The focus of this thesis is the preliminary design optimization and performance analysis of non-cavitating centrifugal turbopumps using a 1D lumped-parameter method. Centrifugal pumps are critical components in many engineering applications due to their high efficiency in converting mechanical energy into fluid pressure. This study presents the development and validation of a computationally efficient model to design and predict the flow properties along different stations of a centrifugal pump. The methodology minimizes the reliance on expensive CFD simulations, making use of multiple design parameters to control the impeller, diffuser, volute, and exit cone configurations to ensure a robust and efficient performance.

A common challenge in turbopump design is the prediction and mitigation of cavitation, which occurs when the fluid static pressure falls below its vapor pressure. This leads to the formation and subsequent collapse of vapor bubbles, which can cause severe damage to pump components. Given the complex physics involved, this work makes use of reduced-order models to predict, and avoid cavitating regimes through design adjustments.

This thesis provides a comprehensive framework for optimizing the design of centrifugal turbopumps by integrating validated loss models and a reduced-order modeling approach. The proposed design methodology is applied to develop a centrifugal pump for the TU Delft ORCHID facility, demonstrating its feasibility and effectiveness. This research contributes a practical modeling tool for centrifugal turbopump optimization and performance analysis.

Climate change is a pressing issue. Hydrogen aircraft are an excellent alternative to current kerosene aircraft, and appear to be the most viable long-term solution for net-zero flight. One of the main challenges for hydrogen aircraft is to sustain a low boil-off rate. This research explores the solution of active cooling of the LH2 mixture in the fuel tank. It focusses on the construction of a thermodynamic model for cryogenic liquid hydrogen fuel storage in aircraft, a system model for single-stage Reverse Turbo-Brayton Cryocoolers (RTBC), and the conceptual design of the RTBC’s miniature high-speed compressor. This is used for the integrated modelling of the RTBC, compressor and LH2 fuel tank for an exploration study of the carbon neutral hydrogen concept of the long-range Flying-V aircraft. Results show that the RTBC might offer a valuable addition to the Flying-V design space for boil-off control in addition to careful design of the insulation and tank shape.

In the scope of global decarbonisation, hydrogen has been identified as an essential energy carrier. Not only as an energy storage solution for further electrification in vehicles but also as a primary fuel source in processes that rely on chemical energy which cannot be easily electrified. However, at ambient conditions, hydrogen is also a very sparse gas with a low energy density. This requires it to be either liquified or compressed as a gas for most storage and transport solutions, both of which are rather energy-intensive processes. In the case of compressed hydrogen this leads to a significant amount of potential energy stored in the storage tanks. In current applications, the high pressure hydrogen is then expanded through a valve to reach the system’s desired working pressure. A process in which most of the potential energy stored in the compressed is lost to thermal effects.

The research in this thesis is focused on identifying a suitable application in which an expander could be applied to recover part of the potential energy stored in compressed hydrogen and to provide a conceptual design and a thermodynamical analysis of this expander to assess its efficiency and feasibility and has been caried out in collaboration with Ayed Engineering GmbH.
The literature study provided an overview of the current hydrogen landscape and the potential applications in which an expander could be applied. These have been evaluated and led to the selection of a hydrogen refuelling station as a suitable application for this purpose.

A system model has been developed to replicate a refuelling process in a hydrogen refuelling station and to serve as an operating environment for the to-be-designed expander. Based on the operating parameters of the hydrogen refuelling station, a number of expander designs have been developed, each optimized for the operating conditions in the station at a certain timestep. Empirical loss models have been applied to assess the performance of each of these designs across the entire operating range. From this, it was possible to find which potential design would provide the best overall performance. This selected design and the operating conditions at its optimal performance point have then been used in a 3D CFD validation case using Ansys CFX.

The results indicate that employing a radial inlet turbine for the recovery of potential energy stored in compressed hydrogen in a hydrogen refuelling station can indeed lead to notable operational cost savings but also that there are several practical challenges which remain to be solved. Specifically, the extremely high rotational speeds that are required in operation and the miniature design features of the turbine design. To address these, a sensitivity analysis of several system parameters and design assumptions has been included to provide guidance for future work.

