Numerical Investigation to Derive Correlations for Hydrodynamic Entrance Length in Very Low Reynolds Number Regime in Rectangular Microchannels

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Dustin R. Ray ◽  
Debendra K. Das
Keyword(s):  
Three Dimensional ◽  
Numerical Data ◽  
Reynolds Numbers ◽  
Maximum Error ◽  
Entrance Length ◽  
Fully Developed Flow ◽  
Rectangular Microchannels ◽  
Mean Error ◽  
Aspect Ratios ◽  
Laminar Flow Model

Abstract A three-dimensional laminar flow model was used for 37 Reynolds numbers (0.1, 0.2…1, 2…10, 20…100, and 200…1000) through six rectangular microchannels (aspect ratios: 1, 0.75, 0.5, 0.25, 0.2, and 0.125) to develop correlations for hydrodynamic entrance length. The majority of the Reynolds numbers are in the low regime (Re < 100) to fulfill the need to determine the hydrodynamic entrance length for microchannels. Examination of the fully developed flow condition was considered using the velocity or fRe criteria. Numerical results from the present simulations were validated by comparing the fRe results. Two new correlations were developed from a vast amount of numerical data (222 simulations). The velocity criterion correlations predict entrance length with a mean error of 4.67% and maximum error of 10.28%. The fRe criterion generated better correlations and were developed as a function of aspect ratio to predict entrance length with a mean error less than 2% and maximum error of 5.75% for 0.1 ≤ Re ≤ 1000 and 0 ≤ α ≤ ∞.

Numerical simulation of pressure drop for three-dimensional rectangular microchannels

2018 ◽  
Vol 35 (6) ◽  
pp. 2234-2254 ◽  
Author(s):  
Zhipeng Duan ◽  
Peng Liang ◽  
Hao Ma ◽  
Niya Ma ◽  
Boshu He
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Three Dimensional ◽  
Numerical Data ◽  
Rectangular Microchannels ◽  
Content Type ◽  
Aspect Ratios ◽  
Rectangular Channels

Purpose The purpose of this paper is to numerically investigate the flow characteristics and extend the data of friction factor and Reynolds number product of hydrodynamically developing laminar flow in three-dimensional rectangular microchannels with different aspect ratios. Design/methodology/approach Using a finite-volume approach, the friction factor characteristics of Newtonian fluid in three-dimensional rectangular ducts with aspect ratios from 0.1 to 1 are conducted numerically under no-slip boundary conditions. A simple model that approximately predicts the apparent friction factor and Reynolds number product fappRe is referenced as a semi-theoretical fundamental analysis for numerical simulations. Findings The accurate and reliable results of fappRe are obtained, which are compared with classic numerical data and experimental data, and the simple semi-theoretical model used and all comparisons show good agreement. Among them, the maximum relative error with the classic numerical data is less than 3.9 per cent. The data of fappRe are significantly extended to other different aspect ratios and the novel values of fappRe are presented in the tables. The characteristics of fappRe are analyzed as a function of a non-dimensional axial distance and the aspect ratios. A more effective and accurate fourth-order fitting equation for the Hagenbach's factor of rectangular channels is proposed. Originality/value From the reliable data, it is shown that the values of fappRe and the model can be references of pressure drop and friction factor for developing laminar flow in rectangular channels for researchers and engineering applications.

Symmetry breaking and instability mechanisms in medium depth torsionally driven open cylinder flows

2011 ◽  
Vol 672 ◽  
pp. 521-544 ◽  
Author(s):  
STUART J. COGAN ◽  
KRIS RYAN ◽  
GREGORY J. SHEARD
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Symmetry Breaking ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Interfacial Region ◽  
Nonlinear Stability Analysis ◽  
Aspect Ratios ◽  
Instability Modes

A numerical investigation was conducted into the different flow states, and bifurcations leading to changes of state, found in open cylinders of medium to moderate depth driven by a constant rotation of the vessel base. A combination of linear stability analysis, for cylinders of numerous height-to-radius aspect ratios (H/R), and nonlinear stability analysis and three-dimensional simulations for a cylinder of aspect ratio 1.5, has been employed. Attention is focused on the breaking of SO(2) symmetry. A comprehensive map of transition Reynolds numbers as a function of aspect ratio is presented by combining a detailed stability analysis with the limited existing data from the literature. For all aspect ratios considered, the primary instabilities are identified as symmetry-breaking Hopf bifurcations, occurring at Reynolds numbers well below those of the previously reported axisymmetric Hopf transitions. It is revealed that instability modes with azimuthal wavenumbers m = 1, 3 and 4 are the most unstable in the range 1.0 < H/R < 4, and that numerous double Hopf bifurcation points exist. Critical Reynolds numbers generally increase with cylinder aspect ratio, though a decrease in stability occurs between aspect ratios 1.5 and 2.0, where a local minimum in critical Reynolds number occurs. For H/R = 1.5, a detailed characterisation of instability modes is given. It is hypothesized that the primary instability leading to transition from steady axisymmetric flow to unsteady three-dimensional flow is related to deformation of shear layers that are present in the flow, in particular at the interfacial region between the vortex breakdown bubble and the primary recirculation.

