Analytic Prediction of the Friction Factor for Turbulent Flow in Internally Finned Channels

1981 ◽  
Vol 103 (3) ◽  
pp. 423-428 ◽  
Author(s):  
M. J. Scott ◽  
R. L. Webb
Keyword(s):  
Turbulent Flow ◽  
Friction Factor ◽  
Analytical Model ◽  
Analytical Models ◽  
Turbulent Friction ◽  
Law Of The Wall ◽  
Finned Tubes ◽  
Rectangular Channels ◽  
Factor Data ◽  
Analytic Prediction

This work develops an analytical model for the friction factor with turbulent flow in internally finned channels. Such channels are an important class of enhanced heat transfer surfaces. Until this work, no analytical models for the turbulent friction factor have been proposed. The present model assumes the validity of the Law of the Wall and applies the logarithmic velocity distribution to the interfin and core regions of the flow. Theoretically based friction factor equations are developed for internally finned circular tubes and rectangular channels. The model predicts Carnavos data for 21 internally finned tubes within ± 10 percent. Friction factor data were taken for five internally finned, rectangular channels. The analytical model predicts these data within ± 10 percent, except for the case of a very high fin.

Prediction of Turbulent Flow-Induced Noise in Aircraft Cabins

2010 ◽  
Author(s):  
Joana da Rocha ◽  
Afzal Suleman ◽  
Fernando Lau
Keyword(s):  
Turbulent Flow ◽  
Analytical Model ◽  
Sound Pressure ◽  
Real Life ◽  
Interior Noise ◽  
Analytical Models ◽  
Aircraft Cabins ◽  
Wide Range ◽  
Flow Induced Noise ◽  
Cabin Interior

Flow-induced noise in aircraft cabins can be predicted through analytical models or numerical methods. However, the analytical methods existent nowadays were obtained for simple structures and cabins, in which, usually, a single panel is excited by the turbulent flow, and coupled with an acoustic enclosure. This paper discusses the development of analytical models for the prediction of aircraft cabin noise induced by the external turbulent boundary layer (TBL). The coupled structural-acoustic analytical model is developed using the contribution of both structural and acoustic natural modes. While, in previous works, only the contribution of an individual panel to the cabin interior noise was considered, here, the simultaneous contribution of multiple flow-excited panels is also analyzed. The analytical models were developed for rectangular and cylindrical cabins. The mathematical models were successfully validated through the good agreement with several independent experimental studies. Analytical predictions are presented for the interior sound pressure level (SPL) at different locations inside the cabins. It is shown that identical panels located at different positions have dissimilar contributions to the cabin interior noise, showing that the position of the vibrating panel is an important variable for the accurate prediction of cabin interior noise. Additionally, the results show that the number of vibrating panels significantly affects the interior noise levels. It is shown that the average SPL, over the cabin volume, increases with the number of vibrating panels. The space-averaged SPL is usually accepted to provide the necessary information for the noise prediction. However, in some real life applications, the local sound pressure may be desirable. To overcome this point, the model is also able to predict local SPL values, at specific locations in the cabin, which are also affected by number of vibrating panels, and often differ from the average SPL values. The developed analytical model can be used to study a wide range of different systems involving a cabin coupled with vibrating panels, excited by the TBL. The properties of the external flow, acoustic cabin, and panels, as well as the number of vibrating panels, can be easily changed to represent different systems. These abilities of the model make it a solid basis for future investigations involving the implementation of noise reduction techniques and multidisciplinary design optimization analyzes.

Turbulent Friction Factor for a Rod Bundle in Consideration of a Subchannel Geometry

2002 ◽  
Author(s):  
Joo Hwan Park ◽  
Chang Joon Jeong ◽  
Myung Seung Yang ◽  
Dong Suk Oh
Keyword(s):  
Friction Factor ◽  
Measurement Data ◽  
Experimental Results ◽  
Flow Area ◽  
Theoretical Derivation ◽  
Turbulent Friction ◽  
Law Of The Wall ◽  
Rod Bundle ◽  
Two Parameters ◽  
Geometry Parameter

A generalized turbulent friction factor for a rod bundle was developed based on “Law of the Wall” for a tube. It was included two parameters which are one parameter of hydraulic diameter and flow area of a subchannel and rod bundle and another parameter (called geometry parameter hereinafter) of subchannel configuration and pitch-to-diameter ratio (P/D) for a single subchannel. The turbulent geometry parameter for a single subchannel has been used as a constant on the previous works but it was found to be dependent on subchannel shapes and P/D from the present work. Hence, it was modeled as a function of the subchannel shapes and P/D from 1.0 to 1.5. The turbulent geometry parameters for single subchannels were validated by the theoretical derivation of a triangular and square subchannel. Those are compared and agreed well with the previous measurement data for 4 kinds of subchannel types such as a triangular, a square, a wall and a corner subchannel. The present model of turbulent friction factor for a rod bundle included the turbulent geometry parameter has been compared with the various experimental results for circular tubes and hexagonal tubes with various rod numbers. The predicted turbulent friction factors for those rod bundles were agreed excellently with experimental results.

