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. ... Read more

Organic Rankine Cycle systems are gaining increasing attention as a modular, cost-effective and decentralised thermal energy recovery solution. The design of an efficient expander in the ORC system is crucial to its rapid uptake by the industry. Compared to volumetric expanders, a radial turbine provides advantages in terms of flexibility and better part-load performances. The design of ORC radial turbines is faced with two challenges. Firstly, the expansion in the stator occurs close to the vapour-liquid dome and the critical point, where the ideal gas assumption is no longer valid. Such expansions fall under the Non-ideal thermodynamic regime. Secondly, due to the lower speed of sound in the working fluid, the expansions are supersonic and are accompanied by compressible flow features such as shock waves, expansion fans which generate entropy and reduce the performance of the expander. There exists significant validated design methodologies and empirical relations for conventional turbomachinery. However this is not the case for unconventional turbomachinery where established loss correlations are not applicable. Hence, there is a knowledge gap in validated design tools for unconventional turbomachinery like ORC radial turbines. The thesis forms a part of the validation campaign of the open-source flow solver, SU2 and approaches the exercise by studying expansions in two paradigmatic test cases, namely (i) a linear stator cascade and (ii) a converging - diverging nozzle.

The study of expansions through a linear cascade is a preceding step to the study of a rotating radial turbine. Consequently, a RANS simulation on the single channel blade passage is studied under the validated assumption of flow periodicity. The expansion takes place from inlet total conditions of 18.4 bara and 525 K (Z =0.558) to a static pressure of 1.95 bara (Z = 0.951) and exit flow of Mach 2. Two types of response quantities are studied namely direct and system response quantities. Direct response quantities are those that can be measured directly such as the pressure, Mach, density. System response quantities are derived from direct measurements and provide information to characterise the performance of the stator. The selected system response quantities are: (i) Pressure loss coefficient (C_p= 0.074), (ii) Kinetic energy loss coefficient (ζ_KE= 0.115), (iii) Entropy loss coefficient (ζs=0.118), (iv) Base pressure loss coefficient (C_pb= -0.065), (v) Standard deviation of exit flow angle (σ_β2 = 1.244) and (vi) Standard deviation of exit Mach (σ_M2= 0.033). Experimentally, it is possible to measure the pressure loss coefficient, base pressure loss coefficient and the flow uniformity at the outlet using a combination of pressure and direct velocity measurements. Through a Design of Experiments approach, the sensitivity of the flow to input uncertainties was studied through a stochastic collocation based forward propagation of the uncertainty. The input uncertainties considered are the inlet total pressure, fluid viscosity and critical point properties. The Sobol indices from the uncertainty quantification indicate the more dominant influence of the critical point properties over other inputs considered. The results also validate the use of a constant viscosity assumption for the RANS simulation. The subsequent planned unit test case was to characterise the expansion through an optimised stator blade row. To this end, a deterministic adjoint based optimisation was performed with the objective function of minimising entropy generation. The resulting geometry was studied and resulted in a pressure loss coefficient improvement of around 4%, although stator flow uniformity at the exit was compromised. The uncertainty quantification performed on the optimised blade geometry yielded robustness improvements on the pressure loss coefficient and reduction in uncertainties associated with direct response quantities, although no strong correlations can be drawn between the improvements in uncertainty and the deterministic optimisation. Given current machining tolerances, the realisation of such a negligible geometry change is not viable from an experimental
perspective.
The second section of the thesis deals with experimental investigation of expansions in a converging-diverging nozzle through a matrix of isobars with increasing degree on non-ideality. Two isentropes with inlet pressure of 2.73 bara (Z = 0.9526) and 6 bara (Z = 0.901) with pressure ratio of 8.76 were performed with recording of pressure, temperature, flowrate and density measurements along the ORCHID. The flow field was visualised using the schlieren method using a z-type layout. The thesis reports the first measurements of total pressure before the nozzle inlet and vapour density and flowrate measurements. The experimental data was post-processed to identify steady-state and quantify the Type A and Type B uncertainties. The schlieren images were used to extract information on the Mach distribution along the nozzle mid-plane using an inhouse line extraction tool. Lastly, a 2.5^o wedge at the exit of the nozzle is used to generate oblique shock waves that are then manually measured. The flow field at the exit of the nozzle is in the ideal region where the shock angle only depends on upstream Mach number. Hence, the experimentally observed oblique shock angles for the off-design case are close to on-design (Inlet pressure = 18.4 bara) predictions. ... Read more

