# Pressure Losses and Flow Maldistribution in Ducts with Sharp Bends

TL;DR: In this paper, a large number of calculations of typical flow situations has been carried out in the present study to address such issues as the optimum location of guides vanes, the influence of an upstream bend on the loss coefficient and the scaling laws for proper extrapolation of laboratory results to industrial scale applications.

Abstract: Pipelines and ducting systems used in process industry applications are characterized by large sizes, sharp bends and successive bends connected by short straight sections. Systematic studies of such flow situations have not been reported in the literature and the design of such ducting systems is based on rules of thumb and scaled-model testing. Taking advantage of the potential size-insensitivity of CFD-based calculations, a large number of calculations of typical flow situations has been carried out in the present study to address such issues as the optimum location of guides vanes, the influence of an upstream bend on the loss coefficient and the scaling laws for proper extrapolation of laboratory results to industrial scale applications. It is shown that the ideal radial location of a vane for a square duct is given by (RiRo)0.5 and that the influence of an upstream bend on the loss coefficient is beneficial in most cases. Thus, the calculation of bend losses treating each bend as being isolated is likely to be conservative. The velocity profile is uniformly improved by the use of vanes. The loss coefficient is not very sensitive to the fluid scaling, but the effect of wall roughness has to be considered carefully in scaled-down conditions.

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TL;DR: In this article, a three-regime correlation is developed for the excess bend loss coefficient as a function of Reynolds number, aspect ratios, curvature ratios and spacer lengths between the channels.

Abstract: The pressure losses in the flow distributor plate of the fuel cell depend on the Reynolds number and geometric parameters of the small flow channels. Very little information has been published on the loss coefficients for laminar flow. This study reports a numerical simulation of laminar flow though single sharp and curved bends, 180° bends and serpentine channels of typical fuel cell configurations. The effect of the geometric parameters and Reynolds number on the flow pattern and the pressure loss characteristics is investigated. A three-regime correlation is developed for the excess bend loss coefficient as a function of Reynolds number, aspect ratios, curvature ratios and spacer lengths between the channels. These have been applied to calculate the pressure drop in typical proton-exchange membrane fuel cell configurations to bring out the interplay among the important geometric parameters.

147 citations

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TL;DR: In this article, the authors proposed a guide vane in dividing flow tees in a ventilation and air-conditioning duct to reduce the local resistance represented by the tees, and the results showed that the resistance reduction rate was 4.3% −263.8% under different flow ratios (5:1-1:3) and different aspect ratios (4:1−1:4) compared with that of a tee without the guide-vane.

Abstract: Because of the significant resistance effect and the energy consumption effect, increasing attention has been paid to the local resistance represented by tees in ventilation and air-conditioning duct systems in recent years. The resistance reduction method involving installation of a guide vane in dividing flow tees in a ventilation and air-conditioning duct is studied. A reasonable position for installing the guide vane is proposed. The form of the guide vane is optimized. The resistance characteristics of the tee are analyzed under different flow velocities and different aspect ratios of the duct. The implementation effect of optimizing a tee is verified through a full-scale experiment. The results show that the resistance reduction rate of the proposed guide vane is 4.3%–263.8% under different flow ratios (5:1–1:3) and different aspect ratios (4:1–1:4) compared with that of a tee without the guide vane. In some cases, the resistance reduction rate exceeds 100%; the mechanism responsible for this phenomenon is also analyzed. The tee with the proposed guide vane reduces deformation of the fluid, the mechanical energy converted to internal energy and turbulent energy dissipation. The study results are verified through a full-scale experiment; the experimental data are in good agreement with the simulated values and the results reported in previous studies.

41 citations

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TL;DR: In this paper, the structural vibration and fluid-borne noise induced by turbulent flow through a 90° piping elbow is studied and the effect of guide vanes in different positions installed at the elbow on the flowinduced vibration and flow-induced noise is investigated.

