In this study, a sensitivity analysis based on Reynolds Averaged Navier-Stokes (RANS) equations has been conducted to model the reacting turbulent flow in a swirler used in a (Disk-Oriented) gas-turbine using propane-air mixture. Several popular turbulence models and combustion models have been compared at different equivalence ratios. The effects of simulation parameters such as turbulence intensity, TKE Prandtl number, Schmidt number, and gravity direction have been studied. The contour plots of the species mass fraction (H 2 , OH) and temperature distributions from the CFD results are compared against the experimental visual results. The results showed that the realizable k-ε model and the steady diffusion flamelet model (SDF) are more suitable to model the turbulence combustion in the swirl domain. The computations further showed that the TKE Prandtl number and gravity are sensitive parameters to model the combustion from the swirler, while the Schmidt number and turbulence intensity showed less sensitivity.

The investigated generic configuration consists of cylindrical film cooling holes with a diameter of D = 8.4 mm and an inclination angle of α = 35°. The jets are characterized by a momentum flux ratio of I = 0.63, a density ratio of DR = 0.94 and a cross-flow Reynolds number of Re = 5500. Stereoscopic PIV allows creating a (pseudo) three dimensional image of the flow field. High resolution PIV is used to evaluate velocity fluctuations. The numerical model uses the SST and an EARSM turbulence model. The turbulent scalar fluxes are computed by a constant turbulent Prandtl number as well as algebraic models for the turbulent heat flux. The presented results consist of field cuts and line profiles of the velocity, vorticity and turbulent kinetic energy. All considered numerical options can predict the velocity field accurately, the SST turbulence model is the numerically most stable model and has the lowest demands in computational costs.

A counterflow diffusion flame for supercritical CO 2 combustion is investigated at various CO 2 dilution levels and pressures by accounting for realgas effects into both thermal and transport properties. The UCF 1.1 24-species mechanism is used to account the chemistry. The nature of important non-premixed combustion characteristics such as Prandtl number, thermal diffusivity, Lewis number, stoichiometric scalar dissipation rate, flame thickness, and Damköhler number are investigated with respect to CO 2 dilution and pressure. The result show that, the aforementioned parameters are influenced by both dilution and pressure; the dilution effect is more dominant. Further, result shows that Prandtl number increases with CO 2 dilution and at ninety percent CO 2 dilution, the difference between the Prandtl number of the inlet jets and the flame is minimal. Also, the common assumption of unity Lewis number in the theory and modeling of non-premixed combustion does not hold reasonable for sCO 2 applications due to large difference of Lewis number across the flame and the Lewis number on the flame drop significantly with increase in the CO 2 dilution. An interesting relation between Lewis number and CO 2 dilution is observed. The Lewis number of species drops by 15% when increasing the CO 2 dilution by 30%. Increasing the CO 2 dilution increases both the flow and chemical timescales; however chemical timescale increases faster than the flow time scales. The magnitudes of the Damköhler number signifies the need to consider finite rate chemistry for sCO 2 applications. Further, the Damköhler numbers at 90% sCO 2 dilution are very small, hence laminar flamelet assumptions in turbulent combustion simulations are not physically correct for this application. Also, it is observed that the Damköhler number drops non-linearly with increasing CO 2 dilution in the oxidizer stream. This is a very important observation for the operation of sCO 2 combustors. Further, the flame thickness is found to increase with CO 2 dilution and reduce with pressure.

The design of film cooling systems relies heavily on Reynolds-Averaged Navier-Stokes (RANS) simulations, which solve for mean quantities and model all turbulent scales. Most turbulent heat flux models, which are based on isotropic diffusion with a fixed turbulent Prandtl number (Pr t ), fail to accurately predict heat transfer in film cooling flows. In the present work, machine learning models are trained to predict a non-uniform Pr t field, using various datasets as training sets. The ability of these models to generalize beyond the flows on which they were trained is explored. Furthermore, visualization techniques are employed to compare distinct datasets and to help explain the cross-validation results.

