Flow Development Time Research Articles

Transient behavior and steady-state rheology of dense frictional suspensions in pressure-driven channel flow

AbstractResults from particle-resolved Direct numerical simulations are presented for dense suspensions of frictional non-colloidal spheres in viscous pressure-driven channel flow. The bulk solid volume fraction varies between $$\phi _b=0.2$$ ϕ b = 0.2 and 0.6, and the Coulomb friction coefficient is either $$\mu _c = 0$$ μ c = 0 or 0.5. The main objectives are to unravel the influence of (1) $$\phi _b$$ ϕ b and $$\mu _c$$ μ c on the flow development time and of (2) heterogeneous shear on the steady-state suspension rheology. Starting from an initially homogeneous distribution, the particles show shear-induced migration toward the core until equilibrium is reached. The flow development time decays exponentially with increasing $$\phi _b/\Phi _R$$ ϕ b / Φ R , where $$\Phi _R$$ Φ R is a friction-dependent reference bulk concentration beyond which particle contacts cause a rapid increase in the particle stress. The steady-state rheology is studied by means of the ‘viscous’ and ‘frictional’ rheology frameworks. Excluding the central core and wall regions, the data for the local relative suspension viscosity collapse onto a single curve as function of the normalized local concentration $${\bar{\phi }}/\phi _m$$ ϕ ¯ / ϕ m , where $$\phi _m$$ ϕ m is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number $$I_v$$ I v in the core region, where the macroscopic friction coefficient $$\mu $$ μ drops below the minimal value found for homogeneous shear flows. A modified frictional rheology model is presented that captures subyielding. Finally, a model is presented for $${\bar{\phi }}/\phi _{mp}$$ ϕ ¯ / ϕ mp as function of $$I_v$$ I v , where $$\phi _{mp}$$ ϕ mp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond $$\phi _{m}$$ ϕ m at high $$\phi _b$$ ϕ b and maximum core concentrations below $$\phi _m$$ ϕ m at lower $$\phi _b$$ ϕ b .

Transient Natural Convection in an Enclosure with Variable Thermal Expansion Coefficient and Nanofluid Properties

Transient natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity, and the thermal expansion coefficient of Al2O3-water nanofluid. The study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ ϕ ≤ 7%), the enclosure aspect ratio (AR =1), and temperature differences between the cold and hot walls (∆T= 30). Transient parameters such as development time and time-average Nusselt number along the cold wall are also presented as a non-dimensional form. Increasing the Rayleigh number shortens the non-dimensional time of the initializing stage. By increasing the volume fraction of nanoparticles, the flow development time shows different behaviors for various Rayleigh numbers. The non-dimensional development time decreases by enhancing the concentration of nanoparticles.

Characterizing dynamic hysteresis and fractal statistics of chaotic two-phase flow and application to fuel cells

In this study, we analyze the stability of two-phase flow regimes and their transitions using chaotic and fractal statistics, and we report new measurements of dynamic two-phase pressure drop hysteresis that is related to flow regime stability and channel water content. Two-phase flow dynamics are relevant to a variety of real-world systems, and quantifying transient two-phase flow phenomena is important for efficient design. We recorded two-phase (air and water) pressure drops and flow images in a microchannel under both steady and transient conditions. Using Lyapunov exponents and Hurst exponents to characterize the steady-state pressure fluctuations, we develop a new, measurable regime identification criteria based on the dynamic stability of the two-phase pressure signal. We also applied a new experimental technique by continuously cycling the air flow rate to study dynamic hysteresis in two-phase pressure drops, which is separate from steady-state hysteresis and can be used to understand two-phase flow development time scales. Using recorded images of the two-phase flow, we show that the capacitive dynamic hysteresis is related to channel water content and flow regime stability. The mixed-wettability microchannel and in-channel water introduction used in this study simulate a polymer electrolyte fuel cell cathode air flow channel.

