Effect of Non-Axisymmetric Endwall Profiling on Heat Transfer and Film Cooling Effectiveness of a Transonic Rotor Blade

Effects of non-axisymmetric endwall profiling on total pressure loss, heat transfer, and film cooling effectiveness of a transonic rotor blade were numerically investigated. The numerical methods, including the turbulence model and grid sensitivity, were validated with the existing experimental data. To reduce the thermal load on endwall, non-axisymmetric endwall profiling near leading edge and at pressure-side corner area was performed with a range of contour amplitudes. Heat transfer and flow fields near the profiled endwalls were analyzed and also compared with the plain endwall configuration. On the profiled endwall, three kinds of cooling holes, i.e., cylindrical holes, rounded-rectangular holes, and elliptical holes, were arranged, and film cooling effect was investigated at three blowing ratios. Results indicate that, with endwall profiling, the area-averaged Stanton number on endwall is reduced by 7.71% and total pressure loss in cascade is reduced by 11.07%. Among three kinds of cooling holes, the arrangement of the elliptical hole performs the best film cooling effect on the profiled endwall. Compared with the plain endwall, non-axisymmetric endwall with elliptical cooling holes improves film cooling coverage by 10.87%, reduces the Stanton number by 8.88%, and increases the net heat flux reduction performance by 4% at M = 0.7.

Direct Numerical Simulation of Turbine Cascade Flow with Heat Transfer

Two- and three-dimensional direct numerical simulation (DNS) of turbine cascade flow at low Reynolds number with heat transfer are performed using high-order finite difference method. Two-dimensional laminar computation which is used to construct the initial flow of three-dimensional DNS fails to predict Stanton number on the second half of suction side where the flow is turbulent in experiment. In three-dimensional DNS, transition is triggered by periodic blow-and-suction disturbances. Numerical experiments show that phase randomness of the disturbance is not necessary to trigger the transition which can be induced by disturbances with fixed phases. In a range of time fundamental frequency of disturbance, when increasing the frequency, transition moves downstream. When time fundamental frequency is big enough, transition disappears. With fixed space phases, time phases and selected time fundamental frequency, time averaged pressure and Stanton number distributions of three-dimensional DNS coincide with the experimental datum. Averaged velocity and temperature, Root-Mean-squares (RMS) of velocity pulse，temperature pulse, Reynolds shear stress and heat flux are extracted from the DNS database. All statistics agree well with experimental and theoretical results which verify the accuracy of present database.

Effect of Non-Axisymmetric Endwall Profiling on Heat Transfer and Film Cooling Effectiveness of a Transonic Rotor Blade

Effects of non-axisymmetric endwall profiling on total pressure loss, heat transfer and film cooling effectiveness of a transonic rotor blade were numerically investigated. The numerical methods, including the turbulence model and grid sensitivity, were validated with the existing experimental data. To reduce thermal load on endwall, non-axisymmetric endwall profiling near leading edge and at pressure-side corner area were performed with a range of contour amplitudes. Heat transfer and flow fields near the profiled endwalls were analyzed and also compared to the plain endwall configuration. On the profiled endwall, three kinds of cooling-holes, i.e. cylindrical holes, rounded-rectangular holes and elliptical holes, were arranged, and film cooling effect was investigated at three blowing ratios. Results indicate that, with endwall profiling, the area-averaged Stanton number on endwall is reduced by 7.71% and total pressure loss in cascade is reduced by 11.07%. Among three kinds of cooling holes, arrangement of elliptical hole performs the best film cooling effect on profiled endwall. Compared with plain endwall, non-axisymmetric endwall with elliptical cooling holes improves film cooling coverage by 10.87%, reduces the Stanton number by 8.88% and increases the net heat flux reduction performance by 4% at M = 0.7.

Roughness effects in turbulent forced convection

We conducted direct numerical simulations of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal-span channel is used to circumvent the high cost of simulating high-Reynolds-number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, $k^{+}$, is increased, the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$, increases in the transitionally rough regime before tending towards the fully rough asymptote of $\unicode[STIX]{x1D705}_{m}^{-1}\log (k^{+})+C$, where $C$ is a constant that depends on the particular roughness geometry and $\unicode[STIX]{x1D705}_{m}\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $Re_{b}$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}^{+}$, appears to tend towards a constant value, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $Re_{b}$ in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat-transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness $k_{s}/k$ and the temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, $z_{0m}/z_{0h}$, being linearly proportional to the inner-normalised momentum roughness length, $z_{0m}^{+}$, where the constant of proportionality is related to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress are observed. Instantaneous visualisations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.

Effects of Flow Oscillations in the Mainstream on Film Cooling

The objective of this study is to investigate the effects of oscillations in the main flow and the coolant jets on film cooling at various frequencies (0 to 2144 Hz) at low and high average blowing ratios. Numerical simulations are performed using LES Smagorinsky–Lilly turbulence model for calculation of the adiabatic film cooling effectiveness and using the DES Realizable k-epsilon turbulence model for obtaining the Stanton number ratios (St/Sto). Additionally, multi-frequency inlet velocities are applied to the main and coolant flows to explore the effects of multi-frequency unsteady flows and the results are compared to those at single frequencies. The results show that at a low average blowing ratio (M = 0.5) if the oscillation frequency is increased from 0 to 180 Hz, the effectiveness decreases and the Stanton number ratio increases. However, when the frequency goes from 180 to 268 Hz, the effectiveness sharply increases and the Stanton number ratio increases slightly. If the frequency changes from 268 to 1072 Hz, the film cooling effectiveness decreases and the Stanton number ratio increases slightly. If the frequency goes from 1072 to 2144 Hz, the film cooling effectiveness climbs up and the Stanton number ratio decreases. The results show that at high average blowing ratio (M = 1.0) the trends of the film cooling effectiveness are similar to those at low blowing ratio (M = 0.5) except from 0 to 90 Hz. If the frequency goes from 0 to 90 Hz at M = 1.0, the film cooling effectiveness increases and the Stanton number ratio decreases. It can be said that it is important to include the effects of oscillating flows when designing film cooling systems for a gas turbine.

