• Author / Uploaded
• Antonio L. Negron

Citation preview

Contents

Solving Engineering Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Setting Up Engineering Problem in Flow Simulation . . . . . . . . . . . . . . . Selecting Geometrical and Physical Features of the Problem . . . . . . . . . . . . . . . . . Creating the Model and the Flow Simulation Project . . . . . . . . . . . . . . . . . . . . . . . 2 Solving Engineering Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strategy of Solving Engineering Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1-1 1-4 1-4 1-4 1-6 1-6

Settings for Resolving the Geometrical Features of the Model and for Obtaining the Required Solution Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 Monitoring the Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9 Viewing and Analyzing the Obtained Solution . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10 Estimating the Reliability and Adequacy of the Obtained Solution . . . . . . . . . . . . . 1-10

3 Frequent Errors and Improper Actions . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11

Advanced Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 1 Mesh - Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 Types of Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 Mesh Construction Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Basic Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Control Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Resolving Small Features by Using the Control Planes . . . . . . . . . . . . . . . . . . . . . 2-5 Contracting the Basic Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Resolving Small Solid Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7 Curvature Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7 Tolerance Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9 Narrow Channel Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Local Mesh Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12

Solving Engineering Problems with Flow Simulation 2013

i

Recommendations for Creating the Computational Mesh .

.................. 2 Mesh-associated Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visualizing the Basic Mesh Before Constructing the Initial Mesh . . . . . . . . . . . . . Enhanced Capabilities of the Results Loading . . . . . . . . . . . . . . . . . . . . . . . . . . Viewing the Initial Computational Mesh Saved in the .cpt Files . . . . . . . . . . . . . . Viewing the Computational Mesh Cells with the Mesh Option . . . . . . . . . . . . . . . Visualizing the Real Computational Geometry . . . . . . . . . . . . . . . . . . . . . . . . . Switching off the Interpolation and Extrapolation of Calculation Results . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Meshing - Additional Insight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial Mesh Generation Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Mesh Generation and Resolving the Interface . . . . . . . . . . . . . . . . . . . . Narrow Channel Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thin walls resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Square Difference Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mesh Diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refinements at Interfaces Between Substances . . . . . . . . . . . . . . . . . . . . . . . . . Small Solid Features Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Curvature Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SSFRL or CRL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tolerance Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Local Mesh Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The "Optimize thin walls resolution" option . . . . . . . . . . . . . . . . . . . . . . . . . . . Postamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Calculation Control Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finishing the Calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refinement of the Computational Mesh During Calculation . . . . . . . . . . . . . . . . . 5 Flow Freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What is Flow Freezing? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How It Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Freezing in a Permanent Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow Freezing in a Periodic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-13 2-14 2-14 2-14 2-14 2-16 2-16 2-17 2-19 2-20 2-20 2-21 2-21 2-23 2-25 2-26 2-28 2-28 2-28 2-29 2-30 2-31 2-31 2-32 2-33 2-33 2-33 2-33 2-34 2-37 2-40 2-40 2-40 2-41 2-42

Advanced Features Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1 1 Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Engineering Cavitation Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isothermal Cavitation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

3-1 3-2 3-2 3-2 3-3

Examples of use. . Recommendations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8 2 Steam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 3 Humidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11 Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-12 Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 4 Real Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15 Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16 Example of use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19 5 Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20 Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20 Local Rotating Regions - Additional Information. . . . . . . . . . . . . . . . . . . . . . . 3-21 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22 Global Rotating Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22 Local Rotating Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 Examples of Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-26

Solving Engineering Problems with Flow Simulation 2013

iii

iv

1 Solving Engineering Problems

Introduction The most common problem, which almost every engineer faces every day, is to design a device or process with the desired parameters, having only limited resources both for the design effort itself and for the resulting device or process operation. Various tools and methods are used to solve this problem. Flow Simulation can help the engineer to predict and optimize fluid flows and heat transfer in a wide variety of applications, and makes solving the engineering problems easier and faster. In general, there are three approaches to solving engineering problems: • an experimental approach: a hardware rig or prototype, i.e., the full-scale object and/or its model, is manufactured and the experiments needed for designing the object are conducted with this hardware; • a computational approach: the computations needed for designing the object are performed and their results are directly used for designing the object, without conducting any experiments; • a computational-experimental approach combines computations and experiments (with the manufactured full-scale object and/or its model) needed for designing the object; their sequence and contents depend on the solved problem and iterative procedures may be run. Each of the first two approaches has advantages and disadvantages. The purely experimental approach, being properly conducted, does not require additional validation of the obtained results, but is very expensive, even if it is performed on the object models, since testing facilities and hardware are required anyway. Moreover, if the object models are tested, the obtained results must be scaled to the full-scale object, so some computations are still involved.

Solving Engineering Problems with Flow Simulation 2013

1-1

Solving Engineering Problems

The purely computational approach, being properly performed, is substantially less expensive than the experimental one, both in terms of finances and time, but it requires assurance in adequacy of the obtained computational results. Naturally, such assurance must be based on numerous verifications and validations of the used computational codes, both on the mathematical accuracy of the obtained results (the results adequacy to the used mathematical model) and on the adequacy of the used mathematical model to the governing physical processes, which is validated by comparing the computation results to the available experimental data. The third approach, if it combines experiments and computations reasonably, joins the advantages of both of the first two above-mentioned approaches and avoids their disadvantages. Complex engineering problems are solved mainly in this way. A computational code validated on available experimental data allows quickly selecting the optimal object design and/or its optimal operating mode. Then necessary experiments are conducted to verify the selection. When selecting a computational code most suitable for solving your problems, it is necessary to consider the following suggestions. Any computational code is based, firstly, on a mathematical model of the governing physical processes (expressed in the form of a set of differential and/or integral equations derived from physical laws, and include, if necessary, semi-empirical and empirical constants and relationships) and, secondly, on a method of solving these equations. Since the equations of the mathematical model cannot be solved analytically, they are solved numerically, in a discrete form on a computational mesh, and the solution of the mathematical problem is obtained with a certain degree of accuracy. Naturally, the accuracy of the solution of a mathematical problem depends on both the method of discretising the differential and/or integral equations and on the method of solving the obtained discrete equations. Once these methods have been selected, the accuracy of solution of the mathematical problem depends on how well the computational mesh resolves the regions of a non-linear behavior in the problem. To provide a good accuracy, the mesh has to be rather fine in these regions. Moreover, the usual way of estimating the accuracy of the solution consists in obtaining solutions on several different meshes, from coarse to fine. So, if beginning from some mesh in this set, the difference in the physical parameters of interest between the solutions obtained on the finer and coarser meshes becomes negligible from the standpoint of the solved problem (the solution flattens), then the accuracy of the solution of the mathematical problem required for solving this engineering problem is considered to be attained, since the so-called solution mesh convergence is attained. Naturally, the solution of the mathematical problem can differ from the experimental values, and this difference depends, firstly, on the conformity of the mathematical model and the simulated physical processes, and, secondly, on the error, which these experimental values have been measured with, and which is known and tends to decrease upon increasing the number of tests performed to measure them.

1-2

Correspondingly, the computational codes differ from each other not only in their cost, but also in the accuracy of the mathematical simulation of physical problems, as well as in the procedure of specifying the initial data, in the amount of the user time needed for this specification, in the procedure of solving a problem and the computer memory and CPU time needed for obtaining a solution of the required accuracy, and in the procedures of processing and visualization of the obtained results and the user time needed for that. Naturally, a highly accurate solution requires a fine computational mesh, and, consequently, substantial computer memory and CPU time, as well as, in some cases, increased user time and efforts for specifying the initial data for the calculation. As the result, if the time needed to solve an engineering problem with a computational code exceeds some threshold time, then either the engineering problem becomes irrelevant (for instance, because your competitors have outpaced you by that time), or alternative approaches, which may be not so accurate, but are surely faster, are used instead to solve the problem within given time limits. Before getting acquainted with the recommended procedure of obtaining a reliable and accurate solution of an engineering problem with Flow Simulation, it is expedient to consider Flow Simulation features governing the below-described strategy of solving engineering problems with Flow Simulation. Since Flow Simulation is based on solving time-dependent Navier-Stokes equations, steady-state problems are solved through a steady-state approach. To obtain the steady-state solution quicker, a method of local time stepping is employed over the computational domain considered. A multigrid method is used for accelerating the solution convergence and suppressing parasitic oscillations. The computational domain is designed as a parallelepiped enveloping the model with planes orthogonal to the axes of the Cartesian Global coordinate system of the model. The computational mesh is built by dividing the computational domain into parallelepiped cells with its sides orthogonal to the Global coordinate system axes. (The cells lying outside the fluid-filled regions and outside solids with heat conduction specified do not participate in the calculations). Procedures of the computational mesh refinement (splitting) are used to resolve the model features better, such as high-curvature surfaces in contact with fluid, thin walls surrounded by fluid, narrow flow passages (gaps), and the specified insulator boundaries. During the calculation the computational mesh can be refined additionally (if that is allowed by the user-defined settings) to better resolve the high-gradient flow and solid regions revealed in the calculation (Solution-Adaptive Meshing). Since steady-state problems are solved in Flow Simulation through the steady-state approach, it is necessary to determine the termination moment for the calculation properly. If the calculation is finished too early, when the steady state solution has not been attained yet, then the obtained solution can depend on the specified initial conditions and so be not very reliable. On the contrary, if the calculation is finished too late, then some time is wasted. To optimize the termination moment for the calculation and to determine physical parameters of interest (such as a force acting on a model surface, or a model hydraulic resistance) with a sufficient accuracy, you can specify them as the calculation goals.

