scholarly journals The second curvature correction for the straight segment approximation of periodic vortex wakes

2018 ◽  
Vol 3 (1) ◽  
pp. 345-352 ◽  
Author(s):  
David H. Wood
Keyword(s):  
Approximate Expression ◽  
Operating Conditions ◽  
Vortex Rings ◽  
Local Curvature ◽  
Curvature Correction ◽  
Order Of Magnitude ◽  
Small Vortex ◽  
Straight Segments ◽  
Number Of Segments ◽  
Far Wake

Abstract. The periodic, helical vortex wakes of wind turbines, propellers, and helicopters are often approximated using straight vortex segments which cannot reproduce the binormal velocity associated with the local curvature. This leads to the need for the first curvature correction, which is well known and understood. It is less well known that under some circumstances, the binormal velocity determined from straight segments needs a second correction when the periodicity returns the vortex to the proximity of the point at which the velocity is required. This paper analyzes the second correction by modelling the helical far wake of a wind turbine as an infinite row of equispaced vortex rings of constant radius and circulation. The ring spacing is proportional to the helix pitch. The second correction is required at small vortex pitch, which is typical of the operating conditions of large modern turbines. Then the velocity induced by the periodic wake can greatly exceed the local curvature contribution. The second correction is quadratic in the inverse of the number of segments per ring and linear in the inverse spacing. An approximate expression is developed for the second correction and shown to reduce the errors by an order of magnitude.

scholarly journals The Second Curvature Correction for the Straight Segment Approximation of Periodic Vortex Wakes

2018 ◽  
Author(s):  
David H. Wood
Keyword(s):  
Approximate Expression ◽  
Operating Conditions ◽  
Vortex Rings ◽  
Local Curvature ◽  
Curvature Correction ◽  
Order Of Magnitude ◽  
Small Vortex ◽  
Straight Segments ◽  
Number Of Segments ◽  
Far Wake

Abstract. The periodic, helical vortex wakes of wind turbines, propellers, and helicopters are often approximated using straight vortex segments which cannot reproduce the binormal velocity associated with the local curvature. This leads to the need for the first curvature correction which is well known and understood. It is less well known that under some circumstances, the binormal velocity determined from straight segments needs a second correction when the periodicity returns the vortex to the proximity of the point at which the velocity is required. This paper analyzes the second correction by modeling the helical far-wake of a wind turbine as an infinite row of equispaced vortex rings of constant radius and circulation. The ring spacing is proportional to the helix pitch. The second correction is required at small vortex pitch, which is typical of the operating conditions of modern large turbines. Then the velocity induced by the periodic wake can greatly exceed the local curvature contribution. The second correction is quadratic in the inverse of the number of segments per ring and linear in the inverse spacing. An approximate expression is developed for the second correction and shown to reduce the errors by an order of magnitude.

Parametric height influence analysis on thermal radiation and convection applied to real ovens

2021 ◽  
pp. 095440892110375
Author(s):  
Sílvio Aparecido Verdério Júnior ◽  
Vicente Luiz Scalon ◽  
Santiago del Rio Oliveira ◽  
Elson Avallone ◽  
Paulo César Mioralli ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Numerical Models ◽  
Radiation Heat Transfer ◽  
Geometric Optimization ◽  
Operating Conditions ◽  
High Productivity ◽  
Order Of Magnitude ◽  
Lower Height ◽  
Heat Exchanges

Due to their greater flexibility in heating and high productivity, continuous tunnel-type ovens have become the best option for industrial processes. The geometric optimization of ovens to better take advantage of the heat transfer mechanisms by convection and thermal radiation is increasingly researched; with the search for designs that combine lower fuel consumption, greater efficiency and competitiveness, and lower costs. In this sense, this work studied the influence of height on heat exchanges by radiation and convection and other flow parameters to define the best geometric height for the real oven under study. From the dimensions and real operating conditions of continuous tunnel-type ovens were built five numerical models of parametric variation, which were simulated with the free and open-source software OpenFOAM®. The turbulent forced convection regime was characterized in all models. The use of greater heights in the ovens increased and intensified the recirculation regions, reduced the rates of heat transfer by thermal radiation, and reduced the losses of heat by convection. The order of magnitude of heat exchanges by radiation proved to be much higher than heat exchanges by convection, confirming the results of the main references in the technical-scientific literature. It was concluded that the use of ovens with a lower height provides significant increases in the thermal radiation heat transfer rates.

scholarly journals Correcting Bias in Log-Linear Instrument Calibrations in the Context of Chemical Ionization Mass Spectrometry

