Bounding sectional curvature along a Kahler-Ricci flow

1.You can easily edit the display of datums on screen to make them easier to work with. Use Tools > Datums > Modify Datum Display and try translating, scaling and rotating some of your axes and planes.e Modify Mesh Resolution under the CAD menu to refine the display of the CAD model. This function can refine the model if it appears too coarse (e.g. cylinders and arcs appear too faceted).3、Use one or more of the various sampling functions to reduce the size of the scan data set. Sampling the point cloud to remove redundant or unnecessary data will help speed up the alignment and analysis processes.4、You can make changes to the color spectrum on the result model by using the Analysis > Edit Spectrum command. This allows you to change options such as the number of segments, tolerance values and the range of individual color bands5、Use the Ellipse selection tool to select points around holes or similar features. To select points within a ring, hold down the CTRL key to deselect the interior points.6、When creating a point datum using Best Fit Circle Center, select a large flat area surrounding the circular void. This will help to establish the plane of the circle.7、You do not have to select the entire perimeter of a circle to create a point datum using Best Fit Circle Center. The largest arc in the selection will drive the definition of the circle center.8、The 3-2-1 Alignment command can be use to define three orthogonal planes and an origin on each object and align the objects accordingly.9、Use the Alt+6 and Alt+7 hotkeys to Show All Datums or Hide All Datums.10、The World object can be used as an alignment fixture to align an object to a specified coordinate system without using a reference object.11、Dynamic zooming on a point: hold down the Shift key and the right mouse button to zoom in at the location where the mouse was clicked. Move the mouse up or down to zoom in or out.13、If two objects are closely aligned, use the 'Fine Adjustments Only' option in Auto Create Datums/Features or Best Fit Alignment to minimize the processing time.14、A Location Set can be used to create a table of deviation results at critical locations. This information can be included in reports and exported for use in statistical analysis programs.15、Company logos can be automatically placed in reports by customizing the header images in the Create Report customization options.16、Enable the 'Prompt Before Overwriting' option to prevent accidentally overwriting existing work. The option is in Tools > Options menu under the General > Directories heading.17、The Ellipse selection tool helps in selecting circular or oval-shaped regions, and the new Lasso selection tool can select freeform regions.18、Toolbars can be moved and positioned in different locations on the application.19、You can activate the right mouse button menu in the toolbar region to select which toolbars you want displayed.20、The Tools > Alignment > To Viewer command helps quickly orient the view so it is perpendicular to a specific portion of the object.21、You can undock and float the Manager and Info Panels to increase the size of your workspace. Simply click and drag the top of each panel out of the main application window. Double-click the top of each panel to return it to the docked position.22、The Select Bounded Components tool lets you select areas bounded by marked edges and can be instrumental in selecting entire faces precisely and easily. To use the tool, select at least one polygon within the area bounded by curves and then choose Edit > Select > Bounded Components.23、Changing the Selection Tool (Rectangle, Ellipse, Line, Paintbrush, and Lasso) can help when selecting complex areas of a model. You can also change some parameters of the selection tools under Tools > Options > Display > Selection.24、You can greatly increase your graphics performance by working with a small portion of the model. Simply select the desired region and click View > Selected Only.25、A movable light source is available for inspecting the model. Consult the General > Themes > Mouse Themes under Tools > Options to determine the correct key combination.26、The Advanced Screen Capture command in the File menu allows you to capture images at much higher resolution than the monitor display. This is very useful for high-resolution printing.27、Multiple views make it easier to position a plane or properly orient a model. The layout can be adjusted via the View > Frame Layout menu or the Frame Layout toolbar.28、Increasing the picking zoom in the Tools > Options > Graphics Picking heading allows you to select smaller triangles more accurately.29、To quickly get an idea of model size (possibly to set correct units), you can view the dimensions of the bounding box on the 'Bounding Box' tab of the Info Panel.30、Make extensive use of Set Rotation Center when magnifying, especially when performing local polygon or boundary editing operations.31、The Alt+1 key combination will make only the currently active object visible; all other objects in the Model Manager will be hidden. Alt+2 can be used to proceed to the next object in the tree.32、Holding down the CTRL key when selecting a file from the 'recent file list' in the File menu will Import the file as opposed to Opening it. This is very useful for importing commonly used objects and templates.33、Every display color can now be configured. Go to Tools > Options > General > Themes and edit an existing color theme.34、To streamline your workflow, customize your toolbars and right click menu. Right-click on any toolbar and select "Customize...".35、When aligning multiple data sets (10+), it may be easier to only register several at a time by selecting them in the Model Manager prior to invoking the Manual Registration dialog.36、When registering data, the Floating set will be rotated and transformed to align with the Fixed set.37、Use the Modify button in the Manual Registration dialog to make manual adjustments to the alignment of the two data sets.38、Use the Shaded Points checkbox in the Registration dialogs to view point clouds with shading. This will make it easier to see common features in regions of overlap.39、Use the Merge function to automatically merge multiple, registered data sets into a single polygon model.40、When performing 1-Point Registration, try picking a point near lockable features, avoiding points at the boundaries of the data set.41、Remember, you can select Unregister when your data sets don't appear close enough, then try again in a region with more overlap.42、Overlapping data is necessary for successful 1-Point Registration and Global Registration.43、When manually aligning a large number of objects, you can improve processing time and the end result by achieving a good alignment of all objects prior to running the global registration command.44、In the manual "Create Feature" command on a polygon model use triangle selection if the feature has a lip that differs from the surrounding surface area. It helps to define the plane of the feature.45、When using Datum/Feature Alignment, if a feature pair constrains your model in an incorrect way, then turn off the 'Use Feature Axis' option in the dialog to relax the constraint.46、When using Datum/Feature Alignment, if the model appears flipped after matching some feature pairs, use either the Flip Plane or Flip Axis buttons on one of the pairs to correct it.47、To check GD&T parallelism, perpendicularity, angularity or runout tolerance, align the test data to the reference object and then compare the selected set of points against the corresponding datum on the reference object with the "Evaluate GD & T" command.48、The Uniform Sampling command now provides enhanced capabilities, including determining the spacing by target point count, keeping points in high curvature areas, and retaining points along boundaries.49、You can automatically save your files at any interval of minutes that you specify. Look for the Autosave option under Tools > Options > File I/O.50、The Measure Distance function can now calculate distance along a surface, in addition to straight line distances.51、If Detect Targets fails to find some of the spheres, or detects extraneous regions as spheres, adjust the sensitivity and reapply.52. If Global Registration gives unsatisfactory results on the full set of scans, apply it independently to two or more subsets of the scans which represent parts of the model, e.g., front & back, top & bottom, etc. before applying to the whole model.53. If you are trying to align a freeform object, such as a car door, based on datums and features, try creating Datum Targets in the Create Datums command and then use the RPS Alignment command to align them.54. You can add tolerances to locations in a location set by selecting the location set in the model manager and then clicking on a cell in the tolerance columns. Type in the desired tolerance and then hit Enter.55. You can now move or delete multiple annotations from one annotation view to another. Just hold down CTRL while selecting the annotations. To clear the selection release the CTRL button and click on the background.56. When using Average Polygon Objects, the Weighted Average option will greatly reduce the effect of outliers on the shape of the final model.57. In Evaluate Callouts, if you modify the view or callout positions, the views and callout positions will be updated in the Reference model as well.58. In all GD&T callout views, you can sort the tables by any column value by clicking on the column title.59. 2D Dimensions support multiple rectangle and lasso selection regions by using Shift and Ctrl keys to add or remove new regions.60. A unique datum symbol (A, B, C, etc.) can be assigned along with datum and feature names and used for GD&T callouts.61. The Results > Export Deviations command can be used to save a CSV file of all of the reference and test points after a 3D Comparison without using location sets.62. The Multiple Sections command allows multiple parallel sections to be made from an existing 2D Comparison or 2D Dimensioning cross section.63. The Offset Points command can be used to compensate for material thickness in cases where the B-side of a sheet metal part is scanned instead of the A-side.64. The Background Grid can be enabled on the Display tile to show the position and size of the model. The 2 Panel mode allows for two panes of the background grid to be displayed in any 3D view.65. The color of a datum indicates whether or not it is supported by the automation system. A green datum can be automatically recreated; an orange datum cannot.。

1FME ® Workbench Transformers Quick-Reference Booklet1 3DThese transformers create and modify three-dimensional surface and solid geometries.1 calculatorsThese transformers calculate a value and supply it to a new attribute on a feature. 3 collEctorsThese transformers operate on collections of features at the same time. The collection of features may be replaced by new features based upon them, have their attributes or geometries merged, or have their orders altered.4 DatabasEThese transformers allow interaction with external databases. Data can be extracted from databases and merged into the feature stream or merged onto features. Arbitrary SQL statements can also be executed.5 filtErsThese transformers perform tests on feature geometry and/or attributes, and allow the feature to be routed to different destinations depending on the outcome of the test.6 gEomEtric opEratorsThese transformers operate on thegeometry of individual features or groups of features.10 infrastructurEThese transformers provide interaction with the underlying FME translation engine facilities. These include functionality to log features, set feature colors, createindividual features and grids of features from nothing, and invoke the FME Viewer on features flowing by.12 linEar rEfErEncingThese transformers work with linear referencing data structures on FME features.12 listsThese transformers operate on FME attribute lists.13 manipulatorsThese transformers modify (manipulate) the geometry or attributes of individual features in isolation from other features. 19 rastErsThese transformers create, use, and output rasters. They operate on data consisting of a regularly spaced grid of values. 