scholarly journals Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

2021 ◽  
Vol 11 (9) ◽  
pp. 4237
Author(s):  
Mingjie Zhang ◽  
Jiangang Yang ◽  
Wanfu Zhang ◽  
Qianlei Gu
Keyword(s):  
Circular Orbit ◽  
Present Method ◽  
Decomposition Method ◽  
Parameter Analysis ◽  
Elliptical Orbit ◽  
Computational Time ◽  
Solution Technique ◽  
Rotordynamic Coefficients ◽  
Cfd Method ◽  
Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

Comparisons of Rotordynamic Characteristics Predictions for Annular Gas Seals Using the Transient Computational Fluid Dynamic Method Based on Different Single-Frequency and Multifrequency Rotor Whirling Models

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Computational Fluid Dynamic ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Single Frequency ◽  
Solution Technique ◽  
Model Parameters ◽  
Multiple Frequency ◽  
Rotordynamic Coefficients ◽  
Gas Seals ◽  
Cfd Method

The three-dimensional (3D) transient computational fluid dynamic (CFD) method was proposed to predict rotordynamic coefficients for annular gas seals. This transient CFD method uses unsteady Reynolds-Averaged Navier–Stokes (RANS) solution technique and mesh deformation theory, which requires a rotor whirling model as the rotor excitation signal to solve the transient leakage flow field in seal and obtain the transient fluid response forces on the rotor surface. A fully partitioned pocket damper seal (FPDS) was taken as the test object to validate the present numerical method. Comparisons were made between experimental data and rotordynamic coefficient predictions using the three variations of the single-frequency and multiple-frequency rotor whirling models: (1) one-dimensional whirling model, (2) circular orbit whirling model, and (3) elliptical orbit whirling model. The numerical results show that the rotordynamic coefficients predicted by the present CFD method and six different rotor whirling models all agree well with the experiment data, and nearly coincide for all rotor whirling models. The proposed transient CFD method can be used to perform a reasonably accurate prediction of the frequency-dependent rotordynamic coefficients for annular gas seals based on any one of the present six rotor whirling models, as long as ensuring the combination of these whirling model parameters captures the small perturbation theory. The rotor whirling parameters such as whirling orbit, amplitude, and frequency number are important in predicting rotor whirling motion and fluid response forces, but have almost no effect on the computed rotordynamic coefficients. The benefit of the multiple-frequency rotor whirling models is the ability to calculate accurate rotordynamic coefficients of annular gas seals in a wide frequency range with a simulation time on the order of one-tenth the cost of the single-frequency whirling models.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

Prediction of Rotordynamic Performance of Smooth Stator-Grooved Rotor Liquid Annular Seals Utilizing Computational Fluid Dynamics

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Farzam Mortazavi ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Excitation Frequency ◽  
Computationally Efficient ◽  
Operational Conditions ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Liquid Seal ◽  
Frequency Ratios ◽  
Annular Seals

Circumferentially grooved, annular liquid seals typically exhibit good whirl frequency ratios (WFRs) and leakage reduction, yet their low effective damping can lead to instability. The current study investigates the rotordynamic behavior of a 15-step groove-on-rotor annular liquid seal by means of computational fluid dynamics (CFD), in contrast to the previous studies which focused on a groove-on-stator geometry. The seal dimensions and working conditions have been selected based on experiments of Moreland and Childs (2016, “Influence of Pre-Swirl and Eccentricity in Smooth Stator/Grooved Rotor Liquid Annular Seals, Measured Static and Rotordynamic Characteristics,” M.Sc. thesis, Texas A&M University, College Station, TX). The frequency ratios as high as four have been studied. Implementation of pressure-pressure inlet and outlet conditions make the need for loss coefficients at the entrance and exit of the seal redundant. A computationally efficient quasi-steady approach is used to obtain impedance curves as functions of the excitation frequency. The effectiveness of steady-state CFD approach is validated by comparison with the experimental results of Moreland and Childs. Results show good agreement in terms of leakage, preswirl ratio (PSR), and rotordynamic coefficients. It was found that PSR will be about 0.3–0.4 at the entrance of the seal in the case of radial injection, and outlet swirl ratio (OSR) always converges to values near 0.5 for current seal and operational conditions. The negative value of direct stiffness coefficients, large cross-coupled stiffness coefficients, and small direct damping coefficients explains the destabilizing nature of these seals. Finally, the influence of surface roughness on leakage, PSR, OSR, and stiffness coefficients is discussed.

