Direct Numerical Simulation of Real-gas Effects within Turbulent Boundary Layers for Fully-developed Channel Flows

Real-gas effects have a significant impact on compressible turbulent flows of dense gases, especially when flow properties are in proximity of the saturation line and/or the thermodynamic critical point. Understanding of these effects is key for the analysis and improvement of performance for many industrial components, including expanders and heat exchangers in organic Rankine cycle systems. This work analyzes the real-gas effect on the turbulent boundary layer of fully developed channel flow of two organic gases, R1233zd(E) and MDM - two candidate working fluids for ORC systems. Compressible direct numerical simulations (DNS) with real-gas equations of state are used in this research. Three cases are set up for each organic vapour, representing thermodynamic states far from, close to and inside the supercritical region, and these cases refer to weak, normal and strong real-gas effect in each fluid. The results within this work show that the real-gas effect can significantly influence the profile of averaged thermodynamic properties, relative to an air baseline case. This effect has a reverse impact on the distribution of averaged temperature and density. As the real-gas effect gets stronger, the averaged centre-to-wall temperature ratio decreases but the density drop increases. In a strong real-gas effect case, the dynamic viscosity at the channel center point can be lower than at channel wall. This phenomenon can not be found in a perfect gas flow. The real-gas effect increases the normal Reynolds stress in the wall-normal direction by 7–20% and in the spanwise direction by 10–21%, which is caused by its impact on the viscosity profile. It also increases the Reynolds shear stress by 5–8%. The real-gas effect increases the turbulence kinetic energy dissipation in the viscous sublayer and buffer sublayer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo><</mml:mo><mml:mn>30</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> but not in the outer layer. The turbulent viscosity hypthesis is checked in these two fluids, and the result shows that the standard two-function RANS model (<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ω</mml:mi></mml:math></inline-formula>) with a constant <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>C</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.09</mml:mn></mml:math></inline-formula> is still suitable in the outer layer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>></mml:mo><mml:mn>70</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, with an error in ±10%.

Unsteady phenomena at the combustor-turbine interface

The combustor-turbine interface in a gas turbine is characterised by complex, highly unsteady flows. In a combined experimental and large eddy simulation (LES) study including realistic combustor geometry, the standard model of secondary flows in the nozzle guide vanes (NGV) is found to be oversimplified. A swirl core is created in the combustion chamber which convects into the first vane passages. Four main consequences of this are identified: variation in vane loading; unsteady heat transfer on vane surfaces; unsteadiness at the leading edge horseshoe vortex, and variation in the position of the passage vortex. These phenomena occur at relatively low frequencies, from 50–300 Hz. It seems likely that these unsteady phenomena result in non-optimal film cooling, and that by reducing unsteadiness designs with greater cooling efficiency could be achieved. Measurements were performed in a high speed test facility modelling a large industrial gas turbine with can combustors, including nozzle guide vanes and combustion chambers. Vane surfaces and endwalls of a nozzle guide vane were instrumented with 384 high speed thin film heat flux gauges, to measure unsteady heat transfer. The high resolution of measurements was such to allow direct visualisation in time of large scale turbulent structures over the endwalls and vane surfaces. A matching LES simulation was carried out in a domain matching experimental conditions including upstream swirl generators and transition duct. Data reduction allowed time-varying LES data to be recorded for several cycles of the unsteady phenomena observed. The combination of LES and experimental data allows physical explanation and visualisation of flow events.

Unsteady flow phenomena in turbine shroud cavities

This paper presents those flow parameters at which coherent structures appear in the blade tip cavities of shrouded turbine blades. To the authors’ knowledge, this is reported for the first time in the open literature. The unsteady flow in a shroud cavity is analysed based on experimental data recorded in a labyrinth seal test rig. The unsteady static wall pressure in the shroud cavity inlet and outlet is measured using time-resolving pressure sensors. Sensors are located at staggered circumferential positions to allow cross-correlation between signals. The unsteady pressure signals are reduced using Fourier analysis and cross-correlation in combination with digital filters. Based on the data, a theory is formulated explaining the phenomena reflected in the measurements. The results suggest that pressure fluctuations with distinct numbers of nodes are rotating in the shroud cavity outlet. Moreover, modes with different node numbers appear to be superimposed, rotating at a common speed in circumferential direction. The pressure fluctuations are not found at all operating points. Further analysis indicates that the pressure fluctuations are present at operating points matching distinct parameters correlating with the cavity flow coefficient. Unsteady RANS simulations predict similar flow structures for the design operating point of the test rig.

