Model Validation and Decision Making: An Example Using the Twin Lakes Tracer Test

1992 ◽  
Vol 294 ◽  
Author(s):  
Natalie E. Olague ◽  
Paul A. Davis ◽  
Darrla Smith ◽  
Tom Feeney
Keyword(s):  
Dispersion Model ◽  
Three Dimensional ◽  
Tracer Test ◽  
Two Dimensional ◽  
Transport Models ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Advection Dispersion ◽  
Two Dimensional Flow ◽  
Similar Site

ABSTRACTAn approach to the validation of ground-water flow and transport models that are used in support of licensing a radioactive waste site is proposed and demonstrated. The approach attempts to interpret modeling results in light of their intended purpose. Instead of trying to find the ‘best’ fit model to the experimental data, we attempt to determine the conservativeness or bias invoked by applying different models to simulate the same experiment. In this way we are able to provide guidance to the regulatory community on where they should expect model results to fall relative to actual data and provide some evidence that certain model approaches lead to conservative results while other modeling approaches lead to non-conservative results. Applying this approach to the Twin Lakes Tracer Test demonstrated that a simple one-dimensional flow and one-dimensional dispersion model consistently over-predicts the maximum concentration. A one-dimensional flow with three-dimensional dispersion and two dimensional flow with two dimensional advection-dispersion are conservative only if they employ laboratory scale dispersivities. Therefore, if a decision-maker were to accept a similar site based on results from these types of models, there would be a relatively low chance that he has accepted an unsafe site. However, if decision-makers were to reject a similar site based on these types of results, there would be a relatively large chance that they rejected a safe site.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Theoretical Aspects of Thrust Vector Control by Secondary Gas Injection in Rocket Nozzles

1968 ◽  
Vol 72 (686) ◽  
pp. 171-177 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Vector Control ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Thrust Vector Control ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Thrust Vector ◽  
Secondary Injection

This work deals with theoretical aspects of thrust vector control in rocket nozzles by the injection of secondary gas into the supersonic region of the nozzle. The work is concerned mainly with two-dimensional flow, though some aspects of three-dimensional flow in axisymmetric nozzles are considered. The subject matter is divided into three parts. In Part I, the side force produced when a physical wedge is placed into the exit of a two-dimensional nozzle is considered. In Parts 2 and 3, the physical wedge is replaced by a wedge-shaped “dead water” region produced by the separation of the boundary layer upstream of a secondary injection port. The modifications which then have to be made to the theoretical relationships, given in Part 1, are enumerated. Theoretical relationships for side force, thrust augmentation and magnification parameter for two- and three-dimensional flow are given for secondary injection normal to the main nozzle axis. In addition, the advantages to be gained by secondary injection in an upstream direction are clearly illustrated. The theoretical results are compared with experimental work and a comparison is made with the theories of other workers.

Circulation Generation and Vortex Ring Formation by Conic Nozzles

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Moshe Rosenfeld ◽  
Kakani Katija ◽  
John O. Dabiri
Keyword(s):  
Vortex Ring ◽  
Vortex Generator ◽  
Ring Formation ◽  
Vortex Rings ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Vortex Ring Formation ◽  
Exit Nozzle ◽  
Two Dimensional Flow

Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

scholarly journals Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

2011 ◽  
Vol 278 (1725) ◽  
pp. 3670-3678 ◽  
Author(s):  
Brooke E. Flammang ◽  
George V. Lauder ◽  
Daniel R. Troolin ◽  
Tyson Strand
Keyword(s):  
Three Dimensional ◽  
Flow Patterns ◽  
Wake Flow ◽  
Ring Vortex ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Volumetric Imaging ◽  
Dimensional Flow ◽  
Classic Problem ◽  
Two Dimensional Flow

Understanding how moving organisms generate locomotor forces is fundamental to the analysis of aerodynamic and hydrodynamic flow patterns that are generated during body and appendage oscillation. In the past, this has been accomplished using two-dimensional planar techniques that require reconstruction of three-dimensional flow patterns. We have applied a new, fully three-dimensional, volumetric imaging technique that allows instantaneous capture of wake flow patterns, to a classic problem in functional vertebrate biology: the function of the asymmetrical (heterocercal) tail of swimming sharks to capture the vorticity field within the volume swept by the tail. These data were used to test a previous three-dimensional reconstruction of the shark vortex wake estimated from two-dimensional flow analyses, and show that the volumetric approach reveals a different vortex wake not previously reconstructed from two-dimensional slices. The hydrodynamic wake consists of one set of dual-linked vortex rings produced per half tail beat. In addition, we use a simple passive shark-tail model under robotic control to show that the three-dimensional wake flows of the robotic tail differ from the active tail motion of a live shark, suggesting that active control of kinematics and tail stiffness plays a substantial role in the production of wake vortical patterns.

Extension of the Prandtl–Batchelor theorem to three-dimensional flows slowly varying in one direction

2010 ◽  
Vol 654 ◽  
pp. 351-361 ◽  
Author(s):  
M. SANDOVAL ◽  
S. CHERNYSHENKO
Keyword(s):  
Flow Field ◽  
Small Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Leading Order ◽  
Dimensional Flow ◽  
Two Dimensional Flow

According to the Prandtl–Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl–Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation.

A Theory for the Side Force produced in Two-Dimensional Nozzles by Secondary Gas Injection

1968 ◽  
Vol 72 (687) ◽  
pp. 267-274
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Gas Injection ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Dimensional Flow ◽  
Increase With Increase ◽  
Two Dimensional Flow ◽  
Secondary Port ◽  
Theoretical Side

Summary:This work is concerned with the side force produced in rocket nozzles by secondary gas injection. A new theory for determining the side force is presented for two-dimensional flow and this is considered to be an important step towards a theory applicable to three-dimensional flow. The proposed theory is based on a double wedge model for the separated region upstream of the secondary port. The principal feature of the model is that it accounts tor the fact that the angle of the shock wave, originating from the separated region, is observed to increase with increase in secondary mass flow rate. Theoretical side force results are shown to compare favourably with experimental results obtained using two-dimensional nozzles and a comparison is made between the proposed theory and the theories of other workers.

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