CFD: a complex mix of Physics, Engineering and Art! Results need validation and sanity checks!
The word "Computational" in the phrase "Computational Fluid Dynamics" is simply an adjective to "Fluid Dynamics". Hence, while dealing with aspects of CFD tool or process, it is vitally important to keep the physical understanding of fluid dynamics uppermost in user's mind as CFD has to do with physical problems. -- Adapted from John D. Anderson, Jr (Computational Fluid Dynamics - The Basics with Applications).
Any numerical simulation process is not just "Meshing, setting Boundary Conditions, Running Solver and Making Colourful Contour / Vector Plots". The results ultimately needs to be converted into a set of inputs for a robust design of the component of system. The sound knowledge of "underlying fluid mechanics principles and operating conditions of the problem set-up" are more important than just knowing how to use the software. Some of the requirements which will help a "CFD practitioners" take correct design decisions based on CFD results are:
Though the industrial flow configurations are far from being closer to these simple geometries, the fundamental ideas contained in them are indispensable to a good understanding of modern computation methods. The methods and results arrived at are important not only for these simple flows but also for the extension of our fundamental knowledge of turbulent flows in general. Methods for dealing with turbulent flows for any industrial applications could be devised only on the basis of the detailed experimental results obtained for them.
For example, according to measurements performed by H. Kirsten, the entrance length of a turbulent flow in a pipe is about 50 to 100 diameters. This knowledge is very important in deciding the inlet boundary condition for any industrial internal flow configuration.
CFD is a great tool when used with appropriate procedure and guidelines because of its inherent nature of multi-disciplinary science leading to technically unlimited potential and applications. Yet, "CFD is not a panacea of all the Flow and Heat Transfer problems without experience-base insight". Any result must be looked at by an experienced engineer in that field and must go through an "order-of-magnitude-check" before accepting the results.
All methods for the calculation of turbulent boundary layers are approximate ones and are based on the integral forms of the momentum and energy equations. Since, however, no general expressions for shear and dissipation in turbulent flow can be deduced by purely theoretical considerations, it is necessary to make additional suitable assumptions. These can only be obtained from the results of systematic measurements and, consequently, the calculation of turbulent boundary layers is semi-empirical.
While the usage of CFD simulations in industry is on rise at rapid pace, the credibility of results of any such calculation is still an area of concern. Most organizations using such codes, over time have evolved their own best practice guidelines to minimize the chances of "critical errors". There are many such guidelines issued by ERCOFTAC and AIAA. Following diagram summarizes classifications used to designate the types of error which needs to be addressed when CFD simulations are used to make design decisions beyond extant know-how of the company.
Error: A recognisable deficiency that is not due to lack of knowledge. For example, common known errors are the round-off errors in a computers and the convergence error in an iterative numerical scheme. CFD analyst should be capable of estimating the likely magnitude of the error. It may also arise due to mistakes in input (such as material property variation with temperature).
Uncertainty: A potential deficiency that is due to lack of knowledge. Uncertainties arise because of incomplete knowledge of a physical characteristic, such as the turbulence structure at inlet to a flow domain or because there is uncertainty in the validity of a particular flow model being used. Uncertainty cannot be removed as it is rooted in lack of knowledge (wither physics of the flow or the behaviour of numerical codes).
Verification: It is the procedure intended to ensure that the program solves the equations correctly. As per AIAA, G-077-1998: the process of determining if a simulation accurately represents the conceptual model. A verified simulation does not make any claim relating to the representation of the real world by the simulation. In other words: "it solves the equation right"
Validation: This procedure is intended to test the extent to which the model accurately represents reality. As per AIAA, G-077-1998: it is the process of determining how accurately a simulation represents the real world. In other words: "it solves the right equations"
Accuracy: This is the measure of the similarity of a simulation to the physical flow it is expected to represent.
Calibration: This procedure to assess the ability of a CFD code to predict global quantities of interest for specific geometries of engineering design interest.
MESH CONVERGENCE STUDY: The formal method of establishing mesh convergence requires a curve of a critical result parameter (typically some kind of coefficient such as skin friction coefficient) in a specific location, to be plotted against some measure of mesh density. At least three convergence runs will be required to plot a curve which can then be used to indicate how convergence is achieved or how far away the most refined mesh is from full convergence. However, if two runs of different mesh density give the same result, (mesh) convergence must already have been achieved and no mesh convergence curve is necessary.
Define target variables (usually scalars like Force, Drag Coefficient, Heat Flux, HTC, MAX Temperature, etc). Check the variation in target variable (e.g. mass flow rate at any plane) for various refinements of mesh, keep ITERATION ERROR limit constant say 0.00001
In addition to the turbulence parameter, the inlet velocity profile itself is very important to study the accuracy of CFD result for a particular application. One should check the effect of velocity profile as per power-law such as u = U_{MEAN}*(y/d)^{1/n}, where n = 6, 7, 8, … depending upon Re value. These sensitivity studies are particularly important in cases where separation and reattachment are likely to occur. For Example, in case of a flow over Backward Facing Step, there is decreases in location of reattachment length as the turbulence intensity increases and is sensitive to TI value specified at inlet.
Heat flux and surface heat transfer coefficient is one of the critical output from a thermal simulation. Understanding of the temperature field near the wall and how its gradient is used to calculate the heat transfer rate is important to identify source of errors. Heat transfer at walls is a combination of "heat diffusion due to conduction" and "heat diffusion due to mixing or convection". This is expressed as described below. Here, T is 'local' time-averaged value. α is thermal diffusivity defined as k/ρCp, ε_{h} is eddy diffusivity of heat - analogous to eddy diffusivity of momentum.
Pr_{t} = ε_{m}/ε_{h} is the turbulent Prandtl number defined as ratio of eddy diffusivity of momentum and eddy diffusivity of heat. Note that ε here is eddy diffusivity and not the turbulent eddy dissipation rate. Analogous to wall function for momentum, the wall function (available in textbooks) for temperature is described below and the equation used to calculate heat flux is also explained.The wall function definition used in ANSYS CFX is:
In ANSYS FLUENT, the laws-of-the-wall for mean velocity and temperature are based on the wall unit y^{*} rather than y^{+}. The definition of y^{*} uses u^{*} instead of u^{+} where y^{*} = ρC_{μ}^{1/4}k^{1/2}y/μ and u^{*} = ρC_{μ}^{1/4}k^{1/2}/τ_{W}. These two quantities are approximately equal in equilibrium turbulent boundary layers. κ is von Karman constant in the equation given below.
The steps followed in calculation of temperature or heat flux are as follows:
Step-1: Molecular Prandtl number is calculated based on specified fluid properties: Pr = μ / Cp / k where k is thermal conductivity (not turbulent kinetic energy though k used in law of wall for temperature above is TKE)
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Step-2: For the calculated molecular Prandtl number, thermal sub-layer thickness is estimated which is nothing but the intersection of the linear and logarithmic profiles
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Step-3: Depending upon (momentum) boundary layer height, y* is calculated at the centroid of the near wall cell. As mentioned above, in FLUENT, the laws-of-the-wall for mean velocity and temperature are based on the wall unit y^{*} rather than y^{+}.
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Step-4: Once y* is calculated, velocity at the centroid of the near wall cell is calculated as per law-of-wall for velocity. Thus, Pr, y* and u(y_{P}) are calculated and stored now. Temperaure at near wall cell is, T(y_{P}) still not known.
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Step-5: T(y_{P}) is known by solution of of energy equations in the interior domain. For specified wall temperature boundary condition, heat flux is calculated from the linear equation arising from the law-of-the-wall.
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