Dans un contexte d'amélioration des moteurs aéronautiques en termes de consommation et de pollution, les simulations numériques apparaissent comme un outil intéressant pour mieux comprendre et modéliser les phénomènes turbulents qui se produisent dans les turbomachines. La simulation aux grandes échelles (SGE) d’un étage de turbomachine à des conditions réalistes (nombre de Mach, nombre de Reynolds…) reste toutefois hors de portée dans le cadre industriel. La méthode chorochronique, aujourd’hui largement utilisée pour les calculs URANS, permet de réduire le coût des simulations numériques, mais elle implique de stocker le signal aux frontières du domaine pendant une période complète de l’écoulement. Le stockage direct de l’information étant exclu étant donné la taille des maillages et les pas de temps mis en jeu, la solution la plus courante actuellement est de décomposer le signal sous la forme de séries de Fourier. Cette solution ne retient du signal qu’une fréquence fondamentale (la fréquence de passage de la roue opposée) et un nombre limité d’harmoniques. Dans le cadre d’une SGE, elle implique donc une grande perte d’énergie, et le filtrage des phénomènes décorrélés de la vitesse de rotation comme par exemple un lâcher tourbillonnaire. Le remplacement de la décomposition en séries de Fourier par une décomposition aux valeurs propres (POD pour Proper Orthogonal Decomposition) permet de stocker le signal aux interfaces sans faire d’hypothèse sur les fréquences contenues dans le signal et donc de réduire la perte d’énergie liée à l’utilisation d’un modèle réduit. La compression s’effectue en supprimant les plus petites valeurs singulières et les vecteurs associés. Cette nouvelle méthode est validée sur la simulation URANS d'étages de turbomachines et comparée aux conditions classiques utilisant les séries de Fourier et à des calculs de références contenant plusieurs aubes par roue. Elle est ensuite appliquée à la simulation aux grandes échelles de l'écoulement d'un cylindre. Les erreurs causées par l'hypothèse chorochronique et par la compression sont séparées et on montre que l'utilisation de la POD permet de réduire de moitié le filtrage des fluctuations de vitesses par rapport aux séries de Fourier pour un même taux de compression. Enfin, la simulation aux grandes échelles d'un étage de turbomachine avec des conditions chorochroniques POD est réalisée afin de valider la méthode dans le cadre d'une configuration industrielle. / The more and more restrictive standards in terms of fuel consumption and pollution for aircraft engines lead to a constant improvement of their design. Numerical simulations appear as an interesting tool for a better understanding and modeling of the turbulent phenomena which occur in turbomachinery. The large-eddy simulation (LES) of a turbomachinery stage at realistic conditions (Mach number, Reynolds number...) remains out of reach for industrial congurations. The phase-lagged method, widely used for unsteady Reynolds-averaged Navier--Stockes (URANS) calculations, is a good candidate to reduce the computational cost. However, it needs to store the signal at all the boundaries over a full passage of the opposite blade. A direct storage of the information being excluded given the size of the mesh grid and timesteps involved, the most used solution currently is to decompose the signal into Fourier series. This solution retains the fundamental frequency of the signal (the opposite blade passage frequency) and a limited number of harmonics. In the frame of a LES, as the spectra are broadband, it implies a loss of energy. Replacing the Fourier series decomposition by a proper orthogonal decomposition (POD) allows the storage of the signal at the interfaces without making any assumptions on the frequency content of the signal, and helps to reduce the loss of energy caused by the phase lagged method. The compression is done by removing the smallest singular values and the associated vectors. This new method is first validated on the URANS simulations of turbomachinery stages and compared with Fourier series-based conditions and references calculations with multiple blades per row. It is then applied to the large eddy simulation of the flow around a cylinder. The error caused by the phase-lagged assumption and compression are separated and it is showed that the use of the POD allows to halve the filtering of the velocity fluctuations with respect to the Fourier series, for a given compression rate. Finally, the large eddy simulation of a compressor stage with POD phase-lagged conditions is carried out to validate the method for realistic turbomachinery configurations.