This study strives to provide a critical review and evaluation of influential constituent components in the two-equation k-ε turbulence model class, which are often employed in large full-fidelity gas turbine simulations in industry. All conjectures made, regarding the turbulence model behavior, will be compared to in-house experimental film effectiveness data from a novel film cooling array configuration. This experimental data set is comprised of high resolution adiabatic film cooling effectiveness measurements throughout two film cooling arrays comprised of diffused film holes of modern shape (streamwise inclination of α = 30°, expansion of Φ 1,2,3 = 10°, AR = 3.4, and β = 0° relative to the crossflow direction). The difference between each film cooling array is only a staggered verses inline pattern for the film holes, whereby each has a uniform spacing of X/D = P/D = 8. Local coverage, laterally averaged film cooling effectiveness, and superposition analysis was quantified over a variety of testing conditions (M = 0.5, 0.75, 1.0, 1.5, 2.0, 2.5 at DR = 0.9). First, rendered quantifications of the anisotropic nature of the turbulence are shown throughout the near-field injection region, by leveraging the Reynolds stresses to form anisotropic-invariant maps. Next, results from k-ε models using a linear, a cubic, and a quadratic constitutive relation are compared. Furthermore, effective and conservative scaling of the production and destruction terms in the turbulent transport equations was performed, within reasonable bounds, and the resulting impact on the adiabatic film effectiveness was quantified. This scaling encompasses the C ε2 coefficient, as well as the Durbin realizibility coefficient used in the turbulent viscosity definition. Finally, various formulations of the turbulent Prandtl number were compared, with the resulting adiabatic film effectiveness observed.

High Reynolds flow over a nozzle guide-vane with elevated inflow turbulence was simulated using wall-resolved large eddy simulation (LES). The simulations were undertaken at an exit Reynolds number of 0.5×10 6 and inflow turbulence levels of 0.7% and 7.9% and for uniform heat-flux boundary conditions corresponding to the measurements of (Varty, J. W., and Ames, F. E., 2016, ASME Paper No. IMECE2016-67029). The predicted heat transfer distribution over the vane is in excellent agreement with measurements. At higher freestream turbulence, the simulations accurately capture the laminar heat transfer augmentation on the pressure surface and the transition to turbulence on the suction surface. The bypass transition on the suction surface is preceded by boundary layer streaks formed under the external forcing of freestream disturbances which breakdown to turbulence through inner mode secondary instabilities. Underneath the locally formed turbulent spot, heat transfer coefficient spikes and generally follows the same pattern as the turbulent spot. The details of the flow and temperature fields on the suction side are characterized and first and second order statistics are documented. The turbulent Prandtl number in the boundary layer is generally in the range of 0.7–1, but decays rapidly near the wall.

The cooling protection of the hot end is the key technique for ultra-supercritical steam turbine. Tangential direction cooling chamber has a simple form and stable cooling effectiveness. The influence of inlet Mach number, turbulent Prandtl number, rotational speed, and inlet turbulence intensity on cooling effect of the structure in ideal air model have been made by previous work. The cooling mechanism and the flow characteristic in the ideal air chamber were investigated. In this paper, the focus of the study is to investigate the flow and heat transfer characteristics of the tangential direction cooling chamber in the real steam model. The cooling chamber coupled with the whole steel shaft are simulated. Different boundary condition are compared. The heat transfer coefficients of the hub are acquired at some different rotational speeds and different hub conditions. The distribution of heat transfer coefficients and wall temperature are mainly affected by the viscous force and the velocity gradient near the hub.

A numerical study, based on experimental work of Inanli et al. [1] is conducted to understand the heat transfer characteristics of film cooled test plates that represent the gas turbine combustor liner cooling system. Film cooling tests are conducted by six different slot geometries and they are scaled-up model of real combustor liner. Three different blowing ratios are applied to six different geometries and surface cooling effectiveness is determined for each test condition by measuring the surface temperature distribution. Effects of geometrical and flow parameters on cooling effectiveness are investigated. In this study, Conjugate Heat Transfer (CHT) simulations are performed with different turbulence models. Effect of the turbulent Prandtl Number is also investigated in terms of heat transfer distribution along the measurement surface. For this purpose, turbulent Prandtl number is calculated with a correlation as a function of local surface temperature gradient and its effect also compared with the constant turbulent Prandtl numbers. Good agreement is obtained with two-layered k – ϵ with modified Turbulent Prandtl number.

