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.

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 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.

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.

Measurement and Analysis of Flame Transfer Function in a Sector Combustor Under High Pressure Conditions

2003 ◽  
Author(s):  
W. S. Cheung ◽  
G. J. M. Sims ◽  
R. W. Copplestone ◽  
J. R. Tilston ◽  
C. W. Wilson ◽  
...  
Keyword(s):  
High Pressure ◽  
Transfer Function ◽  
Heat Release ◽  
Gas Turbine ◽  
Mass Flow ◽  
Atmospheric Pressure ◽  
Acoustic Waves ◽  
Gas Turbines ◽  
Transfer Functions ◽  
Unsteady Pressure

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. A flame transfer function describes the change in the rate of heat release in response to perturbations in the inlet flow as a function of frequency. It is a quantitative assessment of the susceptibility of combustion to disturbances. The resulting fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can result. Flame transfer functions for LPP combustion are poorly understood at present but are crucial for predicting combustion oscillations. This paper describes an experiment designed to measure the flame transfer function of a simple combustor incorporating realistic components. Tests were conducted initially on this combustor at atmospheric pressure (1.2 bar and 550 K) to make an early demonstration of the combustion system. The test rig consisted of a plenum chamber with an inline siren, followed by a single LPP premixer/duct and a combustion chamber with a silencer to prevent natural instabilities. The siren was used to induce variable frequency pressure/acoustic signals into the air approaching the combustor. Both unsteady pressure and heat release measurements were undertaken. There was good coherence between the pressure and heat release signals. At each test frequency, two unsteady pressure measurements in the plenum were used to calculate the acoustic waves in this chamber and hence estimate the mass-flow perturbation at the fuel injection point inside the LPP duct. The flame transfer function relating the heat release perturbation to this mass flow was found as a function of frequency. The same combustor hardware and associated instrumentation were then used for the high pressure (15 bar and 800 K) tests. Flame transfer function measurements were taken at three combustion conditions that simulated the staging point conditions (Idle, Approach and Take-off) of a large turbofan gas turbine. There was good coherence between pressure and heat release signals at Idle, indicating a close relationship between acoustic and heat release processes. Problems were encountered at high frequencies for the Approach and Take-off conditions, but the flame transfer function for the Idle case had very good qualitative agreement with the atmospheric-pressure tests. The flame transfer functions calculated here could be used directly for predicting combustion oscillations in gas turbine using the same LPP duct at the same operating conditions. More importantly they can guide work to produce a general analytical model.

An Advanced Frequency-Domain Code for BWR Stability Analysis and Design

2013 ◽  
Author(s):  
Behrooz Askari ◽  
George Yadigaroglu
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Transfer Functions ◽  
Density Wave ◽  
System Stability ◽  
Reactor Kinetics ◽  
Analysis And Design ◽  
Drift Flux ◽  
Reactor Transfer ◽  
Phase Instabilities

Density Wave Oscillations in BWRs are coupled with the reactor kinetics. A new analytical, frequency-domain tool that uses the best available models and methods for modeling BWRs and analyzing their stability is described. The steady state of the core is obtained first in 3D with two-group diffusion equations and spatial expansion of the neutron fluxes in Legendre polynomials. The time-dependent neutronics equations are written in terms of flux harmonics (nodal-modal equations) for the study of “out-of-phase” instabilities. Considering separately all fuel assemblies divided into a number of axial segments, the thermal-hydraulic conservation equations are solved (drift-flux, non-equilibrium model). The thermal-hydraulics are iteratively fully coupled to the neutronics. The code takes all necessary information from plant files via an interface. The results of the steady state are used for the calculation of the transfer functions and system transfer matrices using extensively symbolic manipulation software (MATLAB). The resulting very large matrices are manipulated and inverted by special procedures developed within the MATLAB environment to obtain the reactor transfer functions that enable the study of system stability. Applications to BWRs show good agreement with measured stability data.

Transfer impedances between different regions of branched excitable cells

1988 ◽  
Vol 59 (3) ◽  
pp. 689-705 ◽  
Author(s):  
L. E. Moore ◽  
K. Yoshii ◽  
B. N. Christensen
Keyword(s):  
Resonant Frequency ◽  
Voltage Clamp ◽  
Growth Cone ◽  
Transfer Functions ◽  
Excitable Cells ◽  
Resonant Frequencies ◽  
Steady State Current ◽  
Branching Patterns ◽  
Voltage Dependent ◽  
Impedance Functions

