Drag Coefficient and Two-Phase Friction Multiplier on Tube Bundles Subjected to Two-Phase Cross-Flow

2010 ◽  
Author(s):  
W. G. Sim ◽  
W. Mureithi Njuki
Keyword(s):  
Drag Coefficient ◽  
Void Fraction ◽  
Euler Number ◽  
Tube Bundle ◽  
Cross Flow ◽  
Water Mixture ◽  
Two Phase ◽  
Mass Fluxes ◽  
Wide Range ◽  
Tube Bundles

An approximate analytical model for upward two-phase cross-flow through horizontal bundles, to predict drag coefficient on a cylinder and two-phase Euler number, has been developed. To verify the model, two sets of experiments were performed for various pitch mass fluxes of air-water mixture with void fraction. The experiments were undertaken with rotated triangular array of cylinders. The pitch to diameter ratio is 1.5 and the cylinder diameter 38 mm. The void fraction model proposed by Feenstra et al. (2000) is utilized to estimate the void fraction for the cross-flow in the tube bundle. An important variable on the drag coefficient is the two-phase friction multiplier. An empirical formulation of non dimensional pressure drop (Euler number) for single phase flow in tube bundles was proposed by Zukauskas et al. (1988) and two-phase friction multiplier in duct flow was formulated by various researchers. Considering the formulations, the present model was developed. It is found that Marchaterre’s model (1961) for two-phase friction multiplier is applicable to air-water mixtures. The analytical results agree well with experimental drag coefficients and Euler numbers in air-water mixtures for a sufficiently wide range of pitch mass fluxes and qualities. This model will allow researcher to provide analytical estimates of the drag coefficient, which is related to two-phase damping.

Drag Coefficient and Two-Phase Friction Multiplier on Tube Bundles Subjected to Two-Phase Cross-Flow

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
W. G. Sim ◽  
Njuki W. Mureithi
Keyword(s):  
Drag Coefficient ◽  
Void Fraction ◽  
Euler Number ◽  
Tube Bundle ◽  
Cross Flow ◽  
Water Mixture ◽  
Duct Flow ◽  
Two Phase ◽  
Mass Fluxes ◽  
Wide Range

An approximate analytical model, to predict the drag coefficient on a cylinder and the two-phase Euler number for upward two-phase cross-flow through horizontal bundles, has been developed. To verify the model, two sets of experiments were performed with an air–water mixture for a range of pitch mass fluxes and void fractions. The experiments were undertaken using a rotated triangular (RT) array of cylinders having a pitch-to-diameter ratio of 1.5 and cylinder diameter 38 mm. The void fraction model proposed by Feenstra et al. was used to estimate the void fraction of the flow within the tube bundle. An important variable for drag coefficient estimation is the two-phase friction multiplier. A new drag coefficient model has been developed, based on the single-phase flow Euler number formulation proposed by Zukauskas et al. and the two-phase friction multiplier in duct flow formulated by various researchers. The present model is developed considering the Euler number formulation by Zukauskas et al. as well as existing two-phase friction multiplier models. It is found that Marchaterre's model for two-phase friction multiplier is applicable to air–water mixtures. The analytical results agree reasonably well with experimental drag coefficients and Euler numbers in air–water mixtures for a sufficiently wide range of pitch mass fluxes and qualities. This model will allow researchers to provide analytical estimates of the drag coefficient, which is related to two-phase damping.

Vibration of Tube Bundles in Two-Phase Cross-Flow: Part 3—Turbulence-Induced Excitation

1989 ◽  
Vol 111 (4) ◽  
pp. 488-500 ◽  
Author(s):  
C. E. Taylor ◽  
I. G. Currie ◽  
M. J. Pettigrew ◽  
B. S. Kim
Keyword(s):  
Void Fraction ◽  
Tube Bundle ◽  
Cross Flow ◽  
Vibration Response ◽  
Experimental Program ◽  
Two Phase ◽  
Design Guideline ◽  
Tube Bundles ◽  
Vibration Responses ◽  
Flow Part

An extensive experimental program was carried out to study the vibration behavior of tube bundles subjected to two-phase cross-flow. Turbulence-induced excitation is discussed in Part 3 of this series of three papers. Random vibration response to turbulence-induced excitation is a significant vibration mechanism in heat exchanger tube bundles subjected to two-phase cross-flow. The vibration responses of centrally located tubes in four tube bundle configurations subjected to air-water cross-flow was measured. The results are presented in the form of a normalized forced-excitation spectrum which can be used as a design guideline over a void fraction range from 25 percent to 99 percent and over a practical range of flow rates. The data are further analyzed to determine the dependence of the vibration response on Reynolds number, void fraction and frequency. Measurements taken on a single tube, a row of tubes and on tubes having varying end conditions were used to assist in interpreting the bundle data.

