Christian Helcig

The Effect of the Incidence Angle on the Flow Over a Rotating Disk Subjected to Forced Air Streams

The flow over a stationary and a rotating disk subjected to an outer forced air stream was investigated particular with a look to the effect of incidence angle β. The experiments were carried out with an electrically heated disk placed in a wind tunnel. The measurement of the mean and the local convective heat transfer coefficient enabled a clear study of the flow behavior. The incidence angle β was scanned with high resolution over the entire range, and a large number of crossflow and rotational Reynolds numbers were covered. It was found that a well defined transition incidence angle β existed leading to a symmetry breaking of the flow. The resulting mean heat transfer was in agreement with the phenomenological Landau-de Gennes model in case of small rotational Reynolds numbers. In case of large rotational effects, a different type of transition occurred. Based on the experimental and theoretical results, a discussion of the different phenomena due to the involved flow parameters is given in the paper.© 2013 ASME

Convective Heat Transfer From a Free Rotating Disk Subjected to a Forced Crossflow

The understanding of the heat transfer and flow field behavior of rotating systems is essential from a fundamental point of view and for turbo machinery design. The majority of the publications considers enclosed rotating disk systems and only little is known about the convective heat transfer of free rotating disk systems in a forced flow. In this paper, a free rotating disk system, with particular look on the angle of incidence was investigated. The convective heat transfer from a rotating disk depends at least on three characteristic variables, namely the crossflow, rotational Reynolds numbers and the angle of incidence which are determining the mean Nusselt number. A clear study of the symmetry behavior of the flow field was conducted based on the measurement of the convective heat transfer coefficients. The angle of incidence was scanned with high angular resolution over the entire range between the both extreme cases of a perpendicular disk and a disk in a parallel forced flow. A large number of crossflow and rotational Reynolds numbers were covered by the experiments, too. Based on the experimental and theoretical results, a discussion of the different phenomena and heat transfer regimes is given in this paper.Copyright

Rotating Disk in Air Stream

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.

Effect of Prandtl Number on the Heat Transfer From a Rotating Disk: An Experimental Study

Heat transfer coefficients were experimentally determined for a free rotating disk in still air and water. These were obtained with an electrically heated disk placed in a cylindrical pool. The accuracy of the employed experimental apparatus was assessed by heat transfer measurements in air. For this fluid, an excellent agreement with reliable literature data was found. Essentially new experimental data were obtained for water as fluid. Based upon the experimental data, the validity of theoretical correlations and the effect of the Prandtl number on the convective heat transfer from a rotating disk were discussed. It was found that in laminar water flow, the value of the correlation exponent for the Prandtl number is practically identical to 1/2 as theoretically predicted in 1948 by Dorfman. In turbulent flow, its value is better given by 1/3 as in case of the classical turbulent boundary layer theory.Copyright

Heat Transfer Correlations for Practical Applications

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.

Stationary Disk in Air Stream

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.

Wind Tunnel Experiments with Rotating Disks

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.

Large-Eddy-Simulation (LES) Analysis

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.