LES Study of the Laminar Heat Transfer Augmentation on the Pressure Side of a Turbine Vane Under Freestream Turbulence

Vane pressure side heat transfer is studied numerically using Large Eddy Simulation (LES) on an aft loaded vane with a large leading edge over a range of turbulence conditions. Numerical simulations are performed in a linear cascade at exit chord Reynolds number of Re = 5.1 × 105 at low (Tu≈0.7%), moderate (Tu≈7.9%) and high (Tu≈12.4%) freestream turbulence with varying length scales as prescribed by the experimental measurements of Varty and Ames (2016). Heat transfer predictions (i.e. Stanton number based on exit condition) on the vane pressure side are in a very good agreement with the experimental measurements and the heat transfer augmentation due to the freestream turbulence is well captured. At Tu≈12.4%, freestream turbulence enhances the Stanton number on the pressure surface without boundary layer transition to turbulence by a maximum of about 50% relative to the low freestream turbulence case (Tu≈0.7%). Higher freestream turbulence generates elongated structures and high-velocity streaks wrapped around the leading edge that contain significant energy. Amplification of the velocity streaks is observed further downstream with max r.m.s of 0.3 near the trailing edge but no transition to turbulence or formation of turbulence spots is observed on the pressure side. The heat transfer augmentation at the higher freestream turbulence is primarily due to the initial amplification of the low-frequency velocity perturbations inside the boundary layer that persist along the entire chord of the airfoil. Stanton numbers appear to scale with the streamwise velocity fluctuations inside the boundary layer. Görtler vortices are not observed for this airfoil geometry.

Effects of Oscillations in the Main Flow on Film Cooling at Various Frequencies at a Low Blowing Ratio

The objective of this study was to investigate the effects of oscillations in the main flow on film cooling at various single frequencies at a low average blowing ratio of M = 0.5. The oscillations in the main flow could be a result of combustion instabilities that have been one of the major concerns for gas turbine industry. Understanding the effect of the instabilities on film cooling is important for better design of the gas turbine engines. The frequencies from 268 to 2144 Hz were identified as the dominant frequencies from a Fourier analysis of a combustor instability data on pressure oscillations. Lastly, the experimental data on gas turbine combustor instabilities is applied to the main flow using Fourier Series and the results are compared to those at single frequencies. Numerical simulations are carried out using LES Smagorinsky-Lilly and URANS k-epsilon models. This study is focused on film cooling effectiveness and heat transfer coefficient which are very important in calculation of the blade temperatures. The results show that as the frequency of the main flow goes from 0 to 180 Hz, the film cooling effectiveness is decreased due to enhancement of jet lift off with increasing frequency. However, when the frequency goes from 180 to 268 Hz, the film cooling effectiveness climbs up sharply because a thin coolant film near the wall is overlapped by large vortices containing the coolant. If the frequency changes from 268 to 1072 Hz, the effectiveness drops because the large vortices generated catch up with each other and they start overlapping and they are moved away from the wall. Main flow frequencies from 1072 to 2144 Hz cause an increase of the film cooling effectiveness since the coolant jet could not respond to these very high frequencies and the coolant behavior starts to return to that at 0 Hz gradually along with the effectiveness. In terms of heat transfer coefficients, when the oscillation frequency climbs from 0 to 536 Hz, the spanwise-averaged Stanton number ratio (Stm/Sto) increases due to growing disturbances in the flow. If the frequency is increased from 536 to 2144, the spanwise-averaged Stanton number ratio is decreased. When the oscillation frequency exceeds 536 Hz, the mixing between the hot mainstream and the coolant is reduced because jets do not respond to the flow oscillations as quickly by very short period.

A CFD technique to investigate the chocked flow and heat transfer characteristic in a micro-channel heat sink

In this research, a Computational Fluid Dynamics (CFD) technique was used to investigate the effect of choking on the flow and heat transfer characteristics of a typical micro-channel heat sink. Numerical simulations have been carried out using Spalart–Allmaras model. Comparison of the numerical results for the heat transfer rate, mass flow rate and Stanton number with the experimental data were conducted. Relatively good agreement was achieved with maximum relative error 16%, and 8% for heat transfer and mass flow rate, respectively. Also, average relative error 9.2% was obtained for the Stanton number in comparison with the experimental values. Although, the results show that the majority of heat was transferred in the entrance region of the channel, but the heat transfer in micro-channels can also be affected by choking at channel exit. Moreover, the results clearly show that, the location where the flow is choked (at the vicinity of the channel exit) is especially important in determining the heat transfer phenomena. It was found that Spalart–Allmaras model is capable to capture the main features of the choked flow. Also, the effects of choking on the main characteristics of the flow was presented and discussed.