Compressible flows of fluids whose thermophysical properties are related by complex equations are quantitatively and can be qualitatively different from high-speed flows of ideal gases. Nonideal compressible fluid dynamics (NICFD) is concerned with these fluid flows, which are relevant in many processes and power and propulsion systems. Typically, NICFD effects occur if the fluid is an organic compound and its vapor state is close to the vapor–liquid critical point, at high-reduced temperature and pressure (even supercritical). Current design and analysis of devices operating in the nonideal compressible regime demand for validated simulation software, characterized in terms of uncertainty. Moreover, experiments are needed to further validate related theory. Experimental data are limited as generating and measuring these flows is challenging given their high pressure or temperature or both. In addition, flows of organic compounds can be flammable, can thermally decompose, and sealing may demand for special materials. Recently, more research has been devoted to the measurement of these flows using both intrusive and less intrusive techniques relying on optical access and lasers. The transparency and refractive properties of these dense vapors pose additional problems. The ORCHID (organic Rankine cycle hybrid integrated device) at the Aerospace Propulsion and Power Laboratory of Delft University of Technology is a closed-loop facility, used to generate a continuous nonideal supersonic flow of siloxane MM with the vapor at 4bar and 220 °C at the inlet of the test section. Within this work, we have employed particle image velocimetry for the first time to obtain the velocity field in a de Laval nozzle in such flows. Measured velocity fields (expanded uncertainty within 1.1% of the maximum velocity) have been compared with those resulting from a CFD simulation. The comparison between experimental and simulated data is satisfactory, with deviation ranging from 0.1 to 10 % from the throat to the outlet, respectively. This discrepancy is attributed to hardware limitations, which will be overcome in the future experiments. The feasibility of PIV with uncontrolled but fixed seeding density to measure high-speed vapors of organic vapors has been demonstrated, and future experimental campaigns will target flows for which nonideal effects are more pronounced, other paradigmatic configurations, and improvements to the measurement techniques.

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This paper describes an experiment conducted within the nozzle test section of the Organic Rankine Cycle Hybrid Integrated Device (ORCHID) aimed at providing accurate data for the validation of NICFD flow solvers [5]. A supersonic flow of the dense vapor siloxane MM established in the nozzle of the setup was characterized by means of the schlieren technique and by pressure taps along the nozzle profile. The nozzle inlet conditions corresponded to a stagnation temperature and pressure of T0=253∘C and P0=18.36bara. At these inlet conditions, the compressibility factor of the fluid is Z₀= 0.58. The nozzle backpressure was equal to Pb=2.2bara. The experimental data-set includes: 1) the average mid-plane local Mach number, which was derived from the schlieren images by estimating the angle of the Mach waves originating from the roughness of the upper and lower nozzle surfaces, 2) the angle of a shock wave generated by a 5^∘ wedge placed at the nozzle exit, also detectable in the schlieren images, and 3) the static pressure distribution along the flow expansion acquired with a Scanivalve DSA3218 pressure scanner device. The Mach number at the nozzle exit estimated based on the schlieren images is M= 1.95 ± 0.05, very close to the expected value of M= 2 according to the design conditions of the experiment. The static pressure measurements have a maximum absolute uncertainty amounting to ± 1.80 kPa in the initial stages of the expansion. This information was used to assess the capability of the open-source SU2 flow solver in evaluating the NICFD effects in a supersonic flow of MM when the fluid thermodynamic properties are modeled with a cubic equation of state. For this purpose, two-dimensional Euler simulations were carried out with SU2 for the operating conditions achieved in the experiment. The numerical results are in good agreement with the experimental data. The largest deviation between the simulation and experiment is observed in the nozzle uniform region, where two dips in the Mach number occur due to a slight local decrease in flow velocity owing to two weak shock waves. The shock wave generated by the wedge located at the nozzle outlet propagates with two different angles, namely, β_above= 37. 6^∘± 0.86, and β_below= 31. 6^∘± 0.64, due to the axial misalignment of the wedge with respect to the flow.

