Isentropic Mach Number Distribution Research Articles

Aerodynamic Optimization Framework for a Three-Dimensional Nacelle Based on Deep Manifold Learning-Assisted Geometric Multiple Dimensionality Reduction

As a core component of an aero-engine, the aerodynamic performance of the nacelle is essential for the overall performance of an aircraft. However, the direct design of a three-dimensional (3D) nacelle is limited by the complex design space consisting of different cross-section profiles and irregular circumferential curves. The deep manifold learning-assisted geometric multiple dimensionality reduction method combines autoencoders (AE) with strong capabilities for non-linear data dimensionality reduction and class function/shape function transformation (CST). A novel geometric dimensionality reduction method is developed to address the typical constraints of nacelle parameterization. Low-dimensional latent variables are extracted from the high-dimensional design space to achieve a parametric representation of 3D nacelle manifolds. Compared with traditional parametric methods, the proposed geometric dimensionality reduction method improves the accuracy and efficiency of geometric reconstruction and aerodynamic evaluation. A multi-objective optimization framework is proposed based on deep manifold learning to increase the efficiency of 3D nacelle design. The Pareto front curves under drag divergence constraints reveal the correlation between the geometry distribution and the surface isentropic Mach number distribution of 3D nacelles. This paper demonstrates the feasibility of the proposed geometric dimensionality reduction method for direct multi-objective optimization of 3D nacelles.

Turbulence anisotropy analysis at the middle section of a highly loaded 3D linear turbine cascade using Large Eddy Simulation

This study analyzes the flow over a three-dimensional linear low-pressure turbine cascade blade using large eddy simulation at Re = 90,000. The computational model consists of one blade passage with periodic boundaries and synthetic turbulence is generated at the inlet of the domain. Various flow metrics, including isentropic Mach number distribution at mid-span and wake total pressure losses are compared with available experimental data and found to be in good agreement. A more detailed analysis of the turbulence with particular attention to the separation bubble region is subsequently presented. The analysis revealed that the turbulence is in a nearly two-component state very close to the wall region and gradually follows a certain anisotropy trajectory, as the distance from the wall increases. Even in the free-stream region no fully isotropic state is reached, due to large acceleration and flow turning. The results give a new insight into the state of turbulence within the separation region on the blade suction side and emphasize the deficiencies of the Reynolds-averaged Navier Stokes (RANS) turbulence models in reproducing the turbulence anisotropy. This insight is of relevance for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separation region.

Effect of inflow conditions on transonic turbine airfoil limit loading

To better understand airfoil limit loading and the effect inflow conditions have on local efficiency, a computational fluid dynamic investigation was performed for four different transonic turbine airfoils under sub-critical, critical, and supercritical conditions. A computational baseline was established using data previously collected at the Pratt and Whitney Canada High-Speed Wind Tunnel at Carleton University near design conditions using the Reynolds-Averaged Naiver-Stokes shear stress transport k − ω turbulence model with γ transition. The effects of inflow conditions on aerodynamic performance were examined by varying incidence by ± 20°, mainstream turbulence intensity from 5 to 20% and mainstream turbulent length scale from 1 to 100% of the airfoil pitch. Quantitative data of mass-flow averaged Mach numbers, mass-flow averaged flow angles, surface isentropic Mach number distributions and mass-flow averaged total pressure loss coefficients were collected and are presented alongside flow visualizations of numerical Schlieren images to allow for a detailed description of the entire flow domain. Similar to previous experimental work the limit loading pressure ratio and the mass-flow averaged outlet flow angle were strongly correlated with the airfoil outlet metal angle. The influence of inflow conditions was minimal on the exit flow profile with the exception of the mass-flow averaged total pressure loss coefficients. Results show incidence variation to change the total pressure loss coefficient depending on the airfoil, whereas, turbulence intensity and turbulent length scale predicted a drastic increase in loss with increased turbulence level for all airfoils considered.