La prise en compte de la transition laminaire-turbulent dans les codes Navier-Stokes demeure problématique d’un point de vue numérique dès lors qu’on s’intéresse à des géométries complexes tridimensionnelles tel qu’un étage de turbomachine. Le modèle à équations de transport Re se propose de résoudre ces difficultés et d’ouvrir la voie à la modélisation automatique du phénomène pour des simulations RANS. Le travail exposé dans ce mémoire de thèse a consisté à développer dans le code elsA le modèle de transition Re et à évaluer l’aptitude de ce modèle à capturer avec précision le phénomène de la transition laminaire-turbulent dans le cadre de simulations RANS en turbomachine. Après une étude bibliographique, l’implémentation du modèle dans le code elsA est décrite ainsi que des premières simulations validant les développements réalisés. Par la suite, des cas documentés relatifs à des applications en aérothermique sont traités. Les prévisions par CFD des flux de chaleur à la paroi sont en bon accord avec l’expérience, démontrant ainsi la capacité du modèle à capturer avec précision la nature de la couche limite. Dans une dernière partie, le modèle est appliqué à la prévision de la transition par bulbe de décollement sur des aubages de turbine basse pression. Les résultats obtenus indiquent que le modèle doit être amélioré afin de modéliser correctement le phénomène de transition par bulbe de décollement. Ces travaux ont permis de valider l’utilisation du modèle de transition Re dans le code elsA pour une large gamme d’applications en turbomachine, et laissent entrevoir la perspective d’utiliser ce modèle. / The modelisation of laminar to turbulent transition is still difficult in RANS computations while dealing with three dimensional computational domains like turbomachinery domains. The laminar to turbulent transition model Re has been proposed to solve these issues and permit the automatic modeling of laminar to turbulent transition in RANS codes. The Re model has been introduced into the code elsA and evaluated thanks to several computations relative to turbomachinery. After a bibliographical study, the implementation of the model into the code elsA and the inital results are described in this document. In a third part, aerothermal issues in turbomachinery are investigated. The estimations of the heat fluxes by CFD are in good agreement with the experimental data which demonstrate the capability of the model to capture laminar and turbulent regions. In a last part the phenomenon of separation induced transition occuring on low pressure turbine blade is studied. The results obtained while employing the Re model show that the model need to be refined for these applications. The studied performed have permited the validation the use of the laminar to turbulent transition model Re with the code elsA for very different applications in turbomachinery.

Neste trabalho é realizada a concepção, projeto, construção e ensaio de turbinas de múltiplos discos para a verificação dos principais parâmetros e metodologias utilizadas para o projeto e análise do equipamento, além de estudar formas de otimização do equipamento. Assim, uma turbina de múltiplos discos é construída e testada com diferentes configurações de rotores, em uma bancada experimental construída e dimensionada especialmente para esse fim, além da implementação dos métodos analíticos pesquisados no software Engineering Equation Solver (EES). Assim, uma comparação entre os resultados experimentais obtidos por Rice e os modelos de analíticos disponíveis, mostra que o modelo do fator de atrito (FA) é o que melhor representa a operação do equipamento, além de ser o mais versátil dos métodos testados, permitindo que a turbina seja dimensionada e otimizada para várias configurações de construção. Já os resultados experimentais obtidos com um dos protótipos de turbina construído e operado com ar comprimido, mostram que, com modificações simples da geometria, configuração e acabamento superficial dos discos que compõem o rotor, é possível aumentar a eficiência isentrópica em até 35% em relação a turbina padrão montada com a configuração padrão de rotor (discos lisos), sem acarretar prejuízo em alguns dos principais benefícios da utilização deste tipo de equipamento. Os resultados experimentais obtidos mostram também que a eficiência diminui significativamente com o aumento da folga entre o raio externo do rotor e a parte interna da carcaça. / This work is performed conception, design, construction and testing of multiple-disks turbines (MDTs) for the verification of key parameters and methodologies used for the design and analysis of machine as well as consider ways to equipment optimization. Thus, a multiple-disk turbine is constructed and tested with different impeller configurations, in a test rig especially constructed and dimensioned for this purpose, besides the implementation of the analytical methods in software Engineering Equation Solver (ESS). Thus, a comparison between the experimental results obtained by Rice and analytical models available, shows that the friction factor model (FF) is what best represents the operation of the equipment, and is the most versatile of the tested methods, allowing the turbine is sized and optimized for various building configurations. Since the experimental results obtained with one of the turbine prototypes built and operated with compressed air, show that with simple modifications of geometry, configuration and surface finish of the disks that make up the rotor, it is possible to increase the isentropic efficiency by up to 35% compared the standard turbine rotor mounted with the default configuration (flat disks), without causing damage in some of the major benefits of using this type of equipment. The experimental results also show that efficiency decreases significantly with increasing clearance between the outer radius of the rotor and the internal part of the housing.