Solving Engineering Problems with Flow Simulation 2013

1-3

Solving Engineering Problems

The way to simulate an engineering problem with SolidWorks+Flow Simulation correctly and adequately from the physical standpoint, i.e. to state the corresponding model problem, and to solve this model problem properly and reliably with Flow Simulation, is described in the chapters Setting Up Engineering Problem in Flow Simulation and Solving Engineering Problem.

1 Setting Up Engineering Problem in Flow Simulation It is necessary to remember that a fast but inaccurate beginning will cost you more efforts and time spent not only for specifying the initial data, but, even worse, for the subsequent calculations, until they finally become reliable. Therefore, we strongly recommend that you carefully read this section.

Selecting Geometrical and Physical Features of the Problem Before you open or create a SolidWorks model and define a Flow Simulation project, it is necessary to understand which geometrical and physical features most substantially influence the problem solution - first of all, those that are important for estimating the possibility of solving the problem with Flow Simulation. For example, • if the problem contains movable parts, then it is necessary to estimate the importance of taking into account their motions when solving the problem, and, if these motions are important, to estimate the possibility of solving this problem with a quasi-stationary approach, since model parts motions during the calculation are not considered in Flow Simulation (however, you may specify a translational and/or rotational motion of the specific wall or a rotating reference frame), • if the problem includes fluids of different types (for example, a gas and a liquid), and there is an interface between them or these fluids are mixing, then it is necessary to estimate the importance of taking this into account, since Flow Simulation does not consider a free fluid surface, or mixing of fluids of different types. We can present other examples of a clear impossibility of solving some engineering problems with Flow Simulation, as well as of simplifying the engineering problems for solving them with Flow Simulation, but it is impossible to envision and describe all the possible situations in the present document, so in each particular case you will have to make decision by yourself.

Creating the Model and the Flow Simulation Project If a SolidWorks model has already been created when designing the object, and it is fully adequate to the object, then, to solve the engineering problem with Flow Simulation, it can be required: • to simplify the model by removing the parts, which do not influence the problem solution, but consume computer resources, i.e. memory and CPU time. For 1-4

example, a corrugated model surface which will result in an exceedingly large number of mesh cells required to resolve it can be specified instead as a smooth surface with equivalent wall roughness. If the model has narrow fluid-filled blind holes, whose influence on the overall flow pattern is, by rough estimate, barely perceptible, it would be better to remove these features in order to avoid the excessive mesh splitting around them. • to add auxiliary parts to the model such as inlet and outlet tubes for stabilization of the flow, lids to cover the inlet and outlet openings, and parts to denote rotating regions, local initial meshes or other areas where special conditions are applied. All these actions, being executed properly, can be very pivotal in obtaining a reliable and accurate solution. On the contrary, adding auxiliary parts to a model will inevitably cause an increase of the computational mesh cells and, consequently, the required computer memory and CPU time, therefore these parts dimensions must be adequate to the stated problem. If a model has not been created yet, it is expedient to consider all the above-mentioned factors when creating it. If all effects of these actions are not clear enough, it can be worthwhile to vary the model parts and/or their dimensions in a series of calculations in order to determine their influence on the obtained solution. Then, in accordance with the problem physical features revealed and adapted to Flow Simulation capabilities, the basic part of the Flow Simulation project is specified: the problem type (internal or external), fluids and solids involved in the problem, physical features considered (such as heat conduction in solids, time-dependent analysis, gravitational effects, etc.), boundaries of the calculation domain, initial and boundary conditions, and, if necessary, fluid subdomains, rotating regions, volume and/or surface heat sources, fans and other features and conditions. The specified boundary conditions, as well as heat sources, fans, and other conditions and features must correspond to the statement of the physical problem and must not conflict with each other. Eventually, you specify the physical parameters of interest as the Flow Simulation project goals. They can be local or integral, defined within the whole computational domain or in a certain volume, on a surface or in a point. The parameters determined over some region are expressed in the form of their minimum, or maximum, average, or bulk average values. This allows you to increase the reliability and accuracy of determination of these parameters, since the goal values are saved on each iteration during the calculation and can be analyzed later. On the contrary, the convergence behavior of the parameters not specified as goals cannot be analyzed afterwards, as they are saved only at the last iteration and, optionally, at the user-specified iterations in transient simulations.

Solving Engineering Problems with Flow Simulation 2013

1-5

Solving Engineering Problems

2 Solving Engineering Problem As soon as you have specified the basic part of the Flow Simulation project that is unlikely to be changed in the subsequent calculations, the next step is to select the strategy of solving the engineering problem with Flow Simulation to obtain a reliable and accurate solution of the problem.

Strategy of Solving Engineering Problems As it is mentioned in Introduction, by performing a series of calculations on a set of computational meshes ranging from coarse to fine ones, we can estimate the accuracy of the solution of the mathematical problem. As soon as the calculation on a finer mesh does not yield a noticeably different (from the engineering problem standpoint) solution, i.e. the solution flattens with respect to the mesh cell number, we can conclude that the solution of the mathematical problem has achieved mesh convergence, which means that the required mathematical solution accuracy is attained. Naturally, first you must determine the threshold for the solution-vs.-mesh change, so that the change smaller than this threshold will be considered as negligible. Since the determination of this threshold is only possible in relation to some physical parameter, it is natural to connect it to the physical parameters of interest in the engineering problem, in particular, with the admissible error in determination of these physical parameters. Moreover, since steady-state problems are solved in Flow Simulation through the steady-state approach, monitoring the behavior of the calculation goals during the calculation can serve two purposes. Firstly, if these parameters oscillate during the calculation, it will allow you to determine their values and observation errors more accurately by averaging them over a number of iterations and determining their deviation from this average value. Secondly, you may want to intervene in the calculation process by finishing the calculation manually if you see that either the solution is unacceptable for you by some reasons, or, vice versa, if the solution has already converged, so that there is no reason to continue the calculation any further. Therefore, the strategy of solving an engineering problem with Flow Simulation consists, first of all, in performing several calculations on the same basic project (with the same model, inside the same computational domain, and with similar boundary and initial conditions) varying only the computational mesh. Since the computational mesh is built automatically in Flow Simulation, it can be changed by varying the project parameters that govern the mesh (the initial computational mesh on which the calculation starts, and maybe its refinement during the calculation): Result Resolution Level, Minimum Gap Size, Minimum Wall Thickness and other.

1-6

An additional item in this strategy of solving an engineering problem with Flow Simulation consists in varying the auxiliary elements added to the model as needed to solve the problem with Flow Simulation (such as inlet and outlet tubes attached to the inlet and outlet openings, for internal problems), the dimensions of which are questionable from the standpoint of their necessity and sufficiency. Those physical parameters of the engineering problem, whose values are not known exactly and which, in your opinion, can influence the problem solution, must be varied also. When performing these calculations, there is no need to investigate the solution-vs.-mesh convergence again, since it has already been achieved before. It is enough to just perform these calculations with the project mesh settings that provided the solution with satisfactory accuracy during the solution-vs.-mesh convergence investigation. The same applies also to the parametric engineering calculations where you change the model geometry and/or flow parameters. However, you must keep in mind the potential necessity for checking the solution-vs.-mesh convergence, because in doubtful cases it must be checked again. In spite of the apparent simplicity of the proposed strategy, its full implementation is usually troublesome due to the substantial difficulties including, first of all, a dramatic increase in the requirements for computer memory and CPU time when you substantially increase the number of cells in the computational mesh. Since both the computer memory and the time for which the engineering problem must be solved are usually restricted, the specific implementation of this strategy eventually governs the accuracy of the problem solution, whether it will be satisfactory or not. Perhaps, a further simplification of the model and/or reducing the computational domain will be required. Some specific description of this strategy is presented in the next sections of this document.

