Supercritical Mode Research Articles

A weakly supercritical mode in a branching random walk

The case of weakly supercritical branching random walks is considered. A theorem on asymptotic behavior of the eigenvalue of the operator defining the process is obtained for this case. Analogues of the theorems on asymptotic behavior of the Green function under large deviations of a branching random walk and asymptotic behavior of the spread front of population of particles are established for the case of a simple symmetric branching random walk over a many-dimensional lattice. The constants for these theorems are exactly determined in terms of parameters of walking and branching.

Nonlinear Excitation of Subcritical Instabilities in a Toroidal Plasma.

In a collisionless plasma, it is known that linearly stable modes can be destabilized (subcritically) by the presence of structures in phase space. However, nonlinear growth requires the presence of a seed structure with a relatively large threshold in amplitude. We demonstrate that, in the presence of another, linearly unstable (supercritical) mode, wave-wave coupling can provide a seed, which is significantly below the threshold, but can still grow by (and only by) the collaboration of fluid and kinetic nonlinearities. By modeling the subcritical mode kinetically, and the impact of the supercritical mode by simple wave-wave coupling equations, it is shown that this new kind of subcritical instability can be triggered, even when the frequency of the supercritical mode is rapidly sweeping. The model is applied to the bursty onset of geodesic acoustic modes in a LHD experiment. The model recovers several key features such as relative amplitude, time scales, and phase relations. It suggests that the strongest bursts are subcritical instabilities, driven by this mechanism of combined fluid and kinetic nonlinearities.

Модификация свойств конструкционных материалов интенсивными потоками заряженных частиц и плазмы

The analysis of the experimental and theoretical work state-of-the-art in the field of the constructional materials modification with the intensive flows of charged particles and plasma with the power density ranging in interval 0.1–1000 MWt/cm 2 is carried out. The irradiation modes with the inherent physical processes and the role of different mechanisms in formation of the properties of treated materials are surveyed. The irradiation can be divided onto two modes: subcritical and supercritical. In the subcritical irradiation mode a target material remains in the solid state or melts. In the supercritical regime the formation of plasma torch and its subsequent expansion at a rate of more than 103 m/s are observed. The transition from subcritical to supercritical mode has a threshold character. The mechanisms of mechanical stresses formation under irradiation are discussed, these stresses are the shock wave propagating with a sound velocity and the localized near the irradiated surface stresses arising due to the nonhomogeneous space distribution of the temperature in target material. The reasons of target surface smoothing and of crater formation are given. It is shown that the manifestation of one or another phenomenon of irradiation is determined by its mode. The analysis of mass transfer occurring due to diffusion, thermocapillary convection or development of Richtmyer-Meshkov instability is carried out in accordance with the irradiation mode. The irradiation of the solids leads to the deformation hardening mainly at the expense of shear component of the localized stresses. The decrease of the irradiation duration provokes the high strain rate and the high level of shear stresses that both provide more effective generation of dislocations.

Boundary layers for the 3D primitive equations in a cube: The supercritical modes

In this article we study the boundary layers for the viscous Linearized Primitive Equations (LPEs) when the viscosity is small. The LPEs are considered here in a cube. Besides the usual boundary layers that we analyze here too, corner layers due to the interaction between the different boundary layers are also studied.

Measurements of convective heat transfer to vertical upward flows of CO2 in circular tubes at near-critical and supercritical pressures