Analysing and developing turbomachinery at off-design conditions requires the usage of robust and efficient Computational Fluid Dynamics (CFD) solvers. With the introduction of the computer, many advancements have been made in the field of numerical methods involving these flow problems. These numerical methods are used in order to solve these complex flow structures that are formed due to the interaction between the rotating machinery and the fluid. With the emergence of new design paradigms using computer-aided optimisation, novel solver methods are required which are able to deal with the increase in computational cost and the convergence difficulties following off-design conditions. One of the CFD solvers that is used for turbomachinery design is the open-source software SU2. SU2 is currently developed partially at the Delft University of Technology, where an increase in solver performance with respect to turbomachinery aerodynamics is greatly desired. The current work provides a numerical study of SU2's current performance with respect to turbomachinery analysis, as this is currently unknown.

The current performance of SU2 is to be analysed using steady RANS turbomachinery simulations. The research conducted by Xu et al. \cite{Xu2020} will be used as reference data in order to validate SU2's performance together with data obtained from the CFD solvers CFX and Numeca. The research conducted by Xu et al. resulted in the development of their NUTSCFD solver, which showed strong performance with respect to turbomachinery analysis. Four test cases are set up and used in order to analyse SU2. The test cases that are considered for the numerical study include: the NACA 0012 airfoil, the LS89 turbine cascade, the MTU centrifugal compressor and the 1.5 stage ETH turbine. The first three test cases are validated using the results obtained by the NUTSCFD solver, where the ETH turbine is validated using CFX and Numeca. Following these test cases, SU2's performance is analysed using the residual behaviour. Xu et al. dedicate their performance increase to be the result of the Newton-Krylov method that is implemented in their NUTSCFD solver. SU2 also includes a Newton-Krylov solver, but its performance with respect to turbomachinery is also unknown. A performance assessment with respect to SU2's Newton-Krylov method involving turbomachinery analysis is therefore conducted as well.

The results obtained using the NACA 0012 and LS89 test cases show a discrepancy in solver performance involving SU2. With respect to SU2's Newton-Krylov solver, the NACA 0012 test case shows a reduction in non-linear iterations where this is not found for the LS89 test case. Both results showed however a large difference in performance when compared to the NUTSCFD solver, where SU2's standard solver was also unable to match NUTSCFD. The results obtained following these test cases have led to the development of the MTU test case, where the MTU test case was to be used in order to provide a more accurate comparison between SU2 and NUTSCFD. Instead, SU2 was unable to run the MTU test case, where the solver showed stalling behaviour...

In the pursuit of reducing the climate impact of aviation, there has been an increased interest in the adoption of renewable energy technologies. Examples of revolutionary technologies include hydrogen fuel cell systems and waste heat recovery using the organic Rankine cycle. The design of viable energy conversion systems for aviation poses unique challenges in terms of efficiency, weight and size. To this end, research on small-scale turbomachinery operating at high rotational speeds is increasingly pursued in the context of, for example, fuel cell air compressors or organic Rankine cycle turbines. Such machines typically call for oil-free operation to avoid contamination of the process fluid. Gas foil bearings can prove to be an enabling technology due to their reliability, oil-free operation and compatibility with high rotational speeds.

The use of gas foil bearings to support organic Rankine cycle turbines requires lubrication with complex working fluids at operating conditions near the saturated vapour line or thermodynamic critical point. Although there has been an increased interest in high-pressure gas lubrication in recent scientific literature, there is still a lack of understanding of the effects of non-ideal compressible flows on the performance of (gas foil) journal bearings. In order to further address this knowledge gap, this work focuses on the modelling of such bearings lubricated with dense fluids made by complex molecules like those adopted for waste heat recovery at high temperatures in aviation.

The compressible Reynolds equation governing the thin-film flow within the bearing is discretized using a finite difference method. The solution to the non-linear problem is obtained using a relaxation method in which a thermodynamic software program updates the non-ideal thermodynamic state properties after each iteration. The load-carrying capacity of the bearing is obtained by integrating the resulting steady-state pressure field around the rotor shaft. A perturbation method is applied to obtain the stiffness and damping coefficients used in a linearized rotor-dynamic analysis. The developed computational tool allows for the analysis of bearing performance under varying operating conditions.

The conclusions of this work emphasize the challenge of generating sufficient load-carrying capacity and rotor-dynamic stability associated with high-pressure gas lubrication in journal bearings. Bearings operating with compressible lubricants near the thermodynamic critical point are typically characterized by turbulent thin-film flows with non-negligible molecular interactions. Reduced peak pressures within the gas film are anticipated, resulting in a reduced load-carrying capacity as compared to ideal gas lubrication flows. It is shown that non-ideal thermodynamic effects have an impact on rotor-dynamic stability by affecting the steady-state attitude angle of the bearing.