Settings for Resolving the Geometrical Features of the Model and for Obtaining the Required Solution Accuracy The computational mesh variation described in the previous section is the key item of the proposed strategy for solving engineering problems with Flow Simulation. The result resolution level governs the number of basic mesh cells, the criteria for refinement (splitting) of the basic mesh to resolve the model geometry, creating the initial mesh, as well as the criteria for refinement (splitting) of the initial mesh during the problem solution. The Result resolution level parameter, specified in the Wizard, defines the following parameters in the created project: the Level of initial mesh and the Results resolution level. The Level of initial mesh only governs the initial mesh and is accessible (after the Wizard is finished) from the Initial Mesh dialog. The Results resolution level is accessible from the Calculation Control Options dialog and controls the refinement of computational mesh during the calculation and the calculation finishing conditions. The geometry resolution options that also influence the initial mesh can be changed both in the Wizard and on the Automatic Settings tab of the Initial Mesh and Local Initial Mesh dialogs. The effects of the geometry resolution options can be altered on the other tabs of these dialogs.

Solving Engineering Problems with Flow Simulation 2013

1-7

Solving Engineering Problems

Before creating the initial mesh, Flow Simulation automatically determines the Minimum gap size and the Minimum wall thickness for the walls contacting the fluid with both sides. This is required for resolving the geometrical features of the model with the computational mesh. Flow Simulation creates the initial mesh so that the number of the mesh cells along the normal to the model surface must not be less than a certain number, if the distance along this normal from this surface to the opposite wall is not less than the minimum gap size. This insures that a flow passage or gap with the width larger than the specified minimum gap size will be resolved with a certain number of cells across it. The Minimum wall thickness governs the resolution of the sharp edges such as tips of thin fins or, if the Optimize thin walls resolution option is not selected, the overall resolution of the thin walls in the same way as the minimum gap size governs resolution of the flow passages and gaps in the model. In the automatic mode these mesh parameters are determined from the dimensions of the surfaces with the boundary conditions specified, such as the model inlet and outlet openings in an internal analysis, as well as the surfaces and volumes with the heat sources, local initial conditions, surface and/or volume goals and some of the other conditions and features. If you select the options to specify the Minimum gap size and the Minimum wall thickness manually, you can see the their values determined by Flow Simulation. If these values cannot provide an adequate resolution of the model geometry, you can change them. At that, it is necessary to remember that the number of the computational mesh cells generated to resolve the model geometrical features depends on the specified result resolution level. Evidently, when creating a Flow Simulation project, it is always worthwhile to make sure that both the minimum gap size and the minimum wall thickness are relevant to the model geometry. However, if the model geometry is complicated (for instance, there are non-circular flow passages, sharp edges protruding into the stream, etc.), it can be difficult to determine these parameters unambiguously. In this case it can be useful to perform several calculations by varying these parameters within a reasonable range in order to reveal their influence on the problem solution. In accordance with the strategy of solving engineering problems, these calculations must be performed at various result resolution levels. The initial mesh created at the result resolution levels of 3…5 is not changed during the calculation, so it is not adapted to the solution. Result resolution levels of 5…7 yield the same initial mesh, but at the result resolution levels of 6 and 7 the mesh is refined during the calculation in the regions of increased physical parameters gradients. At level 8, a finer initial mesh is generated and refinements during calculation take place. It makes sense to perform calculations at the result resolution level of 3 if both the model geometry and the flow field are relatively smooth. For more complex problems we recommend, first of all, to perform the calculation at the result resolution level of 4 or 5 (naturally, explicitly specifying the minimum gap size and minimum wall thickness). After that, if the calculation at the result resolution level of 5 is finished properly, we recommend, in order to ascertain the mesh convergence, to perform the calculation at the result resolution level of 7 and, if the computer resources allow you to do this, at the result 1-8

resolution level of 8.

Monitoring the Calculation Monitoring the calculation - at least, monitoring the behavior of the physical parameters specified by you as the project goals (you can also inspect physical parameters fields at the specified planar cross-sections) is useful for the following reasons: • you can intervene in the process of calculation - for instance, manually finish the calculation before it finishes automatically, if you see that either the calculation is unacceptable for you for some reasons (for example, if Flow Simulation generates warnings), or, vice versa, when solving a steady-state problem (and some transient problems also), the solution has already converged, so that there is no reason to continue the calculation; • if a steady-state problem is solved, and the physical parameters specified by you as the project goals oscillate with iterations, then inspecting the behavior of these parameters during the calculation will allow you to determine their values and determination errors more accurately by averaging their values over the iterations and determining their deviations from these average values; • if the physical parameters of interest do not change substantially during the calculation, you can obtain their intermediate (preliminary) values beforehand and use them for engineering analysis, while letting the calculation to continue until the final values are reached; • if you solve a time-dependent problem, you can see the calculation results obtained at the current physical time moment before the calculation is finished. The first above-mentioned reason is particularly useful since it allows you to substantially reduce the CPU time in some cases. For example, if you do not specify the high Mach number gas flow in the project settings, whereas in fact the flow reaches high Mach numbers, or if Flow Simulation warns you about a vortex at the model outlet, both situations substantially reducing the calculation accuracy and making it necessary to change some of the problem settings (specify high Mach number flow for the first case or lengthen the model outlet tube for the second one). If you solve a steady-state problem at the result resolution level of 7 or 8 and you see that the computational mesh refinements performed during the calculation do not increase the number of cells in the mesh and, therefore, do not noticeably improve the problem solution (the values of the project goals do not change), you can finish the calculation relatively early (say, after 1…2 travels have been performed).

Solving Engineering Problems with Flow Simulation 2013

1-9

Solving Engineering Problems

Viewing and Analyzing the Obtained Solution When viewing and analyzing the obtained solution after finishing the calculation, it is recommended to plot the history of the project goals during the calculation, if you did not monitor them directly as the calculation went on. If a steady-state problem is solved, and you specified the physical parameter of interest as the project goal, then, if this parameter oscillated during the calculation, you can determine its value more accurately by averaging it over the last iterations interval, in which its steady-state oscillation is seen. This way you can also determine the variance of this goal, i.e. its deviation from the average value, that characterizes the goal determination error in the obtained solution. It is also useful to check for vortices at the model outlet, as well as to see the flow pattern in the model and, if heat transfer in solids is considered, the temperature distribution through the solid parts of the model. Naturally, first of all it is expedient to see the obtained field of the physical parameter of interest, not only in the region of interest, but also in a broader area, in order to check this field for apparently inconsistent results. It is also worthwhile to examine the obtained fields of other physical parameters related to the parameter of interest. For example, if you are interested in the total pressure loss, you may want to see the velocity field, whereas if you are interested in the temperature of solid, a picture of the fluid-to-solid heat flux field is also useful.

Estimating the Reliability and Adequacy of the Obtained Solution In accordance with the general approach to estimating the reliability and accuracy of the engineering problem solution obtained with a computational code, this estimation consists of the following two parts: an estimation of how accurate is the solution of the mathematical problem corresponding to the mathematical model of the physical process, and an estimation of the accuracy of simulating the physical process with the given mathematical model. The accuracy of solution of the mathematical problem is determined by mathematical methods, independently of the consistency of the model to the physical process under consideration. In our case, this accuracy estimation is based on analyzing the mesh convergence of the problem solutions obtained on different computational meshes. Then, since steady-state problems are solved with Flow Simulation via a steady-state approach by employing local time steps, it is useful to verify additionally the accuracy of the obtained solution by solving the similar time-dependent problem not employing local time steps. As soon as the mathematical problem solution of a satisfactory accuracy is obtained, the next step consists in estimating the accuracy the physical process simulation with the mathematical model employed in the computational code. To do this, the obtained solution is compared with the available experimental data (considering the errors which consist of measurement errors and experimental errors arising from possible spurious influences). Naturally, since experimental data are always restricted, for the validation it is desirable to select the data which are as close to the engineering problem being solved as possible. To validate the computational code against the available experimental data, you must solve 1-10

the corresponding test problem in addition to the practical engineering problem you are solving (preferably before you start to solve the practical problem following the above-mentioned strategy). This operation increases the reliability of estimating the obtained solution of the engineering problem so substantially that the required additional time and efforts will fully pay back later on, in particular when solving similar engineering problems. If after solving the test problem you see that the accuracy of its solution obtained with Flow Simulation is not satisfactory from your standpoint, check to see that you have properly specified the Flow Simulation project, that all substantial features of the engineering problem hare considered, and, finally, that Flow Simulation restrictions do not impede solving this engineering problem.