An extensive experimental program of heat transfer measurements has been completed recently at the University of Ottawa's supercritical pressure test facility (SCUOL). Thermal–hydraulics tests were performed for vertical upflow of carbon dioxide in directly heated tubes with inner diameters of 8 and 22mm, at high subcritical, near-critical and supercritical pressures. The test conditions, when converted to water-equivalent values, correspond to conditions of interest to current Super-Critical Water-Cooled Reactor designs, and include many measurements under conditions for which few data are available in the literature. These data significantly complement the existing experimental database and are being used for the derivation and validation of a new heat transfer prediction method in progress at the University of Ottawa. The same data are also suitable for the assessment of the accuracy of other heat transfer prediction methods and fluid-to-fluid scaling laws for near-critical and supercritical pressures. In addition, they permit further examination of previously suggested relationships describing the critical heat flux and post-dryout heat transfer coefficient at high subcritical pressures and the boundaries of the deteriorated/enhanced heat transfer regions for near-critical and supercritical pressures. The measurements reported in this paper cover several subcritical heat transfer modes, including single phase liquid heat transfer, nucleate boiling, critical heat flux, post-dryout heat transfer and superheated vapor heat transfer; they also cover several supercritical heat transfer modes, including heat transfer to liquid-like supercritical fluid and heat transfer to vapor-like supercritical fluid, which occurred in the downstream sections of the tubes. The collected data were reduced and compiled. The reported heat transfer database consists of more than 17,000 data points in the 8 and 22mm tubes, along with pressure drop data for the 8mm tube. The tables of heat transfer and pressure drop data are provided as separate files in electronic format. The results are presented in plots of wall temperature and heat transfer coefficient vs. bulk fluid enthalpy. The parametric trends of diameter, mass flux, pressure and heat flux on these wall temperature and heat transfer coefficient profiles have been plotted and discussed. The present supercritical heat transfer measurements are in good agreement with corresponding results reported by other investigators.

Effect of folds and pockets on the topology and propagation of premixed turbulent flames

Propagation of premixed turbulent flames is examined using a hybrid Navier–Stokes/front tracking methodology, within the context of a hydrodynamic model. The flame, treated as a surface of density discontinuity separating the burned and unburned gases, propagates relative to the fresh mixture at a speed that depends on the local mixture (through a Markstein length) and flow conditions (through the stretch rate), and the flow field is modified in turn by gas expansion; only positive Markstein length are considered, where thermo-diffusive instabilities are absent. Depending on the Markstein length, we have identified in a previous publication two modes of propagation – sub-critical and super-critical, based on whether the effects of the Darrieus–Landau instability are absent or dominant, respectively. The results were limited to low turbulence intensities where the mathematical representation of the flame front was based on an explicit single-valued function. In the present paper we utilize a generalized representation of the flame surface that allows for multivalued and disjointed interfaces, thus extending the results to higher turbulence intensities. We show that when increasing the turbulence intensity the influence of the Darrieus–Landau instability on the super-critical mode of propagation progressively decreases and in the newly identified highly-turbulent regime the flame is dominated completely by the turbulence for all values of Markstein numbers; i.e., with no distinction between sub- and super-critical conditions. Primary importance is given to the determination of the turbulent flame speed and its dependence on turbulence intensity which, when increasing the turbulence level, transitions from a quadratic to a sub-linear scaling. Moreover, the exponent of the sub-linear scaling for the turbulent flame speed is generally lower than the corresponding exponent for the scaling of the flame surface area ratio, which is often used for experimentally determining the turbulent flame speed. We show that the leveling in the rate of increase of the turbulent flame speed with turbulence intensity, is due to frequent flame folding and detachment of pockets of unburned gas that cause a reduction in the average main surface area of the flame, while the lower exponents in the scaling law for the turbulent flame speed compared to that of the flame surface area ratio is due to flame stretching. Disregarding the effect of flame stretch for mixtures of positive Markstein length results in overestimating the turbulent flame speed. Finally, we characterize the flame turbulence interaction via quantities such as the mean vorticity and mean strain, illustrating the effects of incoming turbulence on the flame and the modification of the flow by the flame on the unburned and burned sides.

Acoustic response of vortex breakdown modes in a coaxial isothermal unconfined swirling jet