Neste trabalho é realizada a concepção, projeto, construção e ensaio de turbinas de múltiplos discos para a verificação dos principais parâmetros e metodologias utilizadas para o projeto e análise do equipamento, além de estudar formas de otimização do equipamento. Assim, uma turbina de múltiplos discos é construída e testada com diferentes configurações de rotores, em uma bancada experimental construída e dimensionada especialmente para esse fim, além da implementação dos métodos analíticos pesquisados no software Engineering Equation Solver (EES). Assim, uma comparação entre os resultados experimentais obtidos por Rice e os modelos de analíticos disponíveis, mostra que o modelo do fator de atrito (FA) é o que melhor representa a operação do equipamento, além de ser o mais versátil dos métodos testados, permitindo que a turbina seja dimensionada e otimizada para várias configurações de construção. Já os resultados experimentais obtidos com um dos protótipos de turbina construído e operado com ar comprimido, mostram que, com modificações simples da geometria, configuração e acabamento superficial dos discos que compõem o rotor, é possível aumentar a eficiência isentrópica em até 35% em relação a turbina padrão montada com a configuração padrão de rotor (discos lisos), sem acarretar prejuízo em alguns dos principais benefícios da utilização deste tipo de equipamento. Os resultados experimentais obtidos mostram também que a eficiência diminui significativamente com o aumento da folga entre o raio externo do rotor e a parte interna da carcaça. / This work is performed conception, design, construction and testing of multiple-disks turbines (MDTs) for the verification of key parameters and methodologies used for the design and analysis of machine as well as consider ways to equipment optimization. Thus, a multiple-disk turbine is constructed and tested with different impeller configurations, in a test rig especially constructed and dimensioned for this purpose, besides the implementation of the analytical methods in software Engineering Equation Solver (ESS). Thus, a comparison between the experimental results obtained by Rice and analytical models available, shows that the friction factor model (FF) is what best represents the operation of the equipment, and is the most versatile of the tested methods, allowing the turbine is sized and optimized for various building configurations. Since the experimental results obtained with one of the turbine prototypes built and operated with compressed air, show that with simple modifications of geometry, configuration and surface finish of the disks that make up the rotor, it is possible to increase the isentropic efficiency by up to 35% compared the standard turbine rotor mounted with the default configuration (flat disks), without causing damage in some of the major benefits of using this type of equipment. The experimental results also show that efficiency decreases significantly with increasing clearance between the outer radius of the rotor and the internal part of the housing.

La prise en compte des couplages dynamiques entre les différents organes constituant une turbomachine s’inscrit dans le processus d’optimisation des designs moteur. L’amélioration des performances des turboréacteurs passe souvent par l’utilisation d’architectures multi-rotors. Dans le contexte des moteurs avec une architecture bi-rotor, des résultats d’essais expérimentaux montrent qu’il est nécessaire de considérer, dès la conception, l’influence de la dynamique de l’arbre Haute Pression (HP) sur les aubages de l’arbre Basse Pression (BP). Dans ce cadre d’étude, un premier modèle simplifié de bi-rotor aubagé est développé dans le repère tournant lié au rotor BP. Ce modèle est composé de deux rotors modélisés par des équivalents poutres - masses - ressorts et d’une roue aubagée constituée d’aubes souples modélisées par des poutres encastrées sur un disque rigide. Desnon-linéarités de type jeu radial avec contact au niveau des paliers sont également considérées et la réponse des aubes soumises à des excitations multi-fréquentielles de type balourd BP et HP est analysée. La présence de non-linéarités dans le système conduit à mettre en oeuvre des algorithmes adaptés, basés sur des techniques de résolution dans le domaine fréquentiel avec l’évaluation des efforts non-linéaires dans le domaine temporel. Afin d’avoir une meilleure description de la dynamique de la roue aubagée, une méthode spécifique de couplage est proposée, permettant de coupler un modèle réduit de roue aubagée 3D à un modèle simplifié de bi-rotor. Une démarche adaptée à la modélisation de la roue aubagée en symétrie cyclique est implémentée afin de considérer des non-linéarités de type contact en tête d’aube. La méthode de couplage proposée est ensuite illustrée sur un exemple simple puis validée dans un cadre linéaire et non-linéaire. Enfin, cette méthode de couplage est appliquée au cas d’une structure industrielle, constituée d’un modèle d’ensemble simplifié représentatif d’un moteur et d’un modèle éléments finis d’une roue de turbine BP. Les résultats obtenus mettent en évidence le