3 Frequent Errors and Improper Actions Let us consider the most common errors and improper actions that can occur when solving engineering problems with Flow Simulation.  When Specifying Initial Data:

• not considering physical features which are important for the engineering problem under consideration: for instance, high Mach number gas flow (it must be considered if M>3 for steady-state and M>1 for transient problems or if the supersonic flow occurs in about a half of the computational domain or greater), gravitational effects (must be considered if either the fluid velocity is small, the fluid density is temperature-dependent, and a heat source is considered, or several fluids having substantially different densities are considered in a gravitational field), necessity of a time-dependent analysis (for instance, at the moderate Reynolds numbers, when unsteady vortices are generated); • incorrectly specifying symmetry planes as the computational domain boundaries (for instance, at the moderate Reynolds numbers, when unsteady vortices are generated; you should keep in mind that the symmetry of model geometry and initial and boundary conditions does not guarantee the symmetry of the flow field); • if you specify symmetry planes and intend to specify a mass or volume flow rate at a model inlet or outlet opening, please do not forget to adjust the flow rate accordingly, instead of specifying the total flow rate: for instance, if the symmetry plane crosses the inlet opening and splits it in two halves, specify a half of the flow rate value; • if you specify integral boundary or volume conditions (heat transfer rates, heat generation rate, etc.), please remember that their values specified in the Flow Simulation dialog boxes correspond to the fraction of area or volume laying inside the computational domain;

Solving Engineering Problems with Flow Simulation 2013

1-11

Solving Engineering Problems

• if you specify a flow swirl on a model inlet or outlet opening (in the Fans or Boundary Conditions dialogs), please do not forget to properly specify their swirl axes and the coordinate system; • if you specify a Unidirectional or Orthotropic porous medium, please do not forget to specify their directions; • please make sure that the specified boundary conditions do not conflict with each other. For example, if you deal with gas flows and the model inlet flow is subsonic, whereas the flow inside the model becomes supersonic, it is incorrect to specify flow velocity or volume flow rate as the boundary condition at the model inlet, since they are fully determined by the geometry of the model flow passage and the fluid specific heat ratio; • if you solve a time-dependent problem, and this problem has cyclic-in-time boundary conditions, thus leading to a steady-state cyclic-in-time solution, to obtain which you have to calculate the flow several times in cycle, every time specifying the solution from the previous calculation as the initial condition for the next calculation, there is no need to specify the boundary conditions for several cycles. Instead it is more convenient to specify them for a cycle and perform a series of calculations, running each calculation with the Take previous results check box selected in the Run dialog; • when specifying Surface Goals, Volume Goals, Point Goals or Equation Goals, it is better to give them sensible names to identify these goals unambiguously; • if you want to monitor the intermediate calculation results at certain sections of the model during the calculation, it is better to determine these sections positions in the Global coordinate system before actually running the calculation, since during the calculation it is more difficult;  When Monitoring a Calculation:

• when monitoring intermediate calculation results during a calculation, please do not forget the spatial nature of the problem being solved (of course, if the problem itself is not 2D). To take a look at the full pattern it is expedient to see the results at least in 2 or 3 intersecting planes;  When Viewing the Obtained Solution after Finishing a Calculation:

• to view different result features in different panes simultaneously, you can split the SolidWorks graphics area into 2 or 4 panes and build different result features in different graphical areas through their individual Cut Plots, 3D Plots, Surface Plots, Flow Trajectories, Isosurfaces defined in these areas; • if you intend to see integral physical parameters (such as area, mass or volume flow rates, heat generation rates, forces, etc.) with the Surface Parameters dialog box, please remember that: • the shown values are determined over the parts of the surface that belong to the computational domain;

1-12

• their determination errors include errors of representing these surfaces in SolidWorks and Flow Simulation, the latter depends on the computational mesh;

Solving Engineering Problems with Flow Simulation 2013

1-13

Solving Engineering Problems

1-14

2 Advanced Knowledge

Introduction The present document supplies you with our experience of employing the advanced Flow Simulation capabilities, organized in the following topics:  Manual adjustment of the initial computational mesh settings  Mesh-associated tools (viewing the mesh before and after the calculation and

advanced post-processing tools)  Calculation control options (refinement of the computational mesh during calculation,

conditions of finishing the calculation)  Flow freezing

1 Mesh - Introduction This chapter provides the fundamentals of working with the Flow Simulation computational mesh, describes the mesh generation procedure and explains the use of parameters governing both automatically and manually controlled meshes. First, let us introduce a set of definitions.

Types of Cells Any Flow Simulation calculation is performed in a rectangular parallelepiped-shaped computational domain which boundaries are orthogonal to the axes of the Cartesian Global Coordinate System. A computational mesh splits the computational domain with a set of planes orthogonal to the Cartesian Global Coordinate System's axes to form rectangular parallelepipeds called cells. The resulting computational mesh consists of cells of the following four types:

Solving Engineering Problems with Flow Simulation 2013

2-1

Advanced Knowledge

• Fluid cells are the cells located entirely in the fluid. • Solid cells are the cells located entirely in the solid. • Partial cells are the cells which are partly in the solid and partly in the fluid. For each partial cells the following information is kept: coordinates of intersections of the cell edges with the solid surface and normal to the solid surface within the cell. As an illustration let us look at the original model (Fig.1.1) and the generated computational mesh (Fig.1.2).

Fig.1.1

The original model.

Fluid cell

First level cell

Partial cell Partial cell

Solid cell

Zero level cell (basic cell)

Fig.1.2 The computational mesh cells of different types

2-2

Mesh Construction Stages Refinement is a process of splitting a rectangular computational mesh cell into eight cells by three orthogonal planes that divide the cell's edges in halves. The non-split initial cells that compose the basic mesh are called basic cells or zero level cells. Cells obtained by the first splitting of the basic cells are called first level cells, the next splitting produces second level cells, and so on. The maximum level of splitting is seven. A seventh level cell is 87 times smaller in volume than the basic cell. During the solution-adaptive meshing the cells can be refined and merged. See ”Refinement of the Computational Mesh During Calculation’ on page 37. The following rule is applied to the processes of refinement and merging: the levels of two neighboring cells can only be the same or differ by one, so that, say, a fifth level cell can have only neighboring cells of fourth, fifth, or sixth level. The mesh is constructed in the following steps:  Construction of the basic mesh taking into account the Control Planes and the

respective values of cells number and cell size ratios.  Resolving of the interface between substances, including refinement of the basic mesh

at the solid/fluid and solid/solid boundaries to resolve the relatively small solid features and solid/solid interface, tolerance and curvature refinement of the mesh at a solid/fluid, solid/porous and a fluid/porous boundaries to resolve the interface curvature (e.g. small-radius surfaces of revolution, etc). If you switch on or off heat conduction in solids, or add/move insulators, you should rebuild the mesh.  Narrow channels refinement, that is the refinement of the mesh in narrow channels

taking into account the respective user-specified settings.  Refinement of all fluid, and/or solid, and/or partial mesh cells up to the user-specified

level.  Mesh conservation, i.e. a set of control procedures, including check for the difference

in area of cell facets common for the adjacent cells of different levels. After each of these stages is passed, the number of cells is increased to some extent. In Flow Simulation you can control the following parameters and options which govern the computational mesh: 1 Nx, the number of basic mesh cells (zero level cells) along the X axis of the Global

Coordinate System. 1 ≤ Nx ≤ 1000 2 Ny, the number of basic mesh cells (zero level cells) along the Y axis of the Global

Coordinate System. 1 ≤ Ny ≤ 1000. 3 Nz, the number of basic mesh cells (zero level cells) along the Z axis of the Global

Coordinate System. 1 ≤ Nz ≤ 1000. Solving Engineering Problems with Flow Simulation 2013

2-3

Advanced Knowledge

4 Control planes. By adding and relocating them you can contract and/or stretch the

basic mesh in the specified directions and regions. Six control planes coincident with the computational domain's boundaries are always present in any project. 5 Small solid features refinement level (Lb). 0 ≤ Lb ≤ 9. 6 Curvature refinement level (Lcur). 0 ≤ Lcur ≤ 9.

