Prediction of Deswirled Radial Inflow in Rotating Cavities With Hysteresis

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
David May ◽  
John W. Chew ◽  
Timothy J. Scanlon
Keyword(s):  
Steady State ◽  
Flow Characteristic ◽  
Steady State Solution ◽  
Negative Resistance ◽  
Operating Conditions ◽  
Operating Characteristics ◽  
Transient Model ◽  
Rotating Cavity ◽  
1D Model ◽  
Flow Effects

Deswirl nozzles are sometimes used in turbomachinery to reduce the pressure drop when air is drawn radially inwards through a rotating cavity. However, this can lead to nonunique steady state solutions with operating conditions achieved depending on how the steady point is approached. In the present study, a novel transient, 1D model of flow in a rotating cavity has been created. The model was validated for two distinct cases: a smooth rectangular cavity and an engine-representative case. The transient model reproduced experimentally observed hysteresis, discontinuity in operating characteristics, and regions where no steady-state solution could be found. In the case of the engine-representative rig, part of the flow characteristic could not be obtained in testing. This was determined to be due to the interaction of the negative resistance region of the vortex and the flow-modulating valve characteristic. Measures that allow the full capture of the flow characteristic in rig testing are identified. These results show that inclusion of transient rotating flow effects can be important in turbomachinery air systems modeling. To the authors' knowledge, this is the first model to capture these effects.

Prediction of De-Swirled Radial Inflow in Rotating Cavities With Hysteresis

2012 ◽  
Author(s):  
David May ◽  
John W. Chew ◽  
Timothy J. Scanlon
Keyword(s):  
Steady State ◽  
Flow Characteristic ◽  
Pressure Ratio ◽  
Tangential Velocity ◽  
Flow Characteristics ◽  
Steady State Solution ◽  
Operating Conditions ◽  
Operating Characteristics ◽  
Transient Model ◽  
Rotating Cavity

De-swirl nozzles are sometimes used in turbomachinery to reduce the pressure drop when air is drawn radially inwards through a rotating cavity. However, this can lead to non-unique steady state solutions with operating conditions achieved depending on how the steady point is approached. In the present study, a transient, 1D model of flow in a rotating cavity has been created. The model allows the vortex profile to change with through flow rate, and links this to estimates of disk windage, tangential velocity and, consequently, the vortex pressure gradient. The model was applied to the simulation of de-swirl nozzle fed, rotating cavities with radial inflow. The steady vortex flow characteristics (non-dimensional flow versus pressure ratio) predicted by the model were validated for 2 distinct cases. For a smooth rectangular cavity the flow characteristic was predicted using the model’s default parameters. For an engine-representative case with non-axisymmetric geometric features, the flow characteristic of the cavity was reproduced with some alignment of the model. The transient model reproduced experimentally observed hysteresis, discontinuity in operating characteristics, and regions where no steady-state solution could be found. A transient model is required as a steady state model would choose one of the possible solutions without physical justification. In the case of the engine-representative rig, part of the flow characteristic could not be obtained in testing. This is determined to be due to the interaction of the negative resistance region of the vortex and the flow modulating valve characteristic. Measures that allow the full capture of the flow characteristic in rig testing are identified.

Rotary Lip Seal Operation With an Ingested Meniscus

1997 ◽  
Vol 119 (1) ◽  
pp. 205-210 ◽  
Author(s):  
R. F. Salant
Keyword(s):  
Steady State ◽  
Operating Conditions ◽  
Multiple Equilibrium ◽  
Asperity Contact ◽  
Shaft Speed ◽  
Operating Characteristics ◽  
Lip Seal ◽  
History Of ◽  
Sealing Zone ◽  
Operating Points

Previous numerical simulations and experimental observations have shown that the meniscus in a rotary lip seal will be ingested into the sealing zone when the shaft speed exceeds a critical value. The present numerical analysis shows that once the meniscus is ingested, multiple equilibrium operating points exist, so the steady-state operating characteristics of the seal will depend on the history of the seal as well as on the steady-state operating conditions and seal properties. The analysis also shows that if the meniscus moves too close to the liquid-side of the seal, asperity contact between the lip and the shaft will occur.

Validation of On-line Respiration Meter and its Applications by Computer Simulation

1992 ◽  
Vol 26 (5-6) ◽  
pp. 1355-1363 ◽  
Author(s):  
C-W. Kim ◽  
H. Spanjers ◽  
A. Klapwijk
Keyword(s):  
Steady State ◽  
Activated Sludge ◽  
Respiration Rate ◽  
Oxygen Demand ◽  
Operating Conditions ◽  
Mass Balances ◽  
Short Term ◽  
Respiration Rates ◽  
On Line ◽  
Made In

An on-line respiration meter is presented to monitor three types of respiration rates of activated sludge and to calculate effluent and influent short term biochemical oxygen demand (BODst) in the continuous activated sludge process. This work is to verify if the calculated BODst is reliable and the assumptions made in the course of developing the proposed procedure were acceptable. A mathematical model and a dynamic simulation program are written for an activated sludge model plant along with the respiration meter based on mass balances of BODst and DO. The simulation results show that the three types of respiration rate reach steady state within 15 minutes under reasonable operating conditions. As long as the respiration rate reaches steady state the proposed procedure calculates the respiration rate that is equal to the simulated. Under constant and dynamic BODst loading, the proposed procedure is capable of calculating the effluent and influent BODst with reasonable accuracy.

