Favre-Averaged Fourier-Based Methods for Gas Turbine Flows

2019 ◽  
Author(s):  
Feng Wang ◽  
Luca di Mare ◽  
Paolo Adami
Keyword(s):  
Gas Turbine ◽  
Linear Time ◽  
Computational Cost ◽  
Navier Stokes ◽  
Design Stage ◽  
Mean Flow ◽  
Non Linear ◽  
Time Marching ◽  
Turbine Design ◽  
Turbomachinery Design

Abstract Steady Reynolds-Averaged Navier-Stokes (RANS) simulations are the workhorse of turbomachinery design. Recent trends in gas turbine design require full consideration of flow unsteadiness at the design stage to address issues of performance as well as integrity. Unsteady calculations using non-linear time marching methods are too computationally expensive to be used at the design stage. An alternative way is needed to reduce computational cost whilst retaining control on the accuracy of the simulations. To address this need, this paper presents a framework of Fourier-based methods for turbomachinery flows. The method is based on the non-linear harmonic (NLH) method. The method uses the favourable properties of Favre-averaging to obtain a simpler and more flexible formulation of the time-averaged system for NLH. This is ideal for implementing NLH in a CFD code where minimum modifications are desired. The approach allows the fidelity of the simulations to be tuned by switching on or off the coupling between the flow perturbations and the mean flow or the cross-coupling among the harmonics. This leads to a range of modelling fidelity for unsteady flows. For example, if the unsteady flow is linear, a linear harmonic method is sufficient for the design instead of using a harmonic balance simulation which has extra computational cost and slower convergence. The method has been tested on compressors and turbines which covers gas turbine flows in a range of flow regimes. Good agreement with data from non-linear time marching simulations are observed for all cases.

scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

Numerical Study of Deterministic Fluxes in Compressor Passages

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Feng Wang ◽  
Mauro Carnevale ◽  
Luca di Mare
Keyword(s):  
High Speed ◽  
Numerical Study ◽  
Navier Stokes ◽  
Design Stage ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Radial Profiles ◽  
And Performance ◽  
Stage Matching ◽  
Unsteady Effects

Computational fluid dynamics (CFD) has been widely adopted in the compressor design process, but it remains a challenge to predict the flow details, performance, and stage matching for multistage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and unsteady RANS (URANS) calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious values of flow quantities (e.g., whirl angle). The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore, the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS mixing plane solutions. The magnitudes of divergence of Reynolds stresses (RS) and deterministic stresses (DS) are compared. The effect of deterministic fluxes is demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes is also observed. The effect of deterministic fluxes is confirmed via the nonlinear harmonic (NLH) method which includes the deterministic fluxes in the mean flow, and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

Unsteady RANS Analysis of Particles Deposition in the Coolant Channel of a Gas Turbine Blade Using a Non-Linear Model

2014 ◽  
Author(s):  
Domenico Borello ◽  
Paolo Capobianchi ◽  
Marco De Petris ◽  
Franco Rispoli ◽  
Paolo Venturini
Keyword(s):  
Gas Turbine ◽  
Turbine Blade ◽  
Solid Particles ◽  
Navier Stokes ◽  
Internal Cooling ◽  
Gas Turbine Blade ◽  
Two Phase ◽  
Cooling Channels ◽  
Non Linear ◽  
Elliptic Relaxation

The two-phase flow in a geometry representing the final portion of the internal cooling channels of a gas turbine blade is here presented and discussed. In the configuration under scrutiny, the coolant flows inside the duct in radial direction and it leaves the blade through the trailing edge after a 90 deg turning. An unsteady Reynolds Averaged Navier-Stokes (URANS) simulation of the flow inside such channel was carried out. An original non-linear version of the well-established ζ-f elliptic relaxation model was developed and applied here. The new model was implemented in the well-validated T-FlowS code currently developed by the authors’ group at Sapienza Università di Roma. The predictions demonstrated a good accuracy of the non-linear URANS model, clearly improving the results of the baseline linear ζ-f model and of the Launder Sharma k-ε model used as reference. The obtained unsteady flow field was adopted to track a large number of solid particles released from several selected sections at the inlet and representing the powders usually dispersed (sand, volcanic ashes) in the air spilled from the compressor and used as cooling fluid. The well-validated particle-tracking algorithm here adopted for determining the trajectories demonstrated to be very sensitive to the flow unsteadiness. Finally, the fouling of the solid surfaces was estimated by adopting a model based on the coefficient of restitution approach.

scholarly journals Three Dimensional Time-Marching Inviscid and Viscous Solutions for Unsteady Flows Around Vibrating Blades

1993 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Thin Layer ◽  
Stokes Equations ◽  
Linear Time ◽  
Correction Method ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Blade Passage ◽  
Time Marching ◽  
Viscous Solutions