The modelling of a gas foil journal bearing used to potentially support the turbine of the organic Rankine cycle hybrid integrated device (ORCHID) of the TU Delft has finally been considered. The results show the utility of a numerical model in assessing bearing performance and understanding the associated physics. This work can be used as a basis for future analysis and design of gas foil journal bearings lubricated with high-pressure process fluids.

Developments in computational capabilities and the always increasing demand for higher performance of internal flow applications has meant that Computational Fluid Dynamics (CFD) has become an essential tool within the design process. A key point of interest is to couple the fluid solver with numerical optimisation techniques in order to obtain a more automated design process that can handle a vast amount of different design aspects. The open source CFD suite SU2 has emerged as an enabler for aerodynamic shape optimisation involving a large number of design variables, due to its efficient, accurate and flexible discrete adjoint solver. 
For the adjoint-based aerodynamic design optimisation of internal flow applications the deformation of the volumetric mesh has to be performed in an robust and efficient manner. Often small wall clearance gaps and periodic domains are encountered in internal flow domains, which could potentially lead to the deterioration of the mesh. Sliding boundary node methods can be applied in order to maintain the mesh quality in case of small wall clearance gaps. Additionally, periodic boundaries can be displaced in a periodic manner following the applied deformation in order to prevent low quality cells near the periodic interface. Therefore, it would be of interest to implement the sliding boundary node methods and periodic conditions in a Radial Basis Function (RBF) interpolation method, one of the most robust mesh deformation methods available. 
Additionally, the computational efficiency should be considered, since high computational times should be prevented for large and complex three-dimensional cases with a high number of design variables. 
The aim of this thesis project is therefore to develop a robust and computationally efficient mesh deformation method suitable within the discrete adjoint optimisation framework of SU2 for internal flow applications by means of developing an implementation of the RBF interpolation method including sliding boundary node algorithms, periodic boundary conditions and data reductions methods.
The sliding is achieved by replacing the interpolation condition for the sliding nodes with a planar slip condition. Or alternatively, by freely displacing the sliding nodes based on the known deformation and subsequently projecting the nodes back onto the boundary. The periodic displacement of the boundaries is ensured by making the distance function of the RBF periodic. The periodic nodes are then treated as internal nodes to allow them to move.
The developed RBF-SliDe tool is able to generate higher minimum mesh qualities compared with the regular RBF interpolation method. The sliding of the boundary nodes reduces the degree of skewing of the mesh elements in case of drastic deformations, resulting in a higher minimum mesh quality. Furthermore, the introduction of the periodic displacement prevents low quality skewed or compressed mesh elements, as the periodic boundaries move along with the deformation. 
The Aachen turbine stator blade is considered as a realistic three-dimensional test case. For this stator blade an optimised geometry was available, which was obtained with an adjoint-based aerodynamic optimisation performed with SU2. Therefore, the resulting minimum mesh quality is compared to the one obtained with the more conventional linear elasticity equation method as used in SU2. The minimum mesh quality obtained with the RBF-SliDe tool is nearly three times higher compared to the minimum mesh quality of the linear elasticity equations methods. This highlights the potential of the periodic sliding RBF interpolation method in terms of preserving the mesh quality.

Propeller propulsion systems combined with Boundary layer ingestion (BLI) have been proposed as a propulsive system to reduce the CO2 emissions of aircraft by 50% by 2050. BLI leads to increased disturbances at the propeller disk and causes more noise due to the fluctuating blade loading. Using the APPU project as a test case, unsteady inflow is used to determine whether a metric to lower the blade loading fluctuation on an airfoil level is possible. Therefore, an optimisation was created using an Euler solver reliant on the harmonic balance method and the adjoint method to lower the computing time of the simulation. The combination of these methods has proven successful in turbomachinery applications. The optimisation scheme uses the modelled APPU inflow conditions to optimise for the drag coefficient while lowering the Root Mean Squared Error of the lift coefficient during the simulations by applying a constraint in various optimisation runs.