A comparison of flow development in high density gas‐solids circulating fluidized bed downer and riser reactors

Comparison of flow development in high density downer and riser reactors is experimentally investigated using fluid catalytic cracking particles with very high solids circulation rate up to 700 kg/m2s for the first time. Results show that both axial and radial flow structures are more uniform in downers compared to riser reactors even at very high density conditions, although the solids distribution becomes less uniform in the high density downer. Solids acceleration is much faster in the downer compared to the riser reactor indicating a shorter length of flow development and residence time, which is beneficial to the chemical reactions requiring short contact time and high product selectivity. Slip velocity in risers and downers is also first compared at high density conditions. The slip velocity in the downer is much smaller than in the riser for the same solids holdup indicating less particle aggregation and better gas‐solids contacting in the downer reactors. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1172–1183, 2015

Physical and computational modelling of residence and flow development time in a large municipal disinfection clearwell

In this study, a two-dimensional, depth-averaged computational model (River2DMix) was used to predict the flow pattern and residence time distribution for flow through the Calgary Glenmore Water Treatment Plant northeast clearwell. Results are compared to those from flow visualization and tracer studies in a 1 : 19 scale model of the clearwell, as well as tracer studies conducted at the plant. Tests were carried out for three flow rates that ranged from minimum to maximum operating conditions. A key observation in the physical model was that it was necessary to let the flow fully develop before starting a tracer test to determine the residence time distribution. This flow development time to achieve steady-state results was approximately 10·5 h at the minimum flow rate tested. Results also show that it was unnecessary to model the structural columns either in the simulation or the scale model for developed flow in this clearwell, although for undeveloped or transient flow conditions the columns were important to consider.

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a horizontal concentric annulus

A numerical study of transient natural convection heat transfer of aqueous nanofluids in a horizontal annulus between two coaxial cylinders is presented. The effective thermophysical properties of water in the presence of copper oxide nanoparticles with four different volume fractions are predicted using existing models, in which the effects of the Brownian motion of nanoparticles are taken into consideration. The predicted development of convective flow and heat transfer of nanofluids is presented by means of the average Nusselt number over the outer cylinder. The flow development time towards a steady state and the time-averaged Nusselt number are predicted and scaled with Rayleigh number. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is gradually lowered as the volume fraction of nanoparticles is increased. In addition, the time-averaged Nusselt number will be overestimated if the Brownian motion effects are not considered.

Scaling Analysis of the Unsteady Natural Convection Boundary Layer Adjacent to an Inclined Plate for Pr > 1 Following Instantaneous Heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage, and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

Unsteady natural convection heat transfer from a heated horizontal circular cylinder to its air-filled coaxial triangular enclosure

Unsteady natural convection heat transfer in a horizontal annular region bounded by a heated inner circular cylinder and a coaxial outer triangular cylinder is numerically studied for a wide range of Grashof numbers, aspect ratios, and inclination angles of the triangular enclosure. Different phases are identified during the course of flow development through the evolutions of the average Nusselt number over the inner circular wall. Snapshots of streamlines and isotherms for two typical cases are presented to exhibit identification among these phases. The flow development time and time-averaged Nusselt number over the inner circular wall are predicted and scaled with Grashof number. Additionally, the onset and evolution of pitchfork bifurcation are quantitatively investigated.

Unsteady natural convection in a triangular enclosure under isothermal heating

The fluid flow and heat transfer inside a triangular enclosure due to instantaneous heating on the inclined walls are investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer under the inclined walls may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. A new triple-layer integral approach of scaling analysis has been considered to obtain major scaling relations of the velocity, thicknesses, Nusselt number and the flow development time of the natural convection boundary layer and verified by direct numerical simulations over a wide range of flow parameters.

Numerical study of transient buoyancy-driven convective heat transfer of water-based nanofluids in a bottom-heated isosceles triangular enclosure

A numerical study of transient buoyancy-driven convective heat transfer of water-based nanofluids inside a bottom-heated horizontal isosceles triangular cylinder is presented. Nano-sized copper oxide (CuO) particles suspended in water with two different volume fractions are considered. The thermophysical properties of water in the presence of nanoparticles are predicted using existing models, in which the effects of the Brownian motion of nanoparticles are taken into account. It is shown that pitchfork bifurcation appears for relatively high Grashof numbers and the critical Grashof number is found to be 5.60 × 10 4. The predicted development of convective flow of nanofluids is presented by means of the average Nusselt number over the bottom. Additionally, the flow development time towards a steady/quasi-steady state and the time-averaged Nusselt number are scaled with Grashof number. It is also shown that at constant Grashof numbers the time-averaged Nusselt number is lowered as more nanoparticles are added to the base liquid and will be overestimated if the Brownian motion effects are not considered.

