Evaluation of CFD Methods for Prediction of Total Temperature and Total Pressure Distribution in Gas Turbines

Master of Science Thesis

KTH School of Industrial Engineering and Management Energy Technology TRITA-ITM-EX 2019:439

Division of Heat and Power SE-100 44 STOCKHOLM

Evaluation of CFD Methods for

Prediction of Total Temperature and

Total Pressure Distribution in Gas

Turbines

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Master of Science Thesis TRITA-ITM-EX 2019:439

Evaluation of CFD Methods for Prediction of Total Temperature and Total Pressure Distribution in

Gas Turbines

Lars Fredrik Wahlgren Approved

20190801 Examiner Björn Laumert Supervisor Jens Fridh Commissioner

Siemens Industrial Turbomachinery AB Contact person Ken Flydalen

Abstract

This thesis work was performed as a collaboration between the Royal Institute of Technology in Stockholm and Siemens Industrial Turbomachinery in Finspång. It was undertaken with the purpose of investigating the use of CFD methods in ANSYS CFX to predict flow mixing in gas turbines.

The results were evaluated against experimental data gathered as part of an international collaboration; The FACTOR project. The experimental data investigated were total temperature and total pressure at nozzle guide vane inlet and outlet.

The results thus focus mainly on nozzle guide vane inlet and outlet due to the nature of the available experimental data.

The distribution of these parameters was also investigated in the NGV flow channel and on the vane surface, but it is appreciated that any conclusions drawn from these results are speculative in nature due to the lack of experimental data. Any conclusions drawn must be placed in perspective of the evaluation of NGV inlet and outlet, for which experimental data is available.

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Sammanfattning

Detta examensarbete utfördes som ett samarbete mellan KTH i stockholm och Siemen Industrial Turbomachinery i Finspång. Det undertogs med syftet att undersöka användning av CFD-metoder i ANSYS CFX för att förutspå flödesmixning i gasturbiner.

Resultaten utvärderades mot experimentel data som samlats genom ett internationellt samarbete: FACTOR-projektet. Den experimentella data som undersökts var totaltemperatur och totaltryck vid in- och utloppet till ett statorblad.

Resultaten fokuserar huvudsakligen vid in- och utlopp till statorbladed på grund av den tillgängliga experimentella datan. Distributionen av totaltemperatur och totaltryck mellan dessa plan undersöktes också, men det måste lyftas att alla slutsatser som dras av dessa resultat är till någon grad spekulativ på grund av tillgängliga datans natur. Alla slutsatser som dras härutav måste utvärderas i samband med den tillgängliga datan.

Det huvudsakliga focuser låg vid mixningen av totaltemperature och totaltryck i ett statorbland anslutet till en brännkammarsimulator. De undersöka metoderna var RANS-SST, SBES och LES-WALE.

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Acknowledgements

I would like to begin by thanking Jens Fridh and Ken Flydalen for giving me the opportunity to do this master’s thesis work. I could not have hoped for a more interesting subject, a better end to my student life and a better start to my career.

During the course of the work my supervisors at Siemens Industrial Turbomachinery, Arman Farhanieh and Navid Mikaillian, have proven invaluable in providing their support and expertise, thank you.

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Table of Contents

Abstract ... 2 Sammanfattning ... 3 Acknowledgements ... 4 Table of Contents ... 5 Nomenclature ... 6 1 Introduction ... 7 1.1 Literature Study ... 7 1.2 Objectives ... 10 1.3 Methodology ... 10 1.4 Limitations ... 10

1.5 Benefits, Ethics & Sustainability ... 11

2 Theoretical Background ... 12 2.1 Gas Turbines ... 12 2.2 CFD ... 14 3 Experimental setup ... 18 4 Numerical setups ... 20 4.1 Domain ... 20 4.2 Mesh ... 20 4.3 Boundary Conditions ... 24 4.4 General settings ... 26 4.5 RANS – SST ... 26

4.6 SBES and LES-WALE ... 27

4.7 Y+ ... 27

5 Results ... 28

5.1 Total temperature and total pressure contours ... 28

5.2 Circumferential averages ... 37

5.3 Streamwise temperature distribution ... 41

5.4 NGV cooling velocity lines ... 44

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Nomenclature

Abbreviations

CFD – Computational Fluid Dynamics LE – Leading Edge

LES-WALE – Large Eddy Simulation - Wall-Adapting Local Eddy-viscosity HRSG – Heat Recovery Steam Generator

ISO – International Standard Organization (15 degree and 1 atm ambient conditions) NGV / V – Nozzle Guide Vane / Vane

RANS – Reynolds-Averaged Navier-Stokes RMS – Root Mean Square

RTR / B – RoToR / Blade TE – Trailing Edge

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1 Introduction

The global power production faces great changes in the near future. The balance between renewable, reliable and financially viable power generation is a multifaceted problem, and the potential solutions are hotly debated.

Although current gas turbine technology is mainly based on fossil fuel, the use of natural gas allows for relatively clean fossil fueled power production, and through CHP plants a high net efficiency of close to 60% can be reached (Siemens, 2019). Add in the possibility of running gas turbines on pure hydrogen, the technology holds the potential for clean and fully renewable power generation (Cappelletti & Martelli, 2017). Gas turbines play a vital role in current power generation in a wide variety of energy systems, among others as a reliable supply of power where connection to a main power grid is unfeasible, such as for off shore oil rigs as well as to handle peak power demand in national power grids.

Computational Fluid Mechanics in turn play a significant part in the design process, used together with empirical studies to validate the design choices at an early stage, before costly and time-consuming production has begun.

As CFD is a fairly young field, having its roots in the mid-20th _{century, much is still developing, in particular}

due to the fast development of computational power. This means that continuous evaluation and development of these tools and methods are required.

Ansys CFX is an established CFD software tool used in gas turbine design, and was the main tool used during this project.

The aim of this thesis was to evaluate current methods for modelling the total temperature and total pressure distribution in gas turbines. The evaluation was done against experimental data gathered during the FACTOR project. The FACTOR project (short for Full Aerothermal Combustor Turbine interactiOns Research) is a joint effort EU project aimed to increase knowledge regarding the design of turbines. Specifically, it aims to increase the understanding of combustion chamber and turbine interactions (Wucherpfennig & Krumme, 2017).

1.1 Literature Study

The literature study is divided into two sections, one detailing previous work performed at or in collaboration with Siemens, and which this thesis is a direct continuation of, as well as a section detailing other relevant work. These are named internal and external work respectively.

1.1.1 Internal work

This report is a continuation of the work of several other reports, the most relevant of which are detailed below.

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To evaluate the SAS cases an initial RANS-SST case was run. These results are presented here to act as an evaluation background, see Figure 1 and Figure 2 (Faba, 2018). Plane 41 refers radial-circumferential plane located directly behind the nozzle guide vane (Figure 9).