The use of CFD-based optimizations is becoming a standard for turbomachinery design. Although the use of such optimizations can lead to great improvements of the machine performances, there are still several shortcomings in the common design procedure of turbomachines. In fact, this entails the optimization of the component shape, and only a retrospective check on manufacturing feasibility and structural viability. This might lead to several design iterations and lot of time wasted.
This thesis project aims at developing a multidisciplinary optimization method where the structural behaviour of the part can be checked already in the first part of the design process. This is done by using the "cold" design as first guess of the optimization, and by performing a fluid-structure interaction to predict the deformations of the part, and simultaneously investigating the behaviour of the flow field, in order to obtain the performances achieved by the operating "hot" design.

This work sets out the creation, verification and demonstration of an automated end-to-end tool for the multi-point fluid-dynamic optimization of turbomachinery. Taking into account multiple operating conditions during optimization aims to benefit the overall performance of turbomachines which are characterized by off-design operation and to produce more robust designs with respect to deviations in operating conditions. The feasibility and effectiveness of the tool is demonstrated by a two-point fluid-dynamic optimization of a two-dimensional Aachen turbine stator cascade, performed on the High-Performance Computing cluster of the TU Delft. By utilizing the stochastic NSGA2 optimization algorithm, the numerically noisy problem is successfully optimized. The entropy generation of the blade is reduced at both nominal and off-design operating condition by an average of 7.57%, while satisfying a constraint on the flow turning when passing through the stator cascade. Additionally, a numerical noise analysis shows that disregarding the most noisy design variables increases the probability of obtaining an improved design.

To cater to the increasing demand in short-range passenger air transport and the research in electric and hybrid aircraft, there is a renewed interest in the research of propellers. Propellers are known to have high aerodynamic efficiency, which translates to lower fuel burn in comparison to other jet engines, making it an attractive option for airlines to operate it in regional transport. With such a heightened interest in the research of propellers for future applications, it is crucial to study the effect of the shape-design of the blades on its aerodynamic performance parameters. The combination of advanced numerical methods with computational fluid dynamics allows determining the sensitivity of cost function to variations of the design parameters. In this thesis, a RANS-based CFD methodology incorporating the adjoint method is developed to perform the sensitivity analysis of the propeller's aerodynamic performance to the variation in the shape design of the blade. This methodology is applied to two propeller test cases- straight and swept blade. The propeller aerodynamic analysis is performed with SU2 for a range of advance ratios and compared against ANSYS Fluent's. Based on the verification and validation of SU2's flow solver, a larger discretization error was obtained with SU2 in comparison with ANSYS Fluent, for the simulations on the same computational mesh. Once SU2's flow solver is verified and validated using the two propeller cases, it is used to draw a comparison between the aerodynamic performance of the two blades. the swept blade operated with higher aerodynamic efficiency at high advance ratios with the largest gain of 0.47% at J=1.2. While it experiences a marginal loss in the efficiency at lower advance ratios with the largest decrement being 0.37% at J=0.6.

SU2’s adjoint solver is used to perform discrete adjoint-based sensitivity analysis of the propellers at multiple design points with thrust coefficient and torque coefficient as the objective functions. The sensitivity analysis of the thrust coefficient suggested that the regions of high sensitivity are located along the leading-edge and outboard portions of the blade's suction side. The concentration of the regions of high sensitivity varied with the advance ratio. For a given blade, similar trends were seen for the surface sensitivities of the torque coefficient. Both blades exhibit similar trends for surface sensitivities of both objective functions. Whereas based on the gradient information, the highest gradients of thrust coefficient are attained for the design variables located near the trailing edge of the straight blade, at a given radial position. Swept blade shows a chordwise gradient trend similar to the straight blade at most radial positions, except the tip region. It was inferred that the introduction of sweep at the tip results in the shift of the dominant design variable from trailing edge to mid-chord. Similar to surface sensitivities, trends of the chordwise gradient of two objective functions were alike for a given blade. Based on this study, the resulting understanding of the sensitivity of the propeller’s performance parameters to the variation in blade shape design can be used as an input for future design studies aimed at designing efficient propellers. Likewise, the RANS-based CFD methodology incorporating the adjoint method used in this work can be aimed at developing adjoint-based multidisciplinary design capabilities for propellers.

