Savas Yavuzkurt

Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part I: Simulation of the Vortex Rope

Numerical simulations and analysis of the vortex rope formation in a simplified draft tube of a model Francis turbine are carried out in this paper, which is the first part of a two-paper series. The emphasis of this part is on the simulation and investigation of flow using different turbulence closure models. Two part-load operating conditions with same head and different flow rates (91% and 70% of the best efficiency point (BEP) flow rate) are considered. Steady and unsteady simulations are carried out for axisymmetric and three-dimensional grid in a simplified axisymmetric geometry, and results are compared with experimental data. It is seen that steady simulations with Reynolds-averaged Navier–Stokes (RANS) models cannot resolve the vortex rope and give identical symmetric results for both the axisymmetric and three-dimensional flow geometries. These RANS simulations underpredict the axial velocity (by at least 14%) and turbulent kinetic energy (by at least 40%) near the center of the draft tube, even quite close to the design condition. Moving farther from the design point, models fail in predicting the correct levels of the axial velocity in the draft tube. Unsteady simulations are performed using unsteady RANS (URANS) and detached eddy simulation (DES) turbulence closure approaches. URANS models cannot capture the self-induced unsteadiness of the vortex rope and give steady solutions while DES model gives sufficient unsteady results. Using the proper unsteady model, i.e., DES, the overall shape of the vortex rope is correctly predicted and the calculated vortex rope frequency differs only 6% from experimental data. It is confirmed that the vortex rope is formed due to the roll-up of the shear layer at the interface between the low-velocity inner region created by the wake of the crown cone and highly swirling outer flow.

Comparison of Four Different Two-Equation Models of Turbulence in Predicting Film Cooling Performance

The capabilities of four two-equation turbulence models in predicting film cooling effectiveness were investigated and their limitations as well as relative performance are presented. The four turbulence models are the standard, RNG, and realizable k-e models as well as the standard k-ω model all found in the FLUENT CFD code. In all four models, the enhanced wall treatment has been used to resolve the flow near solid boundaries. A systematic approach has been followed in the computational setup to insure grid-independence and accurate solution that reflects the true capabilities of the turbulence models. Exact geometrical and flow-field replicas of an experimental study on discrete-jet film cooling were generated and used in FLUENT. A pitch-to-diameter ratio of 3.04, injection length-to-diameter ratio of 4.6 and density ratios of 0.92 and 0.97 were some of the parameters used in the film cooling analysis. Furthermore, the study covered two levels of blowing ratio (M = 0.5 and 1.5) at an environment of low free-stream turbulence intensity (Tu = 0.1%). The standard k-e model had the most consistent performance among all considered turbulence models and the best centerline film cooling effectiveness predictions with the results deviating from experimental data by only ±10% and about 20–60% for the low (M = 0.5) and high (M = 1.5) blowing ratio cases, respectively. However, centerline side-view and surface top-view contours of non-dimensional temperature for the standard k-e cases revealed that the good results for film cooling effectiveness η compared to the experimental data were due to a combination of an over-prediction of jet penetration in the normal direction with an under-prediction of jet spread in the lateral direction. The standard k-ω model completely failed to produce any results that were meaningful with under-predictions of η that ranged between 80 and 85% for the low blowing ratio case and over-predictions of about 200% for the high blowing ratio case. Even though the RNG and realizable models showed to have better predicted the jet spread in the lateral direction compared to the standard k-e model, there were some aspects of the flow, such as levels of turbulence generated by cross-flow and jet interaction, that were not realistic resulting in errors in the η prediction that ranged from −10% to +80% for the M = 0.5 case and from −80% to +70% for the M = 1.5 case. As a result of this study at this point it was concluded that the standard k-e model have the most promising potential among the two-equation models considered. It was chosen as the best candidate for further improvement for the simulation of film cooling flows.Copyright

Numerical Simulations of the Near-Field Region of Film Cooling Jets Under High Free Stream Turbulence: Application of RANS and Hybrid URANS/Large Eddy Simulation Models

