal explosive underwater explosion shockwave model incorporating a non-ideal explosive shockwave parameter correction function controlled by the Al/O ratio. First, we conducted underwater explosion tank experiments to obtain four groups of Al/O ratios of shockwave parameters of underwater explosion with aluminized explosives and analyzed the effect of the Al/O ratio on them. Subsequently, we calculated the equation of state of aluminized explosives and established a one-dimensional simulation model of underwater explosion. We verified the reliability of the mesh quality and equation of state using the experimental data. Finally, we used the model to calculate the underwater explosion shockwave parameters of aluminized explosives with Al/O ratios of 0.1–1.3. Based on data analysis, we established a calculation model of the pressure peak and energy flow density of the underwater explosion shockwave of aluminized explosives containing non-ideality correction functions. Our results demonstrate that shockwave pressure peak and energy increase and then decrease with an increase in the Al/O ratio, and the non-ideal behavior of aluminized explosives makes the shockwave energy of underwater explosion more sensitive to the Al/O ratio. The proposed model can better predict the experimental results and can be of high practical value as a general structure for underwater explosion shockwave models of other aluminized or metalized explosives.

Effects of an Explosion-Proof Wall on Shock Wave Parameters and Safe Area Prediction

To study the influences of an explosion-proof wall on shock wave parameters, an air explosion protection experiment was performed, the time history of shock wave pressure at different positions before and after the explosion-proof wall was established, and the characteristics of shock wave impulse and dynamic pressure were analyzed. The explosion-proof working conditions of five different diffraction angles were simulated and analyzed using Autodyn software(2019R3). Results indicated the following findings. The explosion-proof wall exerted an evident attenuation effect on the explosion shock wave, but considerable pressure still existed at the top of the explosion-proof wall. Overpressure behind the wall initially increased and then decreased. The larger the diffraction angle, the faster the attenuation speed of the diffraction overpressure of the shock wave in the air behind the wall. The history curve of shock wave pressure exhibited an evident bimodal structure. The shock wave diffraction of the wall made the shock wave bimodal structure behind the wall more prominent. The characteristics of the bimodal structure behind the wall (the interval time of overpressure peak Δt was less than the normal phase time of the diffracted shock wave T+) caused the shock wave impulse to stack rapidly, significantly improving its damage capability. The peak value of dynamic pressure on the oncoming surface was approximately two times the peak value of overpressure, and the inertia of air molecules resulted in a longer positive duration of dynamic pressure than overpressure. The maximum overpressure on the ground behind the explosion-proof wall appeared at approximately two times the height of the explosion-proof wall, while the maximum overpressure in the air behind the explosion-proof wall appeared at approximately one times the height of the explosion-proof wall. The relatively safe areas on the ground and in the air behind the wall were approximately 4–4.5 times and 3.5–4 times the height of the explosion-proof wall, respectively.

Experimental investigation of nanosecond laser-induced shock waves in water using multiple excitation beams.

Revealing the expansion and interaction dynamics of multiple shock waves induced by a nanosecond laser is important for controlling laser surgery. However, the dynamic evolution of shock waves is a complex and ultrafast process, making it difficult to determine the specific laws. In this study, we conducted an experimental investigation into the formation, propagation, and interaction of underwater shock waves that are induced by nanosecond laser pulses. The effective energy carried by the shock wave is quantified by the Sedov-Taylor model fitting with experimental results. Numerical simulations with an analytic model using the distance between adjacent breakdown locations as input and effective energy as fit parameters provide insights into experimentally not accessible shock wave emission and parameters. A semi-empirical model is used to describe the pressure and temperature behind the shock wave taking into account the effective energy. The results of our analysis demonstrate that shock waves exhibit asymmetry in both their transverse and longitudinal velocity and pressure distributions. In addition, we compared the effect of the distance between adjacent excitation positions on the shock wave emission process. Furthermore, utilizing multi-point excitation offers a flexible approach to delve deeper into the physical mechanisms that cause optical tissue damage in nanosecond laser surgery, leading to a better comprehension of the subject.

Effects of content and particle size of TiH2 powders on the energy output rules of RDX composite explosives

In order to improve the detonation characteristics of RDX, a RDX-based composite explosive with TiH2 powders was prepared. The effects of content and particle size of TiH2 powders on thermal safety, shock wave parameters and thermal damage effects of RDX-based composite explosive were studied with the C80 microcalorimeter, air blast experiment system and colorimetric thermometry method. Experimental results showed that TiH2 powders could enhance the thermal stability of RDX-based composite explosive and increase its ultimate decomposition heat. The content and particle size of TiH2 powders also had significant effects on the thermal safety, detonation velocity, shock wave parameters, fireball temperature and duration of RDX-based composite explosives. Furthermore, the differences of TiH2 and Ti powders on the detonation energy output rules of RDX-based composite explosives were also compared, showing that TiH2 powders had better influences on improving the explosion power and thermal damage effect of RDX-based composite explosives than Ti powders, for the participation of free H2 released by TiH2 powders in the detonation process. TiH2 powders have important research values as a novel energetic additive in the field of military composite explosives.