Blade Envelopes Part II: Multiple Objectives and Inverse Design

AbstractBlade envelopes offer a set of data-driven tolerance guidelines for manufactured components based on aerodynamic analysis. In Part I of this two-part paper, a workflow for the formulation of blade envelopes is described and demonstrated. In Part II, this workflow is extended to accommodate multiple objectives. This allows engineers to prescribe manufacturing guidelines that take into account multiple performance criteria. The quality of a manufactured blade can be correlated with features derived from the distribution of primal flow quantities over the surface. We show that these distributions can be accounted for in the blade envelope using vector-valued models derived from discrete surface flow measurements. Our methods result in a set of variables that allows flexible and independent control over multiple flow characteristics and performance metrics, similar in spirit to inverse design methods. The augmentations to the blade envelope workflow presented in this paper are demonstrated on the LS89 turbine blade, focusing on the control of loss, mass flow, and the isentropic Mach number distribution. Finally, we demonstrate how blade envelopes can be used to visualize invariant designs by producing a 3D render of the envelope using 3D modeling software.

New approach of inverse design of transonic compressor rotor blade via prescribed isentropic Mach distributions without modification of governing equations

Shock loss is the primary source of total pressure loss of transonic axial compressors. Reducing the shock by redesigning the geometry of rotor is of great interest for turbomachinery designers. However, the complex flow field involving shock waves, shock-boundary interaction, intense secondary flows, etc., in the compressor makes the design of rotor difficult. The conventional method of design and optimization is computationally intensive and time-costly. This study introduces an inverse design method to design rotor blades corresponding to prescribed isentropic Mach number distributions with no modification of flow-governing equations. An artificial neural network is trained to predict the isentropic Mach number distributions of any deformed blades. Then, with the pattern search optimization, the blade corresponding to the prescribed isentropic Mach number distributions can be achieved. When the aerodynamic parameter database is calculated and the neural network is obtained, this method can design large numbers of blades of changed isentropic Mach number distributions immediately, without modifying the computational fluid dynamics (CFD) flow solver. The design process is fully automatic and efficient. In this study, NASA Rotor 37 is redesigned and optimized as test cases. Some analysis on the influence of blade shape on aerodynamic characteristics of the rotor is represented in this study.

High-order accurate direct numerical simulation of flow over a MTU-T161 low pressure turbine blade

Reynolds Averaged Navier-Stokes (RANS) simulations and wind tunnel testing have become the go-to tools for industrial design of Low-Pressure Turbine (LPT) blades. However, there is also an emerging interest in use of scale-resolving simulations, including Direct Numerical Simulations (DNS). These could generate insight and data to underpin development of improved RANS models for LPT design. Additionally, they could underpin a virtual LPT wind tunnel capability, that is cheaper, quicker, and more data-rich than experiments. The current study applies PyFR, a Python based Computational Fluid Dynamics (CFD) solver, to fifth-order accurate petascale DNS of compressible flow over a three-dimensional MTU-T161 LPT blade with diverging end walls at a Reynolds number of 200,000 on an unstructured mesh with over 11 billion degrees-of-freedom per equation. Various flow metrics, including isentropic Mach number distribution at mid-span, surface shear, and wake pressure losses are compared with available experimental data and found to be in agreement. Subsequently, a more detailed analysis of various flow features is presented. These include the separation/transition processes on both the suction and pressure sides of the blade, end-wall vortices, and wake evolution at various span-wise locations. The results, which constitute one of the largest and highest-fidelity CFD simulations ever conducted, demonstrate the potential of high-order accurate GPU-accelerated CFD as a tool for delivering industrial DNS of LPT blades.

A New Method for Rapid Optimization Design of a Subsonic Tandem Blade

Tandem blade technology has been developed for years due to its capacity to bear higher aerodynamics than conventional configurations. Even so, there is still the tough problem of how to design tandem blades effectively and further improve blade performance. This paper tries to further understand the flow characteristics of tandem blades in order to present a new method of designing them under subsonic inflow conditions. Firstly, efforts were made to reveal the aerodynamic interaction between the forward blade (FB) and the aft blade (AB). Secondly, considering this aerodynamic interaction, the design principles and the camber line modification method were put forward, with which typical controlled diffusion airfoil (CD airfoil) isentropic Mach number distributions can be achieved for both FB and AB. Lastly, the optimizations were conducted on a 2D tandem blade and a transonic compressor with a tandem blade, respectively. The computation fluid dynamic (CFD) results show that the optimized tandem blade achieves a significant improvement for both 2D blade performance and transonic compressor characteristics at low speeds.