Figure 1: Total temperature, Plane 41, RANS (Faba, 2018)

Figure 2: Total Pressure, Plane 41, RANS (Faba, 2018)

A report written during the spring semester of 2018 evaluated a number of different turbulence models for steady RANS: the k-ε, the Wilcox k-ω and the Menter SST k- ω (Hallbäck, 2018).

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There were however differences in the magnitude of the error between the examined turbulence models. Particularly it is noted that the poor performance of the SST model could be caused by an underutilization of the k-epsilon model due to the setup (Hallbäck, 2018).

The report written by Hallbäck evaluated mainly total temperature of plane 41 and 42 (see chapters regarding Experimental setup, page 18). For this reason, the results for plane 41 will be used in this report for comparison. Plane 41 refers radial-circumferential plane located directly behind the nozzle guide vane (Figure 9).

Figure 3: Total temperature results for several RANS setups (Hallbäck, 2018)

1.1.2 External work

This section details relevant studies not undertaken at Siemens Industrial Turbomachinery.

A report titled ‘Numerical investigation of fluid flow parameters in a combustor simulator’ highlights the problems in predicating temperature distributions in gas turbines and the resulting need for a large safety factor in turbine cooling, reducing the performance of the turbine. A combustor simulator was investigated in ANSYS CFX using RANS-SST, SAS-SST and LES-WALE SGS turbulence models. The subsequent results are evaluated against empirical data provided by the FACTOR project. The conclusions of this report were that neither steady nor unsteady RANS is capable of accurately predicting the experimental flows, but that the SAS and LES models show much greater potential. It is noted that SST k-omega turbulence models underpredict the mixing resulting in high temperature gradients at combustor exits (Barhaghi, 2018). Another report, ‘Integrated large eddy simulation of combustor and turbine interactions: Effect of turbine stage inlet condition’, which also uses the FACTOR test rig as the basis of its CFD domain as well as for experimental evaluation, focuses on the effects of the nozzle guide vane inlet conditions by studying the effects of combustor integration as compared to the same mean inlet conditions applied directly to the nozzle guide vane. The LES method with Smagorinsky turbulence modelling is used, and the report concludes that the temperature distribution for both stator and rotor passages and blade walls are significantly impacted by these conditions. It is argued that a main cause is a lack of turbulence injection into the NGV passage when the combustion simulator is not modelled (Duchaine, et al., 2017).

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Hybrid RANS-LES models are investigated in an effort to mitigate the known limitations of pure RANS methods as well as the computational load of pure LES methods. Also undertaken as part of the FACTOR project, this report only investigates the combustor simulator and concludes that the hybrid method investigated shows promise for future work that could include the nozzle guide vane in the domain, as the mixing and temperature distribution in the combustor was greatly affected (Andreini, et al., 2016).

1.2 Objectives

The objective of this study is to evaluate the modelling methods used to predict total temperature and total pressure distributions in gas turbines, specifically regarding combustor chamber and first turbine stage. The goal will be to add to the existing body of knowledge and to present the necessary simulation results for RANS-SST, SBES and LES-WALE methods to be able to adequately evaluate the effects of the inclusion of the combustion chamber for steady RANS-SST, as well as to compare these to results acquired from the transient Scale Resolving Simulation methods SBES and LES-WALE.

The specific objectives are set as:

 Evaluate the effects of inclusion of the combustion chamber simulator for steady RANS-SST with regards to mixing of the total temperature and total pressure in a radial-circumferential plane, and as a circumferential average.

 Compare and evaluate the main discrepancies between transient simulations and steady RANS-SST for two sets of transient methods:

o SBES o LES-WALE

1.3 Methodology

The procedure of this project is iterative in nature. The steps being; Meshing, Simulation setup, Simulation, Evaluation.

After evaluation of the results any weakness in the setup is identified and adjustments made, either to the mesh or to the simulation setup, and the process repeated. The evaluations are ultimately done against experimental data, with the desire to achieve a higher fidelity to this empirical data when compared to earlier simulations. Earlier simulations refer to both those performed during the course of this project and other projects (see Literature study).

A focus is put on the mixing of the main hot flow with the cooling flows, and the main parameters investigated were total temperature and total pressure at nozzle guide vane inlet and outlet.

The mesh was created in ICEM CFD and the simulations performed in ANSYS CFX.

1.4 Limitations

This report lacks an in-depth mesh sensitivity study. The results were evaluated continuously according to business practice and expertise along the way, and two separate meshes were evaluated for the RANS-SST case. This however remains a limitation in the results of the study.

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Several of the investigated CFD methods are computationally heavy, and easily become time-consuming. This limits the amount of cases that can be simulated over the course of time limited project such as this. An obvious limitation is the unprecise nature of current generation CFD methods, being the very focus of this study. However, since the results are evaluated specifically for their predictive accuracy, this limitation needs to be addressed.

The two combustor simulator meshes used were provided and thus the creation of them was outside the scope of this project. This means no direct control was possible of these meshes.

1.5 Benefits, Ethics & Sustainability

Even though current gas turbines operate mainly on fossil fuels, and assuming a pressing need to abandon such fuels on a larger scale, there are both environmental and social arguments for pursuing research in these areas.

All fields of engineering operating with turbomachinery stands to gain from advances in CFD modelling in this field. Such fields include but are not limited to; freshwater and wastewater handling as well as vast majority of power generation, such as nuclear, wind and hydro power. This is especially valid due to this report’s connection to the FACTOR project, a collaborative effort undertaken by several universities and companies operating in different fields.

When considering fuels themselves, large parts of the world will still be dependent on fossil energy sources for the foreseeable future, and amongst these fuel sources natural gas has lower levels of pollution and CO2 emissions when compared to for instance coal.

Certain current gas turbines operate with a mixture of fossil fuels and hydrogen, and future technology holds the potential of 100% hydrogen fuel turbines. This creates the potential for a clean, renewable and reliable power generation.

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2 Theoretical Background

This chapter details the most relevant concepts underlying this report.

2.1 Gas Turbines

Gas turbines are a type of airbreathing combustion engines. The most common uses include the production of electricity in power plants and thrust in aircraft. They differ from the more commonly known piston engines (seen in most private vehicles) by not using a reciprocating motion, but rather continuous rotation to extract energy from the working fluid.

2.1.1 Brayton cycle

Gas turbines typically operate under an open Brayton Cycle. In the most general case (Figure 4), air at ambient conditions enters the compressor where its temperature and pressure is raised through compression. Fuel is burned and the heat increases the temperature further. The air, now mixed with combustion products, enters the turbine where the work is extracted by lowering the temperature and pressure, and finally the gas is exhausted (Moustapha, et al., 2003).