A 3-dimensional non-linear time-marching method of solving the thin-layer Navier-Stokes equations in a simplified form has been developed for blade flutter calculations. The discretization of the equations is made using the cell-vertex finite volume scheme in space and the 4-stage Runge-Kutta scheme in time. Calculations are carried out in a single-blade-passage domain and the phase-shifted periodic condition is implemented by using the shape correction method. The 3-D unsteady Euler solution is obtained at conditions of zero viscosity, and is validated against a well-established 3-D semi-analytical method. For viscous solutions, the time-step limitation on the explicit temporal discretization scheme is effectively relaxed by using a time-consistent two-grid time-marching technique. A transonic rotor blade passage flow (with tip-leakage) is calculated using the present 3-D unsteady viscous solution method. Calculated steady flow results agree well with the corresponding experiment and with other calculations. Calculated unsteady loadings due to oscillations of the rotor blades reveal some notable 3-D viscous flow features. The feasibility of solving the simplified thin-layer Navier-Stokes solver for oscillating blade flows at practical conditions is demonstrated.

scholarly journals Cooling Air Flow in a Multi Disc Industrial Gas Turbine Rotor

1998 ◽  
Author(s):  
D. Brillert ◽  
A. W. Reichert ◽  
H. Simon
Keyword(s):  
Simple Model ◽  
Gas Turbine ◽  
Boundary Layers ◽  
Mass Flow ◽  
Radial Flow ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Mean Flow ◽  
Flow Through ◽  
Secondary Air

The objective of this paper is to investigate the secondary air system in a multidisc rotor. The investigation was performed using Navier-Stokes calculations, network modeling and measurements taking into account new test data from Siemens’ Model V84.3A gas turbine prototype. The objective of the investigation was to better the understanding of flow patterns and to generate a simple model for describing mean flow values. The flow patterns predicted on the basis of Navier-Stokes calculations are described and the losses associated with fluid flow through rotating cavities of multidisc rotors are evaluated. High losses are generated in the radial flow through the corotating discs, and this investigation therefore concentrates on this flow. The investigated mass flowrates are relatively high when compared with the mass flow naturally transported on rotating discs (Cw > 105). One part of the mass flow is forced to flow along the boundary layers. The other part is transported outside of the boundary layers like a free potentially inviscid flow. On the basis of the investigation of the Navier Stokes-calculations, a simple analytical model of the radial flow through the corotating discs is developed. Good agreement was found to exist between the experimental data and the results of the simple model.

Application of Machine Learning in Turbulent Combustion for Aviation Gas Turbine Combustor Design

2021 ◽  
Author(s):  
Vishwas Verma ◽  
Kiran Manoharan ◽  
Jaydeep Basani
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Flow Field ◽  
Gas Turbine ◽  
Computational Cost ◽  
Data Driven ◽  
Navier Stokes ◽  
Computational Time ◽  
Reacting Flow ◽  
Data Driven Approach

Abstract Numerical simulation of gas turbine combustors requires resolving a broad spectrum of length and time scales for accurate flow field and emission predictions. Reynold’s Averaged Navier Stokes (RANS) approach can generate solutions in few hours; however, it fails to produce accurate predictions for turbulent reacting flow field seen in general combustors. On the other hand, the Large Eddy Simulation (LES) approach can overcome this challenge, but it requires orders of magnitude higher computational cost. This limits designers to use the LES approach in combustor development cycles and prohibits them from using the same in numerical optimization. The current work tries to build an alternate approach using a data-driven method to generate fast and consistent results. In this work, deep learning (DL) dense neural network framework is used to improve the RANS solution accuracy using LES data as truth data. A supervised regression learning multilayer perceptron (MLP) neural network engine is developed. The machine learning (ML) engine developed in the present study can compute data with LES accuracy in 95% lesser computational time than performing LES simulations. The output of the ML engine shows good agreement with the trend of LES, which is entirely different from RANS, and to a reasonable extent, captures magnitudes of actual flow variables. However, it is recommended that the ML engine be trained using broad design space and physical laws along with a purely data-driven approach for better generalization.

scholarly journals Global analysis of Navier–Stokes and Boussinesq stochastic flows using dynamical orthogonality

2013 ◽  
Vol 734 ◽  
pp. 83-113 ◽  
Author(s):  
T. P. Sapsis ◽  
M. P. Ueckermann ◽  
P. F. J. Lermusiaux
Keyword(s):  
Global Analysis ◽  
Computational Cost ◽  
Fluid Flows ◽  
Projection Methods ◽  
Navier Stokes ◽  
Mean Flow ◽  
Field Equations ◽  
Stochastic Fluctuations ◽  
Low Dimensionality ◽  
Orthogonal Field