Field inversion for data-augmented RANS modelling in turbomachinery flows

Turbulence modelling in turbomachinery flows remains a challenge, especially when transition and separation phenomena occur. Recently, several research efforts have been devoted to the improvement of closure models for Reynolds-averaged Navier-Stokes (RANS) equations by means of machine learning approaches which make it possible to extract the knowledge hidden inside the available high-fidelity data (from experiments or from scale-resolving simulations). In this work the use of the field inversion approach is investigated for the augmentation of the Spalart–Allmaras RANS model applied to the flow in low pressure gas turbine cascades. As a first step, the field inversion method is applied to the T106c cascade at two different values of Reynolds number (80000-250000): An adjoint-based gradient method is employed in order to minimise the prediction error on the wall isentropic Mach number distribution. The data obtained by the correction field are then analysed by means of an Artificial Neural Network (ANN) which makes it possible to generalise the correction by finding correlations which depend on physical variables. A study on the definition of the input variables and on the architecture of the ANN is performed. Different kind of corrections are evaluated and a particularly robust correction factor is obtained by limiting the range of the correction in the spirit of intermittency models. Finally, the ANN is introduced in an augmented version of the Spalart–Allmaras model which is tested on the T106c cascade (for values of the Reynolds number not considered during the training) and for the T2 cascade. The prediction ability of the method is investigated by comparing the numerical predictions with the available experimental data not only in terms of wall isentropic Mach number distribution (which was used as goal function during the field inversion) but also in terms of mass-averaged exit angle and kinetic losses.

Fan–Intake Interaction Under High Incidence

In this paper, we present an extensive numerical study on the interaction between the downstream fan and the flow separating over an intake under high incidence. The objectives of this investigation are twofold: (a) to gain qualitative insight into the mechanism of fan–intake interaction and (b) to quantitatively examine the effect of the proximity of the fan on the inlet distortion. The fan proximity is altered using the key design parameter, L/D, where D is the diameter of the intake, and L is the distance of the fan from the intake lip. Both steady and unsteady Reynolds-averaged numerical simulations (RANS) were carried out. For the steady calculations, a low-order fan model has been used, while a full 3D geometry has been used for the unsteady RANS. The numerical methodology is also thoroughly validated against the measurements for the intake-only and fan-only configurations on a high bypass ratio turbofan intake and fan, respectively. To systematically study the effect of fan on the intake separation and explore the design criteria, a simplified intake–fan configuration has been considered. In this fan–intake model, the proximity of the fan to the intake separation (L/D) can be conveniently altered without affecting other parameters. The key results indicate that, depending on L/D, the fan has either suppressed the level of the postseparation distortion or increased the separation-free operating range. At the lowest L/D (∼0.17), around a 5 deg increase in the separation-free angle of incidence was achieved. This delay in the separation-free angle of incidence decreased with increasing L/D. At the largest L/D (∼0.44), the fan was effective in suppressing the postseparation distortion rather than entirely eliminating the separation. Isentropic Mach number distribution over the intake lip for different L/D's revealed that the fan accelerates the flow near the casing upstream of the fan face, thereby decreasing the distortion level in the immediate vicinity. However, this acceleration effect decayed rapidly with increasing upstream distance from the fan-face.

