Convective Heat Transfer From Rotating Disks Subjected To Streams Of Air

Configurations based on rotating disks are widely used in engineering applications, and convective heat transfer from a rotating disk has been studied extensively in the scientific literature for several decades. In addition to a large number of technical papers, several monographs [1–4] about this topic are also available. Today, research dedicated to flow and heat transfer phenomena in rotating disk systems is still being performed, as demonstrated by the increasing number of corresponding scientific and technical conference contributions and research articles.

This chapter briefly reviews some basic principles that are useful when studying flow and heat transfer in rotating disk systems. Further details about these principles can be found in the literature, and it is therefore not necessary to present all of their implications here. The flow over an inclined disk with finite thickness is in general three-dimensional and characterized by flow separation. The transitions between different flow and heat transfer regimes can be described in terms of the critical point theory proposed for the first time in the early 1950s. This approach has been developed further over the last decades, and its connections to bifurcation theory became apparent. Its great potential for analyzing rotating disk systems has been recently realized, and its basic principles are given here.

Investigating convective heat transfer from a rotating disk subjected to streams of air requires placing a heated disk apparatus in the test section of a wind tunnel. This approach was employed for the first time by Dennis et al. [1] in 1970. Although this general experimental approach is fairly straightforward, the performance of accurate measurements is not free of challenges or technical issues. In this section, the approach and procedure are briefly presented and illustrated by examples obtained by the authors and co-workers. Special attention is also given to the importance of the inflow turbulence level because several flow transition and bifurcation phenomena can only be investigated in wind tunnel streams with very low inflow turbulence at the test section.

For axisymmetric configurations of rotating disk systems, fluid flow and heat transfer can be analyzed using powerful mathematical methods such as the self-similar solutions. These solutions cover the free rotating disk without any additional forced flow and the rotating disk placed perpendicular to a uniform stream. They represent important limit cases for the more general configuration of an inclined rotating disk, and since there are a lot of reliable data for these cases, they are useful for validating experimental or numerical methods. However, sometimes the analytical treatment is only valid under certain conditions that might not be fulfilled in practical applications, for example, in the case of a stagnation flow onto an orthogonal disk. A closed self-similar solution is only known for an infinite disk, and its application to finite disks in uniform streams still has to be confirmed.

No general solution for the three-dimensional flow field is known for an inclined disk with finite radius R subjected to streams of air. In their pioneering papers on parallel rotating disks subjected to air streams, Dennis et al. [1] and Booth and de Vere [2] recognized how important the effect of flow separation at the rim of the blunt disk is for flow and heat transfer behavior. In general, the angle of attack (i.e., the inclination) of the disk β represents a third major parameter in addition to rotational and translational Reynolds numbers Re _ω and Re _u . Furthermore, the disk thickness ratio d/R is also relevant for the occurrence of flow separation and reattachment of a turbulent boundary. It is therefore useful to organize the following discussion into two separate chapters: a discussion of the phenomena involved in a stationary disk (Chap. 5) followed by an extension to rotating disks (Chap. 6) based on the results for stationary disks.

The flow and heat transfer behavior for a stationary disk subjected to a uniform stream of air was discussed in Chap. 5. The various phenomena could be explained on the basis of a critical point and bifurcation theory and fundamental boundary layer considerations because mainly the translational Reynolds number Re _u and the incidence β govern the flow field. The extension to a rotating disk requires substantial efforts because a third major parameter, the rotational Reynolds number Re _ω , is now involved. Correspondingly, the flow behavior becomes much more complicated in comparison to the stationary disk. However, to a large extent it is possible to systematically discuss the new phenomena within the framework given by the limited case of a stationary disk. The rotational effects are then considered as perturbations. This approach is chosen in the present chapter as a start into the complex field of the flow over an inclined rotating disk.

Computational Fluid Dynamics, usually abbreviated as CFD, has become a “third” approach in addition to the classic analytical treatment and the experimental investigation of flow and heat transfer phenomena. CFD is a branch of fluid mechanics that uses numerical methods and mathematical algorithms to solve and analyze problems that involve flow phenomena. This approach is especially attractive since powerful computers for performing the calculations are now widely available. However, the direct numerical simulation (DNS) of turbulent flows resolving the entire range of turbulent length scales at high Reynolds numbers is still not feasible, and appropriate simulation strategies for such flows are still required.

The previous chapters clearly demonstrated that, in the case of rotating disks subjected to forced streams, complex flow and convective heat transfer phenomena exist. It is possible to a large extent to formulate separately adequate heat transfer correlations for the different flow and heat transfer regimes, but these correlations are limited to the considered phenomena. For instance, in the case of a stationary disk, the mean convective heat transfer can well be described by a phenomenological Landau-de Gennes model (see Chap. 5), but the presence of rotation might introduce completely new phenomena, as discussed in Chap. 6. With a look to engineering applications, it is desirable to obtain suitable heat transfer correlations that are accurate enough for practical purposes but still easy to handle for a wide class of users. This chapter discusses issues connected to that purpose.