¾ Before using a CFD code incorporating a specific model for a particular application, validate it against test data for a similar application with similar flow structures and flow physics. A design application, where accurate performance and flow-field data is needed, will require more detailed validation than an application involving a preliminary investigation of a flow. Validation of engineer-ing cases should be aimed to check the most prominent and relevant flow features, rather than to capture every detail in the calculation.
¾ For the improved validation of complex flows, consider the taxonomy of the flow and validate the models being used on relevant simpler flows. For example, the validation of a code and turbulence model for a radial pump application should include not only a similar radial pump test case, but also test cases demonstrating the typical flow structures found in the pump, such as decelerating flow in a cascade of blades, flow in a rotating channel, secondary flow in bends, and leading and trailing edge flows. Simple test cases used in validation will allow finer grids than those used in real applications so that results of calculations at the typical grid resolution expected in the appli-cation should also be investigated.
¾ Carefully check the quality and accuracy of any experimental data used as a validation test case, to provide confidence in the experiment and the quality experimental data. The experiments should attempt to capture the relevant boundary conditions and initial conditions where appropri-ate. If the experimental results are found to be sensitive to the boundary conditions and experi-mental set-up then this should be reported. The experiexperi-mental data should include measurements of the quantity which is of interest and needed for CFD validation. This is best done by close col-laboration between experimentalists and CFD analysts. If colcol-laboration between experimentalists and CFD analysis is not possible care should be taken that the physically relevant quantities have been measured and that the quality and accuracy of the data is known.
¾ The validation data set should be independent of any data set used to construct the CFD model.
¾ Carry out the validation simulations in accordance with the guidelines outlined in this document. In particular, one of the validation calculations should use about the same mesh size as will be used in the real application.
¾ A simple test of validity should be carried out by examining particular flow features. The global mass balance should be checked, the total temperature should not vary if no heat or work is being added to the flow, and in areas away from solid boundaries the total pressure may often be as-sumed to be constant. Predictions of the entropy in a flow field can also be a helpful validation check.
¾ When using CFD for a design application, examine the flow of a well understood and well tested baseline design comprising the same important flow features as a means of calibrating the
ex-pected accuracy of the code to this application. The reliability of predictions of a new design can then be assessed by taking into account the calibration of the code with the baseline design. Such a calibration allows a more accurate estimate of the predicted performance of the new design to be made by consideration only of the differences and trends between the new design and the baseline design.
¾ Document the validation efforts. In any CFD calculations which are carried out without undergoing a thorough validation process (which is sometimes necessary as there may be no suitable meas-urements, or the time available allows no alternative), then attention should be drawn in the documentation of the results to the speculative nature of the simulation, with comments on why the user believes that the results are correct.
11.6. Guidelines on turbulence modelling
11.6.1. General guidelines on turbulence modelling
¾ Ensure that low numerical and convergence errors have been achieved in turbulent flow simula-tions. The relevance of turbulence modelling only becomes significant in CFD simulations when other sources of error, in particular the numerical and convergence errors, have been removed or properly controlled. Clearly no proper evaluation of the merits of different turbulence models can be made unless the discretisation error of the numerical algorithm is known, and grid sensitivity studies become crucial for all turbulent flow computations.
¾ Be aware that there is no universally valid general model of turbulence that is accurate for all classes of flows. Validation and calibration of the turbulence model with test data are necessary for all applications5.
¾ If possible, examine the effect and sensitivity of results to the turbulence model by changing the turbulence model being used.
¾ When using a particular turbulence model, check the published literature with regard to the known weaknesses of the model. The weaknesses of the standard k-ε model (Launder and Spalding [1974]) ,which is the most commonly used model in industrial applications, are listed below to-gether with some indications of possible palliative actions which might be fruitfully considered.
¾ Decide whether a wall function method, in which the near-wall region is bridged with wall func-tions, or a low Reynolds number model, in which the flow structure in the viscous sub-layer is re-solved, is to be used. This decision will be based on the available resources and the requirements for resolution of the boundary layer. Wall function methods are not valid in the presence of sepa-rated regions and/or strong three dimensional flows. The validity of the wall function approach or the use of a low Reynolds number model should be examined for the flow configuration under study.
11.6.2. Guidelines on wall functions
¾ Check the lower limit of y+. In the commonly used applications of wall functions, the meshing should be arranged so that the values of y+ at all the wall-adjacent integration points is only slightly above the recommended lower limit given by the code developers, typically between 20 and 30 (the form usually assumed for the wall functions is not valid much below these values). This pro-cedure offers the best chances to resolve the turbulent portion of the boundary layer. It should be noted that this criterion is impossible to satisfy close to separation or reattachment zones because y+ will approach zero there, independent of the distance to the wall.
