Current design methods for oblique manifolds were first presented in the paper of London et al. in 1968. This method presents a single equation to shape the dividing manifold of several manifold configurations. However, current literature shows a potential to improve the current design method by implementing advanced techniques. This paper aims to bridge this gap by presenting an innovative design methodology incorporating these advanced techniques. The proposed design method integrates free-form deformation and adjoint-based methods within a 1st-order shape optimization framework. The objective function focuses on the minimization of mass flow mal-distribution, evaluated by an incompressible Reynolds-Averaged Navier-Stokes solver. Through three initial tests, this paper demonstrates a consistent improvement in the objective for all obtained designs. Noteworthy is the finding that small changes to the initial design lead to significant enhancements, evidenced by an 82.5\% decrease in the mass flow mal-distribution. Off-design testing further substantiates the effectiveness of the design method, showcasing superior performance under varying initial conditions for the optimized designs. Further testing not only exhibits improved objectives but also reveals common features among results for diverse initial designs. This paper shows a novel and effective design methodology for consecutive manifold systems, laying a robust foundation for an improved design method.

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.

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.

As aircraft manufacturers push for better fuel economy, novel aircraft concepts, like the propulsive fuselage concept have emerged. One of the prime component of such concepts is the boundary layer ingestion (BLI) engine. Such engine operates by ingesting the low-momentum fluid emerging from the surface of the aircraft fuselage which enables to enhance its propulsive efficiency. The design of a BLI engine is fundamentally different than that of a conventional aircraft engine as the BLI fan experiences distorted airflow at every revolution. Therefore, when its performance are analyzed by means of CFD, single passage simulations become insufficient to represent the flow characteristics. and extremely expensive simulation of the entire annulus become necessary for analysis and design purposes. Especially during conceptual design, where several BLI engine configurations must be investigated in combination with their airframe integration, new reduced-order methods are required to alleviate the computational burden while retaining a sufficient level of accuracy.

An alternative, computationally efficient approach capable of coping with the full-annulus simulation is the well-established body-force modelling (BFM). BFM is a technique through which the physical blade rows are replaced by a volumetric force field which mimics the flow turning imparted by the physical blade rows. Thanks to this simplification, BFM does not require the physical blades to be accurately reproduced in the mesh, thus offering substantial computational cost reduction. Due to the associated gains in computational efficiency, this method is commonly used for the analysis and off-design performance prediction of full-annulus geometries, which are computationally demanding through conventional methods. Although the method has been established for analysis purposes, its capability as a design tool was never assessed.

Implementation of BFM in a CFD code that can be automatically differentiated to attain design sensitivities via the adjoint method may enable efficient BFM-based design of complex engine configurations.

In this research, the BFM model originally developed by Ref. \cite{Hall2015AnalysisIngestion} and improved by Ref. \cite{Thollet2017BodyInteractions} was implemented into open-source CFD software SU2, which is equipped with a discrete adjoint solver based on operator overloading. In addition, parallel force and a metal blockage source term were added to the existing formulation to increase the fidelity of the BFM. The implementation was validated by comparing the results obtained from the BFM and the physical blade computation on an exemplary axial turbine test case.

The results show that the BFM was capable of providing static and stagnation pressure and temperature trends with an accuracy of approximately 94\%. Furthermore, the absolute flow deflection by the stator and rotor rows were found to deviate by $\SI{5}{\degree}$ and $\SI{17}{\degree}$. The BFM was found to be 3 orders of magnitude faster than the equivalent physical blade computation.

The current high demands for the energy and transportation industries make it imperative to design efficient and reliable turbomachinery. Aeroelastic phenomena such as forced response and flutter are one of the main concerns when designing these machines, and the incorrect prediction of these effects generates vibrations that can lead to structural failure due to high cycle fatigue. Furthermore, the search for unconventional energy sources is also of great relevance to meet these demands. Power generation using the Rankine cycle with organic fluids is one example of these technologies. The different thermodynamic properties, when comparing to water, of these fluids, make it possible to use low temperature energy sources, having many practical applications such as waste heat recovery and combined power cycles. Organic fluids, due to their high molecular weight, are also characterized by a low speed of sound which results in a supersonic flow, leading to shock waves. This unsteadiness propagates onto rotating blade rows downstream and acts as a harmonic forcing. Investigating the impact of these effects on the structural integrity of small scale radial machines operating with organic fluids has not been done in the past and is the goal of this thesis. The assembly of a forced response analysis chain is made and is based in three main points. First, finding and characterizing resonant conditions. Second, determining aerodynamic harmonic forcing and aerodynamic damping, and finally, place alternating and mean stresses against structural limits. This method was applied to two test cases, the NASA rotor 67 and the ORCHID turbine. The NASA rotor 67 is used as a benchmark case to assemble and validate the analysis chain due to the large amount of openly available experimental data. ORCHID is a small scale ORC turbine designed at TU Delft and is used to explore the influence of the aeroelastic effects on this category of machines. For the ORCHID turbine, high unsteady pressures in the turbine rotor blades were observed by the simulations made. This is due to the shock waves in the upstream supersonic stator, from tip leakage and from potential interactions. In terms of flutter, a stable system was found for the resonant conditions studied. The regions of higher unsteadiness were confined to the upstream most part of the rotor blade being excited, which correspond to areas of small modal displacements. Furthermore, even with high rotational speeds, the small scale of the machine resulted in small centrifugal effects, and so in high allowable margins for alternating stresses. In sum, even with a high unsteady pressure content, the mismatch between these and the mode shapes, and the positive aerodamping values, result in a safe system in terms of high cycle fatigue for the resonant conditions studied. The current work should be continued for the manufacture of the ORC turbine by investigating precise material properties, hub geometry and upstream inlet geometries that can lead to lower frequency resonant crossings. Furthermore, the investigation of the influence of the aeroelastic issues identified on the efficiency and the incorporation of the work developed on multi­disciplinary optimization procedures is also of great relevance and a main recommendation for further studies.