Investigations on the Rotordynamic Characteristics of a Hole-Pattern Seal Using Transient CFD and Periodic Circular Orbit Model

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xin Yan ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Circular Orbit ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Numerical Approach ◽  
Deformation Method ◽  
Rotordynamic Coefficients ◽  
Forward Orbit ◽  
Reaction Forces ◽  
Orbit Model

Numerical investigations on the rotordynamic characteristics of a typical hole-pattern seal using transient three-dimensional Reynolds-averaged Navier–Stokes (RANS) solution and the periodic circular orbit model were conducted in this work. The unsteady solutions combined with mesh deformation method were utilized to solve the three-dimensional RANS equations and obtain the transient reaction forces on a typical hole-pattern seal rotor at five different excitation frequencies. The relation between the periodic reaction forces and frequency dependent rotordynamic coefficients of the hole-pattern seal was obtained by considering the rotor with a periodic circular orbit (including forward orbit and backward orbit) of the seal center. The rotordynamic coefficients of the hole-pattern seal were then solved based on the obtained unsteady reaction forces and presented numerical method. Compared with the experimental data, the predicted rotordynamic coefficients of the hole-pattern seal are more agreeable with the experiment than that of the ISO-temperature (ISOT) bulk flow analysis and numerical approach with one-direction-shaking model. Furthermore, the unsteady leakage flow characteristics in the hole-pattern seal were also illustrated and discussed in detail.

Non-Negative Matrix Factorization Based Uncertainty Quantification Method for Complex Networked Systems

2015 ◽  
Author(s):  
Arpan Mukherjee ◽  
Rahul Rai ◽  
Puneet Singla ◽  
Tarunraj Singh ◽  
Abani Patra
Keyword(s):  
Matrix Factorization ◽  
Decomposition Method ◽  
Uncertainty Propagation ◽  
Networked Systems ◽  
Computational Time ◽  
State Variables ◽  
System Decomposition ◽  
Cluster Interaction ◽  
Quantifying Uncertainty ◽  
Non Negative Matrix Factorization

The behavior of large networked systems with underlying complex nonlinear dynamic are hard to predict. With increasing number of states, the problem becomes even harder. Quantifying uncertainty in such systems by conventional methods requires high computational time and the accuracy obtained in estimating the state variables can also be low. This paper presents a novel computational Uncertainty Quantifying (UQ) method for complex networked systems. Our approach is to represent the complex systems as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. First, we apply Non-negative Matrix Factorization (NMF) based decomposition method to partition the domain of the dynamical system into clusters, such that the inter-cluster interaction is minimized and the intra-cluster interaction is maximized. The decomposition method takes into account the dynamics of individual nodes to perform system decomposition. Initial validation results on two well-known dynamical systems have been performed. The validation results show that uncertainty propagation error quantified by RMS errors obtained through our algorithms are competitive or often better, compared to existing methods.

scholarly journals Dynamic analysis of liquid annular seals with herringbone grooves on the rotor based on the perturbation method

2018 ◽  
Vol 5 (6) ◽  
pp. 180101 ◽  
Author(s):  
Lulu Zhai ◽  
Zhang Zhenjie ◽  
Chi Zhonghuang ◽  
Guo Jia
Keyword(s):  
Dynamic Characteristics ◽  
Operating Conditions ◽  
Geometric Parameters ◽  
Leakage Flow ◽  
Flow Rates ◽  
Rotordynamic Coefficients ◽  
Sealing Performance ◽  
Spiral Angle ◽  
Herringbone Grooves ◽  
Annular Seals

Annular seals have significant effects on the hydraulic and rotordynamic performances of turbomachinery. In this paper, an analysis method for calculating the leakage flow rates and dynamic characteristics of liquid annular seals with herringbone grooves on the rotor is proposed and verified. Leakage flow rates and dynamic characteristics of the model seals under different operating conditions are theoretically analysed and compared with those of plain and spiral-grooved seals of the same size. In addition, the influence of geometric parameters such as spiral angle and the lengths of the constituent parts on the sealing and rotordynamic coefficients of seals with herringbone grooves are also discussed. The results show that seals with herringbone grooves have better sealing performance, while providing better support actions and damping characteristics than the other two seal types under the same operating conditions. The seal geometric parameters including spiral angle, the lengths of the constituent parts and the clearance value have a significant influence on the dynamic characteristics of seals with herringbone grooves.

scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

scholarly journals ANFIS grid partition framework with difference between two sigmoidal membership functions structure for validation of nanofluid flow

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Mahboubeh Pishnamazi ◽  
Meisam Babanezhad ◽  
Ali Taghvaie Nakhjiri ◽  
Mashallah Rezakazemi ◽  
Azam Marjani ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Logic ◽  
Ant Colony ◽  
Computational Time ◽  
Membership Functions ◽  
Square Cavity ◽  
Grid Partition ◽  
Anfis Method ◽  
Cfd Method ◽  
Method R

Abstract In this study, a square cavity is modeled using Computational Fluid Dynamics (CFD) as well as artificial intelligence (AI) approach. In the square cavity, copper (Cu) nanoparticle is the nanofluid and the flow velocity characteristics in the x-direction and y-direction, and the fluid temperature inside the cavity at different times are considered as CFD outputs. CFD outputs have been assessed using one of the artificial intelligence algorithms, such as a combination of neural network and fuzzy logic (ANFIS). As in the ANFIS method, we have a non-dimension procedure in the learning step, and there is no issue in combining other characteristics of the flow and thermal distribution beside the x and y coordinates, we combine two coordinate parameters and one flow parameter. This ability of method can be considered as a meshless learning step that there is no instability of the numerical method or limitation of boundary conditions. The data were classified using the grid partition method and the MF (membership function) type was dsigmf (difference between two sigmoidal membership functions). By achieving the appropriate intelligence in the ANFIS method, output prediction was performed at the points of cavity which were not included in the learning process and were compared to the existing data (the results of the CFD method) and were validated by them. This new combination of CFD and the ANFIS method enables us to learn flow and temperature distribution throughout the domain thoroughly, and eventually predict the flow characteristics in short computational time. The results from AI in the ANFIS method were compared to the ant colony and fuzzy logic methods. The data from CFD results were inserted into the ant colony system for the training process, and we predicted the data in the fuzzy logic system. Then, we compare the data with the ANFIS method. The results indicate that the ANFIS method has a high potentiality compared to the ant colony method because the amount of R in the ANIFS system is higher than R in the ant colony method. In the ANFIS method, R is equal to 0.99, and in the ant colony method, R is equal to 0.91. This shows that the ant colony needs more time for both the prediction and training of the system. Also, comparing the pattern recognition in the two systems, we can obviously see that by using the ANFIS method, the predictions completely match the target points. But the other method cannot match the flow pattern and velocity distribution with the CFD method.

Optimization of the spacecraft final orbit and the trajectory of the apsidal impulse launch, with due regard to spent stage jettisons into the atmosphere

2019 ◽  
Author(s):  
I.S. Grigoryev ◽  
A.I Proskuryakov
Keyword(s):  
Circular Orbit ◽  
Parametric Analysis ◽  
Artificial Satellite ◽  
Optimal Number ◽  
Elliptical Orbit ◽  
Additional Mass ◽  
Fuel Distribution ◽  
Mass Consumption ◽  
Earth Space ◽  
Near Earth Space

The article considers the idea of reducing littering the near-Earth space by means of spent stage jettisons into the Earth's atmosphere. A solution to the problem of optimization of the apsidal impulse transfer between the reference circular orbit of an Earth’s artificial satellite and the final elliptical orbit is proposed. A parametric analysis of the obtained solutions is performed, a simple pulse choice scheme close in functionality to the optimal one is proposed. Questions about the optimal number and location of pulses and the optimal mass of the first stage are investigated. An assessment of the additional mass consumption associated with the stage jettisons into the atmosphere comparing with the simple separation of the stages is performed. It was found that in the case of optimal fuel distribution among the tanks such mass consumption is small when a final ascent pulse is 1.5 km/s.

Sign in / Sign up

Export Citation Format

Share Document