AbstractWe provide a new framework for the study of fluid flows presenting complex uncertain behaviour. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal field equations. By numerically solving these equations, we evolve in a fully coupled way the mean flow and the statistical and spatial characteristics of the stochastic fluctuations. This set of equations is formulated for the general case of stochastic boundary conditions and allows for the application of projection methods that considerably reduce the computational cost. We analyse the transformation of energy from stochastic modes to mean dynamics, and vice versa, by deriving exact expressions that quantify the interaction among different components of the flow. The developed framework is illustrated through specific flows in unstable regimes. In particular, we consider the flow behind a disk and the Rayleigh–Bénard convection, for which we construct bifurcation diagrams that describe the variation of the response as well as the energy transfers for different parameters associated with the considered flows. We reveal the low dimensionality of the underlying stochastic attractor.

Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach

2000 ◽  
Author(s):  
T. Chen ◽  
P. Vasanthakumar ◽  
L. He
Keyword(s):  
Stokes Equations ◽  
Linear Time ◽  
Three Dimensional ◽  
Axial Flow ◽  
Interaction Effects ◽  
Navier Stokes ◽  
Linear Interaction ◽  
Blade Row ◽  
Non Linear ◽  
Blade Row Interaction

An efficient non-linear harmonic methodology has been developed for predicting unsteady blade row interaction effects in multistage axial flow compressors. Flow variables are decomposed into time averaged variables and unsteady perturbations, resulting in time averaged equations with deterministic stress terms depending on the unsteady perturbation. The non-linear interaction between the time averaged flow field and the unsteady perturbations are included by a simultaneous pseudotime integration approach, leading to a strongly coupled solution. The stator/rotor interface treatment follows a flux averaged characteristic based mixing plane approach and includes the deterministic stress terms due to upstream running potential disturbances and downstream running wakes, resulting in the continuous nature of all parameters across the interface. The basic computational methodology is applied to the three-dimensional Navier-Stokes equations and validated against several cases. Results show that this method is much more efficient than the non-linear time-marching methods while still modeling the nonlinear unsteady blade row interaction effects.

Numerical Study of Deterministic Fluxes in Compressor Passages

2018 ◽  
Author(s):  
Feng Wang ◽  
Mauro Carnevale ◽  
Luca di Mare
Keyword(s):  
High Speed ◽  
Numerical Study ◽  
Navier Stokes ◽  
Design Stage ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Multi Stage ◽  
Radial Profiles ◽  
Stage Matching ◽  
Unsteady Effects

Computational Fluid Dynamics (CFD) has been widely adopted at the compressor design process, but it remains a challenge to predict the flow details, performance and stage matching for multi-stage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and URANS calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious mixed-out variables, e.g. whirl angle. The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS solutions. The magnitude of divergence of Reynolds stresses and deterministic stresses are compared. The effect of deterministic fluxes are demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes are also observed. The effect of deterministic fluxes are confirmed via the non-linear harmonic method which includes the deterministic fluxes in the mean flow and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

Unsteady Methods to Investigate Inlet Distortion in a Transonic Tail Cone Thruster Fan Stage With Boundary Layer Ingestion

2020 ◽  
Author(s):  
Ritangshu Giri ◽  
Mark G. Turner ◽  
Mark L. Celestina
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Aerodynamic Performance ◽  
Navier Stokes ◽  
High Fidelity ◽  
Accurate Analysis ◽  
Inlet Distortion ◽  
Fuel Burn ◽  
Time Marching ◽  
Turbomachinery Design

Abstract Boundary Layer Ingestion (BLI) engines have the potential to offer significantly reduced fuel burn, but the fan stage must be designed to run efficiently with a distorted inflow. It must also be able to withstand unsteady aerodynamic loads resulting from a non-uniform flowfield. In a multidisciplinary turbomachinery design cycle involving such a complicated flowfield, high fidelity numerical solutions are required. Two high fidelity unsteady Reynolds Averaged Navier-Stokes (URANS) methods for accurate analysis of a Tail Cone Thruster (TCT) transonic fan stage subjected to inlet distortion have been implemented. They are frequency domain based non-linear harmonic (NLH) and full-annulus complete time domain based time marching methods. This paper demonstrates that the relevant parameters required to accurately compute aerodynamic performance of a fan stage in distorted conditions can be accurately modelled with a few harmonics using the NLH method in a fraction of time compared to the full annulus time marching method. However, the complete aerodynamics of distortion transfer across different blade rows of a fan stage can only be analyzed using the time marching solution. Several physical mechanisms which govern the fan response to an inlet distortion and how different distortion profiles impact the aerodynamic performance of this fan stage are also explained.

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