Search results for: normalized modulus

Authors: Ali Kadir, S. R. Mishra, M. Shamshuddin, O. Anwar Beg

Abstract:

Motivation- Rotating disk bio-reactors are fundamental to numerous medical/biochemical engineering processes including oxygen transfer, chromatography, purification and swirl-assisted pumping. The modern upsurge in biologically-enhanced engineering devices has embraced new phenomena including bioconvection of micro-organisms (photo-tactic, oxy-tactic, gyrotactic etc). The proven thermal performance superiority of nanofluids i.e. base fluids doped with engineered nanoparticles has also stimulated immense implementation in biomedical designs. Motivated by these emerging applications, we present a numerical thermofluid dynamic simulation of the transport phenomena in bioconvection nanofluid rotating disk bioreactor flow. Methodology- We study analytically and computationally the time-dependent three-dimensional viscous gyrotactic bioconvection in swirling nanofluid flow from a rotating disk configuration. The disk is also deformable i.e. able to extend (stretch) in the radial direction. Stefan blowing is included. The Buongiorno dilute nanofluid model is adopted wherein Brownian motion and thermophoresis are the dominant nanoscale effects. The primitive conservation equations for mass, radial, tangential and axial momentum, heat (energy), nanoparticle concentration and micro-organism density function are formulated in a cylindrical polar coordinate system with appropriate wall and free stream boundary conditions. A mass convective condition is also incorporated at the disk surface. Forced convection is considered i.e. buoyancy forces are neglected. This highly nonlinear, strongly coupled system of unsteady partial differential equations is normalized with the classical Von Karman and other transformations to render the boundary value problem (BVP) into an ordinary differential system which is solved with the efficient Adomian decomposition method (ADM). Validation with earlier Runge-Kutta shooting computations in the literature is also conducted. Extensive computations are presented (with the aid of MATLAB symbolic software) for radial and circumferential velocity components, temperature, nanoparticle concentration, micro-organism density number and gradients of these functions at the disk surface (radial local skin friction, local circumferential skin friction, Local Nusselt number, Local Sherwood number, motile microorganism mass transfer rate). Main Findings- Increasing radial stretching parameter decreases radial velocity and radial skin friction, reduces azimuthal velocity and skin friction, decreases local Nusselt number and motile micro-organism mass wall flux whereas it increases nano-particle local Sherwood number. Disk deceleration accelerates the radial flow, damps the azimuthal flow, decreases temperatures and thermal boundary layer thickness, depletes the nano-particle concentration magnitudes (and associated nano-particle species boundary layer thickness) and furthermore decreases the micro-organism density number and gyrotactic micro-organism species boundary layer thickness. Increasing Stefan blowing accelerates the radial flow and azimuthal (circumferential flow), elevates temperatures of the nanofluid, boosts nano-particle concentration (volume fraction) and gyrotactic micro-organism density number magnitudes whereas suction generates the reverse effects. Increasing suction effect reduces radial skin friction and azimuthal skin friction, local Nusselt number, and motile micro-organism wall mass flux whereas it enhances the nano-particle species local Sherwood number. Conclusions - Important transport characteristics are identified of relevance to real bioreactor nanotechnological systems not discussed in previous works. ADM is shown to achieve very rapid convergence and highly accurate solutions and shows excellent promise in simulating swirling multi-physical nano-bioconvection fluid dynamics problems. Furthermore, it provides an excellent complement to more general commercial computational fluid dynamics simulations.

Keywords: bio-nanofluids, rotating disk bioreactors, Von Karman swirling flow, numerical solutions

Procedia PDF Downloads 156

Authors: Nanine Fouche

Abstract:

The Cape Flats is a low-lying sand-covered expanse of approximately 460 square kilometres, situated to the southeast of the central business district of Cape Town in the Western Cape of South Africa. The aeolian sands masking this area are often loose and compressible in the upper 1m to 1.5m of the surface, and there is a general exceedance of the maximum allowable settlement in these sands. The settlement of shallow foundations on Cape Flats sands is commonly predicted using the results of in-situ tests such as the SPT or DPSH due to the difficulty of retrieving undisturbed samples for laboratory testing. Varying degrees of accuracy and reliability are associated with these methods. More recently, shear wave velocity (Vs) profiles obtained from seismic testing, such as continuous surface wave tests (CSW), are being used for settlement prediction. Such predictions have the advantage of considering non-linear stress-strain behaviour of soil and the degradation of stiffness with increasing strain. CSW tests are rarely executed in the Cape Flats, whereas SPT’s are commonly performed. For this reason, and to facilitate better settlement predictions in Cape Flats sand, equations representing shear wave velocity (Vs) as a function of SPT blow count (N60) and vertical effective stress (v’) were generated by statistical regression of site investigation data. To reveal the most appropriate method of overburden correction, analyses were performed with a separate overburden term (Pa/σ’v) as well as using stress corrected shear wave velocity and SPT blow counts (correcting Vs. and N60 to Vs1and (N1)60respectively). Shear wave velocity profiles and SPT blow count data from three sites masked by Cape Flats sands were utilised to generate 80 Vs-SPT N data pairs for analysis. Investigated terrains included sites in the suburbs of Athlone, Muizenburg, and Atlantis, all underlain by windblown deposits comprising fine and medium sand with varying fines contents. Elastic settlement analysis was also undertaken for the Cape Flats sands, using a non-linear stepwise method based on small-strain stiffness estimates, which was obtained from the best Vs-N60 model and compared to settlement estimates using the general elastic solution with stiffness profiles determined using Stroud’s (1989) and Webb’s (1969) SPT N60-E transformation models. Stroud’s method considers strain level indirectly whereasWebb’smethod does not take account of the variation in elastic modulus with strain. The expression of Vs. in terms of N60 and Pa/σv’ derived from the Atlantis data set revealed the best fit with R2 = 0.83 and a standard error of 83.5m/s. Less accurate Vs-SPT N relations associated with the combined data set is presumably the result of inversion routines used in the analysis of the CSW results showcasing significant variation in relative density and stiffness with depth. The regression analyses revealed that the inclusion of a separate overburden term in the regression of Vs and N60, produces improved fits, as opposed to the stress corrected equations in which the R2 of the regression is notably lower. It is the correction of Vs and N60 to Vs1 and (N1)60 with empirical constants ‘n’ and ‘m’ prior to regression, that introduces bias with respect to overburden pressure. When comparing settlement prediction methods, both Stroud’s method (considering strain level indirectly) and the small strain stiffness method predict higher stiffnesses for medium dense and dense profiles than Webb’s method, which takes no account of strain level in the determination of soil stiffness. Webb’s method appears to be suitable for loose sands only. The Versak software appears to underestimate differences in settlement between square and strip footings of similar width. In conclusion, settlement analysis using small-strain stiffness data from the proposed Vs-N60 model for Cape Flats sands provides a way to take account of the non-linear stress-strain behaviour of the sands when calculating settlement.

Keywords: sands, settlement prediction, continuous surface wave test, small-strain stiffness, shear wave velocity, penetration resistance

Procedia PDF Downloads 175