Abstract: The structural vibration and fluid-borne noise induced by turbulent flow through a 90° piping elbow is studied and the effect of guide vanes in different positions installed at the elbow on the flow-induced vibration and flow-induced noise is investigated. Large Eddy Simulation (LES) model is adopted to solve for time varying pressure and velocity fields. The structural vibration is investigated based on a fluid–structure interaction (FSI) code using harmonic response analysis. The computation of hydrodynamic noise is based on a hybrid LES/Lighthill's acoustic analogy method and sound sources are solved as volume sources in commercial software ACTRAN. The numerical results indicate that the guide vane at the right location is effective in reducing vibration and flow-induced noise in the 90° piping elbow with water. The ideal position of the guide vane is determined and some useful engineering conclusions are drawn.

36 citations

### Additional excerpts

...[5] conducted some experiments and CFD-based calculations to clarify the pressure losses in the elbow installed with the guide vane....

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TL;DR: In this article, the impact of geometrical characteristics of wind catchers on their flow features to enhance the effectiveness of cross-ventilation strategies of buildings is investigated, and the authors show that the use of straight and nozzle-shaped inlet extensions can significantly increase the airflow rate.

Abstract: This paper presents a detailed parametric analysis of the impact of geometrical characteristics of wind catchers on their flow features to enhance the effectiveness of cross-ventilation strategies of buildings. The following geometrical characteristics are evaluated in detail: (i) ceiling tilt angle, (ii) radius of the outer-corner bend, (iii) leeward-side tilt angle, (iv) straight inlet extension length, (v) nozzle-shaped inlet extension radius, and (vi) radius of the inner-corner bend. In addition, the impact of using guide vanes at the bend of wind catchers is systematically investigated. High-resolution coupled (outdoor wind flow and indoor airflow) 3D steady RANS CFD simulations are performed for 40 different wind catcher geometries. The CFD simulations are based on a grid-sensitivity analysis and are validated by comparing with two wind-tunnel measurements. The results show that the use of straight and nozzle-shaped inlet extensions can significantly increase the airflow rate. The maximum increase is about 23%, which is achieved for the straight inlet extension length S/D = 1 (D is wind-catcher depth). Guide vanes are also found to effectively improve the flow uniformity inside the wind catcher and significantly enhance the airflow rate. This enhancement can go up to 29% when guide vanes are implemented in combination with a straight inlet extension with S/D = 0.375. The results of the present study support the optimal aerodynamic design of wind catchers.

28 citations

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TL;DR: In this article, a thermal resistance network analytical model is proposed to investigate the thermal resistance and pressure drop in serpentine channel heat sinks with 180 deg bends, where the bend loss coefficient is obtained as a function of the Reynolds number, aspect ratios, widths of fins, and turn clearances.

Abstract: In this paper, a thermal resistance network analytical model is proposed to investigate the thermal resistance and pressure drop in serpentine channel heat sinks with 180 deg bends. The total thermal resistance is obtained using a thermal resistance network model based on the equivalent thermal circuit method. Pressure drop is derived considering straight channel and bend loss because the bends interrupt the hydrodynamic boundary periodically. Considering the effects of laminar flow development and redevelopment, the bend loss coefficient is obtained as a function of the Reynolds number, aspect ratios, widths of fins, and turn clearances, through a three-regime correlation. The model is then experimentally validated by measuring the temperature and pressure characteristics of heat sinks with different Reynolds numbers and different geometric parameters. Finally, the temperature-rise and pressure distribution of the thermal fluid with Reynolds numbers of 500, 1000, and 1500 are examined utilizing this model. [DOI: 10.1115/1.4027508]

26 citations

### Cites methods from "Pressure Losses and Flow Maldistrib..."

...CFD is proven to be an efficient method for calculating the pressure loss at the bends, being used, for instance, to compute the pressure drop between upstream and downstream bends [18], calculating the bend loss coefficient [19], and optimizing the surface of channel [20,21]....