scholarly journals Numerical Prediction of Two-Phase Flow through a Tube Bundle Based on Reduced-Order Model and a Void Fraction Correlation

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1355
Author(s):  
Claire Dubot ◽  
Cyrille Allery ◽  
Vincent Melot ◽  
Claudine Béghein ◽  
Mourad Oulghelou ◽  
...  
Keyword(s):  
Void Fraction ◽  
Grassmann Manifold ◽  
Tube Bundle ◽  
Cross Flow ◽  
Horizontal Tube ◽  
Phase Flow ◽  
Two Phase ◽  
Tube Bundles ◽  
Flow Through ◽  
Phase Mixture

Predicting the void fraction of a two-phase flow outside of tubes is essential to evaluate the thermohydraulic behaviour in steam generators. Indeed, it determines two-phase mixture properties and affects two-phase mixture velocity, which enable evaluating the pressure drop of the system. The two-fluid model for the numerical simulation of two-phase flows requires interaction laws between phases which are not known and/or reliable for a flow within a tube bundle. Therefore, the mixture model, for which it is easier to implement suitable correlations for tube bundles, is used. Indeed, by expressing the relative velocity as a function of slip, the void fraction model of Feenstra et al.and Hibiki et al. developed for upward cross-flow through horizontal tube bundles is introduced and compared. With the method suggested in this paper, the physical phenomena that occur in tube bundles are taken into consideration. Moreover, the tube bundle is modelled using a porous media approach where the Darcy–Forchheimer term is usually defined by correlations found in the literature. However, for some tube bundle geometries, these correlations are not available. The second goal of the paper is to quickly compute, in quasi-real-time, this term by a non-intrusive parametric reduced model based on Proper Orthogonal Decomposition. This method, named Bi-CITSGM (Bi-Calibrated Interpolation on the Tangent Subspace of the Grassmann Manifold), consists in interpolating the spatial and temporal bases by ITSGM (Interpolation on the Tangent Subspace of the Grassmann Manifold) in order to define the solution for a new parameter. The two developed methods are validated based on the experimental results obtained by Dowlati et al. for a two-phase cross-flow through a horizontal tube bundle.

Random Excitation Forces in Tube Bundles Subjected to Two-Phase Cross-Flow

1996 ◽  
Vol 118 (3) ◽  
pp. 265-277 ◽  
Author(s):  
C. E. Taylor ◽  
M. J. Pettigrew ◽  
I. G. Currie
Keyword(s):  
Flow Regime ◽  
Void Fraction ◽  
Flow Rate ◽  
Large Scale ◽  
Power Spectra ◽  
Cross Flow ◽  
Random Excitation ◽  
Two Phase ◽  
Wide Range ◽  
Tube Bundles

Data from two experimental programs have been analyzed to determine the characteristics of the random excitation forces associated with two-phase cross-flow in tube bundles. Large-scale air-water flow loops in France and Canada were used to generate the data. Tests were carried out on cantilevered, clamped-pinned, and clamped-clamped tubes in normal-square, parallel-triangular, and normal-triangular configurations. Either strain gages or force transducers were used to measure the vibration response of a centrally located tube as the tube array was subjected to a wide range of void fractions and flow rates. Power spectra were analyzed to determine the effect of parameters such as tube diameter, frequency, flow rate, void fraction, and flow regime on the random excitation forces. Normalized expressions for the excitation force power spectra were found to be flow-regime dependent. In the churn flow regime, flow rate and void fraction had very little effect on the magnitude of the excitation forces. In the bubble-plug flow regime, the excitation forces increased rapidly with flow rate and void fraction.