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This work assessed the accuracy of the SU2 flow solver in predicting the isentropic expansion of Siloxane MM through the converging-diverging nozzle test section of the Organic Rankine Cycle Hybrid Integrated Device (ORCHID) [9]. The expansion is modeled using compressible Euler equations, and assuming adiabatic flow, while the fluid thermodynamic properties are estimated using the Peng-Robinson equation of state. The boundary conditions for the experiment and simulations correspond to a stagnation temperature and pressure of T¯0=253.7∘C and P¯0=18.36bar. At these inlet conditions the compressibility factor of the fluid is Z₀= 0.58. The back pressure was equal to P¯b=2.21bar. The Mach number along the centreline, and static pressure along the nozzle surface were used as the system response quantities for the validation exercise. The studied SU2 model provides valid predictions for Mach number and static pressure. The largest deviation observed in the Mach number comparison between the simulation and experiment is in the uniform flow region of the nozzle and is equal to E_Mach= 0.045. Regarding the pressure trend, the largest discrepancy occurs in the kernel region and is equal to E_pressure= 9 kPa. At the same time, the simulated Mach number and static pressure reach a maximum absolute uncertainty of ± 0.015 and of ± 20 kPa, respectively. For both quantities, these values are reached in the region close to the throat. All the uncertainties calculated for the simulated pressure profile were larger than those of the experiments. The static pressure is particularly sensitive to the geometrical uncertainties of the nozzle profile, especially inside the kernel region. A proper characterisation of the nozzle geometry was therefore required to perform a meaningful validation of the fluid dynamic solver. The developed infrastructure can be used in the future for the validation of SU2 in different operating conditions and flow cases.

