Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed b...Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed by scalar product of vectors which does not depend on a choice of system of co-ordinates. Taking into account the necessary corrections in record of a phase of plane waves, it is shown that the decision of the homogeneous wave equation in the form of “belated” potentials is simultaneously and the decision of the equations of movement of a liquid, and “outstripped” potentials does not satisfy them. The analysis of coefficients of reflection and passage of running waves in non-uniform space is carried out. It is shown that on boundary of spaces with different sound speeds, a turning point of a sound wave is the point of full internal reflection. The way of calculation of coefficients of reflection and passage is offered by consideration of all three waves on boundary of spaces as vectors with the set directions and amplitude of a falling wave. Calculation of coefficients of reflection and passage of a sound wave in a wave-guide of canonical type along the chosen trajectory by two methods—under traditional formulas and a vector method is carried out. Results of calculation practically coincide.展开更多
This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspecti...This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric GaussSeidel/Gauss-Seidel(LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-countreduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.展开更多
It is consider that, from the standpoint of the law of conservation of energy, the process of converting sound wave falls on the boundary between two spaces in two, leaving the boundary, reflected and passage. It is a...It is consider that, from the standpoint of the law of conservation of energy, the process of converting sound wave falls on the boundary between two spaces in two, leaving the boundary, reflected and passage. It is assumed that the simultaneous presence of three waves is impossible, and that the process of converting one wave in two waves occurs instantaneously. Based on this concept, enter the following boundary conditions for the calculation of amplitudes (coefficients) of the reflected and passage waves. The initial phases of the reflected and passage waves coincide with the phase of the falling wave. The energy of the falling wave is equal to the sum of the energies of the reflected and passage waves. The normal component velocity amplitude of the particle of the liquid under the influence of the falling wave is equal to the sum of the normal component of particle velocity amplitudes of the reflected and passage waves. It was found that the character of dependence of the reflection coefficient on the angle of departure of the initial wave is the same as in the traditional formulas, but the coefficient of passage does not exceed unity. Calculations of reflection and passage coefficients for different values of the refractive coefficient at the boundary between two homogeneous spaces as well as the canonical form of the waveguide, wherein the speed of sound which is minimum at predetermined depth is carried out.展开更多
This paper is proposed to consider the propagation of sound waves in the liquid as a result of special deformation of the medium. Mechanical vibrations of the membrane, (diaphragm) creating a sound wave, transfer from...This paper is proposed to consider the propagation of sound waves in the liquid as a result of special deformation of the medium. Mechanical vibrations of the membrane, (diaphragm) creating a sound wave, transfer from layer to layer in medium without causing synchronous oscillations of the fluid particles. It can be assumed that the deformation of the liquid is similar to the driving force (pressure) in the direction perpendicular to the plane of the vibrating membrane. Usually, the running wave functions are used to describe the sound waves, but they do not contain the direction of propagation. It is proposed to consider that the amplitude of the wave is a vector coinciding with the vector tangent to the path of the wave. This would allow for a change of direction of propagation without changing its phase, in which the direction of wave is not present. It proposed a method of calculating a vector of amplitudes of the reflected and transmitted sound waves based on the laws of conservation of impulse and energy of the waves and the boundary conditions defined by Snell’s law. It is shown that one of the two solutions of the wave equation does not apply to real physical process of sound wave’s propagation in the liquid.展开更多
文摘Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed by scalar product of vectors which does not depend on a choice of system of co-ordinates. Taking into account the necessary corrections in record of a phase of plane waves, it is shown that the decision of the homogeneous wave equation in the form of “belated” potentials is simultaneously and the decision of the equations of movement of a liquid, and “outstripped” potentials does not satisfy them. The analysis of coefficients of reflection and passage of running waves in non-uniform space is carried out. It is shown that on boundary of spaces with different sound speeds, a turning point of a sound wave is the point of full internal reflection. The way of calculation of coefficients of reflection and passage is offered by consideration of all three waves on boundary of spaces as vectors with the set directions and amplitude of a falling wave. Calculation of coefficients of reflection and passage of a sound wave in a wave-guide of canonical type along the chosen trajectory by two methods—under traditional formulas and a vector method is carried out. Results of calculation practically coincide.
基金co-supported by the National Natural Science Foundation of China(No.51976172)the National Science and Technology Major Project of China(No.2017-Ⅱ-0009-0023)。
文摘This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric GaussSeidel/Gauss-Seidel(LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-countreduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.
文摘It is consider that, from the standpoint of the law of conservation of energy, the process of converting sound wave falls on the boundary between two spaces in two, leaving the boundary, reflected and passage. It is assumed that the simultaneous presence of three waves is impossible, and that the process of converting one wave in two waves occurs instantaneously. Based on this concept, enter the following boundary conditions for the calculation of amplitudes (coefficients) of the reflected and passage waves. The initial phases of the reflected and passage waves coincide with the phase of the falling wave. The energy of the falling wave is equal to the sum of the energies of the reflected and passage waves. The normal component velocity amplitude of the particle of the liquid under the influence of the falling wave is equal to the sum of the normal component of particle velocity amplitudes of the reflected and passage waves. It was found that the character of dependence of the reflection coefficient on the angle of departure of the initial wave is the same as in the traditional formulas, but the coefficient of passage does not exceed unity. Calculations of reflection and passage coefficients for different values of the refractive coefficient at the boundary between two homogeneous spaces as well as the canonical form of the waveguide, wherein the speed of sound which is minimum at predetermined depth is carried out.
文摘This paper is proposed to consider the propagation of sound waves in the liquid as a result of special deformation of the medium. Mechanical vibrations of the membrane, (diaphragm) creating a sound wave, transfer from layer to layer in medium without causing synchronous oscillations of the fluid particles. It can be assumed that the deformation of the liquid is similar to the driving force (pressure) in the direction perpendicular to the plane of the vibrating membrane. Usually, the running wave functions are used to describe the sound waves, but they do not contain the direction of propagation. It is proposed to consider that the amplitude of the wave is a vector coinciding with the vector tangent to the path of the wave. This would allow for a change of direction of propagation without changing its phase, in which the direction of wave is not present. It proposed a method of calculating a vector of amplitudes of the reflected and transmitted sound waves based on the laws of conservation of impulse and energy of the waves and the boundary conditions defined by Snell’s law. It is shown that one of the two solutions of the wave equation does not apply to real physical process of sound wave’s propagation in the liquid.