With an increasing complexity of systems, systematic design space exploration is required for fair analysis and comparison of architecture design options. However, there is still a need for a benchmark problem to support the development & evaluation of optimization algorithms and system architecture design space modeling methods, and to educate stakeholders in system architecture optimization. The thesis focus lies on the creation of such benchmark problem with an application to aircraft jet engine design, which is subsequently tackled by developing an MDO tool using a system architecting approach with mixed-discrete and multi-objective capabilities. The tool was built with the open-source software pyCycle and OpenMDAO and can generate, analyze and compare different aircraft engine architectures on several disciplines including engine thermodynamic cycle analysis, weight, geometry, emissions and noise. Therefore, it is able to tackle the black-box, mixed-discrete, multi-objective and hierarchical nature of system architecture optimization problems.

”To provide a novel remotely controlled aircraft for in-situ and remote sensing atmospheric
measurements at high altitudes designed for researching and monitoring climate change.”
“To design a costeffective unmanned subsonic aircraft for atmospheric measurements
at altitudes exceeding 25 km using sustainable fuels”.

The objective of this thesis was to further the validation effort on the SU2 flow solver for non-ideal compressible flows. To do so, an uncertainty quantification infrastructure based on the V&V20 validation standard was developed. To determine whether a model error was present, the different sources of uncertainty were combined and then compared to the error between the SU2 simulations and the experiments. A variety of paradigmatic test cases were proposed which, together, would constitute a robust validation of the SU2 flow solver. Two paradigmatic unit test cases were analyzed; namely, a supersonic inviscid flow and a Mach 2.0 flow over a 2.5 degree wedge. The operating conditions of the experiments were as follows: an inlet total temperature and pressure of T_0=252°C and P_0=18.4 bara, and a back pressure of P_out=2.1 bara, for the first case, and T_0=180°C, P_0=3.5 bara and P_out=1.0 bara, for the second. The solver is able to predict the shock wave angle accurately. This step towards the validation was successful because the calculated total expanded uncertainty of 1.79% is higher the comparison error of 0.57%.In the second part of the thesis, the uncertainty quantification infrastructure was adapted to a test case constituted by more complicated flow features; namely, a supersonic flow through a 5-channel blade row. The computed uncertainties were on the same order of magnitude as in the supersonic inviscid flow test case. The simulations were verified with state-of-the-art CFD software for the quantities pressure and the Mach number. The positive result of the validation represents a step forward in the validation of the flow solver for non-ideal turbomachinery cases. The adaptation of the infrastructure to the cascade blade row paves the way for complex cases and for system response quantities of interest in industrial applications of CFD software, such as efficiency, to be assessed.

Dawn Aerospace is developing a small launch vehicle in the form of a spaceplane, which is powered by a turbopump driven rocket. To reach higher engine efficiency and save weight, there is a need for a small highly-power dense turbine. The efficiency of small turbines strongly depends on the tip gap sizes compared to the blade height. Existing turbine loss models predict large efficiency penalties due to excessive clearance losses, caused by the relatively large tip gap over blade height ratio. To build a competitive small launch vehicle, it is necessary to develop a highly efficient turbine.The objective of the work presented here is to first analyse and then minimize the clearance losses occurring in a representative small turbine for the spaceplane by applying seals on top of the shroud. Turbine loss models presented in the literature are limited to predicting losses for labyrinth seals only. As more advanced seals, like the brush seal, are being used more regularly there is a need for more accurate modelling of clearance losses in shrouded rotors.In order to calculate the leakage through seals, first bulk flow models (BFM) were developed for the labyrinth, annular and brush seal. BFMs use the zeroth-order of a perturbation equation to calculate leakage. Two- and three-dimensional numerical models were developed to simulate the mass flow rate through the seals with the help of commercially available software. Next, the BFMs and numerical models were validated against experimental data obtained from literature. BFMs could predict leakage rates through seals with an accuracy up to 15\%, when suitable empirically determined constants/equations were used. The numerical models performed slightly worse for the annular seals with a minimum accuracy of 25\%, while good predictions were obtained for labyrinth seals and brush seals. Little difference could be seen between 2D and 3D CFD when assessing leakage through shaft seals.The turbine design of Dawn Aerospace was evaluated in CFD and compared to the loss model of Dunham\&Came. First, an unshrouded case was designed to assess the profile and secondary losses arising in the turbine. In the unshrouded case the loss model agreed with CFD. In the case of the shrouded turbine a large discrepancy existed between CFD and the loss model. The difference in loss was attributed to the fact that the loss model massively over predicted the clearance loss of the turbine, by over predicting the leakage over the shroud. A new loss model has been developed which can be used to more accurately predict the clearance loss of a turbine. This improvement is achieved by using Denton's equation for clearance loss and Dunham\&Came's equations for profile and secondary loss. Denton requires the determination of the leakage mass flow rate through the shroud. The leakage mass flow rate is dependent on the inlet, the seal and the outlet. The leakage through the shroud can be calculated with the usage of BFMs. The inlet and outlets of the shrouds are modelled as labyrinth seals while placing the actual sealing system in between. This means that now not only simple labyrinth seals can be predicted, but brush seals as well and possible other seals for which leakage equations are available. It has been shown that the model can accurately predict losses for a range of turbines. The efficiency predictions of the loss model for a range of designed turbines were within 5.6\% when compared to CFD.During the sensitivity analysis on the model it was found that the influence of the inlet and outlet cavity width on the mass flow rate is significant in small turbines. Especially if the sealing mechanism on top of the shroud is simple, which is the case for an annular seal or a single finned labyrinth seal. Whenever multiple fins were adopted or the brush seal is used the inlet and outlet width become less important in the sealing system for reducing leakage rate over shrouds in small axial turbines.