Figure 4: Overview of simple gas turbine system (Farhanieh, 2015)

In the ideal Brayton cycle (Figure 5) the system is closed, and the steps are in turn:  Isentropic compression (1 → 2)

 Constant-pressure heat addition (2 → 3)  Isentropic expansion (3 → 4)

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Figure 5: Ideal Brayton cycle (Farhanieh, 2015)

2.1.1.1 Brayton cycle efficiency

The thermal efficiency of the ideal Brayton cycle (Figure 5) is expressed as

𝜂_𝑡ℎ=𝑤𝑜𝑟𝑘𝑛𝑒𝑡 ℎ𝑒𝑎𝑡𝑖𝑛 = 1 −ℎ𝑒𝑎𝑡𝑜𝑢𝑡 ℎ𝑒𝑎𝑡𝑖𝑛 =𝑐𝑝(𝑇4− 𝑇1) 𝑐𝑝(𝑇3− 𝑇2) = 1 − 𝑇₁(𝑇4 𝑇₁− 1) 𝑇_b(𝑇_𝑇3 2− 1) (2.1)

Where 𝑐𝑝 is the specific heat capacity of the operating medium, and T is temperature.

Since the ideal Brayton cycle is adiabatic, the temperature-pressure relation for an adiabatic reversible process can be used

𝑃 ₄ 𝑃₃ = 𝑃₁ 𝑃₂ ⇔ ( 𝑇₄ 𝑇₃) 𝛾 𝛾−1 = (𝑇1 𝑇₂) 𝛾 𝛾−1 (2.2)

and thus the Brayton cycle efficiency can be expressed using 𝛾 as the ratio of specific heats as

𝜂_𝑡ℎ = 1 − 1 (𝑃_𝑃2 1) 𝛾 𝛾−1 (2.3)

As can be seen there is clear dependency of the efficiency on the pressure ratio. This leads directly to the desire to increase the 𝑃2 which in turn increases 𝑇2 and finally 𝑇3. This is the Turbine Inlet Temperature

-14- 2.1.2 Vane cooling

As mentioned in the previous section, the highest temperature in the turbine is the Turbine Inlet Temperature (TIT). This temperature is limited by the material of the combustor as well as the first stage turbine blades (Moustapha, et al., 2003).

Even with advances in materials such as with single-crystal blades and ceramic coatings, current gas turbines operate at a higher temperature and stress than these materials can withstand. The way this is addressed is by introducing cooling airflows at several places in the turbine. One example is directly to the blades by a method called film cooling. This film cooling works by directing cool air into the blades and out into the passage through small holes in the blades (Figure 6) creating the protective film covering the blade from which the name comes from. However, since this cooling air is drawn for the turbine itself, the cooling is associated with losses, approximately 1% cooling air drawn engine air flow results in 1% increase in specific fuel consumption. The cooling air drawn be as high as 30% of engine air flow when multiple blade rows demand cooling (Moustapha, et al., 2003).

As such, the vane cooling and the degree to which it is mixed with the main flow is a major factor influencing the temperature distribution within a turbine.

Figure 6: Vane cooling streamlines

2.2 CFD

Computational Fluid Dynamics uses a wide variety of numerical methods to simulate fluid flow, heat transfer and other phenomena connected to the flow of certain parameters. These methods are developed in large part to circumvent current computer limitations, as direct numerical simulations (DNS) for any but the most limited scenarios lead to impossibly long computation times (Versteeg & Malalasekera, 2007).

Many CFD methods work by dividing the investigated domain into a grid (also known as mesh), after which all the relevant physical phenomena and fluid properties are defined. Boundary conditions are set to give a reference framework from which calculation can be performed. The solution can now be calculated at each connecting node of this grid or mesh structure (Versteeg & Malalasekera, 2007).

-15- 2.2.1 FVM: Finite Volume Method

The FVM works by dividing a domain into a number of volumes. This is done by placing several nodal points over the relevant geometry, around which arbitrary volumes are created with interfaces midway in-between adjacent points (Versteeg & Malalasekera, 2007).

The relevant differential equations are now discretized over the volumes (Versteeg & Malalasekera, 2007). An advantage of the FVM is the direct discretization of the conservation laws regarding mass, momentum and energy. This leads to the conservation of these properties in this method.

2.2.2 The Navier-Stokes equations

The Navier-Stokes equations are a set of differential equations that describe fluid motion for incompressible Newtonian fluids. These are in essence Newtons second law regarding conservation of momentum applied to a three-dimensional fluid flow (Munson, et al., 2013). With 𝜌 being density, u being velocity, p being pressure and t being time these equations can be expressed as

𝜌 (𝛿𝑢 𝛿𝑡 + 𝛿𝑢 𝛿𝑥+ 𝛿𝑢 𝛿𝑦+ 𝛿𝑢 𝛿𝑧) = − 𝛿𝑝 𝛿𝑥+ 𝜌𝑔𝑥+ ( 𝛿2_𝑢 𝛿𝑥2+ 𝛿2_𝑢 𝛿𝑦2+ 𝛿2_𝑢 𝛿𝑧2) (2.4) 𝜌 (𝛿𝑣 𝛿𝑡 + 𝛿𝑣 𝛿𝑥+ 𝛿𝑣 𝛿𝑦+ 𝛿𝑣 𝛿𝑧) = − 𝛿𝑝 𝛿𝑦+ 𝜌𝑔𝑦+ ( 𝛿2_𝑣 𝛿𝑥2+ 𝛿2_𝑣 𝛿𝑦2+ 𝛿2_𝑣 𝛿𝑧2) (2.5) 𝜌 (𝛿𝑤 𝛿𝑡 + 𝛿𝑤 𝛿𝑥+ 𝛿𝑤 𝛿𝑦+ 𝛿𝑤 𝛿𝑧) = − 𝛿𝑝 𝛿𝑧+ 𝜌𝑔𝑧+ ( 𝛿2_𝑤 𝛿𝑥2 + 𝛿2_𝑤 𝛿𝑦2 + 𝛿2_𝑤 𝛿𝑧2) (2.6)

It is known that these equations are too complex for analytical solutions in most cases as they are non-linear second-order partial differential equations, and direct numerical calculation quickly become too time-consuming for current generation computers in all but the simplest cases (Munson, et al., 2013).

2.2.3 RANS: Reynolds Average Navier-Stokes

The Reynolds Averaged Navier-Stokes equation, as the name implies solves the Navier-Stokes equation by Reynolds-averaging. The most commonly used Reynolds-averaging for turbulence modelling is time-averaging, here in its most recognizable form with 𝜇 being the dynamic viscosity and S being the mean rate of strain 𝜌∂𝑈𝑖 ∂t + 𝜌𝑈𝑗 ∂Ui ∂𝑥𝑗 = −∂P ∂xi + ∂ ∂xj (2𝜇𝑆𝑗𝑖− 𝜌𝑢𝑗′𝑢𝑖′) (2.7)

This equation gives rise to the Reynolds-stress tensor

𝜏𝑖𝑗= −𝜌𝑢𝑗′𝑢𝑖′ (2.8)

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Turbulence is a probabilistic flow phenomenon that involves highly random eddies that manifest over a wide range of scales (Wilcox, 2006). Figure 7 illustrates smoke that as it rises transitions from laminar flow with parallel flow lines, to a turbulent flow with clearly visible eddies of varying sizes.