Analytic Prediction of the Friction and Heat Transfer for Turbulent Flow in Axial Internal Fin Tubes

1993 ◽  
Vol 115 (3) ◽  
pp. 553-559 ◽  
Author(s):  
Nae-Hyun Kim ◽  
R. L. Webb
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Analytic Model ◽  
Algebraic Form ◽  
Law Of The Wall ◽  
Finned Tubes ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Transfer Equations ◽  
Fin Tubes

An analytic model is developed to predict the friction factors and Nusselt numbers for turbulent flow in axial internal fin tubes. The present model uses the Law of the Wall and applies the logarithmic universal velocity and temperature profile to the interfin and core regions of the flow. The fin shape is assumed trapezoidal, and the fin parameters such as fin height, fin root thickness and fin tip thickness are determined from the tube dimensional data. Theoretically based friction and heat transfer equations are developed for internally finned tubes in an algebraic form. The analytic model predicts Carnavos friction data for 11 axial internal fin tubes within ± 10 percent, and heat transfer data of air, water, and water-glycol within ± 15 percent when proper velocity and temperature profiles are used.

An Experimental Study of Taylor Vortices and Turbulence in Flow Between Eccentric Rotating Cylinders

1968 ◽  
Vol 90 (1) ◽  
pp. 285-296 ◽  
Author(s):  
J. H. Vohr
Keyword(s):  
Experimental Study ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Experimental Work ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Rotating Cylinders ◽  
Taylor Vortices ◽  
Torque Measurements ◽  
Factor Data

The critical speeds for onset of Taylor vortices inflow between eccentric rotating cylinders are determined by means of torque measurements for various eccentricity ratios and clearance ratios of the cylinders. Results are compared with the theoretical and experimental work of other investigators. Visual studies are made of the flow in both the Taylor vortex and turbulent flow regimes. Friction factor data are obtained for Reynolds numbers up to 40,000.

scholarly journals Friction Factor Estimation for Turbulent Flows in Corrugated Pipes with Rough Walls

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Maxim Pisarenco ◽  
Bas van der Linden ◽  
Arris Tijsseling ◽  
Emmanuel Ory ◽  
Jacques Dam
Keyword(s):  
Boundary Condition ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Flow Behavior ◽  
Turbulence Models ◽  
Computational Grids ◽  
Law Of The Wall ◽  
Fully Developed Turbulent Flow ◽  
The Right

The motivation of the investigation is the critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models (k−ϵ and k−ω) are used in the computations. First, the fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions, and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, the turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: The friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric, which is wrapped around the spiral.

Analytical Prediction of Turbulent Friction Factor in Circular Pipe Under Supercritical Conditions

2012 ◽  
Author(s):  
Jinguang Zang ◽  
Xiao Yan ◽  
Shanfang Huang ◽  
Zejun Xiao ◽  
Yanping Huang
Keyword(s):  
Friction Factor ◽  
Viscous Sublayer ◽  
Circular Pipe ◽  
Main Role ◽  
Analytical Prediction ◽  
Flow Area ◽  
Algebraic Form ◽  
Supercritical Conditions ◽  
Turbulent Friction ◽  
Law Of The Wall

An analytical method was proposed for the prediction of the turbulent friction factor in a circular pipe under supercritical conditions. The friction factor equation was based on the new wall function by Van Direst transformation which is widely used in compressed flow. The law of the wall of two layers was used and integrated over the entire flow area to obtain the algebraic form of the turbulent friction factor. The new turbulent friction formula was first adjusted to Colebrook equation in isothermal flow at supercritical pressures. And then it was validated in heated supercritical flow by several existing correlations. Similar trends were found between them, which confirms the physical validity of the new frictional formula. The theoretical analysis also shows that the friction factor due to the variation of fluid property at supercritical pressures is mainly caused by the density and viscosity variation. In viscous sublayer, both the viscosity play the main role, while in turbulent sublayer, only the density do.

scholarly journals Friction Factor Estimation for Turbulent Flows in Corrugated Pipes With Rough Walls