1. The excitable properties of branched cells were measured using a combination of voltage-clamp and frequency-domain techniques. Point impedance functions from either the soma or growth cone of NG-108 cells were curve fitted with a reduced cable model at different membrane potentials to establish kinetic parameters. 2. Transfer impedance functions between the soma and growth cone were measured and simulated with a morphologically determined model. In these experiments the membrane potential was controlled by a single-electrode voltage clamp thus allowing an estimate of transfer functions for any arbitrary input, such as a single synaptic current for differing degrees of tonic synaptic drive. Furthermore, the integration of different regional inputs was evaluated based on the transfer functions between different locations on an individual cell. 3. The activation of an outward steady-state current leads to resonating impedance functions that were used to evaluate the kinetic properties of ionic channels in different regions of branched excitable cells. For simple branching patterns the point and transfer impedances show lower resonant frequencies for active growth cones compared with active somas. 4. More complex branching patterns showed the unexpected result that the voltage-dependent resonant frequency was higher for the growth cone recording than the soma. The presence of a higher resonant frequency when the growth cone is activated does not require more rapid kinetics of the active potassium conductance, since the time constant of the active conductance can be the same in the growth cone and the soma membrane. 5. In conclusion, the resonant frequencies, as well as all other aspects of the impedance functions, are complicated interactions of the detailed branching patterns and active conductances. In general, these interactions are not predictable from a passive electrotonic analysis, especially when the voltage-dependent conductances are distributed throughout the dendritic tree.

Controller Design of a Distributed Slewing Flexible Structure—A Frequency Domain Approach

1997 ◽  
Vol 119 (4) ◽  
pp. 809-814 ◽  
Author(s):  
S. M. Yang ◽  
J. A. Jeng ◽  
Y. C. Liu
Keyword(s):  
Frequency Domain ◽  
Transfer Functions ◽  
Controller Design ◽  
System Stability ◽  
Feedback Gain ◽  
Flexible Structure ◽  
Control Law ◽  
Discrete Parameter ◽  
Locus Method ◽  
Beam Experiment

The vibration control of a slewing flexible structure by collocated and noncollocated feedback is presented in this paper. A stability criterion derived from the root locus method in frequency domain is applied to predict the closed-loop system stability of the distributed parameter model whose analytical transfer functions are formulated. It is shown that the control law design requires neither distributed state sensing/estimation nor functional feedback gain; moreover, the spillover problem associated with discrete parameter model can be prevented. Implementation of the noncollocated feedback in a slewing beam experiment validates that the control law is effective in pointing accuracy while suppressing the tip vibration.

Simultaneous Turbine Speed Regulation and Fuel Cell Airflow Tracking of a SOFC/GT Hybrid Plant With the Use of Airflow Bypass Valves

2011 ◽  
Vol 8 (6) ◽  
Author(s):  
Alex Tsai ◽  
David Tucker ◽  
David Clippinger
Keyword(s):  
Fuel Cell ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Transfer Functions ◽  
Nonlinear Models ◽  
Cell Mass ◽  
Hybrid Plant ◽  
Simultaneous Control ◽  
Turbine Speed

This paper studies a novel control methodology aimed at regulating and tracking turbo machinery synchronous speed and fuel cell mass flow rate of a SOFC/GT hardware simulation facility with the sole use of airflow bypass valves. The hybrid facility under consideration consists of a 120 kW auxiliary power unit gas turbine coupled to a 300 kW SOFC hardware simulator. The hybrid simulator allows testing of a wide variety of fuel cell models under a hardware-in-the-loop configuration. Small changes in fuel cell cathode airflow have shown to have a large impact on system performance. Without simultaneous control of turbine speed via load or auxiliary fuel, fuel cell airflow tracking requires an alternate actuator methodology. The use of bypass valves to control mass flow rate and decouple turbine speed allows for a greater flexibility and feasibility of implementation at the larger scale, where synchronous speeds are required. This work utilizes empirically derived transfer functions (TF) as the system model and applies a fuzzy logic (FL) control algorithm that can be easily incorporated to nonlinear models of direct fired recuperated hybrid plants having similar configurations. This methodology is tested on a SIMULINK/matlab platform for various perturbations of turbine load and fuel cell heat exhaust.

Frequency Dependence of Mass Flow Gain Factor and Cavitation Compliance of Cavitating Inducers

1996 ◽  
Vol 118 (2) ◽  
pp. 400-408 ◽  
Author(s):  
S. Otsuka ◽  
Y. Tsujimoto ◽  
K. Kamijo ◽  
O. Furuya
Keyword(s):  
Mass Flow ◽  
Present Model ◽  
Cavity Length ◽  
Incidence Angle ◽  
Low Frequency ◽  
Gain Factor ◽  
Cavity Model ◽  
Frequency Limit ◽  
Closed Cavity ◽  
Reduced Frequency

Unsteady cavitation characteristics are analyzed based on a closed cavity model in which the length of the cavity is allowed to oscillate. It is shown that the present model blends smoothly into quasi-steady calculations at the low frequency limit, unlike fixed cavity length models. Effects of incidence angle and cavitation number on cavitation compliance and mass flow gain factor are shown as functions of reduced frequency. The cavity volume is evaluated by three methods and the results are used to confirm the accuracy and adequacy of the numerical calculations. By comparison with experimental data on inducers, it is shown that the present model can simulate the characteristics of unsteady-cavitation qualitatively.

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