22 stringsThese transformers operate on character strings held in FME attributes.23 surfacEsThese transformers create, use, and output surfaces. They operate on data thatdefines a surface through the z coordinate, and then either outputs this surface in a variety of ways or applies the surface to other data.24 WEb sErVicEsThese transformers access web services using the HTTP protocol.25 WorKfloWThese transformers run workspaces either locally or on an FME server.25 XmlThese transformers work with XML data by mapping XML elements into FME features, using stylesheets to convert XML documents, and querying collections of XML data.fmE ® Workbench transformers Quick-reference bookletThis booklet contains a high-level summary of each transformer’s functionality. For detailed information, please visit or select FME Transformers from the Workbench Help menu.2Properties buttonWhat is a transformer?A transformer is an FME Workbench object that carries out the restructuring of features. FME contains over 300 different transformers to carry out different types of restructuring. In the Workbench interface, transformers are stored in the Transformer Gallery, and grouped in categories applicable to their associated functionality.common Elements used in transformer parameter DialogsEvery transformer has a Properties button on the right of the transformer.When you click the Properties button, most transformers display an Edit Parameters dialog. The content of this dialog depends on the transformer, and sometimes even on connections to the transformer. Most transformers have some common user interface elements, however, and those are described here.The Properties button at the top-right of the transformer is color-coded to show the status of the settings. If the Properties button is the same color as the transformer, you can use the transformer with its existing parameters.A yellow Properties button indicates that the transformer contains default settings, but you have not yet accepted them. You can use the transformer in this state, but the workspace results may be unpredictable.A red Properties button means that there is at least one parameter for which FME cannot supply a default value. You must provide a value in the required field(s) before the transformer can be used.When you click a Properties button, the Edit Parameters dialog that appears will usuallyhave some of the common elements shown in this example.You can edit the default transformer name.Required fields are highlighted. If this field is not filled in, the OK button at the bottom of the dialog is disabled.Click OK to accept changes and close the dialog. Note that this button is disabled if required fields have not been populated.The Defaults menu allows you to replace FME defaults for thistransformer with your own parameter defaults. You can always reset the dialog to FME defaults.Click this Help button to open the FME Workbench Transformer helptopic.Replaces the geometry of a feature that has CSG.Creates long, surface or solidgeometries with a fixed cross-sectional profile taken from theoriginal geometry of the feature.Replaces the geometry of a feature from donut or polygon to face.These transformers calculate a value and supply it to a new attribute on a feature.1 FME® Workbench Transformers Quick-Reference BookletConverts an attribute’s value from one numeric system (base) to another,Extracts the minimum and maximum values of the feature’s coordinatesinto new attributes.2Combines feature attributes.Creates bounding boxes for groups of features. One bounding box feature3 FME® Workbench Transformers Quick-Reference BookletDecomposes an aggregate feature into its components.Stores incoming features until they have all arrived and then releasesthem in their original order.Merges the attributes of one feature onto another feature.Finds the closest two CANDIDATE features within some maximum distanceof each BASE feature and some minimum separation in heading between 4Removes duplicate features based on the value of a key attribute.Separates the features routed to it into their original feature types, ifDiscards input features, preserving only every <sample rate>th feature.5 FME® Workbench Transformers Quick-Reference BookletEvaluates one or more FME-style tests on a feature, and routes the featureaccording to the outcome of the tests.These transformers operate on the geometry of individual features or groups ofPerforms warping operations on the spatial coordinates of features. Itis used to adjust a set of observed features so they more closely matchSnaps endpoints of features entering through the CANDIDATE port toendpoints of features entering through the ANCHOR port. ANCHORPerforms a geometric clipping operation.6Builds connections between donut holes with the outer boundary ofa donut, resulting in a polygon-equivalent representation of the input donut.Cuts holes in polygonal features by making polygons completely enclosedSplits an area feature that has holes into its component rings.Interpolates labels along a linear or polygonal feature.7 FME® Workbench Transformers Quick-Reference BookletPerforms a line-on-area overlay.Performs a line-on-line overlay.Takes features as input and processes them based on the specifiedEach point receives the attributes of the area(s) it is contained in, andeach containing area receives the attributes of each point it contains. 8Performs warping operations on the spatial coordinates of features.Checks each feature and removes self-intersections.Snaps end points of lines together if they are within the <tolerance>distance of each other.Cleans up feature geometries by removing spikes in two dimensions.9 FME® Workbench Transformers Quick-Reference BookletComputes topology on input point, line, and/or area features.Breaks an input geometry into triangular units.1011FME ®Workbench Transformers Quick-Reference Booklet12Replaces the geometry of the feature with a two-dimensional box whoseminimums and maximums are fixed values or are taken from attributes inReplaces the feature geometry with a two-dimensional ellipse whoseRemoves any elevation z coordinates that may or may not have beenAdds a two-dimensional point as the last vertex of the feature. Thecoordinates are taken from attributes in the original feature.Replaces the feature’s geometry with a two-dimensional point whosecoordinates are taken from attributes in the original feature.Performs 3D affine transformation on the coordinates of the feature. Thetransformation results in the x and y coordinates being modified as follows:x’ = Ax + By + Cz + Dy’ = Ex + Fy + Gz + H13 FME® Workbench Transformers Quick-Reference BookletPerforms an affine transformation on the feature’s coordinates.Converts angles of a feature’s geometry and/or attributes from oneSets the given attributes to the properties of an arc geometry.Sets the properties of an arc geometry to those specified.Simulates the ArcSDE conversion on a feature by performing ArcSDEtranslation, scaling, and coordinate snapping.Removes all attributes on incoming features that match a given regularRemoves all attributes from the feature, except those chosen in the list.Adds a prefix or suffix to all attributes coming into the transformer.Removes the attributes chosen from the feature. This is not normallynecessary unless the feature will later be processed by a transformer thatmerges attributes onto it from other features.14Replaces the geometry of an area feature with a line that threads throughthe center of the feature. Works best with long, thin features.Replaces the feature’s geometry with a point that is the feature center ofgravity. The center of gravity is the average x, y, and possibly z coordinateReplaces the feature’s geometry with a point that is in the center of thefeature’s bounding box.Ensures that all features output have less than or equal to <maximumvertices> vertices.15 FME® Workbench Transformers Quick-Reference BookletRemoves one or more coordinates from the geometry of the feature.Rounds off the feature’s coordinates to the specified number of decimalConverts coordinate system strings between representations.Adds vertices to the feature by interpolating new coordinates along itsdefinition at some interval of distance.16Provides two types of algorithms: Smoothing and Generalizing. Thesmoothing algorithms determine a new location for each vertex. ThePerforms the following refinements on the feature’s geometry:- Any homogeneous IFMEAggregate will become a multi(IFMEMultiCurve, IFMEMultiArea, IFMEMultiPoint, or IFMEMultiText).- Any IFMEAggregate or multi with only one member is replaced by itssingle part.- Any IFMEDonut with no holes becomes an IFMEPolygon or IFMEEllipse.- Any IFMEPath with only one segment is replaced by that segment.- Consecutive IFMELine segments within an IFMEPath are combined.17 FME® Workbench Transformers Quick-Reference BookletCalculates a Military Grid Reference System (MGRS) code based on the Calculates a Military Grid Reference System (MGRS) code based on the feature’s geometry.Rotates features in a counterclockwise direction about the specified point by the rotation angle measured in degrees.Calls the specified FME Function, optionally putting the resulting value in the Result Attribute. This is a safe way to run FME functions as they areBuilds and queries surfaces, drapes features or changes the surface representation between DEM, TIN, and CONTOURS.Point features are input with the following data contained in the chosenattributes: site name, sector name, azimuth, and radius. Within pointshaving the same site name, points have their geometry changed topolygons approximating sector shapes.Generates a Voronoi diagram or Thiessen polygon from the input POINTS. These transformers access web services using the HTTP protocol.2D2DArcReplacer (Manipulators category), 132DBoxReplacer (Manipulators category), 132DEllipseReplacer (Manipulators category), 132DForcer (Manipulators category), 132DGridCreator (Infrastructure category), 102DGridReplacer (Collectors category), 32DPointAdder (Manipulators category), 132DPointReplacer (Manipulators category), 133D3DAffiner (Manipulators category), 133DArcReplacer (Manipulators category), 133DForcer (Manipulators category), 133DInterpolator (Manipulators category), 133DPointAdder (Manipulators category), 143DPointReplacer (Manipulators category), 14AAffiner (Manipulators category), 14 AffineWarper (Geometric Operators category), 6 AggregateFilter (Filters category), 5Aggregator (Collectors category), 3 AnchoredSnapper (Geometric Operators category), 6 AngleConverter (Manipulators category), 14 ArcEstimator (Manipulators category), 14 ArcPropertyExtractor (Manipulators category), 14 ArcPropertySetter (Manipulators category), 14 ArcSDEGridSnapper (Manipulators category), 14 ArcSDEQuerier (Database category), 4 ArcStroker (Manipulators category), 14 AreaBuilder (Geometric Operators category), 6 AreaCalculator (Calculators category), 1 AreaFillColorSetter (Infrastructure category), 10 AreaOnAreaOverlayer (Geometric Operators category), 6 AttributeAccumulator (Collectors category), 3 AttributeClassifier (Strings category), 22 AttributeCopier (Infrastructure category), 10 AttributeCreator (Infrastructure category), 10 AttributeDereferencer (Infrastructure category), 10 AttributeExploder (Lists category), 12 AttributeExposer (Infrastructure category), 10AttributeExpressionRemover (Manipulators category), 14 AttributeFileReader (Infrastructure category), 10 AttributeFileWriter (Infrastructure category), 10 AttributeFilter (Filters category), 5 AttributeKeeper (Manipulators category), 14 AttributePrefixer (Manipulators category), 14 AttributeRemover (Manipulators category), 14 AttributeRenamer (Infrastructure category), 10 AttributeReprojector (Manipulators category), 14 AttributeRounder (Calculators category), 2 AttributeSetter (Infrastructure category), 10 AttributeSplitter (Strings category), 22 AttributeTrimmer (Strings category), 22BBaseConverter (Calculators category), 2 BoundingBoxAccumulator (Collectors category), 3 BoundingBoxReplacer (Manipulators category), 14 BoundsExtractor (Calculators category), 2 Bufferer (Manipulators category), 15CCaseChanger (Strings category), 22 CenterLineReplacer (Manipulators category), 15 CenterOfGravityReplacer (Manipulators category), 15 CenterPointReplacer (Manipulators category), 15 ChangeDetector (Filters category), 5 CharacterCodeExtractor (Strings category), 22 CharacterEncoder (Strings category), 22Chopper (Manipulators category), 15 CircularityCalculator (Calculators category), 2 Clipper (Geometric Operators category), 6Cloner (Infrastructure category), 10 CommonSegmentFinder (Collectors category), 4 Concatenator (Strings category), 22 ContourGenerator (Surfaces category), 23 ConvexHullAccumulator (Collectors category), 4 ConvexHullReplacer (Manipulators category), 16 CoordinateConcatenator (Calculators category), 2 CoordinateCounter (Calculators category), 2 CoordinateFetcher (Calculators category), 2 CoordinateRemover (Manipulators category), 16CoordinateRounder (Manipulators category), 16 CoordinateSystemDescriptionConverter(Manipulators category), 16 CoordinateSystemFetcher (Manipulators category), 16 CoordinateSystemRemover (Manipulators category), 16 CoordinateSystemSetter (Manipulators category), 16 Counter (Calculators category), 2 CRCCalculator (Calculators category), 2Creator (Infrastructure category), 10 CSGBuilder (3D category), 1CSGEvaluator (3D category), 1Curvefitter (Manipulators category), 16DDateFormatter (Calculators category), 2 Deaggregator (Collectors category), 4 Decelerator ( Web Services category), 24 DecimalDegreesCalculator (Calculators category), 2 DEMDistanceCalculator (Calculators category), 2 DEMGenerator (Surfaces category), 23Densifier (Manipulators category), 16 DimensionExtractor (Calculators category), 2 Dissolver (Geometric Operators category), 7 DistanceSnipper (Linear Referencing category), 12 DMSCalculator (Calculators category), 2 DonutBridgeBuilder (Geometric Operators category), 7 DonutBuilder (Geometric Operators category), 7 DonutHoleExtractor (Geometric Operators category), 7 DuplicateCoordinateRemover (Manipulators category), 17 DuplicateRemover (Filters category), 5EElevationExtractor (Calculators category), 2 EllipsePropertyExtractor (Manipulators category), 17 EllipsePropertySetter (Manipulators category), 17 EnvironmentVariableRetriever (Calculators category), 2 ESRIReprojector (Manipulators category), 17 ExpressionEvaluator (Calculators category), 2 Extender (Manipulators category), 17Extruder (3D category), 1FFaceReplacer (3D category), 1FeatureHolder (Collectors category), 4 FeatureMerger (Collectors category), 4 FeatureTypeExtractor (Infrastructure category), 11 FeatureTypeFilter (Filters category), 5 FMEFunctionCaller (Strings category), 22GGeneralizer (Manipulators category), 17 GeometryCoercer (Manipulators category), 17 GeometryExtractor (Manipulators category), 17 GeometryFilter (Filters category), 5 GeometryOGCValidator (Filters category), 5 GeometryRefiner (Manipulators category), 17 GeometryRemover (Manipulators category), 17 GeometryReplacer (Manipulators category), 18 GeometryTraitFetcher (Manipulators category), 18 GeometryTraitRemover (Manipulators category), 18 GeometryTraitSetter (Manipulators category), 18 GeoRSSFeatureExtractor ( Web Services category), 24 GeoRSSFeatureReplacer ( Web Services category), 24 GMLFeatureExtractor (Manipulators category), 18 GMLFeatureReplacer (Manipulators category), 18 GOIDGenerator (Strings category), 22 GridInQuestReprojector (Manipulators category), 18 GtransAttributeReprojector (Manipulators category), 18 GtransReprojector (Manipulators category), 18HHexDecoder (Strings category), 22 HexEncoder (Strings category), 22 HoleCounter (Calculators category), 2 HTTPDeleter ( Web Services category), 24 HTTPFetcher ( Web Services category), 24 HTTPFileUploader ( Web Services category), 24 HTTPUploader ( Web Services category), 24IImageFetcher ( Web Services category), 24 ImageRasterizer (Rasters category), 19 InsidePointExtractor (Calculators category), 2 InsidePointReplacer (Manipulators category), 18 Intersector (Geometric Operators category), 7JJoiner (Database category), 4JSONExploder ( Web Services category), 24 JSONExtractor ( Web Services category), 24KKMLStyler ( Web Services category), 25LLabeller (Geometric Operators category), 7 LabelPointReplacer (Manipulators category), 18 LatLongToMGRSConverter (Manipulators category), 18 LengthCalculator (Calculators category), 3 LengthToPointCalculator (Linear Referencing category), 12 LineCloser (Manipulators category), 18 LineJoiner (Geometric Operators category), 8 LineOnAreaOverlayer (Geometric Operators category), 8 LineOnLineOverlayer (Geometric Operators category), 8 ListBuilder (Lists category), 12 ListConcatenator (Lists category), 12ListCopier (Lists category), 12 ListDuplicateRemover (Lists category), 12 ListElementCounter (Lists category), 12 ListExploder (Lists category), 12 ListHistogrammer (Lists category), 12ListIndexer (Lists category), 12ListPopulator (Lists category), 12 ListRangeExtractor (Lists category), 12 ListRemover (Lists category), 12ListRenamer (Lists category), 12ListSearcher (Lists category), 13ListSorter (Lists category), 13ListSummer (Lists category), 13Logger (Infrastructure category), 11MMatcher (Filters category), 5 MeasureExtractor (Linear Referencing category), 12 MeasureGenerator (Linear Referencing category), 12 MeasureSetter (Linear Referencing category), 12 MGRSGeometryExtractor (Manipulators category), 18 MGRSGeometryReplacer (Manipulators category), 18MGRSToLatLongConverter (Manipulators category), 18 MinimumSpanningCircleReplacer(Manipulators category), 18 ModuloCounter (Calculators category), 3 MRFCleaner 2D and 3D(Geometric Operators category), 8NNeighborColorSetter (Geometric Operators category), 8 NeighborFinder (Collectors category), 4 NeighborhoodAggregator (Collectors category), 4 NeighborPairFinder (Collectors category), 4 NullAttributeReplacer (Strings category), 22 NumericRasterizer (Rasters category), 20OOffsetter (Manipulators category), 19 OracleQuerier (Database category), 4 OrientationExtractor (Calculators category), 3 Orientor (Manipulators category), 19PParameterFetcher (Infrastructure category), 11 PartCounter (Manipulators category), 19 PathBuilder (Geometric Operators category), 8 PathSplitter (Manipulators category), 19 PenColorSetter (Infrastructure category), 11Player (Infrastructure category), 11 PointConnector (Geometric Operators category), 8 PointOnAreaOverlayer (Geometric Operators category), 8 PointOnLineOverlayer (Geometric Operators category), 8 PointOnPointOverlayer (Geometric Operators category), 8 PointOnRasterValueExtractor (Rasters category), 20 PolygonBuilder (Geometric Operators category), 9 PythonCaller (Infrastructure category), 11 PythonCreator (Infrastructure category), 11RRandomColorSetter (Infrastructure category), 11 RandomNumberGenerator (Calculators category), 3 RasterBandAdder (Rasters category), 20 RasterBandCombiner (Rasters category), 20 RasterBandInterpretationCoercer (Rasters category), 2028RasterBandKeeper (Rasters category), 20 RasterBandMinMaxExtractor (Rasters category), 20 RasterBandNodataSetter (Rasters category), 20 RasterBandOrderer (Rasters category), 20 RasterBandPropertiesExtractor (Rasters category), 20 RasterBandRemover (Rasters category), 20 RasterBandSeparator (Rasters category), 20 RasterCellCoercer (Rasters category), 20 RasterCellOriginSetter (Rasters category), 20 RasterCellValueReplacer (Rasters category), 20 RasterCheckpointer (Rasters category), 20 RasterConsumer (Rasters category), 20 RasterDEMGenerator (Surfaces category), 23 RasterExpressionEvaluator (Rasters category), 20 RasterExtractor (Rasters category), 20 RasterGCPExtractor (Rasters category), 20 RasterGCPSetter (Rasters category), 20 RasterGeoreferencer (Rasters category), 20 RasterInterpretationCoercer (Rasters category), 21 RasterMosaicker (Rasters category), 21 RasterNodataRemover (Rasters category), 21 RasterNumericCreator (Rasters category), 21 RasterPaletteGenerator (Rasters category), 21 RasterPaletteInterpretationCoercer (Rasters category), 21 RasterPaletteNodataSetter (Rasters category), 21 RasterPaletteRemover (Rasters category), 21 RasterPaletteResolver (Rasters category), 21 RasterPropertiesExtractor (Rasters category), 21 RasterPyramider (Rasters category), 21 RasterReader (Rasters category), 21 RasterReplacer (Rasters category), 21 RasterResampler (Rasters category), 21 RasterRGBCreator (Rasters category), 21 RasterRotationApplier (Rasters category), 21 RasterSelector (Rasters category), 21 RasterSubsetter (Rasters category), 21 RasterTiler (Rasters category), 21Recorder (Infrastructure category), 11 ReprojectAngleCalculator (Calculators category), 3 ReprojectLengthCalculator (Calculators category), 3 Reprojector (Manipulators category), 19Rotator (Manipulators category), 19RubberSheeter (Geometric Operators category), 9SSampler (Filters category), 5Scaler (Manipulators category), 19 SchemaMapper (Database category), 5 SecondOrderConformer (Manipulators category), 19 SectorGenerator (Surfaces category), 23 SelfIntersector (Geometric Operators category), 9 ServerJobSubmitter (Workflow category), 25 Snapper (Geometric Operators category), 9Sorter (Collectors category), 4SpatialFilter (Filters category), 6SpatialRelator (Calculators category), 3 SpikeRemover (Geometric Operators category), 9 SQLExecutor (Database category), 5 StatisticsCalculator (Calculators category), 3 StringFormatter (Strings category), 22 StringLengthCalculator (Strings category), 22 StringPadder (Strings category), 22 StringPairReplacer (Strings category), 22 StringReplacer (Strings category), 22 StringSearcher (Strings category), 22 SubstringExtractor (Strings category), 22 SummaryReporter (Infrastructure category), 11 SurfaceDraper (Surfaces category), 23 SurfaceModeller (Surfaces category), 23 SystemCaller (Infrastructure category), 11TTCLCaller (Infrastructure category), 11 Terminator (Infrastructure category), 11Tester (Filters category), 6TextAdder (Manipulators category), 19 TextLocationExtractor (Manipulators category), 19 TextPropertyExtractor (Manipulators category), 19 TextPropertySetter (Manipulators category), 19 TextStroker (Manipulators category), 19Tiler (Geometric Operators category), 10 TimeStamper (Strings category), 23 TINGenerator (Surfaces category), 24 TopologyBuilder (Geometric Operators category), 1029FME® Workbench Transformers Quick-Reference BookletTransporterReceiver (Infrastructure category), 11 TransporterSender (Infrastructure 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New Method of Water Purification Based on the Particle-Exclusion PhenomenonI V A N K L Y U Z H I N,A N D R E W S Y M O N D S,†J E F F R E Y M A G U L A,A N DG E R A L D H.P O L L A C K*Department of Bioengineering,Box355061,University of Washington,Seattle,Washington98195Received December17,2007.Revised manuscript received April29,2008.Accepted May7,2008.Colloidal particles in suspension are excluded from the vicinity of various hydrophilic surfaces.On the basis of this phenomenon,a novel method of water purification is proposed and tested.Proof-of-concept is demonstrated using a custom-made extractor that collected clean water from the annular “exclusion zone”within a Nafion tube.Up to99.6%of particles could be removed from the suspension.The experimental results suggest that particle exclusion may provide a new framework for water purification from both organic and inorganic matter,as well as from harmful pathogens.IntroductionRecent studies have shown unexpected particle behavior next to various hydrophilic surfaces(1–3).Particles,such as microspheres,migrate away from these surfaces,leaving unexpectedly large regions of particle-free water(Figure1). At equilibrium,these regions may be as large as several hundred micrometers,and their physical properties differ from those of bulk water.These interfacial areas have been termed“exclusion zones”because of their distinctive ability to exclude particles and solutes.Exclusion zones had in fact been noted as early as1970,when microspheres were shown to be excluded from the vicinity of certain biological tissues (4).More recently,extensive studies have shown that the exclusion phenomenon is quite general,both in biological and non-biological systems(1,2).The phenomenon of exclusion provides a new basis for water purification.With a large enough exclusion zone next to the exclusion-generating surface,clean water can be easily collected,leaving behind particle-containing and solute-containing water.We chose Nafion as the excluding surface. Nafion is a perfluorosulfonic ionomer that consists of a polytetrafluoroethylene backbone and regularly spaced side chains terminated by sulfonate ionic groups(5).Previous studies have demonstrated that Nafion has negative charge in deionized water,with a surface electrical potential of-160 mV(2).The advantages of using Nafion as the excluding surface are its relatively large exclusion zone and its com-mercially availability in convenient tubular shape.We developed a system in which water could be drawn continu-ously along the tube’s annular exclusion zone and extracted at the end of the tube,with promising levels of separation of both artificial and natural water-borne particles. Materials and MethodsThe purification process employed a Nafion tube.With a pressure gradient imposed along the tube,suspensions could be forced toflow inside.An annular exclusion zone developed with distance along the tube(Figure2).By drawing water from the annular zone using an extractor at the end,virtually particle-free water could be obtained.Flow Chamber.To observe whether various particle types were excluded from the zones next to the Nafion surface, both in static conditions and duringflow,the experimental chamber illustrated schematically in Figure2was used.A 5-mm-thick transparent plastic sheet with window cut out was set on a glass plate.A3-mm hole was drilled on either end of the sheet,allowing the Nafion tube(O.D.2.5mm, TT-110,Perma Pure LLC,NJ)to traverse the chamber.The chamber wasfilled with distilled,deionized water and sealed with a second glass plate.The tube was connected via Tygon tubing to a container on the input end and to a syringe pump (YA-12,Yale Apparatus)on the output end.The pump worked in the withdraw mode,diminishing the pressure and forcing thefluid suspension toflow through the tube.To observe particle behavior near the Nafion surface in static situations,the syringe pump was engaged until the tube was primed;then,after5to10min,the equilibration time required to ensure that the exclusion zone was fully formed,the near-surface regions were examined.To observe particle behavior duringflow,the syringe pump was set to operate at a constant rate.Once theflow was established, the interfacial region within the Nafion tube was examined in an inverted microscope(Diaphot,Nikon)equipped with a5×objective lens.Images were acquired and analyzed using a digital CMOS camera(DFC290,Leica).Images were also taken occasionally using a digital camera(EasyShare P880, Kodak)through an eyepiece of the microscope.Observations of bacterial and viral suspensions were made in a biosafe laboratory,where high magnification objectives (20×or higher)were the only ones available for use.The short focal distances prompted the use of thinner Nafion tubes(TT-030,ID0.64mm,Perma Pure)that werefixed between a microscope slide and a coverslip.The Nafion tube was superfused with the bacterial suspension and observed under an upright microscope(Axioskop,Zeiss).Bacteria were imaged close to the Nafion tube under both brightfield and fluorescent illumination.Adenoviruses were also studied and imaged via a laser scanning confocal microscope(Leica SP-1,Keck Imaging Center at University of Washington).Because they were small(cylindrical,80nm long)and could not therefore be resolved with light microscopy,the viruses were fluorescently labeled so that the exclusion zone would appear as afluorescence“void”next to the surface of the Nafion tube.Differential Extractor and Separation.The experimental setup used for the separation experiments is shown in Figure 3.A custom-made“differential extractor”was employed to separate exclusion zone water and bulk solution.The extractor was made of two concentric stainless steel tubes of different diameter held together by low temperature silver solder.The Nafion tube clasped the extractor’s outer tube. The extractor’s inner tube extended out0.5mm into the Nafion tube,which made it possible to visualize the purification process under the microscope.The inner and outer channels of the extractor led to separate outputs,each connected to a syringe pumps via Tygon tubing.