The scientific community is consistently focused on identifying new sources of energy, which can reduce the consequences of climate change and depleting natural resources. Organic Rankine Cycle (ORC) based power systems have been touted as one of the promising technologies of extracting thermal energy from waste-heat and renewable sources such as geothermal, solar radiation and biomass, to name a few. Use of an organic fluid makes it theoretically possible to design a compact, high volumetric flow turbine that can extract energy from sources with low temperature head. However, realization of this turbine becomes challenging because of their unsteady nature which stems from high expansion ratio across the cascade and low speed of sound in organic fluids. The expansion of fluid in these turbines occur in the dense gas supersonic regime where ideal gas assumptions do not hold and the flow is characterized by shock waves and expansion fans. The success of ORC systems thus depends on how well these effects are modeled into the design stage. Stator vanes have a major contribution to the stage losses in these high-expansion low reaction turbines. In current literature, there exists no co-relation that takes into account dense gas effects for the preliminary design of these stator vanes. Thus the objective of this thesis is to study the trend of stator losses with the variation of geometric de- sign variables and inlet conditions, subsequently to qualitatively and quantitatively assess the performance of the blade and finally to propose new design correlations for the organic fluid Toluene. To achieve this objec- tive, the stator design variables affecting 2D loss mechanisms are identified and a design space is constrained. It was hypothesized that the total losses are minimum for an optimum vane design corresponding to a unique value of post-expansion ratio. A semi-automated analysis framework was made, that assessed the fluid dy- namic performance of vanes with varying post-expansion ratio, which upon analysis backed the hypothesis successfully. Further, the trend behavior of this optimum post-expansion ratio with design variables such as stator blade angle, total-static expansion ratio, nozzle solidity and fluid non-ideality is investigated and val- ues of post-expansion ratio corresponding to optimum design vanes are obtained. These discrete optimum points are interpolated to obtain a continuous second order function which is the proposed co-relation that can be used for the preliminary design of a stator vane in an ORC turbine.

In order to reduce the carbon foot-print of turbo-generators to global warming, a step-change in the design process is needed. Extensive CFD simulations coupled with optimization algorithms are required, resorting to novel techniques to capture the complex flow phenomena occurring in the passage. However, the computation of the optimization gradients and the imposition of geometrical constrains is computationally expensive and non-trivial due to the large number of design variables. In the 1980s, the adjoint method arose as an alternative technique to compute the sensitivities at a cost independent of the number of design variables. This technique is extremely popular in external aerodynamic applications. However, its full potential is yet to be exploited to internal flows. The use of an adjoint solver, together with a surface parametrization technique based on traditional blade design parameters, presents a unique opportunity towards a fully-automated design methodology based on high-fidelity models for turbomachinery applications. Stemming from the above considerations, the aim of this thesis is to develop a common open-source numerical framework for the optimization of both axial and radial turbomachinery. In order to achieve so, the open-source CFD suite SU2, that includes an adjoint solver, is coupled with ParaBlade, an open-source blade parametrizer based on traditional turbomachinery design variables. The proposed methodology is successfully applied in an axial turbine stator, where a reduction of 7.59% in the entropy generation across the passage is achieved. The study performed in a mixed-flow turbine rotor highlights the need to parametrize the hub and shroud surfaces. However, its optimization revealed a reduction in the objective function value, showing the robustness of the proposed methodology in two types of turbomachinery.