Improving reservoir permeability by electric pulse controllable shock wave

Controllable shock wave (CWS) parameters such as amplitude, operating area and number of operations are easy to control and have received extensive attention as a potential new technology for reservoir permeability enhancement. Based on the continuous-discontinuous element method (CDEM) and considering the coupling mechanism of reservoir deformation, failure, pore seepage and fracture flow, a multiphysical field coupling model of reservoir permeability enhancement under CWS is proposed. Under the fluid–solid coupling condition, the formation and development dynamic process of reservoir fractures are obtained, and the change of reservoir permeability is also obtained. The compression fracture zone, tensile fracture zone and undamaged zone are formed around the wellbore. After repeated impact, the number of fractures is more sensitive to tectonic stress, the fracture aperture is more sensitive to reservoir strength. Different from hydraulic fracturing, a large number of fractures in different directions will appear around the main fracture after repeated impact, forming a complex fracture network similar to spider web, which may be beneficial to improve reservoir permeability. The permeability of reservoirs with different tectonic stresses and strengths increases nonlinearly and monotonicly with repeated impacts. Based on CDEM, the change of reservoir permeability with tectonic stress, strength and impact times is obtained, which is a nonlinear monotonic three-dimensional relationship. Based on that relationship, the parameters of CWS can be controlled to predict the change of reservoir permeability, such as peak pressure, duration, impact times, etc. Therefore, it can optimize the reservoir fracturing scheme and improve the reservoir fracturing efficiency, which has considerable practical significance in engineering.

Influence of combination of coaxial cylindrical explosives on fragmentation and shock waves of a shelled composite charge

AbstractThis paper investigates fragmentation and shock waves generated by a novel coaxial cylindrical composite charge composed of an inner explosive, an intermediate inert material and an outer explosive widely used in tunable ammunition. Charges containing two types of explosive combinations were designed, and explosion experiments were conducted in two initiation modes: detonating only an inner explosive and detonating inner and outer explosives simultaneously. Results suggest the composite charge with higher inner‐detonation velocity and lower outer‐detonation velocity achieves more differentiated power output under different initiations. The differences in the average fragment mass and peak overpressure are as high as 34.5 % and 39.9 %, respectively, which are larger than 4.4 % and 8.4 % under the contrary explosive combination. On the basis of this observation, corresponding 2‐D and 3‐D models were simulated using AUTODYN code to investigate the evolution of the detonation waveform and detonation energy release. The numerically simulated initial shell expansion and later shock wave propagation of the composite charge agreed well with the experimental data. The errors in expansion radius and shock wave parameters (peak overpressure and specific impulse) are less than 6.6 % and 16.9 %, respectively, between the simulations and experiments. It was found that the particle velocity profile in the charge with lower outer‐detonation velocity lagged behind that of the charge with higher inner‐detonation velocity under inner initiation, while a wave front collision zone close to the outer charge appeared in the non‐detonation layer under simultaneous initiation.

Effect of Obstructed Space on the Parameters of Shock Waves from the Deflagration of Hydrogen–Air Clouds

Effect of Obstructed Space on the Parameters of Shock Waves from the Deflagration of Hydrogen–Air Clouds

Моделирование волн давления при дефлаграционном горении облаков топливно- воздушных смесей

The paper examines the assumptions underlying a whole group of methods for estimating the parameters of shock waves (pressure waves) during the combustion of spherical fuel-air clouds - the so-called parametric formulas. The formulas allow to determine the parameters of pressure waves from the given energy release and combustion rate. To do this, a complete system of gas-dynamic equations is solved using high-precision numerical simulation. In this case, the combustion front is explicitly distinguished in the form of an infinitely thin discontinuity, on which the laws of conservation of mass, momentum, and energy are satisfied. The results of such a numerical calculation are compared with calculations using the corresponding parametric formulas. Clouds of a stoichiometric mixture hydrogen-air are considered. It is shown that the parametric formulas describe the expansion of clouds of hot products with a good degree of accuracy. Here, there is complete agreement with the direct numerical simulation. It is also shown that the parameters of pressure waves are satisfactorily described both in the calculation by parametric formulas and in direct numerical simulation. In this case, within the cloud, there is a greater increase in pressure than the parametric formulas predict. This is explained by the fact that the assumptions used in the formulas regarding the behavior of the flame front as an impenetrable piston do not fully reflect the physical processes: the combustion front is a semipermeable piston, and some of the mass of the initial mixture still penetrates through it. The third factor considered, which determines the achieved pressures, is the rarefaction wave that occurs in the air after the cloud burns out. This wave propagates in combination with the leading pressure front formed during combustion initiation. The extent of this complex remains practically constant, and its attenuation during spherical propagation is adequately described by the parametric formulas.