The accuracy and parametric sensitivity of algebraic models for turbulent flow and convection

Abstract Predictions of turbulent flow and convection in round tubes, channels and concentric circular annuli based on a correlating equation for the fraction of the shear stress due to turbulence have previously been shown to be within the scatter of the best experimental data. However, the sufficiency of this agreement has been questioned because of the scatter and limitations in scope of that data. As a supplementary test, the sensitivity of the predictions to each of the numerical empiricisms and arbitrary functions of the model has been investigated. On the whole, the uncertainties in these values and functions are not found to influence the predictions significantly.

[1]  Stuart W. Churchill,et al.  Theoretically Based Correlating Equations for the Local Characteristics of Fully Turbulent Flow in Round Tubes and between Parallel Plates , 1995 .

[2]  Michael Jischa,et al.  About the prediction of turbulent prandtl and schmidt numbers from modeled transport equations , 1979 .

[3]  E. V. Murphree.  Relation between Heat Transfer and Fluid Friction , 1932 .

[4]  Stuart W. Churchill,et al.  A general expression for the correlation of rates of transfer and other phenomena , 1972 .

[5]  Walter Tollmien,et al.  Über ein neues Formelsystem für die ausgebildete Turbulenz , 1961 .

[6]  R. G. Deissler,et al.  Analytical and experimental investigation of adiabatic turbulent flow in smooth tubes , 1950 .

[7]  Bo Yu,et al.  The computed characteristics of turbulent flow and convection in concentric circular annuli. Part III. Alternative thermal boundary conditions , 2005 .

[8]  W. Willmarth,et al.  Reynolds-number effects on the structure of a turbulent channel flow , 1989, Journal of Fluid Mechanics.

[9]  Alexander Smits,et al.  Further observations on the mean velocity distribution in fully developed pipe flow , 2004, Journal of Fluid Mechanics.

[10]  Bo Yu,et al.  The characteristics of fully developed turbulent convection in a round tube , 2001 .

[11]  S. Churchill.  A Reinterpretation of the Turbulent Prandtl Number , 2002 .

[12]  Brian Launder,et al.  A Reynolds stress model of turbulence and its application to thin shear flows , 1972, Journal of Fluid Mechanics.

[13]  A. Smits,et al.  Mean-flow scaling of turbulent pipe flow , 1998, Journal of Fluid Mechanics.

[14]  W. Kays,et al.  Turbulent Prandtl number : where are we ? , 1994 .

[15]  M. V. Zagarola,et al.  Friction factors for smooth pipe flow , 2004, Journal of Fluid Mechanics.

[16]  Prediction of fully developed turbulent convection with minimal explicit empiricism , 2002 .

[17]  A. Kolmogorov,et al.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[18]  T. Elperin,et al.  Isotropic and anisotropic spectra of passive scalar fluctuations in turbulent fluid flow. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  S. Churchill.  New simplified models and formulations for turbulent flow and convection , 1997 .

[20]  S. Pai.  On turbulent flow in circular pipe , 1953 .

[21]  W. Tollmien,et al.  Bericht über Untersuchungen zur ausgebildeten Turbulenz , 1961 .

[22]  J. Kampé De Fériet.  SUR L'ÉCOULEMENT D'UN FLUIDE VISQUEUX INCOMPRESSIBLE ENTRE DEUX PLAQUES PARALLÈLES INDÉFINIES , 1948 .

[23]  L. Prandtl.  7. Bericht über Untersuchungen zur ausgebildeten Turbulenz , 1925 .

[24]  K. Rehme.  Turbulent flow in smooth concentric annuli with small radius ratios , 1974, Journal of Fluid Mechanics.

[25]  W. Kays,et al.  Heat transfer in annular passages—hydrodynamically developed turbulent flow with arbitrarily prescribed heat flux , 1963 .

[26]  N. Arai,et al.  Exact formulations and nearly exact numerical solutions for convection in turbulent flow between parallel plates , 2000 .

[27]  E. R. V. Driest.  On Turbulent Flow Near a Wall , 1956 .

[28]  Charles A. Sleicher,et al.  Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls , 1993 .

[29]  C. Sleicher,et al.  A solution to the turbulent Graetz problem—III Fully developed and entry region heat transfer rates , 1972 .

[30]  G. Whan,et al.  Characteristics of transition flow between parallel plates , 1959 .

[31]  B. Launder,et al.  Mathematical Models of turbulence , 1972 .

[32]  Steven A. Orszag,et al.  Heat transfer in turbulent fluids—I. Pipe flow , 1987 .

[33]  G. I. Barenblatt,et al.  Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data , 1993, Journal of Fluid Mechanics.

[34]  G. Batchelor,et al.  The theory of homogeneous turbulence , 1954 .

[35]  Bo Yu,et al.  The computed characteristics of turbulent flow and convection in concentric circular annuli. Part II. Uniform heating on the inner surface , 2005 .

[36]  Bo Yu,et al.  The computed characteristics of turbulent flow and convection in concentric circular annuli. Part IV: Generalizations , 2005 .

[37]  Bo Yu,et al.  The characteristics of turbulent flow and convection in concentric circular annuli. Part I: flow , 2003 .