couplage entre la dynamique d’ensemble et la dynamique de la roue aubagée et permettent de prédire la réponse non-linéaire des aubes de turbine BP en présence d’une excitation multi-fréquentielle, dans des configurations de co-rotation et de contra-rotation. / The design and optimization process of high efficiency turbomachinery has become a major challenge and a topical issue at both industrial and research levels. Performance improvement has motivated the use of multi-shaft architecture in engines. In the context of dual-shaft aircraft engines, the interaction between dynamics occurring within shafts and bladed disks seems to play an important role at the design stage. The present research work deals with the coupling of these components involving several unbalances in the dynamic response of blades. Within this framework, a simplified analytical model of a bladed dual-shaft developed in the rotating frame is presented. The dual-shaft is modelled by spring - mass- beam systems and connected to a bladed disk composed of a set of flexible blades modelled by Euler-Bernoulli beams clamped in a rigid disk. Nonlinearities coming from bearings are also considered and modelled as a radial clearance and contact stiffness. Considering nonlinearities requires the implementation of dedicated algorithms and specific resolution techniques in the frequency domain as well as the computation of nonlinear forces in the time domain. The nonlinear response of blades subjected to unbalances excitations is investigated and analysed. To have a finer description of the bladed disk dynamics, a specific coupling method is proposed allowing to connect a bladed disk finite element model with the simplified dual-shaft model. A cyclic symmetry approach well-suited to the nonlinear dynamics of bladed disks is developed in order to consider blade tip contact nonlinearities. Performances of the proposed method are illustrated through an academic example and validated in both linear and nonlinear settings. Eventually, the coupling technique is applied to a complex industrial case involving a classical simplified dual-shaft model and a finite element model of the low pressure turbine bladed disk. Numerical results clearly demonstrate the coupling between dynamics and enable to predict the nonlinear response of low pressure turbine blades to several unbalances, for both co-rotating and counter-rotating engines.

Malgré les progrès faits dans les dernières décennies en CFD, les techniques RANS instationnaires pour les turbomachines multi-étages sont toujours très couteuses en temps de calcul, réduisant leur intérêt en conception industrielle. Grâce à une analyse de Fourier, les équations instationnaires de Navier-Stokes peuvent être considérées comme 2N+1 équations stationnaires couplées par un terme source. Cette approche calcule efficacement les écoulements instationnaires périodiques et montre de forts gains en terme de temps de calcul. Cependant, l’expression du terme source est algébrique, ce qui provoque des difficultés dans le calcul de l’inverse de la transformée de Fourier directe. Afin d’améliorer la robustesse et la précision de la méthode, une approche basée sur un échantillonnage temporel non-uniforme est adoptée. Pour réduire le domaine de calcul à un unique passage inter-aube des conditions aux limites de chrochronicité sont développées. Dans un premier temps, un rotor et un stator sont simules avec en une entrée du domaine de calcul une injection qui modélise le sillage de la roue directrice d’entrée. Ainsi, deux fréquences fondamentales sont vues par le rotor. L’influence du contenu fréquentiel dans le rotor (i.e. le nombre d’harmoniques de la fréquence de passage des roues et leurs combinaisons) est analysée. Les résultats sont valides contre ceux obtenus avec des simulations instationnaires classiques. Ensuite, la méthode est appliquée a deux compresseurs industriels, le compresseur transsonique ECL4 et le compresseur d’étude CREATE. / Despite the progress made in the last decades in CFD, the unsteady RANS techniques for multistage turbomachines are still very costly in computation time. Thanks to Fourier analysis, the unsteady Navier-Stokes equations can be seen as 2N + 1 equations coupled by a source term. This approach efficiently computes unsteady flows and showed significant savings in computation time. However, the source term of the method is algebraic, thus entailing some difficulties in the computation of the inverse of the direct Fourier transform. In order to enhance the robustness and the precision of the HBT, non-uniformly sampled time levels are chosen. To reduce the computational domain to a single blade passage, phaselag boundary conditions are developped. First, a rotor and a stator configuration with a wake injection at the inlet (accounting for an inlet guide vane) is modelled. Thus, two fundamental frequencies are seen by the rotor. The influence of the spectrum in the rotor is addressed. The results are validated against classical unsteady RANS simulations. Then the method is applied to two industrial : the transonic compressor ECL4 and the study compressor CREATE.