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The vast number of pioneering theoretical developments inthe area of non-classical gas dynamics together with the rising number ofapplications of organic Rankine cycle (ORC) technology have shaped a new branchof fluid mechanics called non-ideal compressible fluid dynamics (NICFD). Thisfield of fluid mechanics is concerned with flows of dense vapors, whoseproperties do not comply with the ideal gas model. These types of flows occurin dense vapors, supercritical fluids and liquid-vapor mixtures. NICFD is encountered in a variety of industrial processes,the most relevant in the power and propulsion sector, and is of interest forfundamental research.  Chapter 2documents an extensive literature review which covers the main developments inthe numerical, theoretical and experimental areas. In particular, the review ofcurrent and past experiments was aimed at summarizing the lessons learned.Despite the relevance of NICFD applications, experimental information regardingthis type of flows is scarce, due to the challenges inherent with the operatingconditions of such experiments. The main objective of the research documented in thisdissertation was to perform accurate measurements of NICFD flows which can thenbe used to assess the predictive capabilities of state-of-the art numericaltools. To this end, the design and commissioning of suitable and fullyinstrumented facilities capable of generating NICFD flows in a multitude ofsteady, controlled conditions is necessary in order to provide high-quality andwell characterised data. Arguably, state-of-the-art optical techniques are mostsuited for this goal, together with more conventional temperature, pressure andmass flow rate measurements.Advanced laser diagnostic techniques such as particle imagevelocimetry (PIV) are possibly the measurement technique of choice whenaccurate measurements with a high spatial and temporal resolution are needed.However, the use of PIV or other optical techniques capable of providing localand instantaneous information within the flow is not documented. Therefore, afeasibility study was conducted by means of a simpler experiment:  the planar PIV technique was applied tocharacterise the dense vapor of an organic fluid (D4, a siloxane) stirred withina transparent container. Chapter 3 documents the successful results of thisexperiment. The optical properties of the dense vapor make PIV possible.Titanium dioxide (TiO2) seeding particles were used to track the low-speed motionof the fluid around a rotating disk. Vector fields of the natural convectionflow and of the superposition of natural convection and rotating flow wereacquired and studied as exemplary cases. The particles adequately trace theflow since the calculated Stokes number is 6.5×10-5. The quality ofthe experimental data was assessed by means of particle seeding density andparticle image Signal to Noise ratio (S/N). The results are deemed acceptablein view of envisaged high-speed flow experiments. In order to obtain measurement data of high-speed vaporflows in the NICFD regime, new experimental facilities must be conceived,designed, realized and tested. Chapter 4 presents the organic Rankine cyclehybrid integrated device (ORCHID), which was designed, built and commissionedat the Delft University of Technology. The facility can operate continuouslyand with a wide range of operating conditions. The maximum operating pressureand temperature are 25 bara and 350 °C. The facility has been designedto operate with siloxane MM as the working fluid, but it was numericallyverified that it may also be operated with other working fluids such as MDM, MD2M,D4, D5, D6, pentane, cyclopentane, NOVEC649, PP2, PP80, PP90, and toluene. Twotest sections allow to operate the ORCHID either as a supersonic/transonicvapor tunnel or as an ORC turbine test bed. Currently, a supersonic nozzlefeaturing a throat of 150 mm2 with optical access allows to perform gasdynamic experiments for the validation of numerical simulation codes. A secondtest section, a test-bench for mini-ORC expanders,  is being designed and will accommodate afully instrumented 10 kWe machine, however machines of any configuration andwith a rated power of up to approximately 80 kWe can be tested. Chapter 5 documents the achievements reached during thecommissioning of the ORCHID. The successful commissioning of the setup with MMas the working fluid is detailed and discussed based on the recordings ofseveral test runs, including the start up and shut down of the facility.  Data were acquired during the operation atsteady state at the two main operating conditions typical of supersonic nozzleand ORC turbine tests. The operation of the facility is characterized withregards to the process stability, moreover process variables are assessed fortheir uncertainties. The correct operation of the nozzle test section wasverified with a mass flow rate of fluid of m = 1.15 kg / s, and at a thermodynamic state at the nozzle inletcorresponding to T = 252 °C and P =18.36 bara. The test sectionconditions typical of a turbine experiment were T = 275 °C, P =20.8 bara, with a mass flow rate of m = 0.17 kg / s. All therelevant process variables of the test section are affected by a relativeuncertainty that is lower than 0.6 %.Chapter 6 reports the results of the first supersonic nozzleexperiments. Schlieren images of the MM flow through the two-dimensionalconverging-diverging nozzle with the inlet in the NICFD regime were recorded,together with the static pressure profile along the nozzle. A series ofschlieren photographs displaying Mach waves in the supersonic flow wereobtained and are documented at two operating conditions, namely, for inletconditions corresponding to a stagnation temperature and pressure of T0  = 252 °C and P0 = 18.4 bara, and to a back pressure of 2.1bara. Furthermore, static pressure values were measured along the expansionpath for operating conditions given by T0 = 252 °C and P0 = 11.2 bara at the nozzle inletand by a back pressure of 1.2 bara. The two inlet conditions of the fluidcorrespond to a compressibility factor of Z0 = 0.58 and Z0 = 0.79.These Mach number values together with the values of thestatic pressure along the top and the bottom profile of the nozzle were usedfor a first assessment of the capability of evaluating NICFD effects occurringin dense organic vapor flows by comparison with the results of CFD simulations.The outcome of this initial comparison was deemed satisfactory.Chapter 7 introduces the first steps towards the validationof a CFD solver for non-ideal compressible flows. In particular, anindustry-standard validation method was used together with syntheticexperimental data (experimental data were not available yet) to illustrate, asan exercise, how the uncertainty of NICFD software can be quantified. Theassessment is limited to determining how the uncertainties in model inputs,e.g., fluctuations in boundary conditions and thermodynamic property modelsinfluence the overall accuracy of NICFD simulations. The assessment of theuncertainty of the other sub-models is left for a successive phase of thisresearch program. The validation exercise confirmed the applicability of theproposed method, but also pointed out that the adopted validation metricsshould be complemented with additional statistical indicators. The errorsources in the designed experiment are identified and all the uncertainties areadequately quantified.The final chapter summarizes the answers to the researchquestions listed in the first chapter, above all that the ORCHID facility wassuccessfully commissioned and can generate stable dense vapor flows of organicfluids for both fundamental gas dynamic experiments and ORC turbine testing.The first experiments demonstrate that it can be used to obtain accurateoptical and non-optical measurements of supersonic nozzle flows for thevalidation of CFD codes, including flows in the NICFD regime.  An overview of the next phases of theresearch program is also provided.@en