Cross-Wind Influence on Low Aspect Ratio Wings at Low Reynolds Numbers

2013 ◽  
Author(s):  
Amir Karimi Noughabi ◽  
Mehran Tadjfar
Keyword(s):  
Aspect Ratio ◽  
Numerical Study ◽  
Three Dimensional ◽  
Micro Air Vehicles ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Low Aspect Ratio ◽  
Aspect Ratios ◽  
Lift And Drag ◽  
Lift And Drag Coefficient

The aerodynamics of the low aspect ratio (LAR) wings is of outmost importance in the performance of the fixed-wing micro air vehicles (MAVs). The flow around these wings is widely influenced by three dimensional (3D) phenomena: including wing-tip vortices, formation of laminar bubble, flow separation and reattachment, laminar to turbulent transition or any combination of these phenomena. All the recent studies consider the aerodynamic characteristics of the LAR wings under the effect of the direct wind. Here we focus on the numerical study of the influence of cross-wind on flow over the inverse Zimmerman wings with the aspect ratios (AR) between 1 and 2 at Reynolds numbers between 6×104 and 105. We have considered cross-wind’s angles from 0° to 40° and angle of attack from 0° to 12°. The results show that lift and drag coefficient generally decrease when the angle of the cross-wind is increased.

Efficient Computation of Three-Dimensional Flow in Helically Corrugated Hoses Including Swirl

2009 ◽  
Author(s):  
Bas J. van der Linden ◽  
Emmanuel Ory ◽  
Jacques Dam ◽  
Arris S. Tijsseling ◽  
Maxim Pisarenco
Keyword(s):  
Friction Factor ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Efficient Computation ◽  
Time Saving ◽  
Fully Developed Flow ◽  
High Reynolds ◽  
Positive Effect ◽  
Moody Diagram

In this article we propose an efficient method to compute the friction factor of helically corrugated hoses carrying flow at high Reynolds numbers. A comparison between computations of several turbulence models is made with experimental results for corrugation sizes that fall outside the range of validity of the Moody diagram. To do this efficiently we implement quasi-periodicity. Using the appropriate boundary conditions and matching body force, we only need to simulate a single period of the corrugation to find the friction factor for fully developed flow. A second technique is introduced by the construction of an appropriately twisted wedge, which allows us to furthermore reduce the problem by a further dimension while accounting for the Beltrami symmetry that is present in the full three-dimensional problem. We make a detailed analysis of the accuracy and time-saving that this novelty introduces. We show that the swirl inside the flow, which is introduced by the helical boundary, has a positive effect on the friction factor. Furthermore, we give a prediction for which corrugation angles the assumption of axisymmetry is no longer valid. It then has to make place for Beltrami-symmetry if accurate results are required.

Prediction of Heat Transfer and Friction for the Louver Fin Geometry

1992 ◽  
Vol 114 (4) ◽  
pp. 893-900 ◽  
Author(s):  
A. Sahnoun ◽  
R. L. Webb
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Maximum Error ◽  
Transfer Coefficients ◽  
Mean Error ◽  
The Heat Transfer Coefficient

This paper is concerned with prediction of the air-side heat transfer coefficient of the louver fin geometry used in automotive radiators. An analytical model was developed to predict the heat transfer coefficient and friction factor of the louver fin geometry. The model is based on boundary layer and channel flow equations, and accounts for the “flow efficiency” in the array, as previously reported by Webb and Trauger. The model has no empirical constants. The model allows independent specifications of all of the geometric parameters of the louver fin. This includes the number of louvers over the flow depth, the louver width and length, and the louver angle. The model was validated by predicting the heat transfer coefficient and friction factor of 32 louver arrays tested by Davenport, which spanned hydraulic diameter based Reynolds numbers of 300–2800. At the highest Reynolds number, all of the heat transfer coefficients were predicted within a maximum error of −14 / + 25 percent, and a mean error of ± 8 percent. The high Reynolds number friction factors were predicted with a maximum error −22 /+ 26 percent, with a mean error of ± 8 percent. The error ratios were slightly higher at the lowest Reynolds numbers.

Transient growth in developing plane and Hagen Poiseuille flow

2005 ◽  
Vol 461 (2057) ◽  
pp. 1311-1333 ◽  
Author(s):  
Peter W Duck
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Alternative Mechanism ◽  
Fully Developed Flow ◽  
Circular Pipes ◽  
Flow Disturbances ◽  
High Reynolds ◽  
The Stability

The stability of developing entry flow in both two-dimensional channels and circular pipes is investigated for large Reynolds numbers. The basic flow is generated by uniform flow entering a channel/pipe, which then provokes the growth of boundary layers on the walls, until (far downstream) fully developed flow is attained; the length for this development is well known to be (Reynolds number)×the channel/pipe width/diameter. This enables the use of high-Reynolds-number theory, leading to boundary-layer-type equations which govern the flow; as such, there is no need to impose heuristic parallel-flow approximations. The resulting base flow is shown to be susceptible to significant, three-dimensional, transient (initially algebraic) growth in the streamwise direction, and, consequently, large amplifications to flow disturbances are possible (followed by ultimate decay far downstream). It is suggested that this initial amplification of disturbances is a possible and alternative mechanism for flow transition.

