Introduction to Fluid Analysis

Flow simulations are widely used in engineering applications ranging from flow around airplane wings and hydraulic turbines to flow in blood vessels and other circulatory systems. We may gain a better understanding of the motion of fluid around objects as well as the fluid behavior in complex circulatory systems by conducting fluid analysis.

Computational fluid dynamics (CFD) simulation complements experimental testing, helps reduce cost and turnaround time for design iterations, and has become an indispensable tool whenever practical design involving fluids is required.

In fluid dynamics, the motion of a fluid is mathematically described using physical quantities such as the flow velocity u, flow pressure p, fluid density ρ, and fluid viscosity ν. The flow velocity or flow pressure is different at a different point in a fluid volume. The objective of fluid simulation is to track the fluid velocity and pressure variations at different points in the fluid domain.

CFD is useful in a wide variety of applications and here we note a few to give you an idea of its use in industry.  The simulations shown below have been performed using the FLUENT software.  CFD can be used to simulate the flow over a vehicle. For instance, it can be used to study the interaction of propellers or rotors with the aircraft fuselage.  The following figure shows the prediction of the pressure field induced by the interaction of the rotor with a helicopter fuselage in forward flight. Rotors and propellers can be represented with models of varying complexity.

The temperature distribution obtained from a CFD analysis of a mixing manifold. This mixing manifold is part of the passenger cabin ventilation system on the Boeing 767. The CFD analysis showed the effectiveness of a simpler manifold design without the need for field testing.

Bio-medical engineering is a rapidly growing field and uses CFD to study the circulatory and respiratory systems. The following figure shows pressure contours and a cutaway view that reveals velocity vectors in a blood pump that assumes the role of heart in open-heart surgery. 

CFD is attractive to industry since it is more cost-effective than physical testing. However, one must note that complex flow simulations are challenging and error-prone and it takes a lot of engineering expertise to obtain validated solutions.

Aircraft design was traditionally based on theoretical aerodynamics and wind tunnel testing, with flight-testing used for final validation. CFD emerged in the late 1960's. Its role in aircraft design increased steadily as speed and memory of computers increased. Today CFD is a principal aerodynamic technology for aircraft configuration development, along with wind tunnel testing and flighttesting.

State-of-the-art capabilities in each of these technologies are needed to achieve superior performance with reduced risk and low cost.

The application of CFD to reduce the drag of a wing by adjustment of pressure gradient by shaping and by suction through slotted or perforated surfaces. The drag of an aircraft can be reduced in a number of ways to provide increased range, increased speed, decreased size and cost, and decreased fuel usage. The adjustment of pressure gradient by shaping and using laminar boundary-layer control with suction are two powerful and effective ways to reduce drag. This is demonstrated with a calculation method for natural laminar flow (NLF) and hybrid laminar flow control (HLFC) wings.

The application of CFD to ground-based vehicles, in particular to automobile aerodynamics development. The use of CFD in this area has been continuously increasing because the aerodynamic characteristics have a significant influence on the driving stability and fuel consumption on a highway. Since the aerodynamic characteristics of automobiles are closely coupled with their styling, it is impossible to improve them much once styling is fixed. Therefore, it is necessary to consider aerodynamics in the early design stage.

CFD also finds applications in internal flows and has been used to solve real engineering problems such as subsonic, transonic and supersonic inlets, compressors and turbines, as well as combustion chambers and rocket engines.

UNDERSTANDING THE PROBLEM

You can save lots of time and money if you first spend a little time with a piece of paper and a pencil to try to understand the problem you are planning to analyze. Before initiating numerical modeling on the computer and generating a finite element model, it is imperative that you develop a sense of or a feel for the problem. There are many questions that a good engineer will ask before proceeding with the modeling process: Is the material under axial loading? Is the body under bending moments or twisting moments or a combination of the two? Do we need to worry about buckling? Can we approximate the behavior of the material with a two-dimensional model? Does heat transfer play a significant role in the problem? Which modes of heat transfer are influential? If you choose to employ FEA,  " back-of-the-envelope" calculations will greatly enhance your understanding of the problem, in turn helping you to develop a good, reasonable finite element model, particularly in terms of your selection of element types.

