Evaluation of a Dynamic Transfer Matrix for a Hydraulic Turbine

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Keita Yamamoto ◽  
Koichi Yonezawa ◽  
Andres Müller ◽  
François Avellan ◽  
Yoshinobu Tsujimoto
Keyword(s):  
Transfer Matrix ◽  
Mass Flow ◽  
Excitation Frequency ◽  
Hydraulic Turbine ◽  
Gain Factor ◽  
System Stability ◽  
Dynamical Response ◽  
Matrix Elements ◽  
Full Load ◽  
Hydraulic Machines

Abstract It is well known that hydraulic machines experience various types of flow instabilities causing a negative influence on the system under off-design operations. The transfer matrix method correlating the flow properties in upstream and downstream of hydraulic machines is widely adopted as a first step to investigate dynamical characteristics of flow. Transfer matrix elements are the key to understand hydraulic system stability. This study focuses on measurements of transfer matrix elements for a hydraulic turbine. The oscillations of the flowrate are produced by two flow exciters located in upstream and downstream of the turbine, and evaluated from the fluctuations of the pressure difference across two streamwise locations. It is shown that the transfer matrices are successfully evaluated at part load and full load operations in the presence and absence of cavitation. In particular, cavitation compliance and mass flow gain factor, which determine the dynamical response of cavitation to the change of pressure and flowrate, are calculated from the measured transfer matrix elements. The absolute value of both cavitation compliance and mass flow gain factor is found to increase with respect to the decrease of the cavitation number. The phase of the mass flow gain factor is delayed as the excitation frequency increases. This suggests that hydraulic systems may be stabilized when the oscillation frequency increases. As a result of stability analyses, it is demonstrated that the mass flow gain factor plays a crucial role, especially in the full load cavitation surge.

scholarly journals A Review of the Dynamics of Cavitating Pumps

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Christopher Earls Brennen
Keyword(s):  
Resonant Frequency ◽  
Mass Flow ◽  
Transfer Functions ◽  
Gain Factor ◽  
System Stability ◽  
Global Oscillation ◽  
Recent Developments

This paper presents a review of some of the recent developments in our understanding of the dynamics and instabilities caused by cavitation in pumps. Focus is placed on presently available data for the transfer functions for cavitating pumps and inducers, particularly on the compliance and mass flow gain factor, which are so critical for pump and system stability. The resonant frequency for cavitating pumps is introduced and contexted. Finally, emphasis is placed on the paucity of our understanding of pump dynamics when the device or system is subjected to global oscillation.

scholarly journals Backflow effects on mass flow gain factor in a centrifugal pump

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042199886
Author(s):  
Wenzhe Kang ◽  
Lingjiu Zhou ◽  
Dianhai Liu ◽  
Zhengwei Wang
Keyword(s):  
Centrifugal Pump ◽  
Mass Flow ◽  
Flow Rate ◽  
Low Frequency ◽  
Gain Factor ◽  
Low Flow ◽  
Cavity Volume ◽  
Cavitating Flows ◽  
Inlet Tube ◽  
Low Flow Rate