The use of centrifugal compressors is widespread in many different industrial applications, namely refrigeration cycles, oil and gas rotating equipments, automotive turbochargers and small aero-engines. Compared to their axial counterpart, centrifugal compressors can provide the same compression ratio within less compression stages, trading-off efficiency with compactness. Current development in this sector involves the tuning of design process to accommodate analysis of turbomachinery operating with non-conventional working fluids that exhibit non-ideal fluid-dynamic behaviour. However, best practices for the preliminary design of centrifugal compressors still rely on the perfect gas assumption. On the other hand, the improvement of the preliminary design tools may result in significant reduction of time and resources spent during the detailed design step by leveraging Computational Fluid Dynamics (CFD). In this scenario, the present research aims to devise guidelines for the preliminary design of centrifugal compressors operating with non-ideal compressible flows by assessing the performance limits of the machine using a meanline design framework, coupled, where possible, to physics-based loss models. Loss models derived from first principles are preferred to semi-empirical loss correlations as they require less tuning with machine-specific (thus, also working fluid-specific) experimental data. In this work, two major loss sources, namely the blade boundary layer loss and the tip leakage loss, are analyzed in detail. For both loss mechanisms, the physics-based loss model are derived, and their results are compared to CFD results to check their validity and accuracy. Due to time constraints, the remaining loss sources are modelled using semi-empirical correlations available in literature. The outcome of this work are design maps for centrifugal compressors operating with different working fluids and thermodynamic conditions, which highlight the impact of non-ideal compressible fluid dynamics (NICFD) on the optimum design region as well as the maximum theoretical stage efficiency. The novel framework could be further extended and replace the traditional design guidelines based on the perfect gas assumption, aiming to improve compressor preliminary design and contribute to the development of next-generation high-performance turbomachinery.

Turbomachines are prevalent within the aerospace industry and vital for both power production and flight systems. To achieve better performance and higher efficiency, a numerical optimization technique is used to optimize designs. Previous work has primarily focused on performing steady-state optimization of turboma- chinery using Reynolds Averaged Navier Stokes simulations. In efforts for further performance increases, the next step of turbomachinery optimization is to incorporate time-accurate solvers. These time-accurate solvers are computationally more expensive than steady solvers, which hinders usage in optimization. The harmonic balance method was developed to reduce computational requirements compared to a time-accurate solver while maintaining unsteady flow characteristics in the simulation results. Optimization using the harmonic balance method has shown better performance in 2D cases, but there has not been work reporting on a 3D case. Fur- ther analysis of how optimization changes flow irreversibility in a design has not been shown between harmonic balance and mixing plane based optimization. This work’s novel contribution is to perform a comparative study of harmonic balance and mixing plane based optimization of a 3D multistage turbine and perform a loss quantification comparison of the optimized designs. In this work, the flow around a 3D 1.5 stage axial turbine in the subsonic to transonic flow regime was simulated and optimized using the mixing plane and harmonic balance methods. The turbine blade shapes are parameterized using a CAD-based NURBS parameterization and optimized using a gradient-based adjoint algorithm. Flow features, entropy trends, and computational costs between harmonic balance and mixing plane simulation and optimization were compared. This study shows that most entropy creation differences between harmonic balance and mixing plane methods occur in the rotating domain. A turbine design optimized using the harmonic balance method has better fluid-dynamic performance than a design optimized using the mixing plane method. Turbine designs combining blades from both harmonic balance and mixing plane based optimization show better performance than a design using a single flow simulation method for optimization. Results also indicate that a grid converged mesh may not be necessary for entropy generation minimization of turbomachinery designs for transonic flow.

