Influence of the main parameters of a parallel-plate dialyser under laminar flow conditions
A mathematical model describing the mass transfer in a parallel-plate dialyser with co-current laminar flow in both channels based on the Navier-Stokes equations and Fick's second law was developed. Numerical solutions are presented for pulse- and stepwise concentration changes of the solute in one of the channels using the Laplace transform technique. By simulation the influence of the main design and operational parameters of the dialyser and the most important physical constants for the mass transfer process were investigated. Conclusions with regard to optimum design and operation were drawn and some possibilities for simplifying the model were established
Numerical solution of hydraulic models based on the axially-dispersed plug flow model by Laplace transforms
Abstract The problem of solving hydraulic models based on the axially-dispersed plug flow model which are applicable for the mathematical modelling of different flow-through systems both in chemical analysis (e.g., chromatography, flow injection analysis) and chemical industry (e.g., different tubular reactors) is discussed. Methods for numerical inversion of the model solution in the Laplace domain by expanding it into series of orthogonal functions are compared. Best results with respect to precision and consumption of computation time are given by the methods employing Chebyshov polynomials of the first kind and Fourier sine series. These methods were found to be better in these respects than some other frequently used numerical inversion methods.
Flow-Induced Slider Vibration in a Functional Hard Disk Drive: Influence of Air Shroud
An air shroud is designed and placed within a commercially available hard disk drive operating at 15 000 rpm. Large eddy simulations of the turbulent airflow characteristics resulting from both the models, with and without air shroud, are carried out by assuming the read/write head is at the disk middle diameter. The numerical model consists of about nine million tetrahedral cells with the largest and smallest sizes of the cell volumes being 2.5 mm3 and 0.35 mm3 , respectively. The dynamic Smagorinsky-Lily model is employed to mimic the effect of small-scale eddies in the turbulent airflow. Numerically predicted airflow characteristics are compared against the LDA measurements and found to be in good agreement. The wind blowing on the surfaces of the head gimbals assembly is converted into aerodynamic forces and the resulting slider displacement in the off-track and out-of-plane directions are investigated. It is inferred that the disk drive model with air shroud results in a maximum of 44% and 10% less off-track and out-of-plane slider displacements, respectively.