An introduction to heat transfer

The function of the engineering profession is to manipulate materials, energy, and information, thereby creating benefit for humankind. To do this successfully, engineers must have a knowledge of nature that goes beyond mere theory—knowledge that is traditionally gained in educational laboratories. Over the years, however, the nature of these laboratories has changed. This paper describes the history of some of these changes and explores in some depth a few of the major factors influencing laboratories today. In particular, the paper considers the lack of coherent learning objectives for laboratories and how this lack has limited the effectiveness of laboratories and hampered meaningful research in the area. A list of fundamental objectives is presented along with suggestions for possible future research.

http://web.stanford.edu/group/asee/wikiupload/6/69/Feisel_LabsInEngEd.pdf

The Role of the Laboratory in Undergraduate Engineering Education

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits dependence over a short range in wavenumber . Further, consistent with previous experimental observations, when these spectra are multiplied by (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the range.

Direct numerical simulation of turbulent channel flow up to

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Karman “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

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Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface. DOI: 10.1115/1.4001492

https://www.usna.edu/NAOE/_files/documents/Faculty/schultz/Flack,%20Schultz%20-%20Hydraulic%20Roughness%20Scales,%202010.pdf

Review of Hydraulic Roughness Scales in the Fully Rough Regime

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a three-dimensional rough surface geometrically similar to the honed pipe roughness used by Shockling, Allen & Smits (J. Fluid Mech. vol. 564, 2006, p. 267). The present work covers a wide Reynolds-number range (Re θ = 2180–27 100), spanning the hydraulically smooth to the fully rough flow regimes for a single surface, while maintaining a roughness height that is a small fraction of the boundary-layer thickness. In this investigation, the root-mean-square roughness height was at least three orders of magnitude smaller than the boundary-layer thickness, and the Karman number (δ+), typifying the ratio of the largest to the smallest turbulent scales in the flow, was as high as 10100. The mean velocity profiles for the rough and smooth walls show remarkable similarity in the outer layer using velocity-defect scaling. The Reynolds stresses and higher-order turbulence statistics also show excellent agreement in the outer layer. The results lend strong support to the concept of outer layer similarity for rough walls in which there is a large separation between the roughness length scale and the largest turbulence scales in the flow.

The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime

The Reynolds number similarity hypothesis of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness δ is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Reθ of ∼14000. The boundary layers on the rough walls were in the fully rough flow regime (ks+⩾100) with the ratio of the boundary layer thickness to the equivalent sand roughness height δ∕ks greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3ks. Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y<5ks. The present results provide support for Townsend’s Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where δ∕ks⩾40.

Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a threedimensional rough surface geometrically similar to the honed pipe roughness used by Shockling, Allen & Smits (J. Fluid Mech. vol. 564, 2006, p. 267). The present work covers a wide Reynolds-number range (Reθ =2180–27 100), spanning the hydraulically smooth to the fully rough flow regimes for a single surface, while maintaining a roughness height that is a small fraction of the boundary-layer thickness. In this investigation, the root-mean-square roughness height was at least three orders of magnitude smaller than the boundary-layer thickness, and the Karman number (δ), typifying the ratio of the largest to the smallest turbulent scales in the flow, was as high as 10 100. The mean velocity profiles for the rough and smooth walls show remarkable similarity in the outer layer using velocitydefect scaling. The Reynolds stresses and higher-order turbulence statistics also show excellent agreement in the outer layer. The results lend strong support to the concept of outer layer similarity for rough walls in which there is a large separation between the roughness length scale and the largest turbulence scales in the flow.

https://www.usna.edu/NAOE/_files/documents/Faculty/schultz/Schultz,%20Flack%20-%20Rough%20Wall%20Turbulent%20Boundary%20Layer,%202007.pdf

The existence of a critical roughness height for outer layer similarity between smooth and rough wall turbulent boundary layers is investigated. Results are presented for boundary layer measurements on flat plates covered with sandgrain and woven mesh with the ratio of the boundary layer thickness to roughness height (δ∕k) varying from 16 to 110 at Reθ=7.3×103–13×103. In all cases tested, the layer directly modified by the roughness (the roughness sublayer) is confined to a region <5k or <3ks from the wall (where ks is the equivalent sandgrain roughness height). In the larger roughness cases, this region of turbulence modification extends into the outer flow. However, beyond 5k or 3ks from the wall, similarity in the turbulence quantities is observed between the smooth and rough wall boundary layers. These results indicate that a critical roughness height, where the roughness begins to affect most or all of the boundary layer, does not exist. Instead, the outer flow is only gradually modified with increas...

https://www.usna.edu/NAOE/_files/documents/Faculty/schultz/Flack,%20Schultz,%20Connelly%20-%20Critical%20Roughness%20Height,%202007.pdf

Karen A. Flack

Papers

Review of Hydraulic Roughness Scales in the Fully Rough Regime

The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime

Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls

The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime

Examination of a critical roughness height for outer layer similarity