Unsteady Analysis of Blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes

The effect of the upstream wake on the blade heat transfer has been numerically examined. The geometry and the flow conditions of the first stage turbine blade of GE’s E3 engine with a tip clearance equal to 2% of the span was utilized. Based on numerical calculations of the vane, a set of wake boundary conditions were approximated which were subsequently imposed upon the downstream blade. This set consisted of the momentum and thermal wakes as well as the variation in modeled turbulence quantities of turbulence intensity and the length scale. Using a one blade periodic domain, the distributions of unsteady heat transfer rate on the turbine blade and its tip, as affected by the wake, were determined. Such heat transfer coefficient distribution was computed using the wall heat flux and the adiabatic wall temperature to desensitize the heat transfer coefficient to the wall temperature. For the determination of the wall heat flux and the adiabatic wall temperatures, two set of computations were required. The results were used in a phase-locked manner to compute the unsteady or steady heat transfer coefficients. It has been found that the unsteady wake has some effect on the distribution of the time averaged heat transfer coefficient on the blade and that this distribution is different from the distribution that is obtainable from a steady computation. This difference was found to be as large as 20 percent of the average heat transfer on the blade surface. On the tip surface, this difference is comparatively smaller and can be as large as four percent of the average.

The geometry and the flow conditions of the first stage turbine blade of GE’s E3 engine have been used to obtain the unsteady three-dimensional blade and tip heat transfer. The isothermal wall boundary condition was used. The effect of the upstream wake of the first stage vane was of interest and was simulated by provision of a “gust” type boundary condition upstream of the blades. A one blade periodic domain was used. The consequence of this choice was explored in a preliminary study which showed little difference in the time mean heat transfer between a 1:1 and 2:3 vane/blade domains. The full three-dimensional computations are of the blade having a clearance gap of 2% the span. Comparison between the time averaged unsteady and steady heat transfer is provided. It is shown that there is a significant difference between the steady and time mean of unsteady blade heat transfer in localized regions. The differences on the suction side of the blade in the near hub and near tip regions were found to be rather significant. Steady analysis underestimated the blade heat transfer by as much as 20% as compared to the time average obtained from the unsteady analysis. As for the blade tip, the steady analysis and the unsteady analysis gave results to within two percent.

The necessity of performing an unsteady simulation for the purpose of predicting the heat transfer on the endwall surfaces of a turbine passage is addressed. This is measured by the difference between the two solutions obtained from a steady simulation and time average of an unsteady simulation. The heat transfer coefficient (Nusselt number) based on the adiabatic wall temperature is used as the basis of the comparison. As there is no film cooling in the proposed case, a heat transfer coefficient so computed should be a better measure of such difference than say, wall heat flux. Results show that the effect of unsteadiness due to wake passage on the pressures and recovery temperatures on both the hub and casing is negligible. Heat transfer on the endwalls, however, is affected by the unsteady wake; the time-average results yield higher heat transfer; in some regions up to 15% higher. The results for the endwall heat transfer were compared to results in the open literature and are found to be comparable.

The necessity of performing an unsteady simulation for the purpose of predicting the heat transfer on the endwall surfaces of a turbine passage is addressed. This is measured by the difference between the two solutions obtained from a steady simulation and the time average of an unsteady simulation. The heat transfer coefficient (Nusselt number) based on the adiabatic wall temperature is used as the basis of the comparison. As there is no film cooling in the proposed case, a computed heat transfer coefficient should be a better measure of such difference than, say, a wall heat flux. Results show that the effect of unsteadiness due to wake passage on the pressures and recovery temperatures on both hub and casing is negligible. Heat transfer on the endwalls, however, is affected by the unsteady wake; the time-averaged results yield higher heat transfer; in some regions, up to 15% higher. The results for the endwall heat transfer were compared with results in open literature and were found to be comparable.