Some practicing engineers still use finite element analysis to solve a problem that could have been solved more easily by hand by someone with a good grasp of the fundamental concepts of the mechanics of materials and heat transfer. To shed more light on this very important point, consider the following examples.

A BRIEF HISTORYOF THE FINITE ELEMENT METHOD AND ANSYS.

The finite element method (FEM) is a numerical technique that can be applied to obtain solutions to a variety of problems in different engineering branch. Steady state, transient, linear, or nonlinear problems in stress analysis, vibrational, heat transfer, fluid flow, electrical and electromagnetism problems may be analyzed with finite element methods. The origin of the modern finite element method may be traced back to the early 1900s when some investigators approximated and modeled elastic continua using discrete equivalent elastic bars. However, Courant (1943) has been credited with being the first person to develop the finite element method.

In a paper published in the early 1940s, Courant used piecewise polynomial interpolation over triangular subregions to investigate torsion problems. 

The next significant step in the utilization of finite element methods was taken by Boeing in the 1950s when Boeing, followed by others, used triangular stress elements to model airplane wings. Yet, it was not until 1960 that Clough made the term finite element popular. During the 1960s, investigators began to apply the finite element method to other areas of engineering, such as heat transfer and seepage flow problems. Zienkiewicz and Cheung (1967) wrote the first book entirely devoted to the finite element method in 1967.

 In 1971, ANSYS was released for the first time. ANSYS is a comprehensive general-purpose finite element computer program that contains more than 100,000 lines of code. ANSYS is capable of performing static, dynamic, vibrational, heat transfer, fluid flow, and electromagnetism analyses. ANSYS has been a leading FEA program for well over 45 years. The current version of ANSYS 17.0 has a completely new look, with multiple windows incorporating a graphical user interface (GUI), pull-down menus, dialog boxes, and a tool bar. Today, you will find ANSYS in use in many engineering fields, including aerospace, automotive, electronics, and nuclear. In order to use ANSYS or any other "canned" FEA computer program intelligently, it is imperative that one first fully understands the underlying basic concepts and limitations of the finite element methods. 

ANSYS is a very powerful and impressive engineering tool that may be used to solve a variety of problems. However; a user without a basic understanding of the finite element methods will find himself or herself in the same predicament as a computer technician with access to many impressive instruments and tools, but who cannot fix a computer because he or she does not understand the inner workings of a computer!

Introduction to FEM

The finite element method is a numerical procedure that can be used to obtain solutions to a large class of engineering problems involving stress analysis, heat transfer, electro­magnetism, and fluid flow. Having a clear understanding of the basic concepts will enable you to use a general-purpose finite element software, such as ANSYS.

In general, engineering problems are mathematical models of physical situations. Mathematical models of many engineering problems are differential equations with a set of corresponding boundary and/or initial conditions. The differential equations are derived by applying the fundamental laws and principles of nature to a system or a control volume. These governing equations represent balance of mass, force, or energy. When possible, the exact solution of these equations renders detailed behavior of asystem under a given set of conditions.

The analytical solutions are composed of two parts:

a homogenous part and

a particular part

In any given engineering problem, there are two sets of design parameters that influence the way in which a system behaves. First, there are those parameters that provide information regarding the natural behavior of a given system. These parameters include material and geometric properties such as modulus of elasticity, thermal conductivity, viscosity, and area, and second moment of area.

On the other hand, there are parameters that produce disturbances in a system.

Problem Type	Examples of Parameters that Produce Disturbances in a System
Solid Mechanics	external forces and moments; support reaction
Heat Transfer	temperature difference; heat input
Fluid Flow and Pipe Networks	pressure difference; rate of flow
Electrical Network	voltage difference

TABLE Parameters causing disturbances in various engineering systems

It is important to understand the role of these parameters infinite element modeling in terms of their respective appearances in stiffness or conductance matrices and load or forcing matrices. The system characteristics will always show up in the stiffness matrix, conductance matrix, or resistance matrix, whereas the disturbance parameters will always appear in the load matrix.

There are many practical engineering problems for which we cannot obtain exact solutions. This inability to obtain an exact solution may be attributed to either the complex nature of governing differential equations or the difficulties that arise from dealing with the boundary and initial conditions. To deal with such problems, we resort to numerical approximations. In contrast to analytical solutions, which show the exact behavior of a system at any point within the system, numerical solutions approximate exact solutions only at discrete points, called nodes. The first step of any numerical procedure is discretization.