This paper investigates the flow field and thermal characteristics in the near-field regionof film cooling jets through numerical simulations using Reynolds-averaged Navier–Stokes (RANS) and hybrid unsteady RANS (URANS)/large eddy simulation (LES) models.Detailed simulations of flow and thermal fields of a single-row of film cooling cylindricalholes with 30deg inline injection on a flat plate are obtained for low (M¼0.5) and high(M¼1.5) blowing ratios under high free stream turbulence (FST) (10%). The realizablek- emodel is used within the RANS framework and a realizable k- -based detached eddysimulation (DES) is used as a hybrid URANS/LES model. Both models are used togetherwith the two-layer zonal model for near-wall simulations. Steady and time-averagedunsteady film cooling effectiveness obtained using these models are compared with avail-able experimental data. It is shown that hybrid URANS/LES models (DES in the presentpaper) predict more mixing both in the wall-normal and spanwise directions compared toRANS models, while unsteady asymmetric vortical structures of the flow can also be cap-tured. The turbulent heat flux components predicted by the DES model are higher thanthose obtained by the RANS simulations, resulting in enhanced turbulent heat transferbetween the jet and mainstream, and consequently better predictions of the effectiveness.Nevertheless, there still exist some discrepancies between numerical results andexperimental data. Furthermore, the unsteady physics of jet and crossflow interactionsand the jet lift-off under high FST is studied using the present DES results.[DOI: 10.1115/1.4028646]Keywords: film cooling, unsteady simulation, turbulence modeling, high free streamturbulence, detached eddy simulation

Effect of Computational Grid on Performance of Two-Equation Models of Turbulence for Film Cooling Applications

The effect of the computational grid on the performance of two-equation models of turbulence in predicting film cooling effectiveness has been investigated. The four turbulence models are: the standard, RNG, and realizable k-e, and the standard k-ω models in the CFD code FLUENT. The geometry and flow-field were taken from an experimental study on discrete-hole film-cooling on a flat plate and are simulated in FLUENT. Some of the parameters are: Pitch-to-diameter ratio of 3.04, injection tube length-to-diameter ratio of 4.6. Two blowing ratios of M = 0.5 and 1.5 were considered. In earlier studies presented in Turbo Expo 2006 and 2007, a hexahedral grid for the main flow and tetrahedral grid for the short injection tubes and plenum were used as suggested by the FLUENT users’ manual. The results of predictions both under low and high freestream turbulence and for high and low blowing ratios were not that good. It was decided that some of these differences arise from the use of “hybrid mesh” with a non-conformal interface boundary between them. Also tetrahedral mesh in the injection tube could not resolve the boundary layer there leading to incorrect injection profiles at the hole exit. In order to correct this deficiency, in the current study a single hexahedral grid is used both in the injection tube, plenum and the main flow regions eliminating the need for merging two different meshes and also leading to correct boundary layer resolution in the tube resulting in more realistic jet exit profiles. The difference between the model calculations and data for effectiveness are reduced to within 40% in the near field (∼x/D 8). This shows the importance of using correct mesh which fits the problem physics and expected flow pattern for the accurate solutions and indicated the necessity of using CFD codes such as FLUENT with care and experience. There were still differences between the results for four models. It looks like k-e and k-ω models give the best predictions and the trend of the data for the centerline effectiveness in the near field, whereas all models give good (within 5–10%) predictions of the centerline effectiveness in the far field.Copyright

Evaluation of Two-Equation Models of Turbulence in Predicting Film Cooling Performance Under High Free Stream Turbulence

The capabilities of four two-equation turbulence models in predicting film cooling effectiveness under high free stream turbulence (FST) intensity (Tu = 10%) were investigated and their performance are presented and discussed. The four turbulence models are: the standard k-e, RNG, and realizable k-e models as well as the standard k-ω model all four found in the FLUENT CFD code. In all models, the enhanced wall treatment has been used to resolve the flow near solid boundaries. A systematic approach has been followed in the computational setup to insure grid-independence and accurate solution that reflects the true capabilities of these models. Exact geometrical and flow-field replicas of an experimental study on discrete hole film cooling were generated and used in FLUENT. A pitch-to-diameter ratio of 3.04, injection tube length-to-diameter ratio of 4.6 and density ratios of 0.92 and 0.97 were some of the parameters used in the film cooling analysis. The study covered two levels of blowing ratios (M = 0.5 and 1.5) at an environment of what is defined as high initial free-stream turbulence intensity (Tu = 10%). Performance of these models under a very low initial FST were presented in a paper by the authors in Turbo Expo 2006. In that case, the standard k-e model had the most consistent performance among all considered turbulence models and the best centerline film cooling effectiveness predictions under very low FST. However, after the addition of high FST in the free-stream, even the standard k-e model started to deviate greatly from the experimental data (up to 200% over-prediction) under high blowing ratios (M = 1.5). The model which performed the best under high FST but low blowing ratios (M = 0.5) is still the standard k-e model. In all cases only standard k-e model results match the trends of data for both cases. It can be said that under high FST with high M all the models do not do a good job of predicting the data. It was concluded that these deviations resulted from the effects of both high FST and high M. Under high M, near the injection holes deviations could result from the limitations of Boussinesq hypothesis relating the direction of Reynolds stress to the mean strain rate. Also, it seems like all models have trouble including the effects of high FST by not being able to take into account high levels of diffusion of turbulence from the free stream. However, standard k-e model still looks like the best candidate for further improvement with the addition of new diffusion model for TKE under high FST.Copyright

