Performance comparisons are composed of two parts: the first part contains the systematically investigation of six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fl...Performance comparisons are composed of two parts: the first part contains the systematically investigation of six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow and heat transfer based on the finite volume method using staggered and Rhie-Chow’s momentum interpolation collocated grids, the second part contains the comparative computations being conducted on Rhie-Chow’s momentum interpolation collocated grid and Thiart’s finite difference scheme based nonstaggered grid. Three 3-D cases that have analytical or benchmark solutions are adopted. For the first part, the results of computations indicate that, all the six schemes have the same numerical accuracy when the diffusion term is predominant. With the increase of convection, the FUDS, HDS and PLDS almost have the same accuracy in two of those grid systems, while the SUDS and QUICK have higher accuracy than the former. The accuracy of CDS is something in between. For the same under-relaxation factors and convergence criterion, the convergence rate of each scheme on those two grid systems are nearly equal with that on the staggered grid being a little bit faster. For QUICK and CDS, smooth, non-oscillating solutions can be obtained even when local Peclet number may be as large as 31.2-31.3. For the second part, it is concluded that simplified collocated grid system is preferable from numerical accuracy, grid Peclet number limit, sensitivity to the underrelaxation factor and the freedom in choosing finite difference scheme for convection term.展开更多
The presented research was focused on a comparison between different means of obtaining a Nusselt number distribution,in a situation where neither temperature nor heat flux density is constant.Two fundamentally differ...The presented research was focused on a comparison between different means of obtaining a Nusselt number distribution,in a situation where neither temperature nor heat flux density is constant.Two fundamentally different measurement techniques have been utilized,alongside a CFD simulation,in order to designate temperature distributions in a horizontal rod.Dry air under normal pressure,regarded as a perfect gas,was chosen as the working fluid,whereas the rod's cross-section was restricted to a ring.In this scenario heat exchange between the rod and the fluid is driven predominantly by natural convection,with a slight impact of thermal radiation,particularly at temperatures approaching the top end of the available range.Temperature margins achieved at the heated end of the rod ranged from 60 K up to 150 K,resulting in local Rayleigh numbers falling in-between 6.0xl03 and 2.6xl04.Reconstruction of Nusselt numbers from a discrete temperature distribution was possible thanks to a dedicated method implemented using a Scilab script.A segregated,steady-state solver based on the SIMPLE scheme was utilized for the purpose of numerical simulations on the fluid side,whereas a heat conduction equation was solved over solid domain in the considered conjugated heat transfer problem.A corresponding set of empirical data has been obtained,using both resistance temperature detectors and a thermal imaging camera,both for the sake of numerical model validation and comparison of individual methods.The Nusselt numbers resulting from each approach were compared against values computed using available correlations valid for horizontal configuration.展开更多
This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities hav...This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into "dead knots" in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.展开更多
The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where ...The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where G is a real simple Lie Group, W∈ g, C(W) 0 is the identity component of the centralizer C(W) of W in G .展开更多
文摘Performance comparisons are composed of two parts: the first part contains the systematically investigation of six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow and heat transfer based on the finite volume method using staggered and Rhie-Chow’s momentum interpolation collocated grids, the second part contains the comparative computations being conducted on Rhie-Chow’s momentum interpolation collocated grid and Thiart’s finite difference scheme based nonstaggered grid. Three 3-D cases that have analytical or benchmark solutions are adopted. For the first part, the results of computations indicate that, all the six schemes have the same numerical accuracy when the diffusion term is predominant. With the increase of convection, the FUDS, HDS and PLDS almost have the same accuracy in two of those grid systems, while the SUDS and QUICK have higher accuracy than the former. The accuracy of CDS is something in between. For the same under-relaxation factors and convergence criterion, the convergence rate of each scheme on those two grid systems are nearly equal with that on the staggered grid being a little bit faster. For QUICK and CDS, smooth, non-oscillating solutions can be obtained even when local Peclet number may be as large as 31.2-31.3. For the second part, it is concluded that simplified collocated grid system is preferable from numerical accuracy, grid Peclet number limit, sensitivity to the underrelaxation factor and the freedom in choosing finite difference scheme for convection term.
文摘The presented research was focused on a comparison between different means of obtaining a Nusselt number distribution,in a situation where neither temperature nor heat flux density is constant.Two fundamentally different measurement techniques have been utilized,alongside a CFD simulation,in order to designate temperature distributions in a horizontal rod.Dry air under normal pressure,regarded as a perfect gas,was chosen as the working fluid,whereas the rod's cross-section was restricted to a ring.In this scenario heat exchange between the rod and the fluid is driven predominantly by natural convection,with a slight impact of thermal radiation,particularly at temperatures approaching the top end of the available range.Temperature margins achieved at the heated end of the rod ranged from 60 K up to 150 K,resulting in local Rayleigh numbers falling in-between 6.0xl03 and 2.6xl04.Reconstruction of Nusselt numbers from a discrete temperature distribution was possible thanks to a dedicated method implemented using a Scilab script.A segregated,steady-state solver based on the SIMPLE scheme was utilized for the purpose of numerical simulations on the fluid side,whereas a heat conduction equation was solved over solid domain in the considered conjugated heat transfer problem.A corresponding set of empirical data has been obtained,using both resistance temperature detectors and a thermal imaging camera,both for the sake of numerical model validation and comparison of individual methods.The Nusselt numbers resulting from each approach were compared against values computed using available correlations valid for horizontal configuration.
基金supported, in part, by the National Science Foundation of the United States (DMR-0821697, CMMI-0926522, DMR-1105135)
文摘This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into "dead knots" in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.
文摘The semisimple structure, which generalizes the complex and the paracomplex structures, is considered. The authors classify all the homogeneous semisimple spaces whose underlying spaces are G/C(W) 0 , where G is a real simple Lie Group, W∈ g, C(W) 0 is the identity component of the centralizer C(W) of W in G .