2021 ◽  
Author(s):  
Chenyang Bi ◽  
Jordan E. Krechmer ◽  
Manjula R. Canagaratna ◽  
Gabriel Isaacman-VanWertz
Keyword(s):  
Chemical Ionization ◽  
Correction Method ◽  
Operating Conditions ◽  
Oxidation Products ◽  
Mathematical Work ◽  
Ionization Mass ◽  
Individual Compound ◽  
Linear Calibration ◽  
Order Of Magnitude ◽  
Log Linear

Abstract. Quantitative calibration of analytes using chemical ionization mass spectrometers (CIMS) has been hindered by the lack of commercially available standards of atmospheric oxidation products. To accurately calibrate analytes without standards, techniques have been recently developed to log-linearly correlate analyte sensitivity with instrument operating conditions. However, there is an inherent bias when applying log-linear calibration relationships that is typically ignored. In this study, we examine the bias in a log-linear based calibration curve based on prior mathematical work. We quantify the potential bias within the context of a CIMS-relevant relationship between analyte sensitivity and instrument voltage differentials. Uncertainty in three parameters has the potential to contribute to the bias, specifically the inherent extent to which the nominal relationship can capture true sensitivity, the slope of the relationship, and the voltage differential below which maximum sensitivity is achieved. Using a prior published case study, we estimate an average bias of 30%, with one order of magnitude for less sensitive compounds in some circumstances. A parameter-explicit solution is proposed in this work for completely removing the inherent bias generated in the log-linear calibration relationships. A simplified correction method is also suggested for cases where a comprehensive bias correction is not possible due to unknown uncertainties of calibration parameters, which is shown to eliminate the bias on average but not for each individual compound.

scholarly journals Correcting bias in log-linear instrument calibrations in the context of chemical ionization mass spectrometry

2021 ◽  
Vol 14 (10) ◽  
pp. 6551-6560
Author(s):  
Chenyang Bi ◽  
Jordan E. Krechmer ◽  
Manjula R. Canagaratna ◽  
Gabriel Isaacman-VanWertz
Keyword(s):  
Chemical Ionization ◽  
Correction Method ◽  
Operating Conditions ◽  
Oxidation Products ◽  
Mathematical Work ◽  
Ionization Mass ◽  
Individual Compound ◽  
Linear Calibration ◽  
Order Of Magnitude ◽  
Log Linear

Abstract. Quantitative calibration of analytes using chemical ionization mass spectrometers (CIMSs) has been hindered by the lack of commercially available standards of atmospheric oxidation products. To accurately calibrate analytes without standards, techniques have been recently developed to log-linearly correlate analyte sensitivity with instrument operating conditions. However, there is an inherent bias when applying log-linear calibration relationships that is typically ignored. In this study, we examine the bias in a log-linear-based calibration curve based on prior mathematical work. We quantify the potential bias within the context of a CIMS-relevant relationship between analyte sensitivity and instrument voltage differentials. Uncertainty in three parameters has the potential to contribute to the bias, specifically the inherent extent to which the nominal relationship can capture true sensitivity, the slope of the relationship, and the voltage differential below which maximum sensitivity is achieved. Using a prior published case study, we estimate an average bias of 30 %, with 1 order of magnitude for less sensitive compounds in some circumstances. A parameter-explicit solution is proposed in this work for completely removing the inherent bias generated in the log-linear calibration relationships. A simplified correction method is also suggested for cases where a comprehensive bias correction is not possible due to unknown uncertainties of calibration parameters, which is shown to eliminate the bias on average but not for each individual compound.

Parallel Multi-Cycle LES of an Optical Pent-Roof DISI Engine Under Motored Operating Conditions

2017 ◽  
Author(s):  
Noah Van Dam ◽  
Wei Zeng ◽  
Magnus Sjöberg ◽  
Sibendu Som
Keyword(s):  
Experimental Data ◽  
Direct Injection ◽  
Operating Conditions ◽  
New Strategy ◽  
Long Time ◽  
Order Of Magnitude ◽  
Structure Index ◽  
Number Of Cycles ◽  
The Many ◽  
Direct Injection Spark Ignition