Unsteady Numerical Simulation of Flow in Draft Tube of a Hydroturbine Operating Under Various Conditions Using a Partially Averaged Navier–Stokes Model

The variable energy demand requires a great flexibility in operating a hydroturbine, which forces the machine to be operated far from its design point. One of the main components of a hydroturbine where undesirable flow phenomena occur under off-design conditions is the draft tube. Using computational fluid dynamics (CFD), the present paper studies the flow in the draft tube of a Francis turbine operating under various conditions. Specifically, four operating points with the same head and different flow rates corresponding to 70%, 91%, 99%, and 110% of the flow rate at the best efficiency point (BEP) are considered. Unsteady numerical simulations are performed using a recently developed partially averaged Navier–Stokes (PANS) turbulence model, and the results are compared to the available experimental data, as well as the numerical results of the traditionally used Reynolds-Averaged Navier–Stokes (RANS) models. Several parameters including the pressure recovery coefficient, mean velocity, and time-averaged and fluctuating wall pressure are investigated. It is shown that RANS and PANS both can predict the flow behavior close to the BEP operating condition. However, RANS results deviate considerably from the experimental data as the operating condition moves away from the BEP. The pressure recovery factor predicted by the RANS model shows more than 13% and 58% overprediction when the flow rate decreases to 91% and 70% of the flow rate at BEP, respectively. Predictions can be improved significantly using the present unsteady PANS simulations. Specifically, the pressure recovery factor is predicted by less than 4% and 6% deviation for these two operating conditions. A similar conclusion is reached from the analysis of the mean velocity and wall pressure data. Using unsteady PANS simulations, several transient features of the draft tube flow including the vortex rope and associated pressure fluctuations are successfully modeled. The formation of the vortex rope in partial load conditions results in severe pressure fluctuations exerting oscillatory forces on the draft tube. These pressure fluctuations are studied for several locations in the draft tube and the critical region with highest fluctuation amplitude is found to be the inner side of the elbow.

Calculation of Disk Temperatures in Gas Turbine Rotor-Stator Cavities Using Conjugate Heat Transfer

The present study deals with the numerical modeling of the turbulent flow in a rotor-stator cavity with or without imposed through flow with heat transfer. The commercial finite volume based solver, ANSYS/FLUENT is used to numerically simulate the problem. A conjugate heat transfer approach is used. The study specifically deals with the calculation of the heat transfer coefficients and the temperatures at the disk surfaces. Results are compared with data where available. Conventional approaches which use boundary conditions such as constant wall temperature or constant heat flux in order to calculate the heat transfer coefficients which later are used to calculate disk temperatures can introduce significant errors in the results. The conjugate heat transfer approach can resolve this to a good extent. It includes the effect of variable surface temperature on heat transfer coefficients. Further it is easier to specify more realistic boundary conditions in a conjugate approach since solid and the flow heat transfer problems are solved simultaneously. However this approach incurs a higher computational cost. In this study, the configuration chosen is a simple rotor and stator system with a stationary and heated stator and a rotor. The aspect ratio is kept small (around 0.1). The flow and heat transfer characteristics are obtained for a rotational Reynolds number of around 106 . The simulation is performed using the Reynolds Stress Model (RSM). The computational model is first validated against experimental data available in the literature. Studies have been carried out to calculate the disk temperatures using conventional non-conjugate and full conjugate approaches. It has been found that the difference between the disk temperatures for conjugate and non-conjugate computations is 5 K for the low temperature and 30 K for the high temperature boundary conditions. These represent differences of 1% and 2% from the respective stator surface temperatures. Even at low temperatures, the Nusselt numbers at the disk surface show a difference of 5% between the conjugate and non-conjugate computations, and far higher at higher temperatures.Copyright

FILM COOLING CALCULATIONS WITH AN ITERATIVE CONJUGATE HEAT TRANSFER APPROACH USING EMPIRICAL HEAT TRANSFER COEFFICIENT CORRECTIONS