Previous researches has shown that inlet backflow may occur in a centrifugal pump when running at low-flow-rate conditions and have nonnegligible effects on cavitation behaviors (e.g. mass flow gain factor) and cavitation stability (e.g. cavitation surge). To analyze the influences of backflow in impeller inlet, comparative studies of cavitating flows are carried out for two typical centrifugal pumps. A series of computational fluid dynamics (CFD) simulations were carried out for the cavitating flows in two pumps, based on the RANS (Reynolds-Averaged Naiver-Stokes) solver with the turbulence model of k- ω shear stress transport and homogeneous multiphase model. The cavity volume in Pump A (with less reversed flow in impeller inlet) decreases with the decreasing of flow rate, while the cavity volume in Pump B (with obvious inlet backflow) reach the minimum values at δ = 0.1285 and then increase as the flow rate decreases. For Pump A, the mass flow gain factors are negative and the absolute values increase with the decrease of cavitation number for all calculation conditions. For Pump B, the mass flow gain factors are negative for most conditions but positive for some conditions with low flow rate coefficients and low cavitation numbers, reaching the minimum value at condition of σ = 0.151 for most cases. The development of backflow in impeller inlet is found to be the essential reason for the great differences. For Pump B, the strong shearing between backflow and main flow lead to the cavitation in inlet tube. The cavity volume in the impeller decreases while that in the inlet tube increases with the decreasing of flow rate, which make the total cavity volume reaches the minimum value at δ = 0.1285 and then the mass flow gain factor become positive. Through the transient calculations for cavitating flows in two pumps, low-frequency fluctuations of pressure and flow rate are found in Pump B at some off-designed conditions (e.g. δ = 0.107, σ = 0.195). The relations among inlet pressure, inlet flow rate, cavity volume, and backflow are analyzed in detail to understand the periodic evolution of low-frequency fluctuations. Backflow is found to be the main reason which cause the positive value of mass flow gain factor at low-flow-rate conditions. Through the transient simulations of cavitating flow, backflow is considered as an important aspect closely related to the hydraulic stability of cavitating pumping system.

scholarly journals Complex response analysis of a non-smooth oscillator under harmonic and random excitations

2021 ◽  
Vol 42 (5) ◽  
pp. 641-648
Author(s):  
Shichao Ma ◽  
Xin Ning ◽  
Liang Wang ◽  
Wantao Jia ◽  
Wei Xu
Keyword(s):  
Excitation Frequency ◽  
System Stability ◽  
Response Analysis ◽  
External Excitation ◽  
Stochastic Response ◽  
Impact Oscillator ◽  
Nonlinear Parameters ◽  
Bifurcation Phenomena ◽  
Mc Simulation ◽  
Smooth System

AbstractIt is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Backward Traveling Rotating Stall Waves in Centrifugal Compressors

2002 ◽  
Author(s):  
Z. S. Spakovsky
Keyword(s):  
Mass Flow ◽  
Centrifugal Compressor ◽  
First Principles ◽  
Rotating Stall ◽  
Air Injection ◽  
System Stability ◽  
Centrifugal Compressors ◽  
Injection Scheme ◽  
Surge Margin ◽  
Low Order

Rotating stall waves that travel against the direction of rotor rotation are reported for the first time and a new, low-order analytical approach to model centrifugal compressor stability is introduced. The model is capable of dealing with unsteady radially swirling flows and the dynamic effects of impeller-diffuser component interaction as it occurs in centrifugal compression systems. A simple coupling criterion is developed from first principles to explain the interaction mechanism important for system stability. The model findings together with experimental data explain the mechanism for first-ever observed backward traveling rotating stall in centrifugal compressors with vaned diffusers. Based on the low-order model predictions, an air injection scheme between the impeller and the vaned diffuser is designed for the NASA Glenn CC3 high-speed centrifugal compressor. The steady air injection experiments show an increase of 25% in surge-margin with an injection mass flow of 0.5% of the compressor mass flow. In addition, it is experimentally demonstrated that this injection scheme is robust to impeller tip-clearance effects and that a reduced number of injectors can be applied for similar gains in surge-margin. The results presented in this paper firmly establish the connection between the experimentally observed dynamic phenomena in the NASA CC3 centrifugal compressor and a first principles based coupling criterion. In addition, guidelines are given for the design of centrifugal compressors with enhanced stability.

Calculation of the excitation transfer matrix elements between the S2 or S1 state of carotenoid and the S2 or S1 state of bacteriochlorophyll

1993 ◽  
Vol 98 (10) ◽  
pp. 8012-8023 ◽  
Author(s):  
Hiroyoshi Nagae ◽  
Toshiaki Kakitani ◽  
Tetzuya Katoh ◽  
Mamoru Mimuro
Keyword(s):  
Transfer Matrix ◽  
Excitation Transfer ◽  
Matrix Elements

A Study on the Leakage and Rotordynamic Performance of a Long Labyrinth Seal Under Mainly Air Conditions

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Labyrinth Seal ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
The Impact