The use of Large-eddy Simulations (LES) has increased due to their ability to resolve the turbulent fluctuations of engine flows and capture the resulting cycle-to-cycle variability. One drawback of LES, however, is the requirement to run multiple engine cycles to obtain the necessary cycle statistics for full validation. The standard method to obtain the cycles by running a single simulation through many engine cycles sequentially can take a long time to complete. Recently, a new strategy has been proposed by our research group to reduce the amount of time necessary to simulate the many engine cycles by running individual engine cycle simulations in parallel. With modern large computing systems this has the potential to reduce the amount of time necessary for a full set of simulated engine cycles to finish by up to an order of magnitude. In this paper, the Parallel Perturbation Methodology (PPM) is used to simulate up to 35 engine cycles of an optically accessible, pent-roof Direct-injection Spark-ignition (DISI) engine at two different motored engine operating conditions, one throttled and one un-throttled. Comparisons are made against corresponding sequential-cycle simulations to verify the similarity of results using either methodology. Mean results from the PPM approach are very similar to sequential-cycle results with less than 0.5% difference in pressure and a magnitude structure index (MSI) of 0.95. Differences in cycle-to-cycle variability (CCV) predictions are larger, but close to the statistical uncertainty in the measurement for the number of cycles simulated. PPM LES results were also compared against experimental data. Mean quantities such as pressure or mean velocities were typically matched to within 5–10%. Pressure CCVs were under-predicted, mostly due to the lack of any perturbations in the pressure boundary conditions between cycles. Velocity CCVs for the simulations had the same average magnitude as experiments, but the experimental data showed greater spatial variation in the root-mean-square (RMS). Conversely, circular standard deviation results showed greater repeatability of the flow directionality and swirl vortex positioning than the simulations.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 2: Analysis

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Jieun Song ◽  
Seung Jin Song
Keyword(s):  
Pressure Distribution ◽  
Centrifugal Compressor ◽  
Axisymmetric Flow ◽  
Mass Conservation ◽  
Labyrinth Seal ◽  
Operating Conditions ◽  
New Model ◽  
Flow Coupling ◽  
Order Of Magnitude ◽  
Rotordynamic Forces

AbstractAn integrated analytical model to predict non-axisymmetric flow fields and rotordynamic forces in a shrouded centrifugal compressor has been newly developed and validated. The model is composed of coupled, conservation law-based, bulk-flow submodels, and the model takes into account the flow coupling among the blades, labyrinth seals, and shroud cavity. Thus, the model predicts the entire flow field in the shrouded compressor when given compressor geometry, operating conditions, and eccentricity. When compared against the experimental data from part 1, the new model accurately predicts the evolution of the pressure perturbations along the shroud and labyrinth seal cavities as well as the corresponding rotordynamic stiffness coefficients. For the test compressor, the cross-coupled stiffness rotordynamic excitation is positive; the contribution of the shroud is the highest; the contribution of the seals is less than but on the same order of magnitude as that of the shroud; and contribution of impeller blades is insignificant. The new model also enables insight into the physical mechanism for pressure perturbation development. The labyrinth seal pressure distribution becomes non-axisymmetric to satisfy mass conservation in the seal cavity, and this non-axisymmetry, in turn, serves as the influential boundary condition for the pressure distribution in the shroud cavity. Therefore, for accurate flow and rotordynamic force predictions, it is important to model the flow coupling among the components (e.g., impeller, shroud, labyrinth seal, etc.), which determines the non-axisymmetric boundary conditions for the components.

CFD Simulations of the Cold Neutron Source at the OPAL Reactor

2020 ◽  
Author(s):  
James L Spedding ◽  
Mark Ho ◽  
Weijian Lu
Keyword(s):  
Neutron Source ◽  
Cold Neutron ◽  
Operating Conditions ◽  
Convergence Time ◽  
Cfd Model ◽  
Cfd Simulations ◽  
Cold Neutron Source ◽  
Order Of Magnitude ◽  
Computational Fluid Dynamics Cfd ◽  
Polyhedral Mesh

Abstract The Open Pool Australian Light-water (OPAL) reactor Cold Neutron Source (CNS) is a 20 L liquid deuterium thermosiphon system which has performed consistently but will require replacement in the future. The CNS deuterium exploits neutronic heating to passively drive the thermosiphon loop and is cryogenically cooled by forced convective helium flow via a heat exchanger. In this study, a detailed computational fluid dynamics (CFD) model of the complete thermosiphon system was developed for simulation. Unlike previous studies, the simulation employed a novel polyhedral mesh technique. Results demonstrated that the polyhedral technique reduced simulation computational requirements and convergence time by an order of magnitude while predicting thermosiphon performance to within 1% accuracy when compared with prototype experiments. The simulation model was extrapolated to OPAL operating conditions and confirmed the versatility of the CFD model as an engineering design and preventative maintenance tool. Finally, simulations were performed on a proposed second-generation CNS design that increases the CNS moderator deuterium volume by 5 L, and results confirmed that the geometry maintains the thermosiphon deuterium in the liquid state and satisfies the CNS design criteria.

