Influence of Floating Ring Seal Working Condition Parameters on the Dynamic Characteristics of Transient Gas Film

The high requirements for sealing performance in high-speed rotating machinery has led to the design of floating seal with annular spiral groove that offer the advantages of low leakage and extended stability. However, efforts to model the dynamic performance of these floating seal have suffered from the great complexity of the flow field. The present work addresses this issue by establishing a transient Reynolds formulation of a floating seal with annular spiral groove in a rotating coordinate system based on the small perturbation method. In addition, the influence of radial eccentricity and film thickness on the solution divergence and calculation accuracy is calculated. The dynamic stiffness and dynamic damping matrixes are built. Then the variation rules of the dynamic stiffness and damping coefficient of the gas film with structure and working conditions are investigated in detail. The results show that the floating ring seal is more suitable for the service conditions of small film thickness, low pressure, high speed and large eccentricity. Accordingly, the results obtained lay a theoretical foundation for evaluating real-world applications of floating ring seal.

Thermo-elastohydrodynamic analysis of the inhomogeneous foil bearing with misalignment

Purpose The misalignment is generally inevitable in the process of machining and assembly of rotor systems with gas foil bearings, but the exploration on this phenomenon is relatively less. Therefore, the purpose of this paper is to carry out the thermo-elastohydrodynamic analysis of the foil bearing with misalignment, especially the inhomogeneous foil bearing. Design/methodology/approach The rotor is allowed to misalign in two non-rotating directions. Then the static and dynamic performance of the inhomogeneous foil bearing is studied. The thermal-elastohydrodynamic analysis is realized by combining the Reynolds equation, foil deformation equation and energy equation. The small perturbation method is used to calculate the dynamic coefficients, then the critical whirl ratio is obtained. Findings The gas pressure, film thickness and temperature distribution distort when the misalignment appears. The rotor misalignment can improve the loading capacity but rise the gas temperature at the same time. Furthermore, the rotor misalignment can affect the critical whirl ratio which demonstrates that it is necessary to analyze the misalignment before the rotordynamic design. Originality/value The value of this paper is the exploration of the thermo-elastohydrodynamic performance of the inhomogeneous foil bearing with misalignment, the analysis procedure and the corresponding results are valuable for the design of turbo system with gas foil bearings.

Sea Echoes for Airborne HF/VHF Radar: Mathematical Model and Simulation

Currently, shore-based HF radars are widely used for coastal observations, and airborne radars are utilized for monitoring the ocean with a relatively large coverage offshore. In order to take the advantage of airborne radars, the theoretical mechanism of airborne HF/VHF radar for ocean surface observation has been studied in this paper. First, we describe the ocean surface wave height with the linear and nonlinear parts in a reasonable mathematical form and adopt the small perturbation method (SPM) to compute the HF/VHF radio scattered field induced by the sea surface. Second, the normalized radar cross section (NRCS) of the ocean surface is derived by tackling the field scattered from the random sea as a stochastic process. Third, the NRCS is simulated using the SPM under different sea states, at various radar operating frequencies and incident angles, and then the influences of these factors on radar sea echoes are investigated. At last, a comparison of NRCS using the SPM and the generalized function method (GFM) is done and analyzed. The mathematical model links the sea echoes and the ocean wave height spectrum, and it also offers a theoretical basis for designing a potential airborne HF/VHF radar for ocean surface remote sensing.

A Derivation of Stiffness and Damping Coefficients for Short Hydrodynamic Journal Bearings with Pseudo-Plastic Lubricants

ABSTRACTA new derivation considering the non-linear terms has been proposed to calculate stiffness and damping coefficients for short hydrodynamic journal bearings lubricated with pseudo-plastic fluids. The proposed method has relaxed the constraint of small perturbation method applicable to only small values of non-Newtonian factor α. An analytical solution is also given. The non-linear Reynolds equation is solved with a more reasonable boundary condition ∂p*/∂z* = 0 at the location of z*=0 while the analytical pressure distribution is obtained by seven-point Gauss-Legendre integral formula. When the non-dimensional non-Newtonian factor α is small, the stiffness and damping coefficients of computed by the proposed method can agree well with those from small perturbation method, which could verify the proposed derivation. As for large non-dimensional non-Newtonian factor α, the stiffness coefficients $K_{XX}^*$ , $K_{XY}^*$ and $K_{YX}^*$ as well as the damping coefficients $C_{XX}^*$ , $C_{XY}^*$ and $C_{YX}^*$ decrease with the increasing of non-dimensional non-Newtonian factor α. The significance of the derivation is that it can relax the constraint of small α and simplify the computation process.