Slot film cooling in an accelerating boundary layer with high free-stream turbulence is studied numerically using Large Eddy Simulations (LES). Recent cooling designs of turbine airfoils (such as double-wall cooling) enable slot cooling configurations that are known to provide improved cooling effectiveness over discrete hole cooling systems. Calculations are done for a symmetrical leading edge geometry with the slot fed by a plenum populated with pin fins. To generate the inflow turbulence, the Synthetic Eddy Method (SEM) is used by which the turbulence intensity and length scales in each direction can be specified at the inflow. Different levels of turbulence are imposed at the inflow cross-plane. For the inflow at the plenum, an a priori simulation has been performed in the plenum with pin fins, and the velocity signals are stored at a plane downstream of the pin fins over a sufficient period of time, and are used as the inflow boundary condition in the plenum. Calculations are done for a Reynolds number of 250,000 and freestream turbulence levels of 0.7%, 3.5%, 7.8% and 13.7% are reported. These conditions correspond to the experimental measurements of Busche and Ames (2014). Numerical results show good agreement with experiment data and show the observed decay of thermal effectiveness with turbulence intensity. The turbulence and non-uniformity exiting the slot are shown to play an important role in the cooling effectiveness distributions downstream of the slot. To provide a better understanding of the flow physics and heat transfer, the mean flowfield and turbulence statistics are studied. Generation of freestream structures is observed at the leading edge, and the amplification of the corresponding fluctuations downstream is identified as one of the parameters influencing the slot cooling performance. Predictions show the higher growth rate of the thermal boundary layer with increasing turbulence which is a clear indication of the increase in turbulent thermal diffusivity and reduction of the effective turbulence Prandtl number. The self-similar temperature profiles deviate from those measured under low freestream turbulence condition.

The cooling protection of the hot end is the key technique for ultra-supercritical steam turbine to cool the hot components. In this paper, the internal flow mechanism and cooling characteristics in the tangential direction cooling channel in the intermediate pressure cylinder (IPC) are investigated using the method of computational fluid dynamics. Various turbulence models and mesh sizes are evaluated (the k-ε model, the k-ω model, the SST model). Also, calculated results of the nonrotating bottom wall are compared with the experimental results in a previous research to show the reliability of the CFD program used. Detailed predictions of the contours of velocity, pressure and temperature are carried out. The focus of this study is to investigate the effects of inlet Mach number, turbulent Prandtl number, rotational wall speed, and inlet turbulence intensity on the cooling effectiveness of the vortex channel. The inlet Mach number, the turbulent Prandtl number, the rotational wall speed and the inlet turbulence intensity varied from 0.315 to 0.512, from 0.71 to 1.0, from 0 to 3000rpm, and from 1% to 10%, respectively. Results show that the parameters have different effects on the cooling effectiveness of the vortex cooling chamber. The cooling effect of the vortex channel increases with increasing inlet Mach number and rotational wall speed, while decreases with the increasing turbulent Prandtl number. As the inlet turbulence intensity increases, the cooling effect increases firstly, and then decreases.

Algebraic closures for the turbulent scalar fluxes were evaluated for a discrete hole film cooling geometry using the results from the high-fidelity Large Eddy Simulation (LES) of Bodart et al. [1]. Several models for the turbulent scalar fluxes exist, including the widely used Gradient Diffusion Hypothesis, the Generalized Gradient Diffusion Hypothesis [2], and the Higher Order Generalized Gradient Diffusion Hypothesis [3]. By analyzing the results from the LES, it was possible to isolate the error due to these turbulent mixing models. Distributions of the turbulent diffusivity, turbulent viscosity, and turbulent Prandtl number were extracted from the LES results. It was shown that the turbulent Prandtl number varies significantly spatially, undermining the applicability of the Reynolds analogy for this flow. The LES velocity field and Reynolds stresses were fed into a RANS solver to calculate the fluid temperature distribution. This analysis revealed in which regions of the flow various modeling assumptions were invalid and what effect those assumptions had on the predicted temperature distribution.