Increasing concerns about the effects of freeing large quantities of greenhouse gases into the atmosphere have sparked interest in organic Rankine cycle for renewable power systems. Single-stage radial inflow turbines appear as suitable expansion devices for this type of application. However, supersonic conditions can be reached in the stator of these devices, causing non-ideal fluid-dynamic behavior. This makes it necessary to explore unconventional architectures, for which only a limited number of design methods have been proposed.
In this context, the principal activity of this study was to formulate guidelines, and thereby reduce the preliminary design space, of supersonic radial stator vanes. This was done by first identifying the relevant loss mechanism and design parameters through an examination of the available literature. This led to the formulation of a research hypothesis, which was studied by means of two-dimensional, steady computational fluid dynamic simulations.
To this end, a parametric study was devised, in which any design parameter can be varied to study its effect on the blade performance. This is done analyzing the trends resulting from the post-processing of simulation generated data. The data production is based on a workflow consisting of finding a condition-specific convergent-divergent nozzle, which is used to build a mean-line radial vane, for which a mesh grid is generated and utilized by a previously validated numerical solver to perform the simulations. The complete process was overseen by a semi-automated design chain constructed to manage and execute the necessary steps.
It was assumed that profile losses would be the most influential loss characteristic, given that two-dimensional flow is predominant in mean-line geometries. According to the literature, both its major components, viscous dissipation and mixing losses should have an impact on the stator’s efficiency. Likewise, the degree of expansion along the embedded nozzle present between adjacent blades, was identified as the main design specifications to be analyzed. A trade-off between the contribution of the main loss mechanisms based on the variation of this parameter was predicted to exist.
Applying the generalized research method on a candidate test case resulted in the generation of data from almost 500 different simulations. This led to several findings, including that it is not possible to vary the nozzle design Mach number without causing simultaneous changes to other relevant geometrical features, such as the throat width. This rendered invalid some of the initial assumptions used to set up the experiments.
Similarly, this finding was expected to be the reason behind large differences between the calculated and imposed pressure ratio on the boundary conditions, as well as large variations in the mass flow of each set of blades. Additional simulations were required to analyze these deviations, based on varying other relevant parameters, including the imposed pressure ratio and outflow boundary location. The results seem to suggest that, due to the supersonic nature of the flow, an additional geometrical constraint influences the expansion process.
Performance analyzes were then possible by adapting the definition of valid designs to blade configurations matching or exceeding the imposed pressure ratio. Based on these results, the relevance of the post-expansion ratio (defined as the ratio between the pressure level at the nozzle exit and the stator outflow) became apparent. This was also the case when this ratio was manipulated by changing the imposed back pressure on the system. Moreover, when quantified with respect to this parameter, the flow deviation showed a linear behavior and the losses exhibited a plateau of higher performance.
Finally, this project provides a foundation for this line of research, both in a theoretical and practical sense. Future studies should focus on validating claims made regarding the supersonic expansion process and extending the data to determine the generality of the found performance trends. Only then will it be possible to conclusively establish the dependence between design parameters and performance for this unconventional type of blade.

The growing environmental concerns has put a lot of political & ethical pressure on the conventional industrial practices. The research community is ever so eager to investigate new technologies that can offer an efficient and environmentally sound solution to the issues caused by the polluting industrial processes. One of the potential solution is an Organic Rankine Cycle (ORC) which is proven to be an effective technology to efficiently extract energy from low-temperature sources. The ORC is basically a Rankine cycle but employs a high molecular weight organic fluid as the energy carrier. The peculiar non-classical gas dynamics behaviour of these fluids during dry expansion close to the vapour saturation line (in the dense gas region) poses certain challenges on the turbine design. Furthermore, the low speed of sound in organic fluids and high expansion ratio required in an ORC turbine leads to highly supersonic flows in the turbine. Such high speed flows within a turbine stage are susceptible to high shock losses, if necessary corrective steps are not taken during early design phase. This has sparked a wave of interest in the scientific community to come up with an efficient supersonic ORC turbine design guidelines. The design of a supersonic turbine rotor is crucial to ensure efficient performance of the turbine. In the mid-20th century, a supersonic impulse rotor design methodology for axial turbines was proposed that boasts shock-free turning of supersonic flows using the vortex-flow theory. This procedure relies on Method of Characteristics (MOC) to solve hyperbolic governing PDEs. The method got enriched later with the capability to account for dense gas effects on the rotor geometry which is essential for ORC applications. However, there are no such design guidelines available in the literature to generate a radial rotor blade especially for supersonic flows. The conventional 1D preliminary design methods, generally available for radial rotor blades, are not very reliable in supersonic flow regime. This calls for a novel design philosophy for supersonic radial rotors that accounts for supersonic flow phenomenon early in the design phase to ensure efficient turbine performance. The objective of this thesis is to put forth a design methodology for supersonic radial rotors that acknowledges the flow equations in the design procedure. The proposed design ideology is to extend the supersonic axial rotor design procedure by including the fictitious forces' effects in the governing equations to generate a radial rotor using MOC. These pseudo forces (Centrifugal & Coriolis) are experienced by the flow in the radial runner if seen from the rotor's rotating frame of reference. Furthermore, the dense gas effects are also included in the design using the properties from CoolProp library. A design tool is developed in PYTHON that implements the aforementioned ideology in the design procedure. This thesis takes the first step towards developing a fully functional design methodology for supersonic radial rotors. Therefore, a simple case of a constant force's influence on the rotor geometry is studied in this work and compared with the CFD simulations in both perfect & dense gas region. Future research will focus on understanding the complex behaviour of organic fluids in the presence of an external force and modify the design procedure accordingly.