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##### References

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01 Jan 1980

TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.

Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.

21,858 citations

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01 Jan 1955

TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.

Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

17,321 citations

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TL;DR: In this paper, the authors present a review of the applicability and applicability of numerical predictions of turbulent flow, and advocate that computational economy, range of applicability, and physical realism are best served by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour.

Abstract: The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.

11,866 citations

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01 Jan 1996

TL;DR: This text develops and applies the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice, including advanced techniques in computational fluid dynamics.

Abstract: Preface. Basic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.- Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flow.- Efficiency and Accuracy Improvement. Special Topics.- Appendeces.

7,066 citations

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01 Jan 2006

TL;DR: In this article, Navier and Stokes this article proposed a solution to the problem of finding a solution for the problem in a three-dimensional (3-dimensional) boundary layer.

Abstract: Important Nomenclature Kinematics of Fluid Motion Introduction to Continuum Motion Fluid Particles Inertial Coordinate Frames Motion of a Continuum The Time Derivatives Velocity and Acceleration Steady and Nonsteady Flow Trajectories of Fluid Particles and Streamlines Material Volume and Surface Relation between Elemental Volumes Kinematic Formulas of Euler and Reynolds Control Volume and Surface Kinematics of Deformation Kinematics of Vorticity and Circulation References Problems The Conservation Laws and the Kinetics of Flow Fluid Density and the Conservation of Mass Principle of Mass Conservation Mass Conservation Using a Control Volume Kinetics of Fluid Flow Conservation of Linear and Angular Momentum Equations of Linear and Angular Momentum Momentum Conservation Using a Control Volume Conservation of Energy Energy Conservation Using a Control Volume General Conservation Principle The Closure Problem Stokes' Law of Friction Interpretation of Pressure The Dissipation Function Constitutive Equation for Non-Newtonian Fluids Thermodynamic Aspects of Pressure and Viscosity Equations of Motion in Lagrangian Coordinates References Problems The Navier--Stokes Equations Formulation of the Problem Viscous Compressible Flow Equations Viscous Incompressible Flow Equations Equations of Inviscid Flow (Euler's Equations) Initial and Boundary Conditions Mathematical Nature of the Equations Vorticity and Circulation Some Results Based on the Equations of Motion Nondimensional Parameters in Fluid Motion Coordinate Transformation Streamlines and Stream Surfaces Navier--Stokes Equations in Stream Function Form References Problems Flow of Inviscid Fluids Introduction Part I: Inviscid Incompressible Flow The Bernoulli Constant Method of Conformal Mapping in Inviscid Flows Sources, Sinks, and Doublets in Three Dimensions Part II: Inviscid Compressible Flow Basic Thermodynamics Subsonic and Supersonic Flow Critical and Stagnation Quantities Isentropic Ideal Gas Relations Unsteady Inviscid Compressible Flow in One-dimension Steady Plane Flow of Inviscid Gases Theory of Shock Waves References Problems Laminar Viscous Flow Part I: Exact Solutions Introduction Exact Solutions Exact Solutions for Slow Motion Part II: Boundary Layers Introduction Formulation of the Boundary Layer Problem Boundary Layer on 2-D Curved Surfaces Separation of the 2-D Steady Boundary Layers Transformed Boundary Layer Equations Momentum Integral Equation Free Boundary Layers Numerical Solution of the Boundary Layer Equation Three-Dimensional Boundary Layers Momentum Integral Equations in Three Dimensions Separation