An iterative conjugate heat transfer technique has been developed to predict the temperatures on film cooled surfaces such as flat plates and turbine blades. Conventional approaches using a constant wall temperature to calculate heat transfer coefficient and applying it to solid as a boundary condition can result in errors around 14% in uncooled blade temperatures. This indicates a need for conjugate heat transfer calculation techniques. However, full conjugate calculations also suffer from inability to correctly predict heat transfer coefficients in the near field of film cooling holes and require high computational cost making them impractical for component design in industrial applications. Iterative conjugate heat transfer (ICHT) analysis is a compromise between these two techniques where the external flow convection and internal blade conduction are loosely coupled. The solution obtained from solving one domain is used as boundary condition for the other. This process is iterated until convergence. Flow and heat transfer over a film cooled blade is not solved directly and instead convective heat transfer coefficients resulting from external convection on a similar blade without film cooling and under the same flow conditions are corrected by use of experimental data to incorporate the effect of film cooling in the heat transfer coefficients. The effect of conjugate heat transfer is taken into account by using this iterative technique. Unlike full conjugate heat transfer (CHT) the ICHT analysis doesn’t require solving a large number of linear algebraic equations at once. It uses two separate meshes for external convection and blade conduction and thus problem can be solved in lesser time using less computational resources. A demonstration of this technique using a commercial CFD solver FLUENT is presented for simulations of film cooling on flat plates. Results are presented in form of film cooling heat transfer coefficients and surface temperature distribution which are compared with results obtained from conventional approach. For uncooled surfaces, the deviations were as high as 3.5% between conjugate and conventional technique results for the wall temperature. For film cooling simulations on a flat plate using the ICHT approach showed deviations up to 10% in surface temperature compared to constant wall temperature technique for a high temperature difference case and 3% for a low temperature difference case, since surface temperature is not constant over the surface when conjugate heat transfer is considered. Results show that conjugate heat transfer effect is significant for film cooling flows involving high temperature differences for the current blade materials and application of film cooling correction obtained from experimental data is very useful in obtaining realistic blade temperatures.Copyright

Dependence of Pressure Losses on Angle of Attack for Flow Through Perforated Plates

We have measured the dependence of pressure losses on angle of attacks in pipe flow through a set of seven perforated metal plates. Pressure losses were measured in air flow at temperature and pressure about 24°C and 736 mm Hg. The nominal pipe diameter is 3.5″ resulting an internal pipe diameter of 90.17 mm. Specifically, the plates differ in type of metal, thickness, hole size, and hole spacing. Using a pipe-flow apparatus in which the angle of attacks for the plate was set at either, 0°, or 45°, or 22.5°, we measured the pressure losses over speeds ranging up to approximately 30 m/s. Generally, the pressure loss increases linearly with the square of the air speed; and, in this context, the ratio of pressure loss to air speed squared represents a classical loss coefficient, K, for perforated plates. For a specific air speed, the magnitude of the loss coefficients positively with the ratio of the distance between hole centers to the hole diameter, s/D. The geometric effects associated with changing the angle of attack are complex, and a single dimensionless ratio such as s/D provides insufficient information to describes this effect. However, the measurements do indicate that the loss coefficient K depends on the ratio, s/D, raised to a power of approximately 4.8. Flow visualization may provide some more insight into the specific physical phenomena responsible for these pressure losses.Copyright

An axisymmetric model for draft tube flow at partial load

A new Reynolds-averaged Navier-Stokes (RANS) turbulence model is developed in order to correctly predict the mean flow field in a draft tube operating under partial load using 2-D axisymmetric simulations. It is shown that although 2-D axisymme- tric simulations cannot model the 3-D unsteady features of the vortex rope, they can give the average location of the vortex rope in the draft tube. Nevertheless, RANS simulations underpredict the turbulent kinetic energy (TKE) production and diffusion near the center of the draft tube where the vortex rope forms, resulting in incorrect calculation of TKE profiles and, hence, poor prediction of the axial velocity. Based on this observation, a new k-ε turbulence RANS model taking into account the extra production and diffusion of TKE due to coherent structures associated with the vortex rope formation is developed. The new model can successfully predict the mean flow velocity with significant improvements in comparison with the realizable k-ε model. This is attributed to better prediction of TKE production and diffusion by the new model in the draft tube under partial load. Specifically, the new model calculates 31% more production and 46% more diffusion right at the shear layer when compared to the k-ε model.