The present experimental work is concerned with the study of amplitude dependent acoustic response of an isothermal coaxial swirling jet. The excitation amplitude is increased in five distinct steps at the burner’s Helmholtz resonator mode (i.e., 100 Hz). Two flow states are compared, namely, sub-critical and super-critical vortex breakdown (VB) that occur before and after the critical conical sheet breakdown, respectively. The geometric swirl number is varied in the range 2.14-4.03. Under the influence of external pulsing, global response characteristics are studied based on the topological changes observed in time-averaged 2D flow field. These are obtained from high resolution 2D PIV (particle image velocimetry) in the longitudinal-mid plane. PIV results also illustrate the changes in the normalized vortex core coordinates (rvcc/(rvcc)0 Hz, yvcc/(yvcc)0 Hz) of internal recirculation zone (IRZ). A strong forced response is observed at 100 Hz (excitation frequency) in the convectively unstable region which get amplified based on the magnitude of external forcing. The radial extent of this forced response region at a given excitation amplitude is represented by the acoustic response region (b). The topological placement of the responsive convectively unstable region is a function of both the intensity of imparted swirl (characterized by swirl number) and forcing amplitude. It is observed that for sub-critical VB mode, an increase in the excitation amplitude till a critical value shifts the vortex core centre (particularly, the vortex core moves downstream and radially outwards) leading to drastic fanning-out/widening of the IRZ. This is accompanied by ∼30% reduction in the recirculation velocity of the IRZ. It is also observed that b < R (R: radial distance from central axis to outer shear layer-OSL). At super-critical amplitudes, the sub-critical IRZ topology transits back (the vortex core retracts upstream and radially inwards) and finally undergoes a transverse shrinkage (rvcc/rvcc0Hz decreases by ∼20%) when b ≥ R. In contrast, the vortex core of super-critical breakdown mode consistently spreads radially outwards and is displaced further downstream. Finally, the IRZ fans-out at the threshold excitation amplitude. However, the acoustic response region b is still less than R. This is explained based on the characteristic geometric swirl number (SG) of the flow regimes. The super-critical flow mode with higher SG (hence, higher radial pressure drop due to rotational effect which scales as ΔP ∼ ρuθ2 and acts inwards towards the center line) compared to sub-critical state imposes a greater resistance to the radial outward spread of b. As a result, the acoustic energy supplied to the super-critical flow mode increases the degree of acoustic response at the pulsing frequency and energizes its harmonics (evident from power spectra). As a disturbance amplifier, the stronger convective instability mode within the flow structure of super-critical VB causes the topology to widen/fan-out severely at threshold excitation amplitude.

Scale-up on mixing in rotating microchannel under subcritical and supercritical operating modes

The factors affecting flow and mixing of two different fluids in a rotating radial microchannel are investigated using numerical simulation, experiments, analytical approach and dimensional analysis. As has been verified by both numerical simulation and experiments, depending on the channel width-to-height aspect ratio there are two distinctly different modes of operation, subcritical and supercritical modes, that yield identical mixing quality with the supercritical mode providing higher volumetric throughput. Four dimensionless groups (namely, rotational Reynolds number, channel length-to-height, channel width-to-height, and channel initial radial-location-to-height) are found to be important for correlating the quality of mixing of fluids in the rotating microchannel operating in either mode in form of scale-up laws. The latter, which fill the badly needed missing knowledge gap, are useful for design, operation, and optimization of rotating microchannels for fluid mixing.

Square Turing patterns in reaction-diffusion systems with coupled layers.

Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.

Broad absorption features in wind-dominated ultraluminous X-ray sources?

Abstract The luminosities of ultraluminous X-ray sources (ULXs) require an exotic solution with either supercritical accretion modes on to stellar-mass black holes or subcritical accretion on to intermediate-mass black holes (IMBHs) being invoked. Discriminating between the two is non-trivial due to the present lack of a direct mass measurement. A key expectation of the supercritical mode of accretion is the presence of powerful radiatively driven winds. Here we analyse XMM–Newton data from NGC 5408 X-1 and NGC 6946 X-1 and find that strong soft residuals present in the X-ray spectra can be reconciled with broadened, blueshifted absorption by a partially ionized, optically thin phase of this wind. We derive initial values for the physical parameters of the wind; we also discuss other possible origins for the observed features.

CRITICAL FIELDS AND GROWTH RATES OF THE TAYLER INSTABILITY AS PROBED BY A COLUMNAR GALLIUM EXPERIMENT

Many astrophysical phenomena (such as the slow rotation of neutron stars or the rigid rotation of the solar core) can be explained by the action of the Tayler instability of toroidal magnetic fields in the radiative zones of stars. In order to place the theory of this instability on a safe fundament it has been realized in a laboratory experiment measuring the critical field strength, the growth rates as well as the shape of the supercritical modes. A strong electrical current flows through a liquid-metal confined in a resting columnar container with an insulating outer cylinder. As the very small magnetic Prandtl number of the gallium-indium-tin alloy does not influence the critical Hartmann number of the field amplitudes, the electric currents for marginal instability can also be computed with direct numerical simulations. The results of this theoretical concept are confirmed by the experiment. Also the predicted growth rates of the order of minutes for the nonaxisymmetric perturbations are certified by the measurements. That they do not directly depend on the size of the experiment is shown as a consequence of the weakness of the applied fields and the absence of rotation.