7 Curvature refinement criterion (Ccur). 0 ≤ Ccur ≤ . 8 Tolerance refinement level (Ltol). 0 ≤ Ltol ≤ 9. 9 Tolerance refinement criterion (Ctol). 0 ≤ C tol. 10 Narrow channels refinement: Characteristic number of cells across a narrow channel,

Narrow channels refinement level, The minimum and maximum height of narrow channels to be refined. These options are described in more detail below in this chapter.

Basic Mesh The basic mesh is a mesh of zero level cells. In case of 2D calculation (i.e. if you select the 2D plane flow option in the Computational Domain dialog box) only one basic mesh cell is generated automatically along the eliminated direction. By default Flow Simulation constructs each cell as close to cubic shape as possible. The number of basic mesh cells could be one or two less than the user-defined number (Nx, Ny, Nz). There is no limitation on a cell oblongness or aspect ratio, but you should carefully check the calculation results in all cases for the absence of too oblong or stretched cells.

b) 40x36x1

a) 10x12x1

Fig.1.3 Basic mesh examples.

2-4

Control Planes The Control Planes option is a powerful tool for creating an optimal computational mesh, and the user should certainly become acquainted with this tool if he is interested in optimal meshes resulting in higher accuracy and decreasing the CPU time and required computer memory. Control planes allow you to resolve small features, contract the basic mesh locally to resolve a particular region by a denser mesh and stretch the basic mesh to avoid excessively dense meshes.

Resolving Small Features by Using the Control Planes If the level of splitting is not high enough, small solid features may be not resolved properly. In this case, two methods can be used to improve the mesh: • increase the level of splitting. However, this may result in unnecessary increase of the number of cells in other regions, creating a non-optimal mesh, or • set a control plane crossing the relevant small feature (e.g. a solid's sharp edge). This will allow you to resolve this feature better without creating an excessively dense mesh elsewhere. It is especially convenient in cases of sharp edges oriented along the Global Coordinate System axes. It is recommended that you place a control plane slightly submerged into the solid, and avoid placing it coincident with the solid surface.

Contracting the Basic Mesh Using control planes you may contract the basic mesh in the regions of interest. To do this, you need to set control planes surrounding the region and assign the proper Ratio values to the respective intervals. The cell sizes on the interval are changed gradually so that the proportion between the first and the last cells of the interval is close (but not necessarily equal) to the entered Ratio value. Negative values of the ratio correspond to the reverse order of cell size increase. Alternatively, you may explicitly set the Number of cells for each interval, in which case the Ratio value becomes mandatory. For example, assume that there are two control planes Plane1 and Plane2 (see Fig.1.4) and the ratio on the interval between them is set to 2. Then the basic mesh cells adjacent to the Plane1 will be approximately two times longer than the basic mesh cells adjacent to the Plane2.

Solving Engineering Problems with Flow Simulation 2013

2-5

Advanced Knowledge

Default control plane

Plane 4

Interval 3: number of cells=3 (automatic) ratio=1

Plane 3

Custom control plane Interval 2: number of cells=12 (manual) ratio=1

Custom control plane

Plane 2

Interval 1: number of cells=12 (automatic) ratio=2

Default control plane

Plane 1

Fig.1.4 Specifying custom control planes.

Use of control planes is especially recommended for external analyses, where the computational domain may be substantially larger than the model.

Fig.1.5

Default control planes.

Fig.1.6 Two custom control planes.

In the Fig.1.6 two custom control planes are set through the center of the body with the ratio set to 5 and -5, respectively, on the intervals to the both sides of each plane.

2-6

Resolving Small Solid Features The procedure of resolving small solid features refines only the cells where the solid/fluid (solid/solid, solid/porous as well as fluid/porous) interface curvature is too high: the maximum angle between the normals to a solid surface inside the cell exceeds 120, i.e. the solid surface has a protrusion within the cell. Such cells are split until the the Small solid features refinement level of splitting mesh cells is achieved.

Curvature Refinement The curvature refinement level is the maximum level to which the cells will be split during refinement of the computational mesh until the curvature of the solid/fluid or fluid/porous interface within the cell becomes lower than the specified curvature criterion (Ccur). The curvature refinement procedure has the following stages: 1 Each solid surface is triangulated: Flow Simulation gets triangles that make up the

SolidWorks surfaces. The performance settings do not govern the triangulation performance. 2 A local (for each cell) interface curvature is determined as the maximum angle

between the normals to the triangles within the cell. 3 If this angle exceeds the specified Ccur, and the curvature refinement level is not

reached then the cell is split.

Solving Engineering Problems with Flow Simulation 2013

2-7

Advanced Knowledge

The curvature refinement is a powerful tool, so that the competent usage of it allows you to obtain proper and optimal computational mesh. Look at the following illustrations to the curvature refinement by the example of a sphere.

Fig.1.7 Curvature refinement level is 0;

Fig.1.8 Curvature refinement level is 1;

Total number of cells is 64.

Total number of cells is 120.

Fig.1.9 Curvature refinement level is 2; Curvature criterion is 0.317; Total number of cells is 120.

2-8

Fig.1.10 Curvature refinement level is 2; Curvature criterion is 0.1; Total number of cells is 148.

Tolerance Refinement Tolerance refinement allows you to control how well (with what tolerance) mesh polygons approximate the real interface. The tolerance refinement may affect the same cells that were affected by the small solid features refinement and the curvature refinement. It resolves the interface's curvature more effectively than the small solid features refinement, and, in contrast to the curvature refinement, discerns small and large features of equal curvature, thus avoiding refinements in regions of less importance (see images below).

Fig.1.11 Curvature refinement level is 3; Curvature criterion is 0.1;

Fig.1.12 Tolerance refinement level is 3; Tolerance criterion is 0.1 mm;

Any surface is approximated by a set of polygons which vertices are surface's intersection points with the cells' edges. This approach accurately represents flat faces though curvature surfaces are approximated with some deviations (e.g. a circle can be approximated by a polygon). The tolerance refinement criterion controls this deviation. A cell will be split if the distance (h, see below) between the outermost interface's point within the cell and the polygon approximating this interface is larger than the specified criterion value.

Solving Engineering Problems with Flow Simulation 2013

2-9

Advanced Knowledge

Narrow Channel Refinement The narrow channel refinement is applied to each flow passage within the computational domain (or a region, in case that local mesh settings are specified) unless you specify for Flow Simulation to ignore passages of a specified height. The Narrow Channels term is conventional and used for the definition of the flow passages of the model in the direction normal to the solid/fluid interface. The basic concept of narrow channel refinement is to resolve the narrow channels with a sufficient number of cells to provide a reasonable level of solution accuracy. It is especially important to have narrow channels resolved in analyses of low Reynolds numbers or analyses with long channels, i.e. in such analyses where the boundary layer thickness becomes comparable to the size of the partial cells where the layer is developed. The narrow channel settings available in Flow Simulation are the following: • Narrow channels refinement level – the maximum level of cells refinement in narrow channels with respect to the basic mesh cell. • Characteristic number of cell across a narrow channel – the number of cells (including partial cells) that Flow Simulation will attempt to set across the model flow passages in the direction normal to the solid/fluid interface. If possible, the number of cells across narrow channels will be equal to the specified characteristic number, otherwise it will be as close to it as possible. The Characteristic number of cells across a narrow channel (let us denote it as Nc) and the Narrow channels refinement level (let us denote it as L) both influence the mesh in narrow channels in the following manner: the basic mesh in narrow channels will be split to have Nc number per channel, if the resulting cells satisfy the specified L. In other words, whatever the specified Nc, the smallest possible cell in a narrow channel is 8L times smaller in volume (or 2L times smaller in each linear dimension) than the basic mesh cell. This is necessary to avoid undesirable mesh splitting in very fine channels that may cause the number of cells to increase to an unreasonable value. • The minimum height of narrow channels, The maximum height of narrow channels – the minimum and maximum bounds for the height outside of which a flow passage will not be considered as a narrow channel and thus will not be refined by the narrow channel resolution procedure. For example, if you specify the minimum and maximum height of narrow channels, the cells will be split only in those fluid regions where the distance between the opposite walls of the flow passage in the direction normal to wall lies between the specified minimum and maximum heights. The narrow channel refinement operates as follows: the normal to the solid surface for each partial cell is extended up to the next solid surface, which will be considered to be the opposite wall of the flow passage. If the number of cells per this normal-to-wall direction is less than the specified Nc, the cells will be split to satisfy the narrow channel settings as described above.

