EVALUATING RESIDUALS AND IMBALANCE FORCES BY INFORM

1. EVALUATING RESIDUALS AND IMBALANCE FORCES BY INFORM Residuals These are imbalances (errors) in the finite-volume equations which are computed during the solution procedure, the aim of which, of course, is to reduce them to an acceptable magnitude. Their magnitudes can be reported to the user, variable-by-variable, in two ways, namely as: • Global values, which are the sums of the absolute values for all cells; or • Fields of values, which can be printed in the RESULT file, or viewed by means of PHOTON, AUTOPLOT or the VR-Viewer, in the same manner as for other SOLVEd or STOREd variables. The global values appear both in the result file, where they are influenced by the setting of ITABL and in the graphical monitor, if that is activated. The most convenient means of printing and plotting the field values of residuals (and of "corrections" also) is to make use of the In-Form function RESI (and the function CORR for corrections.)

2. GETTING RESIDUALS • the residuals, are obtained with the In-Form Statement : • (STORED of name is RESI (varname)) • The usefulness of having residual field instead of a global residual ensures to the user the places where its numerical solution achieved or not the desired accuracy. • In complex flow geometries sometimes is quite difficult to get low residual for the whole domain, but if one is interested in some specific regions of the domain he or she may decide if the residuals are low enough to quit the solver.

3. WORKSHOP TO GET RESIDUALS USING INFORM The workshops are based on a single case: steady cross flow of air (IMAT=0) around a 2D cylinder The parameters are described below: • Cylinder diameter and length is 0.1 m x 0.1m. The domain is (xy) plane with 2x1 m with 60x30 grid. • The inlet velocity is 0.001m/s. The north and south walls have flow symmetry. You can start your In-Form programming lines in the q1 file available for download (wksh_if_resi)

4. WRITING IN-FROM LINES FOR WKSH_IF_RESI(1) Inform19Begin (STORED OF RESU IS RESI(U1)) (STORED OF RESV IS RESI(V1)) (STORED OF RESP IS RESI(P1)) Inform19End To start with use 20 sweeps only with FALSTD(U1) = FALSDT(V1) =10.

5. WKSH_IF_RESI(1) • Pressure residuals field for 20 sweeps. • Increase the sweeps to 500 and compare the results. • Also inspect the U1 and V1 residuals. • Check if PARSOL on/off affects the residuals. . For a ‘rescue’ situation a q1 file of this case is available for download (wksh_if_resi)

6. VIRTUAL WIND TUNNEL APPLICATIONS • PHOENICS solves equations which express, cell-by-cell throughout the computational grid, the balances of conserved quantities such as mass, momentum and energy. • An "imbalance patch" is such a patch of cells for which the imbalances of the conserved quantities, at a defined instant in the calculation, is computed and printed.

7. VIRTUAL WIND TUNNEL APPLICATIONS Such patches provide interesting information of the following kinds: • If the patch encloses a volume of material which is free from any source of the quantity in question, if the flow is steady, and if the solution is converged, the printed-out imbalance should be as close to zero as round-off error permits. Larger imbalances are therefore a measure of lack of convergence which it may be useful to know about. • For transient flow, the printed imbalance represents the contribution of the transient terms of the equations, integrated over the patch volume. • If the patch encloses a volume of fluid within which a solid object is held at rest, the imbalances of momentum in three different directions represent the forces exerted by the fluid on the body.

8. PHOENICS IMPLEMENTATION • If a patch name in the Q1 file begins with the four characters IMBL, it will be treated as an imbalance patch. • Associated COVAL commands are necessary in order to indicate the variables for which imbalances must be computed; but the values of CO and VAL appearing in them are immaterial

9. WKSH_IF_RESI(2) • The task of wksh_if_RESI(2) is to evaluate the drag coefficient of the cylinder of wksh-if-resi(1). • The center of the cylinder is at IX=25 and IY=15. The IMBL patches must encompass the cylinder body. Two patches with distinct lengths were chosen: IMBL1 and IMBL2. Group 13. Boundary & Special Sources Imbalance patches enclosing a solid object enable the drag on the object to be deduced. All boxes should report the same momentum balance, if the solution has converged PATCH (IMBL1 ,VOLUME,15,35,8,22,1,1,1,1) COVAL (IMBL1 ,U1 , 0.000000E+00, 0.000000E+00) COVAL (IMBL1 ,V1 , 0.000000E+00, 0.000000E+00) PATCH (IMBL2 ,VOLUME,10,40,5,25,1,1,1,1) COVAL (IMBL2 ,U1 , 0.000000E+00, 0.000000E+00) COVAL (IMBL2 ,V1 , 0.000000E+00, 0.000000E+00)

10. WKSH_IF_RESI(2) • For comparison purposes also activate the ‘ forces in objects’ in OUTPUP .

11. WKSH_IF_RESI(2) • Check below an extract from the result file: • x-wise force on IMBL1 is 2.117E-08 [N] • x-wise force on IMBL2 is 2.264E-08 [N] • y-wise force on IMBL1 is 2.990E-10 [N] • y-wise force on IMBL2 is 6.235E-10[N] • Notice that X-Force on IMBL1 and IMBL2 are close to but not coincident. They result from a integration along the IMB boundary. Perhaps larger boundaries reduce the error, to be investigated. On the other hand, due to the flow symmetry, is not expected any y-wise force, consequently the deduced y-wise forces for both patch are two orders of magnitude lower. • The X-Force evaluated automatically by Phoenics is 2.28E-08 N

12. THE DRAG COEFFICIENT • The uniform flow of air results a Reynolds number (based on the cylinder diameter) of 6.5 CDexp ~ 4.0 see next slide. • The drag coefficient is estimated from the imbalance force: • Which bears a good agreement against the experimental CD data . . For a ‘rescue’ situation a q1 file of this case is available for download (wksh_if_resi)

13. DRAG COEFFICIENT FOR A CYLINDER IN CROSS FLOW

14. END OF THE RESIDUALS & IMBALANCES WORKSHOPS