Screening Strategy for Chiral and Achiral Separations in Supercritical Fluid Chromatography Mode

Supercritical fluid (SF) was discovered 200 years ago, but the use of this fluid as a mobile phase in chromatography only became popular fifty years ago. The development of the supercritical fluid chromatography (SFC) was progressing slowly due to technological problems since ten years; the interest for this chromatographic mode has been growing up as the construction of the SFC instruments is more or less similar with HPLC instruments. The main difference in SFC is the installation of a back pressure regulator which is implemented to control the pressure above the critical pressure. SFC is widely used in chiral chromatography where Polysaccharide phases are the most versatile in use. The mobile phase is mainly composed by CO(2) but the polarity can be increased by adding alcohol. The nature of the alcohol can change drastically the selectivity. The choice of the best tandem stationary phase / mobile phase is difficult to predict. Hence a full screening with different stationary phases and mobile phase solvents is often mandatory. For the achiral separation, SFC is more and more used. Achiral SFC can be classified as normal phase mode, it means that stationary phases are more polar than mobile phase and retention times decrease as polarity of the mobile phase increases. Most popular stationary phases are silica linked with polar group such as aminopropyl, cyanoprpyl, diol or 2-ethylpyridine. Mobile phase are generally composed by CO(2) and methanol. SFC can be used as a complementary technique for reversed phase HPLC or sometimes even to replace HPLC.

Effects of Flow Patterns on Aerodynamic Forces of a Square Cylinder at Incidence

ABSTRACTThe pressure distributions around a square cylinder in a crossflow were experimentally studied in a wind tunnel. The subject of study was conventional, but the results presented new findings. The experiments were performed by using a home-made linear pressure scanner. The ranges of Reynolds number and incidence angle were 2 × 104- 9.4 × 104and 0° - 45°, respectively. According to the topological flow patterns, the flows around the square cylinder at incidence showed three characteristic regimes: The subcritical, supercritical, and wedge flows. A critical incidence angle αcri= 15° separated the regimes of subcritical and supercritical modes. The results of current study provided information regarding the effects of the topological flow patterns on surface pressure distribution, drag, and lift characteristics. The pressure distributions, drag, and lift presented different characteristics in different characteristic flow regimes and had close correlations with the flows. At the critical incidence angle 15° which separated the subcritical and supercritical regimes, the surface-averaged pressure coefficient on each face displayed local extreme value—The drag coefficient attained a minimum of 1.6, the lateral force coefficient reached a maximum of 0.9. The appearance of the minimum drag at the critical incidence angle was attributed to the reduction of wake width which was induced by two surface flow phenomena: (1) reattachment of the separated boundary layer on the lateral surface facing windward at the critical incidence angle and (2) flow pattern change on the lateral surface facing leeward.

Nonlinear stability and patterns in granular plane Couette flow: Hopf and pitchfork bifurcations, and evidence for resonance