Vibration of Tube Bundles in Two-Phase Cross-Flow: Part 1—Hydrodynamic Mass and Damping

1989 ◽  
Vol 111 (4) ◽  
pp. 466-477 ◽  
Author(s):  
M. J. Pettigrew ◽  
C. E. Taylor ◽  
B. S. Kim
Keyword(s):  
Tube Bundle ◽  
Damping Ratio ◽  
Cross Flow ◽  
Design Guidelines ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Mixture Density ◽  
Void Fractions ◽  
Mass Fluxes ◽  
Tube Bundles

Two-phase cross-flow exists in many shell-and-tube heat exchangers, such as condensers, reboilers and nuclear steam generators. An understanding of damping and of flow-induced vibration excitation mechanisms is necessary to avoid problems due to excessive tube vibration. Accordingly, we have undertaken an extensive program to study the vibration behavior of tube bundles subjected to two-phase cross-flow. In this paper we present the results of experiments on four tube bundle configurations; namely, normal triangular of pitch over diameter ratio, p/d, of 1.32 and 1.47, and parallel triangular and normal square of p/d of 1.47. The bundles were subjected to air-water mixtures to simulate realistic mass fluxes and vapor qualities corresponding to void fractions from 5 to 99 percent. Hydrodynamic mass and damping are discussed in Part 1 of this series of three papers. We found that hydrodynamic mass is roughly related to the homogeneous mixture density. The damping characteristics of all tube bundles are generally similar. Damping is maximum between 40 and 80 percent void fraction where the damping ratio reaches about 4 percent. The effect of mass flux is generally weak. Design guidelines are proposed for hydrodynamic mass and for damping.

scholarly journals On Damping and Fluidelastic Instability in a Tube Bundle Subjected to Two-Phase Cross-Flow

2007 ◽  
Author(s):  
Joaquin E. Moran ◽  
David S. Weaver
Keyword(s):  
Flow Regime ◽  
Void Fraction ◽  
Tube Bundle ◽  
Damping Ratio ◽  
Pressure Fluctuations ◽  
Cross Flow ◽  
Phase Changes ◽  
Working Fluid ◽  
Two Phase ◽  
Fluidelastic Instability

An experimental study was conducted to investigate damping and fluidelastic instability in tube arrays subjected to two-phase cross-flow. The purpose of this research was to improve our understanding of these phenomena and how they are affected by void fraction and flow regime. The working fluid used was Freon 11, which better models steam-water than air-water mixtures in terms of vapour-liquid mass ratio as well as permitting phase changes due to pressure fluctuations. The damping measurements were obtained by “plucking” the monitored tube from outside the test section using electromagnets. An exponential function was fitted to the tube decay trace, producing consistent damping measurements and minimizing the effect of frequency shifting due to fluid added mass fluctuations. The void fraction was measured using a gamma densitometer, introducing an improvement over the Homogeneous Equilibrium Model (HEM) in terms of density and velocity predictions. It was found that the Capillary number, when combined with the two-phase damping ratio (interfacial damping), shows a well defined behaviour depending on the flow regime. This observation can be used to develop a better methodology to normalize damping results. The fluidelastic results agree with previously presented data when analyzed using the HEM and the half-power bandwidth method. The interfacial velocity is suggested for fluidelastic studies due to its capability for collapsing the fluidelastic data. The interfacial damping was introduced as a tool to include the effects of flow regime into the stability maps.

Vibration Excitation Forces in a Normal Triangular Tube Bundle Subjected to Two-Phase Cross Flow

2011 ◽  
Author(s):  
E. S. Perrot ◽  
N. W. Mureithi ◽  
M. J. Pettigrew ◽  
G. Ricciardi
Keyword(s):  
Tube Bundle ◽  
Cross Flow ◽  
Random Excitation ◽  
Two Phase ◽  
Constant Frequency ◽  
Fluid Forces ◽  
Drag Forces ◽  
Wide Range ◽  
Drag And Lift ◽  
Lift And Drag

This paper presents test results of vibration forces in a normal triangular tube bundle subjected to air-water cross-flow. The dynamic lift and drag forces were measured with strain gage instrumented cylinders. The array has a pitch-to-diameter ratio of 1.5, and the tube diameter is 38 mm. A wide range of void fraction and fluid velocities were tested. The experiments revealed significant forces in both the drag and lift directions. Constant frequency and quasi-periodic fluid forces were found in addition to random excitation. These forces were analyzed and characterized to understand their origins. The forces were found to be dependent on the position of the cylinder within the bundle. The results are compared with those obtained with flexible cylinders in the same tube bundle and to those for a rotated triangular tube bundle. These comparisons reveal the influence of quasi-periodic forces on tube motions.