and Attachment in Three Dimensions Boundary Layers on Bodies of Revolution and Yawed Cylinders Three-Dimensional Stagnation Point Flow Boundary Layer On Rotating Blades Numerical Solution of 3-D Boundary Layer Equations Unsteady Boundary Layers Second-Order Boundary Layer Theory Inverse Problems in Boundary Layers Formulation of the Compressible Boundary Layer Problem Part III: Navier--Stokes Formulation Incompressible Flow Compressible Flow Hyperbolic Equations and Conservation Laws Numerical Transformation and Grid Generation Numerical Algorithms for Viscous Compressible Flows Thin-Layer Navier--Stokes Equations (TLNS) References Problems Turbulent Flow Part I: Stability Theory and the Statistical Description of Turbulence Introduction Stability of Laminar Flows Formulation for Plane-Parallel Laminar Flows Temporal Stability at In nite Reynolds Number Numerical Algorithm for the Orr--Sommerfeld Equation Transition to Turbulence Statistical Methods in Turbulent Continuum Mechanics Statistical Concepts Internal Structure in Physical Space Internal Structure in the Wave-Number Space Theory of Universal Equilibrium Part II: Development of Averaged Equations Introduction Averaged Equations for Incompressible Flow Averaged Equations for Compressible Flow Turbulent Boundary Layer Equations Part III: Basic Empirical and Boundary Layer Results in Turbulence The Closure Problem Prandtl's Mixing-Length Hypothesis Wall-Bound Turbulent Flows Analysis of Turbulent Boundary Layer Velocity Pro les Momentum Integral Methods in Boundary Layers Differential Equation Methods in 2-D Boundary Layers Part IV: Turbulence Modeling Generalization of Boussinesq's Hypothesis Zero-Equation Modeling in Shear Layers One-Equation Modeling Two-Equation (K-Ae) Modeling Reynolds' Stress Equation Modeling Application to 2-D Thin Shear Layers Algebraic Reynolds' Stress Closure Development of A Nonlinear Constitutive Equation Current Approaches to Nonlinear Modeling Heuristic Modeling Modeling for Compressible Flow Three-Dimensional Boundary Layers Illustrative Analysis of Instability Basic Formulation of Large Eddy Simulation References Problems Mathematical Exposition 1: Base Vectors and Various Representations Introduction Representations in Rectangular Cartesian Systems Scalars, Vectors, and Tensors Differential Operations On Tensors Multiplication of A Tensor and A Vector Scalar Multiplication of Two Tensors A Collection of Usable Formulas Taylor Expansion in Vector Form Principal Axes of a Tensor Transformation of T to the Principal Axes Quadratic Form and the Eigenvalue Problem Representation in Curvilinear Coordinates Christoffel Symbols in Three Dimensions Some Derivative Relations Scalar and Double Dot Products of Two Tensors Mathematical Exposition 2: Theorems of Gauss, Green, and Stokes Gauss' Theorem Green's Theorem Stokes' Theorem Mathematical Exposition 3: Geometry of Space and Plane Curves Basic Theory of Curves Mathematical Exposition 4: Formulas for Coordinate Transformation Introduction Transformation Law for Scalars Transformation Laws for Vectors Transformation Laws for Tensors Transformation Laws for the Christoffel Symbols Some Formulas in Cartesian and Curvilinear Coordinates Mathematical Exposition 5: Potential Theory Introduction Formulas of Green Potential Theory General Representation of a Vector An Application of Green's First Formula Mathematical Exposition 6: Singularities of the First-Order ODEs Introduction Singularities and Their Classi cation Mathematical Exposition 7: Geometry of Surfaces Basic De nitions Formulas of Gauss Formulas of Weingarten Equations of Gauss Normal and Geodesic Curvatures Grid Generation in Surfaces Mathematical Exposition 8: Finite Difference Approximation Applied to PDEs Introduction Calculus of Finite Differences Iterative Root Finding Numerical Integration Finite Difference Approximations of Partial Derivatives Finite Difference Approximation of Parabolic PDEs Finite Difference Approximation of Elliptic Equations Mathematical Exposition 9: Frame Invariancy Introduction Orthogonal Tensor Arbitrary Rectangular Frames of Reference Check for Frame Invariancy Use of Q References for the Mathematical Expositions Index

283 citations