¾ Check the upper limit on y+. In the case of moderate Reynolds number, where the boundary layer only extends to y+ of 300 to 500, there is no chance of accurately resolving the boundary layer if the first integration point is placed at a location with the value of y+ of 100.
¾ Check the resolution of the boundary layer. If boundary layer effects are important, it is recom-mended that the resolution of the boundary layer is checked after the computation. This can be achieved by a plot of the ratio between the turbulent to the molecular viscosity, which is high in-side the boundary layer. Adequate boundary layer resolution requires at least 8-10 points in the layer.
5 Calibration in this sentence refers to testing the ability of a CFD code to predict global quantities of interest for specific geometries of engineering design interest (see definition in chapter 2) and not to tuning the coefficients of a turbulence model, which cannot be recommended for a novice user.
¾ Exercise care when calculating the flow using different schemes or different codes with wall func-tions on the same mesh. Cell centred schemes have their integration points at different locafunc-tions in a mesh cell than cell vertex schemes. Thus the y+ value associated with a wall-adjacent cell dif-fers according to which scheme is being used on the mesh.
¾ Check that the correct form of the wall function is being used to take into account the wall rough-ness. An equivalent roughness height and a modified multiplier in the law of the wall must be used.
11.6.3. Guidelines on low Reynolds number models
¾ The value of y+ at the first node adjacent to the wall should be less than 4, and preferably close to unity.
¾ Depending on the Reynolds number, there should be between five and ten mesh points between the wall and y+ equal to 20, which likely results in thirty to sixty points inside the boundary layer for adequate boundary layer resolution.
11.6.4. Guidelines on weaknesses of the standard k- ε model
¾ The turbulent kinetic energy is over-predicted in regions of flow impingement and re-attachment leading to poor prediction of heat transfer and the development of boundary layer flow around leading edges and bluff bodies. The high turbulence levels predicted upstream of a stagnation point are transported around the body and the real boundary layer development is swamped by this effect. Kato and Launder [1993] have proposed an ad-hoc modification (called the Yap correc-tion) to the equation for the production term of k appearing in the k and ε equation, which is de-signed to tackle this problem. The RNG k-ε model (Yakhot et al. [1992]) includes a modification to the transport equation for ε and may also improve predictions in this area. The problems depend on the free-stream values of k and ε and may not always occur.
¾ Highly swirling flows are often poorly predicted due to the complex strain fields and regions of re-circulation in a swirling flow are often under-estimated. These deficiencies require turbulence models with improved physics, such as non-linear k-ε models, algebraic Reynolds stress models, or full Reynolds stress models with low Reynolds number capability limitation (for example, the re-views in Patel et al. [1985] and Wilcox [1998]).
¾ Mixing is often poorly predicted in flows with strong buoyancy effects or high streamline curvature.
Again this deficiency requires improved physics, see comment above.
¾ Flow separation from surfaces under the action of adverse pressure gradients is often poorly pre-dicted. The real flow is likely to be much closer to separation (or more separated) than the calcula-tions suggest. The SST version of Menter's k-ω based, near wall resolved model (Menter [1993, 1996]) can offer a considerable improvement.
¾ Flow recovery following re-attachment is often poorly predicted. If possible, avoid the use of wall functions in these regions, but low Reynolds number models may also have some problems. A promising possibility is the use of a length-scale limiting device (Ince and Launder [1995]).
¾ The far-field spreading rates of round jets are predicted incorrectly. The use of non-linear k-ε models should be investigated for these problems (Apsley et al. [1995]).
¾ Turbulence driven secondary flows in straight ducts of non-circular cross section are not predicted at all. Linear eddy viscosity models cannot capture this feature. Use RSTM or non-linear eddy vis-cosity modelling.
¾ Dilation effects on turbulence production, which may become important for compressible flows, are not accounted for. These may be important in mixing layers at moderate Mach numbers.
Sarkar et al. [1989] and Zeman [1990] have proposed modifications to the k-ε model that correct this deficiency but the database is small.
¾ Laminar and transitional regions of flow cannot be calculated with the standard k-ε model but non-linear modelling may help in this respect. Transition is an active area of research in turbulence modelling. Some simple practical advice is given in section 4.7 below.
¾ The vertical heat flux in a buoyancy affected horizontal boundary layer, or in a thermal plume, is poorly represented by an eddy viscosity model which assumes a turbulent Prandtl number to cal-culate the turbulent transport of heat. RSTM models including the solution of equations for the three heat fluxes is currently the only option if this is important.
11.6.5. Guidelines on transitional flows
¾ Use experimental data to check whether the flow contains extensive regions of laminar or transi-tion flow which would be incorrectly estimated by the k-ε model with wall functions, or poorly pre-dicted by low Reynolds number k-ε models.
¾ Model transiton by intervention in the code to switch the turbulence model on or off at predeter-mined locations deterpredeter-mined by experiment