Wall procedure iteration

The procedure is the following Eq. (3.13) is calculated for given p and q. Then the resulting concentration at the respective walls cA w is compared with the assumptions in Eqs. (3.14). If the result is not satisfactory, either p or q can be changed individually or the global fit parameter d can be changed to execute another iteration. 

A significant number of the detected events are invalid, as either they correspond to a "random coincidence" between two unrelated y-rays or else one or both of the y-rays has been scattered before detection. The PEPT algorithm attempts to discard these invalid events, using an iterative procedure in which the centroid of the events is calculated, the y-rays passing furthest from the centroid are discarded, and this process is repeated until a specified fraction / of the original events remains. The optimum value of / depends on the mass of material between the tracer and the detectors, which adds to the number of scattered events. For example, when studying flow inside a vessel with 15 mm thick steel walls, 80% of the detected events must be discarded, so that the fraction/ of useful events is 0.2. The precision A of a PEPT location is given approximately by... 

The iterative procedure for the solution of the inverse problem by the regular conjugate gradient method was performed assuming the functions T(x,y), AT(x,y), X(x,y), and J x) are available at the -th iteration. The wall heat flux, q(x), at step n+1 is obtained from... 

Boundary conditions are 5T/0n = 0 (n is the normal to interface surface) on the gas-solid interface and on the symmetry lines as far as on the external wall surface (for case of channel with heat production in the wall) continuity both of heat flux and temperature on solid-liquid interface and the continuity of temperature on gas-liquid interface. Gauss-Zeidel iterative procedure has been used to solve the heat problem numerically. We used a non-uniform grid pattern near the vapor-liquid interface for higher computational accuracy. 

Laminar flow conditions cease to exist at Rcmod = 2100. The calculation of the critical velocity corresponding to Rcmod = 2100 requires an iterative procedure. For known rheology (p, m, n, Xq) and pipe diameter (D), a value of the wall shear stress is assumed which, in turn, allows the calculation of Rp, from equation (3.9), and Q and Qp from equations (3.14b) and (3.14a) respectively. Thus, all quanties are then known and the value of Rcmod can be calculated. The procedure is terminated when the value of x has been found which makes RCjnod = 2100, as illustrated in example 3.4 for the special case of n = 1, i.e., for the Bingham plastic model, and in example 3.5 for a Herschel-Bulkley fluid. Detailed comparisons between the predictions of equation (3.34) and experimental data reveal an improvement in the predictions, though the values of the critical velocity obtained using the criterion Rqmr = 2100 are only 20-25% lower than those predicted by equation (3.34). Furthermore, the two... 

Since the apparent viscosity is a function of the impeller properties and 1/Fow cannot be calculated immediately, an iterative procedure must be made. This can be simplified because there are a limited number of possible gearbox output speeds. Once the impeller type and diameter have been chosen, the torque at each speed can be calculated followed by the shear stress and shear rate at the wall. Then the viscosity and 1/Fow can be calculated and the regime in which the impeller would operate can be identified. The appropriate correlation can then be used to calculate Po Rew, and this can be rearranged to solve for the impeller speed. The condition where the output speed from rearranging Po Rew is just less than the input speed used to calculate 1/Fow is the one on which the design will be based. An example of this method is given in Section 9-3.7. 

---