Loads Applied to Clogged Steam Generators Internal Structures

2009 ◽  
Author(s):  
Olivier Brunin ◽  
Geoffrey Deotto
Keyword(s):  
Cooling Capacity ◽  
Operating Conditions ◽  
Steam Generators ◽  
Numerical Application ◽  
Flow Area ◽  
Internal Structures ◽  
Order Of Magnitude ◽  
Water Mass Balance ◽  
Side Flow ◽  
Secondary Side

During their commissioning, steam generators are clean, which means there is no fouling of the heat transfer surface of tubes and no clogging of the flow area on the secondary side. Then sludge appears steadily at a slow pace during operation. Sludge initiates a partial loss of cooling capacity which is modeled by a fouling factor and which mainly results in vapor pressure decrease. Sludge also initiates a reduction of the secondary side flow area, known as clogging. Four safety-related issues are dependant on clogging [1]: the secondary water mass balance, the thermohydraulics oscillations, the tube vibration risk and the resistance of internal structures. This paper focuses on the last of these issues. A numerical application, based on the modeling of a fictitious steam generator, is detailed in this presentation. The order of magnitude is an 8-times increase of the loads in normal operating conditions in case of a typical 60% clogging ratio of the upper tube support plate, and a 12-times increase in case of incidental depressurization transient. These theoretical results emphasize the need to take these loads properly into account in the checking of the mechanical behavior of the internal structure of the steam generators in operation in case of significant sludge deposits.

Distinctions Between Two Types of Self Excited Gas Oscillations in Vaneless Radial Diffusers

1979 ◽  
Author(s):  
A. N. Abdelhamid ◽  
J. Bertrand
Keyword(s):  
Static Pressure ◽  
Pressure Fluctuations ◽  
Rotating Stall ◽  
Operating Conditions ◽  
Flow Coefficient ◽  
Width Ratio ◽  
Flow Conditions ◽  
Oscillating Flows ◽  
Frequency Domains ◽  
Order Of Magnitude

Experiments were conducted to determine the characteristics of oscillating flows in a centrifugal compression system with vaneless diffusers. The system was operated without a diffuser and with eight different diffuser configurations to determine the effects of diffuser diameter and width ratios on the unsteady behavior of the system. Mean and fluctuating velocity and static pressure measurements were carried out in the time and frequency domains. The system without a diffuser was found to be stable at all operating conditions. The installation of any of the eight diffusers resulted in the generation of self-excited oscillations at some operating conditions. It was found that the critical flow coefficient at which onset of oscillations was observed increased as the diffuser width ratio was decreased and as the diameter ratio was increased. Comparison between the characteristics of the oscillations observed in the present study and those observed by other investigators indicate that rotating stall in two geometrically similar diffusers can be an order of magnitude different in the non-dimensional rotational speed and level of unsteady pressure fluctuations. These differences point towards the possibility of existence of more than one set of flow conditions which could lead to the occurrence of the unsteady phenomena.

Shock cavity implosion morphologies and vortical projectile generation in axisymmetric shock–spherical fast/slow bubble interactions

1998 ◽  
Vol 362 ◽  
pp. 327-346 ◽  
Author(s):  
N. J. ZABUSKY ◽  
S. M. ZENG
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Mach Disk ◽  
Vortex Rings ◽  
Tvd Scheme ◽  
Downstream Side ◽  
Bubble Interactions ◽  
Vortex Layer ◽  
Mesh Resolution ◽  
Order Of Magnitude

Collapsing shock-bounded cavities in fast/slow (F/S) spherical and near-spherical configurations give rise to expelled jets and vortex rings. In this paper, we simulate with the Euler equations planar shocks interacting with an R12 axisymmetric spherical bubble. We visualize and quantify results that show evolving upstream and downstream complex wave patterns and emphasize the appearance of vortex rings. We examine how the magnitude of these structures scales with Mach number. The collapsing shock cavity within the bubble causes secondary shock refractions on the interface and an expelled weak jet at low Mach number. At higher Mach numbers (e.g. M=2.5) ‘vortical projectiles’ (VP) appear on the downstream side of the bubble. The primary VP arises from the delayed conical vortex layer generated at the Mach disk which forms as a result of the interaction of the curved incoming shock waves that collide on the downstream side of the bubble. These rings grow in a self-similar manner and their circulation is a function of the incoming shock Mach number. At M=5.0, it is of the same order of magnitude as the primary negative circulation deposited on the bubble interface. Also at M=2.5 and 5.0 a double vortex layer arises near the apex of the bubble and moves off the interface. It evolves into a VP, an asymmetric diffuse double ring, and moves radially beyond the apex of the bubble. Our simulations of the Euler equations were done with a second-order-accurate Harten–Yee-type upwind TVD scheme with an approximate Riemann Solver on mesh resolution of 803×123 with a bubble of radius 55 zones.

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