2-10

Although the settings that produce an optimal mesh depends on a particular task, here are some ’rule-of-thumb’ recommendations for narrow channel settings: 1 Set the number of cells across narrow channel to a minimum of 5. 2 Use the minimum and maximum heights of narrow channels to concentrate on the

regions of interest. 3 If possible, avoid setting high values for the narrow channels refinement level, since it

may cause a significant increase in the number of cells where it is not necessary.

Fig.1.13 Small solid features refinement level is 3; Narrow channel refinement is disabled.

Fig.1.14 Small solid features refinement level is 3; Narrow channel refinement is on: 5 cells across narrow channels, Narrow channels refinement level is 2.

Solving Engineering Problems with Flow Simulation 2013

2-11

Advanced Knowledge

Fig.1.15 Small solid features refinement level is 3; Narrow channel refinement is on: 5 cells across narrow channels, Narrow channels refinement level is 5.

Local Mesh Settings The local mesh settings option is one more tool to help create an optimal mesh. Use of local mesh settings is especially beneficial if you are interested in resolving a particular region within a complex model. The local mesh settings can be applied to a component, face, edge or vertex. You can apply local mesh settings to fluid regions and solid bodies. To apply the local mesh settings to a fluid region you need to specify this region as a solid part or subassembly and then disable this component in the Component Control dialog box. The local mesh settings are applied to the cells intersected with the selected component, face, edge, or a cell enclosing the selected vertex. However, cells adjacent to the cell of the local region may be also affected due to the refinement rules described in the Mesh Construction Stages chapter.

2-12

Fig.1.16 The local mesh settings used: Two narrow channels are refined to have 10 cells across them.

Recommendations for Creating the Computational Mesh 1 At the beginning create the mesh using the default (automatic) mesh settings. Start with the Level of initial mesh of 3. On this stage it is important to recognize the appropriate values of the minimum gap size and minimum wall thickness which will provide you with the suitable mesh. The default values of the minimum gap size and minimum wall thickness are calculated using information about the overall model

dimensions, the Computational Domain size, and area of surfaces where conditions (boundary conditions, sources, etc.) and goals are specified. Don't switch off the Optimize thin walls resolution option, since it allows you to resolve the model's thin walls without the excessive mesh refinement. 2 Closely analyze the obtained automatic mesh, paying attention to the total numbers of

cells, resolution of the regions of interest and narrow channels. If the automatic mesh does not satisfy you and changing of the minimum gap size and minimum wall thickness values do not give the desired effect you can proceed with the custom mesh. 3 Start to create your custom mesh with the disabled narrow channel refinement, while the Small solid features refinement level and the Curvature refinement level are

both set to 0. This will produce only zero level cells (basic mesh only). Use control planes to optimize the basic mesh. 4 Next, adjust the basic mesh by step-by-step increase of the Small solid features refinement level and the Curvature refinement level. Then, enable the narrow

channels refinement. 5 Finally, try to use the local mesh settings.

Solving Engineering Problems with Flow Simulation 2013

2-13

Advanced Knowledge

2 Mesh-associated Tools Introduction Since the mesh settings is an indirect way of constructing the computational mesh, to better visualize the resulting mesh various post-processing tools are offered by Flow Simulation. In particular, these tools allow to visualize the mesh in detail before the calculation, substantially reducing the CPU and user time. The computational mesh constructed by Flow Simulation or other CFD codes cannot resolve the model geometry at the mesh cell level exactly. A discrepancy can lead to prediction errors. To facilitate an analysis of these errors and/or to avoid their appearance, Flow Simulation offers various options for visualizing the real computational geometry corresponding to the computational mesh used in the analysis. Since the numerical solution is obtained inevitably in the discrete form, i.e., in the centers of computational mesh cells, it is interpolated and extrapolated by the post-processor to present the results in a smooth form, which is typically more convenient to the user. As a result, some prediction errors can stem from these interpolations and extrapolations. To facilitate an analysis of such errors and/or to prevent their appearance, Flow Simulation offers an option to visualize the physical parameters’ values calculated at the centers of computational mesh cells, so that when presenting results by coloring an area with a palette, the results are considered constant within each cell.

Visualizing the Basic Mesh Before Constructing the Initial Mesh Using this option the user can inspect the Basic mesh and its Control planes corresponding to the mesh settings, which can be made manually or retained by default. The plot appears as soon as these settings have been made or changed, so you immediately see the resulting mesh. (See Help or User’s Guide defining the Basic mesh and its Control planes). To enable this option, select the Show basic mesh option in the Flow Simulation, Project menu, or in the Initial Mesh dialog box. The option is accessible both before and after the calculation. Using this option, you may shifting the Control planes to desired positions to assure that certain features of the model geometry are captured by the computational mesh.

Enhanced Capabilities of the Results Loading Flow Simulation allows to view not only the calculation results and the current computational mesh, which they have been obtained on, but also the initial computational mesh (i.e., which the calculation begins on). The latter can be viewed either before or after the calculation, allowing the user to compare the initial and current (i.e., refined during the calculation) computational meshes.

2-14

Fig.2.1 The Basic mesh (left) and the Initial mesh (right).

To view various meshes, you must open the corresponding file via the Load results dialog box. The calculation results, including the current computational mesh, are saved in the .fld files, whereas the initial computational mesh is saved separately in the .cpt file. All these files are saved in the project folder, which name (a numeric string) is formed by Flow Simulation and must not be changed. The .cpt files and the final (i.e., with the solution obtained at the last iteration) .fld files have the name similar to that of the project folder, whereas the solutions obtained during the calculation at the previous iterations (corresponding to certain physical time moments, if the problem is time-dependent) are saved in the .fld files with names “r_”, e.g. the project initial data are saved in the r_000000.fld file. Do not try to load the calculation results obtained in another project with a different geometry; the effect will be unpredictable.

Fig.2.2 The Load Results dialog box.

Solving Engineering Problems with Flow Simulation 2013

2-15

Advanced Knowledge

Viewing the Initial Computational Mesh Saved in the .cpt Files To optimize the process of solving an engineering problem and to save time, in some cases it may be useful to view the initial computational mesh before performing the calculation, particularly to be sure that the model features are resolved well by this mesh. To view the initial computational mesh after loading the .cpt file, Flow Simulation offers you Cut Plots, Surface Plots, and the Mesh option (see below), which are also used for viewing the calculation results.

Viewing the Computational Mesh Cells with the Mesh Option To view fluid cells of the computational mesh cells (i.e. the cells lying fully in the fluid), solid cells (lying fully in the solid), and partial cells lying partly in the fluid and partly in the solid, Flow Simulation offers you the Mesh option. Different colors can be used to better differentiate between the computational mesh cells of each of the above-mentioned types. To see the cells in a certain parallelepiped region, the user must specify the coordinates of the region boundaries in the Global Coordinate System. Visualization of a large amount of computational mesh cells (e.g. all fluid cells in the whole computational domain) may be impractical, since it could require substantial time and memory, and even then you might not be able to see all the visualized cells because the majority of them will likely be screened from view by other cells. Using the Mesh option, you can also save the information concerning the mesh cells, including the physical parameters values obtained in their centers, in ASCII or Microsoft® Excel® files.

2-16

Visualizing the Real Computational Geometry Since the SolidWorks model geometry, especially its high-curvature parts, cannot be resolved exactly at the cell level by the rectangular (parallelepiped) computational mesh, the real computational geometry corresponding to the computational mesh used in the analysis can be viewed after the calculation to avoid or estimate the prediction errors stemming from this discrepancy. If no solution-adaptive meshing occurs during the calculation, the real computational geometry can be viewed just after the mesh generation. This option is employed by clearing the Use CAD geometry check box in Cut Plots, 3D Plots, Surface Plots, Flow Trajectories, Point Parameters and XY Plots. The result is especially clear when colored Contours are used to visualize a physical parameter values (see Fig.2.3).

Fig.2.3 Cut Plots around the SolidWorks model outer surface (left) and on its computational realization (right).

This capability is especially useful for revealing important surface regions in the model, which are inadequately resolved by the computational mesh. On the other hand, this option may be useful when creating Surface Plots for SolidWorks models containing rippled surfaces, where ripples, which are supposed to be not essential from the problem solution viewpoint, were not resolved by the computational mesh. In this case, coloring of the simplified solid/fluid interface instead of coloring the actual SolidWorks model faces can lead to substantial reduction of the CPU time and memory requirements.

