Aroon K. Viswanathan

Investigation of Detached Eddy Simulations in Capturing the Effects of Coriolis Forces and Centrifugal Buoyancy in Ribbed Ducts

The predictive capability of Detached Eddy Simulations (DES) is investigated in stationary as well as rotating ribbed ducts with relevance to the internal cooling of turbine blades. A number of calculations are presented at Re =20,000 and rotation numbers ranging from 0.18 to 0.67 with buoyancy parameters up to 0.29 in a ribbed duct with ribs normal to the main flow direction. The results show that DES by admitting a LES solution in critical regions transcends some of the limitations of the base RANS model on which it is based. This feature of DES is exemplified by its sensitivity to turbulence driven secondary flows at the rib side-wall junction, to the effect of Coriolis forces, and centrifugal buoyancy effects. It is shown that DES responds consistently to these non-canonical effects when RANS and URANS with the same model cannot, at a cost which is about a tenth of that of LES for the geometry and Reynolds number considered in this study.

A Comparative Study of DES and URANS for Flow Prediction in a Two-Pass Internal Cooling Duct

The capabilities of the detached eddy simulation (DES) and the unsteady Reynolds averaged Navier-Stokes (URANS) versions of the 1988 k-ω model in predicting the turbulent flow field in a two-pass internal cooling duct with normal ribs is presented. The flow is dominated by the separation and reattachment of shear layers; unsteady vorticity induced secondary flows and strong streamline curvature. The techniques are evaluated in predicting the developing flow at the entrance to the duct and downstream of the 180 deg bend, fully developed regime in the first pass, and in the 180 deg bend. Results of mean flow quantities, secondary flows, and the average friction factor are compared to experiments and large-eddy simulations (LES)

Capturing Effects of Rotation in Sudden Expansion Channels Using Detached Eddy Simulation

T HE effects of system rotation are of interest in flows in hydro/ turbo machinery especially in the design of centrifugal compressor impellers and runner blades. When the direction of rotation is in tandem with the fluid rotation vector, that is, the vorticity, the flow is stabilized, whereas the flow is destabilized if the directions are opposing. As with boundary layers, shear layers are also stabilized or destabilized by rotation. Rotation (or streamline curvature) generates extra strain rates that significantly affect turbulent stress production. Bradshaw [1] formulated an analogy between meteorological parameters and parameters describing rotation about the axis normal to the plane of rotation. He defined an effective Richardson number (Ri) for flows undergoing rotation that is used to define amodifiedmixing length [l l0 1 Ri ].Most of the later studies also propose a similar definition, where the effects of rotation are modeled by formulating corrections using a rotation Richardson number. Nilsen and Andersson [2] used an algebraic second moment closure model to predict the rotational effects on backward facing step flows. It was observed that rotation induced variation in the mean flow pattern was a result of significant changes in turbulent fluctuations in the free shear layer. However quantitative predictions of the reattachment length showed only partial agreement with the experimental data (Rothe and Johnston [3]). A similar study was carried out on rotating flows using a v–f model by Iaccarino et al. [4]. Both the original and a modified version of the model were used to predict the reattachment length downstream of a backward facing step. The modified model predicted the reattachment length better than the originalmodel. However itwas observed that the predictions of the modified model, like the algebraic second moment (ASM) model of Nilsen and Andersson [2] showed only partial agreement with the experiments. Therefore in spite of the continual development of Reynolds-averagedNavier–Stokes (RANS)models, predicting the effects of rotation in turbulent flows is a major challenge. The eddies formed in themassively separated regions downstream of the step are geometry specific. The “detached” eddies are not as universal as the eddies in typical thin shear layers where RANS models are calibrated. This is the reasonwhyRANSmodels are often observed to fail in flows undergoing massive separation. Large eddy simulation (LES) resolves the large energy carrying eddies while modeling the smaller isotropic eddies using a subgrid scale stress model. LES is a viable and a reliable method for simulating flows undergoing massive separation. However the near-wall resolution necessary for LESmakes it prohibitively expensive at high Reynolds numbers. A solution to the computational challenges associated with the reliable prediction ofmassively separated turbulent flows is detached eddy simulations (DES). DES sensitizes a RANS model to grid length scales, thereby allowing it to function as a subgrid scalemodel in critical regions of interest. This allows the natural instabilities of the flow in this region to develop, the energy cascade to grow, and improves the quality of the solution in this region. Though DES was initially proposed for the Spalart–Allmaras model, it can be easily extended to other models (Strelets [5]), by appropriately defining a turbulent length scale. The credibility of the approach has been validated by numerous applications in the literature for external and internal flows. The objective of the current study is to investigate the capabilities of DES in capturing the effects of rotation induced Coriolis forces on turbulent separation and reattachment in a backward facing step geometry. To evaluate the accuracy of the scheme in predicting the effects, the reattachment lengths predicted by DES are compared with experimental measurements by Rothe and Johnston [1] and also compared with other RANS models from the literature.

