Publisher Summary Heating or cooling of large surface area products is often carried out in devices consisting of arrays of round or slot nozzles, through which air impinges vertically upon the product surface. This chapter presents a comprehensive survey emphasizing the engineering applications and empirical equations, presented for the prediction of heat and mass transfer coefficients within a large and technologically important range of variables. The local variations of the transfer coefficients are based on the experimental data for single round nozzles (SRN), arrays of round nozzles (ARN), single slot nozzles (SSN), and arrays of slot nozzles (ASN). The variation of local transfer coefficients is graphically represented. It also explores how to apply these equations in heat exchanger and dryer design as well as in optimization. The flow field of impinging flow is diagrammatically represented. External variables influencing heat and mass transfer in impinging flow depends on mass flow rate, kind and state of the gas and on the shape, size, and position of the nozzles relative to each other and to the solid surface. The design of high-performance arrays of nozzles is also discussed.

Heat and Mass Transfer between Impinging Gas Jets and Solid Surfaces

Approximate layer-averaged equations describing the mechanics of turbid underflows are derived. Closure of the equations describing the balance of fluid mass, sediment mass, and mean flow momentum provides for the delineation of a three-equation model. A description of sediment exchange with the bed allows for the possibility of a self-accelerating turbidity current in which sediment entrainment from the bed is linked to flow velocity. A consideration of the balance of the mean energy of the turbulence yields a constraint on physically realistic solutions to the three-equation model. It is shown that the self-acceleration predicted by the three-equation model is so strong that the energy constraint fails to be satisfied. In particular, the turbulent energy consumed in entraining new bed sediment exceeds the supply of energy to the turbulence, so that the turbulence, and thus the turbidity current, must die. The problem is rectified by the formulation of a four-equation model, in which an explicit accounting is made of the mean energy of the turbulence. Sediment entrainment from the bed is linked to the level of turbulence in the four-equation model. Self-acceleration is again predicted, although it is somewhat subdued compared with that predicted by the three-equation model. The predictions of both models are summarized over a wide range of conditions.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086001404

Self-accelerating turbidity currents

The profile of the longshore current, as a function of distance from the swash line, is calculated by using the concept of radiation stress (introduced in an earlier paper) together with a horizontal eddy viscosity μe of the form μe = ρNx(gh)1/2, where ρ is the density, x is the distance offshore, g is gravity, h is the local mean depth, and N is a numerical constant. This assumption gives rise to a family of current profiles whose form depends only on the nondimensional parameter P = (Π/2)(sN/αC), where s denotes the bottom slope, α is a constant characteristic of breaking waves (α ≑ 0.41), and C is the drag coefficient on the bottom. The current profiles are of simple analytic form, having a maximum in the surf zone and tending to zero at the swash line. Comparison with the laboratory experiments of Galvin and Eagleson (1965) shows remarkably good agreement if the drag coefficient C is taken as 0.010. The theoretical profiles are insensitive to the exact value of P, but the experimental results suggest that P never exceeds a critical value of 2/5.

Longshore currents generated by obliquely incident sea waves: 2

The turbulent wall jet

The spatial distribution of the mean velocity in a two-dimensional turbulent wall jet was measured for a variety of nozzle Reynolds numbers. It was determined that the bulk of the flow is self-similar and it depends on the momentum flux at the nozzle and on the viscosity and density of the fluid. The width of the nozzle which was commonly used to reduce these data has no part in the similarity considerations as has already been suggested by Narasimha et al. (1973). This type of self-similarity can be easily applied to determine the skin friction, which can otherwise only be determined with considerable difficulty. It was also shown that the ‘law of the wall’ applies only to the viscous sublayer. The Reynolds stress in the inviscid, inner portion of the flow is not constant thus the assumption of a ‘constant stress layer’ is not applicable. The applicability and universality of the ‘outer scaling law’ (i.e. Coles’ law of the wake) has been verified throughout the inviscid inner portion of the wall jet. The logarithmic velocity distribution cannot be derived by making the usual assumptions based on the constancy of the Reynolds stresses or on the thinness of the logarithmic region relative to the thickness of the inner layer.

On the applicability of various scaling laws to the turbulent wall jet

With the aid of a hot-wire anemometer, the mean velocity distribution of the incompressible, turbulent, plane wall-jet has been examined in some detail. As previously reported, this fully developed boundary layer belongs to the class of self-preserving flows. Over the entire range of experimental conditions, a single velocity scale , the Boussinesq exchange coefficient e, and the shear stress at the wall have been evaluated. The Reynolds number based on the maximum velocity and the thickness of the boundary layer varied from 22,000 to 106,000.

W. P. Cosart

Papers

The two-dimensional turbulent wall-jet