This process divides the medium of interest into a number of small sub regions (elements) and nodes. There are two common classes of numerical methods:

Finite difference methods and

Finite element methods.

With finite difference methods, the differential equation is written for each node, and the derivatives are replaced by differential equations. This approach results in a set of simultaneous linear equations. Although finite difference methods are easy to understand and employ in simple problems, they become difficult to apply to problems with complex geometries or complex boundary conditions. This situation is also true for problems with non-isotropic material properties.

In contrast, the finite element method uses integral formulations rather than difference equations to create a system of algebraic equations. Moreover, a continuous function is assumed to represent the approximate solution for each element. The complete solution is then generated by connecting or assembling the individual solutions, allowing for continuity at the interelemental boundaries.

ROLLING TOTAL DEFORMATION

ROLLING STRESS

ROLLING STRAIN

Adaptive Convergence

You can control the relative accuracy of a solution in two ways.

• You can use the meshing tools to refine the mesh before solving, or 
• you can use convergence tools as part of the solution process to refine solution results on a particular area of the model.

Through its convergence capabilities, the application can fully automate the solution process, internally controlling the level of accuracy for selected results. You can seek approximate results or adapted/converged results.

You can control convergence to a predefined level of error for selected results. In the calculation of stresses, displacements, mode shapes, temperatures, and heat fluxes, the application employs an adaptive solver engine to identify and refine the model in areas that benefit from adaptive refinement. The criteria for convergence is a prescribed percent change in results. The default is 20%.

You can continue to refine the mesh based on a specific solution result. When you pick a result (Equivalent Stress, Deformation, Total Flux Density, etc.), indicate that you want to converge on this solution. You pick a value and the solution is refined such that the solution value does not change by more than that value.

To add convergence, click the result you added to your solution; for example, Equivalent Stress, Total Deformation, or Total Flux Density. If you want to converge on deformation, right-click on Total Deformation and select Insert> Convergence. In the Details View, you can specify convergence on either the Minimum or Maximum value. Additionally, you can specify the Allowable Change between convergence iterations.

General Notes

• Adaptive convergence is not supported for orthotropic materials.
• Adaptive convergence is not supported for solid shell elements (the SOLSH190 series elements).
• Adaptive convergence is not valid for linked environments where the result of one analysis is used as input to another analysis.
• Low levels of accuracy are acceptable for demonstrations, training, and test runs. Allow for a significant level of uncertainty in interpreting answers. Very low accuracy is never recommended for use in the final validation of any critical design.
• Moderate levels of accuracy are acceptable for many noncritical design applications. Moderate levels of accuracy should not be used in a final validation of any critical part.
• High levels of accuracy are appropriate for solutions contributing to critical design decisions.
• When convergence is not sought, studies of problems with known answers yield the following behaviors and approximated errors:
• At maximum accuracy, less than 20% error for peak stresses and strains, and minimum margins and factors of safety.
• At maximum accuracy, between 5% and 10% error for average (nominal) stresses and elastic strains, and average heat flows.
• At maximum accuracy, between 1% and 5% error for average stress-related displacements and average calculated temperatures.
• At maximum accuracy, 5% or less error for mode frequencies for a wide range of parts.
• When seeking highly accurate, Converged Results, more computer time and resources will be required than Manual control, except in some cases where the manual preference approaches highest accuracy.
• Given the flexible nature of the solver engine, it is impossible to explicitly quantify the effect of a particular accuracy selection on the calculation of results for an arbitrary problem. Accuracy is related only to the representation of geometry. Increasing the accuracy preference will not make the material definition or environmental conditions more accurate. However, specified converged results are nearly as accurate as the percentage criteria.
• Critical components should always be analyzed by an experienced engineer or analyst prior to final acceptance.
• For magnetostatic analyses, Directional Force results allow seeking convergence based on Force Summation or Torque as opposed to other results converging on Maximum or Minimum values.
• Adaptive convergence is not valid if a Periodic Region or Cyclic Region symmetry object exists in the model.
• Adaptive convergence is not valid if an imported load object exists in the environment.