L’enjeu de cette thèse est d’améliorer la compréhension et la prédiction du phénomène de réponse forcée des aubages de turbomachines en situation de résonance. L’étude a été menée au moyen de simulations numériques U-RANS 3D et en s’appuyant sur le compresseur d’essai ERECA, dédié au phénomène de réponse forcée. Pour prédire les amplitudes de vibration des aubages excités aérodynamiquement, la méthode de prédiction la plus répandue consiste à effectuer séparément un calcul d’excitation et un calcul d’amortissement aérodynamique ; on parle alors de calcul découplé. C’est cette méthode qui a été mise en œuvre dans un premier temps. Les calculs d’excitation et d’amortissement aérodynamiques ont été comparés individuellement aux résultats d’essais. Pour cela une méthode de traitement du signal fréquence/amplitude a été développée dans le but d’extraire l’amortissement et l’excitation des résultats d’essais. Les analyses des simulations ont permis de mieux comprendre les mécanismes d’excitation et d’amortissement aérodynamique. On a ainsi pu montrer que le phénomène d’interaction rotor/stator s’apparente par son caractère discontinu à une percussion périodique. Quant au phénomène d’amortissement, il se caractérise par le bilan des contributions de chaque zone d’échange d’énergie sur la paroi de l’aubage. En outre, les amplitudes vibratoires calculées à partir de cette méthode sont très proches des valeurs d’essais. Toutefois, cette procédure de calcul requiert la mise en œuvre de 2 calculs instationnaires différents et ne permet pas à l’heure actuelle d’être utilisée dans un cycle de conception. Dans le but de simplifier et d’améliorer la qualité de prédiction des analyses de réponse forcée, la méthode du couplage dynamique a été mise en œuvre et évaluée. Avec cette méthode, l’aubage répond librement aux sollicitations engendrées par le fluide. Une fois le régime transitoire évacué, l’aubage oscille en régime permanent. Cette méthode permet donc de prédire une amplitude vibratoire à partir d’un seul calcul instationnaire. En revanche, le calcul s’avère bien plus onéreux que la méthode découplée de par l’existence du régime transitoire. Dans le but de rendre accessible cette méthode à un niveau industriel, deux méthodes d’accélération du calcul ont été mises en place. Les résultats obtenus sont très encourageants et devraient permettre de réduire drastiquement les temps de restitution des analyses de réponse forcée. A la connaissance de l’auteur, cette thèse constitue une étude inédite de comparaison entre méthode découplée et couplage dynamique, qui par ailleurs s’appuie sur des résultats d’essais dédiés exclusivement au phénomène de réponse forcée. / The purpose of this PhD thesis is to provide a better understanding of the forced response phenomena of turbomachinery bladings in resonance conditions. The study will use 3D U-RANS calculations relying on experimental results obtained on the ERECA test case, dedicated to the forced response phenomenon. In order to predict the vibrating amplitudes of aerodynamically excited bladings, the most commonly used prediction methodology consists in separated calculations for the prediction of the aerodynamic excitation and damping ; it is the decoupled method. The predictions of these two components have been compared to the experiment individually. For this, a special signal treatment analysis has been developed so as to extract the damping and excitation from the experimental amplitude/frequency signal. The analysis of the results presented hereafter has provided a better understanding of the mechanisms involved in the aerodynamic damping and excitation. The results obtained match very closely the experiment. However, this procedure requires two different unsteady calculations and is therefore hardly usable within the design process of an engine. In order to simplify and improve the quality of the forced response analysis, the time marching method has been developed and analyzed. With this method, the blade responses freely to the aerodynamic solicitations. Once the transient regime is evacuated, the blade oscillates on its permanent regime. In order to enable access to this methodology on an industrial level, several speed-up methodologies have been implemented and the results are very encouraging. To the knowledge of the author, this thesis is the first comparison between the decoupled and the time marching methods that relies on test results from an experiment dedicated to the forced response phenomenon.