Estimation of snow cover parameters on the earth’s surface with flat and hilly-mountainous terrain using radar interferometry

Исследуется зондирование снежного покрова методом радарной интерферометрии. Предложена приближенная модель интерферометрического зондирования, основанная на методе малых возмущений. Поле обратного рассеяния рассматривается как когерентная сумма волн, рассеянных на неровностях границ раздела “воздух - снег” и “снег - почва”. Представлены результаты определения водного эквивалента снега с помощью радарной интерферометрии на ровной земной поверхности (равнина) и поверхности с уклонами рельефа (холмисто-гористая местность). Проведена оценка вклада рассеяния от поверхности снега в значения амплитуды и интерферометрической фазы. Выполнен анализ влияния уклонов рельефа на оценку параметров снежного покрова. Приведены результаты численных оценок. Показано, что для местности с уклоном рельефа около 45изменения в интерферометрической фазе относительно ровной поверхности достигают 40%. Однако если склоны сравнительно ровные (менее 10), эти изменения не превышают 10% The main characteristics of the snow cover determining its impact on the environment are its thickness and the snow water equivalent (SWE). SWE assesses the water content in the snow cover. Radar interferometry is one of the methods for determining SWE. The paper presents the results of snow cover sensing by radar interferometry on both flat Earth’s surface and terrain with relief. A backscattering model taking into account backscattering from the snow surface is proposed in contrast to the existing methods. The backscattering field is considered as a coherent sum of waves scattered on the irregularities of the air - snow and snow - soil interfaces. These interfaces are statistically rough surfaces with random irregularities, whose heights are described by uncorrelated stationary random functions with their mean values, standard deviations, and correlation radii. It is assumed that the irregularities are small compared to the wavelength, their slopes are small, and the conditions for the applicability of the method of small perturbations are satisfied. It is also supposed that roughness does not affect the coherent field according to the Born approximation. The incident and scattered waves are assumed to follow Snell’s law. The coherent waves reflection and transmission coefficients are determined by Fresnel formulas for a flat interface. The contribution of backscattering from the snow surface to the values of the amplitude and interferometric phase is estimated using small perturbation method. It is shown that the relative error of interferometric phase determination due to the influence of the wave scattered by the air - snow boundary does not exceed 8% for the angles of incidence of 20-45and the density of snow 0.2-0.3 g/cm. The approximate relations show the linear dependence between the interferometric phase and SWE. The model is extended to the general case of backscattering from snow cover on the Earth’s surface with relief. The influence of terrain slopes on the interferometric phase is estimated. It is shown that for hilly terrain with slopes of about 45, the relative changes in the interferometric phase could reach 40%. However, if the slopes are relatively flat (less than 10), these changes do not exceed 10%.

The performance of Generation II journal gas foil bearing with misalignment

Purpose The normal operation of a rotor system is generally vulnerable to misalignment between gas foil bearing (GFB) and rotor. However, most theoretical and experimental researches about the characteristics of GFBs have ignored this phenomenon. Therefore, the main purpose of this paper is to evaluate the static and dynamic performance of GFBs considering misalignment. Design/methodology/approach The shaft is allowed to misalign in two directions. Then the variations of bearing load, friction force, restoring moment, stiffness and damping coefficients are thoroughly explored. The hydrodynamic pressure on the gas film is modeled with compressible Reynolds equation, and the deformation of the flexible bearing is calculated with finite element method. Small perturbation method is used to obtain the displacement and moment dynamic coefficients. Findings The film thickness and pressure distribution distort when misalignments appear. The inclination of GFBs can enhance the restoring moment to withstand the imposed misalignment. Furthermore, the simulation phenomenon demonstrates the misalignment around load direction should be avoided as much as possible, while a small value misalignment around another direction is allowed. Originality/value The value of this paper is the exploration of the influence of misalignments on the static and dynamic performance of the Generation II journal GFB. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-10-2019-0418/

REVIEW OF APPROACHES TO DESCRIPTION OF LIGHT SCATTERING IN BIOLOGICAL TISSUE

The article discusses various approaches to modeling the processes of light scattering in biological tissues. The analytical radiation transfer equation, the Tversky approach, the Bethe–Salpeter equation, and the ladder approximation are considered. For cases of single scattering, the Kubelka–Munk approach, the diffusion approximation, and the small perturbation method are presented. The mathematical principles of the considered methods are disclosed in the paper and the limits of applicability in solving the radiation transfer equation are analyzed.