Steady-state Security Assessment Based on K-Means Clustering Algorithm and Phasor Measurement Units

2020 ◽  
Vol 13 (4) ◽  
pp. 559-570
Author(s):  
Bassam A. Hemade ◽  
Hamed A. Ibrahim ◽  
Hossam E.A. Talaat
Keyword(s):  
Steady State ◽  
Clustering Algorithm ◽  
System Security ◽  
Phasor Measurement Units ◽  
Operating Conditions ◽  
Security Assessment ◽  
State Security ◽  
Phasor Measurement ◽  
Measurement Units ◽  
Silhouette Analysis

Background: The security assessment plays a crucial role in the operation of the modern interconnected power system network. Methods: Hence, this paper addresses the application of k-means clustering algorithm equipped with Principal Component Analysis (PCA) and silhouette analysis for the classification of system security states. The proposed technique works on three principal axes; the first stage involves contingency quantification based on developed insecurity indices, the second stage includes dataset preparation to enhance the overall performance of the proposed method using PCA and silhouette analysis, and finally the application of the clustering algorithm over data. Results: The proposed composite insecurity index uses available synchronized measurements from Phasor Measurement Units (PMUs) to assess the development of cascading outages. Considering different operational scenarios and multiple levels of contingencies (up to N-3), Fast Decoupled Power Flow (FDPF) have been used for contingency replications. The developed technique applied to IEEE 14-bus and 57-bus standard test system for steady-state security evaluation. Conclusion: The obtained results ensure the robustness and effectiveness of the established procedure in the assessment of the system security irrespective of the network size or operating conditions.

Mathematical modelling of salt purification by recrystallization. Countercurrent arrangement

1986 ◽  
Vol 51 (11) ◽  
pp. 2481-2488
Author(s):  
Benitto Mayrhofer ◽  
Jana Mayrhoferová ◽  
Lubomír Neužil ◽  
Jaroslav Nývlt
Keyword(s):  
Steady State ◽  
Simple Model ◽  
Mathematical Modelling ◽  
Distribution Coefficient ◽  
Mother Liquor ◽  
Equilibrium Temperature ◽  
Operating Conditions ◽  
Limiting Case

The paper presents a simple model of recrystallization with countercurrent flows of the solution and the crystals being purified. The model assumes steady-state operating conditions, an equilibrium between the outlet streams of each stage, and the same equilibrium temperature and distribution coefficient for all stages. With these assumptions, the model provides the basis for analyzing the variation in the degree of purity as a function of the number of recrystallization stages. The analysis is facilitated by the use of a diagram constructed for the limiting case of perfect removal of the mother liquor from the crystals between the stages.

scholarly journals Financial Impacts of Net-Metered Distributed PV on a Prototypical Western Utility’s Shareholders and Ratepayers

Energies ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4794 ◽  
Author(s):  
Peter Cappers ◽  
Andrew Satchwell ◽  
Will Gorman ◽  
Javier Reneses
Keyword(s):  
Capital Investment ◽  
Operating Conditions ◽  
Net Energy ◽  
Electricity Pricing ◽  
Operating Characteristics ◽  
Financial Model ◽  
Energy Metering ◽  
Percentage Basis ◽  
Financial Impacts ◽  
Net Energy Metering

Distributed solar photovoltaic (DPV) under net-energy metering with volumetric retail electricity pricing has raised concerns among utilities and regulators about adverse financial impacts for shareholders and ratepayers. Using a pro forma financial model, we estimate the financial impacts of different DPV deployment levels on a prototypical Western U.S. investor-owned utility under a varied set of operating conditions that would be expected to affect the value of DPV. Our results show that the financial impacts on shareholders and ratepayers increase as the level of DPV deployment increases, though the magnitude is small even at high DPV penetration levels. Even rather dramatic changes in DPV value result in modest changes to shareholder and ratepayer impacts, but the impacts on the former are greater than the latter (in percentage terms). The range of financial impacts are driven by differences in the amount of incremental capital investment that is deferred, as well as the amount of incremental distribution operating expenses that are incurred. While many of the impacts appear relatively small (on a percentage basis), they demonstrate how the magnitude of impacts depend critically on utility physical, financial, and operating characteristics.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

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