This degree project in applied physics studies the tip gap flows over the rotor blades of a high-pressure turbine. The rotor blade used in the study has an improved design that utilizes both a cavity tip and an uneven profiling to reduce turbine loss. The designed rotor blade is shown to admit a 21% lower leakage mass flow rate across the tip gap than a reference rotor blade with a flat tip. By studying the designed rotor blade using transient CFD, the flow field of the tip gap region has been studied through one blade passage. The flow field characteristics of particular interest are the leakage mass flow rate across the tip gap region, which is proportional to turbine loss, and the characteristic vortices that reside within the cavity tip. By using post-processing scripts, the leakage mass flow rate has been calculated for every time step across one blade passage, showing a strong time dependence. The characteristic vortices are found using two different vortex detection algorithms, and their respective vorticity magnitude is shown to depend on the leakage mass flow rate. The simulation shows that the vorticity magnitude is increasing above a threshold of leakage mass flow rate, and that it is decreasing under this threshold. This effect is shown to destabilize the leakage mass flow rate, increasing its amplitude over its period of one blade passage.

Accurately predicting fan performance, including bounds of operation, is an important function of any Computational Fluid Dynamics (CFD) package. The presented research uses a CFD code developed as part of the Computational Research and Engineering Acquisition Tools and Environment (CREATE), known as Kestrel, to evaluate a single stage compressor at various operating conditions. Steady-state, single-passage simulations are carried out to validate capabilities recently added to Kestrel. The analysis includes generating speedlines of total pressure ratio and efficiency, as well as radial total temperature and total pressure profiles at two axial locations in the compressor at various operating conditions and fan speeds, and simulation data from the single-passage runs is compared to experimental data. Time-accurate, full annulus simulations are also carried out to capture and analyze the processes leading to stall inception for both uniform and distorted inlet conditions. The distortion profile used contains a 90 degree sector of lower total pressure at the inlet. The observed fan behavior at stall inception is compared to previous research, and it is concluded that the inlet distortion significantly changes the behavior of the part-span stall cells that develop after stall inception. Understanding the physical processes that lead to stall inception allows fan designers to design more robust fans that can safely take advantage of the better performance associated with operating closer to stall.

<div>Vacuum is needed in many applications and, there are many types of pumps that can provide the vacuum level needed. One widely used pump is the liquid-ring vacuum pump, which does not involve any solid-solid contacts at interfaces where moving and stationary parts meet. Though liquid-ring vacuum pumps are efficient and robust, manufacturers have aggressive goals on improving efficiency, performance, and range of operations.</div><div> </div><div> In this research, time-accurate computational fluid dynamic (CFD) analyses were performed to study the flow mechanisms in a liquid-ring vacuum pump to understand how it works and how the design can be improved. Based on the understanding gained, a physics based reduced order model was developed for preliminary design of the liquid ring vacuum pumps.</div><div> </div><div> In the CFD analyses, the liquid (water) was modeled as incompressible, the gas (air) as an ideal gas, and turbulence by the shear-stress transport model. The gas-liquid interface was resolved by using the volume-of-fluid method, and rotation of the impeller was enabled by using a sliding mesh. Parameters examined include the suction pressure (75, 300, and 600 Torr) and the impeller's rotational speed (1150, 1450 and 1750 rpm) with the temperature of the gas at the inlet of the suction chamber kept at 300 K and the pressure at the outlet of the exhaust chamber kept at one atmosphere. The CFD solutions generated were verified via a grid sensitivity study and validated by comparing with experimental data. When compared with experiments, results obtained for the flow rate of the gas ingested by the pump had relative errors less than 6\% and results obtained for the power consumed by the pump had relative errors less than 13\%.</div><div> </div><div> Results obtained show the shape of the liquid ring to play a dominant role in creating the expansion ratio or the vacuum needed to draw air into the pump through the suction port and the compression ratio needed to expel the air through the discharge ports. Results were generated to show how centrifugal force from rotation and how acceleration/deceleration from the difference in pressure at the pump's inlet and outlet along with the eccentricity of the impeller relative to the pump's housing affect the shape of the liquid ring. Results were also generated to show how the rotational speed of the impeller and the pressure at the suction port affect the nature of the gas and liquid flow in the pump and the pump’s effectiveness in creating a vacuum. </div><div> </div><div> With the knowledge gained from the CFD study, a physics-based reduced-order model was developed to predict air ingested and power consumed by the pump as well as the liquid ring shape and pressure of the gas and liquid in the pump as a function of design and operating parameters. This model was developed by recognising and demonstrating that the amount of air ingested and power consumed by the pump is strongly dependent on the shape and location of the liquid ring surface. The flow rates of the gas ingested by the pump and the power consumed by the pump predicted by the model were compared with experimental data and relative errors were less than 12\% and 17\% respectively.</div>