Large Eddy Simulation in a Duct With Rounded Skewed Ribs

Results from Large Eddy Simulation (LES) of fully developed flow in a ribbed duct are presented with rib pitch-to-height ratio (P/e) is 10 and a rib height to hydraulic diameter ratio (e/Dh ) is 0.1. Computations are carried out on a square duct with 45° ribs on the top and bottom walls arranged in a staggered fashion. The ribs have a rounded cross-section and are skewed at 45° to the main flow. The Reynolds number based on bulk velocity is 25,000. Mean flow and turbulent quantities, together with heat transfer and friction augmentation results are presented for a stationary case. The flow is characterized by a helical vortex behind each rib and a complementary cross-sectional secondary flow, both of which result from the angle of the rib with respect to the mean flow and result in a spanwise variation of the heat transfer. The mean flow, the turbulent quantities and the heat transfer in the duct show similar trends as in the duct with square cross-section ribs. However the results show that there is lesser friction in the ducts with rounded ribs. The overall heat transfer on the ribbed wall was augmented by 2.85 times that of a smooth duct, at the cost of friction which increases by a factor of 10. The computed values compare well with the experimental values.© 2005 ASME

Detached Eddy Simulation of Flow and Heat Transfer in a Stationary Internal Cooling Duct With Skewed Ribs

Numerical predictions of a hydrodynamic and thermally developed turbulent flow for a unit period of a stationary duct using Detached Eddy Simulation (DES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) are presented. The domain under consideration is a square duct with 45° ribs on the top and bottom walls arranged in a staggered fashion. Computations are carried out for a bulk Re of 47,000. The rib height to channel hydraulic diameter (e/Dh ) is 0.1 and the rib pitch to rib height (P/e) is 10. DES is applied on two grids 80 × 80 × 80 and 128 × 80 × 80 and the initial results are compared with the experimental results and LES computations. Based on this the 128 × 80 × 80 grid is chosen for the comprehensive study. DES and URANS computations are carried out on the grid. The rib geometry introduces a strong secondary flow along the rib. The presence of the secondary flow introduces a spanwise variation in the heat transfer. DES predicts flow features and heat transfer distribution which is consistent with the experimental observations and LES computations. The average friction and the augmentation ratios predicted by DES also concur with the earlier observations.Copyright

Detached Eddy Simulation of Turbulent Flow and Heat Transfer in a Ribbed Duct

Numerical predictions of a hydrodynamic and thermally developed turbulent flow are presented for a stationary duct with square ribs aligned normal to the main flow direction. The rib height to channel hydraulic diameter (e/Dh ) is 0.1, the rib pitch to rib height (P/e) is 10 and the calculations have been carried out for a bulk Reynolds number of 20,000. Detached Eddy Simulation (DES) has been used to compute the flowfield and the heat transfer. DES calculations are carried out on a 963 grid, a 643 grid and a 483 grid to study the effect of grid resolution. Based on the agreement with earlier LES computations and experimental data the 643 grid is observed to be suitable for the DES computation. DES and RANS calculations carried out on the 643 grid are compared to LES calculations on 963 /1283 grids and experimental measurements. The flow and heat transfer characteristics for the DES cases compare well with the LES results and the experiments. The average friction and the augmentation ratios are consistent with experimental results, predicting values within 15% of the measured quantities, at a cost lower than the LES calculations. RANS fails to capture some key features of the flow.Copyright