Numerical validation of an analytical seal flutter model

An analytical model to describe the flutter onset of straight-through labyrinth seals has been numerically validated using a frequency domain linearized Navier-Stokes solver. A comprehensive set of simulations has been conducted to assess the stability criterion of the analytical model originally derived by Corral and Vega (2018), “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models - Part I: Theoretical Support,” ASME J. Turbomach., 140 (12), pp. 121006. The accuracy of the model has been assessed by using a simplified geometry consisting of a two-fin straight-through labyrinth seal with identical gaps. The effective gaps and the kinetic energy carried over are retained and their effects on stability are evaluated. It turns out that is important to inform the model with the correct values of both parameters to allow a proper comparison with the numerical simulations. Moreover, the non-isentropic perturbations included in the formulations are observed in the simulations at relatively low frequencies whose characteristic time is of the same order as the discharge time of the seal. This effect is responsible for the bending of the stability limit in the <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mn>0</mml:mn><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> ND stability map obtained both in the model and the simulations. It turns out that the analytical model can predict accurately the stability of the seal in a wide range of pressure ratios, vibration mode-shapes, and frequencies provided that this is informed with the fluid dynamic gaps and the energy carried over to the downstream fin from a steady RANS simulation. The numerical calculations show for the first time that the model can be used to predict accurately not only the trends of the work-per-cycle of the seal but also quantitative results.

Enabling the potential of hybrid electric propulsion through lean-burn-combustion turbofans

Hybrid-electric propulsion has emerged as a promising technology to mitigate the adverse environmental impact of civil aviation. Boosting conventional gas turbines with electric power improves mission performance and operability. In this work the impact of electrification on pollutant emissions and direct operating cost of geared turbofan configurations is evaluated for an 150-passenger aircraft. A baseline two-and-a-half-shaft geared turbofan, representative of year 2035 entry-into-service technology, is employed. Parallel hybridization is implemented through coupling a battery-powered electric motor to the engine low-speed shaft. A multi-disciplinary design space exploration framework is employed comprising modelling methods for multi-point engine design, aircraft sizing, performance and pollutant emissions, mission and economic analysis. A probabilistic approach is developed considering uncertainties in the evaluation of direct operating cost. Sensitivities to electrical power system technology levels, as well as fuel price and emissions taxation are quantified at different time-frames. The benefits of lean direct injection are explored along short-, medium-, and long-range missions, demonstrating 32% NO<italic>_x</italic> savings compared to traditional rich-burn, quick-mix, lean-burn technologies in short-range operations. The impact of electrification on the enhancement of lean direct injection benefits is investigated. For hybrid-electric powerplants, the take-off-to-cruise turbine entry temperature ratio is 2.5% lower than the baseline, extending the corresponding NO<italic>_x</italic> reductions to the level of 46% in short-range missions. This work sheds light on the environmental and economic potential and limitations of a hybrid-electric propulsion concept towards a greener and sustainable civil aviation.

Experimental and computational investigation of flow structure of buoyancy induced flow in heated rotating cavities

This paper presents Laser-Doppler Anemometry (LDA) measurements obtained from the Sussex Multiple Cavity test facility. This facility comprises a number of heated disc cavities with a cool bore flow and is intended to emulate the secondary air system flow in an H.P compressor. Measurements were made of the axial and tangential components of velocity over the respective range of Rossby, Rotational and Axial Reynolds numbers, (Ro, <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mtext>R</mml:mtext><mml:msub><mml:mtext>e</mml:mtext><mml:mi>θ</mml:mi></mml:msub></mml:math></inline-formula> and<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">R</mml:mi></mml:mrow><mml:msub><mml:mtext>e</mml:mtext><mml:mi>z</mml:mi></mml:msub></mml:math></inline-formula>),<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/></mml:mrow><mml:mn>0.32</mml:mn><mml:mo><</mml:mo><mml:mtext>Ro</mml:mtext><mml:mo><</mml:mo><mml:mn>1.28</mml:mn></mml:math></inline-formula>,<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">R</mml:mi></mml:mrow><mml:msub><mml:mtext>e</mml:mtext><mml:mi>θ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>7.1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>5</mml:mn></mml:msup></mml:math></inline-formula>, <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mn>1.2</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo><</mml:mo><mml:mrow><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">R</mml:mi></mml:mrow><mml:msub><mml:mtext>e</mml:mtext><mml:mi>z</mml:mi></mml:msub><mml:mo><</mml:mo><mml:mn>4.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup></mml:math></inline-formula> and for the values of the buoyancy parameter <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>β</mml:mi><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mtext>T</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> :<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/></mml:mrow><mml:mn>0.50</mml:mn><mml:mo><</mml:mo><mml:mrow><mml:mspace width="0.25em"/><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mtext>T</mml:mtext><mml:mo><</mml:mo><mml:mn>0.58</mml:mn></mml:math></inline-formula>. The frequency spectra analysis of the tangential velocity indicates the existence of pairs of vortices inside the cavities. The swirl number, <italic>X_k</italic>, calculated from these measurements show that the cavity fluid approaches solid body rotation near the shroud region. The paper also presents results from Unsteady Reynolds-Averaged Navier-Stokes (URANS) calculations for the test case where Ro = 0.64. The time-averaged LDA data and numerical results show encouraging agreement.