*Corresponding author phone:(206)685-1880;fax:(206)685-3300;e-mail:ghp@.†Current address:MRC Centre for Developmental Neurobiology,King’s College London,Strand,London WC2R2LS,England,U.K.Environ.Sci.Technol.2008,42,6160–616661609ENVIRONMENTAL SCIENCE&TECHNOLOGY/VOL.42,NO.16,200810.1021/es703159q CCC:$40.75 2008American Chemical SocietyPublished on Web07/11/2008The pumps generated reduced pressures inside the extractor’s inner and outer channels,forcing the suspension to flow.When the suspension reached the extractor’s interface,the contents of the tube’s core was sucked into the inner channel,while the annular water was sucked into the outer channel (Figure 3).Thus,the solution near the Nafion surface was separated from the core solution.Suspension Preparation.To test the method’s effective-ness,particle suspensions of varied composition were prepared.They included topsoil,clay soil,silt,bacteria,viruses,and microspheres.Turbidity,expressed in NTUs (nephelometric turbidity units)was used as a measure of particle concentration.This approach is commonly used forthat purpose (6–9).Turbidity was measured using a turbi-dimeter (2020i,LaMotte,MD).The instrument was calibrated using 0.5,10,and 100NTU standards (Amco Clear,GFS Chemicals,OH).Although turbidity of river and lake waters can reach hundreds of NTUs during rains and floods,typical values lie within 1-20NTU (7,8),well within the range of calibration.The suspensions of topsoil,clay soil,and silt were prepared by mixing the soil samples (Ward’s Natural Science,Rochester NY)with deionized water in a commercial blender (51BL32,Waring,New Hartford,CT).After they were mixed,the suspensions were filtered through a paper filter with 8-to 12-µm pore size (Sharkskin General-Purpose filter paper,Whatman).This procedure removed the larger particles that would ordinarily settle out inside the Nafion tube.The turbidity of the filtered solutions lay within a 100-300NTU range,and this required further dilution for experiments.Dilution yielded input suspensions with turbidities 5,20,and 100NTU.To supplement the studies of natural particles,carboxy-late-coated 3-µm latex microspheres (Polybead,Polysciences Inc.;coefficient of variance,5%)were used as synthetic test particles.Concentrated stock suspensions (1.68×1012particles/L)were diluted with distilled,deionized water.For the experiments that employed flow,the stock solution was diluted to yield 5,20,and 100NTU suspensions.Water for the experiments (Type 1,HPLC grade,18.2ΜΩ)was obtained from a standard water purification system (Diamond TII,Barnstead).Because of their hazardous nature,bacterial and viral suspensions were observed under static conditions only,near the surface of the Nafion tube.No flow experiments were carried out.Two gram-negative bacterial species were studied,Escherichia coli and Nitrousomonus europea .E.coli were cultured overnight at 37°C in liquid broth media.N.europea were grown in special media at room temperature until fully grown.Cells were spun down and washed three times in 10%glycerol solution to remove salt,which has been shown to reduce the size of exclusion zones (3).The washed bacteria were then diluted 1:1with sterile deionized water,giving a final concentration of approximately 5×108particles/mL.Some bacterial preparations wereincubatedFIGURE 1.Example of development of exclusion zone (EZ)near the edge of Nafion film.An aqueous microsphere suspension was injected between two microscope slides with a flat Nafion film squeezed between.Following injection,the microspheres migrated away from the edges of the Nafion film,leaving a region of particle-free water.Carboxylate-coated 3-µm microspheres were used.Images were acquired with an invertedmicroscope.FIGURE 2.Experimental chamber used for exclusion-zone observations,not to scale.A motor pulled on the syringe plunger at a constant,controllable rate.Particles condensed in the tube’s core,as shown schematically.For exclusion-zone observations in static situations,the syringe motor could be stopped.Observation point marked with dashedcircle.FIGURE 3.Experimental setup used for water purification experiments,not to scale.Syringe pumps (not shown)generated flow through Nafion tube and channels of differential extractor.Arrows denote direction of flow.VOL.42,NO.16,2008/ENVIRONMENTAL SCIENCE &TECHNOLOGY96161with a fluorescent cell-viability marker SYTO-9(Molecular Probes)for 15min.Viral particles were obtained from the University of Washington Molecular Genetics Laboratory.The preparation used was an aerosol adenovirus of rare serotype,usually seen in patients with compromised immune systems.Viral particles were labeled with Cy3dye by dialysis and then frozen in 0.5mL aliquots at -80°C for storage.Once the virus preparation was thawed on ice,it was dialyzed against 500mL sterile deionized water for 3.5h to remove the salt from the virus particle buffer (initially 150mM NaCl).For the preparation used in these experiments,the stock concentra-tion was 1.4×1012viral particles/mL.This was diluted 3:2with deionized water,giving a working concentration of 8.4×1011viral particles/mL.ResultsSolute Exclusion.To determine if topsoil particles,clay soil,and silt are excluded,the Nafion tube was primed with the respective suspension at 100NTU and observed as described in Figure 2.Exclusion zones were seen with all suspensions (Figure 4).Their size at equilibrium depended on suspension type.For clay particles,the size (∼170µm)was generally larger than that of topsoil and silt particles (∼120µm).By comparison,the exclusion zone of 3-µm carboxylate mi-crospheres under the same conditions was greater than 300µm.Soil-exclusion zones were also more ambiguously defined than microsphere-exclusion zones,that is,their termination boundaries were less sharp.Exclusion zones were also seen with bacterial particles.Both bacterial species (N.europea and E.coli )were excluded.An example is shown in Figure 5.The exclusion zone was revealed by a fluorescence gap.Viral suspensions revealed a different kind of behavior.After the viral suspension was superfused around the Nafion tube,“clusters”were observed which were much larger than the individual particles (Figure 6).These fluorescent clusters,2-5µm in diameter,were absent from a region approximately 150-µm wide.They were also adsorbed onto the Nafion tube’s outer wall,possibly as a result of immediate binding to the Nafion upon infusion.Whether or not individual viral particles might be present within the cluster-exclusion zone remains uncertain.Flow Observations.To study particle exclusion during flow,the experimental chamber illustrated in Figure 2wasmodified so that Nafion tubing of different i.d.’s (2.2,1.6and 1.2mm)could be employed.The exclusion zone inside the tube was measured at midlength along the tube and studied at different flow rates.Starting from 5mL/h,the flow rate was increased in 5mL/h increments to 50mL/h.AteachFIGURE 4.Exclusion zones within static colloidal suspensions.Photographs were taken with a 5×objective 5min afterpriming.FIGURE 5.Exclusion of E.coli inside and outside the Nafiontube.FIGURE 6.Medium of viral particles near Nafion surface.Observed fluorescent clusters were absent in the zone next to Nafion (EZ).Some clusters attached to the Nafion surface.61629ENVIRONMENTAL SCIENCE &TECHNOLOGY /VOL.42,NO.16,2008flow rate,approximately five minutes were allowed for the exclusion zone to come to steady state,for measurement.An example showing the development of the steady state is presented in Figure 7.Along the length of the Nafion tube,the exclusion zone was not uniform.At the tube’s entry,particles were evenly distributed over the full cross-section.As particles moved through the tube during steady flow,they were progressively excluded from the vicinity of the wall,both with distance and time.At a flow rate of 15mL/hr,for example,the exclusion zone reached its steady-state size at a distance of 1-2mm.At that position and flow rate,the exclusion-zone size was smaller than in the static condition (see Figure 7).When the flow rate was increased,the exclusion-zone size diminished.This dependence,for each of several tube diameters,is shown in Figure 8.Note that the tube with the largest i.d.showed the largest exclusion zones.When solutions of topsoil,clay soil,or silt were pumped through the Nafion tube,sediment formed.The sedimented particles accumulated progressively on the bottom of the tube in a thin layer.In general,sediment was heavier toward the tube’s distal end,although the amounts were not quantified.Sediment formation did not obscure the flow through the tube.It is apparent from Figure 8that lower flow rates yielded larger exclusion zones.However,lower flow rates also brought lower overall water-collection rates.As a compromise,an intermediate flow rate of 15mL/h was selected for the separation experiments,below.At this flow rate,the linear velocity at the centerline was 1.91(0.06mm/s.Pure-Water Extraction.Extraction experiments were carried out according to the setup shown in Figure 3.When particles reached the differential extractor,the exclusion zone was fully formed (Figure 9).The differential extractor separated the suspension into core and annular fractions (c.f.,Figure 3).The latter fraction contained relatively purified water.We define R as the ratio of turbidity in the collected purified suspension to that in the input suspension.Lower R values mean better purification.It was more convenient to express results in terms of 1-R ,which we define as purification efficacy.Higher values imply higher efficacy.Purified-water yield,on the other hand,depends on how fast water within the exclusion zone is delivered to the differential extractor.Both yield and efficacy are increased with larger exclusion zones.To determine efficacy and yield at various levels of contamination,the turbidities of the input suspensions were varied.Suspensions of topsoil,clay soil,silt,and microspheres were used.The inner channel intake rate was kept at 13mL/h,and the outer channel intake rate was 2mL/h.Together,this created a 15mL/h flow through the Nafion tube.Thus,for every 15mL of input suspension,2mL of purified annular fraction were extracted.Sample collection continued for two hours,yielding 4mL of exclusion-zone water.Because the minimum amount of solution required for turbidity mea-surement was 10mL,the collected annular fractions were diluted with 6mL of deionized water.After the turbidity was measured,the result was multiplied by 2.5to take into account the dilution.The results are presented in Table 1.The purification efficacy depended on suspension type.The highest was achieved with the microspheres.With 100NTU input suspension,99.6%efficacy was achieved.For the input suspensions of lower turbidity (20and 5NTU),efficacy was 98%.Results obtained with the soil suspensions showed the opposite tendency:higher initial particle concentrations resulted in lower efficacy.Approximately 70-90%of particles were removed.Overall,the microsphere suspensions were purified with greater efficacy than the soil suspensions.To determine how efficacy varied with annular flow rate,the ratio of outer/inner intake rate ratio was varied,without changing either input turbidity (20NTU)or overall flow rate (15mL/h).The differential extractor separated an annular layer from the solution in the core.The width of the annular layer collected depended on the outer-channel intake rate:higher intake rates tended to suck water closer to the core,which was “dirtier”.Thus,with lower outer-channel intake rate,cleaner water should be collectible.To test this premise,the outer/inner channel flow ratio was changed in five steps,from 14/1to 7/8mL/hr,and the turbidities were measured.Changing the ratio did not affect the size of exclusion zone because the flow rate was maintained constant.The results are presented in Table 2.With all suspensions,purification efficacy decreased as the intake rate through the outer channel was increased.Values of purification efficacy were always highest for the microsphere suspensions.However,with the 1mL/h intake rate,topsoil and clay results were similar to that of microspheres.In general,reductionFIGURE 7.Development of exclusion zone during flow at a fixed observation point.Flow rate of 15mL/h was used.A steady state was reached after approximately 60s.Right:microsphere exclusion in staticsituation.FIGURE 8.Effect of flow rate on exclusion-zone size.VOL.42,NO.16,2008/ENVIRONMENTAL SCIENCE &TECHNOLOGY96163of the intake rate through the outer channel resulted in cleaner water.This was observed for all particle types.Results varied somewhat among experiments.For ex-ample,the conditions in the second data column of Table 2(2mL/h)and the second data row of Table 1(20NTU)are similar:both represent collection rates of 2mL/h at 20NTU.Yet the results