Due to the complex and random nature of turbulence, accurately solving these fluctuations comes at a high computational cost, and it is these fluctuations that are the physical explanation of the Reynolds stresses mentioned in the previous section (Menter, 2012).

Figure 7: Laminar-turbulent transition (Settles, 2009)

2.2.5 Turbulence models

“An ideal turbulence model should introduce the minimum amount of complexity while capturing the essence of the relevant physics.” (Wilcox, 2006, p. 2).

Many turbulence models have been developed, among these are the k-ε, the k-ω and the Johnson and King (JK) models. These models all have their strengths and weaknesses, for instance the k-ε had poor handling of boundary layer flows, whereas the k-ω model improved accuracy for boundary layers and instead had weaknesses in the modeling of the free stream (Menter, 2009). The JK model was created specifically to for the solving of turbulent boundary layer flows (CFD Online, 2019).

The Shear Stress Transport (from here on SST) model was introduced in the mid 90s to address the need for turbulence model that could adequately handle recent developments in the field, such as increases in processing power (enabling external 3D aerodynamics) as well as developments in meshing with unstructured grids (Menter, 2009).

The goal of the SST model was to combine the strengths of earlier models, namely the k-ε, k-ω and the JK models to achieve an accurate prediction of boundary layer behavior in flows experiencing adverse pressure, even included a small amount of separation (Menter, 2009).

2.2.6 SRS: Scale Resolving Simulation

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2.2.6.1 LES: Large Eddy Simulation

LES is a Scale Resolving method and thus separates the large and small eddy structures and handles them in separate ways as described above. As such it only fully solves turbulence above a certain length scale and models the rest, this is done by applying a low-pass filter to the Navier-Stokes equations. The reasoning being that large eddy structures are geometry dependent, whereas small eddies have a universal character model (Versteeg & Malalasekera, 2007).

2.2.6.2 DES: Detached Eddy Simulation

DES was created in an attempt to improve the accuracy of turbulence models in separated regions. It is a hybrid approach combining RANS with LES, using RANS for the main flow and switching to LES where the flow has detached. Thus combining the strengths of both models, the accuracy of LES with the lesser computational costs of RANS (Menter, 2012).

2.2.6.3 SBES: Stress-Blended Eddy Simulation

The SBES model family is a hybrid RANS-LES setup. It has superseded the DES model family in ANSYS CFX and was developed to address a weakness regarding the shielding of the attached boundary layers from the impact of the RANS zones. As SBES is a function that combines two different existing models, it is not classified as a turbulence model in itself. As a result of SBES there is a faster transition and a clearer distinction between the RANS and LES zones, meaning the RANS boundary layers are protected from influence from the LES parts of the flow, as compared with the DES models. This leads to more accurate solutions.

2.2.6.4 LES-WALE: Wall-adapted local eddy-viscosity model

WALE is a relatively simple LES model that has the benefit of being able to provide zero viscosity for laminar shear flows, an issue that is present in the more widely used Smagorinsky model. The importance of this functionality lies in flows with a laminar turbulent transition, where the lack thereof would negatively impact the laminar flow. This addresses the issue in industrial CFD applications where complex models put a high demand on computational power (Menter, 2012).

2.2.7 Law of the Wall and y+

The Law of the Wall identifies an important behavior for fluid flow near walls in that its velocity varies logarithmically with the distance to the wall. A general equation describing this relationship was found by normalizing the axis representing the velocity and the distance to the wall into u+ and y+ respectively as

𝑢+₌ 𝑢 𝑢_𝜏, 𝑦 +₌𝑦𝑢𝜏 𝜈 (2.9) where 𝑢_𝜏=𝜏𝑤 𝜌 (2.10) is the shear or friction velocity, being a measurement of the shear stress in units of velocity.

The dimensionless wall constant, or y+, is an important parameter for evaluation of the mesh. In sublayer (y+ < 5) the law of the wall is described by a linear relationship

𝑢+_{= 𝑦}+ _(2.11)

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3 Experimental setup

The empirical data was gathered as a part of the FACTOR project and was outside the scope of this project. The experimental setup will however be described below due to its vital role in the evaluation of the CFD results.

The FACTOR test rig features a non-reacting combustor simulator, using compressed and dried air heated to about 250 degrees Celsius to simulate combustion products (Wucherpfennig & Krumme, 2017). This enables the combustor and vane to be investigate as a unit and the usage of sensors that would not be practical in real combustion environment (Wucherpfennig & Krumme, 2017).

The rig (Figure 8) features a setup with 40 NGVs, 60 RTR blades and 20 LPVs. The combustor airflow is swirled to emulate real combustor flows (Faba, 2018).

Figure 8: FACTOR Project Test rig (Wucherpfennig & Krumme, 2017)

3.1.1 Geometry

The main results focus on the total temperature and the total pressure of plane 40 and plane 41 of the factor test rig. Plane 40 acts as the interface between the combustion chamber and the nozzle guide vane, plane 41 in turn is the interface between NGV and RTR (Krumme, 2017).

-19- 3.1.2 Measuring setup

The measurements were taken with a pneumatic 5-hole-probe (Figure 10) equipped with a single front-facing thermocouple which is shown as a red dot in Figure 10. The probe was calibrated before each measurement by making contact with the hub wall at full extension, this to compensate for length changes in the probe arm caused by temperature changes. The measurements were taken in a radial-tangential coordinate system (Scherman & Krumme, 2017).

Figure 10: 5-hole-probe (Scherman & Krumme, 2017)

The 5-hole-probe is sensitive to Mach number variations in the flow, and was therefore calibrated at 6 different intervals between Mach 0.1 and 0.9. A specialized calibration device with a nozzle designed for minimal losses and a highly controlled jet was developed. The same calibration device was used for total temperature calibrations. The tests showed that errors were within 3% for total pressure and 2% for total temperature (Bacci, 2017).

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4 Numerical setups

The following sections details the methods used to generate the results of the project.

4.1 Domain

The domain investigated (Figure 11) corresponds to a section of the FACTOR test rig (Figure 9 Meridional view of FACTOR test rig with numbered planes, modified from ). More precisely a single combustion chamber and two nozzle guide vanes. To this an outlet box was added that does not correspond to any physical feature of the rig. This outlet box was added to allow the simulated flow to stabilize after the nozzle guide vane and avoid any effects at the domain outlet to influence the results.