The first evidence of a variety of nonlinear equilibrium states of travelling and stationary waves is provided in a two-dimensional granular plane Couette flow via nonlinear stability analysis. The relevant order-parameter equation, the Landau equation, has been derived for the most unstable two-dimensional perturbation of finite size. Along with the linear eigenvalue problem, the mean-flow distortion, the second harmonic, the distortion to the fundamental mode and the first Landau coefficient are calculated using a spectral-based numerical method. Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary instabilities, respectively, are analysed using the first Landau coefficient. The present bifurcation theory shows that the flow is subcritically unstable to stationary finite-amplitude perturbations of long wavelengths (kx ~ 0, where kx is the streamwise wavenumber) in the dilute limit that evolve from subcritical shear-banding modes (kx = 0), but at large enough Couette gaps there are stationary instabilities with kx = O(1) that lead to supercritical pitchfork bifurcations. At moderate-to-large densities, in addition to supercritical shear-banding modes, there are long-wave travelling instabilities that lead to Hopf bifurcations. It is shown that both supercritical and subcritical nonlinear states exist at moderate-to-large densities that originate from the dominant stationary and travelling instabilities for which kx = O(1). Nonlinear patterns of density, velocity and granular temperature for all types of instabilities are contrasted with their linear eigenfunctions. While the supercritical solutions appear to be modulated forms of the fundamental mode, the structural features of unstable subcritical solutions are found to be significantly different from their linear counterparts. It is shown that the granular plane Couette flow is prone to nonlinear resonances in both stable and unstable regimes, the signature of which is implicated as a discontinuity in the first Landau coefficient. Our analysis identified two types of modal resonances that appear at the quadratic order in perturbation amplitude: (i) a ‘mean-flow resonance’ which occurs due to the interaction between a streamwise-independent shear-banding mode (kx = 0) and a linear/fundamental mode kx ≠ 0, and (ii) an exact ‘1 : 2 resonance’ that results from the interaction between two waves with their wavenumber ratio being 1 : 2.

ICONE19-43824 EVALUATION AND OPTIMIZATION OF A SUPERCRITICAL CARBON DIOXIDE POWER CONVERSION CYCLE FOR NUCLEAR APPLICATIONS

There have been a number of studies involving the use of gases operating in the supercritical mode for power production and process heat applications. Supercritical carbon dioxide (CO_2) is particularly attractive because it is capable of achieving relatively high power conversion cycle efficiencies in the temperature range between 550℃ and 750℃. Therefore, it has the potential for use with any type of high-temperature nuclear reactor concept, assuming reactor core outlet temperatures of at least 550℃. The particular power cycle investigated in this paper is a supercritical CO_2 recompression Brayton Cycle. The CO_2 recompression Brayton Cycle can be used as either a direct or indirect power conversion cycle, depending on the reactor type and reactor outlet temperature. The advantage of this cycle when compared to the helium Brayton Cycle is the lower required operating temperature; 550℃ versus 750℃. However, the supercritical CO_2 recompression Brayton Cycle requires a high end operating pressure in the range of 20 MPa, which is considerably higher than the required helium Brayton cycle high end operating pressure of 7 MPa. This paper presents results of analyses performed using the UniSim process analyses software to evaluate the performance of the supercritical CO_2 recompression Brayton cycle for different reactor coolant outlet temperatures and mass flow rates. The UniSim model assumed a 600 MW_t reactor power source, which provides heat to the power cycle at a maximum temperature of between 550℃ and 850℃. Sensitivity calculations were also performed to determine the affect of reactor coolant mass flow rates for a reference reactor coolant outlet temperature of 750℃. The UniSim model used realistic component parameters and operating conditions to model the complete power conversion system. CO_2 properties were evaluated, and the operating range for the cycle was adjusted to take advantage of the rapidly changing conditions near the critical point. The UniSim model was then optimized to maximize the power cycle thermal efficiency at the different reactor coolant outlet temperatures and flow rates. The results of the analyses showed that power cycle thermal efficiencies in the range of 40 to 50% can be achieved over the range of temperatures and mass flow rates investigated.

Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equation governing the system dynamics is obtained. The agents are considered to interact with one another implicitly via the reward of one agent depending on the choice of the other agents. The pairwise interaction model is adopted to describe this effect. As a specific example of systems with non-transitive interactions, a two agent and three agent systems of the rock-paper-scissors type are analyzed in detail, including the stability analysis and numerical simulation. Scale-free memory is demonstrated to cause complex dynamics of the systems at hand. In particular, it is shown that there can be simultaneously two modes of the system instability undergoing subcritical and supercritical bifurcation, with the latter one exhibiting anomalous oscillations with the amplitude and period growing with time. Besides, the instability onset via this supercritical mode may be regarded as “altruism self-organization”. For the three agent system the instability dynamics is found to be rather irregular and can be composed of alternate fragments of oscillations different in their properties.