varied somewhat.Variation was typically on the order of 10-20%.Tables 1and 2show the best results among those achieved under nearly similar conditions,typically among five trials.The deviations were mainly the result of technical deficits,such as slightly noncircular tubular cross-section or off-center collector position,and because the goal was to test proof-of-principle,the data presented in the tables report the best results achieved,rather than the means.In the absence of the noted technical deficits,it is estimated that the best results would have been achieved with more consistency.DiscussionSolutes are excluded from an unexpectedly large zone next to many hydrophilic surfaces (1–4).On the basis of this phenomenon,we constructed a device that separates variousparticulates from water and collects the purified fraction.Representative particulates commonly found in water were effectively removed,without the need for a fine physical filter.The scientific basis of this phenomenon is under intense study.Exclusion of particles and solutes from zones spanning hundreds of micrometers from surfaces is not expected from conventional theory,although some aspects such as double-layer and osmotic phenomena may play a role.The bulk of evidence suggests that a major player is a long-range reorganization of water molecules in the vicinity of hydro-philic surfaces,including Nafion,the reorganized,or struc-tured “phase”of water excluding particles and solutes (2).A presentation of the evidence and implications is available at /programs/displayevent.aspx?rID )22222,the link to the 2007/2008University of Washington Annual Lectureship Award,where this phenomenon is featured.Exclusion of Water-Borne Particles.The experiments incorporated various soil suspensions and biological particles.The fact that they were excluded from the region next to Nafion adds to the growing list of particles and solutes confirmed to be excluded from the zone next to hydrophilic surfaces (1–4).Soil suspensions had smaller exclusion zones than mi-crospheres (Figure 4).This difference may result from two factors.One is particle-size distribution.The exclusion-zone size is larger for larger particles (1).Soil suspensions,after having passed through a 12-µm filter,contained an array of smaller particle sizes,including those smaller than the 3-µm microsphere size used here.The presence of these smaller particles may explain the relatively smaller exclusion zones.Another reason for the relatively smaller zones may be the presence of dissolved substances.Soils usually contain salts and other molecular compounds such as proteins,peptides,and polysaccharides (10),which are known to cause dimi-nution of exclusion-zone size (3).We found also that the boundaries of the exclusion zone were less sharp for soil than for microspheres (Figure 4).This fuzziness also may arise from the soil’s particle-size diversity.For the 3-µm carboxylate microspheres,by contrast,the standard deviation of size was only 0.112µm,generating a very distinct border (Figure 4).Exclusion zones observed for bacterial particles and viral clusters imply that a disinfection device may be possible.Currently,bacterial particles are filtered out by membranes or filters,and the residual organisms are deactivated by various disinfectants such as chlorine,ozone,or UV (11,12).If bacterial particles are separable in a same manner as soil particles,then a new disinfection method could be on the horizon.Exclusion-Based Purification.Built on the observation that water-borne particles are excluded fromnear-surfaceFIGURE 9.Photographs of the zones near the extractor.Left:Microsphere suspension.Right:Clay suspension.Intake rate of the outer channel:2mL/h.Inner channel:13mL/h.TABLE 1.Purification Efficacy for Various Suspensions As a Function of Particle Concentration apurification efficacy (%)input turbidity (NTU)microspherestopsoil silt clay soil 598938490209873938410099.6768679aSolution intake rates:inner channel,13mL/h;outer channel,2mL/h.Samples collected for 2h.TABLE 2.Purification Efficacy Achieved with Various Outer Channel Intake Rates apurification efficacy (%)intake rate through outer channel (mL/h)suspension type 12467microsphere 9891807056clay soil 9871474846topsoil9680595039aInner channel intake rate was changed to maintain a 15mL/h flow rate through the tube.Samples were collected for two hours and then diluted to yield 10mL.61649ENVIRONMENTAL SCIENCE &TECHNOLOGY /VOL.42,NO.16,2008regions of hydrophilic substances,the prototypefiltration system performed well.Various soils could be separated, resulting in relatively pure water.Purification of soil suspensions depended on concen-tration(Table1).Lower-concentration suspensions gener-ally showed higher purification efficacy than those with higher concentrations.This may be a result of the lower salt concentration associated with lower soil concentration. On the other hand,the efficacy of microsphere-suspension purification did not depend significantly on concentration. This result agrees with the previous observation that microsphere concentration does not affect the exclusion-zone size(1).The observed relation between exclusion-zone size and flow rate(Figure8)sheds light on the conditions under which pure-water yield may be maximized.Pure-water yield depends mainly on two features:exclusion zone size andflow rger exclusion zones allow extraction of more clean water per unit volume of original suspension. Higherflow rate should allow faster collection.On the other hand,higherflow rate also reduces the size of exclusion zone(Figure8).Hence,to maintain high purification efficacy a lower outer-channel intake rate must be used,which in turn decreases the pure water collection rate.However,the curves on the graph in Figure8suggest a plateau atflow rate of approximately50mL/h;thus,at flow rates higher than50mL/h,the exclusion-zone size should not change significantly.Potentially,this may allow pure water collection at much faster rates.At an expedient outer-channelflow rate of2mL/h,soil turbidity was reduced by90%,whereas the reduction for microspheres was up to99.6%(Table1).This difference stems from the observation that microsphere-exclusion zones were larger than soil-particle exclusion zones;the flow collected by the differential extractor’s outer channel was therefore essentially all exclusion-zone water.If the exclusion zone is smaller than200µm,as in the case of soil suspensions,then the particles from the core are sucked into the outer channel,contaminating the annular fraction. This problem was solved by lowering the outer channel’s intake rate.Although this procedure increased the puri-fication efficacy(Table2),it also reduced pure water yield, the tradeoff between pure water yield and purification efficacy.Methodological Limitations.Execution of the experi-ments revealed several shortcomings of the approach.They arise both from the exclusion phenomenon itself and the specific implementation of the principle.Geometrical Limitations.Geometric uniformity was an important consideration.To prevent particles fromflowing into the extractor’s outer channel,the gap between the extractor’s two concentric tubes had to be uniform over the circumference;otherwise,some core solution couldflow into the outer channel.This contaminates the annular fraction and reduces purification efficacy.To minimize this problem, the setup had to be carefully aligned each time prior to the experiment and not always perfectly.If this concentric approach were adapted for larger scale purification,careful engineering would need to address this limitation.Similarly,the Nafion-tube shape is also critical.If the cross-section is noncircular,then theflow profile will be nonuniform,and particles in some core regions may enter the annulus.Indeed,some samples coming from the manufacturer had a distinctly elliptical cross-section.Such tubes could be forced into an almost circular cross-section by feeding them through a hole made in the chamber wall. When the tube was dry,itfit through the hole easily.Upon swelling in water,the tube sealed the hole and acquired a more circular cross-section.Noncircularity is a lingering problem that could be circumvented by using a system design based onflat surfaces.Sediment Formation.The observed sediment formation is probably caused by the rapid settling of the heavier particles or by some chemical change inside the Nafion tube that created heavier particles.If sedimentation is caused by the weight of the larger particles,then the problem could probably be solved throughfiner prefiltering,or the issue could be circumvented altogether through use of a vertically oriented Nafion tube.Although the amount of sediment was minute relative to the total number of particles within the suspension,its existence must have affected the results presented in Table 1,presumably elevating the apparent purification efficacy. Indeed,one could argue that the turbidity reduction in the annular fraction originated entirely from sediment formation, the clear water arising entirely because of settling.However, sediment fallout was not observed at all with microspheres, which showed the greatest turbidity reduction(Table1). Hence,the effect seems to be relatively minor,although further consideration is warranted.Low Purification Rate.The relatively small size of the exclusion zone places a limit on the water-purification rate.Flow rates were considerably smaller than those involved in standard purification techniques.To increase throughput,multiple units could be arranged in parallel, or relatively larger exclusion zones could be generated by using surfaces that might be better exclusion-zone nuclea-tors than Nafion.On the other hand,the tubular design employed here was adopted solely for obtaining proof of principle,with no consideration given to generating high throughput.For commercial applications,other designs may be more effective.If these improved designs cannot yield purification efficacies beyond the80-90%obtainable here with common particles,then cascading of units in series might eventually be necessary.The current design is preliminary;it reflects only the modest level of engi-neering required for obtaining proof-of-principle.Advantages.The principal advantage of this approach is its inherent simplicity.Removal of particles occurs naturally; in principle,it is merely a matter of collecting the purified water.Modern purification techniques,by contrast require the use of physicalfilters or membranes that eventually become clogged and must be cleaned(backwashed)or replaced(11,13–15).Here,there are no physicalfilters.On the other hand,scaling up this new approach for imple-mentation in realistic settings will evidently require ap-preciable engineering.This is for the future.Another advantage of this approach is its inherent capacity to remove pathogens.Bacterial particles were excluded,and preliminary data indicate that viruses might be excluded as well(Figures7and8).This feature would make the method especially useful in locales where drinking water may contain biological contaminants.In summary,the exclusion-zone phenomenon offers a new,previously unforeseen route toward water purification. Proof-of-principle has been demonstrated,with good sepa-ration ratios in a simple design.The prototype could easily be improved for both faster and cleaner collection,making it a practical approach with considerable promise because of its inherent simplicity.AcknowledgmentsThis research was supported by ONR Grant N00014-05-1-0773and NIH Grant1R21AT-002362.We thank Chenyang Wang,Vincent Thuc Wu,and Iris Pang for help with preliminary measurements that aided in the initial design. Literature Cited(1)Zheng,J.-M.;Pollack,G.H.Long-range forces extending frompolymer-gel surfaces.Phys.Rev.E2003,68,031408.VOL.42,NO.16,2008/ENVIRONMENTAL SCIENCE&TECHNOLOGY96165。