Three-dimensional flow over two spheres placed side by side

1993 ◽  
Vol 246 ◽  
pp. 465-488 ◽  
Author(s):  
Inchul Kim ◽  
Said Elghobashi ◽  
William A. Sirignano
Keyword(s):  
Reynolds Number ◽  
Vortical Structure ◽  
Three Dimensional ◽  
Numerical Data ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Confined Flow ◽  
Small Spacing

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.

scholarly journals Internal Passage Heat Transfer Prediction Using Multiblock Grids and a k-ω Turbulence Model

1996 ◽  
Author(s):  
David L. Rigby ◽  
A. A. Ameri ◽  
E. Steinthorsson
Keyword(s):  
Heat Transfer ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Three Dimensional Flow ◽  
Flow And Heat Transfer ◽  
Aspect Ratios ◽  
Single Block ◽  
Multiblock Grid ◽  
Good Agreement

Numerical simulations of the three-dimensional flow and heat transfer in a rectangular duct with a 180° bend were performed. Results are presented for Reynolds numbers of 17,000 and 37,000 and for aspect ratios of 0.5 and 1.0. A k-ω turbulence model with no reference to distance to a wall is used. Direct comparison between single block and multiblock grid calculations are made. Heat transfer and velocity distributions are compared to available literature with good agreement. The multi-block grid system is seen to produce more accurate results compared to a single-block grid with the same number of cells.

Quasi-periodic cylinder wakes and the Ginzburg–Landau model

1995 ◽  
Vol 291 ◽  
pp. 191-222 ◽  
Author(s):  
Pierre Albarède ◽  
Michel Provansal
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Model Parameters ◽  
Ginzburg Landau ◽  
Phase Measurements ◽  
Low Reynolds Numbers ◽  
Aspect Ratios ◽  
Second Mode ◽  
Time Periodic

The time-periodic phenomena occurring at low Reynolds numbers (Re [lsim ] 180) in the wake of a circular cylinder (finite-length section) are well modelled by a Ginzburg–Landau (GL) equation with zero boundary conditions (Albarède & Monkewitz 1992). According to the GL model, the wake is mainly governed by a rescaled length, based on the aspect ratio and the Reynolds number. However, the determination of coefficients is not complete: we correct a former evaluation of the nonlinear Landau coefficient, we show difficulties in obtaining a consistent set of coefficients for different Reynolds numbers or end configurations, and we propose the use of an ‘influential’ length. New two-point velocimetry results are presented: phase measurements show that a subtle property is shared by the three-dimensional wake and the GL model.Two time-quasi-periodic phenomena – the second mode observed for smaller aspect ratios, and the dislocated chevron observed for larger aspect ratios – are presented and precisely related to the GL model. Only the linear characteristics of the second mode are readily explained; its existence depends on the end conditions. Moreover, through a quasi-static variation of the length, the second mode evolves continuously to end cells (and vice versa). Observations of the dislocated chevron are recalled. A very similar instability is found on the chevron solution of the GL equation, when the model parameters (c1, c2) move towards the phase diffusion unstable region. The early stages of this instability are qualitatively similar to the observed patterns.

On the dynamics of three-dimensional slung prisms under very low and high turbulence flows

2017 ◽  
Vol 816 ◽  
pp. 468-480 ◽  
Author(s):  
Y. Jin ◽  
L. P. Chamorro
Keyword(s):  
Growth Rate ◽  
Vortex Shedding ◽  
Small Amplitude ◽  
Free Stream ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Free Stream Turbulence ◽  
Aspect Ratios ◽  
High Turbulence ◽  
Hotwire Anemometry

The distinctive pendulum-like oscillation and pitching patterns of cubic and rectangular slung prisms were inspected for two aspect ratios at various Reynolds numbers $Re$ under two free-stream turbulence levels. Systematic experiments were performed using high-resolution telemetry and hotwire anemometry to quantitatively characterize the dynamics of the prisms and the wake fluctuation. The results show that the dynamics of the prisms can be characterized by two distinctive regions depending on the prism shape. Specifically, in the case of cubic prisms the regions are defined by the growth rate of the pitching amplitude; whereas the dynamics of the rectangular prisms is more sensitive to the angle of attack. In particular, when the large side initially faces the flow, the regions are defined by the synchronization between the vortex shedding and pure oscillations under very low turbulence. When the smaller side initially faces the flow, the regions are defined by the equilibrium pitching position. Regardless of the geometry of the prism and flow condition the dominant oscillation frequency resulted as being close to the natural frequency of the small-amplitude pendulum-like oscillation.

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