Taylor-Couette-Poiseuille flow heat transfer in a high Taylor number test rig

As technology advances, rotating machinery are operating at higher rotational speeds and increased pressures with greater heat concentration (i.e. smaller and hotter). This combination of factors increases structural stresses, while increasing the risk of exceeding temperature limits of components. To reduce stresses and protect components, it is necessary to have accurately designed thermal management systems with well-understood heat transfer characteristics. Currently, available heat transfer correlations operating within high Taylor number (above 1×10^10) flow regimes are lacking. In this work, the design of a high Taylor number flow experimental test rig is presented. A non-invasive methodology, used to capture the instantaneous heat flux of the rotating body, is also presented. Capability of the test rig, in conjunction with the use of high-density fluids, increases the maximum Taylor number beyond that of previous works. Data of two experiments are presented. The first, using air, with an operating Taylor number of 8.8± 0.8 ×10^7 and an effective Reynolds number of 4.2± 0.5 ×10^3, corresponds to a measured heat transfer coefficient of 1.67 ± 0.9 ×10^2 W/m2K and Nusselt number of 5.4± 1.5×10^1. The second, using supercritical carbon dioxide, demonstrates Taylor numbers achievable within the test rig of 1.32±0.8×10^12. A new correlation using air, with operating Taylor numbers between 7.4×10^6 and 8.9×10^8 is provided, comparing favourably with existing correlations within this operating range. A unique and systematic approach for evaluating the uncertainties is also presented, using the Monte-Carlo method.

Numerical and experimental study of droplet-film-interaction for low pressure steam turbine erosion protection applications

One common approach for anti-erosion measures in low pressure steam turbines is to equip a hollow stator vane with slots on the airfoil surface in order to remove the water film by suction and consequently reduce the amount of secondary droplets. The purpose of this paper is to build an understanding of the predominant effects in fluid-film interaction and to examine the suitability of modern numerical methods for the design process of such slots. The performance of a suction slot in terms of collection rate and air leakage is investigated numerically in a flatplate setup with upstream injection of water. In order to model the relevant phenomena (film transport, edge stripping of droplets, transport of droplets in the surrounding fluid, wall impingement of droplets) an unsteady Eulerian-Lagrangian simulation setup is applied. The accuracy of the numerical approach is assessed by comparison with experimental measurements. The comparison of four cases with the measured data demonstrates that the chosen simulation approach is able to predict the main features of film flow and interaction with the surrounding fluid. The collection rate as well as fluid film properties show the same qualitative dependency from water mass flow rate and air velocity.

Flow instability effects related to purge through a gas turbine chute seal

This paper investigates flow instabilities inside the cavity formed between the stator and rotor disks of a high-speed turbine rig. The cavity rim seal is of chute seal design. The influence of flow coefficient on the sealing effectiveness at constant purge flow rate through the wheel-space is determined. The effectiveness at different radial positions over a range of purge flow conditions and flow coefficients is also studied. Unsteady pressure measurements have identified the frequency of instabilities that form within the rim seal, phenomena which have been observed in other studies. Frequencies of these disturbances, and their correlation in the circumferential direction have determined the strength and speed of rotation of the instabilities within the cavity. Large scale unsteady rotational structures have been identified, which show similarity to previous studies. These disturbances have been found to be weakly dependent on the purge flow and flow coefficients, although an increased purge reduced both the intensity and speed of rotation of the instabilities. Additionally, certain uncorrelated disturbances have been found to be inconsistent (discontinuous) with pitchwise variation.

Impact of volumetric system design on compressor inlet conditions in supercritical CO2 cycles

The paper aims to improve the understanding of the dependency of compressor inlet conditions close to the critical point in supercritical CO₂ (sCO₂) cycles on different volumetric cycle designs. The compressor inlet conditions are fixed by the specific static outlet enthalpy of the main cooler and the static pressure determined by the mass of CO₂ in the closed cycle. While in a previous study the authors analyzed effects on the compressor inlet conditions with respect to the specific static enthalpy in the pseudocritical region for constant inlet pressure, this paper focuses on the influence of the volume of the heater and cooler. The analysis is based on experimental observations from two different experimental sCO₂ cycles, the SUSEN loop and the HeRo loop. The change of compressor inlet pressure upon change of the cooling power is substantially different and caused by the different volumetric design of the cycles. A simple model based on the volumes of the hot and cold sections in the cycle is developed to understand the dependency of compressor inlet conditions on the volumetric design. In terms of the volumetric design of the cycle, the paper will improve the knowledge of the challenges in stable compressor operation close to the critical point.