Hypermesh 命令一览表（上）Geom主面板 (3)Nodes子面板/Distance子界面 (3)Node edit 子界面 (3)Line edit子面板 (4)Lines子面板 (4)Defeature 子界面 (4)Circles 子界面 (4)Surfaces子界面/Surface edit子界面 (5)Midsurface 子界面 (6)Solids 子界面 (6)Solid edit 子界面 (7)Primitives 子界面 (7)Edge edit 子界面/ Point edit 子界面 (8)Auto cleanup 子界面 (9)Quick edit 子界面 (9)1D主面板 (9)Masses 子界面/Shp 子界面 (10)Rigids 子界面 (10)Fe joints 子界面 (10)Bars 子界面 (10)Connectors 子界面 (10)Spotweld 子界面 (13)Hyperbeam 子界面 (13)Line mesh 子界面/Vectors 子界面 (13)Systems 子界面 (14)Edit element 子单元 (14)Split 子单元 (14)Replace子单元/Detach子单元 (14)2D主面板 (14)Cones 子界面 (15)Planes 子界面 (15)Spheres 子界面 (15)Torus 子界面 (15)Drag 子界面 (16)Spin 子界面 (16)Elem offset 子界面 (16)Auto mesh 子界面 (16)Composites子界面 (17)Shrink wrap 子界面 (17)Smooth 子界面 (17)Quality index 子界面 (17)Elem cleanup 子界面 (17)3D 主面板 (18)Solid map 子界面 (18)Linear solid子界面/ Solid mesh 子菜单 (18)Tetramesh子界面 (19)Geom 主面板Nodes 节点Lines 线Surface 曲面Solid 实体Quick edit 快速编辑Node edit 节点编辑Line edit 线编辑Surface edit 曲面编辑Solid edit 实体编辑Edge edit 边编辑Temp nodes 临时节点Circles 圆Defeature简化几何模型Primitives 基本体Point edit 点编辑Distance 距离Length 长度Midsurface 中间面Auto clean up 自动清理Nodes 子面板 Distance 子界面Node edit 子界面Lineedit 子面板Create node 创造节点Create point 创造点 Type in 输入Reject 取消Pick geom.在几何体上建点Number of nodes 节点个数On line 在线上建点Bias intensity 偏置At point 在点上建立节点Number of nodes 建立几个节点Between 两点之间Bias intensity 偏置On plane 在面上建立节点Distance 距离Xdist X 方向的距离Ydist Y 方向的距离Zdist Z 方向的距离Angle节点之间的角度Two nodes 两个节点的距离Nodes between 两点之间放置几个节点Three nodes 三个节点Circle center圆心Two points 两个点的距离Three points 三个点Associate关联Tolerance 公差Move node 移动节点Step size移动尺寸大小Destination surf目标曲面Place node 放置节点Node to place节点到另一个地方Remap 重映射Node list 节点目录Align node 对齐节点Combine 合并Smooth 光滑Split at point指定点分割Split at joint 在连接处分割Split at line 用线分割Cut line剪切线Split at plane 用面分割Lines 子面板DDefeature 子界面Circles 子界面Circle 圆Radius 半径Center & radius 圆心& 半径Offset 偏移量Points & vector 点 & 向量Three points 三个点Find center 寻找中心Smooth corners 平滑转角Smooth line 使线光滑Min tangent angel最小切线角度Extend line 延长线Follow curvature 原有曲率From nodes 通过节点Linear 线性的Offset 偏移Offset by midline 通过中线偏移From surf edges 曲面边缘偏移Original component 偏移到原始组件里Ignore element normal 忽略法向单元Break angle 打断角度From features 通过特性选取Feature angle 特性角度Surfs with plane 面上的曲面Elements with plane 面上的单元Line with plane 面上的线At intersection 交集处Smooth lines 光滑线At tangent 切线Check points 检查点Radius 半径Fillets 圆角Trim original lines 修剪线段Pinholes 小孔Surf fillets 曲面倒角Diameter 直径Find fillets by profile 通过轮廓选取倒角Surf fillets 曲面倒角Find fillets in selected 在选择的部分选取倒角Edge fillets 边倒角Trim-intersect 修剪相交Duplicates 复制Cleanup tolerance 清除公差Find symmetry 寻找对称Reorganize 重组Delete positive 删除当前Symmetry 对称面Delete negative 删除复制体Surfaces 子界面Surface edit 子界面Multiple node 多个节点Trim with nodes 通过节点修剪Node normal to edge 矢量节点到边界Along a vector 沿着矢量Entire surface 全部的曲面Keep line Endpoints 保持线的终点Trim with lines 通过线修剪All attached surface 所有接触面With plane 用平面With surfs 用曲面Trim with surfs/plane 用曲面/平面修剪Self intersecting surfs自定义曲面At cursor 手动选取All trim lines of surfs所有曲面上的修剪线Untrim 还原修剪Internal trim lines 内部修剪线Disjoint offset 部分偏移Offset 偏移Remove degenerations 移除Cross Extension 同过延伸使交叉ExtendExtend selected surf edges延伸选择的曲面边界Shrink 缩放Ruled 规则面Auto reverse自动翻转Spline /filler样条线 / 填充线Auto create （free edges only ）自动创建（自由边）Skin 蒙皮Keep tangency 相切Drag along vector 沿着矢量拉伸Drag / spin 拉伸 / 旋转Drag along line 沿着线拉伸Auto detect features 自动检查特性Mesh-based auto tolerance网格自动调整公差Surface complexity 曲面复杂度Split by components 通过组件分割From FE 通过单元Associate nodes 关联节点auto select whole edge自动选择整个边界Pick angel 拾取角度Fillets 圆角Radius 角度Midsurface 子界面Solids 子界面Closed solid 闭合实体Extract 抽取Auto midsurface 自动抽取中间面Extraction options 提取选项Sort 分类Combine with adjacent plates连接与之相邻的板Combine all adjacent plates 连接所有相邻的板Surface pair 配对曲面Result in middle surface comp结果保存在中面组件中Target type 目标样式Point to offset 指定偏移量Quick edit 快速编辑Target location 目标位置Pilot pointPoint to offset 指定偏移量Accept target 接受目标Assign target 赋值目标Pilot pointRemove target 移除目标Retained edge 要保留的边缘Replace edge 替代边缘Edge to move 要移动的边界Extend surface 延伸曲面Surfaces to extend 延长曲面Max extension distension 最大移动距离View thickness 查看厚度Show surfaces thickness 观察曲面厚度Set thickness 设置厚度Auto select solid surfaces 自动选择实体曲面Bounding surfs 曲面边界Surfs component 保存到曲面组件中Drag along vector 沿着向量拖动Merge solids at shared edges 合并重合实体边界Drag along normal 沿着法向拖动Frame mode 框架模式Reference node 参照节点Drag along line 沿着线拖动Transformation planeSolid edit 子界面Primitives 子界面变换平面Spin 旋转Trim with nodes 通过节点修剪Extend trimmer 延伸修剪With cut line 通过剖切线With bounding lines通过边界线Drag a cut line 手动画剖切线With sweep lines 通过扫率曲线Trim with lines线修剪Sweep to 选择曲线Trim with plane/surf 平面/曲面修剪With plane 通过面With surfs 通过曲面To be merged 选取合并的实体Merge by removal 通过分割面合并实体Merge 合并Remove scratches删除刮伤Detach 分离To Detach 要分离的实体Boolean 布尔运算Operating type 操作类型Operating 具体操作Square/block 正方形/块Full cone 整个圆锥Partial cone 部分圆锥Botton center 底面中心Botton center 底面中心Normal vector 法向量Normal vector 法向量Top radius 顶部半径Major vector 主向量Base radius 根部半径Start angle 起始角度Height 高度End angle 终止角度Cylinder/cone 圆柱体/圆锥Axis ratio 轴比率By center and radius 通过中心和半径For partial sphere部分球体Sphere For 4 nodes sphere 通过四点创建球体Theta begin 起始角度Edge edit 子界面Point edit 子界面Theta end 终止角度Phi begin 起始直径Phi end 终止直径Minor radius 内环半径Major center 外环中心Torus 圆环Major radius 外环半径Minor center 内环中心Add 增加At cursor 光标选取Suppress 废除Multiple points 多重边界Break angle 打断角度Replace 替代Move point 去除的点Retained point 保留的点Release 释放Points to edges 点投影到线Points to surfs 点投影到曲面Distance tolerance 距离公差Angle tolerance 角度公差Project 投影Internal points onto its surfs 内部点映射到曲面At cursor 光标选取Toggle 忽略Cleanup tolerance 公差Suppress 压缩Break angle 打断角度Move edge 要移动的边Replace 替代Retained edge 要保存的边Equiv across comps 通过组件合并Equivalence 合并Equiv free edges only仅合并自由边Unsplit 清除分割Multiple edges 混合边界Min radius 最小半径Max radius 最大半径Min angle 最小角度Edge fillets 边界倒角Trim-intersect 修剪相交Close orphan 关闭孤行Angle surfs 曲面角度Offset surfs 偏移曲面Min filletAuto cleanup 子界面Quick edit 子界面1D 主面板最小倒角Max fillet 最大倒角Angel vertex 顶点角度Shape ratio 形状比例Min edge 最小边缘Topology cleanup parameters 拓扑清理参数Use current parameters 使用当前参数Elements quality criteria 元素质量标准Use current criteria 使用当前标准Split surf-node通过节点分割曲面Adjust/set density 调整/创建密度Split surf-line通过节点和目标线分割曲面Replace point 合并点Washer split 偏置分割线Add/remove point 添加/删除点Unsplit surf 合并分割曲面Add point on line 在线上增加点Toggle edge 忽略自由边Release point 释放点Filler surf 曲面倒角Project point 投影点Delete surf 删除曲面Trim-intersect 切除相交Masses 集中质量Bars 梁单元Connectors 连接器Line mesh 线性网格Edit element 编辑单元Fe joint 铰单元Rods 杆单元Spotweld 点焊单元Linear 1d 一维线性Split 分割Sph 球Rigids 刚性单元Hyperbeam Hyper 梁Replace 替代Rbe3橡胶单元Detach 分离Springs 弹簧单元Order change 改变阶次Gaps 间隙单元Vectors 向量Config edit 配置编辑Systems 坐标系Elem types 单元类型Masses 子界面Shp 子界面Rigids 子界面Fe joints 子界面Bars 子界面Connectors 子界面Organize 管理Spot焊点Add links增加连接Compare比较Find 查询Bolt螺栓Unrealize不真实Quality质量Mask 隐藏Seam 缝焊Delete 删除Area 面连接Translate 移动Apply mass 施加质量Numbers 数量Fe absorb FE吸附Renumbers从编号二级子界面OrganizeCollectors 集合Dest component 目标组件Includes 包括Dest目标Mass质量Create创造Property属性Update 更新System系统Simple cubic简单的立方体Pitch边长Material density材质密度Create创建Independent固定点Dependent连接点Attach dependent nodes as a set连接独立的点做设置Dof自由度Connectivity连接性Switch转换Update更新Attach/detach set连接/分离设置Combine合并Combine rigids with合并刚性单元通过Joint type连接类型Create创造Orientation定位Update 更新Spherical 球形的Bar2二维梁Pins aBar3三维梁Orientation/offsets in basic 简单的定位/偏移Update 更新Offset a a 偏移二级子界面Mask 二级子界面find 二级子界面translate 二级子界面deleteGlobal system 坐标系统Magnitude 偏移量二级子界面renumberStart with 从~~开始Single 单个Increment by 增加到二级子界面spot Location 位置Mesh independent 独立网格Spot 焊点Connect what 与~连接Non-normal projection 非均匀投影Creat 创建Tolerance 公差No systems 无系统Realize 实现Add location nodes as line 增加位置节点产生线Spacing 间距End offset 末端偏移Edit 编辑Retain line 保持线二级子界面boltLocation 位置Hole diameter 孔直径Bolt 螺栓Connect what 与~连接Use dynamic vector 使用动态矢量Creat 创建Tolerance 公差Mask 隐藏Reverse显示与隐藏颠倒Reverse all所有都相反状态Mask not shown 隐藏不显示Unmask all 全部显示Unmask 取消隐藏Reject 放弃Find entities 查找对象Find attached 查找连接Attached to 连接到Between 两者之间Delete associated solids 删除相关的实体Delete entity 删除实体Delete associated elems 删除相关的单元Delete model 删除模型Realize 实现Elems to current comp 创建单元到当前组件中中二级子界面seam Location 位置Mesh independent 独立网格Seam 缝焊Connect with 与~连接Creat 创建Tolerance 公差Realize 实现Elems to current comp 创建单元到当前组件中Spacing 间距Params 参数End offset 末端偏移Edit 编辑Group 组Connect rule 连接规则二级子界面area Location 位置Mesh independent 独立网格Area 面Connect with 与~连接Non-normal projection 非均匀投影Creat 创建Tolerance 公差No systems 无系统Realize 实现Elems to current comp 创建单元到当前组件中Mapped type 映射类型Size and bias 尺寸和偏移量Edit 编辑Free type 自由样式Element size 单元尺寸二级子界面Apply mass二级子界面Add links Location 位置Add links 增加连接Connect when 连接时间Connect what 与~~连接Re-connect rule 重新连接的规则Location 位置Mass type 网格类型Connect method 连接方法Distribution 分布Connect what 与~~连接Search tolerance 查询公差二级子界面QualitySpotweld 子界面Hyperbeam 子界面Merge tolerance 合并公差Cross section plane 通过界面Create node at centroid 创建节点在图心Plane base node 平面基准点Shell section 壳截面Create node at shear center 创建节点在剪切中心Part generation 产生部分Solid section 实体截面Analysis type 分析类型Standard section 标准截面Standarad section library 标准截面数据库Standarad section type 标准截面形式Generic section 普通截面Edit section 编辑截面Plot centroid 显示型心Review sections 审查截面Shear center 切变中心Line mesh 子界面Vectors 子界面Preview duplicates 预览重复单元Preview combine 预览合并Connectors 连接Remove duplicates 移除重复单元Projection check 投影校核Find too long 寻找太长的1D elems 1D 单元Length 长度Angle 角度3D elems 3D 单元Jacobian 雅克比All surfs 所有曲面Element config 单元配置Using geom.使用几何Weld location 焊接位置Using nodes 使用节点Without systems 无系统Using elems 使用单元Attach to shell elems 附在壳上的单元Switch nodes 转换节点Element size 单元格大小Segment is whole line 整个线段分段Peoperty 性质Element config 单元配置Vector update method 矢量修正方法Create 创建Magnitude 量Update 更新Global system 坐标系统Systems 子界面Edit element 子单元Split 子单元Replace子单元Detach子单元2D主面板Planes 平面Ruled规则面Connectors连接器Automesh自动划分网格Edit element编辑单元Cones 圆锥Spline样条线HyperlaminateHyper薄板Shrink wrap收缩翘曲Split分割Spheres 球体Skin三角形Composites复合材料Smooth光滑Replace替代Torus 圆环Drag拉伸Qualityindex质量指标Detach分离Create by axis direction 通过轴方向创建create by node reference通过参照节点创建Rectangular 矩形Set reference 设置参考Assign赋值Set displacement设置位移Material orientation 定义材料Material orientationalmethod定义材料方法Plot绘图Tria三角形Quad正方形Tetra四面体Pyramid棱锥Penta五面体Create创建Hex六面体Combine合并Combine to quad合并成正方体Split分割Displayed elems显示单元Cleanup清理Plate elements 板单元Split all sides 分割所有的边Solid elements 实体单元Split into hexas 分割成六面体Hexa elements 六面体单元Two pentas二个五边形Refine to target element size 改善目标单元的尺寸Refine elements改善单元体Target element edge length目标单元边界长度Replace 移动的点Equivalent 等价With不动的点At mid-point在混合节点Detach分离Detach elements分离单元Detach from从~中分离Spin 旋转Elem cleanup 单元清理Order change 改变阶次Line drag 拉伸Config edit 配置编辑Elem offset 单元偏置Elem types 单元类型Cones 子界面Botton center 底面中心Mesh, keep surf划分网格，保留曲面Normal vector 法向量Radius 半径Top radius 顶部半径Ratio 比率Full cone 完整的圆锥Height 高度Major radius 外环半径Start angle 起始角User controlled 自定义Cone 圆锥End angle 终止角Planes 子界面Spheres 子界面Torus 子界面Mesh, keep surf划分网格 , 保留曲面Trimmed 修剪Calculate plane 估算面Square 正方形Full sphere 整个球Mesh, keep surf 划分网格，保留曲面Four points 四个点画球Radius 半径Theta begin 起始角度Theta end 终止角度Phi begin 起始直径User controlled 自定义Phi end 终止直径Center 中心Mesh, keep surf 划分网格，保留曲面Full torus 整个圆环Normal vector 法向量Minor radius 内环半径User controlledMajor vector 主向量Major radius 外环半径Drag 子界面Spin 子界面Elem offset 子界面Connectors 子界面参照1D Connectors Auto mesh 子界面Minor start 内环起始角Major center 外环中心Minor end 内环结束角Minor center 内环中心Major start 外环起始角Three points 三点确定Minor radius 内环半径Major end 外环结束角Distance 距离Drag geoms 拉伸几何体Mesh, keep surf 划分网格，保留曲面Bias style 偏载类型Drag elems 拉伸单元Bias intensity 偏载强度Angle 角度Spin geoms 旋转几何体Mesh, keep surf 划分网格，保留曲面On spin Bias style 偏载类型Spin elems 旋转单元Bias intensity 偏载强度Number of layer 层的数量Solid layers 实体层Initial offset 初始偏移量Tolal thickness 总体厚度Shell layers 壳层Elems to offset 单元偏移Linear or no biasing 线性或不偏载Bias intensity 偏载强度Shell offset 壳偏移量Elements to current comp 创建创建单元到当前组件中CFD corners CFD 角Thicken shells 加厚壳Along geom to follow 沿着几何偏移Shells are on the midsurfaces壳加在中间层Elements size 单元尺寸Elems to surf component 创建单元到面组件Composites 子界面Shrink wrap 子界面Smooth 子界面Quality index 子界面Elem cleanup 子界面Mesh type 单元类型First order 一阶Break connectivity 打断当前连接Previous settings 先前的设置Link opposite edges 连接对面的边QI optimize QI 优化Use current criteria 使用当前条件Smooth across common edges with feature angle光滑有特性角度的共同边Min elem size 最小单元尺寸Edge deviation 边界偏差Max elem size 最大单元尺寸Max angle 最大角度Closed volume proximity封闭附近的体积Surface deviation曲面偏差Mesh type 网格形式Free edge deviation 自由边的偏差Rigid body mesh 刚性体网格Max feature ang 最大的特性角度Material orientation 指定材料Material orientational method 指定材料方法Ply directions厚度方向Tight 紧的Element size 单元尺寸Loose 松散的Generate solid mesh 产生实体网格Mesh orientation 网格方向Iteration 迭代次数Plates 板AnchorSolids 实体Autodecide 自动决定Min size 最小尺寸Place node 放置节点Max size 最大尺寸Swap edge 交换边界Aspect ratio 长宽比Node optimize 节点优化Warpage 翘曲Element optimize 单元优化Skew 扭曲度Jacobian 雅克比Fix folded elems ，angles 修复折叠的单元，角Use surrounding elems 使用周围的单元Reduce tria elems 减少三角单元Use current criteria 使用现有标准QI smooth elems with target QI 光滑单元的目标Feature angle 特征角Fix elems failing QI check 修复单元QI 故障检查Edit element、split、replace、detach参照1D 3D 主面板Solid map 实体映射Drag拉伸Connectors链接Tetramesh四面体格划分Edit element编辑单元Linear solid 线性实体Spin旋转Smooth光滑Split分割Solid mesh 实体网格Line drag拉伸Replace替代Elem offset单元偏置Detach分离Order change改变阶次Config edit配置编辑Elem types单元类型Solid map 子界面Source geom 起始几何Along parameters 参数设置Dest geom 目标几何体Along bias style 偏置形式General 普遍方法Along geom 沿着几何体Elem size 单元尺寸Line drag沿着线拉伸Show solidmap mesh显示实体网格Linear线性Linear solid 线性实体Apply orthogonality to along 相交延长Ends only 终止处One volume 一个实体Smooth dest目标光滑Interactive互动Stop meshing on bad jacobian在不好的雅可比处停止划分网格Multi solids 混合实体Source shell 壳源Previous setting 先前的设置Linear solid子界面Solid mesh 子菜单Alignment 对齐方式Distribute layer 分布的层Density 密度Bais intensity偏载强度Start region开始区域End region结束区域Connecting连接Uniform mesh统一的网格Drag 、Spin 、Line drag 、Elem offset 、Connectors 参照2DTetramesh 子界面Select trias/quads to tetra mesh 选择三面体/四面体进行四面体网格自动划分Optimize mesh quality 优化网格质量Tetra mesh 四面体网格No fixed trias/quads 不修复三面体/四面体Standard 标准Tetra remesh四面体网格重新自动划分Fixed with boundary layer 修复边界网格Number of layers 层的数量Comps 组件First layer thickness 第一层的厚度Single thickness 单一厚度Growth rate 增长率Float w/o boundary layer 浮动w/o 边界层Simple transition ：ratio 单个旋转比CFD mesh CFD 网格Remesh重新划分网格Enclose volume 闭合的实体Volume tetra 四面体体积Match existing mesh 匹配存在的网格Elems to current comp 创建单元到当前组件中Smooth 参照2D。