Organic Rankine Cycle (ORC) Power Plants can be of greatimportance in the energy transition as they are suitable for converting wasteheat to power and can utilize renewable energy for their operation. To improvethe efficiency of ORC Power Plants, the physical phenomena inside thesemachines must be understood. Understanding the boundary layer of complexorganic fluid flows in these systems is crucial, as it is estimated to beresponsible for one-third of the losses in turbomachinery. n this thesis, two-dimensional steady state boundarylayer flows of nonideal gas have been investigated numerically. The objectivewas to find the influence of complex fluid nonideality, characterized by idealgas departure, on boundary layer flows. In particular, a high-speed densevapour expansion of organic fluid Hexamethyldisiloxane (MM) inside a de Lavalnozzle test section has been studied. The nozzle is part of a measurementcampaign to collect experimental data with the purpose of validation andcalibration of Non-Ideal Compressible Fluid Dynamics (NICFD) software.  MATLAB program was developed for solving thetwo-dimensional steady state boundary layer equations including generalthermophysical properties. Transition prediction methods, the algebraicCebeci-Smith turbulence model (CS-model), and state-of-the-art thermophysicalmodels were implemented. The program was verified and validated for air withliterature. The turbulence model was validated with experimental data oflarge-scale zero pressure gradient adiabatic flows. The results match for theentire Mach-number range from 0.2 up to 2.8. The program also proved to becapable of predicting the turbulent boundary layer along a flat wall inside ade Laval nozzle expanding air. Deterministic simulations of the boundary layer along thecurved wall surface of the aforementioned nozzle expanding MM were performed.The results showed a larger decrease in the newly defined property C_e inthe core flow along expansion compared to air. In contrast, the propertygradients; namely density ratio c and Chapman-Rubesin parameter C,inside the boundary layer were found to be negligible. Furthermore, the resultsshow that the influence of the pressure history upstream of the nozzle throatis relatively small or even negligible in the diverging nozzle section. Theboundary layer displacement thickness for both laminar and turbulent flow wasfound to be negligible compared to the nozzle cross section, which results in anegligible effect on the nozzle core flow. The program needs further validation for flows departingfrom ideal gas. First, the flow condition in de Laval nozzles, laminar orturbulent, needs to be obtained by conducting experiments. Then, sensitivitystudies need to prove if the inviscid nozzle design is a robust design forviscous flows too; namely, being insensitive to changes in total inputconditions, uncertainties in closure coefficients, and variations in upstreampressure history. ... Read more

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. ... Read more

The Organic Rankine Cycle Hybrid Integrated Device (ORCHID) is a small scale power plant that is used to study the fundamental gas dynamic behavior of dense organic fluids, as well as the behavior of turbomachinery. In order to draw accurate conclusions about the raw sensor data generated by the ORCHID one has to know when the system is in steady-state. Currently, determining the steady state over historical data is cumbersome, and difficult to do in real time.
Our application aims to solve the problems with the current information workflow by consolidating the functionality that is currently spread across multiple applications into one main application, as well by offering steady state detection over real-time data. Aside from the lack of steady state detection capabilities, our client indicated that the applications currently in use often lag or crash. Therefore we defined three design goals: Performance, Reliability, and Ease of Use.
The main challenge we encountered during this phase was finding a way to properly connect the different external applications needed to properly process the ORCHID's data. The design goals were continuously referenced during the implementation phase to ensure the quality of our application. Additionally, we used unit, integration, and manual testing. The last category also comprised user tests conducted with our client to ensure that the final product would meet his requirements.
With our final application, we solve the client's main problem: it is now possible to detect whether or not a system is in steady state while an experiment is being conducted. This greatly reduces both the amount of time the client has to invest, as well as the amount of energy needed to conduct a successful experiment. ... Read more

The growing interest in organic Rankine Cycle (ORC) based power systems has encouraged ample amount of literature on the design methodologies for unconventional turbo-machinery. These machines generally operate in the so-called Non-Ideal Compressible Fluid Dynamic (NICFD) region of the working fluid where the thermophysical properties and transport properties models, and optical properties are experimentally unexplored. Therefore, these design methods need to be validated using state-of-the-art measurement techniques like Particle Image Velocimetry (PIV). PIV has not been implemented to study the non-ideal behaviour of such fluids, and therefore a feasibility study of PIV in these unconventional media is required. This work deals with exploring the possible challenges that could occur while applying the PIV technique to measure the flow comprising of non-ideal fluids in low speed and high-speed regime.

The fluids for which the feasibility is studied are Octamethylcyclotetrasiloxane (D4) and Hexamethyldisiloxane (MM) which are frequently used working fluids for ORC power systems. The equation of state used to calculate thermo-physical properties of these fluids is briefly discussed. The viscosity of these fluids is calculated to assess the tracer particle response characteristics and check for large variations of viscosity with the thermodynamic variables. To be able perform optical diagnostics, one also has to explore the optical properties of the working fluid --- especially the refractive index. Therefore, a theoretical study of refractive index and influence of thermodynamic properties on the refractive index is studied. Conventional seeding techniques are reviewed and its feasibility for the fluids of interest is discussed.

A test facility called the Non-Intrusive Vapour Analyser (NIVA) was designed to conduct PIV in low speed vapour flows induced by a rotating disk. A suspension of D4 and 170 nm titania particles was evaporated to obtain a seeded volume of D4 vapour, on which PIV can be performed. The signal-to-noise ratio (SNR) was calculated to verify sufficient light scattering property of the titania particles. The seeding technique of evaporating the suspension of D4 + titania yields sufficiently homogeneous seeding distribution. Mean velocity fields of the vapour flow in the NIVA at different disk rotation speeds could be measured with acceptable uncertainties. Considering a vast difference in flow conditions at high-speeds, a theoretical study of high-speed MM flow in a de-Laval nozzle is done to explore challenges that could occur in application of PIV. Large gradients in density are typical of dense gas expansions. This subsequently results in large gradients in optical properties like refractive index. Challenges to particle imaging due to inhomogeneous refraction of light are investigated by preliminary estimation of position error and velocity error along the nozzle axis. A conceptual design of the seeding system is proposed that can operate at high-pressures and does not risk contamination of the working fluid.

It was concluded from the experimental results in NIVA that PIV is feasible in low-speed vapour flows and can measure velocity fields with an average uncertainty of less than 1%. Also, refractive index gradients in high-speed vapour flows could cause unacceptable errors of greater than 1% in PIV measurements. These errors depend on the complexity of the fluid and the distance between the measurement plane and nozzle wall.
... Read more