Numerical investigations of separation-induced transition on high-lift low-pressure turbine using RANS and LES methods

At low Reynolds numbers, laminar-turbulent transition occurs on the suction side of high-lift low-pressure turbine blades. The prediction of this flow is an important step in low-pressure turbine design. Thus, the laminar-turbulent transition must be modeled or resolved. The flow around the high-lift low-pressure turbine blade T106C is predicted using Reynolds-Averaged Navier-Stokes (RANS) simulations, without and with transition model, and large-eddy simulations (LES). LES are performed in order to predict the laminar separation bubble (LSB) without any laminar-turbulent transition modeling. Only two Reynolds numbers are investigated with LES, and the current study concerns also the validation of the turbulent random flow generation technique of Smirnov et al. Reynolds number and freestream turbulence effects are studied using the analysis of the unsteady behavior of the separated shear layer and the bubble. The steady flow predicted by RANS simulation with transition model and by the time-averaged LES are in good agreement with isentropic Mach number distribution at mid-span, except for the lowest Reynolds number (Re2is = 80,000). For this last case, the separation and transition points are predicted downstream of the experimental points. The spectral analysis of LES results at different locations allows determining specific frequencies of physical mechanisms. LES are able to predict LSB over the high-lift low-pressure turbine blade T106C as RANS simulation with transition model and to capture the Kelvin–Helmholtz instability which is the cause of the transition mechanism.

Steady Vortex-Generator Jet Flow Control on a Highly Loaded Transonic Low-Pressure Turbine Cascade: Effects of Compressibility and Roughness

A new high-speed linear cascade has been developed for low-pressure turbine (LPT) studies at The Ohio State University. A compressible LPT profile is tested in the facility and its baseline performance at different operating conditions is assessed by means of isentropic Mach number distribution and wake total pressure losses. Active flow control is implemented through a spanwise row of vortex-generator jets (VGJs) located at 60% chord on the suction surface. The purpose of the study is to document the effectiveness of VGJ flow control in high-speed compressible flow. The effect on shock-induced separation is assessed by Mach number distribution, wake loss surveys and shadowgraph. Pressure sensitive paint (PSP) is applied to understand the three dimensional flow and shock pattern developing from the interaction of the skewed jets and the main flow. Data show that with increasing blowing ratio, the losses are first decreased due to separation reduction, but losses connected to compressibility effects become stronger due to increased passage shock strength and jet orifice choking; therefore, the optimum blowing ratio is a tradeoff between these counteracting effects. The effect of added surface roughness on the uncontrolled flow and on flow control behavior is also investigated. At lower Mach number, turbulent separation develops on the rough surface and a different flow control performance is observed. Steady VGJs appear to have control authority even on a turbulent separation but higher blowing ratios are required compared to incompressible flow experiments reported elsewhere. Overall, the results show a high sensitivity of steady VGJs control performance and optimum blowing ratio to compressibility and surface roughness.

Predicting High-Lift Low-Pressure Turbine Cascades Flow Using Transition-Sensitive Turbulence Closures

This paper discusses the application of different transition-sensitive turbulence closures to the prediction of low-Reynolds-number flows in high-lift cascades operating in low-pressure turbine (LPT) conditions. Different formulations of the well known γ-R˜eθt model are considered and compared to a recently developed transition model based on the laminar kinetic energy (LKE) concept. All those approaches have been coupled to the Wilcox k-ω turbulence model. The performance of the transition-sensitive closures has been assessed by analyzing three different high-lift cascades, recently tested experimentally in two European research projects (Unsteady Transition in Axial Turbomachines (UTAT) and Turbulence and Transition Modeling for Special Turbomachinery Applications (TATMo)). Such cascades (T106A, T106C, and T108) feature different loading distributions, different suction side diffusion factors, and they are characterized by suction side boundary layer separation when operated in steady inflow. Both steady and unsteady inflow conditions (induced by upstream passing wakes) have been studied. Particular attention has been devoted to the treatment of crucial boundary conditions like the freestream turbulence intensity and the turbulent length scale. A detailed comparison between measurements and computations, in terms of blade surface isentropic Mach number distributions and cascade lapse rates will be presented and discussed. Specific features of the computed wake-induced transition patterns will be discussed for selected Reynolds numbers. Finally, some guidelines concerning the computations of high-lift cascades for LPT applications using Reynolds-averaged Navier–Stokes (RANS)/unsteady RANS (URANS) approaches and transition-sensitive closures will be reported.