Solving Engineering Problems with Flow Simulation 2013

2-17

Advanced Knowledge

If the computational mesh has resolved the SolidWorks model well, so the obtained computational results are adequate, then enable the Use CAD geometry option before performing the final Cut Plots and Surface Plots to obtain smooth pictures which are more convenient for the analysis. Notice that when creating a Surface Plot with the Use CAD geometry option switched off, only the solid/fluid interfaces of partial cells within the computational mesh will be colored. When a Surface Plot is created in the Use all faces mode, solid/fluid interfaces of all partial cells will be colored. However, when a Surface Plot is created on a selected surface, the solid/fluid interfaces are colored only in the partial cells intersected by the SolidWorks model surface approximated by triangles inside SolidWorks, which may differ from the mesh-approximated surface of the model. Depending on the problem considered, there may be such cases when certain partial cells are not intersected by the triangulated surface and therefore the corresponding solid/fluid interfaces would not be colored. Naturally, this circumstance concerns visualization only and does not affect the calculation results.

2-18

Switching off the Interpolation and Extrapolation of Calculation Results Since the numerical solution is obtained inevitably in the discrete form, i.e., in the form of values in the centers of the computational mesh cells in Flow Simulation, it is interpolated and extrapolated by the post-processor to present the results in a smooth form, which is typically more convenient to the user. As a result, prediction errors can stem from and/or be hidden by such interpolation and extrapolation that smoothens the calculation results. To facilitate the revealing, analysis, and elimination of such errors, Flow Simulation offers an option to visualize the physical parameter values ’as is’, i.e. without interpolation, when presenting calculation results in Cut Plots and Surface Plots (other result features, namely, isolines, isosurfaces, flow streamlines and particle trajectories can not be built at all without interpolation), so when coloring a surface with a palette, the results are considered constant within the mesh cells (see Fig.2.4). Since the mesh cells’ centers used in coloring the surface can lie at different distances from the surface, this can introduce an additional variegation into the picture, if the value of the displayed parameter depends noticeably on this distance (see Fig.2.4).

Fig.2.4 The fluid velocity Surface Plots in the near-wall region created with the interpolation of the calculation results (left) and without interolation (right).

Solving Engineering Problems with Flow Simulation 2013

2-19

Advanced Knowledge

Conclusion The presented mesh-associated tools of Flow Simulation are additional tools for obtaining reliable and accurate results with this code. These tools are summarized in the table: Application Basic mesh

Initial mesh

After the calculation

+

+

+

To inspect the Basic mesh and setting its Control planes

Widened capabilities of loading the results

+

+

To view the Initial mesh and the calculation results

Viewing the Initial mesh

+

+

To analyze the Initial mesh

Viewing mesh cells of different type

+

+

To view mesh cells and save the respective physical parameters values

Visualizing the computational geometry

+

+

For analysis of inadequate results and quick post-processing of the results of complicated models

+

For analysis of inadequate results

Option

Visualizing the Basic mesh

Switching off the interpolation of results

Reason

3 Meshing - Additional Insight Flow Simulation considers the real model created in SolidWorks and generates a rectangular computational mesh automatically distinguishing the fluid and solid domains. The corresponding computational domain is generated in the form of a rectangular parallelepiped enclosing the model. In the mesh generation process, the computational domain is divided into uniform rectangular parallelepiped-shaped cells, which form a so-called basic mesh. Then, using information about the model geometry, Flow Simulation further constructs the mesh by means of various refinements, i.e. splitting of the basic mesh cells into smaller rectangular parallelepiped-shaped cells, thus better representing the model and fluid regions. The mesh, which the calculation starts from, so-called initial mesh, is fully defined by the generated basic mesh and the refinement settings.

2-20

Each refinement has its criterion and level. The refinement criterion denotes which cells have to be split, and the refinement level denotes the smallest size, which the cells can be split to. Regardless of the refinement considered, the smallest cell size is always defined with respect to the basic mesh cell size so the constructed basic mesh is of great importance for the resulting computational mesh. The main types of refinements are:  Small Solid Features Refinement  Curvature Refinement  Tolerance Refinement  Narrow Channel Refinement  Square Difference Refinement

In addition, the following two types of refinements can be invoked locally:  Cell Type Refinement  Solid Boundary Refinement

During the calculation, the initial mesh can be refined further using the  Solution-Adaptive Refinement.

Though it depends on a refinement which criterion or level is available for user control, we will consider all of them (except for the Solution-Adaptive Refinement) to give you a comprehensive understanding of how the Flow Simulation meshing works. In the chapter below the most important conclusions are marked with the blue italic font. For abbreviation list refer to the Glossary paragraph.

Initial Mesh Generation Stages Basic Mesh Generation and Resolving the Interface 1 Create basic mesh cells which sizes are governed by the computational domain size,

the user-specified Control Planes and the number of the basic mesh cells. [Nx, Ny, Nz, Control Planes. Parameters which act on each stage are summarized in square brackets at the end of the stage.] 2 Analyze triangulation in each basic mesh cell at the interfaces between different

substances (such as solid/fluid, solid/porous, solid/solid and porous/fluid interfaces) in order to find the maximum angle between normals to the triangles which compose the interface within the cell. 3 Depending on the maximum angle found, the decision whether to split the cell or not is

made in accordance with the specified Small solid features refinement level (SSFRL), Narrow channel refinement level (NCRL), Curvature refinement level (CRL) and Curvature criterion (CRC), Tolerance refinement level (TRL) and Tolerance

Solving Engineering Problems with Flow Simulation 2013

2-21

Advanced Knowledge

Refinement Criterion (TRC) (see the Refinements at Interfaces Between Substances paragraph). [SSFRL, NCRL, CRL and CRC]. If a cell belongs to a local initial mesh area, then the corresponding local refinement levels will be applied (see the Local Mesh Settings paragraph). 4 If a basic mesh cell is split, the resulting child cells are analyzed as described in items 2

and 3, and split further, if necessary. The cell splitting will proceed until the interface resolution satisfies the specified SSFR criterion, CRC and TRC, or the corresponding level of splitting reaches its specified value. The specified levels of splitting denote the maximum admissible splitting, i.e. they show to which level a basic mesh cell can be split if it is required for resolving the solid/fluid interface within the cell. 5 The operations 2 to 4 are applied for the next basic mesh cell and so on, taking into

account the following Cell Mating rule: two neighboring cells (i.e. cells having a common face) can be only cells which levels are similar or differ by one. This rule has the highest priority as it is necessary for simplifying numerical algorithm in solver. The fourth-level red cells appearing after resolving the cog cause the neighboring cells to be split up to third level (yellow cells), that, in turn, causes the subsequent refinement producing second level cells (green cells) and first level cells (blue cells). The white zero level cell (basic mesh cell) remains unsplit since it borders on first level cells only, thus satisfying the rule. Fig.3.1 Fluid cell refinement due to the Cell Mating rule.

The Cell Mating rule is strict and has higher priority than the other cell operations. The rule is also enforced for the cells that are entirely in a solid. The mesh at this stage is called the primary mesh. The primary mesh implies the complete basic mesh with the resolution of the solid/fluid (as well as solid/solid, solid/porous, etc.) interface by the small solid features refinements and the curvature refinement also taking into account the local mesh settings.

2-22

Narrow Channel Refinement After the primary mesh has been created, the narrow channel refinement is put in action. The Narrow Channels term is conventional and used for the definition of the model flow passages which are ’narrow’ in the direction normal to the solid/fluid interface. Regardless of the real solid curvature, the mesh approximation is that the solid boundary is always represented by a set of flat elements, which nodes are the points where the model intersects with the cell edges. Thus, whatever the model geometry, there is always a flat element within a partial cell and the normal to this element denotes the direction normal to the solid/fluid interface for this partial cell. The narrow channel refinement operates as follows: 1 For each partial cell Flow Simulation calculates the “local” narrow channel width as

the distance between this partial cell and the next partial cell found on the line normal to the solid/fluid interface of this cell (i.e. normal to the flat surface element located in the cell). If the line normal to the solid/fluid interface crosses a local initial mesh area, then the corresponding local narrow channel refinement settings is applied to the cells in this direction. 2 If the distance value falls within the range defined by the Minimum height of narrow

channel (NCHmin) and Maximum height of narrow channel (NCHmax) options, the number of cells per this interval is calculated including both partial cells and taking into account which portion of each partial cell is in fluid. [NCHmin, NCHmax]. 3 More precisely, the number of cells across the channel (i.e. on the interval between the

two partial cells) is calculated as N = Nf + np1 + np2, where Nf is the number of fluid cells on the interval, and np1 and np2 are the fluid portions of the both partial cells. This value is compared with the specified Characteristic number of cells across a narrow channel (CNC). If N is less than the specified CNC then the cells on this interval are split. For example, on Fig.3.2 Nf = 2, np1 = np2 = 0.4, and N = 2+0.4+0.4 = 2.8 which is less than the criterion. On Fig.3.3 the partial cells are split, so that the fluid portions of the newly-formed partial cells are np1 = np2 = 9/10, and the criterion is satisfied (N > CNC).