The validation of SU2 for modelling classical non-ideal compressible fluid dynamics will advance the research into efficient ORC turbomachinery design. This study determines the validity of the two-dimensional flow solver for predicting the isentropic expansion of Siloxane MM through a converging-diverging nozzle using compressible Euler equations, adiabatic flow, and the Peng-Robinson equation of state. Two flows with an inlet stagnation temperature of 525K were considered: an expansion from 18.4 bar to 2.1 bar, and an expansion from 11.1 bar to 1.3 bar.  Mach number along the centreline and static pressure along the nozzle surface were used as the direct system response quantities used in the analysis. Experimental data and uncertainty came from the ORCHID, model input uncertainty was quantified using stochastic collocation, and the numerical uncertainty was calculated using the Richardson extrapolation. The conclusions were based on a hybrid of the ASME V&V 20 and Real Space validation metrics, with a novel Engineering Response Quantity analysis based on determining the effects of system uncertainty on performance parameters. The studied SU2 model provide valid predictions for Mach number, and invalid predictions for static pressure. The largest error is in the kernel region, where E_Mach=0.111 and E_Pressure = 112 kPa. Mach number has a maximum simulation uncertainty of 2% at the transition to the reflex region. Pressure has a maximum uncertainty of 3% at the throat. In the context of turbomachinery the simulation uncertainties translate to +/-0.001 and +/-0.02 on a loss coefficient calculated across a theoretical normal shock, for Mach and pressure respectively. Considering +/-0.01 as significant for a loss coefficient the Mach uncertainty is negligible. Input uncertainty is the largest component of the pressure uncertainty, while experimental uncertainty is dominant for Mach. The input parameters which provide the highest contribution to the uncertainty are critical pressure and temperature. The developed infrastructure can be used for expanding the validation of SU2 to different flow cases.

In the pursuit of a new ultra-efficient generation of turbomachines, novel and more sophisticated flow simulation and optimization methods have to be adopted. With the development of harmonic balance (HB) methods and adjoint optimization, questions arise on the concrete benefits of using one method over another. This research investigates the difference in predictive capability and computational cost between unsteady harmonic balance and steady-state flow solving methods in particular. The research is performed using the SU2 software suite. The relevant set of scaling parameters is established based on a dimensional analysis. Variation of several of these nondimensional parameters - namely the flow and work coefficient, specific heat ratio gamma, isentropic pressure-volume exponent gamma-Pv and volumetric flow ratio - constitute the different setups. Given the excessive computational times associated with full optimizations, this large set of case studies is subjected to one flow evaluation. Trends and conclusions are made based on the resulting data. It is found that the accuracy difference between steady and HB solvers decreases slightly with an increase in flow coefficient as reduced frequency goes down, and increases significantly with the stage work coefficient as Mach effects increase. Varying working fluids under the ideal gas law is found not to impact the stage and solver performance given the volumetric flow ratio as a similarity parameter. In cases where gamma-Pv is significantly larger than gamma, a major increase in stage Mach numbers is observed. Consequently, the difference between results found by steady-state and harmonic balance solvers is considerably larger. Upon increasing the volumetric flow ratio over the stage, stage efficiencies have been found to increase and solver performance differences to decrease. A pair of complete optimizations then aims to bring additional insights and to verify the validity of the simulation results. The optimizations illustrate the effects of the behavior observed in flow simulations on a full optimization process and reiterate the difference in computational time between both methods. In both cases, the HB-optimized turbine stages are more efficient than the equivalent steady-optimized cascades, namely by 0.58% and 0.12%. The predictive capability of steady-state solvers in comparison with unsteady solvers is found to be dependent on reduced frequency, work coefficient and stage maximum Mach number. A new parameter consisting of those three quantities, the adjusted reduced frequency, forms a linear relationship with the deviation in steady versus unsteady results. It can thus be used as an indicative parameter in preliminary design to trade off accuracy and computational time and select the right solver for a given case.