Aerodynamic inverse design optimization for turbine cascades based on control theory

Based on control theory, adjoint system for the general problem of turbomachinery aerodynamic optimization was studied and developed in the present paper by using the variation technique in the grid node coordinates combined with Jacobian Matrics of flow fluxes. Then the adjoint system for aerodynamic design optimization of turbine cascade governed by compressible Navier-Stokes equations was derived in detail. With the purpose of saving computation resources, the mathematic method presented in this paper avoids the coordinate system transforming in the traditional derivation process of the adjoint system and makes the adjoint system much more sententious. Given the general expression of objective functions consisting of both boundary integral and field integral, the adjoint equations and their boundary conditions were derived, and the final expression of the objective function gradient including only boundary integrals was formulated to reduce the CPU cost, especially for the complex 3D configurations. The adjoint system was solved numerically by using the finite volume method with an explicit 5-step Runge-Kutta scheme and Riemann approximate solution of Roe’s scheme combined with multi-grid technique and local time step to accelerate the convergence procedure. Finally, based on the aerodynamic optimization theory in the present work, 2D and 3D inviscid and viscous inverse design programs of axial turbomachinery cascade for both pressure distribution and isentropic Mach number distribution on the blade wall were developed, and several design optimization cases were performed successfully to demonstrate the ability and economy of the present optimization system.

Multidisciplinary Optimization of a Turbocharger Radial Turbine

This paper presents a multidisciplinary design optimization of a turbocharger radial turbine for automotive applications with the aim to improve two major manufacturer requirements: the total-to-static efficiency and the moment of inertia of the radial turbine impeller. The search for the best design is constrained by mechanical stress limitations, by the mass flow and power, and by aerodynamic constraints related to the isentropic Mach number distribution on the rotor blade. The optimization of the radial turbine is performed with a two-level optimization algorithm developed at the von Karman Institute for Fluid Dynamics. The system makes use of a differential evolution algorithm, an artificial neural network (ANN), and a database as a compromise between accuracy and computational cost. The ANN performance predictions are periodically validated by means of accurate steady state 3D Navier-Stokes and centrifugal stress computations. The results show that it is possible to improve the efficiency and the moment of inertia only in a few numbers of iterations while limiting the stresses to a maximum value. Based on the large number of evaluated designs during the optimization, this paper provides design recommendations of a turbocharger radial turbine at least for a good preliminary design.

One-pitch passage designed inversely with a single blade for cascade experiments

A linear cascade experimental apparatus often consists of only a few cascade blades. Advantages to this experimental arrangement are increased by the use of larger cascade blades, a lower mass flow rate, a corresponding decrease in required power, and easier optical access within the cascade passage. However, fewer cascade blades in the cascade row make it difficult to establish periodic flow conditions between blades compared to infinite cascade model experiments. Generally, removing fluid from the cascade walls or adjusting tailboards located downstream of the cascade are common methods to establish periodic flow conditions through the cascade blades. In this study, a passage for cascade experiments is designed to satisfy infinite cascade flow conditions without any flow control or tailboards. A one-pitch at cascade row is adopted as its width and only a single cascade blade is installed within the passage. The surface isentropic Mach number distribution on the blade is chosen for the existence of infinite cascade flow conditions, and 14 geometric design variables related to the passage shape are applied to the design of a one-pitch passage by using a genetic algorithm. Flow structures within a passage designed using a genetic algorithm match with those obtained with the infinite cascade flow condition. Computed results obtained with a single cascade blade show that infinite cascade flow conditions can be obtained by modifying only the passage walls of the cascade experimental apparatus.

An inverse design of a double-pitch passage for an infinite cascade model experiment

In this study, sidewalls of a turbine cascade experimental apparatus are designed to satisfy periodic flow conditions with two blades without any flow control or tailboards. Generally, the turbine cascade experimental apparatus needs removing fluid from the cascade walls or adjusting tailboards located downstream of the cascade to establish periodic flow conditions through the cascade blades. If a linear turbine cascade often consists of only a few blades within a passage, advantages to this experimental arrangement are increased from using larger turbine cascades, a lower mass flowrate and corresponding decrease in required power, and easier optical access within the cascade passage. However, fewer blades in the cascade make it difficult to establish periodic flow conditions between blades compared to infinite cascade flow conditions. In order to test a turbine cascade with a few blades without flow control devices, only two turbine blades are installed within a double-pitch passage. Sidewall shape is designed with 12 geometric design variables using a gradient-based optimization method, and surface isentropic Mach number distribution on the blades is chosen for the existence of periodic flow conditions. The computed result shows periodic flow conditions obtained by modifying only the sidewalls of the double-pitch passage as a cascade experimental apparatus.