14. ABSTRACT In a gas turbine engine, the turbine rotor blades are buffeted by the wakes of the vanes located upstream. There is a transient effect from the passing of wakes on the blade heat transfer. This transient effect has been computed for a representative rotor by introducing a wake upstream via an unsteady inlet flow boundary condition, or gust condition. Two cases of turbulent flow and laminar flow with Reynolds numbers of 385,000 and 385 respectively were considered. For the turbulent flow case a quasi-steady calculation was also performed. The variation in the unsteady heat transfer coefficient was found to be as high as 120 percent of the mean. For the turbulent flow case a quasisteady calculation was also performed. The time mean of the unsteady heat transfer, the mean of the quasi-steady variations and the steady results agree reasonably well on all blade locations except for the turbulent results which differ near the leading edge. The quasi-steady heat transfer results do not agree with the instantaneous unsteady results, although the time-mean values are similar.

Steady simulations were performed to investigate tip leakage flow and heat transfer characteristics on the rotor blade tip and casing in a single-stage gas turbine engine. A typical high-pressure gas turbine stage was modeled with a pressure ratio of 3.2. The predicted isentropic Mach number and adiabatic wall temperature on the casing showed good agreement with available experimental data under similar operating condition. The present numerical study focuses extensively on the effects of tip clearance heights and rotor rotational speeds on the blade tip and casing heat transfer characteristics. It was observed that the tip leakage flow structure is highly dependent on the height of the tip gap and the speed of the rotor. In all cases, the tip leakage flow was seen to separate and recirculate just around the corner of the pressure side of the blade tip. This region of re-circulating flow enlarges with increasing clearance heights. The separated leakage flow reattaches afterwards on the tip surface. Leakage flow reattachment was shown to enhance surface heat transfer at the tip. The interaction between tip leakage flow and secondary flows that is induced by the relative casing motion is found to significantly influence the blade tip and casing heat transfer distribution. A region of critical heat transfer exists on the casing near the blade tip leading edge and along the pressure-side edge for all the clearance heights that were investigated. At high rotation speed, the region of critical heat transfer tends to move towards the trailing edge due to the change in inflow angle.

This paper reports on an investigation of the heat transfer on the suction side of a transonic film cooled turbine rotor blade in a linear cascade. Heat transfer coefficient and film effectiveness are first determined for steady conditions. The unsteady effects of a passing shock on the heat transfer are then investigated. The film cooling pattern used is a showerhead design with three rows on the suction side, one row at the stagnation point and two rows on the pressure side. The experiments were performed at engine representative temperature and pressure ratios using air as coolant. Heat transfer measurements are obtained using a Heat Flux Microsensor, and surface temperature is monitored with a surface thermocouple. Static pressure is monitored with a Kulite pressure transducer. The shock emerging from the trailing edge of the NGV and impinging on the rotor blades is modeled by passing a shock wave along the leading edges of the cascade blades. The steady-state heat transfer coefficient is 8% higher with film cooling than without film cooling. Shock heating of the freestream flow is determined to be the major contribution to the unsteady variation of heat flux, leading to an increase of about 30°C to 35°C in recovery temperature and adiabatic wall temperature.

Unsteady heat transfer caused by a confined impinging jet is studied using direct numerical simulation (DNS). The time-dependent compressible Navier-Stokes equations are solved using high-order numerical schemes together with high-fidelity numerical boundary conditions. A sixth-order compact finite difference scheme is employed for spatial discretization while a third-order explicit Runge-Kutta method is adopted for temporal integration. Extensive spatial and temporal resolution tests have been performed to ensure accurate numerical solutions. The simulations cover several Reynolds numbers and two nozzle-to-plate distances. The instantaneous flow fields and heat transfer distributions are found to be highly unsteady and oscillatory in nature, even at relatively low Reynolds numbers. The fluctuation of the stagnation or impingement Nusselt number, for example, can be as high as 20 percent of the time-mean value. The correlation between the vortex structures and the unsteady heat transfer is carefully examined. It is shown that the fluctuations in the stagnation heat transfer are mainly caused by impingement of the primary vortices originating from the jet nozzle exit. The quasi-periodic nature of the generation of the primary vortices due to the Kelvin-Helmholtz instability is behind the nearly periodic fluctuation in impingement heat transfer, although more chaotic and non-linear fluctuations are observed with increasing Reynolds numbers. The Nusselt number distribution away from the impingement point, on the other hand, is influenced by the secondary vortices which arise due to the interaction between the primary vortices and the wall jets. The unsteady vortex separation from the wall in the higher Reynolds number cases leads to a local minimum and a secondary maximum in the Nusselt number distribution. These are due to the changes in the thermal layer thickness accompanying the unsteady flow structures.