Figure 11: Overview of domain

4.2 Mesh

Two already existing meshes was provided for the combustion chamber, one coarser and one finer. The meshing performed by the author of this report was done in ICEM CFD 18.0.0 (nozzle guide vane and outlet box). ICEM CFD was used due to the high degree of control it gives the user when creating the mesh. The general steps taken when generating a mesh in ICEM CFD for this project were:

1. Import geometry 2. Generate surface mesh

a. Repair surface mesh b. Smooth surface mesh 3. Generate Volume mesh

a. Smooth volume mesh 4. Generate Prism mesh

-21- 4.2.1 NGV: Nozzle Guide Vane

The mesh was created from an available negative volume model of the first vane and channel. The model included cooling channels and cooling pins.

Figure 12: Negative volume model of first vane and channel

The nozzle guide vane was duplicated in order for the flow to be able to simulate one full periodic section of combustion chamber and nozzle guide vanes. Periodic surfaces were created on the channel boundaries adjacent to the outermost pressure and section side of the nozzle guide vanes to minimize the computational power needed by avoiding modelling several wanes in the same stage.

An initial patch independent surface mesh using triangle elements was created. A mesh quality of greater than 0.5 was strived form, where mesh quality is a normalized value ranging from 0 at poor quality, and 1 at high quality. An effort was made to manually remove all bad mesh elements that might cause non-convergence.

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Figure 13: Mesh prism layer

To decrease the computational load for the transient simulations (SBES and LES-WALE) a coarser nozzle guide vane mesh was created by increase the size outlet surface mesh and remeshing the volume mesh. The same process was used to create the prism layer as for the initial nozzle guide vane mesh.

Figure 14: NGV mesh, fine (a), coarse (b)

4.2.2 CC: Combustion Chamber

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simulations, the lower element count mesh was later adopted for the second RANS case as well as the SBES and LES simulations.

(a) (b) Figure 15: CC mesh, fine (a), coarse (b)

4.2.3 Outlet box

The outlet box acts a stand-in for the HPR to allow the flow to stabilize after the NGV and thereby avoid any effects from the domain outlet to influence upstream flow.

For mesh iteration 1 (see Table 1) the outlet box was created by extruding the NGV outlet to a total length of 4 cm over 24 layers in the axial direction using same-sized elements. For mesh iteration 2 (see Table 2) the outlet box instead has a two-part design, initially with exponentially growing mesh length in the axial direction, followed by same-sized mesh elements. Due to the aforementioned increase in the nozzle guide vane outlet surface element size, the second outlet box also feature larger elements in the radial-tangential directions. This was done to further reduce the element count and in turn the computational load.

-24- 4.2.4 Mesh iteration 1

The initial mesh was used for RANS case 1 and several rejected transient cases. The reason for abandoning this initial mesh was due to computation demand for transient SBES resulting in unreasonable simulation times, as well as convergence problems in transient LES.

Table 1: Mesh iteration 1, amount of sections, nodes and elements

Section Amount Nodes elements

Combustion

Chamber 1 10 000 309 57 319 176

NGV 2 12 813 564 29 905 144

NGV Outlet box 2 189 525 288 240

4.2.5 Mesh iteration 2

Initial results indicate that it is difficult to combine the demand for grid resolution with the computational limitations. The high mesh count resulted in the need for an unreasonably small time-step. An initial attempt was made to address this problem by increasing the size of the NGV outlet surface mesh and the outlet box element size in the radial-tangential directions. This however was unsuccessful.

More drastic measures were taken. The overall NGV mesh size was increased by 20%. A significantly rougher CC mesh was made available. This addressed the computational demand of the mesh. The savings in mesh elements was used to create a longer outlet box, addressing the issues of reversed flow.

The second mesh attempts to address the computational demand by significantly reducing the size of the combustion chamber mesh as well as the outlet box.

The aforementioned convergence problems in transient LES runs was argued to be due to a drastically increasing CFL number near V1 outlet. This increase in CFL number was argued to be due to the turning of the flow at the NGV resulting in the flow crossing the rather long and narrow outlet box element from an unfavourable direction. To counteract this, the outlet box elements were double in area size in the radial-tangential plane.

Table 2: Mesh iteration 2, amount of sections, nodes and elements

Section Amount Nodes elements

Combustion

Chamber 1 3 853 278 20 896 497

NGV 2 11 789 299 28 267 343

NGV Outlet box 2 63 319 88 286

4.3 Boundary Conditions

The same boundary conditions were used for all sections respectively for the different scenarios.

-25-

Table 3) boundary conditions were set as a single mass flow and temperature value for the whole surface, whereas the outer and inner cavity feeds defined mass flux and temperature over a large number of holes for each region respectively (Figure 17). All inlet flows were defined as flat profiles.

Figure 17: Inner cavity feed (a) and outer cavity feed (b)

Table 3: Boundary conditions - Inlets Type Section Position Name Mass flow

[normalized] Total Temperature [normalized] Inlet Combustion

chamber 1 Main inlet 0.614 1

2 Outer cavity feed 0.186 0.5813 3 Inner cavity feed 0.129 0.5813 NGV1 4 Upstream coolant feed 0.048 0.5820 5 Downstream coolant feed 0.023 0.5820

Table 4: Boundary conditions - Outlets Type Section Position Data Outlet Outlet box exit at

plane 41 6 Radial average of static pressure

Airflow enters the domain at several locations. Hot air enters through the CC main inlet, and cooling air flows through several separate locations; through two cavity feeds connected to the CC, and two separate feeds of the nozzle guide vanes, terminating in many small cooling holes on the vane surface. See

-26-

Figure 18: Domain with numbered positions

4.4 General settings

All simulations used Air Ideal Gas to best correspond to the dried and heated air used by the FACTOR test rig. All boundaries corresponding to physical walls was set to have a smooth wall roughness with a no-slip condition, since wall are designed for minimal friction loss but boundary layers still exist and impact the flow. Otherwise a free slip wall condition was set. Heat transfer was set to adiabatic for all cases since heat loss is assumed to be negligible for these circumstances. The reference pressure was set to 0 atm. The buoyancy model was set to Non Buoyant since buoyancy will not be a main influence on flow effects. Since the domain contained no rotating parts the domain motion was set to Stationary. All cases used the total energy heat transfer setting, which includes the kinetic energy effects. This was used in accordance to recommendations in the Ansys CFX documentation for Mach numbers exceeding 0.3 (Ansys, 2019).

4.5 RANS – SST

Both RANS-SST were identical except for the mesh used. The second RANS case being used to evaluate the effects of the coarser mesh on a steady state simulation before moving on to the transient simulations; SBES and LES.

The SST turbulence model was used with automatic wall function. A RANS simulation was initially run with upwind advection scheme, the results of which was used to initialize the RANS case 1 whereas RANS case 2 used the RANS case 1 results. Bot RANS case 1 and 2 used the high resolution advection scheme. Turbulence intensity was set to Medium (5%).