This paper reports one of the initial NICFD experiments in the nozzle test section of the ORCHID aimed at providing accurate data for the validation of flow solvers, albeit, at this stage of the research, the focus is limited to inviscid phenomena. Notably, a series of schlieren photographs displaying Mach waves in the supersonic flow of the dense vapor of siloxane MM were obtained and are documented here for the commissioning experiment, namely, for inlet conditions corresponding to a stagnation temperature and pressure of T0=252∘C and P0=18.4bara. At these inlet conditions the compressibility factor of the fluid is Z₀= 0.58. The digital processing of the schlieren images allowed to estimate multiple angles formed by the Mach waves stemming from the upper and lower nozzle surfaces because of the infinitesimal density perturbations generated by the, albeit small, roughness of the metal surfaces. These values are related to the local Mach number by a simple geometric relation. Moreover, the total expanded uncertainty in the Mach number was computed. This information together with the estimate of the average Mach number was used for a first assessment of the capability of evaluating NICFD effects occurring in a dense organic vapor flow of MM by comparison with the results of CFD simulations. The outcome of the comparison was satisfactory. It can thus be inferred that the nozzle test section has been commissioned and it is ready for experimental campaigns in which its full potential in terms of measurements accuracy, repeatability, and operational flexibility will be exploited.

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This work assesses the feasibility of the planar PIV technique to study the characteristics of a siloxane vapor D4. Titanium dioxide (TiO2) seeding particles were used to track the motion around a rotating disk in a low speed flow. Vector fields of natural convection (NC) and a superposition of NC and rotating flow were selected as exemplary cases. The particles were capable of tracing the flow since the calculated Stokes number St is 6.5×10-5. The quality of the experimental data is assessed by means of particle seeding density and particle image Signal to Noise ratio (S/N). The final results are deemed acceptable for an accurate assessment of the flow field. Rejected outliers are below 2.3% and the relative uncertainties corresponding to the average velocity fields are below 1%.@en

Mini ORC power systems with the capability to deliver 3-50 kWe are receiving increased recognition for applications such as heat recovery from automotive engines, or distributed power generation from geothermal reservoirs and solar irradiation. Efficient and reliable expanders are the enabling components of such power systems, and all the related developments are currently at the research stage [1]. In the open literature experimental gas dynamic data is limited concerning the fluids and the flow conditions of interest for ORC expanders [2]. Therefore, CFD tools used for the fluid dynamic design of these components cannot be validated against reliable test cases. To bridge this gap, new experimental facilities are currently being built, such as the ORCHID setup [3]. The availability of proper experimental datasets is not, however, the sole requirement for validating a CFD code. Another precondition, equivalently important, is to define an appropriate validation methodology. This paper introduces the first steps towards the validation of a CFD solver for non-ideal compressible flows. Notably, a numerical procedure based on uncertainty quantification analysis has been conceived to assess the accuracy of the thermophysical sub-model of the code, i.e. the equation of state (EoS). Due to the lack of suitable experimental data, a synthetic dataset is generated and used to investigate the validity of the procedure. The associated validation exercise confirms the applicability of the proposed procedure, but also points out that the adopted validation metrics should be complemented with additional statistical indicators.

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Organic Rankine Cycle (ORC) power systems are receiving increased recognition for the conversion of thermal energy when the source potential and/or its temperature are comparatively low. Mini-ORC units in the power output range of 350 kWe are actively studied for applications involving heat recovery from automotive engines and the exploitation of solar energy. Efficient expanders are the enabling components of such systems, and all the related developments are at the early research stage. Notably, no experimental gasdynamic data are available in the open literature concerning the fluids and flow conditions of interest for mini-ORC expanders. Therefore, all the performance estimation and the fluid dynamic design methodologies adopted in the field rely on non-validated tools. In order to bridge this gap, a new experimental facility capable of continuous operation is being designed and built at Delft University of Technology, the Netherlands. The Organic Rankine Cycle Hybrid Integrated Device (ORCHID) is a research facility resembling a state-of-Theart high-Temperature ORC system. It is flexible enough to treat different working fluids and operating conditions with the added benefit of two interchangeable Test Sections (TS's). The first TS is a supersonic nozzle with optical access whose purpose is to perform gas dynamic experiments on dense organic flows in order to validate numerical codes. The second TS is a test-bench for mini-ORC expanders of any configuration up to a power output of 100 kWe. This paper presents the preliminary design of the ORCHID setup, discussing how the required operational flexibility was attained. The envisaged experiments of the two TS's are also described.

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