Based on n-power velocity and temperature profiles a method of computing various turbulent boundary layer thicknesses and shape factors affected by wall temperature and Prandtl number for fully developed subsonic gas flow over a flat plate is presented. Density variation in the boundary layer is given main consideration. Numerical computations include both heating and cooling of gas. Boundary layer thicknesses and shape factors are shown to be significantly affected by wall temperature and to a lesser degree by Prandtl number. An experiment is described which involved air flow up to 30 m/sec over a flat plate maintained at constant wall temperatures up to 250 C. Comparisons between theory and experiment are good.

Characteristic requirements of a closed-cycle gas turbine (CCGT) working fluid were identified and the effects of their thermodynamic and transport properties on the CCGT cycle performance, required heat exchanger surface area and metal operating temperature, cycle operating pressure levels, and the turbomachinery design were investigated. Material compatibility, thermal and chemical stability, safety, cost, and availability of the working fluid were also considered in the study. This paper also discusses CCGT working fluids utilizing mixtures of two or more pure gases. Some mixtures of gases exhibit pronounced synergetic effects on their characteristic properties including viscosity, thermal conductivity and Prandtl number, resulting in desirable heat transfer properties and high molecular weights. Typical examples of such synergetic gas mixture are helium-xenon and helium-carbon dioxide.

Monatomic gas mixtures have low Prandtl numbers, as low as 0.25 or even lower, compared to about 0.7 for air. In a closed Brayton cycle using a low Prandtl number working gas, the three heat exchangers in the cycle will in general be smaller than in a comparable cycle using air. A system study has been made to compare several promising monatomic gases with air, and to explore the economic incentive to replace air in the closed Brayton cycle with a monatomic gas.

Two methods were used to calculate the heat flux to full-coverage film cooled airfoils and, subsequently, the airfoil wall temperatures. The calculated wall temperatures were compared to measured temperatures obtained in the Hot Section Facility operating at real engine conditions. Gas temperatures and pressures up to 1900 K and 18 atm with a Reynolds number up to 1.9 million were investigated. Heat flux was calculated by the convective heat transfer coefficient adiabatic wall method and by the superposition method which incorporates the film injection effects in the heat transfer coefficient. The results of the comparison indicate the first method can predict the experimental data reasonably well. However, superposition overpredicted the heat flux to the airfoil without a significant modification of the turbulent Prandtl number. The results of this research suggests that additional research is required to model the physics of full-coverage film cooling where there is significant temperature/density differences between the gas and coolant.

The paper presents finite-difference predictions for the convective heat transfer in symmetrically-heated rotating cavities subjected to a radial outflow of cooling air. An elliptic calculation procedure has been used, with the turbulent fluxes estimated by means of a low Reynolds number k-ε model and the familiar ‘turbulence Prandtl number’ concept. The predictions extend to rotational Reynolds numbers of 3.7 × 10 6 and encompass cases where the disc temperatures may be increasing, constant or decreasing in the radial direction. It is found that the turbulence model leads to predictions of the local and average Nusselt numbers for both discs which are generally within ± 10% of the values from published experimental data, although there appear to be larger systematic errors for the upstream disc than for the downstream disc. It is concluded that the calculations are of sufficient accuracy for engineering design purposes, but that improvements could be brought about by further optimization of the turbulence model.

Comparisons with experimental heat transfer and surface pressures were made for seven turbine vane and blade geometries using a quasi-three-dimensional thin-layer Navier-Stokes analysis. Comparisons are made for cases with both separated and unseparated flow over a range of Reynolds numbers and freestream turbulence intensities. The analysis used a modified Baldwin-Lomax turbulent eddy viscosity model. Modifications were made to account for the effects of: 1) freestream turbulence on both transition and leading edge heat transfer; 2) strong favorable pressure gradients on re-laminarization; and 3) variable turbulent Prandtl number on heat transfer. In addition, the effect on heat transfer of the near-wall model of Deissler is compared with the Van Driest model.