4.5.1 Convergence criteria

Both RANS cases were considered converged when RMS residuals of momentum, heat transfer, turbulence kinetic energy and turbulence frequency had stabilized at around 1 ∗ 10−5_{. The domain outlet mass flow}

-27-

4.6 SBES and LES-WALE

The SBES and LES-WALE case shared all the basic settings with the RANS cases, and mesh with RANS case 2.

Before starting the time averaging of transient parameters it is a common practice to allow for 5-10 complete flow-throughs, computed as

𝑡_{𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑝𝑎𝑠𝑠} = 𝑉

𝑚̇∗ 𝜌 = 9,131 ∗ 10

−3 _{[𝑠] (4.1)}

Combining this with a timestep of

10−5 𝑠 (4.2) Combining this with a timestep of 10−5 _{𝑠 results in 4566 timesteps, rounded to 5000 steps, or 0.05 s, before}

averaging is started.

4.7 Y+

The y+ plus value was investigated to check that the mesh has achieved a desired refinement at the first prism layer. This was done in CFX investigating only two vanes with outlet boxes.

The y+ values in cooling channels and cooling holes, as well as on blade surfaces was generally below 1 and always below 3. Certain areas on hub and shroud reached a y+ of no larger than 4, this was deemed acceptable. As a result of the coarser mesh created to address to convergence issues with the LES case, the y+ value was improved to below 3 for all areas of the NGV (Figure 19).

-28-

5 Results

In the results the RANS case 1, RANS case 2, SBES and LES-WALE will be referred to as RANS1, RANS2, SBES and LES respectively for ease of reading. In result figures the SBES and LES case will also be referred to as the SBES1 and LES1 case, respectively.

The main results are presented in two types of figures. Figure 20 to Figure 38 plots the distribution of total temperature and total pressure as contours, whereas Figure 42 to Figure 50 show total temperature and total pressure in as a circumferential average with respect to radius.

To this are added several figures showing hot and cold streaks, vane cooling streamlines and vane temperature to assist the analyses of the impact the mixing in the simulated results. It must be considered that the experimental data available only validates the mixing of total temperature and total pressure at plane 40 and plane 41, as such any conclusions drawn from these additional figures must be seen in the context of the main results. To reiterate, plane 40 and plane 41 refers to the inlet and the outlet of the NGV respectively, see Figure 9.

Initially an overview of the general flow trends is given with the help of the radial-circumferential plane to present an intuitive introduction to the results and visualize the mixing of the flow. This is followed by a short analysis of the circumferentially averaged results for each simulated case.

For the radial-circumferential plots the scale is the same for all cases for a specific plane and parameter. This is set to the most preferable parameter interval for the measured data to highlight the differences between the simulations and the measurements. The exception is the temperature difference plots shown on the right for all cases, here the scale is set for each case individually. This was done due to the relatively small and varying nature of these parameter intervals.

5.1 Total temperature and total pressure contours

-29-

Figure 20: Experimental data of Total Temperature at Plane 40

Figure 21: RANS1 data of Total Temperature and Temperature Difference at Plane 40

-30-

Figure 23: SBES1 data of Total Temperature and Temperature Difference at Plane 40

-31-

Considering the total pressure, a good correspondence to the main trends can be found, though with a prominent undermixing of the total pressure parameter. The only noticeable exception is the LES case (Figure 29) which predicts both a lower maximum and minimum total pressure, resulting in plot which more accurately resembles the experimental data with exception of a lower minimum pressure located in the swirl.

Figure 25: Experimental data of Total Pressure at Plane 40

Figure 26: RANS1 data of Total Pressure and Pressure Difference at Plane 40

-32-

Figure 28: SBES1 data of Total Pressure and Pressure Difference at Plane 40

-33-

At plane 41 there is a larger discrepancy in the general mixing trends than was observed at plane 40. It is interesting to note that the righthand passage’s character changes significantly between the two RANS cases (Figure 31 and Figure 32), the major difference in setup being the coarser combustion chamber. The SBES1 case (Figure 33) shows a similar flow pattern to the RANS1 case, which can be explained by the similarity of these cases at plane 40, with the effects of these trends traveling downstream to plane 41. This can be seen as a degree of verification that the changes done to NGV mesh did not significantly impact the results. The LES case (Figure 34) show no significant difference to the SBES case.

Figure 30: Experimental data of Total Temperature at Plane 41

Figure 31: RANS1 data of Total Temperature and Temperature Difference at Plane 41

-34-

Figure 33: SBES1 data of Total Temperature and Temperature Difference at Plane 41

-35-

The total pressure simulations for plane 41 (Figure 36 to Figure 39) show no significant differences to each other, and all cases manage to capture the general trends with a high accuracy.

Figure 35: Experimental data of Total Pressure at Plane 41

Figure 36: RANS1 data of Total Pressure and Pressure Difference at Plane 41

-36-

Figure 38: SBES1 data of Total Pressure and Pressure Difference at Plane 41

-37-

5.2 Circumferential averages

An effort is made to keep color and type of line choice consistent throughout the plots to facilitate reading. For instance, measured data is show as a black whole line in all figures, the RANS1 case a red short-dashed line for all figures and so on.

To give an easier overview all circumferentially averaged results are combined into four separate figures, one for each plane and parameter (Figure 50 to Figure 61).

Individual plots, showcasing the results for each parameter and method for each plane separately can be found in Appendix A, and these will be referenced when discussing the results of the separate cases as compared to the experimental data. However, all relevant results can also be found in the four figures below, Figure 40 to Figure 43.

Figure 40: All cases, circumferential temperature average, Plane 40

Figure 41: All cases, circumferential pressure average, Plane 40 220 230 240 250 260 270 280 320 370 420 470 Radius [mm] Total Temperature [K]

Total Temperature at Plane 40

Combined

Measured RANS1 RANS2 SBES1 LES1 220 230 240 250 260 270 280 142000 143000 144000 145000 146000 147000 Radius [mm]

Total Pressure [Pa]

-38-

Figure 42: All cases, circumferential temperature average, Plane 41

Figure 43: All cases, circumferential pressure average, Plane 41

5.2.1 RANS Case 1

Even with the inclusion of the combustion chamber simulator, the mixing of the flow was underpredicted, and the temperature distributions achieved are similar to earlier results. It can be seen that the general shape of the flow resembles the empirical data, however the maximum and minimum temperatures are exaggerated.

At plane 40 (Figure 50) the highest total temperature discrepancies are found near the hub and shroud. The hub in particular showed the highest deviation, with a close to 100 K temperature difference, with the measured temperature being approximately 30% higher than the simulated.

240 245 250 255 260 265 270 275 280 360 380 400 420 440 460 Radius [mm] Total Temperature [K]

Total Temperature at Plane 41

Combined

Measured RANS1 RANS2 SBES1 LES1 240 245 250 255 260 265 270 275 280 118000 123000 128000 133000 138000 143000 Radius [mm]

Total Pressure [Pa]

-39-

Total temperature at plane 41 (Figure 51) instead shows a very close match at hub and shroud, with discrepancies arising away from the walls. The general pattern with two high temperature spots for the measurements at radius 272 mm and 250 mm appears to be shifted downwards for RANS1 case. These hot spots also appear exaggerated, indicative of an underpredicted flow mixing, the most significant discrepancy arising at a radius of 245 mm. Here the temperature differs approximately 28 K or 7.5%.