AIAA J OURNALV ol.35,No.8,August1997Analysis of Streamline Curvature Effectson Wall-Bounded Turbulent FlowsJiang Luo and Budugur LakshminarayanaPennsylvania State University,University Park,Pennsylvania16802This work deals with numerical analysis for the effects of surface curvature,particularly the concave curvature,on turbulent duct¯ows and boundary layers.A compressible Navier±Stokes code incorporating Reynolds stressmodels has been developed using a four-stage Runge±Kutta scheme.Numerical computations have been carriedout for curved¯ows in180-deg and90-deg turning ducts and a turbulent boundary layer using Reynolds stressmodels with/without modi®cations to the dissipation rate(")equation.Various modi®cations to the"equation arediscussed.A quantitative relationship has been established between two seemingly different modi®cations to the"equation.It is observed that the modeling of concave curvature effect is qualitatively different from the modeling ofconvex curvature effect.Detailed comparisons between computations and data indicate that,to capture the strongampli®cation of turbulence near a concave wall,the standard"equation needs to be modi®ed.NomenclatureC f=skin-friction coef®cient,w/(0.5U2e)C1,C2,C,C c=constants in Eq.(2):1.44,1.92,0.09,0.2C s1,C s2=constants in Eq.(4):0.43,1.90H=duct heightk=turbulent kinetic energy,0.5u i u in=coordinate normal to the surfaceP=static pressureP k=production rate of k,u i u j@U i/@x jR=radius of curvature of reference streamline Re,Re=Reynolds number(U m H/,U m/)Ri t=Richardson number,(k/)2(U/r2)@(Ur)/@n r=local radius of curvature of streamlineS=invariant of strain rate,(2S i j S i j)S i j=strain rate,(@U i/@x j+@U j/@x i)/2s=streamwise coordinate along surfaceU=streamwise mean velocityU e=freestream velocity at inletU m=bulk velocityu,v,w=¯uctuating velocities in streamwise,normal(radial),and cross-stream directions(u,v,wrepresenting rms values in Figs.2±8)u i u j=Reynolds stressy=coordinate normal to test wally+=wall distance variable,yu/=boundary-layerthickness=dissipation rate of turbulent kinetic energy=angle into bend measured from bendentrance/momentum thickness,t=laminar and turbulent kinematic viscosity,C k2/w=wall shear stressIntroductionL ONGITUDINAL surface curvature exerts a signi®cant in¯u-enceon turbulentboundarylayers overcurvedbodiesand¯ows through curved ducts.The skin-friction coef®cient(and heat trans-fer rate),compared with that of a boundary layer on a¯at surface, is decreased on a convex surface due to the damping of turbulence Received Sept.14,1996;revision received May1,1997;accepted for publication May5,1997.Copyright c1997by Jiang Luo and Budugur Lakshminarayana.Published by the American Institute of Aeronautics and Astronautics,Inc.,with permission.Ph.D.Candidate,Department of Aerospace Engineering;currently Se-nior Engineer,Solar Turbines,Inc.,San Diego,CA92101.Member AIAA.Evan Pugh Professor of Aerospace Engineering,and Director,Center for Gas Turbines and Power.Fellow AIAA.by the convex curvature,but it is increased on a concave surface due to the ampli®cation of turbulence by the curvature(Refs.1±3, etc.).Previous computational efforts,e.g.,Refs.1,4,and5,have demonstrated that the effects of curvature on turbulence intensity and structure must be predictedaccurately to capture the boundary-layer development over curved surfaces.To predict the stabilizing and destabilizing curvature effects,it is necessary to make empir-ical modi®cations to eddy viscosity models.1Gibson et al.,6So et al.,7and Shima,8among others,have shown that the Reynoldsstress model(RSM)can account for the curvature effects without empir-ical modi®cations.However,Park and Chung9modi®ed the RSM with an additional curvature time scale to capture the curvature ef-fects accurately.The authorsrecentlyanalyzedthe turbulent¯ows in highlycurved ducts with a RSM and observed that the RSM can successfullycap-ture the large damping of turbulencenear the convex wall but under-predictsthe enhancementof turbulencenear the concavewall.10The modeling of concave curvature effect appears to be quite different from the modelingof convexcurvatureeffect.This may be attributed to the qualitativelydifferent charactersof these two effects,namely, the mere attenuation of preexisting eddies by convex curvature but reorganization of eddy structures by concave curvature,as sug-gested by Gillis and Johnston,11Muck et al.,12and Hoffman et al.,13 etc.As argued by many authors,a concave curved¯ow may become three dimensional due to the possible existence of Taylor±Gortler vortices.However,these longitudinal vortices have not been ob-served in some experiments.Barlow and Johnston3found that large scales in concave boundary layers exhibit a range of behavior from Taylor±Gortler vortices,when upstream nonuniformities are large, to energetic large eddies(radial in¯ows and out¯ows),when the up-stream¯ow is uniform.They have observed that the enhancement of turbulence is mainly due to the large-scale eddies rather than the Taylor±Gortler vortices.These longitudinal vortices are found to cause only minor increases in the spanwise-averaged skin-friction coef®cient.Hoffman et al.13also showed that the secondaryeffectof the vortices is less important than the primary effect of the concave surface curvature for moderately curved¯ows.Barlow and Johnston3suggestedthat,for many applications,two-dimensional models should be adequate,provided that they can ac-count for the slow development of the energetic large-scale eddies in concave boundary layers.The failure of the RSM(with the stan-dard equation)in modeling these large eddies hence appears to be the major reasonfor the underpredictionof turbulenceenhancement by Luo and Lakshminarayana.10The major objective of the present paper is to improve the prediction of the concave curvature effects.Three strongly curved duct¯ows with/without streamwise pressure gradient will be analyzed using the RSM model.The modeling of 12731274LUO AND LAKSHMINARAYANA the equation,includingrecent modi®cationsto it,will be discussedand assessed.Turbulence Models and Numerical ProcedureThe Reynolds stress model employed in the present study is theRSM model of Gibson and Launder14with the exception of the diffusionterm.The turbulentdiffusionterm is modeledwith a simple isotropicstress diffusionmodel followingthe suggestionof Lien andLeschziner.15The standard equation can be written asD D t =Diff()+k(C1P k C2)(1)where D/D t stands for the convection of and Diff()for the turbulent diffusion of.The preceding equation for is modeled in analogy to the equation for turbulent kinetic energy k.As discussed in detail by Launder et al.16and Lumley,17it may be assumed that the local transfer rate of turbulent energy from the large-scale eddies to ner scale motions is essentially equal to the energy dissipation rate itself for steady¯ow close to local equilib-rium,i.e.,P k.Hence,for¯ows that are in local equilibrium,the source term in the equation might be modeled in terms of the tur-bulence production.This essentially implies that the production of dissipationis linearly proportionalto the productionof turbulenten-ergy,whereas the destruction of dissipation is linearly proportional to the destruction of turbulent energy.Modi®cations to Standard"EquationThe modeled equation for,Eq.(1),has been used for over two decades and has been successful in predicting a variety of thin shear¯ows.Its weaknesses,such as the overprediction of the spread rate of the axisymmetric jet,have been recognized before, and a number of ad hoc modi®cations have been proposed.For example,to account for the streamline curvature effects,Launder et al.4(denoted as LPS)modi®ed the destruction term in Eq.(1)to be C2(2/k)(1C c Ri t),where Ri t=(k/)2(U/r2)@(Ur)/@n in curvilinear orthogonal(s,n)coordinate.Hanjalic and Laun-der(HL model5)modi®ed the generation term in Eq.(1)to be C1(/k)t(@U/@n)2.These two models seem to be different.How-ever,for mildly or moderately curved¯ows,a quantitative relation-ship between them might be derived as follows.The additionalsink term in the LPS4model can be added to the generation term,and Eq.(1)can be written asDD t=Diff()+(k){[C1t(@U@n U r)2+(C2C c C)t U r2@(Ur)@n]C2}=Diff()+(k){C1t(@U@n)2[(1A)2+(C2C c C1C)A(1+A)]C2}Diff()+(k){C1t(@U@n)2(1+A)C2}(2)where A is de®ned as(U/r)/(@U/@n),the ratio of the extra strain rate producedby curvatureto the primary shear strain.The empirical values for coef®cients C1,C2,C c,and C have been used and the second-order term is neglected because A is normally very small for mildly to moderately curved¯ows.On the other hand,the HL model is given byDD t=Diff()+(k){C1t(@U@n)2C2}=Diff()+(k){C1t(@U@n)2(1+0A)C2}(3)This is actually an LPS-type model if the coef®cient C c in the LPS model is set to be0.13instead of0.2.Thus,for mildly to moder-ately curved¯ows,the HL model appears to differ from the LPS model only in terms of the magnitude of the coef®cient.Indeed, Rodi and Scheuerer5found that the LPS model is successful for curved boundary-layer¯ows and observed that the LPS model con-sistently has a stronger modi®cation effect than the HL model.This is also consistent with Richmond and Patel’s18observation that the HL model is able to capture the trend of curvature effects but un-derpredicts the magnitude.Lumley17developed a new equation based on the concept of spectralenergytransferfor nonequilibrium¯ows.The sourcetermin this equation is modeled with the invariant strain rate(S)rather than P k,thus removing the rigid linkage between the generation terms of the and k equations.By modeling the dynamic equation of the mean-square vorticity¯uctuation,Shih et al.19derived a transport equation for the dissipation rate,the production term of which is similar to that of the equation by Lumley.17Shih et al.’s model is given asDD t=Diff()+C s1S C s2k+(4)The invariant strain rate S is de®ned as S=(2S i j S i j),which is different from Lumley’s17model,where the value of S is obtained from a separate transport equation.This new production term for the equation in fact modi®es the time scale that controls the rate at which turbulent energy enters the spectral pipeline,as discussed in detail by Lumley.17Numerical ProcedureA Navier±Stokes procedure,incorporating the RSM model,the standard equation,the LPS modi®cation,and the Shih et al. model,has been developedbased on the code describedin Kunz and Lakshminarayana.20The mean-¯ow equationsare integratedin time by the explicitfour-stageRunge±Kutta scheme.The convectionand diffusion terms are discretizedon a nonstaggeredgrid using second-order accurate central differencing.Fourth-order and second-order arti®cial dissipationterms(with coef®cientsaround0.02and0.25)20 are included to damp high wave number errors and to improve the shock capturing,respectively.For the present low-speed¯ows, the second-order arti®cial smoothing actually is not used.Eigen-value scaling and local velocityscaling[using(U/U m)2]of arti®cial dissipation terms are used to avoid contaminationof the solution by arti®cial dissipation.20The RSM equationsare discretizedin space and integratedin time in the same way as the mean-¯ow equations.Because the convection terms in the RSM equationsare discretizedwith centraldifferencing, arti®cial dissipation is needed to prevent odd-even decoupling.It is observed that the inclusion of fourth-order arti®cial dissipation has not resulted in convergent solutions.Hence,a small amount of second-order arti®cial dissipation is added to the RSM equations. The required value of arti®cial dissipation for a convergentsolution is fairly small(with the coef®cient around0.02).Local velocity scaling is also used to reduce the smoothing in the equations to zero inside the boundary layer.The arti®cial dissipation coef®cient in the normal direction is kept as a small fraction,e.g.,110,of that in the streamwise direction,which further reduces the in¯uence of smoothing on the convergentsolution to a negligiblelevel.Note that the current level of second-ordersmoothing is much lower than that brought by the rst-order accurate upwind-differencingscheme. The iteration of the RSM equation in the present time-marching procedureis found to be stable,without the implementationof elab-orate stabilizingmeasuressuch as those required for pressure-based methods.The implementation of the RSM model near the wall,in-cluding the matching of the RSM model with the near-wall model, has followed the proceduredescribedby Lien and Leschziner.21The near-wall region(y+<70)is handled by a one-equation model,in which only the k equation is solved while the near-wall pro®le is prescribed with empirical functions.10Unlike the low-Reynolds-number RSM(such as that used by So et al.7),the current Reynolds stress model is valid only for the fully turbulent region and can-not be used in the near-wall region.In other words,the RSM isLUO AND LAKSHMINARAYANA1275Table1Conditions(at bend entrance)for test casesTurning angle,Authors deg/R in/R out Re Re RemarksSandborn and Shin22180 1.00.3 2.1105 1.2104Constant widthKim and Patel23900.050.04 2.21053103Constant widthJohnson and Johnston2490N/A0.055 3.9104 1.3103Variable width@P@s0on outer walla)180-deg duct22b)90-deg duct23c)Concave boundary layer24Fig.1Duct geometries and grids.solvedin the outerregion(y+>70),and boundaryconditionsfor theReynolds stress components(uu,vv,ww,uv)are speci-ed at y+=70grid line.Hence,the Reynolds stresses for y+<70are not computed in the current code.They are provided from thek equation,which is solved down to the wall.The typical distri-bution for uu,vv,ww,and uv in near-wall turbulence isemployed,i.e.,uu=1.1k,vv=0.25k,ww=0.65k,anduv=0.255k.Convergencecriteriaare takenas fourdecadesdropof rms densityresidualand2.5±3decadesdrop of the rms residualfor.The differ-ence between the computed mass¯ow rates at the duct inlet and theexit is less than0.2%of the inlet mass¯ow rate.The converged k±solution is used to initialize the computation with the RSM equa-tions.It typically takes about9000steps to get a convergent RSMsolution.Results and DiscussionDescription of Test Cases and Numerical DetailsThe cases computed in this paper include the two-dimensional¯ow in the180-deg duct of Sandborn and Shin,22the midspan¯owin the90-deg rectangular duct of Kim and Patel,23and the turbulentboundary layer on the outer(concave)wall of the90-deg