Development of a Numerical Model for Quasi-Periodic Forces of Two-Phase Cross Flow in Tube Bundles

2014 ◽  
Author(s):  
Sarra Zoghlami ◽  
Cédric Béguin ◽  
Stéphane Étienne
Keyword(s):  
Numerical Model ◽  
Tube Bundle ◽  
Cross Flow ◽  
Deep Understanding ◽  
Added Mass ◽  
Dispersed Phase ◽  
Two Phase ◽  
Induced Drag ◽  
Tube Bundles ◽  
Lagrange Approach

To reduce the damage caused by induced vibrations due to two-phase cross flow on tube bundles in heat exchangers, a deep understanding of the different sources of this phenomenon is required. For this purpose, a numerical model was previously developed to simulate the quasi periodic forces on the tube bundle due to two-phase cross flow. An Euler-Lagrange approach is adopted to describe the flow. The Euler approach describes the continuous phase (liquid) using potential flow. The dispersed phase is assumed to have no interaction on liquid flow. Based on visual observation, static vortices behind the tube are introduced. The Lagrange approach describes the dispersed phase (gas). The model allows bubbles to split up or to coalesce. The forces taken into account acting on the bubbles are the buoyancy, the drag and induced drag, the added mass and induced added mass and impact force (bubble-bubble and bubble-tube). Forces taken into account acting on the tubes are impact forces and induced drag and added mass forces. This model allows us to obtain quasi periodic force on tube induced by two-phase cross flow of relative good magnitude and frequency contains. The model still needs improvement to bring us closer to experimental data of force, for example by introducing a dependency between the void ratio and the intensity of the vortex and by taking into account the bubbles deformation.

Effect of Void Fraction on Vibrational Behavior of Tubes in Tube Bundle Under Two-Phase Cross Flow

1997 ◽  
Vol 119 (3) ◽  
pp. 457-463 ◽  
Author(s):  
H. Y. Lian ◽  
G. Noghrehkar ◽  
A. M. C. Chan ◽  
M. Kawaji
Keyword(s):  
Void Fraction ◽  
Two Phase Flow ◽  
Tube Bundle ◽  
Dynamic Pressure ◽  
Damping Ratio ◽  
Cross Flow ◽  
Vibration Measurement ◽  
Phase Flow ◽  
Two Phase ◽  
Vibrational Behavior

The effects of local two-phase flow parameters on the vibrational behavior of tubes have been studied in an in-line 5 × 20 tube bundle subjected to air-water cross-flow. One of the tubes was flexibly mounted and instrumented for vibration measurement and the others were rigid. Parameters obtained include local void fraction fluctuations, RMS amplitude of void fraction fluctuations, void fraction distributions across the tube bundle, flow regimes based on probability density function of void fraction signals, damping ratio, and tube vibration response as a function of mass flux, void fraction and dynamic pressure. Damping and tube vibration amplitude in two-phase flow have been found to be closely related to the RMS amplitudes of the local void fraction fluctuations and dynamic pressure fluctuations, respectively.

Numerical Investigation of Air/Water and Hydrogen/Diesel Flow Across Tube Bundles With Baffles

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Diego N. Venturi ◽  
Waldir P. Martignoni ◽  
Dirceu Noriler ◽  
Henry F. Meier
Keyword(s):  
Void Fraction ◽  
Volume Fraction ◽  
Tube Bundle ◽  
Superficial Velocity ◽  
Intermittent Flow ◽  
Two Phase ◽  
Operational Conditions ◽  
Horizontal Flows ◽  
Tube Bundles ◽  
Experimental Approaches

Two-phase flows across tube bundles are very commonly found in industrial heat exchange equipment such as shell and tube heat exchangers. However, recent studies published in the literature are generally performed on devices where the flow crosses the tube bundle in only a vertical or horizontal direction, lacking geometrical fidelity with industrial models, and the majority of them use air and water as the working fluids. Also, currently, experimental approaches and simulations are based on very simplified models. This paper reports the simulation of a laboratory full-scale tube bundle with a combination of vertical and horizontal flows and with two different baffle configurations. Also, it presents a similarity analysis to evaluate the influence of changing the fluids to hydrogen and diesel in the operational conditions of the hydrotreating. The volume of fluid (VOF) approach is used as the interface phenomena are very important. The air/water simulations show good agreement with classical correlations and are able to show the stratified behavior of the flow in the horizontal regions and the intermittent flow in the vertical regions. Also, the two baffle configurations are compared in terms of volume fraction and streamlines. When dealing with hydrogen/diesel flow using correlations and maps made for air/water, superficial velocity is recommended as similarity variable when a better prediction of the pressure drop is needed, and the modified superficial velocity is recommended for prediction of the volume-average void fraction and the outlet superficial void fraction.

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