The total pressure for RANS1 at plane 40 (Figure 41) shows a high accuracy with respect to the general shape of the temperature distribution. With a slight overprediction of the total pressure at all points. It should be noted that this overestimation of the total pressure is only about 1.5% where greatest, at a radius of 230 mm.

The total pressure for RANS1 at plane 41 (Figure 43) captures the general characteristic of the measured data, with a few caveats. Most noticeably the sharp increase in the measured temperature near the hub, although it can be questioned if this is due to some error in the measured data. The maximum difference is ca 2% in the detached flow, and at maximum ca 3.8% in the boundary layer, at a radius of 277 mm.

5.2.2 RANS Case 2

The RANS2 case features the coarser CC mesh. This significantly impacted the mixing of the flow when viewed as circumferential average, indicating a strong mesh dependence of these results. Here too the general distribution of total temperature is captured but with significantly lower hub and shroud temperatures and a higher mid passage temperature. The greatest underestimation of temperature was at the hub wall with 54 K, or 12.4%. The highest overestimation of temperature was at a radius 255 mm with 35 K, or 7.6% (Figure 40Figure 54).

At plane 41, similar to the RANS1 case, there is a general down-shifting of the general trend in a radial direction for the total temperature (Figure 55), although here there is greater underestimation of the hub and shroud temperatures. The two hotspots in the measured data are also less pronounced.

Similar to the RANS1 case, the total pressure at plane 40 is captured with a high accuracy. The exception being the shroud pressure deviating from the general pattern, but instead being highly accurate when compared to the measured data (Figure 56).

The total pressure for RANS2 at plane 41 captures the general characteristic of the measured data near exactly to the RANS1 case. As such the maximum difference is ca 2% in the detached flow, and at maximum ca 3.8% in the boundary layer, at a radius of 277 mm.

5.2.3 SBES

The total temperature for the SBES case for plane 40 shows some improvement in the mixing as compared to the RANS cases. Particularly the near shroud temperature shows good match with the experimental data. Above a radius of 250 mm, approximately mid passage, there is a slight overprediction of the total temperature of around 10 to 20 K. Below the same radius there is a slight underprediction of the total temperature, the greatest difference arising at the hub wall, with a underprediction of the total temperature with about 44 K, or 11% (Figure 40).

The total temperature for the SBES case for plane 41 shows some improvement in the mixing overall, in particular the temperature near both hub and shroud closely match the experimental data (Figure 59). As with both RANS cases, the total pressure at plane 40 is simulated with only a very slight overprediction, also capturing the general trend accurately (Figure 60).

-40- 5.2.4 LES-WALE

The LES-WALE case shows a good match to the earlier SBES data. Similarly the near shroud temperature show good match with the experimental data. Above a radius of 250 mm, approximately mid passage, there is a slight overprediction of the total temperature of around 10 to 20 K. Below the same radius there is a slight underprediction of the total temperature, the greatest difference arising at the hub wall, with a underprediction of the total temperature with about 44 K, or 11% (Figure 58).

Similar as for the SBES case the total temperature results for the LES1 case at plane 41 shows a good match to the experimental data near the hub and shroud (Figure 63).

The total pressure at plane 40 for the LES case show an exceptionally good match. The largest discrepancy is at a radius of 234 mm where the total pressure is overestimated by less than 1% (Figure 64).

-41-

5.3 Streamwise temperature distribution

The figures below show hot and cold flow migration over the NGV for all cases. On set of figures illustrate a constant temperature of 465 K (Figure 44) and one 345 K (Figure 45). These temperatures were arbitrarily chosen to give a sense of the distribution of temperatures in the flow channel.

As can be seen the two RANS cases features iso-surfaces that spread out more into the flow channel than the SBES and LES case. Both for the hot and cold flow migration. This is in line with what would be expected if a higher degree of mixing has been achieved, as we must move further into the centralized hot spot to reach a certain hot temperature, and further out into the cooling to reach cool temperature. This result is supported by the transient average for the planes where experimental data exists for verification.

-42-

Figure 45: Cold flow migration, NGV, 345 K, (a) RANS1, (b), RANS2, (c) SBES, (d) LES

The following figures illustrate the temperature distribution in a meridional view, set mid-passage between the two NGV. The temperature scale is set between the minimum and maximum temperature of domain, representing the main inlet and cooling flows temperatures respectively (Figure 46).

-43-

Figure 46: Total temperature, meridional view, (a) RANS1, (b) RANS2, (c) SBES, (d) LES

The following figures illustrate the total temperature distribution in a circumferential plane at approximately mid radius (Figure 47). Here the impact of the differences in mixing becomes apparent. Comparing the two RANS (Figure 47 a and b) cases to the SBES (Figure 47 c) and LES case (Figure 47 d), it becomes apparent that the two later cases show a significant increase in mixing. The general trend being that the flow nearest the NGV is warmer, and the main hot streak is cooler. This is in line with the mixing trend observed in Figure 46.

-44-

Figure 47: Circumferential NGV total temperature distribution at mid radius

5.4 NGV cooling velocity lines

-45-

-46-

5.5 NGV temperature

Figure 49 illustrates the NGV surface temperatures for all cases. These figures demand some extra attention since the NGV temperature is one of the main limiting factors gas turbines, and one of the main underlying reasons for the desire to develop more accurate predictive methods for flow mixing.

This figures clearly demonstrate the effects of the observed mixing. The SBES (Figure 49 c) and LES case (Figure 49 d) show a more even temperature distribution, with less pronounced cold and hotspots when compared to the two RANS cases (Figure 49 a and b).

Figure 49: NGV surface temperature, (a) RANS1, (b) RANS2, (c) SBES, (d) LES

-47-

For the RANS2 case the increase in temperature can attributed to the higher temperature observed at the leading edge, which in turn can be attributed to wider spreading of the hot flow as observed in Figure 47 (b). For the SBES and LES case the higher degree of mixing is attributed, as this has been seen to increase the near wall temperatures for both the SBES and LES case at plane 40 in particular.

Table 5: Average NGV temperature

Case: Area Average of temperature [K] Fraction of RANS1 [1]

RANS1 359.763 1

RANS2 374.624 1.041

SBES 375.456 1.044

-48-

6 Discussion

The findings point to the difficulty of combining the need for a necessary physical and temporal resolution. The desire of a satisfactory physical resolution demands a finer mesh, this however places increasing demands on a shorter time-step, demanding ever increasing computational power.