Transient natural convective heat transfer of a low-Prandtl-number fluid inside a horizontal circular cylinder with an inner coaxial triangular cylinder

A numerical study of transient natural convection of liquid gallium (Pr = 0.023) from a horizontal triangular cylinder to its coaxial cylindrical enclosure is performed. The aspect ratio is fixed at 2 and two positions of the inner triangular cylinder are considered. The development of the convective flow and heat transfer is shown via the time histories of the average Nusselt number over the outer circular wall for various Grashof numbers. Temporal phases of the flow development are identified as: initializing, developing, transitioning, and steady/quasi-steady state or oscillating. Typical flow patterns and temperature distributions at these phases are presented by means of streamlines and isotherms, respectively. Pitchfork bifurcation is present for both positions of the inner triangular cylinder when Gr ⩾ 5 × 10 4. The time-averaged Nusselt number over the outer circular cylinder, the flow development time, and the onset time of pitchfork bifurcation are predicted and scaled with the Grashof number. It is found that the time-averaged Nusselt number is apparently increased by horizontally placing the top side of the inner triangular cylinder for Gr ⩾ 1 × 10 5.

Physical and computational modelling of residence and flow development time in a large municipal disinfection clearwell

In this study, a two-dimensional, depth-averaged computational model (River2DMix) was used to predict the flow pattern and residence time distribution for flow through the Calgary Glenmore Water Treatment Plant northeast clearwell. Results are compared to those from flow visualization and tracer studies in a 1 : 19 scale model of the clearwell, as well as tracer studies conducted at the plant. Tests were carried out for three flow rates that ranged from minimum to maximum operating conditions. A key observation in the physical model was that it was necessary to let the flow fully develop before starting a tracer test to determine the residence time distribution. This flow development time to achieve steady-state results was approximately 10.5 h at the minimum flow rate tested. Results also show that it was unnecessary to model the structural columns either in the simulation or the scale model for developed flow in this clearwell, although for undeveloped or transient flow conditions the columns were important to consider.

SHROUD TECHNIQUE USING THE TRANSIENT METHOD FOR LOCAL HEAT TRANSFER MEASUREMENTS

A new technique for measuring local heat transfer coefficients on complex-shaped models is described. This technique is referred to as the shroud technique and is a variation on the well-known transient method. The technique involves preheating a model inside a shroud while it is installed in a wind tunnel. The shroud is then ejected, exposing the model to ambient temperature air. The transient temperature on the surface of the model is measured using liquid crystals and recorded with a video system. Although an infinite variety of model shapes can be used, measurements on a cylinder in cross-flow are used to demonstrate this technique. The measurements are compared with earlier measurements, which used different techniques. Good agreement is found at the stagnation point and in the front laminar boundary-layer region. In the separation region, the heat transfer rate is dependent an the thermal boundary condition, which in the transient method is affected by the selection of the nondimensional liquid crystal temperature. In the wake region, it was found that the results depend on the flow development time relative to the transient measurement time.

Some experimental results on the development of Couette flow for non-Newtonian fluids

This paper reports some experimental results on the time development of a Couette flow following the start-up of shear flow using the technique of two-color flow birefringence. Measurements obtained on collagen solutions are consistent with two theoretical studies which predict that for some viscoelastic liquids, momentum is transferred from the moving Couette cell boundary to the interior of the fluid through a velocity wave propagating and reflecting between the cell boundaries. This non-Newtonian phenomenon, exhibited as an oscillatory response in the measured birefringence and orientation angle, is observed at shear rates above a critical value when the response time of the polymer solution approaches the flow development time in the Couette flow cell.

Approximate Analysis of Transient Laminar Boundary-Layer Development

Transient development of the boundary layer on a flat plate following the impulsive start of motion of the surrounding fluid is analyzed approximately. The Howarth-Dorodnitzin transformation and a Crocco Integral are used to relate the temperature field to the approximate velocity field which is obtained in a “constant density” plane. The solution for the velocity field is determined using the unsteady Momentum Integral equation with a new type of profile. Expressions for the boundary-layer development time and model surface temperature at the end of the development time are presented. Good agreement with a roughly determined experimental flow development time is achieved.