Separation and Transition Control on an Aft-Loaded Ultra-High-Lift LP Turbine Blade at Low Reynolds Numbers: High-Speed Validation

This paper presents the second part of an investigation of the combined effects of unsteadiness and surface roughness on an aft-loaded ultra-high-lift low-pressure turbine (LPT) profile at low Reynolds numbers. The investigation has been performed using low- and high-speed cascade facilities. The low- and high-speed profiles have been designed to have the same normalized isentropic Mach number distribution. The low-speed results have been presented in the first part (Zhang, Vera, Hodson, and Harvey, 2006, ASME J. Turbomach., 128, pp. 517–527). The current paper examines the effect of different surface finishes on an aft-loaded ultra-high-lift LPT profile at Mach and Reynolds numbers representative of LPT engine conditions. The surface roughness values are presented along with the profile losses under steady and unsteady inflow conditions. The results show that the use of a rough surface finish can be used to reduce the profile loss. In addition, the results show that the same quantitative values of losses are obtained at high- and low-speed flow conditions. The latter proves the validity of the low-speed approach for ultra-high-lift profiles for the case of an exit Mach number of the order of 0.64. Hot-wire measurements were carried out to explain the effect of the surface finish on the wake-induced transition mechanism.

Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model

A new transonic turbine cascade model that accurately produces infinite cascade flow conditions with minimal compressor requirements is presented. An inverse design procedure using the Favre-averaged Navier-Stokes equations and k‐ε turbulence model based on the method of steepest descent was applied to a geometry consisting of a single turbine blade in a passage. For a fixed blade geometry, the passage walls were designed such that the surface isentropic Mach number (SIMN) distribution on the blade in the passage matched the SIMN distribution on the blade in an infinite cascade, while maintaining attached flow along both passage walls. An experimental rig was built that produces realistic flow conditions, and also provides the extensive optical access needed to obtain detailed particle image velocimetry measurements around the blade. Excellent agreement was achieved between computational fluid dynamics (CFD) of the infinite cascade SIMN, CFD of the designed double passage SIMN, and the measured SIMN.

Three-dimensional calculations of the flow field around a turbine blade with film cooling injection near the leading edge

Injection of coolant air from a showerhead injection system at the leading edge of a high pressure turbine blade is investigated using a fully implicit three-dimensional finite-volume method on multi-block grids. For various blowing rates, the calculation results for the velocity and pressure fields and turbulence intensity are compared with available experimental data. The present method yields excellent agreement with the experiments for the isentropic Mach number distributions on the blade surface. The standardk–e turbulence model with wall functions is already capable of capturing the major details of the flow field including the injection-induced secondary-flow vortices, particularly so on the suction side. On the pressure side, however, the lateral jet spreading is under-predicted somewhat together with an exaggeration of the near-wall sink-flow vortices. On this side with convex walls, where turbulence anisotropy is appreciable according to the experiments, overall better predictions were obtained with the anisotropy correction of Bergeles et al. [23] promoting the Reynolds stress in the lateral direction. The correction has no beneficial effect on the suction side with concave walls where the turbulence anisotropy was observed to be much smaller.

Calculation of the Flow around a High-Pressure Turbine Blade with Cooling-Jet Injection from Slots at the Leading Edge

A fully vectorised, basically three-dimensional finite-volume multi-block method for flows with complex boundaries is applied in a stripped-down two-dimensional version for the investigation of the flow field in the leading-edge region of a high-pressure turbine blade with slot cooling-jet injection. The calculation results are compared with experiments and the numerical results of other investigators. The present method yields excellent agreement with the experiments for the isentropic Mach number distributions on the blade surface. All numerical results for the velocity field were found to be in very good agreement with each other and with experiments on the suction side, while the agreement is not as good on the pressure side.