The mixing problem experienced in RANS simulations are shown to be mitigated by including the combustion chamber when compared to results from other work (Figure 3: Total temperature results for several RANS setups ). However, care must be taken to not end up with a mesh that prohibits the necessary convergence, especially for the transient cases. This is highly problem specific, both with regards to the domain and physics resolved, but also with regards to computational power and real-time available for the project.

A source of error for this work is the lack of an extensive mesh sensitivity study. Two different mesh setups, one fine and one significantly coarser, were investigated in RANS cases 1 and 2 respectively, and the coarser mesh was later used for the SBES and LES cases. When viewing the effects of the coarser mesh on the plane 40 total temperature and total pressure, the effects were not clear and showed both minor increases and decreases in accuracy. As only the coarser combustor mesh was investigated for the SBES and LES case, these have no corresponding results for the fine mesh, and can only be compared to the results for the RANS case when investigating the effects of the coarser mesh. Here the SBES and LES case showed a general improvement. For plane 41 the effects of the course NGV and outlet box were also unclear, here the total temperature for the RANS1, SBES and LES all showed a similar flow pattern while the RANS2 case deviated from the other cases.

Even with coarser mesh the SBES and LES simulation resulted in generally improved mixing when compared to the RANS1 case. Due to the similarity between the SBES and LES case, and the known tendency of LES to produce significantly better results, it cannot be ruled out that the coarser combustor mesh impacts the SBES and LES results negatively. This also highlights the need of a proper mesh sensitivity study.

-49-

7 Conclusion

At plane 40 the results show a clear undermixing of the flow with regards to total temperature for all cases. With regards to the circumferentially averaged results, all cases show too high mid-passage temperatures and too low hub temperatures. At the shroud, both RANS cases predicts to low total temperature, while the SBES and LES manages to accurately predict the total temperature.

At plane 41 the inclusion of the combustor simulator for the first RANS case, using the finer mesh, does show a good match at both hub and shroud temperature and a generally closer match to experimental temperatures, indicating a generally better mixing. It does however also show a higher maximum temperature. The second RANS case, using the coarser mesh, shows a different though similarly bad match to the experimental data as what has been seen in earlier studies. The more advanced SBES and LES methods, using the same mesh as the second RANS case, show a good match at hub and shroud temperatures, and a better match overall than what has been seen in earlier studies.

For total pressure, all cases show a good match at all planes. Deviations are only a few percent, and within the error margin of the measurements.

 The inclusion of a chamber in the domain does improve the steady RANS-SST results of total temperature mixing at plane 41, depending on the refinement of the CC mesh.

-50-

8 Future work

The results indicate there might be significant dependence on the mesh in the current setup. A thorough mesh sensitivity study should be performed to investigate the effects thereof.

The domain should be extended to include the full combustor simulator. As the currently used geometry did increase the mixing when compared to the results achieved when not including the combustor, it would be interesting to study the effects of including the cooling cavities.

-51-

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Appendix A

Figure 50: RANS case 1, Circumferential temperature average, Plane 40

Figure 51: RANS case 1, Circumferential temperature average, Plane 41 220 230 240 250 260 270 280 320 370 420 470 Radius [mm] Total Temperature [K]

Total Temperature at Plane 40

RANS1

RANS1 Measured 240 245 250 255 260 265 270 275 280 360 380 400 420 440 460 Radius [mm] Total Temperature [K]

Total Temperature at Plane 41

RANS1

-53-

Figure 52: RANS case 1, Circumferential pressure average, Plane 40

Figure 53: RANS case 1, Circumferential temperature average, Plane 41 220 230 240 250 260 270 280 142000 143000 144000 145000 146000 147000 Radius [mm]

Total Pressure [Pa]

Total Pressure at Plane 40

RANS1

Measured RANS1 240 245 250 255 260 265 270 275 280 118000 123000 128000 133000 138000 143000 Radius [mm]

Total Pressure [Pa]

Total Pressure at Plane 41

RANS1

Measured

-54-

Figure 54: RANS case 2 Circumferential temperature average, Plane 40

Figure 55: RANS case 2, Circumferential temperature average, Plane 41 220 230 240 250 260 270 280 320 370 420 470 Radius [mm] Total Temperature [K]

Total Temperature at plane 40

RANS2

Measured RANS2 240 245 250 255 260 265 270 275 280 360 380 400 420 440 460 Radius [mm] Total Temperature [K]

Total Temperature at Plane 41

RANS2

-55-

Figure 56: RANS case 2, Circumferential pressure average, Plane 40

Figure 57: RANS case 2, Circumferential pressure average, Plane 41 220 230 240 250 260 270 280 142000 143000 144000 145000 146000 147000 Radius [mm]

Total Pressure [Pa]

Total Pressure at Plane 40

RANS2

Measured RANS2 240 245 250 255 260 265 270 275 280 118000 123000 128000 133000 138000 143000 Radius [mm] Total Pressure [K]

Total Pressure at Plane 41

RANS2

-56-

Figure 58: SBES case 1, Circumferential temperature average, Plane 40

Figure 59: SBES case 1, Circumferential temperature average, Plane 41 220 230 240 250 260 270 280 320 370 420 470 Radius [mm] Total Temperature [K]

Total Temperature at Plane 40

SBES1

Measured SBES1 240 245 250 255 260 265 270 275 280 360 380 400 420 440 460 Radius [mm] Total Temperature [K]

Total Temperature at Plane 41

SBES1

-57-

Figure 60: SBES case 1, Circumferential total pressure average, Plane 40

Figure 61: SBES case 1, Circumferential total pressure average, Plane 41 220 230 240 250 260 270 280 142000 143000 144000 145000 146000 147000 Radius [mm]

Total Pressure [Pa]

Total Pressure at Plane 40

SBES1

Measured SBES1 240 245 250 255 260 265 270 275 280 118000 123000 128000 133000 138000 143000 Radius [mm]

Total Pressure [Pa]

Total Pressure at Plane 41

SBES1

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Figure 62: LES-WALE case 1, Circumferential total temperature average, Plane 40

Figure 63: LES-WALE case 1, Circumferential total temperature average, Plane 41 220 230 240 250 260 270 280 320 370 420 470 Radius [mm] Total Temperature [K]

Total Temperature at Plane 40

LES1

Measured LES1 240 245 250 255 260 265 270 275 280 360 380 400 420 440 460 Radius [mm] Total Temperature [K]

Total Temperature at Plane 41

LES1

-59-

Figure 64: LES-WALE case 1, circumferential total pressure average, Plane 40

Figure 65: LES-WALE case 1, circumferential total pressure average, Plane 41 220 230 240 250 260 270 280 142000 143000 144000 145000 146000 147000 Radius [mm] Total Pressure [K]

Total Pressure at Plane 40

LES1

Measured LES1 240 245 250 255 260 265 270 275 280 118000 123000 128000 133000 138000 143000 Radius [mm]

Total Pressure [Pa]

Total Pressure at Plane 41

LES1