2009 ◽  
Author(s):  
Maxim Pisarenco ◽  
Bas van der Linden ◽  
Arris Tijsseling ◽  
Emmanuel Ory ◽  
Jacques Dam
Keyword(s):  
Boundary Condition ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Flow Behavior ◽  
Turbulence Models ◽  
Computational Grids ◽  
Law Of The Wall ◽  
Fully Developed Turbulent Flow ◽  
The Right

The motivation of the investigation is critical pressure loss in cryogenic flexible hoses used for LNG transport in offshore installations. Our main goal is to estimate the friction factor for the turbulent flow in this type of pipes. For this purpose, two-equation turbulence models (k–ε and k–ω) are used in the computations. First, fully developed turbulent flow in a conventional pipe is considered. Simulations are performed to validate the chosen models, boundary conditions and computational grids. Then a new boundary condition is implemented based on the “combined” law of the wall. It enables us to model the effects of roughness (and maintain the right flow behavior for moderate Reynolds numbers). The implemented boundary condition is validated by comparison with experimental data. Next, turbulent flow in periodically corrugated (flexible) pipes is considered. New flow phenomena (such as flow separation) caused by the corrugation are pointed out and the essence of periodically fully developed flow is explained. The friction factor for different values of relative roughness of the fabric is estimated by performing a set of simulations. Finally, the main conclusion is presented: the friction factor in a flexible corrugated pipe is mostly determined by the shape and size of the steel spiral, and not by the type of the fabric which is wrapped around the spiral.

An Improvement in the Calculation of Turbulent Friction in Rectangular Ducts

1976 ◽  
Vol 98 (2) ◽  
pp. 173-180 ◽  
Author(s):  
O. C. Jones
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Circular Tube ◽  
Hydraulic Diameter ◽  
Published Data ◽  
Turbulent Friction ◽  
Frictional Pressure Drop ◽  
Aspect Ratios

Frictional pressure drop in rectangular ducts is examined. Using correspondence between theory and experiment in laminar flow as a means for acceptance of published data, turbulent flow data for smooth rectangular ducts were compared with smooth circular tube data. Data for ducts having aspect ratios between unity and 39:1 were obtained in the literature and, in conjunction with new experimental data, were examined for deviations from the smooth circular tube line (smooth Moody). It was found that at constant Reynolds number based on hydraulic diameter the friction factor increases monotonically with increasing aspect ratio. It was thus concluded that the hydraulic diameter is not the proper length dimension to use in the Reynolds number to insure similarity between the circular and rectangular ducts. Instead, it was determined that if a modified Reynolds number Re* was obtained so that geometric similarity was provided in laminar flow by the relation f = 64/Re* for all geometries, that this Reynolds number also provided good similarity in fully developed turbulent flow within a ∼ 5 percent scatter band about the smooth tube line. By using this “laminar equivalent” Reynolds number, Re*, it is demonstrated that circular tube methods may be readily applied to rectangular ducts eliminating large errors in estimation of friction factor.

scholarly journals Novel Structure and Thermal Design and Analysis for CubeSats in Formation Flying

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 150
Author(s):  
Yeon-Kyu Park ◽  
Geuk-Nam Kim ◽  
Sang-Young Park
Keyword(s):  
Analytical Model ◽  
Formation Flying ◽  
Thermal Environment ◽  
Thermal Analyses ◽  
Thermal Design ◽  
Analytical Models ◽  
Test Results ◽  
Solar Panels ◽  
Novel Structure ◽  
Micro Propulsion

The CANYVAL-C (CubeSat Astronomy by NASA and Yonsei using a virtual telescope alignment for coronagraph) is a space science demonstration mission that involves taking several images of the solar corona with two CubeSats—1U CubeSat (Timon) and 2U CubeSat (Pumbaa)—in formation flying. In this study, we developed and evaluated structural and thermal designs of the CubeSats Timon and Pumbaa through finite element analyses, considering the nonlinearity effects of the nylon wire of the deployable solar panels installed in Pumbaa. On-orbit thermal analyses were performed with an accurate analytical model for a visible camera on Timon and a micro propulsion system on Pumbaa, which has a narrow operating temperature range. Finally, the analytical models were correlated for enhancing the reliability of the numerical analysis. The test results indicated that the CubeSats are structurally safe with respect to the launch environment and can activate each component under the space thermal environment. The natural frequency of the nylon wire for the deployable solar panels was found to increase significantly as the wire was tightened strongly. The conditions of the thermal vacuum and cycling testing were implemented in the thermal analytical model, which reduced the differences between the analysis and testing.

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