Abstract This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure Pi = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients Hij are measured. The real parts of Hij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness KΩ and cross-coupled stiffness kΩ. The imaginary parts of Hij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m˙ of the test seal steadily increases as inlet LVF increases. KΩ is negative under all test conditions, and the magnitude of KΩ increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, kΩ is a small negative value. Injecting oil into the air increases kΩ slightly and make the magnitude of kΩ closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on kΩ. C normally increases as inlet LVF increases. The value of the effective damping Ceff = C − kΩ/Ω near 0.5ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5ω. Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of Ceff near 0.5ω. Also, the liquid presence does not change the insensitiveness of m˙, KΩ, kΩ, C, and Ceff to change in ω; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m˙, KΩ, kΩ, C, and Ceff.

A Novel Strategy for Passive Control of Combustion Instabilities Through Modification of Flame Dynamics

2008 ◽  
Author(s):  
Nicolas Noiray ◽  
Daniel Durox ◽  
Thierry Schuller ◽  
Se´bastien Candel
Keyword(s):  
Passive Control ◽  
Full Range ◽  
Premixed Flames ◽  
Perforated Plate ◽  
Operating Conditions ◽  
System Stability ◽  
Injection System ◽  
Coherent Motion ◽  
Dynamical Response ◽  
Combustion Instabilities

Passive control of combustion instabilities is explored in the case of systems featuring a collection of premixed flames. The method devised in this research differs from the general strategies employed to passively hinder the growth of acoustic-combustion oscillations by augmenting acoustic damping. Dissipation of acoustic energy is usually obtained by connecting Helmholtz resonators or quarter wave type cavities or by placing perforated plate linings around the system. While these systems effectively reduce pressure oscillations, optimum performance is not always obtained over the full range of operating conditions and their implementation requires substantial space which is not often available in practice. Conceptually, these standard techniques deal with the consequences of combustion instabilities but not with the driving sources. It is shown here that an alternative solution may be to directly act on the causes of the onset of thermo-acoustic coupling. The basic idea is to modify the flames dynamics using the dynamical response of the injection system. The principle of the passive control strategy proposed on this basis is to counteract the onset of oscillations by tackling the underlying causes. The injection system is modified to avoid a coherent motion of the flames when they are submitted to an acoustic modulation and reduce the coupling between acoustic perturbations and heat release fluctuations. Numerical simulations and experimental data are presented and one may infer that the method could bring a substantial improvement to the system stability. The efficiency of this technique is demonstrated in the case of small premixed flames anchored on a multipoint injection system (the configuration is that of a premixed gaseous-fueled multipoint dump combustor), but the principle is more general and can be extended to larger scale turbulent combustors featuring a collection of flames.

A Study for Rotordynamic and Leakage Characteristics of a Long-Honeycomb Seal With Two-Phase, Mainly Air Mixtures

2019 ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Volume Fraction ◽  
Silicone Oil ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Liquid Volume Fraction ◽  
Honeycomb Seal ◽  
The Impact

Abstract This paper investigates the impact of the oil (silicone oil PSF-5cSt) presence in the air on the leakage and rotordynamic characteristics of a long-honeycomb seal with length-to-diameter ratio L/D = 0.748 and diameter D = 114.656 mm. Tests are carried out with inlet pressure Pi = 70.7 bars, pressure ratio PR = 0.35 and 0.25, inlet liquid volume fraction LVF = 0%, 3.5%, and 7%, and shaft speed ω = 10, 15, and 20 krpm. During the tests, the seal is centered. Test results show that leakage mass flow rate ṁ increases (as expected) as inlet LVF increases. Increasing inlet LVF makes direct stiffness K increase more rapidly with increasing excitation frequency Ω. Increasing inlet LVF has a negligible effect on K at low Ω values, but increases K at high Ω values. The value of effective damping Ceff at about 0.5ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5ω. Increasing inlet LVF increases the value of Ceff at about 0.5ω, reducing the possibility of sub-synchronous vibrations SSVs at about 0.5ω. San Andrés’s model is used to produce predictions. The model assumes that the test fluid in the seal clearance is an isothermal-homogenous mixture. The model adequately predicts ṁ, K, and the value of Ceff at about 0.5ω.

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