Steady simulations have been performed to investigate tip leakage flow and heat transfer characteristics on the casing and rotor blade tip in a single stage turbine engine. A turbine stage of stator and rotor was modeled with a pressure ratio of 3.2. The predicted isentropic Mach number and adiabatic wall temperature on the casing showed good agreement with available experimental data. The effects of tip clearance height and rotor rotational speed on the blade tip and casing heat transfer characteristics are mainly considered. It is observed that the tip leakage flow structure is highly dependent on the height of the tip gap as well as speeds of the rotor blade. In all cases, flow separates just around the corner of the pressure side of the blade tip. The region of recirculating flow increases with the increase of the clearance height. Then the flow reattaches on the tip surface near the suction side beyond the flow separation. This flow reattachment enhances surface heat transfer. The leakage flow interaction with the reverse cross flow, induced by relative casing motion, is found to have significant effect on the blade tip and casing heat transfer distribution. Critical region of high heat transfer on the casing exists near the blade tip leading edge and along the pressure side edge at all clearance height. Whereas, at high speed rotation, it tends to move towards the trailing edge due to the change of inflow angle.

Control of over-tip leakage flow between turbine blade tips and the stationary shroud is one of the major challenges facing gas turbine designers today. The flow imposes large thermal loads on unshrouded high pressure turbine blades and is significantly detrimental to turbine blade life. This paper presents results from a computational study performed to investigate the detailed blade tip heat transfer on a sharp-edged, flat tip HP turbine blade. The tip gap is engine representative at 1.5% of the blade chord. Nusselt number distributions on the blade tip surface have been obtained from steady flow simulations and are compared to experimental data carried out in a super-scale cascade, which allows detailed flow and heat transfer measurements in stationary and engine representative conditions. Fully structured, multiblock hexahedral meshes were used in the simulations, performed in the commercial solver Fluent. Seven industry-standard turbulence models, and a number of different tip gridding strategies are compared, varying in complexity from the one-equation Spalart-Allmaras model to a seven-equation Reynolds Stress model. Of the turbulence models examined, the standard k-ω model gave the closest agreement to the experimental data. The discrepancy in Nusselt number observed was just 5%. However, the size of the separation on the pressure side rim was underpredicted, causing the position of reattachment to occur too close to the edge. Other turbulence models tested typically underpredicted Nusselt numbers by around 35%, although locating the position of peak heat flux correctly. The effect of the blade to casing motion was also simulated successfully, qualitatively producing the same changes in secondary flow features as were previously observed experimentally, with associated changes in heat transfer to the blade tip.

Control of over-tip leakage flow between turbine blade tips and the stationary shroud is one of the major challenges facing gas turbine designers today. The flow imposes large thermal loads on unshrouded high pressure (HP) turbine blades and is significantly detrimental to turbine blade life. This paper presents results from a computational study performed to investigate the detailed blade tip heat transfer on a sharp-edged, flat tip HP turbine blade. The tip gap is engine representative at 1.5% of the blade chord. Nusselt number distributions on the blade tip surface have been obtained from steady flow simulations and are compared with experimental data carried out in a superscale cascade, which allows detailed flow and heat transfer measurements in stationary and engine representative conditions. Fully structured, multiblock hexahedral meshes were used in the simulations performed in the commercial solver FLUENT. Seven industry-standard turbulence models and a number of different tip gridding strategies are compared, varying in complexity from the one-equation Spalart–Allmaras model to a seven-equation Reynolds stress model. Of the turbulence models examined, the standard k-ω model gave the closest agreement to the experimental data. The discrepancy in Nusselt number observed was just 5%. However, the size of the separation on the pressure side rim was underpredicted, causing the position of reattachment to occur too close to the edge. Other turbulence models tested typically underpredicted Nusselt numbers by around 35%, although locating the position of peak heat flux correctly. The effect of the blade to casing motion was also simulated successfully, qualitatively producing the same changes in secondary flow features as were previously observed experimentally, with associated changes in heat transfer with the blade tip.

