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Introduction / Specific Instructions / Notes / Changes from 1.0/ Changes from 2.0

    The motion of most fluid flows of engineering interest is completely described by the Navier Stokes equations. Except in very simple situations, however, these equations are too difficult to solve. At the beginning of the 20th century Ludwig Prandtl proposed a division of the problem to make it more tractable. He hypothesized that viscous effects (associated with the most troublesome terms in the Navier Stokes equations) are only important in a thin region immediately adjacent to a solid surface, termed the boundary layer. Here the velocity reduces rapidly to zero at the surface (the no-slip condition). As long as this region remains thin then a number of approximations can be made that greatly simplify the equations. This idea has turned out to be an extremely powerful one, to the extent that a huge number of engineering flow calculations today are performed by combining an inviscid solution for the outer flow with a viscous boundary layer solutions to provide the flow near the body. The present applets implement several different boundary layer calculation methods. Along with the Vortex Panel Method Applet (or another inviscid solver) they can be used to obtain complete flow solutions of the type envisaged by Prandtl.

    The boundary-layer equations (the thin-layer approximation to the Navier Stokes) are partial differential equations. They can be solved directly by finite difference method. Alternatively, if the form of the boundary layer velocity and/or temperature profile is assumed, they can be reduced to ordinary differential equations with respect to distance along the body surface that can be numerically integrated. Techniques that use this second approach are termed 'integral methods'. They are more empirical (i.e. approximate) than finite difference methods but are much faster.

    Boundary layers can be either laminar or turbulent. Laminar boundary layers usually form near the leading edge or nose of a body. The flow in a laminar boundary layer is smooth and steady. Turbulent boundary layers are formed when the laminar boundary reaches a certain age (Reynolds number) and becomes unstable, undergoing transition. The flow inside a turbulent boundary layer is unsteady and irregular and it is the time-averaged boundary layer equations that must be solved in this case. However, the time-averaging process (which is necessary to make the equations soluble) introduces a new term into the equations (the Reynolds stress term) that must be estimated using empirical information, known as a turbulence model. In a finite difference method an explicit turbulence model is used. In an integral method, the turbulence model is implicit in the assumed form of the velocity profile.

    When a temperature difference exists between a body and the flow through which it is moving, or when compressibility effects are significant, both thermal and aerodynamic boundary layers are formed. In low-speed flow when the temperature differences do not significantly influence the boundary layer dynamics, the thermal boundary layer can be estimated through a fairly straightforward extension of a boundary layer method. In high-speed flow the thermodynamics and aerodynamics become coupled and are solved simultaneously.

    Here we present nine applets for calculating boundary layer flows, four for laminar boundary layers (WALZ, ILBLI, CLBL and WALZHT), five for turbulent (MOSES, ITBL, JETMIX, CTBL and MOSESHT). Out of these, 4 employ integral methods (WALZ, MOSES, WALZHT, MOSESHT), 4 finite difference methods (ILBLI, CLBL ITBL, CTBL), 7 are for incompressible flow (WALZ, ILBLI, WALZHT, MOSES, ITBL, JETMIX and MOSESHT), 2 for compressible flow (CLBL, CTBL) and 4 have the capability of computing thermal boundary layers (WALZHT, MOSESHT, CLBL and CTBL). Detailed descriptions of the theory and methods behind the seven basic methods (WALZ, MOSES, ILBLI, ITBL, CLBL, JETMIX, CTBL), along with Fortran programs that implement these methods (except CTBL) are found in  "Boundary Layer Analysis, Revised" by J. A. Schetz, AIAA, 2010. Indeed, these applets were originally developed as supplementary material for that text, although they can be used in a stand-alone manner. Descriptions of the theory behind the extensions of WALZ and MOSES to handle heat transfer (WALZHT and MOSESHT) are provided in our paper HEAT TRANSFER CODES FOR STUDENTS IN JAVA and its references.

Specific Instructions
   The following instructions describe the six incompressible methods (WALZ, ILBLI, WALZHT, MOSES, ITBL, JETMIX, and MOSESHT). The operation of the two compressible methods (CTBL and CLBL) is very similar and can easily be inferred from the incompressible codes. Furthermore, explicit instructions for CLBL and CTBL will be added in the near future.

Any of the applets can be launched by pressing the appropriate button on the applet page. You can launch any number of the same or different applets at the same time. Each applet opens in a window that will remain open until you close it, or your browser. Otherwise this window is browser independent. All the applets have the same basic interface, illustrated on the below for ITBL.

    The bulk of the applet window consists of a panel containing three graphs which display the results of or inputs to the calculation (to change the quantities plotted, simply click on the graphs). The lower of these three graphs always displays the boundary layer thicknesses and their development. The three laminar methods also include routines for estimating when transition occurs. Transition is also indicated on this graph by a vertical arrow labelled "T". All of the methods detect (and stop at) boundary layer separation. Separation is indicated on this graph by a vertical arrow labelled "S".
    The lower part of the panel contains a list of all the properties/quantities that are needed to perform the boundary layer calculation. These include items such as the properties of the fluid, the reference properties of the flow (on which the inputs and outputs are scaled), the characteristics of the surface on which the boundary layer is growing, calculation parameters (step sizes etc.) and initial boundary layer parameters (for methods that do not start at the leading edge). All numerical items can be changed simply by selecting them, typing the new value into the text area to the right of the list, and clicking the "Change" button. To change a non-numerical item (e.g. anything listed under Surface Characteristics), select the item and click the "Change" button. This will bring up an appropriate dialog box. Note that items in the list in black text only serve as headings and cannot be selected.  The three laminar methods (WALZ, ILBLI and WALZHT) base their transition predictions on Michel's method (see "Boundary Layer Analysis, Revised" by J. A. Schetz, AIAA, 2010). Michel's method predicts that transition occurs when Re(theta)=2.9*(Rex)0.4. Here Re(theta) is the momentum thickness Reynolds number and Rex is the Reynolds number based on distance from the origin of the boundary layer (the leading edge), both based on the local edge velocity. The constant of 2.9 assumes that a boundary layer on a flat plate would undergo transition at Rex = 2,500,000. This value is rather high for most applications so we have included the flat plate transition Reynolds number (and therefore this constant) as an input in this list for these laminar methods.
    At the bottom of the applet there are two buttons "Run" and "Step" and a slidebar. Pressing the "Run" button instructs the applet to proceed with the calculation (results are plotted as the calculation proceeds) during which the label on this button changes to "Pause". Once the calculation is complete the label changes to "Reset". Pressing "Pause" causes the calculation to pause, pressing "Reset" returns the applet to the start of the calculation. The step button causes one streamwise (x) step of the calculation to be performed before pausing. Repeatedly pressing this button allows one to proceed through the calculation step by step. The slidebar controls the speed of the calculation. It can be instructive to watch the boundary layer develop as the calculation proceeds, but on most computers the calculation speed is to fast to see this. The calculation speed can be artificially slowed by moving the slidebar to the left.
    At the top of the applet window are menus each containing a list of items. The function of each of these items is explained below:

File Menu

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Changes from Version 2.0
Changes from Version 1.0
The applet interfaces are quite different than in Version 1.0 :- However, the underlying numerical methods are identical to those used in version 1.0 - the same calculation performed with the versions 1.0 and 2.1 will produce identical results. If, for some reason, you would like to run one of the applets in its version 1.0 form, they are still available here.

Current Applet Version 2.1. Last HTML/Applet update 4/19/02. Questions or comments please contact William J. Devenport