Large Eddy Simulation of Fully Developed Flow and Heat Transfer in a Rotating Duct With 45° Ribs

This paper concerns itself with investigating the effect of rotation on flow and heat transfer in a 45° ribbed square duct. Large-Eddy Simulations (LES) are used to investigate why rotation does not have any effect on heat transfer augmentation unlike 90 degree ribs, in which considerable changes are observed in augmentation at the trailing and leading walls of the duct. It is found that unlike 90 degree ribbed ducts, in which the heat transfer augmentation is strongly dependent on streamwise momentum, spanwise momentum dominates heat transfer in skewed ribs. Since Coriolis forces under orthogonal rotation about the z-axis do not directly contribute to spanwise momentum, they do not have as much of an effect on heat transfer at the ribbed walls at the trailing and leading sides. However, because of the augmentation of turbulence at the trailing side, the vortices which are produced in the separated shear layer of the rib and which move from the inside to the outside of the duct, break down and diffuse before they can impinge on the outer wall. Turbulence attenuation at the leading wall has the opposite effect which allows the vortices to maintain their coherence and impinge on the outer wall. This effect taken together with the streamwise flow being pushed to the leading side, produces an extended region of high heat transfer at the outer wall near the leading side. This is countered by lower heat transfer at the trailing side of the outer wall. Hence, although local variations are present due to rotation, the overall augmentation remains the same.Copyright

Large Eddy Simulation of Flow and Heat Transfer in an Internal Cooling Duct With High Blockage Ratio 45° Staggered Ribs

Numerical predictions of a hydrodynamic and thermally developed turbulent flow are presented for a unit period of a stationary duct with square ribs aligned at 45° to the main flow direction. The rib height to channel hydraulic diameter (e/Dh ) is 0.375 and the rib pitch to rib height (P/e) is 10. The domain under consideration is a rectangular passage of aspect ratio 1:2.5 with 45° ribs on the top and bottom walls arranged in a staggered fashion. The computations are carried out for a bulk Re of 27,000. The rib geometry introduces a strong secondary flow along the rib. A large helical vortex develops behind the rib which breaks down before it reaches the outer wall. This results in higher heat transfer at the inner wall as compared to the outer wall, which is in contrast to the trend observed in a square channel with low blockage ribs. In a square duct with low blockage ribs the secondary flow has two counter-rotating cells which do not change direction through the channel. However in this case only one rotating cell is observed in this case, which changes direction as it passes over successive ribs. The average friction and the heat transfer augmentation ratios are consistent with the experimental results [1], predicting values within 15% of the measured quantities.© 2005 ASME

A Comparative Study of DES and URANS in a Two-Pass Internal Cooling Duct With Normal Ribs

The capabilities of the Detached Eddy Simulation (DES) and the Unsteady Reynolds Averaged Navier-Stokes (URANS) versions of the 1988 κ-ω model in predicting the turbulent flow field and the heat transfer in a two-pass internal cooling duct with normal ribs is presented. The flow is dominated by the separation and reattachment of shear layers; unsteady vorticity induced secondary flows and strong streamline curvature. The techniques are evaluated in predicting the developing flow at the entrance to the duct and downstream of the 180° bend, fully-developed regime in the first pass, and in the 180° bend. Results of mean flow quantities, secondary flows, friction and heat transfer are compared to experiments and Large-Eddy Simulations (LES). DES predicts a slower flow development than LES, while URANS predicts it much earlier than LES computations and experiments. However it is observed that as fully developed conditions are established, the capability of the base model in predicting the flow and heat transfer is enhanced by switching to the DES formulation. DES accurately predicts the flow and heat transfer both in the fully-developed region as well as the 180° bend of the duct. URANS fails to predict the secondary flows in the fully-developed region of the duct and is clearly inferior to DES in the 180° bend.Copyright