This study focuses on local heat transfer characteristics on the tip and near-tip regions of a turbine blade with a flat tip, tested under transonic conditions in a stationary, 2-D linear cascade with high freestream turbulence. The experiments were conducted at the Virginia Tech transonic blow-down wind tunnel facility. The effects of tip clearance and exit Mach number on heat transfer distribution were investigated on the tip surface using a transient infrared thermography technique. In addition, thin film gages were used to study similar effects in heat transfer on the near-tip regions at 94% height based on engine blade span of the pressure and suction sides. Surface oil flow visualizations on the blade tip region were carried-out to shed some light on the leakage flow structure. Experiments were performed at three exit Mach numbers of 0.7, 0.85, and 1.05 for two different tip clearances of 0.9% and 1.8% based on turbine blade span. The exit Mach numbers tested correspond to exit Reynolds numbers of 7.6 × 105, 9.0 × 105, and 1.1 × 106 based on blade true chord. The tests were performed with a high freestream turbulence intensity of 12% at the cascade inlet. Results at 0.85 exit Mach showed that an increase in the tip gap clearance from 0.9% to 1.8% translates into a 3% increase in the average heat transfer coefficients on the blade tip surface. At 0.9% tip clearance, an increase in exit Mach number from 0.85 to 1.05 led to a 39% increase in average heat transfer on the tip. High heat transfer was observed on the blade tip surface near the leading edge, and an increase in the tip clearance gap and exit Mach number augmented this near-leading edge tip heat transfer. At 94% of engine blade height on the suction side near the tip, a peak in heat transfer was observed in all test cases at s/C = 0.66, due to the onset of a downstream leakage vortex, originating from the pressure side. An increase in both the tip gap and exit Mach number resulted in an increase, followed by a decrease in the near-tip suction side heat transfer. On the near-tip pressure side, a slight increase in heat transfer was observed with increased tip gap and exit Mach number. In general, the suction side heat transfer is greater than the pressure side heat transfer, as a result of the suction side leakage vortices.

An unsteady numerical investigation was performed to examine time dependent behaviors of the tip leakage flow structures and heat transfer on the rotor blade tip and casing in a single stage gas turbine engine. A transonic, high-pressure turbine stage was modeled and simulated using a stage pressure ratio of 3.2. The rotor’s tip clearance was 1.2 mm in height (3% of the rotor span) and its speed was set at 9500 rpm. Periodic flow is observed for each vane passing period. Tip leakage flow as well as heat transfer data showed highly time dependent behaviors. A stator trailing edge shock appears as the turbine stage is operating at transonic conditions. The shock alters the flow condition in the rotor section, namely, the tip leakage flow structures and heat transfer rate distributions. The instantaneous Nusselt number distributions are compared to the time averaged and steady-state results. The same patterns in tip leakage flow structures and heat transfer rate distributions were observed in both unsteady and steady simulations. However, the unsteady simulation captured the locally time-dependent high heat transfer phenomena caused by the unsteady interaction with the upstream vane trailing-edge shock and the passing wake.

Impact of the injector size on the transfer functions of premixed laminar conical flames

This paper discusses the problem of heat transfer in service based on unsteady heat transfer theory. Firstly, the unsteady partial differential heat transfer equations are established according to the law of conservation of energy, and the initial values and boundary conditions are determined. Two unknown convective heat transfer coefficients are involved in the heat transfer model of the work suit. The optimal heat transfer coefficient is determined by describing the numerical relationship and solving the optimization problem, which can be applied to the thickness design of the work suit. The relationship between the convective heat transfer coefficient and the measured temperature is established by the least square method. Furthermore, the unsteady heat transfer model is solved numerically by explicit difference method, and the stability and accuracy of the model are verified. Finally, according to the solution results, the temperature distribution and parameter fitting effect of the work suit are shown, which proves the effectiveness and reliability of the model in practical application.