Jimmy C. K. Tong

Breakdown of Laminar Pipe Flow into Transitional Intermittency and Subsequent Attainment of Fully Developed Intermittent or Turbulent Flow

The breakdown of laminar pipe flow into transitional intermittency is predicted numerically here for the first time. Subsequent to transitional intermittency, a fully developed regime is achieved wherein the flow may be either intermittent or fully turbulent. Fully developed friction factors are predicted as a function of the Reynolds number throughout the intermittent regime. These predictions successfully bridge the gap between well-established laminar friction factors and turbulent friction factors. Definitive numerical information is provided about the locations in the pipe at which both laminar breakdown and fully developed attainment occur. These locations are a function of the Reynolds number. The streamwise changes in the velocity profiles reflect the complex evolution of the flow as it passes through the successive regimes. For design purposes, information is provided for the pressure drop that characterizes the evolving flow. The numerical results correspond to an inlet turbulence intensity level of 5%.

Fluid Flow in a System with Separate Laminar and Turbulent Zones

Attention is focused on physical situations in which separate zones of laminar and turbulent flow coexist within a given device. The specific motivating application for this study is a complex fluid-flow manifold used in the thermal management of electronic equipment. The adopted approach to the solution of this fluid-flow problem was to employ a turbulent-flow model for the entire solution space but to use several turbulence models as inputs. The goal of the study was to quantify the behavior of popular turbulence models in regions where the flow is laminar according to the accepted Reynolds number criteria. Three models were considered: 1) standard k-ϵ, 2) k-ω, and 3) SST. Evaluation of the models was based on the values of the ratio μ t /μ in nominally laminar regions, where μ t and μ are, respectively, the turbulent and molecular viscosities. Values of this ratio well below one in a nominally laminar region would indicate that a turbulence model reduces, in effect, to a laminar model. It was found that the standard k-ϵ model failed to provide values of μ t /μ << 1 for channel Reynolds numbers as low as 370. On the other hand, both the k-ω and SST models yielded values of μ t /μ << 1 for Re = 370. For these models, acceptably small values of the ratio were encountered for Reynolds numbers up to 370. At still higher Reynolds numbers, these turbulence models did not reduce to laminar models. Results for the relationship between the overall pressure drop and the system flowrate are also presented for use in practical applications.

Attainment of Flowrate Uniformity in the Channels That Link a Distribution Manifold to a Collection Manifold

A logic-based systematic method of designing manifold systems to achieve flowrate uniformity among the channels that interconnect a distribution manifold and a collection manifold has been developed, implemented, and illustrated by case studies. The method is based on tailoring the flow resistance of the individual channels to achieve equal pressure drops for all the channels. The tailoring of the flow resistance is accomplished by the use of gate-valve-like obstructions. The adjustment of the valve-like obstructions is determined here by means of numerical simulations. Although the method is iterative, it may converge in one cycle of the iterations. Progress toward the goal of per channel uniformity can be accelerated by tuning a multiplicative constant. The only departure of the method from being fully automatic is the selection of the aforementioned multiplicative constant. The method is described in detail in a step-by-step manner. These steps are illustrated both generically and specifically for four case studies. As an example, in one of the case studies, an original flow imbalance of over 100% in an untailored manifold system was reduced to a flow imbalance of less than 10% in one cycle of the method.

A Quasi-Analytical Method for Fluid Flow in a Multi-Inlet Collection Manifold

This paper sets forth a fully validated quasianalytical method for determining the fluid flow in a multi-inlet collection manifold. The method is based on first principles, which are the conservation laws for mass and momentum. Although it is necessary to use numerical means to extract results from the model, the solution task is accomplished by the use of a spreadsheet, without the need for complex software or large computer assets. The validation of the method was achieved by comparing the key results with those from a numerically exact simulation. The comparison included both local results and global results. For the local results, the accuracy of the model was found to be in the 1% range, while the global results from the model were accurate to about 4%. The investigated manifold was a case study drawn from a problem involving thermal management of electronic equipment, in which an array of coldplates discharged spent air into the manifold. It was found, from both the quasianalytical method and the numerical simulation, that there is a variation in the per-coldplate flowrate due to axial pressure variations in the manifold. These pressure variations can be attributed to the streamwise acceleration of the manifold flow due to the accumulation of the flow entering the manifold from the coldplate array. The utility of the quasianalytical method was further demonstrated by applying it to a number of other cases. In particular, the method was used to design a manifold capable of producing a uniform mass flowrate through all of its ports. DOI: 10.1115/1.2717620

Unified Treatment of Natural Convection in Tall Narrow and Flat Wide Rectangular Enclosures

Numerical simulation was used to investigate natural convection in rectangular enclosures ranging in aspect ratio from tall, narrow shapes to flat, wide shapes. For each of the selected aspect ratios, the Rayleigh number was varied over a range of approximately four decades. Two fundamental thermal boundary conditions were considered. One of these, commonly designed as heating from below, involved the imposition of a temperature at the lower bounding wall that is higher than that at the upper bounding wall. The side walls of the enclosure were maintained adiabatic for this case. The second employed boundary condition was side walls at different uniform temperatures and adiabatic upper and lower boundaries. For each aspect ratio and for both types of boundary conditions, the onset of natural convection from the regime of pure conduction occurred at a definitive value of the Rayleigh number, termed the critical Rayleigh number. Once that threshold value was exceeded, the Nusselt number increased markedly with increasing Rayleigh number, the sharpness of the increase being greater for the bottom-heated case. For that case and for aspect ratios (height/width) greater than one, the breakdown of a flow pattern characterized by a single recirculation zone caused a sudden halt to the increase of the Nusselt number. This breakdown was followed by a rapid reformation of the flow pattern into a pair of recirculation zones, one situated above the other. The critical Rayleigh number was insensitive to the aspect ratio for flat, wide enclosures but, on the contrary, the critical value increased markedly with increasing aspect ratio for tall, narrow enclosures. In general, a critical Rayleigh number for the bottom-heated case exceeded that for the side-heated case by a factor of 12.

Intermittent flow modeling. Part 1: Hydrodynamic and thermal modeling of steady, intermittent flows in constant area ducts

A model for predicting fluid flow and convective heat transfer in all flow regimes has been implemented for steady mainflows in pipes and ducts of constant cross section. The key feature of the model is its capability to predict transitions between purely laminar and purely turbulent flow, while the latter flows are also predicted with high accuracy. The flow regime need not be specified in advance but is determined automatically as the flow evolves during its passage along the pipe or duct. Intermittently in the transition regime is fully accounted. It was shown that fully developed flows are necessarily restricted to either the laminar regime or the turbulent regime, but that a fully developed intermittent regime exists. The effects of the flow conditions at the inlet of the pipe or duct, velocity profile shape and turbulence intensity, on the subsequent transitions were quantified. To facilitate the heat transfer analysis, the turbulent-Prandtl-number concept, widely used to inter-relate the turbulent viscosity and thermal conductivity, was extended to encompass both intermittent and laminar flows. The presented results include all-flow-regime fully developed friction factors and fully developed Nusselt numbers. The locations where laminar-flow breakdown occurs and where fully developed begins are also presented.Copyright