duct mea-sured by Johnson and Johnston.24The details of these test cases aregiven in Table1.The current Navier±Stokes code with the RSM model and thestandard k±model has been validated against benchmark-qualitydata for¯at-plate boundary-layer¯ows.25The computations of thepreceding cases with different Reynolds numbers were carried outwith an averageinlet Mach number of approximately0.2,to accom-modate the compressible formulation of the current code.The inlettotal pressure was adjusted to keep the Reynolds number the sameas that in the measurement.The geometries and grids of the ducts are shown in Fig.1,wherethe bend region is plotted.The251141(streamwise normal)and241141grids were generated by an algebraic method for the180-deg duct and the two90-deg ducts,respectively.A systematicgrid independence study has been performed.For Kim and Patel’s90-deg duct¯ow,further re®nement of the mesh(such as281141and281161)has resulted in negligible difference in the solution.For instance,the relative difference in the computed skin-frictioncoef®cients(C f)at the bend exit,i.e.,90-deg location,is less than0.5%.The rst grid point near the wall is located around y+=1.The inlet pro®les for streamwise velocity,four individual Reynoldsstress,and dissipation rate are obtained by computation of the de-veloping¯ow in a long straight channel with the correspondingReynolds number.10180-deg Duct FlowThe predictions at two locations inside the bend(=30and90deg)for Sandborn and Shin’s22180-deg duct¯ow(Re=2.1105)are presented in this section.The predictions by the standardk±model are also included to highlight the performance of thethree RSM models,namely,the RSM model with the standardequation,the LPS modi®cation,4and the Shih et al.19model,respectively.The predicted pro®les of uv,uu,vv,and U at=30degare shown in Figs.2a±2d,respectively.Near the inner wall,the tur-bulence has been greatly damped by convex curvature as well asby large¯ow acceleration,and the measured turbulent shear stressis close to zero over a large region(Fig.2a).On the other hand,a large ampli®cation of turbulence is observed near the concavewall.The k±model fails to account for the curvature effects andpredicts a near-symmetric pro®le of uv,which is much higherthan the data near the convex wall but lower than the data nearthe concave wall.The RSM with the standard model capturesthe turbulence damping very well but underpredicts the ampli®-cation of turbulence as stated earlier.The two modi®ed mod-els are seen to provide signi®cant improvement in capturing theconcave curvature effects over the standard model(Figs.2a±2c).As seen in Figs.2b and2c,the predicted streamwise¯uctua-tion velocity(u=uu)by all the RSM models is larger than thenormal¯uctuation velocity(v=vv)near the concave wall,inagreement with the data.The isotropic k±model predicts closevalues for all the three normal stresses,among which uu is un-derpredicted near the concave wall,whereas vv is overpredictednear the convex wall.The mean velocity pro®les(Fig.2d)predictedby all the models are in good agreement with the data because themean¯ow at this location is dominated by large pressure gradientsand is not sensitive to the predicted levels of turbulence.The major features of the¯ow at=90deg(Fig.3)are similarto those observed at=30deg.All the RSM models capture thecomplete damping of turbulence near the convex wall very well.Both the predicted and measured mean velocity pro®les show verythin boundarylayersnearthe convexwall(Fig.3d).Nearthe concavewall,strong turbulent mixing brings high-momentum¯uid towardsthe wall,creating full velocity pro®le.The RSM with LPS modeland the Shih et al.model predict the highest level of turbulenceampli®cation(Figs.3a±3c)and hence the fullest velocity pro®lenear the concave wall,being in the closest agreement with the data.The RSM with the standard model is seen to capture the trend ofthe effect of concave curvature on turbulence but underpredicts themagnitude.1276LUO AND LAKSHMINARAYANAa)Turbulent shear stressb)Streamwise rms turbulent velocityc)Radial rms turbulent velocityd)Streamwise mean velocityFig.2Pro®les of180-deg duct¯ow atµ=30deg(Ref.22).Many authors have observed a very large increase in the radialcomponent of Reynolds stress(vv)in concave boundary layers,which can also be seen in Fig.3c.Unlike the location=30deg,the radial¯uctuation velocity v at=90deg is now as large as1.5times the streamwise¯uctuation velocity u.This feature is quiteunusual for attached turbulent shear¯ows.The high value of radial¯uctuation velocity is caused by the large-scale radial in¯ows andout¯ows,which are induced directly by the centrifugal instability.The RSM with the standard model is seen to underpredict thevalues for both u and v(Figs.3b and3c).The underpredictionof vseems to be more serious than that of u.This may be attributed tothe near-wall model for pressure±strain correlation(i j w)in Gibsonand Launder’s14model,which is known to have excessive dampingeffect for normal Reynolds stress,i.e.,vv,even far away from thewall.However,a test run has been made using the RSM with i jwset to zero near the concave wall and the standard model.As seenin Figs.3b and3c,this ad hoc model provides only slight improve-mentin predictingthe valueof vv,whileprovidingless satisfactorypredictions for uv and uu.This numerical experiment indicatesthat the underprediction of turbulence by the RSM with the stan-dard model should not be attributed to the near-wall modelingfor pressure±strain correlation.The underprediction is more likelyto be caused by the problem with the standard model.Indeed,the two modi®ed models are seen to capture the ampli®cation ofturbulence much better than the standard model(Figs.3a±3c).a)Turbulent shear stressb)Streamwise rms turbulent velocityc)Radial rms turbulent velocityd)Streamwise mean velocityFig.3Pro®les of180-deg duct¯ow atµ=90deg(Ref.22).It is somewhat surprising to see that the LPS model4and theShih et al.model19provide similar predictions for turbulence am-pli®cation,although the developmentof these two models followeddifferent arguments.The source term of the Lumley17and the Shihet al.19models differs from that of the standard model becausethe former modi®es the time scale for spectral energy transfer.17Bymodifying the sink term,the LPS model essentially increases thetime scale for spectral energy transfer in the concave region and re-duces it in the convex region as seen in Eq.(2).Both modi®cationshave removed the rigid linkage between the generation terms ofand k equations.Note that,unlike the LPS model,the extensionof the Lumley17and the Shih et al.19models to three-dimensional¯ows is straightforward.Indeed,the failure of the standard model should be attributedmainly to the modeling of its generation term,which is based onthe assumption that the production of dissipation should keep pacewith the production of turbulent energy,i.e.,without any lag in theprocess of spectral energy transfer.This assumption is known to beaccurate only for the¯ows in local equilibrium.But the¯ow nearthe concave wall is not in local equilibrium.If there is no lag in the transfer of energy from large eddies tosmall eddies,then the energy level at small eddies(hence the levelof dissipation)in a concave boundary layer should be signi®cantlyhigher than that in a¯at boundary layer because it is well knownthat the energy level of large eddies in a concave boundary layer isLUO AND LAKSHMINARAYANA1277a)Turbulent shear stressb)Streamwise rms turbulent velocityc)Radial rms turbulent velocityd)Streamwise mean velocityFig.4Pro®les of90-deg duct¯ow atµ=45deg(Ref.23).much higher than that in a¯at boundary layer.However,throughthe measurement of energy spectra,Barlow and Johnston3foundthatªat high frequencies,the energy content of the turbulence isabout the same as in the¯at boundary layer for all y-locations,suggesting that the small-scale turbulence structure is essentiallyunaffectedby curvature.ºIn theirdirectnumericalsimulation(DNS)of a mildly curved channel¯ow,Moser and Moin26concluded thatªthe dissipation terms,which are dominated by the small scales,are in good agreement on the two walls(convex and concave)....This suggests that curvature has a minimal effect on small scale ofturbulence.ºAll of these observations indicate that there is a lag in the devel-opment of true dissipationin concave boundary layers as suggestedby Lumley17for evolving nonequilibrium¯ows.Thus,to capturethe large ampli®cation of turbulence in concave boundary layers,the generationterm in the equation should not keep pace with thatin the k equation.This is the reason for the signi®cant improvementobtained by both the LPS model and Lumley and Shih et al.’smodel,as has been demonstrated in Fig.3.90-deg Duct FlowThe predictedpro®les for uv,uu,vv,and U at=45degand0.5H downstream of the bend for Kim and Patel’s23¯ow arepresented in Figs.4and5,respectively.The curvature parameter(/R)of this¯ow is considerablysmaller than that of Sandborn andShin22(Table1).The opposite effects of convex and concave curva-a)Turbulent shear stressb)Streamwise rms turbulent velocityc)Radial rms turbulent velocityd)Streamwise mean velocityFig.5Pro®les of90-deg duct¯ow at0.5H downstream of bend.23tures are still quite signi®cant as seen from the highly nonsymmetricpro®les of turbulencequantities.The experimentaluncertaintyis re-ported to be1.5%in streamwise mean velocity(U),5%in uu,and10%in other turbulence stresses.23At both streamwise locations,the turbulence level near the concave wall is signi®cantly underpre-dicted by the RSM with the standard model.The predictions bythe RSM with both modi®ed models are in signi®cantly closeragreement with the data.This gives further support to the argumentmade earlier.At=45deg,the measurement has nearly equal values for thethree Reynolds stress components.The RSMs with both modi®edmodels capture uu quite well but still underpredict the val-ues of vv near the concave wall(Figs.4a±4c).At0.5H down-stream of the bend,the measured radial¯uctuation velocity v iseven slightly higher than the streamwise velocity u near the con-cave wall(Figs.5a±5c).The RSMs with both modi®ed modelscapture the turbulence quantities near the concave wall much betterthan the RSM with the standard model.The predicted skin-friction coef®cient C f on the convex wall ofthis duct is shown in Fig.6a.The predicted values of C f from allthe RSM models are about the same and in good agreement with thedata.The standard k±model,however,substantially overpredictsthe value of C f due to its overpredictionof the turbulentshear stressas shown earlier.On the concavewall,as seen in Fig.6b,the levelsofC f predicted by different models are seen to be proportionalto thepredicted levels of turbulent energy and uv.The standard k±1278LUO AND LAKSHMINARAYANAa)Inner wall b)Outer wallFig.6Skin-friction coef®cients for90-deg duct¯ow.23a)Turbulent shear stressb)Streamwise rms turbulent velocityc)Radial rms turbulent velocityFig.7Pro®les of concave boundary-layer¯ow atµ=30deg(Ref.24). model underpredicts the value of C f due to its underprediction of uv.The RSM with the standard model also underestimatesthe C f because it has not captured the large ampli®cation of turbulence near the concave wall.The RSMs with the two modi®ed models predict the highest level of turbulence and hence the highest C f, both being in best agreement with the data.Concave Turbulent Boundary LayerIn both the geometries presentedearlier,the boundarylayers near the concave wall are subject to a fairly strong streamwise pressure gradient.To isolate the effects of concave curvature from thoseFig.8Skin-friction coef®cient for concave boundary layer.24 caused by the pressure gradient,the inner wall in Johnson and Johnston’s2490-deg duct was contoured to minimize the pressure gradient on the outer(test)wall.The turbulent velocity¯uctuations and shear stress pro®les are presented in Figs.7a±7c for=30degwhere y starts from outer wall.The four models provide predic-tions in different levels of agreement with the data,similar to what has been observed for the aforementioned cases with the in¯uence of pressure gradient.This further supports the argument that the standard model must be modi®ed to capture the turbulence ampli-cationin concaveboundarylayerswith/withoutpressuregradients. Finally,the predicted C f is shown in Fig.8.The behavior of C f is different from that of Kim and Patel’s23duct because the streamwise pressure gradient is now much lower.The predicted values of C f by different turbulence models are seen to correspond to the predicted turbulence quantities.The RSMs with the modi®ed models provide the best predictions for turbulence quantities and hence for the skin-friction coef®cient.Concluding RemarksNumerical computationsusing Reynoldsstress models have been carried out to investigate the effects of surface curvature,particu-larlyconcavecurvature,on turbulentduct¯ows and boundarylayers. The modeling of concave curvature effect is observed to be qualita-tively different from the modeling of convex curvature effect.The RSM model is very successfulin predictingthe turbulencedamping due to convex curvature but underpredicts the magnitude of turbu-lence ampli®cation due to concave curvature.The present analyses indicate that there is a lag in the development of true dissipation in concave boundary layers.To capture the large ampli®cation of turbulence in concave boundary layers,the generation term in the equation should not keep pace with that in the k equation.A。