Removal of toxic aristolochic acid components from Aristolochia plants by supercritical fluid extraction

This study aimed to assess the feasibility of using supercritical fluid extraction (SFE) to remove the major aristolochic acid components from two Aristolochia herbs, Fructus Aristolochiae and Caulis Aristolochiae manshuriensis. Four operating parameters, viz., vessel pressure ( P), vessel temperature ( T), mole fraction ( X) of entrainer (absolute ethanol) in supercritical carbon dioxide and extraction mode (EM) were investigated for their impact on the AA extraction. Statistical analysis revealed that the extraction mode and the mole fraction of entrainer were the only two dominant factors governing the AA extraction. For a 1-g powdered sample of 100–120 mesh size which had been pretreated with 2 mL absolute ethanol for 12 h, the removal of AA-I and AA-II from the two Aristolochia plants was best carried out in dynamic mode using a vessel pressure of 194 bar, vessel temperature of 50 °C, entrainer concentration of 0.2 mole fraction, and extraction time of 4 h. The removal rates of AA-I and AA-II were respectively 65.2% and 59.1% from Fructus Aristolochiae, and 81.3% and 81.2% from Caulis Aristolochiae manshuriensis.

Transmission of evanescent modes through a subwavelength aperture of a cylindrical waveguide. 2. The influence of dielectric properties of a real metal

The transmission of an evanescent light wave through the subwavelength aperture of a dielectric cylindrical metal-coated waveguide is studied. The theoretical approach to the description of the field structure in such a nanowaveguide is developed, which takes into account the transformation of the initial wave reflected from the output aperture and proves applicable when dielectric properties of a real metal are taken into account. The complex reflection coefficient of a supercritical waveguide mode from the aperture, the complex light flow and the far-field transmission coefficient are calculated for an aluminium-coated waveguide at the light wavelength of λ = 488 nm. It is established that the reflection and transmission coefficients of the nanowaveguide strongly depend on the dielectric constant of its core and differ significantly for transverse-magnetic and transverse-electric modes. It is demonstrated that the characteristics of light fields under study differ essentially from those of a nanowaveguide with ideally conducting walls and the subwavelength aperture in a perfectly conducting screen.

Transmission of evanescent modes through a subwavelength aperture of a cylindrical waveguide. 1. Ideal metal approximation

The transmission of an evanescence electromagnetic wave through the subwavelength aperture of a dielectric cylindrical metal-coated waveguide is studied. In the ideal metal approximation a theoretical approach to the description of the field structure in a nanowaveguide is developed, which takes into account the transformation of the initial wave reflected from the output aperture. The complex reflection coefficient of a supercritical waveguide mode from the subwavelength aperture is calculated. The dependence of the field structure at the waveguide output on the ratio of its radius to the optical wavelength and on the dielectric constants of the waveguide core and the environment is found. The conditions for the appearance of a plasmon resonance in the presence of a medium with the negative dielectric constant in front of the input hole of the waveguide are found.

Dynamic Stability of Cylindrical Shells under Moving Loads by Applying Advanced Controlling Techniques Part I—Using Periodic Stiffeners

The load acting on a cylindrical shell, with added periodic stiffeners, under a transient pressure pulse propelling a pullet (gun case) has been experimentally studied. This study is based on two modes of velocities, the first is subcritical mode and the second is supercritical mode. The stiffeners are added to the gun tube of an experimental gun facility, of 14 mm bore diameter. The radial strains are measured by using high‐frequency strain gage system in phase with a laser beam detection system. Time‐resolved strain measurement of the wall response is obtained and both precursor and transverse hoop strains have been resolved. The time domain analysis has been done using “wavelet transform package” in order to determine the frequency domain modes of vibrations and detect the critical frequency mode. A complete comparison of the dynamic behavior of the shell tube before and after adding periodic stiffeners has been done, which indicated that a significant damping effect reaches values between 61.5 and 38% for subcritical and critical modes. The critical frequency of the stiffened shell is increased, so the supercritical mode is changed to subcritical mode. The amplification and dispersion factors are determined and constructed; there is a reduction in the corresponding speed frequencies by about 10%. Also the radial‐bending vibrations and tube muzzle motions are detected at muzzle velocity ratio of 0.99%, the results indicated that there is a significant improvement in increasing the number of rounds per second by about 36% and increasing the pointing precision by about 47%.