Fig.3.2

Fig.3.3

NCRL = 2; CNC = 3; N = 2.8 < CNC

NCRL = 3; CNC = 3; N = 3.8 > CNC

Solving Engineering Problems with Flow Simulation 2013

2-23

Advanced Knowledge

Like in the other refinements, the Narrow channel refinement level (NCRL) denotes the maximum level to which the cells can be split to satisfy the CNC criterion. The NCRL has higher priority than the CNC, so the refinement will proceed until the CNC criterion is satisfied or all the cells reach the Narrow channel resolution level. The narrow channel refinement is symmetrical with respect to the midpoint of the interval and proceeds from the both ending partial cells towards the midpoint. [CNC, NCRL].

Fig.3.4

Fig.3.5

CNC = 5; NCRL = 1

CNC = 5; NCRL = 3

In Fig.3.4, the specified Characteristic number of cells across a channel is 5 but only two cells were generated since the maximum refinement level of one allows only basic mesh cells and first-level cells to be generated. In Fig.3.5, the specified Narrow channel refinement level is high enough to allow five cells to be placed across the channel. 5 Next, for all the fluid cells within the entire computational domain the following Fluid

Cell Leveling procedure is applied: if a fluid cell is located between two cells of higher level, it is split to be equalized with the level of neighboring smaller cells.

2-24

Thin walls resolution In contrast to the narrow channels, thin walls can be resolved without the mesh refinement inside the wall, since the both sides of the thin wall may reside in the same cell. Therefore, the amount of cells needed to resolve a thin wall is generally lower than the number of cells needed to properly resolve a channel of the same width. See Fig.3.6 - 3.8 illustrating the thin walls resolution technology and its limitations. Solid 2

Fluid 1

Solid 1 Fluid 2

Fig.3.6 One mesh cell can contain more than one fluid and/or solid volume; during calculation each volume has an individual set of parameters depending on its type (fluid or solid).

Fig.3.7 If the wall thickness is greater than the basic mesh cell's size across the wall or if the wall creates only one fluid volume in the cell, then the opposite sides of the wall will not lay within the same cell. Such walls are resolved with two or more cells across.

Solving Engineering Problems with Flow Simulation 2013

2-25

Advanced Knowledge

Model geometry

Meshed geometry

Trimmed edge

Trimmed cell

Fig.3.8 The edges of thin walls ending within a mesh cell may be trimmed in certain cases. These mesh cells are called Trimmed cells.

Square Difference Refinement The Square Difference Refinement checks the neighboring partial cells of different levels for the difference between their fluid passage areas. If the difference between the fluid passage area of the higher-level cell and the total fluid passage areas of the adjacent lower-lever cells exceeds the Square Difference Refinement Criterion (SDRC) then the greater-level cell is split to the level of adjacent cells in order to equalize the fluid passage areas (see Fig.3.9). The Square Difference Refinement is always enabled and cannot be disabled since it is a strict solver requirement. As with the Cell Mating rule, this is another condition imposed by the solver to provide stability for the convergence processes. Though you cannot turn off the Square Difference Refinement, you can control its criterion, which is directly proportional to the Curvature refinement criterion. [CRC].

2-26

Fig.3.9

Fig.3.10

Two adjacent partial cells of different levels at the cylinder surface.

Cut plot of the cylinder. The concerned cells are blue. SSFRL = 2; CRL = 0; CRC = 3.14; NCRL = 1.

Fig.3.9 shows neighboring partial cells of different levels at the cylinder's solid/fluid interface. The fluid passage area of the higher-level cell is the ABDE polygon. The total fluid passage area of the lower-level cells is the ABCDE polygon, so the difference between the fluid passages is the yellow BCD triangle. In this example we have increased the curvature refinement criterion to , thereby increasing the Square Difference Refinement Criterion so that the fluid passage difference (BCD) is smaller than the criterion, and thus, there is no need to split the higher-level cell. Note that the Square Difference Refinement may cause a domino effect when one splitting produces cells which become lower-level cells for the next adjacent cell causing it to split too, and so on, resulting in an increased number of cells.

Fig.3.11

Fig.3.12

SSFRL = 3, CRL = 0; CRC = 0.45 Total cells = 49391.

SSFRL = 3, CRL = 2; CRC = 0.50; Total cells = 41376.

In the Fig.3.11 the total number of cells is nearly 20% more than in the Fig.3.12 in spite of the fact that the Curvature refinement is disabled (CRL = 0) in the first case. Here, the model geometry is similar and before the Square Difference Refinement the mesh is practically the same in both cases and mostly governed by the Small Solid Features Refinement when the SSFRL exceeds the CRL, i.e. changing the CRL from 0 to 3 would not change substantially the number of cells. However, in the first case the curvature criterion is lower, resulting in a more stringent criterion of the Square Difference Refinement. So the smaller Square Difference Refinement criterion leads to a greater number of cells subject to the Square Difference Refinement. In the Fig.3.11 you can see a stripe of the third level cells along the cylinder. This is the result of the Square Difference Refinement and the domino effect when a cell on the cylinder edge involves the neighboring cell in the refinement procedure and so forth along the cylinder. Increase of the curvature criterion will increase the Square Difference Refinement Criterion, and, in turn, decrease the number of cells in both cases. If in the first case we specify the same CRC as in the second case (0.5054 rad), the total number of cells decreases to 40963.

Solving Engineering Problems with Flow Simulation 2013

2-27

Advanced Knowledge

Mesh Diagnostic The mesh diagnostic is intended to inspect the resulting initial mesh but not to change the total number of cells.

Refinements at Interfaces Between Substances Different interface types (solid/fluid, solid1/solid2, solid/porous or porous/fluid) are checked on different refinement criteria, namely: small solid features criterion, curvature refinement criterion, tolerance refinement criterion and narrow channel refinement criterion for solid/fluid and solid/porous interfaces; small solid features criterion for solid1/solid2 interfaces; small solid features criterion and curvature refinement criterion for porous/fluid interfaces. Whereas the specified refinement levels are equally applied to any interface type.

Small Solid Features Refinement The small solid features refinement acts on the cells where the maximum angle between normals to the surface-forming triangles is strictly greater than 120. To make this 120-degree criterion easier to understand, let us consider simple small solid features of planar faces only. The normal to triangles that form the planar face is normal to the planar face too. Therefore, instead of considering the normals to the triangles we can consider normals to faces, or better the angle between faces.

Fig.3.13 SSFRL = 1, CRL = 0, NCRL = 0

In Fig.3.13 the cells with the cogs of 150 and 60 degrees were not split by the small solid features refinement because the maximum angles between the faces (i.e. between normals to the triangles enclosed by the cell) are 30 and 120, respectively. If the angle between the normals becomes greater than 120 (121 for the 59-cog) then the cell is split. The cell with the square spike surely has to be split because the lateral faces of the spike have their normals at the angle of 180, thus satisfying the 120-degree criterion. Note that rectangular corners (like in the rightmost cell) do not satisfy the criterion and therefore will not be resolved by the small solid features refinement.

2-28

Remember that if the Narrow channel refinement is enabled, the maximum level to which the small solid features refinement can split the cells is set as the maximum level from the specified SSFRL and Narrow channel refinement level (NCRL). In other words, if the Narrow channel refinement is enabled, the SSFRL has no effect if it is smaller than the NCRL.

Fig.3.14 SSFRL = 0, CRL = 0, NCRL = 1

From Fig.3.14 it is clear that the cells are split by the 120-degree criterion up to the first level, as defined by the narrow channel refinement level. For the information about how the NCRL influences the narrow channel refinement see the Narrow Channel Refinement paragraph.

Curvature Refinement The curvature refinement works in the same manner as the small solid features refinement with the difference that the critical angle between the normals can be specified by the user (in radians) as curvature refinement criterion (CRC). Here, the smaller the criterion, the better resolution of the solid curvature. To give more precise and descriptive explanation, the following table presents several CRC values together with the corresponding angles between normals and the angles between planar faces. Table 2.1: Influence of the curvature criterion on the solid curvature resolution. Curvature criterion, rad

0.3176

0.4510

0.5548

0.6435

1.0472

1.5708

2.0944

3.1416

' between normals, [degrees]

>19

>25

>31

>36

>60

>90

>120

180

 between faces, [degrees]