Approximate algebraic correlations for the two-dimensional laminar boundary layer flow and heat transfer with favorable pressure gradient at constant K ( ≡ v U e 2 d U e d x ) values were found by using Pohlhausen’s integral method. Two thermal boundary conditions were considered: constant wall heat flux and constant wall temperature. These correlations were tabulated and compared in the limits KRe x → 0 and KRe x → ∞ with the similarity solutions of the Blasius flow and the convergent-channel flow. The comparisons between these correlations and those obtained numerically from the STAN5 code were excellent. The results showed that the momentum boundary layer grows at the leading edge with an initial rate like the Blasius flow to a maximum value, then decreases and asymptotically approaches the behavior of a convergent-channel flow. As KRe x increases, the skin friction coefficient decreases and approaches a constant; the Pohlhausen’s pressure gradient parameter ( Λ ≡ δ 2 v d U e d x ) increases from zero at the leading edge and approaches a constant. While hydrodynamically asymptotical solutions were obtained, no asymptotical thermal similarity was found. Skin friction coefficient and various integral parameters could be collapsed into a corresponding single curve when suitable normalization factors were chosen. The effects of Prandtl number and unheated starting length were also analyzed.

Finite-volume predictions are presented for the convective heat transfer rates in a rotating cavity, formed by two co-rotating plane discs and a peripheral shroud, and subjected to a radial outflow of cooling air. The heating of the discs is asymmetric, the air entering the cavity through a central hole in the cooler (upstream) disc. The predicted Nusselt number distributions for each disc are compared with unpublished data from the University of Sussex for dimensionless mass-flow rates in the range 2800 ≤ C w ≤ 14000 and rotational Reynolds numbers, Re θ , up to 5.2 × 10 6 . A single-grid elliptic procedure was used with turbulent transport represented via a low Reynolds number k-ε model and the turbulence Prandtl number concept. In comparing the predicted and measured convective heat fluxes, it is important to consider the radiative heat exchange between the discs. This is estimated using a conventional view-factor approach based on black-body emission. Under conditions of asymmetric heating, rotationally-induced buoyancy forces can exert significant effect on the flow structure, the induced motion tending to oppose that imposed by the radial outflow. Indeed, flow visualisation studies have revealed that, as the rotational Reynolds number is increased (for a fixed value of C w ), the flow in the source region initially becomes oscillatory in nature, leading eventually to the onset of chaotic flow in which the usual Ekman layer structure does not persist in all angular planes. The extent to which the effects of such flow behaviour can be captured by the steady, axisymmetric calculation approach used here is questionable, but it is found that the turbulence model (used previously for the prediction of heat transfer in symmetrically-heated cavities) still leads to good (±10%) predictive accuracy for the heated (downstream) disc. However, the predicted Nusselt numbers for the cooler (upstream) disc generally show little accord with experimental data, often signifying heat flow into the disc instead of vice-versa. It is concluded that the modelling of the turbulent heat transport across the core region of the flow is erroneous, especially at high rotational Reynolds numbers: this is attributed to overestimated turbulence energy production in that region due to the action of the radial-circumferential component of shear stress ( vw ). Adoption of an algebraic-stress model for this shear stress is partly successful in removing the discrepancies between prediction and experiment.

The effects of elevated free-stream turbulence on flow and thermal structures in transitional boundary layers were investigated experimentally on a heated flat plate. Detailed boundary layer measurements using a three-wire probe and wall heat transfer were made with free-stream turbulence intensities of 0.5, 3.8, 5.5 and 6.4 percent respectively. The onset of transition, transition length and the turbulent spot formation rate were determined. The statistical results of the streamwise and cross-stream velocity fluctuations, temperature fluctuation, Reynolds stresses and Reynolds heat fluxes were presented. The eddy viscosity, turbulent thermal diffusivity and the turbulent Prandtl number were calculated and related physical mechanisms are discussed.