The ultimate state of turbulent permeable-channel flow

Direct numerical simulations have been performed for heat and momentum transfer in internally heated turbulent shear flow with constant bulk mean velocity and temperature, $u_{b}$ and $\theta _{b}$ , between parallel, isothermal, no-slip and permeable walls. The wall-normal transpiration velocity on the walls $y=\pm h$ is assumed to be proportional to the local pressure fluctuations, i.e. $v=\pm \beta p/\rho$ (Jiménez et al., J. Fluid Mech., vol. 442, 2001, pp. 89–117). The temperature is supposed to be a passive scalar, and the Prandtl number is set to unity. Turbulent heat and momentum transfer in permeable-channel flow for the dimensionless permeability parameter $\beta u_b=0.5$ has been found to exhibit distinct states depending on the Reynolds number $Re_b=2h u_b/\nu$ . At $Re_{b}\lesssim 10^4$ , the classical Blasius law of the friction coefficient and its similarity to the Stanton number, $St\approx c_{f}\sim Re_{b}^{-1/4}$ , are observed, whereas at $Re_{b}\gtrsim 10^4$ , the so-called ultimate scaling, $St\sim Re_b^0$ and $c_{f}\sim Re_b^0$ , is found. The ultimate state is attributed to the appearance of large-scale intense spanwise rolls with the length scale of $O(h)$ arising from the Kelvin–Helmholtz type of shear-layer instability over the permeable walls. The large-scale rolls can induce large-amplitude velocity fluctuations of $O(u_b)$ as in free shear layers, so that the Taylor dissipation law $\epsilon \sim u_{b}^{3}/h$ (or equivalently $c_{f}\sim Re_b^0$ ) holds. In spite of strong turbulence promotion there is no flow separation, and thus large-amplitude temperature fluctuations of $O(\theta _b)$ can also be induced similarly. As a consequence, the ultimate heat transfer is achieved, i.e. a wall heat flux scales with $u_{b}\theta _{b}$ (or equivalently $St\sim Re_b^0$ ) independent of thermal diffusivity, although the heat transfer on the walls is dominated by thermal conduction.

Forced Turbulent Convection Along Heated and Cooled Walls with Variable Fluid Properties

The effect of temperature depending material properties on heat and momentum transfer along heated/cooled walls in turbulent pipe flow was investigated using direct numerical simulations (DNS). For the considered thermal wall conditions, always associated with a molecular Prandtl number well over unity Prw = 10, the significantly dampened/enhanced turbulent motion caused by the increase/decrease of the viscosity with distance to the heated/cooled wall, turned out to clearly dominate over the opposite trend of the enthalpy fluctuations. The Nusselt number and, quantitatively less pronounced, the wall friction coefficient are accordingly decreased/increased for the heated/cooled case. A comparison against a well established Nu-correlation unveils the limits of the generally applied approach, which is essentially based on uniform bulk flow conditions and subsequently modified accounting for material property variation, when applied to heated and cooled conditions. An enhanced disparity of the turbulent normal stresses is observed inside the inertial subrange for the heated case, indicating a stronger deviation from isotropic turbulence, which possibly challenges mostly isotropic standard turbulence models.

Internal Diameter Coating by Warm Spraying of Fine WC-12Co Powders (− 10 + 2 µm) with Very Short Spray Distances up to 10 mm

The internal diameter (ID) coating by means of thermal spraying is currently experiencing growing interest in science and industry. In contrast to the well-established plasma- and arc-based spray techniques, there is a lack of knowledge concerning kinetic processes such as HVOF, HVAF and warm spray (WS). A major challenge represents the necessity of short spray distances and the compact design of novel ID spray guns with reduced combustion power. Conventional WC-Co powders (− 45 + 15 µm) are not able to achieve a sufficient heat and momentum transfer. The use of fine powders < 15 µm offers an approach to overcome this drawback as they feature a larger surface-to-volume ratio and a lower mass. However, the processing of fine powders requires suitable spray equipment and a sensitive parameter adjustment. In this study, warm spraying of fine WC-12Co powders (− 10 + 2 µm) with a novel ID spray gun (HVOF + N2) “ID RED” (Thermico Engineering GmbH, Germany) was investigated. First, the flame profile as well as the in-flight behavior of the particles along the spray jet (spray distances SD = 10-80 mm) was analyzed at different nitrogen flows NF = 15-115 L/min to find suitable spray parameter intervals. Subsequently, planar steel samples were coated with SD = 10-50 mm and constant NF = 90 L/min. Analyses regarding the microstructure, the mechanical properties and the phase evolution of the coatings were performed. The aim was to study spraying with the novel ID gun and to scrutinize shortest feasible spray distances. Finally, steel tubes (internal diameter of 81.6 mm and a wall thickness of 10.0 mm) were coated with SD = 20 mm and NF = 90 L/min to investigate in how far the results can be transferred to ID parts. Correlations between the particle behavior, the microstructure and the coating properties were made.

Modeling of chemical and technological processes

In an accessible form, the textbook presents the theoretical foundations of physical and mathematical modeling; considers the modeling of mass, heat and momentum transfer processes, the relationship and analogy between them; studies the theory of similarity, its application in modeling, models of the structure of flows in apparatuses. Experimental-statistical and experimental-analytical modeling methods are also described, which include "black box" methods, planning passive, active full and fractional factor experiments, and adjusting models based on the results of the experiment. At the same time, modeling of chemical reactors, methods of optimization of chemical-technological processes, their selection, comparison and application examples are considered. Examples of modeling and optimization of processes in chemical, petrochemical and biotechnology on a computer in Excel and MathCAD environments are given. The appendices provide the basics of working in the MathCAD environment and elements of matrix algebra. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for bachelors who are trained for the chemical, petrochemical, food, textile and light industries. It can be useful for specialists and undergraduates, as well as for scientists, engineers and postgraduates dealing with the problem under consideration.

Laminar Convection in Circular Tubes With Developing Flow

The combined entry problem for the simultaneous development of heat and momentum transfer in a circular tube has been resolved over an extended range of inverse Graetz number ZH≥10−6 and for a wide range of Prandtl numbers 0.1≤Pr≤500. For the historical range of ZH≥5×10−4 and 0.7≤Pr≤50, earlier studies are within 5% of the current benchmark calculations, but for the new extended range of conditions, the best authoritative sources were in error by as much as 33%. Four new correlations are proposed for the local and average Nusselt numbers, and for the constant temperature and constant heat flux wall condition, which are accurate to 2.2% for all values of inverse Graetz number and Pr≥0.5. In contrast, legacy correlations typically had a 10–20% error range when compared to the results of this work, with many exhibiting larger errors and only few achieving errors as low as 5–10%.